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IV Phenomena of Importance in Reduced Gravity In Chapter III various HEDS technologies are explored and the phenomena likely to affect their operation in reduced gravity are identified. In this chapter, those phenomena and their dependence on, or importance in, reduced gravity are discussed, along with research that would be needed to develop an adequate database as well as predictive models for better characterizing the phenomena. The material in this chapter and in Chapter V provides the basis for the research recommendations outlined in Chapter VI. IV.A GENERAL CONSIDERATIONS Introduction In microgravity research, one is concerned with how, in various circumstances, the relationships or balances among various fundamental phenomena depend on the presence or absence of gravity and, consequently, how particular processes of technical importance depend on gravity level. Some phenomena can therefore be isolated for study if gravity is eliminated. Moreover, knowledge of the underlying physics can often be obtained when it is not masked by phenomena that are induced by terrestrial gravity. This basic scientific goal is emphasized in the NASA microgravity research program (Woodward, 1998~. Understanding and mitigating the technological consequences of low gravity must be one of NASA's primary research goals. If the HEDS program is to be successful, however, its research goals must differ from NASA's purely scientific goals. In particular, the emphasis must be on applied research, which is the focus of this report. Indeed, the report identifies the kinds of enabling technologies required to meet the goals of the HEDS program. The following paragraphs provide an overview of the basic effects of a reduction in gravity; those effects are then treated in more detail in subsequent sections of the chapter. The emphasis is on how the interplay of gravity and other, competing basic physical processes finds expression in various dimensionless combinations of physical parameters. Either explicitly or implicitly, these dimensionless groups will govern the interaction of microgravity with the specific phenomena discussed in this chapter. The overview concludes with some general thoughts about the need for microgravity research to characterize the relationships among these groups. 111
2 MICROGRAVITY RESEARCH Gravity and Density Difference First, the general importance of the combination of gravity with density difference should be noted. Gravity is a body force per unit mass (a virtual acceleration, according to Newtonian mechanics). Therefore, the gravity- force-density is the product of gravity and density (p), and fluid motion is affected by gravity if the density is nonuniform. Accordingly, one expects any change of gravity level coupled with a density difference (whether preexisting or due to the flow process) to affect the phenomena of interest. In other words, a product gyp will be of basic significance, where /\p is a characteristic parameter describing the density difference. Clearly, the larger the density difference the larger will be the effect of a change in gravity level. The largest density differences normally encountered are those due to the presence of different phases, especially gas and liquid, or gas and solids. Thus, one must be especially concerned with multiphase flows. Smaller, but often important, density differences also occur as the result of thermal expansion of a single phase, as will be discussed in a later section of this chapter. Frequently, when gravity is changed, physical phenomena that depend on gravity will change in ways that can be characterized as a change in stability. Stability is an especially useful concept for engineering purposes, since one normally intends a system to stay unchanged over time or to maintain a steady motion. There are many classical books treating stability; for fluids, the work of Chandrasekhar (1961) and of Yih (1965) abounds in stability problems involving gravity. A common issue for the fluid systems discussed in Chapter III is a change of local stability when gravity is reduced or vanishes. In Earth gravity, a liquid/vapor system will tend to stratify stably, with vapor above and liquid below; then, if the interface is displaced it will tend to return. If gravity is absent, the restoring force is absent and the position of the interface is indeterminate. This is the situation in a cryogenic storage tank. If the situation in Earth gravity is initially the reverse, with vapor below the liquid, then the situation is unstable, and the vapor will tend to rise as a consequence of buoyancy. This instability enables a simple boiler to function. As gravity is reduced, this helpful instability is reduced, and boiler performance is impaired. Clearly, either stability or instability associated with gravity on Earth may be desirable, depending on the function considered. In some cases, such as the dispersal of particulates or droplets, neutral stability would be desired, and in such cases, reduced gravity could be helpful. Gravity-Density Coupling in Various Basic Processes Various basic flow processes may now be related to buoyancy as expressed by the gravity-density difference product, and typical dimensionless groups may thus be identified. It will be seen that if such groups are numeri- cally very large or very small, dominance of one process over another is implied. More importantly, such groups are parameters of any theoretical or computational model for system behavior, with effects depending on numeri- cal coefficients, or correlations, derived from the appropriate theories or experiments. · Flow forced by pressure difference. If the velocity of buoyant rise (or fall) through a distance L owing to a given density difference (/\p) is compared with the velocity produced by a given pressure difference, /\p, acting as the only other force on the fluid, the comparison can be expressed in terms of the dimensionless group glYpL/lYp. If this parameter] is much less than unity, then buoyancy is insignificant. This is certainly true in rocket exhausts, for example, where the pressure drop is very large. · Capillarity, wetting, and Marangoni;flows. The role of buoyancy in comparison with that of capillarity, or surface tension (c,j, can be expressed by the dimensionless group g/\pL2/c, when surface tension acts on a curved interface of scale L. This group is the "static" Bond number (Ostrach, 1982) based on density difference. One sees that for a given surface tension coefficient Achy, capillarity becomes more important relative to buoyancy if either 1With pressure drop expressed in terms of the flow velocity it produces, this parameter is the reciprocal, squared, of the Froude number as given by Yih (1965) or the "densimetric" Froude number in the hydraulics literature.
PHENOMENA OF IMPORTANCE IN RED UCED GRA VITY 113 g or L becomes small and less important if L is large, unless g is especially small or zero. In Marangoni flows, it is the gradient of c, that is important (Ostrach, 1982), so in the above group, c, would be replaced by a surface- tension difference /\c,, which in turn varies with temperature or composition. This topic is discussed in more detail in Section IV.B. · Diffusion. Transport by buoyancy may compete with molecular diffusion in affecting composition, tem- perature, or some other local property. If the diffusion coefficient, D, is known for the property difference of interest, the competition is governed by the dimensionless group g/\pL3/pD2. If the diffusing quantity is thermal energy, the foregoing group becomes g/\pL3pcp2/k2, where k is thermal conductivity and cp is specific heat. This subject is discussed more fully in Section IV.B. · Viscosity. Similarly, buoyant transport of momentum may compete with viscosity, according to the group glipL3 /pv2, in which v is the kinematic viscosity coefficient of the fluid.2 · Chemical transformation and combustion. Obviously, chemical change results in density change, and therefore an interaction with gravity can be expected, as discussed above. Consequences of chemical change in low gravity are also discussed in Section IV.F. · Electromagnetic forces. Electric or magnetic fields may exert body forces whose effects can be compared with the gravitational body force, gyp. · Vibration. Time dependence of motion, or unsteady motion in general, introduces yet another degree of freedom of fluid or solid motion, and the accelerations involved clearly compete with the virtual acceleration represented by gravity. Thus, the importance of gravity during vertical vibration of a container with a liquid/vapor interface (Yih, 1965) will be governed by the group g/\p/p£Co2, where £ is the amplitude of the imposed vibration. The higher the imposed frequency co, the less important buoyancy becomes relative to forces due to acceleration. The dynamic behavior of machines or structures also depends on gravitational loading, as a simple pendulum illustrates. Unsteadiness in competition with gravity is an important topic called "jitter, where gravity itself appears to fluctuate owing to imposed accelerations (Woodward, 1998) arising from crew motions, rocket firings, and so on. Acoustics in the presence of gravity furnishes still another important example of time dependence. In general, if a process is time-dependent, new parameters, and hence additional dimensionless groups, will need attention. ~ , i, ~ · Phase change. In a subsequent section, the physical process of solidification and melting is discussed, and it is made clear that the role of buoyancy, and hence of gravity level, is an interactive one: the phase change itself depends on buoyant transport, which in turn depends on the degree of phase change already achieved. · Granular behavior. In Section IV.G, problems of particulate or granular flows are described. Density and gravity are of course coupled in such flows, and particle interactions with each other and with liquid or gaseous media will furnish examples of the static and dynamic phenomena with which buoyancy must be compared. Gravity Regime Boundaries It is obvious from the foregoing discussion that particular combinations of processes must be identified for specific problems. For example, inertia, viscosity, heat conduction, and capillarity may be simultaneously impor- tant, along with buoyancy, in some technically important phenomena. Therefore, many specific dimensionless groups will be needed to describe complex flow regimes of interest (Ostrach, 1982~. Nevertheless, the crude outline given above shows that, generally, gravity level, g, finds itself in a group that includes density difference and some positive power (n) of length scale, that is, g/\pLn. Thus, one may infer that when gravity is reduced, any effect of that reduction will be amplified by large density difference (especially that due to phase difference) and also by large scale. 2This group may be recognized as the classical Grashof number (Eckert and Drake, 1972), to which the previous two groups are related through the Schmidt number (v/D) and the Prandtl number (pcpvlk).
4 MICROGRAVITY RESEARCH Gravity reduction will be significant only in relation to phenomena competing with buoyancy or settling processes. Therefore, in any given reduced-gravity situation, one would like to know whether the dimensionless- group coefficients or correlations used in Earth gravity still apply, or whether a different set of models or correlations needs to be developed. That is, one asks what numerical levels of the various dimensionless groups applicable to a specific technical situation represent critical boundary zones between regimes of essentially terrestrial and essentially microgravity behavior. This is the problem posed by fractional gravity environments, which is where a large proportion of HEDS operations are expected to be carried out. Research Issues It would be useful for NASA to develop a catalog of the regime-change zones for the dimensionless param- eters of all relevant fundamental phenomena. This would presumably entail reviewing and extending the experi- ments performed in microgravity. This effort would provide the basis for assessing the computational design capabilities in the future, capabilities essential for comprehensive and credible designs of efficient, reliable systems and components for HEDS. Clearly the number and the ranges of relevant parameters are very great. Therefore, the development of the suggested catalog would require effort carried out over a long period of time, focused on a great variety of difficult issues and problems. References Chandrasekhar, S. 1961. Hydrodynamic and Hydromagnetic Stability. International Senes Monographs on Physics. Oxford: Clarendon Press. Ostrach, S. 1982. Low-gravity fluid flows. Annul Rev. Fluid Mech. 14:313-346. Woodward, D. 1998. NASA's Microgravity Research Program. NASA Report TM 1998-208418. Huntsville, Ala.: NASA Marshall Space Flight Center. Yih, C.S. 1965. Dynamics of Nonhomogeneous Fluids. London: Macmillan. IV.B INTERFACIAL PHENOMENA Interfacial or capillary phenomena generally refer to the broad field of surface-tension-related phenomena (Maxwell, 1878; Gibbs, 1878; de Gennes, 1985; Haynes and Langbein, 1987~. The terminology derives from the surface-tension-induced rise (fall) of liquid in a capillary tube for contact angles less than (greater than) 90°. These phenomena are not directly influenced by gravity level, but they become increasingly important in determining the configuration and movement of liquid as gravity level is reduced, and they may become dominant in microgravity (Ostrach, 1982~. In some cases, the effects may be utilized to compensate for the loss of gravity in the manage- ment of liquids in microgravity; examples are wicked structures as in heat pipes (Faghri, 1995; also see Figure III.A.5 of this report), capillary pumped loops, and vane structures as in cryogenic storage tanks (Dodge, 1990~. Because of their dominance and practical importance in reduced gravity, the following interracial phenomena are discussed in this section: static and dynamic capillary configurations, wetting, and the Marangoni effect (arising from gradients of the surface free energy). Capillary Equilibrium and Dynamic Forms Most of the problems and work described in this section assume a uniform surface tension and therefore omit Marangoni effects, but in many practical situations these must be included; they are discussed later on. The dimensionless Bond number measures the ratio of (gravity forces)/(capillary forces) and is given by B = pgL2/c,, where p and c, are, respectively, the density and surface tension of the liquid, g is the gravitational strength, and L is a characteristic length; for example, the ratio of height to radius of a liquid in a capillary tube is inversely proportional to B. Similarly, the Bond number enters into a description of equilibrium shapes determined by the
PHENOMENA OF IMPORTANCE IN RED UCED GRA VITY 115 competition of gravitational and capillary forces, as exemplified by sessile and pendant drop shapes (Antar and Nuotio-Antar, 1993; Haynes and Langbein, 1987; Concus and Flinn, 1990~. There is a large literature devoted to static equilibrium capillary shapes in the absence of gravity; these are shapes that minimize the area of the surface of a mass of liquid subject to boundary conditions of a fixed volume and given contact angles at the perimeter of the surface (Antar and Nuotio-Antar, 1993; Haynes and Langbein, 1987; Concus and Flinn, 1990; Carter, 1998~. In some cases (as for a box with a shallow layer of partially wetting liquid), there are multiple solutions: the liquid may cover a face of the box or collect along the edges and/or corners (Martinez et al., 1987~. In addition, there is the question of the stability of equilibrium shapes, as illustrated by the Rayleigh instability of a cylinder or the stability of liquid bridges (Koster, 1990), that arise in containerless processing of materials. In addition to static problems, there are many dynamic problems in capillary theory exemplified by Benard convection, the oscillations of liquid drops or bubbles, resonances between the applied forces or accelerations (e.g., "jitter), and capillary modes of motion of a mass of liquid in a container (Zhang and Vinals, 1997), including so-called sloshing problems (Antar and Nuotio-Antar, 1993~. Benard convection, arising from the heating from below of a layer of liquid with a free surface and leading to a pattern of hexagonal convection cells, is often dominated by Marangoni convection (Antar and Nuotio-Antar, 1993) rather than the buoyancy-driven convection analyzed by Rayleigh. In particular, Benard cells have been studied under microgravity conditions. The stability and dynamics of capillary-dominated configurations of liquids are expected to play an important role in the management of liquids and in the boiling/condensation process in heat exchangers under reduced gravity conditions (Westbye et al., 1995~. As mentioned above, they also underlie the operation of heat pipes, capillary pumped loops, microgrooved heat pipes, and veined structures. Surface-tension-driven free surface flows arise in nature, science, and technology. An important technologi- cal application of free surface flows is the laser printer, and HEDS applications include the liquid-droplet surface radiator and the electrostatic liquid film radiator. It is recognized that drops generally result from the motion of free surfaces. The dynamics and breakup of drops and of other free surface flows, including theoretical develop- ments and experimental work, have recently been reviewed and unresolved problems have been outlined (Eggers, 1997; Stone, 1994~. Research Issues A body of classical knowledge and current results is available, as indicated above, but there are many unsolved problems of capillarity-determined liquid configurations involving practical boundary conditions (e.g., vessel and conduit shapes) that require additional modeling and experiments. Dynamic problems involving resonances between imposed vibrations and accelerations (e.g., "jitter) and capillary modes of liquid masses are important because of the possibility of uncontrolled excursions of the liquid mass; such problems need to be extended. In addition, the inclusion of Marangoni effects will require computer modeling of complex fluid flows as well as a greatly improved knowledge of the Marangoni parameters (e.g., temperature and composition depen- dence of the surface tension). Wetting Wetting is a phenomenon in which one condensed phase spreads over the surface of a second condensed phase (Adamson, 1982; Findenegg and Telo de Gama, 1987~. If the spreading stops at some equilibrium configuration with the surfaces of both phases exposed, it is called partial wetting; this is illustrated in Figure IV.B.1 for the case of a drop of liquid L on the surface of a rigid solid S. both in contact with the vapor V. The contact angle ~ is determined in the classical description by the balance of surface tensions (indicated in the figure) described by the Young equation: ~sv = Ads + Rev cosO.
116 FIGURE IV.B. 1 A liquid drop in equilibrium with a rigid solid sur- face and the vapor; interface free energies are labeled by the adjacent phases. MICROGRAVITY RESEARCH ASH ILLS If the spreading does not stop, which occurs when cash 2 Cal S + Cal v, then complete wetting is said to occur; the liquid phase spreads indefinitely on (i.e., it wets) the solid surface as long as it is thick enough to be described as a macroscopic liquid. In general, the two phases may be liquid or solid. A related phenomenon is the partial or complete penetration of a second phase into a grain boundary between two crystals. Although wetting is a capillary or surface phenomenon not significantly affected by gravity level, it becomes increasingly important when the gravity level is reduced, which makes it one of several phenomena that dominate events under micro- gravity conditions, and for this reason it is included in this report. Wetting, partial or complete, underlies such important technologies as soldering and welding (Nance and Jones, 1993~; liquid-phase sintering (German et al., 1995~; the operation of wicks in capillary pumped loops (Anatar and Nuotio-Antar, 1993) and vanes in the cryogenic storage of liquids (Dodge, 1990~; heat pipes (Faghri, 1999; Peterson et al., 1998~; boiling/condensation heat transfer, including the rewetting of a hot surface (Westbye et al., 1995~; and lubrication. Usually, small contact angles or complete wetting are desired in these techniques. To understand the meaning of complete wetting (de Gennes, 1985; Dietrich, 1988) in the context of the previous illustration, let W = cask + Cal v - Cal S be the work per unit area required to separate the liquid from the solid. Then, the condition for complete wetting becomes W 2 2c,~ v, which means that the adhesion of the liquid to the solid is greater than the cohesion of the liquid. Complete wetting is favored for liquids of low surface energy in contact with solids to which they are strongly attracted. A film of oil or grease that interferes with adhesion will favor partial wetting with a large contact angle. Extensions and modification of the Young description are necessary to account for several important features of wetting that include (1) hysteresis of the contact angle, (2) dynamics of wetting, and (3) breakdown of the macroscopic description on sufficiently small scales. Hysteresis of the contact angle (Decker and Garoff, 1997; Rame and Garoff, 1996) refers to the greater value of the contact angle obtained from measurement if the contact line is advancing (extending the liquid) than if it is receding; the difference between the advancing and receding contact angles makes it possible for a drop on a tilted solid surface in 1 go to be stationary (e.g., raindrops on a window pane). The extent of hysteresis is affected by the microscopic topography and condition of the surface. The dynamics of wetting is exemplified by dependence of the geometry of the liquid configuration in the immediate vicinity of a moving contact line on the velocity of the contact line; in particular, the effective contact angle depends on that velocity. This is particularly true of the ebullition cycle during boiling, where the dynamic contact angle is required to adequately model the nucleation of bubbles on the heated wall. There is also evidence that a spreading liquid drop on a solid surface is preceded by a thin film (Marsh et al., 1993~. The dynamics of wetting has become an important area of investigation (Decker and Garoff, 1997; Rame and Garoff, 1996~. The thermodynamic description of wetting breaks down when the thickness of the liquid becomes comparable to or less than the correlation length in the liquid, i.e., when the liquid in a thin film or filament can no longer be described in macroscopic thermodynamic terms. This can occur if the liquid is imbibed into a porous structure (as in a wick) whose pore dimensions are comparable to or smaller than the correlation length in the liquid (Wiltzius et al., 1989~. Two additional developments in wetting science in recent years are the following: (1) A phenomenon known as premelting (Frenken and van der Veen, 1985) can occur in which the surface layer of a solid loses translational long-range order below the melting point of the solid. As the melting point is approached, the thickness of the
PHENOMENA OF IMPORTANCE IN RED UCED GRA VITY T To Tw A ~1 Ct ~ OC 117 BFIGURE IV.B.2 Miscibility gap with critical and wetting tem- peratures Tc and Tw. layer diverges to become a bulk liquid layer that completely wets the solid at the melting point. Premelting has been confirmed in several systems. (2) A theory of Cahn (1977), now confirmed in several systems, shows that in a binary system with a critical temperature Tc, as shown schematically in Figure IV.B.2, there is a temperature Tw< Tc in the two-phase region above which one of the two phases (say or, rich in A) will be completely wetted by the other (or', rich in phase B). Further, as the two-phase field is approached from the single-phase A side (shown by the arrow), an adsorbed layer of B on the A phase occurs and increases in thickness until at the two-phase boundary, wetting of or by or' occurs. Research Issues Technologies that depend on wetting generally require good or complete wetting of a fluid on solid surfaces (i.e., low or zero contact angle). Based on this requirement and the preceding discussion, areas that would profit from research are the following: (1) the hysteresis effect, which can inhibit the spread of the wetting liquid, (2) the dynamics of wetting, which determines the rapidity with which wetting or rewetting will take place, (3) the 1 ~ ~7 ~7 1 description of wetting in porous materials when the scale of the pores is comparable to or smaller than the correlation length in the liquid, so that a bulk description of the liquid is no longer appropriate, and (4) develop- ment of the molecular theory of wetting, which would enlarge the knowledge base on material combinations and conditions for good wetting and on wetting or tensioactive agents (Schrader and Loeb, 1992; Eustathopoulos et al., 1998~. Marangoni Effect The Marangoni effect (Hondros, 1998; Antar and Nuotio-Antar, 1993; Legros et al., 1987, 1990; Ostrach, 1982) commonly refers to liquid convection caused by surface tension gradients at the free surface of a liquid or at the interface between two liquids. Because this dependence of surface tension on position arises in the presence of temperature or composition gradients along the surface when the surface tension depends on the temperature and/ or on composition, the effect may also be called the thermosolutal, thermocapillary, or solutocapillary effect. When the surface tension is a function of position along a surface or interface, there is a resultant force on an element of the surface or interface. Since the net force on the element must vanish to avoid essentially infinite acceleration of the atomically thin element, a velocity gradient perpendicular to the surface is generated that 1 41 ~ _1_ 1 ~ ~1 1 ~ 41 1 ~ 1 21 21 ~ 41 ~1 21 ~1 supplies the counterbalancing VISCOUS force. l he result IS a tnermosolutal-lnclucecl convection In the ilUlC`. l he Marangoni effect occurs in the absence of gravity and is a dominant cause of convection in microgravity. A special publication of the Philosophical Transactions of the Royal Society, London (Hondros et al., 1998) is
118 MICROGRAVITY RESEARCH devoted entirely to the Marangoni effect and provides a comprehensive look at what is known about this phenom- enon, especially as it affects materials processing. It has been suggested (Ostrach, 1977a,b, 1982) that, for historical reasons, the term Marangoni instability should be used to describe those effects resulting from gradients initially normal to an interface. Terms such as thermocapillary and solutocapillary can be applied to effects resulting from gradients of the corresponding variables initially parallel to the interface. However, the term Marangoni effect (or flow) is commonly applied to the generality of flows induced by any gradient that produces a variation of surface tension with position on the interface, whether directly or through the effect of perturbations, and this is the usage that has been adopted in this report. As an example of the Marangoni effect, consider a single component liquid with a liquid/vapor surface lying in the xy plane with a surface tension c,. Suppose there is a temperature gradient ~T/0x at the surface. Then, the force on a surface element in the x direction per unit length along y is dc,/0x = (0c,/0T)~0T/0x). To balance this, there must be a velocity gradient in the z direction, normal to the surface, of magnitude given by ,u~v/0z = (0c,/0T)~0T/0x), where ,u is the coefficient of viscosity. This velocity gradient serves as a boundary condition that generates a convection pattern in the fluid. It is clear from this simple expression that the induced velocity gradient is proportional to the temperature gradient (0T/0x) and inversely proportional to the viscosity. The actual flow in any given system may be very complicated because the convection affects the surface gradients of temperature and composition which, in turn, generate the convection. This coupling of Marangoni-induced convection with the surface tension via the surface temperature and composition can lead to oscillatory flows (Verlarde,1998~. In the case of a liquid/solid interface, there is no Marangoni effect since the solid exerts forces that balance interface tension gradients (and cause a zero velocity at the interface). In general, the dependence of c, on position arises from both temperature gradients and composition gradients (the latter is exemplified by the tearing of wine in a glass), since c, generally depends on both variables; often the effects are mixed, as in the combustion or gasification of liquid drops (Zhang et al., 1996; Aharon and Shaw, 1996~. In a multicomponent system, temperature gradients may have both a direct effect on c, and an indirect effect through the temperature dependence of the surface composition. Thus, whereas dc,/0T is negative for a pure component, it may be positive in a multicomponent system, because as T increases, c, may increase if the adsorption of a surface-active component decreases sufficiently; a notable example is sulfur in stainless steel above 40 ppm (Mills et al., 1998~. Thus, in multicomponent systems, the Marangoni effect can have either sign (defined as the sign of dc,/0T). The Marangoni effect can lead to the migration of drops and bubbles (Verlarde,1998~. For example, consider a liquid drop with dc,/0T < 0. If it is placed on a plate with a temperature gradient, it will move toward the cold end. If it is suspended in a fluid with a temperature gradient, however, it will move toward the hot end (assuming the same sign for the Marangoni coefficient); in the latter case, the return flow along the drop's center line pushes the nose of the drop forward toward the hot end. Similar phenomena happen with bubbles and can have a strong effect on pool and forced convective boiling heat transfer. Marangoni convection usually dominates gravity-induced convection in weld pools in Earth gravity; it is undiminished in microgravity. When the sign of the effect is negative, the liquid surface is pulled toward the cooler outer edges of the pool, and when it is positive, the reverse is true. The shape of the weld pool is affected (Mills et al., 1998~. The Marangoni effect dominates gravity-induced convection in the Benard instability arising from heating a liquid layer from below, provided the layer is not too deep. The threshold AT required to initiate the flow that was calculated by Rayleigh based on gravity-induced convection is 104 to 105 times larger than that found experimentally by Benard (Legros et al., 1987~; the discrepancy was attributed to the Marangoni effect, which causes warm liquid rising to the top center of a cell to be pulled outward by surface tension to the cooler cell edges, where it then sinks. As the gravity level is reduced, Marangoni convection increasingly dominates gravity- induced convection. The relative strengths of Marangoni convection and gravity-induced convection are quantified by the dimen- sionless Marangoni (Ma) and Rayleigh (Ra) numbers:
PHENOMENA OF IMPORTANCE IN RED UCED GRA VITY 119 Ma= c,TpL2/pvk Ra= goc/\TL3/vk (Legros et al., 1990; Verlarde, 1998), where, in the first formula, (;ST= dc,/0T, ~ = VT, p is the density, v is the kinematic viscosity, k is the thermal diffusivity, and L is a characteristic distance, and in the second formula, g is the gravitational constant, or is the thermal expansion coefficient, AT is a temperature difference over a character- istic distance L, and v and k are defined as above. To initiate surface-tension-induced Benard flow, that is, flow due to Marangoni instability, a critical value of Ma ~ 80 is required, and to initiate buoyancy-induced Benard flow, a critical vale of Ra ~ 1,100 is required. Other characteristics of the flow (e.g., oscillatory and turbulent) are determined by these and other dimensionless numbers of fluid dynamics. As indicated by the above examples, Marangoni effects are ubiquitous wherever liquid/fluid interfaces are subject to temperature and composition gradients. The effects become dominant in reduced gravity, as in the stirring of a weld pool, the migration of liquid in spills, fire control, and two-phase fluid transport, and in capillary- operated devices such as heat pipes or capillary pumped loops (referred to in the subsection on wetting). More- over, multicomponent mixtures may have significantly higher critical heat fluxes than occur for single-component boiling, and this observed increase in critical heat flux is apparently due to the Marangoni-induced flows. Research Issues Based on the previous discussion, the research areas of particular relevance are (1) the modeling and experi- mental study of the complex convection flows induced by the Marangoni effect, (2) the experimental determina- tion of the parameters that enter into the Marangoni and other relevant dimensionless numbers (Egry et al., 1998), (3) investigation of tensioactive agents (Eustathopoulos et al., 1998; Verlarde, 1998) to control the magnitude and sign of the effect, and (4) inclusion of thermal and concentration gradients to assess the merits of designs where the Marangoni-induced flow of fluids can be useful or detrimental. References Adamson, A.W. 1982. Physical Chemistry of Surfaces, 4th Ed. New York: Interscience. Aharon, I., and B.D. Shawl 1996. Phys. Fluids 8:1820. Antar, B.N., and V.S. Nuotio-Antar. 1993. Liquid gas capillary surfaces. Fundamentals of Low Gravity Fluid Dynamics and Heat Transfer. Boca Raton, Fla.: CRC Press. Cahn, J.W. 1977. J. Chem. Phys. 66:3667. Carter, W.C. 1988, The forces and behavior of fluids constrained by solids. Acta Metall. 36(8):2283. Concus, P., and R. Flinn. 1990. Capillary surfaces in microgravity. P. 183 in Low-Gravity Fluid Dynamics and Transport Phenomena: Progress in Astronautics and Aeronautics, Vol. 130. J.N. Koster and R.L. Sani, eds. New York: American Institute of Aeronautics and Astronautics. de Gennes, P.G. 1985. Wetting: statics and dynamics. Rev. Mod. Phys. 57:827. Decker, E., and S. Garoff. 1997. The need for new experimental and theoretical models. J. A&es. 63: 159. Dietrich, S. 1988. P. 1 in Phase Transitions and Critical Phenomena, Vol. XII. C. Domb and J.L. Lebowitz, eds. New York: Academic Press. Dodge, F.T. 1990. Fluid management in low gravity. P. 369 in Low-Gravity Fluid Dynamics and Transport Phenomena: Progress in Astronau- tics and Aeronautics, Vol. 130. J.N. Koster and R.L. Sani, eds. New York: American Institute of Aeronautics and Astronautics. Eggers, J. 1997. Nonlinear dynamics and break-up of free-surface flows. Rev. Mod. Phys. 69:865-929. Egry, I., M. Langen, and G. Lohofer. 1998. Measurements of thermophysical properties of liquid metals relevant to Marangoni effects. Philos. Trans. R. Soc. London, Ser. A 356(1739):845. Eustathopoulos, N., J.P. Garandet, and B. Drevet. 1998. Influence of reactive solute transport on spreading kinetics of alloy droplets on ceramic surfaces. Philos. Trans. R. Soc. London, Ser. A 356(1739):871. Faghri, A. 1995. Heat Pipe Science and Technology. Washington, D.C.: Taylor and Francis. Faghri, A. 1999. Recent advances in heat pipe analysis and simulation. Annual Review of Heat Transfer, Vol. 8. C.-L. Tien, ed. New York: Begell House. Findenegg, G.H., and M.M. Telo de Gama. 1987. Wetting and adsorption phenomena. P. 191 in Fluid Sciences and Materials Science in Space. H.U. Walter, ed. New York: Springer-Verlag. Frenken, J.W.M., and J.F. van der Veen. 1985. Phys. Rev. Lett. 54:134.
120 MICROGRAVITY RESEARCH German, R.M., R.G. Iacocca, J.L. Johnson, Y. Liu, and A. Upa&yaya. 1995. Liquid-phase sintering under microgravity conditions. J. Met. 47(8):46-48. Gibbs, J.W. 1878. On the equilibrium of heterogeneous substances. Republished (1961) in The Scientific Papers of J. Willard Gibbs, Vol. 1. Mineola, N.Y.: Dover, p. 55. Haynes, J.M., and D. Langbein. 1987. Fluid statics and capillarity. P. 53 in Fluid Sciences and Materials Science in Space. H.U. Walter, ed. New York: Springer-Verlag. Hondros, E.D. 1998. Introduction: significance of capillary driven flows in materials processing. Philos. Trans. R. Soc. London, Ser. A 356(1739):815. Hondros, E.D., M. McLean, and K.C. Mills, eds. 1998. Marangoni and interracial phenomena in materials processing. Philos. Trans. R. Soc. London, Ser. A 356(1739):811-1061. Koster, J.N. 1990. P. 369 in Low-Gravity Fluid Dynamics and Transport Phenomena: Progress in Astronautics and Aeronautics, Vol. 130. J.N. Koster and R.L. Sani, eds. New York: American Institute of Aeronautics and Astronautics. Legros, J.C., A. Sanfeld, and M. Verlarde. 1987. Fluid dynamics. P. 109 in Fluid Sciences and Materials Science in Space. H.U. Walter, ed. New York: Springer-Verlag. Legros, J.C., O. Dupont, P. Queeckers, and S. Van Vaerenbergh. 1990. Thermohydrodynamic instabilities and capillary flows. P. 207 in Low- Gravity Fluid Dynamics and Transport Phenomena: Progress in Astronautics and Aeronautics, Vol. 130. J.N. Koster and R.L. Sani, eds. New York: American Institute of Aeronautics and Astronautics. Marsh, J.A., S. Garoff, and E.B. Dussan. 1993. Dynamic contact angles and hydrodynamics near a moving contact line. Phys. Rev. Lett. 70:2778. Martinez, I., J.M. Haynes, and D. Langbein. 1987. P. 53 in Fluid Sciences and Materials Science in Space. H.U. Walter, ed. New York: Springer-Verlag. Maxwell, G.J.C. 1878. Capillary action. Encyclopedia Britannica, 9th Ed. New York: Encyclopedia Britannica. Mills, K.C., B.J. Keene, R.F. Brooks, and A. Shirali. 1998. Marangoni effects in welding. Philos. Trans. R. Soc. London, Ser. A 356(1739):911. Nance, M., and J.E. Jones. 1993. Welding in space and low-gravity environments. P. 1020 in ASM Handbook, Vol. 6: Welding, Brazing and Soldering. Metals Park, Ohio: ASM International. Ostrach, S. 1977a. Motion induced by capillarity. Pp. 571-589 in Physicochemical Hydrodynamics: V.G. Levich Festschrift, Vol. 2. London: Advanced Publications. Ostrach, S. 1977b. Convection due to surface-tension gradients. Pp. 563-570 in Committee on Space Research (COSPAR) Advances in Space Research, Vol. 19. M.J. Rycroft, ed. Oxford and New York: Pergamon. Ostrach, S.A. 1982. Low-gravity flows. Annul Rev. Fluid Mech. 14:313. Peterson, G.G., L.W. Swanson, and F.M. Gerner. 1998. Micro heat pipes. Pp. 295-337 in Microscale Energy Transport. C.-L. Tien, A. Majumdar, and F.M. Gerner, eds. New York and Philadelphia: Taylor and Francis. Rame, E., and S. Garoff. 1996. Microscopic and macroscopic dynamic interface shapes and the interpretation of dynamic contact angles. J. Colloid Interface Sci. 177:234. Schrader, M.E., and G.L. Loeb, eds. 1992. Modern Approaches to Wettability. New York: Plenum Press. Stone, H.A. 1994. Dynamics of drop deformation and breakup of viscous fluids. Annul Rev. Fluid Mech. 26:26-65. Verlarde, M.G. 1998. Drops, liquid layers and the Marangoni effect. Philos. Trans. R. Soc. London, Ser. A 356(1739):829. Westbye, C.S., M. Kawaji, and B.N. Antar. 1995. Boiling heat transfer in the quenching of a hot tube under microgravity. J. Thermophys. Heat Transfer 9:302. Wiltzius, P., S.B. Dierker, and B.S. Dennis. 1989. Wetting and random-field transition of binary liquids in a porous medium. Phys. Rev. Lett. 62(7):804. Zhang, B.L., J.M. Card, and F.A. Williams. 1996. Combust. Flame 105:267. Zhang, W., and J. Vinals. 1997. Pattern formation in weakly damped Faraday waves. J. Fluid Mech. 336:301. IV.C MULTIPHASE FLOW Both single and multiphase3 fluid flows may be used in microgravity environments. While single-phase flows can behave somewhat differently in space (owing, for example, to the absence of natural-convection- induced flows), they can be reliably calculated in most cases. The microgravity issues associated with single-phase flows are primarily those related to heat-transfer- induced density changes. These phenomena are discussed in Section IV.D, which is concerned with heat transfer phenomena. Multiphase flows are inherently more complicated than single-phase flows. Because of differences in phasic density and inertia, multiphase flows may exhibit pronounced phase separation and distribution. Indeed, 3The simultaneous flow of several phases or components, for example, vapor/liquid flows and solid/fluid flows.
PHENOMENA OF IMPORTANCE IN RED UCED GRA VITY 121 multiphase flows normally configure themselves into distinctive flow regimes in which the various phases are nonuniformly distributed across the duct through which they flow. Significantly, the modeling of turbulence, pressure drop, heat transfer, and stability must take flow regimes into consideration. Moreover, surface-tension- induced (e.g., Marangoni) forces and surface phenomena are likely to be much more important in space than they are on Earth. It should be noted that virtually all flow-regime-specific phenomena will be influenced by gravity level during both normal forced-flow operating conditions and various postulated accidents. Although NASA has so far been able to design around the need for the extensive use of multiphase systems and processes in its missions, the agency is well aware of the fact that there are numerous issues and concerns facing space system designers attempting to utilize multiphase flow and heat transfer processes and systems in space (McQuillen, 1999~. However, it is inevitable that such systems and processes will be needed for HEDS proposed interplanetary missions and extraterrestrial colonies. Examples, which are discussed in Chapter III, include Rankine cycle power plants, boilers, evaporators, condensers, multiphase thermal buses, electrolysis units, and various other life support and materials processing systems for which performance and weight are important design considerations. In addition, there is a need to better understand multiphase particulate/fluid systems (e.g., dust transport and deposition) in reduced gravity if extraterrestrial colonies are to be established. Unfortunately the current state of knowledge concerning how multiphase systems behave in reduced and microgravity environments is inadequate to support NASA's proposed missions and goals. Indeed, if one is to have confidence in the performance of multiphase systems and processes in space and at extraterrestrial sites, then a well-coordinated research and development effort will be required to provide the needed mission-enabling technology. To understand why this effort is so crucial, it is important to note that multiphase flow and heat transfer technology is a mature one that has been widely used on Earth during the last century. Nevertheless, it is a field that has been empirically based. Unfortunately, many of the design rules and correlations that are valid on Earth are invalid for microgravity applications. One reason for this is that the flow regimes (i.e., how the phases configure) are quite different on Earth and in space. Moreover, natural circulation and buoyancy are suppressed in space while they play an important role in the performance of many multiphase systems on Earth. It will not be economically viable to develop multiphase systems for space in the same way as these systems have been developed on Earth. That is, it will not be practical to test different configurations in space until an acceptable design is achieved. Rather, physically based analytical models (which can be used in computer codes for design purposes) should be developed to take into account all relevant aspects of reduced-gravity phenomena. These analytical models could then be used to optimize designs and scale up small scale microgravity data to full scale. Phase Separation and Distribution It is well known (Heppner et al., 1975) that buoyancy plays an important role in the phase distributions that lead to the development of the various flow regimes and that, as shown in Figure IV.C. 1, the regimes can be very different in microgravity environments. This subsection focuses on some multiphase flow phenomena that are considered to be of vital importance to the HEDS technologies. Many important and challenging problems in multiphase flow and heat transfer have to do with multidimensional (i.e., three-dimensional) phenomena, in particular, phase separation and distribution phenomena. When a flowing multiphase mixture (vapor/liquid or solid/fluid) changes direction or is subject to other types of accelerations, the phases may separate nonuniformly. This is because of the relatively large differences in the inertia of each phase for sufficiently large dispersed particles or bubbles. A good example of this phenomenon can be seen in Figure IV.C.2, which illustrates phase separation for a bubbly gas/liquid mixture in a piping Tee (Hwang et al., 1988~. Because the gas phase has a lower density, and thus a lower momentum flux, than the liquid phase, it has an easier time changing direction from the inlet section into the side branch of the Tee. Thus the position of the dividing streamline for the gas (6G) is farther into the incoming stream than that for the liquid phase (by. Hence
122 FIGURE IV.C.1 The effect of gravity on flow regimes. Image courtesy of NASA. MICROGRAVITY RESEARCH ~ gO] tAnnularflow, microgravity] the zone of influence of the gas is larger than that of the liquid phase. As a consequence, a preferential phase separation of gas into the side branch occurs such that the volume fraction of gas is higher in the side branch and lower in the run (downstream of the branch) than it was at the inlet of the Tee. Similar phase separation phenomena may occur when there is a change in direction or acceleration of a multiphase mixture. In particular, phase separation should be expected in any phase change equipment that is geometrically complex (e.g., plena). One important source of the acceleration force on a multiphase mixture is gravity. Because of gravity, pronounced phase separation regularly occurs in horizontal ducts on Earth, in which the heavier phase will concentrate and flow in the lower part of the duct. In contrast, gravitational phase separation will not occur in microgravity environments. This, of course, will have a pronounced effect on the flow regime (i.e., the phasic configuration) and thus on the overall behavior of the flow. Reliable multidimensional models of multiphase flow will be required to predict phase separation in micro- gravity and reduced-gravity environments. Fortunately, models of this type have recently been developed and used on Earth. In particular, physically based, multidimensional two-fluid models have been developed (Drew and Passman, 1998) by ensemble-averaging the conservation equations of mass, momentum, and energy, and these models were numerically evaluated using computational fluid dynamics (CFD) techniques (Lahey and Drew, 2000~. It appears that multidimensional CFD models of this type can also be developed for microgravity condi- tions. However, this will require carrying out parametric and separate-effects experiments in reduced-gravity environments to develop the constitutive relations required for closure of the two-fluid model. It should be stressed that NASA must be able to reliably calculate phase separation if multiphase systems and processes are to be used in space, because, as noted previously, significant phase separation may occur in multiphase systems (e.g., in pipes, boilers, and condensers) every time the flow accelerates or changes direction. It is also important to note in Figure IV.C.2 that the gas, which is extracted through the side branch of the Tee, depends on the inlet phase distribution. That is, it depends on the phasic distribution within the zones of influence. It has been known for some time that pronounced lateral phase distribution may occur on Earth (Serizawa, 1974) and in microgravity multiphase conduit flows (Heppner et al., 1975; Colin et al., 1991; Bousman and Dukler, 1993; McQuillen et al., 1998~. Figure IV.C.3 shows a void fraction (i.e., the gas volume fraction, (oc) distribution measured on Earth by Serizawa (1974) for dispensed air/water upflow in a pipe. It can be seen that the gas concentrates near the wall (r/ R = +1) of the pipe for low inlet gas flows (i.e., qualities, <x>) but near the pipe's center line for higher inlet gas flows. Phase distribution phenomena of this type have been reported for many conditions, including laminar flows (Antal et al., 1991) and flows in complex geometry conduits (Lopez de Bertodano et al., 1990~. Lateral phase distribution occurs because of the various lateral forces on the dispersed (i.e., noncontinuous)
PHENOMENA OF IMPORTANCE IN RED UCED GRA VITY D-, Dividing Streamline for Gas y Typical Gas , Streamline ^,~ 1 ~ / \~ ~ Dividing Streamline }A - ~1 A= "Zones of Influence" 123 FIGURE IV.C.2 Phase separation in a piping Tee. SOURCE: Lahey (1992~. Reprinted with permission from Elsevier Science Publishers. and continuous phases. This phenomenon is significant because it can lead to flow regime transition, and the thermal-hydraulic characteristics (e.g., pressure drop and heat transfer) of a flowing multiphase mixture are strongly dependent on flow regime and, thus, gravity (Dukler et al., 1988; Jayawardena et al., 1997; Chen et al., 1991; Zaho and Rezkallah, 1993; Bousman et al., 1996; McQuillen et al., 1998~. In principle it is possible to analyze multiphase flows using Lagrangian (interface tracking) volume of fluid or level set numerical formulations, or using direct numerical simulations. However, predictions of this type are prohibitively time-consuming and expensive. The current state of the art is CFD analysis of multiphase systems based on Eulerian or Eulerian/Lagrangian formulations of multidimensional two-fluid models (Lahey, 1992~. The interracial transfer laws required for closure or two-fluid models must be flow-regime-specific and can be derived using a combination of analytical and numerical models and suitable experiments. In particular, both separate-effects experiments, which isolate the various important physical phenomena (e.g., lift and drag), and integral experiments, in which various phenomena interact, will be required to properly assess and verify the multidimensional two-fluid model. Reduced-scale experiments of this type will need to be performed in micro- gravity to assure their relevance. The resulting two-fluid model can be evaluated using CFD techniques. Indeed, this approach is now widely used for the analysis of single and multiphase flows on Earth. Significant progress has been made on the ability to predict phase distribution phenomena using multidimen-
124 FIGURE IV.C.3 Radial void distribution for 1 g0 and bubbly upflow (Serizawa, 1974), where or is the local void fraction and r/R is the relative radial position. SOURCE: Lahey (1992~. Reprinted with permission from Elsevier Science. MICROGRAVITY RESEARCH 0.4 o . _ ct . _ 0 0.2 o o- e =1.03 m/s Z / D = 30 0.1 ) \< Bubbly Flow _ , ~, ~~ <X> ~ 0 0085 ° 0 01 70 0.0258 0 0341 ~ 0.0427 it, 0 0.0511 SIug Flow <A odd ~ ~ <A ,~Sluq Flow ~ no\ to\ ~11 I A Bubbly Flow cJ6 | 1 ~4 1 ~ o 1.0 Radial Position r\ R signal, two-fluid CFD models (Lahey and Drew, 2000~. This has required the analytical modeling of flow-regime- specific interracial transfer laws (e.g., lift and virtual mass) and multiphase turbulence. Moreover, detailed experiments were required on Earth for the development and assessment of these flow-regime-dependent models. These efforts resulted in the development by the U.S. Department of Energy-Naval Reactors program of a multidimensional, four-field, two-fluid CFD model, which has been extensively used by the U.S. Navy. While these computational models are not directly applicable to reduced gravity, they can be extended for this application once interracial closure laws are developed for microgravity that include all relevant physical phenomena. Developing models will require a better understanding of multiphase fluid mechanics and of interracial mass, momentum, and energy transfer mechanisms in reduced gravity environments. Proper quantification of these models, through experiments and analysis, should give NASA the ability to reliably calculate phase distribution and separation, as well as phasic mixing, in simple and complex geometries. In particular, it should be possible to predict the various flow regimes, as well as multiphase pressure drop, flow regime transitions, and boiling/ condensing heat transfer (Lahey, 1996~. To better appreciate the current state of the art, let us consider some comparisons of a multidimensional, two- fluid model with some multiphase data taken on Earth. Because of its importance in many commercial processes, the bubbly flow regime has been chosen to demonstrate the model's predictive capabilities. (However, similar predictions are possible for other flow regimes.) As can be seen in Figures IV.C.4 through IV.C.8, a properly formulated three-dimensional, two-fluid CFD model is capable of predicting a wide variety of adiabatic multiphase flows on Earth. In particular, Figures IV.C.4 through IV.C.6 show that for bubbly upflow in a pipe, the local void fraction, turbulent intensities, and Reynolds stress (i.e., turbulent shear stress) are well predicted. Similarly, Figure IV.C.7 shows that the same model can also predict bubbly downflows in a pipe in which the void fraction distribution is completely different from that for upflow (see Figure IV.C.4~. Similarly, Figure IV.C.8 shows that the same model also gives excellent predictions for bubbly upflow in complex geometry conduits (in this case, an isosceles triangle). Moreover, as can be seen in Figures IV.C.9 and IV.C.10, when the condition of the boiling surface (i.e., the nucleation site density) is properly characterized, Freon (R-113) and SUVA (R-134a) subcooled boiling data are
PHENOMENA OF IMPORTANCE IN RED UCED GRA VITY 0.25 - 0.20 - 0.15 - ~G 0.10 - 0.05 - 0.00 - 125 Two-fluid model Serizawa's data jL=1.36m/s jG = 0 077 m/s _~ 1 0.00 0.20 0.40 0.60 0.80 1.00 r / R FIGURE IV.C.4 Comparison of model predictions with Serizawa's bubbly upflow data (1974~: void fraction distribution at 1 gO (aG is the local void fraction and r/R is the relative radial position). SOURCE: Lahey and Drew (2000, in press). Courtesy of R.T. Lahey, Jr. also well predicted using the same multidimensional, two-fluid CFD model. The results shown in Figure IV.C.10 are particularly significant since they show that a properly formulated two-fluid model can accurately predict two- phase pressure drop and the developing phase distributions for several different flow regimes (Lahey, 1996~. That is, the heated channel was, in effect, a "once-through evaporator" in which subcooled liquid entered and saturated annular flow exited. It should be noted that all of the above examples are for conditions of forced (i.e., pumped) flows in which buoyancy-driven natural circulation plays no role. It is significant that pronounced phase distribution is seen for forced flow conditions, since only multiphase flows of this type are suitable for microgravity conditions (that is, as discussed previously, natural circulation will not be effective in microgravity environments). The applications for these predictive capabilities are extensive, ranging from the design and analysis of boilers, evaporators, condensers, reprocessing systems, electrolysis units, Rankine cycle power plants, and propul- sion systems. Unfortunately, very little research of the type needed to support the development of multiphase CFD predictive capabilities for reduced and/or microgravity applications has been conducted by NASA in the past. Other Multiphase Phenomena It should be noted that some of the phenomena needed in the closure laws (e.g., surface phenomena such as wetting and surface-tension-induced forces) will also have important applications in the analysis of other pro-
26 MICROGRAVITY RESEARCH 0.250 - 0.200 - u' 0.150 - 0.1 00 - 0.050 - Two-fluid model · ~ ~ ~ v L Serizawa's data (radial) ALAA u'L Serizawa's data (axial) iL = 1.36 m/s 0.012 - 0.010 - 0.008 · ~ ~ ~ Serizawa's data: iG = 0 077 m/s model: iG = 0.0 m/s - -- - model: iG = 0.077 m/s iL= 1.36 m/s 0.000-- iG = 0 077 m/s , 0.00 0.20 0.40 0.60 0.80 1.00 r/R FIGUE IV.C.5 Comparison of model predictions with Seriza- wa's bubbly upflow data (1974~: velocity fluctuation distribu- tions at 1 go (up and v'~ are the local liquid turbulent fluctua- tions in the axial and radial directions, respectively, and r/R is the relative radial position). SOURCE: Lahey and Drew (2000, in press). Courtesy of R.T. Lahey, Jr. 0.15 - 0.13 - aG 0.10--I 0.08 - 0.05 - 0.03 - 0.00- , , _, 0.00 0.20 0.40 0.60 0.80 1.00 - · ~ ~ ~ Wang's downflow data \ jL = 1.0 m/s, jG = 0.1 m/s ~ \ Two-fluid model r/R FIGURE IV.C.7 Comparison of model predictions with Wang's bubbly downflow data (Wang et al., 1987~: void frac- tion distribution at 1 go (OCG is the local void fraction and r/R is the relative radial position). SOURCE: Lahey and Drew (2000, in press). Courtesy of R.T. Lahey, Jr. 0.006~ 0.0043 ~ one 0.000, . . . . . 0.00 0.20 0.40 0.60 0.80 1.00 r/R FIGURE IV.C.6 Comparison of model predictions with Serizawa's bubbly upflow data (1974~: Reynolds stress distribution at 1 go (u'Lv'~ is the local liquid Reynolds stress and r/R is the relative radial position). SOURCE: Lahey and Drew (2000, in press). Courtesy of R.T. La- hey, Jr. 1.00 - . 0.80 - 0.60 - aG l iL = 1.0 m/s ~ _ ~ 0.40 - 0.00 - 40 60 80 100 Two-fluid model ~ ~ ~ ~ Bertodano's data iG = 0.60 m/s · ~ ~ ~ Bertodano's data jet = 0.10 m/s / 0 20 y(mm) FIGURE IV.C.8 Comparison of model predictions with Lopez de Bertodano's bubbly upflow data (1993~: void fraction distribution at 1 go (OCG is the local void fraction and y is the lateral position). SOURCE: Lahey and Drew (2000, in press). Courtesy of R.T. Lahey, Jr.
- ~ lo lo by 1.6 1.4 - 1.2 _% ~ 1.0 Q 0.8 u, 0.6 u) `~ 0.4 0.2 O- ~ -0.2 - _ PHENOMENA OF IMPORTANCE IN RED UCED GRA VITY Axial velocity Liquid temperature 0.6 0.6 0.6 0.6 . 20 10 ~ -10 A\ -30 0.008 0.01 0.012 0.014 0.016 0.018 0 on r (m) 0.008 0.01 0.012 0.014 0.016 0.018 r (m) x 10-3 Turbulence kinetic energy Volume fraction 0 \ 3- \ \o \°r~ ~ C) _ ,. 1- 0.008 0.01 0.012 0.014 0.016 0.018 r (m) 25 20 _~ 15 c' 10 5 O. 0.9 - 0.8 - ·~ 0.7- ~ 0.6- > 0.5- 0' 0.4- ct .~ 0.3- 0.2 - 0.1 - O- 0.8 1 ( l 0 0.2 0 4 0.6 0v 0~ 0.008 0.01 0.012 0.014 0.016 0.018 r (m) _~ /< 1 1 1 1 1 0 0.2 0.4 0.6 0.8 1 Axial Distance (x/L) Axial Distance (x/L) 0.9~ 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 O it. t ~ i, --I ~ i+T,, , 0 0.2 0.4 0.6 0.8 1 Spacing Dimension (y/S) 127 FIGURE IV.C.9 Predictions for sub- cooled boiling R-113 upflow in an an- nulus at 1 go, with data of Velindandla et al. (1995) (u is the local liquid ve- locity, TL is the local liquid tempera- ture, LOG is the local void fraction, kL is the local turbulent kinetic energy of the liquid phase, and r is the radial posi- tion). SOURCE: Lahey (1996~. Re- printed with permission from Begell House. x/L ~ 0.18 - 0.42 0.68 0.92 FIGURE IV.C. 10 Predictions of subcooled boiling SUVA upflow be- tween heated parallel plates at 1 go. SOURCE: Lahey (1996~. Reprinted with permission from Begell House.
28 MICROGRAVITY RESEARCH cesses, such as welding, that will be needed in space. These phenomena are discussed at greater length in Section IV.B. While this discussion has focused on vapor/liquid systems, it should be mentioned that similar phenomena have been seen in solid/fluid systems (Alajbegovic et al., 1994~. Indeed, multidimensional two-fluid CFD models have been developed and successfully applied to solid/fluid flows (Alajbegovic et al., l999~. Moreover, a similar CFD approach that includes aerosol physics (e.g., coagulation and thermophoresis) could also be used. Thus, if desired, multidimensional aerosol (e.g., smoke) and dust transport and deposition models could be developed for space and extraterrestrial application. The theory of aerosol transport and deposition is a fairly mature one (Fuchs, 1964), and numerous aerosol transport codes have been developed, benchmarked against experiments, and applied to the transport and deposition of aerosols (e.g., Croff,1980~. Missions to distant moons, asteroids, or planets such as Mars will require that we develop more soil-specific knowledge of the particulate mechanics associated with dust transport/deposition, filtration, and accumulation, as well as techniques for the cleaning of vital life support systems (e.g., solar cells). In other cases, multidimensional, multiphase CFD models could also be developed and used to analyze the flow of solid/fluid systems, including models for particle transport and deposition, regolith transport and process- ing, particulate flow in hoppers, and flow through porous media. However, the appropriate closure laws will be different from those used for vapor/liquid systems (i.e., particle-to-particle interactions will be very significant), and appropriate particle transport experiments will be needed to establish flow behavior in reduced gravity and for atmospheric conditions relevant to the extraterrestrial site. In other applications for example those associated with powder metallurgy processes, direct metal deposi- tion techniques for rapid, one-of-a-kind manufacture in space, and for some pyrolysis processes ad hoc phenom- enological model development and supporting experiments may be sufficient. In any event, it appears that much of the research that will be needed can be done on Earth, and NASA may be able to take advantage of the ongoing particulate mechanics research programs being sponsored by the National Science Foundation. Research Issues In summary, significant phase separation and distribution should be expected when multiphase systems are used in space. Fortunately, it appears that the multidimensional, multiphase CFD models that have been devel- oped for vapor/liquid flows on Earth can be extended to accommodate reduced-gravity environments. To accom- plish this, however, a well-focused research program would be required to obtain a better understanding of multiphase phenomena in reduced gravities, to build a database for model assessment, and to establish the roles of various dimensionless parameters involving gravity. Mixing Chaotic mixing may occur in both single- and two-phase fluids as a result of turbulence (Ottino, 1990; Lahey and Drew, 2000~. In addition, fluid/fluid mixing may be used to produce materials that have special desirable properties. In particular, plastic blends with novel fibrous or multilayer film microstructures have been produced recently by inducing chaotic motion within multiphase melts (Zumbrunnen, 1998), and it is unclear if they will be affected by gravity. The microstructures have been associated with enhancements in physical properties such as toughness, strength, and electrical conductivity. Owing to the repeated stretching and folding inherent in chaotic motion, initially large minor-phase bodies are eventually transformed into films, which may then subdivide into fibers owing to interracial instabilities. Studies of chaotic mixing have been done by Ottino (1990) and Ottino et al. (1992~. Similar microstructures might also be formed in metallic systems having immiscibility gaps in phase diagrams at elevated temperatures. However, on Earth, phase separation due to gravity has prevented attempts to create these microstructures in metallic systems. Results with plastics demonstrate that it may be possible to create metallic alloys with fibrous or multilayer film microstructures if processing is performed in a microgravity environment.
PHENOMENA OF IMPORTANCE IN RED UCED GRA VITY 129 It is well known that during the flow of mixtures of immiscible liquids (Nadler and Mewes, 1997), droplet entrainment and mixing may cause emulsification of the continuous phase, which leads to significantly higher viscosities and pressure drops. There has been virtually no research on these important phenomena in microgravity environments. Single-phase turbulence is a vast field that has occupied the attention of many outstanding scientists and engineers for over 100 years. As a consequence, modern single-phase CFD codes regularly involve the computa- tion of turbulence phenomena using so-called k-£ and T-£ models, where k is the turbulent kinetic energy, £ iS the dissipation rate, and ~ are the Reynolds stresses (Wilcox, 1998~. Moreover, models are available that allow large eddy simulation and direct numerical simulation of single-phase turbulence, although analysis of this type is currently time-consuming and very expensive (Wilcox, 1998~. In contrast, understanding of turbulence phenomena in multiphase flows is much less advanced. Neverthe- less, it is known (Theofanous and Sullivan, 1982; Lance and Bataille, 1991; Lopez de Bertodano et al., 1994a) that for dilute dispersed particulate and bubbly flows, the shear-induced and particle-induced Reynolds stresses can be superimposed. The shear-induced Reynolds stress can be evaluated using a two-phase k-£ or T-£ model (Lahey and Drew, 2000), and a particle-induced Reynolds stress was derived by Nigmatulin (1979~. It has been found (Lopez de Bertodano et al., 1994b) that the ability to predict lateral phase distribution strongly depends on turbulence modeling. As a consequence, research on flow-regime-specific multiphase turbu- lence is important. Unfortunately, virtually no research on the effect of gravity on multiphase turbulence has been conducted to date. This must be rectified if reliable multidimensional, multiphase CFD models are to be devel- oped for applications in space. Research Issues In summary, experimental and analytical research focused on measuring and modeling flow-regime-specific multiphase turbulent phenomena in reduced-gravity environments is required if reliable predictions are to be made of the multiphase flow and heat transfer phenomena expected to occur in many of the power, propulsion, and life support systems and subsystems to be used for HEDS missions. Multiphase Systems Dynamics Multiphase flow also exhibits important global phenomena, which can affect system/subsystem operation and performance. For example, it is well known that liquid handling and storage is an important issue for NASA, and attempts have been made in the past to address it with wicking structures installed in tanks, for instance. Never- theless, more research is needed, particularly for flashing cryogenic liquids and for the cavitation and/or the release of dissolved gases in liquids, in support of proposed future deep-space missions that may involve the harvesting and storage of water from asteroids, or on colonized extraterrestrial sites, and the handling and treatment of liquids associated with waste management and food production. Other important global thermal-hydraulic phenomena are associated with system dynamics, in particular, the stability of multiphase systems. Such systems may exhibit static instabilities (Lahey and Podowski, 1989) such as the following: · Excursive (i.e., Ledinegg) instabilities, · Flow regime relaxation, and · Geysering/chugging. In addition, there may be dynamic instabilities such as these (Lahey and Podowski, 1989~: · Pressure-drop oscillations, · Density-wave oscillations (DWOs), and · Flow-regime-induced oscillations.
130 MICROGRAVITY RESEARCH Of these instabilities, the most important from the point of view of NASA's HEDS goals are excursive (Ledinegg) instabilities, pressure-drop oscillations, and DWOs. Excursive Instabilities It is known (Lahey and Moody, 1995) that a boiling system may undergo Ledinegg-type flow excursions it 0(/\Psystem ) 0/\Pext ) < Dw Dw where w is the flow rate and /\Pext and /\Psystem are, respectively, the external pressure change (e.g., due to a pump) and the irreversible pressure loss in the system. Four cases are shown in Figure IV.C. l l, where the boiling channels head-flow curve is given by the S-shaped curve and the externally impressed channel pressure is given in cases 1 through 4. Cases 1 and 4, for a positive displacement pump and a high-head centrifugal pump, respectively, are stable. In contrast, cases 2 and 3, for a parallel channel and a low-head centrifugal pump, respectively, are unstable. In particular, the unstable cases have multiple operating states, and CHF may occur for states 2 and 2'. It should be noted that this stability problem may be mitigated by inlet orificing and/or increasing system flow rate (w). However, these fixes can cause a large penalty in terms of increased system pressure drop and reduced boiling heat transfer effectiveness. Pressure-Drop Instabilities The inertia associated with an accumulator's dynamics may cause over/under shoots, which drive system oscillations. As can be seen in Figure IV.C.12, the accumulator can convert a Ledinegg-type flow excursion in a boiling loop into an equally undesirable periodic oscillation between points 2' and 3' (Lahey and Podowski,1989~. Density-Wave Oscillations Density-wave oscillations (DWOs) are caused by the lag introduced into a flowing multiphase system by the finite speed of propagation of density waves (Lahey and Podowski, 1989~. To understand DWO phenomena in a boiling or condensing channel we can consider the channel to be a negative feedback control system (Lahey and Podowski, 1989), in which the inlet liquid velocity is induced by the dynamics of the diabetic system (i.e., the boiling or condensing channel). Similar instability phenomena may occur in electronic and electromechanical systems. Figure IV.C.13 is a schematic of a typical U-tube condenser, and Figure IV.C.14 is the block diagram of the analytical model representing this phase-change system. Similar models and block diagrams can be derived for boiling channels (Lahey and Podowski, 1989~. It is significant to note in Figure IV.C.15 that gravity (g) and inlet velocity (j) appear to have a pronounced effect on DWO in boiling channels (Lahey and Podowski,1989~. That is, variations of the inverse Froude number (Fr-l) can cause a significant change in the linear stability boundary. In particular, it appears that stability is increased as the inlet velocity is increased and/or gravity is reduced. The results shown in Figure IV.C.15 are theoretical results in which homogeneous flow was assumed. It is unlikely that this flow regime will occur in reduced-gravity environments, and thus more detailed analysis and/or experimental confirmation are needed. Nevertheless, gravity can be expected to have a strong influence on channel stability. Significantly, nonlinear supercritical and subcritical Hopf bifurcations (e.g., limit cycles) and chaotic oscilla- tions can also occur in boiling/condensing channels (Achard et al., 1985~. Chaotic (i.e., nonperiodic) instabilities may also occur in phase change systems (Clausse and Lahey, 1991; Chang and Lahey, 1997~. Finally, it should be noted that DWOs may occur not only in channels in which phase change takes place but also in phase-change loops (Lahey and Podowski, 1989~.
PHENOMENA OF IMPORTANCE IN RED UCED GRA VITY 131 l ~j Hi UP tw' / lCASE t 1 i~, ~w1 / 3 / _ _ UP twl EXTE RNAL \` ICASE 2) Van ,~ 3 UP {~' EXTE RNAL {CASE 4) 1~ I/ - lip tw] EXTE RNAL (CASE 3) FIGURE IV.C.ll Excursive instabilities in a boiling channel (where lip is the pressure drop and w is the flow rate). SOURCE: Reprinted with permission of the American Nuclear Society from R.T. Lahey, Jr., and F.J. Moody, The Thermal- Hydraulics of a Boiling Water Nuclear Reactor, Second Edition, p. 329. Copyright (I) 1993 by the American Nuclear Society, La Grange Park, Illinois. Multiphase instabilities in diabetic channels and loops must be avoided since the amplitude of the flow excursions and oscillations can be quite large and dangerous to the integrity of the phase change equipment. Indeed, Ledinegg instabilities have destroyed commercial boilers on Earth (Profos, 1962~. Unfortunately, NASA has performed little research to date on multiphase instabilities in reduced-gravity environments. There are also other potentially important multiphase phenomena that should be studied, including counter- current flow limitations, mixed convection and buoyancy (particularly for the emergency and/or long-term cooling of space-based nuclear power plants), the performance of lubrication films and pumps (e.g., cavitation will be more likely to reduce net positive suction heads), and inertial or condensation-induced loads (e.g., liquid-hammer- type loads). It is also important to note that inertial loads and flow unsteadiness may lead to the flow-induced vibration of piping systems and spacecraft structures. This is particularly true for multiphase flows, where inherent unsteadiness in some flow regimes (e.g., slug flow) may create a forcing function for structural vibrations. These topics are considered in Section V.A.
132 MICROGRAVITY RESEARCH Accumulator (I Condenser 11~ ~ us Test secti on w UP ~ AMPS 1 APo -am) '1 ~ -Aw cow _ Wd' '/Apl~p ___/ _ / Id\ / / / / 1 / ~PpumP , WO ~ FIGURE IV.C.12 Pressure-drop instabilities in a boiling loop. SOURCE: Lahey and Podowski (1989~. Reprinted by permission of Hemisphere Publishing Corporation. Saturated Steam Subcoo_ Water ~ ~ a._ __ -~i_ 1 .~) An _ ~ _ 4 ~ - a\ _ 1 t1~t I ~ I ~ r Egg T3 ~ cast t , ~ FIGURE IV.C.13 Schematic of a U-tube condenser. SOURCE: Lahey and Podowski (1989~. Reprinted by permission of Hemisphere Publishing Corporation. Research Issues In summary, multiphase systems can exhibit global (systemwide) phenomena that are sensitive to gravity level. In particular, both excursive and oscillatory system instabilities are expected to be gravity-dependent. Unfortunately, very little research of this type has been done by NASA. It appears that an experimental and analytical research program focused on, at a minimum, Ledinegg (i.e., excursive) pressure drop and density-wave instabilities is needed if reliable multiphase systems are to be used on HEDS missions.
PHENOMENA OF IMPORTANCE IN RED UCED GRA VITY 133 by. A. IN IS s(~ 1¢ ~ ~ ~ ~ 1 ~ FIGURE IV.C.14 Block diagram for a parallel channel in a U-tube condenser (~ is the single-phase pressure-drop-to-inlet- velocity ratio and 11~ the two-phase pressure-drop-to-inlet velocity ratio). Courtesy of R.T. Lahey, Jr. Leo ..x Loo I.so 1 1 boo ~ .2! 1 Fret Q ( Stable) ~~ 1 >< ~ 14~ 4 (Uns table ) >200 FIGURE IV.C.15 Three-dimensional marginal linear stability surface (J = 0.3; 42.0 < Fr-l = gLH/j 2I < 50.0) where j and LH are the inlet velocity and length of the heated channel, respectively, g is the acceleration of gravity, and Fr is the Froude number. SOURCE: Lahey and Podowski (1989~. Reprinted by permission of Hemisphere Publishing Corporation.
34 MICROGRAVITY RESEARCH Flow in Porous Media Problems involving single- and multiphase flow, heat transfer, and multicomponent mass transport in porous media arise in a number of scientific, geophysical, and engineering disciplines. Important technological applica- tions include geothermal energy exploration, enhanced oil recovery, chemical and drying processes, capillary- assisted thermal management technologies for space exploration, and numerous others (Woodling and Morel- Seytox,1976; Wang and Cheng, 1997; Adler and Brenner, 1998; Masuoka, l999~. For example, porous media in a capillary pumped loop, which is used for thermal management in microgravity, determines the available pump- ing head for transport of heat in the loop. Changes in the wick (porous medium) properties to increase the transport capacity of the loop may affect (positively or adversely) the overall loop performance and system response. Following a depriming or dryout of the structure due to excess heat addition or system transients, rewetting of the capillary must occur for normal operation to resume. Delivery of nutrients to the roots of plants in growth media (i.e., porous root media) is an example of fluid flow in porous media associated with plant cultivation for life support in fractional gravity or microgravity environments (Eckart, 1996~. Two-phase devices such as heat pipes and capillary pumped loops have become key elements in the thermal control systems of space platforms. Capillary and porous structures are necessary and widely used in these devices, especially in high-heat-flux and zero-gravity applications (Faghri, 1995, 1999~. As is discussed in Chapter III, porous media are also used in fuel cells, life support systems, bioregenerative food production, and chemical processing. Because of its diverse and important geophysical and technological applications, flow in porous media has received considerable research attention (Bear and Bachmant, 1990; Dullien, 1992; Nield and Bejan, 1992; de Boer, 1996; Wang and Cheng, 1997~. Single- and multiphase fluid flow in saturated, partially saturated, and unsaturated porous media is of interest, and extensive discussion of the issues can be found in the references cited. Darcy's law, which describes fluid flow in porous media, has been generalized for both steady and unsteady multiphase flow in porous media (Dullien,1992~. The macroscopic-scale Darcy's law for two-phase flows in porous media has, however, been criticized from several perspectives (Wang and Cheng, 1997; Adler and Brenner, 1998), and controversy continues about the extension of the law. Data needed for system designs involving porous media are usually obtained empirically, because pore structure, effective thermophysical charac- teristics, transport coefficients, and other information needed as inputs to flow and transient model equations are not readily available. A number of complex, interacting transport phenomena may take place in a nonisothermal, multiphase system. In general, flow in porous media is driven by gravitational, capillary, and viscous forces. Gravity causes phase separation and migration in the direction of the gravitational field. In microgravity, capillary and viscous forces play fundamental roles in controlling the phase distribution and, hence, multiphase flow and transport in porous media. According to Dullien (1998), surface tension, wettability, pore morphology, and displacement are historically the fundamental parameters that determine the topologies of immiscible fluids in porous media at capillary equilibrium. Steady two-phase flow at a given level of saturation depends on viscosities and fluid velocities, in addition to the parameters listed above. No fundamental experimental studies of fluid flow in porous media under isothermal or nonisothermal flow conditions have been performed in reduced or microgravity envi- ronments. The lack of experimental data constitutes a major impediment for the conceptual development of flow models in porous media. Basic understanding of two-phase flows through porous media is of interest in many chemical processing and geophysical applications (Wang and Cheng,1997~. The early work was primarily motivated by potential applica- tions in absorption towers employed in the chemical industry. More recently, two-phase flow in porous media with heat transfer has become a concern in light-water nuclear reactor accident scenarios in which the reactor core is severely degraded (Tuna and Dhir, 1988; Chung and Catton, 1991~. With respect to HEDS technologies, adiabatic two-phase flows or two-phase flows with heat transfer are relevant to life support systems, fuel cells, AMTEC, in situ resources utilization, heat pipes, and materials processing. For example, the delivery of nutrients to roots of plants in growth media is an example of fluid flow in porous media for life support in fractional or microgravity environments (see Section III.C). However, no fundamental studies of single- or two-phase flows in porous media, with or without heat addition, under reduced or microgravity conditions could be identified in the
PHENOMENA OF IMPORTANCE IN RED UCED GRA VITY 135 literature. Flow regimes (flow patterns), pressure drop, and dryout are also expected to be greatly influenced by gravity and surface tension. Size and shape of particles, porosity, permeability, wetting, type of fluids, etc. are expected to be important factors affecting two-phase flows in porous media. The effect of combined thermal and gravity modulation on the onset of convective flow in porous media has not been studied and is not understood. Recently, it was shown theoretically that low-frequency "jitter can have a significant effect on flow stability (Malashetty and Padmavathi, 1998), but experimental data do not appear to exist in the literature that could be used to validate the theoretical predictions. Knowledge of turbulence is important when predicting flow, heat, and mass transfer characteristics in porous media at high Reynolds numbers. Macroscopic turbulence models have been proposed (Travkin et al., 1993; Masuoka and Takatsu, 1996~. Masuoka and Takatsu in their model introduced the concepts of interstitial vortex and pseudovortex to reflect the micro- scopic vortex behaviors intrinsic to porous media. Their macroscopic turbulence model has been subjected to experimental verification (Takatsu and Masuoka, 1998~. It has been shown that the obstruction of a solid matrix not only imposes spatial restrictions on the magnitude of interstitial vortices but also induces flow distortion. The fluid parcel in the mixing zone is transported by the flow distortion with mixing length being of the order of the particle diameter. This motion produces additional mixing in the interstitial vortex. Practical porous-media turbulence models for predicting transport coefficients such as thermal dispersion and eddy diffusivities have not yet been proposed (Masuoka, 1999~. Research Issues In summary, there are many fundamental research issues for single, multiphase, and multicomponent flows and transport in porous media that are not understood and have not been studied under fractional or microgravity conditions. These issues include the following: (1) There is a need to identify single-phase flow regimes in porous media, in both the presence and absence of forced flow, and express them as a function of operating variables. Such information is required for constructing porous media flow and transport models. (2) The simultaneous flow of gas and liquid through a fixed (packed) bed of particles in microgravity needs to be characterized. To this end, different flow regimes that exist (say, air-water systems) should be determined for a range of conditions of technological interest, and the boundaries between flow regimes should be established. (3) The effects of com- bined capillary and gravitational forces in partially saturated porous media and effects of mechanical surface characteristics such as roughness have not been studied and are not understood. Research is needed to relate pore- scale hydrodynamics to macroscopic-scale flow parameters and to identify flow regimes. (4) The effects of local thermal nonequilibrium, on a macroscopic scale, between the solid and fluid phases, on steady transport processes in saturated porous media need to be assessed and conditions identified for which they are important. (5) Experimental and theoretical work is needed to develop models on a micro- and macroscopic scale to rigor- ously address the coupling between vapor dynamics on the pore level and two-phase transport phenomena on the system level. (6) It would be highly desirable to account for pore-level fluid mechanics and to predict the development of complex flow structures and the two-phase zone at the onset of boiling and dryout when a liquid is heated in a porous medium. This is because various transient effects and flow instabilities may exist in the highly nonlinear system in which two-phase adiabatic or nonadiabatic flow occurs in a porous medium. References Achard, J.-L., D.A. Drew, and R.T. Lahey, Jr. 1985. The analysis of nonlinear density-wave oscillations in boiling channels. J. Fluid Mech. 155:213-232. Adler, P.M., and H. Brenner. 1998. Multiphase flow in porous media. Annul Rev. Fluid Mech. 20:35-59. Alajbegovic, A., A. Assad, R.T. Lahey, Jr., and F. Bonetto. 1994. Phase distribution and turbulence structure for solid/fluid upflow in a pipe. Int. J. Multiph. Flow 20(3):453-479. Alajbegovic, A., D.A. Drew, and R.T. Lahey, Jr. 1999. An analysis of phase distribution and turbulence in dispersed particle/liquid flows. Chem. Eng. Commun. 174:85-133. Antal, S.P., R.T. Lahey, Jr., and J.E. Flaherty. 1991. Analysis of phase distributions in fully developed laminar bubbly two-phase flow. Int. J. Multiph. Flow 17(5):635-652.
136 MICROGRAVITY RESEARCH Bear, J., and Y. Bachmant. 1990. Introduction to Modeling of Transport Phenomena in Porous Media. Dordrecht, Netherlands: Kluwer Academic Publishers. Bousman, W.S., and A.E. Dukler. 1993. Studies of gas-liquid flow in microgravity: Void fracture pressure wrap all flow patterns. ASME Symposium Vol. 174/Fed. Vol. 175. New York: American Society of Mechanical Engineers. Bousman, W.S., J.B. McQuillen, and L.C. Witte. 1996. Gas-liquid flow patterns in microgravity: Effects of tube diameter, liquid viscosity and surface tension. Int. J. Multiph. Flow 22(6):1035-1053. Chang, C.J., and R.T. Lahey, Jr. 1997. The analysis of chaotic instabilities in boiling systems. Nucl. Enc. Des. 167:307-334. - , ~ _ ~ _ Chen, I.Y., R.S. Downing, E. Keshock, and M. Al-Skarij. 1991. Measurements and correlation of two-phase pressure wrap under microgravity conditions. J. Thermonhvs. Heat Transfer 5:514-523. ~ , _ Chung, M., and I. Catton. 1991. Post-dryout heat transfer in a multi-dimensional porous bed. Nucl. Eng. Des. 128:289-304. Clausse, A., and R.T. Lahey, Jr. 1991. The analysis of periodic and strange attractors during density-wave oscillations in boiling flows. J. Chaos, Solitons and Fractals 1(2):167-178. Colin, C., J. Fabre, and A.E. Dukler. 1991. Gas-liquid flow at microgravity conditions I, dispersed bubble and slug flow. Int. J. Multiph. Flow 17(4):533-544. Croff, A.G. 1980. ORIXEN2 A Revised and Updated Version of the Oak Ridge Isotope Generation and Depletion Code. ORNL-5621. Oak Ridge, Tenn.: Oak Ridge National Laboratory. de Boer, R. 1996. Highlights in the historical development of the porous media theory: Toward a consistent macroscopic theory. Appl. Mech. Rev. 49:201-262. Drew, D.A., and S.L. Passman. 1998. Theory of Multicomponent Fluids: Applied Mathematical Sciences Series, Vol. 135. New York: Springer-Verlag. Dukler, A.E., J.A. Fabre, S.B. McQuillen, and R. Vernon. 1988. 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Multiphase Flow 13(3). Wilcox, D.C. 1998. Turbulence Modelling for CFD. La Canada, Calif.: DCW Industries. Woodling, R.A., and H.J. Morel-Seytoux. 1976. Multiphase fluid flow through porous media. Annul Rev. Fluid Mech. 8:233-274. Zaho, L., and K.S. Rezkallah. 1993. Gas-liquid flow patterns at microgravity conditions. Int. J. Multiph. Flow 19(5):751-763. Zumbrunnen, D.A. 1998. Enhanced physical properties of composite materials produced by chaotic mixing. Pp. 689-690 in Proceedings of the . ~ ~ . National Science Foundation Design and Manufacturing Grantees Conference, January 5-8, Monterrey, Mexico. Arlington, Va.: Na- tional Science Foundation. IV.D HEAT TRANSFER Introduction Many of the systems required for HEDS technologies involve single- and two-phase flow, heat and mass transfer (transport phenomena), including power generation and storage, propulsion, life support, thermal manage- ment, and in situ resource utilization. Because fluid flow and heat transfer are affected by reduced gravity or microgravity, they represent critical processes in efficient and reliable active power generation technologies. For example, in the absence of gravity, forced convection or cryogenic cooling of regulators, converters, control circuits, etc. (under "Power Management" in Figure III.A.2) will be required. More specifically, multiphase flow phenomena, which are highly gravity-dependent, are central to heat and mass transfer in many systems. Gas/liquid contacting for air purification plays an important role in chemical processes such as catalysis and in beneficiation techniques. Fundamental studies of such phenomena will contribute to process and system design for microgravity or fractional gravity environments. Fluid mechanics and transport phenomena are inseparable, and both are significantly influenced by gravity (particularly for multiphase flow) and play essential roles in many processes that are important to HEDS mission- enabling technologies. For example, a difference in density caused by temperature and/or composition can produce buoyancy-driven flow, thus giving rise to convective heat transfer. Even for single-phase transport, a reduction of gravitational forces leads to the dominance of other forces normally obscured in terrestrial environ- ments, such as surface tension effects (Ostrach, 1982~. A number of different types of forces and fluid flows have
138 MICROGRAVITY RESEARCH been identified that can occur under microgravity conditions. For example, in such microgravity applications as two-phase flow with heat transfer (e.g., boiling) and thermocapillary migration of bubbles and droplets, thermo- capillary flow is known to play an important role (Kamatoni, 1997~. Extensive discussion of the microgravity issues pertaining to single-phase fluid flows as they relate to materials processing in space can be found in an earlier NRC report (1978), and a detailed account of the gravity effects on fluid flows, including identification of relevant scaling parameters, has been provided by Ostrach (1982~. Within the last decade, the Committee on Microgravity Research has also reviewed the status of microgravity research (NRC, 1992, 1995~; the review need not be repeated here. Of the three modes of heat transfer conduction, convection, and thermal radiation conduction and radia- tion are not directly affected by gravity and will not be discussed, except in passing. Single- and multiphase fluid flow are strongly affected by gravity, but single-phase convective heat transfer can be more readily scaled and is, therefore, treated rather superficially. The discussion in the report will focus on convective heat transfer with phase change. Heat conduction in solids and liquids is not influenced by gravity. Heat conduction in gases is also not affected by gravity, except that, indirectly, low gravity is also associated with low atmospheric pressure. This, in turn, results in low density and thermal conductivity of the gas and reduces the rate of heat transfer by conduction. Heat transfer in highly ratified gases is well understood (Eckert and Drake, 1972~. In a free space (lo-7 torr) environment, the molecular mean free path becomes long, and gaseous heat conduction across a gap becomes negligible. In turn, elastic and plastic deformations can become important and affect thermal contact conductance (resistance), but they have not been studied in microgravity environments. Lack of space experience may, however, cause unexpected problems. For example, nitrogen ice, imbedded in aluminum foam inside a dewar, has been seen to expand more than expected. The expansion of the nitrogen ice apparently caused two originally separated internal components inside the dewar to come in contact, providing a path for heat conduction and the increased evaporation of nitrogen, thereby shortening the life span of one near-infrared camera and multi-object spectrometer (NICMOS) on the Hubble Space Telescope (Harwood,1997~. This occurrence clearly demonstrated the peril of using materials (e.g., aluminum foam-nitrogen ice) in the construction of a high-tech thermos whose thermophysical properties are not understood and not well modeled, in this case shortening the life span of an important instrument. Thermal radiation heat transfer is also not affected by gravity. However, the radiation characteristics of a surface can be modified over time by the space environment, and this needs to be considered in the design of the systems. For example, cryodeposits formed on thermal control surfaces can alter the thermal emittance, and ultraviolet radiation can modify the solar radiation characteristics of thermal control coatings. Solar panels on Mars are expected to accumulate dust and soil, and the performance of the photovoltaic cells would be degraded with time if the panels were not cleaned. Human habitats, cryogenic storage facilities, and other structures would also be affected by dust and their radiation characteristics modified. Effects of Martian soil and dust on the radiation characteristics of structural materials are not understood and should be studied. Even though the phenomena of heat conduction and radiation are not influenced directly by gravity, heat transfer by combined conduction and radiation in porous insulations is relevant to HEDS technologies. High- efficiency thermal insulations are usually associated with the cryogenic storage of liquid H2 to prevent heat penetration and boiloff; they can also be used to reduce heat losses from high-temperature (~1000 °C) fuel cells and can improve the temperature performance and control of furnaces by preventing leakage. To improve engineering design equations for low-pressure heat transfer in porous thermal insulations, void radiation, void gas conduction in intermediate and low pressures, and solid conduction need to be understood and modeled. The phenomenological and technical concerns related to the thermal design of systems for HEDS applications are wide ranging and cannot be addressed fully in this account. Single-phase convective heat transfer is discussed only briefly below. The emphasis of the rest of the section is on convective heat transfer problems where gravity can greatly affect fluid motion, and for the sake of brevity, the discussion is focused on the following specific topics: (1) evaporation, (2) boiling, (3) condensation, (4) two-phase forced convection, (5) phase-change (melting and solidification) heat transfer, and (6) phase-change heat transfer in porous media.
PHENOMENA OF IMPORTANCE IN RED UCED GRA VITY 139 Single-Phase Convection Convective heat and mass transfer, i.e., convection of heat and mass, is always accompanied by fluid motion, and the term is used to describe heat transfer between a surface and a moving fluid or across an interface between two immiscible fluids in relative motion. Hence, convection is always influenced by the fluid motion and the state of the fluid. The literature on low-gravity fluid flows in bulk fluids has been reviewed by Ostrach (1982) and Myshkis et al. (1987) and will not be repeated here, though it should be noted that there have been some significant advances since the appearance of these reviews. State-of-the-art literature reviews of convective heat transfer could not be identified, even though the process is as complex as the accompanying fluid flow. Convective heat and mass transfer phenomena play important roles in many space-based technologies. Applications include subsystems for power generation, propulsion, life support, chemical and materials processing, and thermal man- agement. For example, the weightless condition of space travel eliminates the familiar gravitational body force on liquids and gases, usually causing surface tension and contact angle (capillary effects) to dictate the static equilib- rium shape of a liquid and vapor in a propellant tank. Yet, in this situation, gas-free propellant must still be delivered to thrusters, the center of mass must be predicted and controlled, fuel must be kept above freezing, the remaining fuel must be accurately gauged, and apparent anomalies from telemetry must be diagnosed. Single-phase forced flow at sufficiently high velocities is not directly affected by gravity, but for intermediate velocities (say, a Reynolds number of 104 when based on the diameter of the tube as an element of a heat exchanger) where large temperature gradients exist between the fluid near the wall and the center, gravitational effects could modify the forced flow and heat transfer. The heat exchanger orientation, turbulence, and relaminar- ization could be additional factors. In addition, if temperature gradients exist within a fluid flowing at relatively low Reynolds numbers through a curved conduit, there may be separation into different density regions due to secondary flow effects. This effect will be even more pronounced for multiphase flows, where secondary flow can induce phase separation. Unfortunately, the interplay between gravity and secondary flows has not yet been thoroughly studied. In the absence of forced flow, the existence of temperature and concentration gradients in the presence of a gravitational field can lead to bulk flow of the fluid. Single-phase external and internal natural convection heat transfer has received significant research attention during the last 75 years (Raithby and Hollands, 1998~. Convective heat transfer scaling relations have been developed both experimentally and theoretically for a large number of natural (Jaluria, 1987) and mixed (Chen and Armaly, 1987) convection flow geometries, and these scaling relations can be used for thermal design purposes. For example, the external natural convection heat transfer coefficient for laminar and turbulent convection from a vertical plate scales as gi/4 and "i/3, respectively. However, the existing scaling relations have not been carefully compared against experimental data obtained under reduced gravity conditions. The scaling with gravity of thermal phenomena, i.e., the identification of boundaries at which the physics of phenomena changes with the gravity level, has been recommended by a recent NASA workshop. For example, there may be a need to predict (simulate) convective heat transfer from solar cell arrays, radiator panels, and habitable structures on Mars. Theoretical models are currently available for this task. Recent advances in microfabrication techniques have led to the development of compact, microchannel chemical reactors in the United States, Europe, and Japan (Tuckerman and Pease, 1981; Ehrfeld, 1995; Wegeng et al., 1996; Tonkovich et al., 1998~. Microchannel heat exchangers and chemical processing equipment have the advantages of very efficient heat/mass transfer, compactness, and high specific performance (i.e., productivity per unit volume). Such microchannel-based processing technologies have, as an example, potential application for in situ resource utilization because of their greatly reduced mass. Theoretically, the chemical processing rates in such microreactors should increase significantly owing to a decrease in the resistance to the species transport caused by a drastic reduction in the thickness of thermal and solutal boundary layers. Ideally, one would hope to achieve and to maintain sufficiently large reactor throughput by using parallel chemical processing in many small channels composing the reactor, but fouling of these microchannels is of concern. It is clear that successful design of microchannel-based chemical reactors requires a fundamental understand- ing of the transport processes occurring on the microscale. For example, distinct oscillatory flow has been predicted in microchannels, when heat and mass transfer is accompanied by adsorption/desorption (Fedorov and
140 MICROGRAVITY RESEARCH Viskanta, 1999~. However, a similar physical situation has not been found in macrochannels, and the reasons for the difference are not known. There do not appear to be any direct effects of microgravity on flow and transport phenomena in microchannels, but miniaturization of the components reduces their sensitivity to gravity. An indirect effect of microgravity is that it may be difficult to control the purity of fluids in HEDS applications of the technology. In extended operation, single-phase and phase-change heat exchange surfaces in terrestrial environments invariably experience performance degradation due to fouling. Passive means and active devices for enhancing single- and two-phase heat transfer and for mitigating fouling have recently been discussed (Sommerscales and Bergles, 1997~. The influence of fouling caused by impurities or dust on heat-exchange performance (particularly for microchannels) when the heat exchanger is operated for extended periods of time should be studied in microgravity. Research Issues To understand low-Reynolds-number forced and mixed convection as well as natural convection, theoretical analyses and computational tools for single-phase heat transfer need to be developed and supported by parallel experimental efforts so that the models can be validated. The theoretical models should be able to predict not only microgravity fluid behavior but also the effect of body forces due to artificially imposed force fields. Induced forces such as centrifugal, surface tension, magnetic, electrostatic, and osmotic could be analytically evaluated as to their effectiveness in compensating for the absence of gravity field in various space subsystem applications. This would permit simulation of fractional, micro-, and variable gravity and thus would improve understanding and insight into fundamental phenomena. Theoretical/com~utational models validated against experimental data could then be applied with confidence to physical situations of interest. To meet the future demand for growing active power generation, thermal management, and other systems for HEDS missions, passive and active heat transfer enhancement schemes suitable for microgravity conditions need to be assessed and developed for single-phase fluids to reduce the size and weight of the equipment. Examples of such methods include imposition of electric fields, variable gravity or rotation to enhance thin-film heat transfer, and liquid jet impingement cooling/heating of a surface, among others. Microsystems may allow the size and mass of the needed equipment to be reduced. Of particular interest would be schemes that enhance heat transfer but do not increase pressure drop or pumping power proportionately. Evaporation Heat Transfer Evaporation is a surface (interface) mass transfer process that occurs when the liquid molecules near the surface experience collisions that increase their energy above that needed to overcome the surface binding energy. When the temperature of the vapor/gas mixture is lower than the interface temperature, evaporation may proceed only if the parent liquid is superheated and thus supplies the necessary heat (Lock, 1994~. Evaporative cooling that occurs at the liquid surface as a result of evaporation is a phase-change heat-transfer process that is associated with the latent heat of vaporization of the liquid. The energy required to sustain the evaporation must come from the internal energy of the liquid, which then must experience a reduction in temperature (the cooling effect). Evaporating drops, sprays, and liquid films are widely used industrially and in space devices such as space radiators for life support and waste heat management. For example, thin evaporating liquid films produce high heat transfer rates and are used in heat pipes, sweat coolers, grooved evaporators, and other enhanced heat- transfer-surface devices that depend on the formation of thin-film regions owing to capillary action (Bankoff, 1990; Faghri and Khrustalev, 1997~. As a basic physical process, the evaporation of a thin liquid layer plays a key role in heat transfer. Some transport processes can be modeled using a classical continuum transport model with special modification to boundary conditions to account for nonequilibrium effects. Wayner (1998) discusses recent progress. Obviously, a number of high-efficiency heat-transfer devices are dependent on the heat-transfer
PHENOMENA OF IMPORTANCE IN RED UCED GRA VITY 141 characteristics of the evaporating thin layer. As the space applications of two-phase devices are developed, the importance of convection and heat transfer in evaporating thin liquid films will become more important. The behavior of thin films under the action of various mechanical, thermal, or structural forces has recently been discussed in a comprehensive review (Oron et al., 1997~. Theoretical advances in the evaporation/condensa- tion of thin films were also discussed, including the effects of mass loss/gain, vapor thrust, capillarity, and thermocapillarity. Unsolved problems were identified, but the effects of gravity on thin film evaporation were not considered. Stability and dryout of thin liquid films are an important consideration since they can determine the allowable heat flux in forced-convection, subcooled boiling or concurrent annular flow. Stability regimes of thin liquid films in the presence of surface tension, van der Waals forces, hydration, and elastic strain interactions have been studied theoretically (Majumdar and Mezic, 1998~. The study showed that the interplay among these highly nonlinear forces can result in a wide variety of regime maps, but the maps have not been validated experimentally. An interesting application of thin film evaporation phenomena is the electrostatic liquid-film radiator, an ultralight radiator proposed for electric power generation in space (Kim et al., 1994~. Macroscopic thin liquid films are relevant to some HEDS technologies. For example, a knowledge of micro- and macrolayer evaporation (e.g., at a bubble's base and at a bubble boundary) is necessary for predicting nucleate boiling heat transfer in microgravity when buoyancy is strongly reduced and transport processes are determined by the properties of the interface alone (Straub, 1994~. The effects of thermocapillary and capillary pressure flow, evaporation, condensation, and coalescence mechanics need to be understood for predicting nucleate boiling, and future research needs have been discussed (Dhir,1998~. An understanding of convection driven by evaporation in thin liquid layers may also provide a basis for determining the nucleate boiling mechanisms in the macrolayer. For example, the thin liquid sublayer beneath the bubble is believed to be a key element for enhancement of heat transfer in thin (macro-layer thickness) liquid films. In a microgravity environment, the effects of surface tension forces, thermocapillary forces, and the disjoining pressure force and convection on the microlayer thickness, stability of the liquid film, and mechanisms leading to film rupture or dryout are expected to be different than in go In spite of their relevance to a fundamental understanding of the heat transfer mechanisms in nucleate boiling and in two-phase flow in space applications, the thermal conditions taking place in thin liquid layers with a free surface have not been investigated under microgravity. Heat transfer processes in thin liquid layers (<1 mm) with a free surface, in which convection is driven by the surface tension, have not been studied, and nonequilibrium evaporation (or condensation) in weightless conditions across an interface between a viscous liquid and a viscous gas has not been characterized. In the past, almost all investigators concentrated on the convective instability in the liquid layer rather than heat transfer in the layer and evaporation from the free surface. Evaporation and latent heat are expected to play important roles in the onset of convection, and the convection itself in thin liquid layers will be influenced by surface tension under microgravity conditions. With high heat fluxes, the heat and mass transfer rates may be limited by a critical mechanism forced by a physical process. In a gravity field these phenomena are partially masked, but they can be very significant in microgravity environment. Some examples include the following: · Shear stresses at the liquid/vapor interface in an axially grooved condenser, which are due to vapor/liquid interaction combined with the effects of thermocapillarity, can cause the capillary structure to be flooded with liquid and the appearance of liquid recirculation zones. This will lead to unacceptable thermal resistance in the condenser. · The existence of thick liquid films attached to the extended evaporating meniscus in a capillary tube can significantly change the existing methods of predicting dryout in capillary-driven devices. · Shear stresses induced on the liquid/vapor interface by thermocapillarity and complex three-dimensional vapor flow can cause the recession of the evaporating liquid meniscus in a groove and lead to an unstable mode of operation in the axially grooved evaporator. · Rotating thin films offer enhanced evaporative heat transfer characteristics owing to the film thinning effects associated with rotational body forces.
142 Research Issues Some research MICROGRAVITY RESEARCH li' ssues for surface-tension-driven single-phase free surface flows are identified in Section IV.B. Additional areas of appropriate research include (1) theoretical analyses and experiments to observe evaporation- driven fluid motion in very thin evaporating layers, (2) measurement of heat transfer coefficients in very thin liquid films undergoing evaporation for a range of Marangoni numbers, (3) characterization of the Marangoni instability phenomena in droplets undergoing radiative and/or evaporative cooling, and (4) determination of the induced convection on the droplet evaporation rate, which is required for properly designing droplet radiators. Some unexpected critical phenomena have been encountered in such devices as long heat pipe evaporators, and high thermal resistance has been noted in loop heat pipe evaporators. Fundamental investigations under microgravity conditions are needed to better understand the thermal/fluid behavior in capillary structures during evaporation at high heat fluxes. Heat and mass transport may be restricted by the initiation of critical mechanisms forced by physical phenomena at high fluxes. In a gravity field, these phenomena may be masked but they can be very important in a microgravity environment. Boiling Heat Transfer Boiling is a phase change process in which vapor bubbles are formed in a superheated liquid layer adjacent to a heated surface or on a heated surface. Boiling can also be considered as an evaporation process that involves creation of discrete vapor/liquid interfaces on a heated surface. Single-component boiling, which is a formation of pure vapor from a superheated pure liquid, begins when the wall (surface) temperature exceeds the saturation temperature of the liquid. Boiling is known to be a very efficient mode of heat transfer. Knowledge of boiling heat transfer under microgravity conditions, with gravity levels varying from 1 gO to 1 o-6 go, is needed for the design of power generation (e.g., Rankine cycle), thermal management, fluid handling and control, on-orbit storage and supply systems for cryogenic propellants and life support fluids, and for cooling the electronic packages associated with various instrumentation and control systems. The subsystems affected by the phenomena include heat exchangers-boilers; on-orbit storage and supply systems for cryogenic propellants and life-support fluids; and systems for cooling electronic packages, instrument packages, and control systems. During the past 50 years boiling has been the subject of much research because it is a very efficient and, technologically, a very important heat transfer process. Most of the research was on boiling under normal gravity conditions, and the process has received a lot of attention; however, controversies about the mechanisms control- ling boiling persist, and a complete understanding of the critical heat flux (CHF) phenomena remains elusive. Numerous accounts of boiling are available, including that of Dhir (1998), which discusses boiling fundamentals and cites relevant references. In summary, there are two types of boiling heat transfer pool and forced flow. Pool boiling refers to boiling under natural (buoyancy-driven) convection conditions, whereas in forced-flow boiling (whether internal or external), liquid flow over the heated surface is imposed by external means. The boiling heat transfer data are usually presented in the form of a boiling curve in which the wall heat flux is plotted against the difference between the surface temperature and the liquid saturation temperature. The nucleate, transition, and film boiling regimes as well as the critical (maximum) heat flux are identified from the boiling curve. CHF sets the upper limit of fully developed nucleate boiling for safe operation of equipment. Pool Boiling Gravity is one of a large number of system variables that influence the dependence of the nucleate boiling heat flux on the wall temperature (Siegel, 1967; Dhir, 1991, 1998~. The magnitude and direction of the gravitational acceleration with respect to the heater surface influence the fluid dynamics and thermal boundary layers and, consequently, the bubble trajectory. Pool boiling heat transfer results obtained under reduced gravity conditions have been contradictory (Lee et al., 1997; Sitter et al., 1998~. Some earlier nucleate pool boiling data obtained using terrestrial facilities (i.e., free-fall drop towers, parabolic aircraft flights, and sounding rockets) indicated that nucleate boiling heat transfer was insensitive to reductions in gravity (see Straub et al., 1990; see also Lee et al.,
PHENOMENA OF IMPORTANCE IN RED UCED GRA VITY 1 ()0 _` c - G - X = - ~ 10 1 0.1 o Transient - high subcoolino o Transient - low subcooling · STS-47 aJg~O, Subcool=l I TIC · STS-57 a/g~O, S ubcool= I I °C · STS-60 a/g~O, Subcool=11 °C _ | Microgravity | Pool Boiling :: _ ~ q m~X(CHF) Kurateladze :19481 ~ i' "Reference Curve in aJg = 1 | , ,.. . ~ I ~ / \,/ ~ High Subcool __~_\-,_ it/ STS-47-57-60 ,/Uncertainty for Dryo Low subcool 0 / to 0 \ To Too ~ o offs O /` 0 ~ \\ Natural Convection Nu=O. 15 Rain Nucleate boiling regime, Ho: ,1~_, q",l,,n, Berenson (1961' ' Film Boiling, Berenson (196 10 Heater Surface Superheat(ATw=Tw - Tot) (°C) 43 t l ng l ng ) 100 FIGURE IV.D.1 Approximate composite microgravity pool boiling curves for R-113 from steady and quasi-steady measure- ments made during shuttle flights STS-47, STS-57, and STS-60. SOURCE: Lee et al. (1997~. Reprinted with permission from the American Institute of Aeronautics and Astronautics. 1997, for additional citations), whereas other data (Weinzierl and Straub, 1982; Merte et al., 1994) indicated enhancement of nucleate boiling heat transfer in microgravity. The difference in geometry of the heated surfaces, the variable quality of the gravity, and the short times available for conducting experiments contribute to the apparent contradictions in findings about the role of gravity in nucleate pool boiling heat transfer (Lee et al., 1997~. In recent experiments steady-state pool boiling of R- 113 has been achieved, and a pool boiling curve has been generated (Lee et al., 1997, 1999~. Analysis of the transient data has revealed that steady-state nucleate boiling heat transfer under microgravity conditions is enhanced relative to that in Earth gravity, whereas the CHF is considerably reduced. Approximate microgravity pool boiling curves for R-113 have been constructed using available data from quasi-steady measurements on STS-47, -57, and -60 and available correlations (Lee et al., 1997~. Two curves, one for low and one for high levels of subcooling, are compared in Figure IV.D.1 with a reference curve for normal gravity. Pool boiling with fluids whose wetting characteristics are unlike those of R- 113 and with surfaces different from the highly polished quartz used in these experiments are expected to produce different behavior than indicated in the figure.
44 MICROGRAVITY RESEARCH Controversy persists about the dependence of CHF on gravity. According to the Kutateladze (Verkin and Kirichenko, 1976) and the Zuber (Dhir, 1998) theories, CHF should scale as "i/4. However, for very low gravities, its functional dependence on gravity is weaker than is predicted from these theories. The reasons for the weaker dependence of CHF on gravity under microgravity conditions are not fully understood. On the other hand, Kirichenko and his coworkers took measurements at high pressures and observed a stronger dependence of CHF on gravity (i.e., ~ g2/5) (Verkin and Kirichenko, 1976~. This empirical finding over a range of pressures is consistent with the predictions of a simple theoretical model. The reasons for the disagreement between the two theories are not known. The minimum (film boiling) heat flux, corresponding to complete dryout in microgravity, can also be antici- pated to be much less than that in Earth gravity. Nucleate boiling heat transfer experiments were conducted by Ohta et al. (1998) under 10-4 go conditions using a NASDA TR-1A No. 5 rocket. These investigators observed a marked heat transfer enhancement for ethanol when microlayers underneath the attached primary bubbles occu- pied a large part of the heating surface. However, the heat transfer deteriorated as time progressed owing to the extension of dry patches in the microlayers. Experimental data from five space flights have recently been reported and analyzed (Merte et al., 1997; Lee et al., 1999~. Measurements of parameters associated with bubble dynamics and heat transfer in cool boiling of fluorocarbon R-113 were made at about 10-4 go. Boiling characteristics, including vapor bubble dynamics associated with nucleation, bubble growth/collapse, and surface tension, were examined from a series of photo- graphs, and heat transfer coefficients were determined from measured heater surface temperatures. Steady-state pool boiling was achieved and was attributed to surface tension effects. A large vapor bubble observed to hover near the heater surface produced a maximum 32 percent enhancement in heat transfer. A peculiar phenomenon was discovered that was referred to as vapor bubble migration, in which numerous tiny vapor bubbles nucleated and then moved toward a large bubble attached to the heater. An enhancement of about 30 percent in heat transfer was noted, but there was a significant decrease of the CHF in microgravity. Existing theoretical models are unable to predict CHF under pool boiling conditions. For example, Suzuki et al. (1999) reported that the CHF measured in microgravity experiments is two to four times as great as predicted by the existing theories. It is well established that bubbles suspended in a fluid will move when subjected to a temperature gradient, owing to the action of the resulting interracial tension gradient (Subramanian, 1992~. Such motion, termed capillary migration, may have important implications for pool boiling heat transfer from a heated surface. The driving force for the bubble motion is the shear stress at the interface, which is a consequence of the temperature dependence of the surface tension. Recent results of spacecraft experiments on thermocapillary migration of bubbles have been reported (Balasubramanian et al., 1996), but the effect of the surface-tension-driven bubble motion on pool boiling heat transfer in microgravity has not been studied. Theoretical analyses (Subramanian, 1992) have identified two dimensionless parameters (i.e., Reynolds number and Marangoni number) that govern bubble motion in a liquid. In practical situations for space applications, it is expected that a wide range of values of these parameters will be encountered, depending on the thermophysical properties of the fluids involved and the temperature gradients imposed. Study of bubble motion during nucleate pool boiling is complicated by the fact that there may be mutual interference and distortion of the nearly spherical shape as small vapor bubbles coalesce to form larger ones, as observed by Lee et al. (1999~. Important questions remain to be addressed about the mechanisms and character of nucleation, dynamic behavior of the vapor bubbles, nucleate and transition boiling heat transfer, transition from nucleate to transition boiling, boiling stability, partial dryout behavior, drying/rewetting processes on a heated surface, and critical heat flux under microgravity conditions. The physics of bubble growth and detachment, bubble merger (coalescence) at and away from the heated surface, and vapor removal and the contributions of various mechanisms to the total heat transfer rate for pool and forced flow boiling under reduced gravity conditions are not fully understood. For example, the presence of thin liquid layers under vapor bubbles growing on heater surfaces is believed responsible for the enhancement of nucleate pool boiling observed in microgravity relative to that in Earth gravity. The formation of these large-scale thin layers is poorly understood and has not been adequately described for pool and flow boiling by a theoretical model. No correlations suitable for thermal design purposes for pool and low- velocity-flow boiling heat transfer exist. There is also a need to understand microlayer evaporation when its
PHENOMENA OF IMPORTANCE IN RED UCED GRA VITY 145 thickness is of the same order of magnitude as the root-mean-square value of surface roughness. The heat transfer relations, based on dominating buoyancy and hydrodynamic effects, are not applicable under low-gravity condi- tions. In summary, the available results on pool boiling heat transfer under microgravity conditions are contradic- tory, and a mechanistic understanding of the various regimes of boiling is still lacking. Also, no rational basis exists for predicting pool boiling heat transfer, including CHF. Enhanced understanding of pool boiling requires the ability to model bubble nucleation, bubble dynamics, and heat transfer mechanisms. The mechanisms that need to be considered include microlayer evaporation at the bubble base, evaporation on the bubble boundary, transient conduction, thermocapillary convection, and convection induced by bubble motion. Some processes such as microlayer evaporation and flow induced by thermocapillary forces are greatly impacted by the Marangoni effect (see Section IV.B), but the magnitude of the effect cannot be quantified unless the operating conditions, such as gravity level, fluid, heated surface, and so forth, are specified. Research Issues for Pool Boiling To answer critical questions about pool boiling and CHF, research is needed on the fundamental mechanisms that govern bubble nucleation, growth, and interaction with the force field; bubble departure from the heater surface; and subsequent bubble transport in the superheated fluid. Bubble-bubble interactions, bubble rolling and sliding on macro/micro liquid layers, and bubble agglomeration under microgravity conditions are all in need of study. At higher heat fluxes, the transport mechanisms between the mushroom-shaped larger overhead bubbles and the frothing microlayer (very high density of small bubbles) on the heater surface must be established. Nucleate boiling phenomena in thin and thick films need to be studied in the microgravity environment. Such phenomena are relevant to some types of heat pipes and space radiators; they differ significantly from those observed in pool boiling and remain undefined. Active and passive schemes for enhancing pool boiling heat transfer (including fluid additives, surface coatings, and macro- and microsurface geometry modifications) are recommended for study. Such schemes have a potential of reducing the size and mass of the devices needed for thermal management. Flow Boiling Forced-convection boiling heat transfer and the pressure drop in uniform and nonuniform cross-section channels (conduits) under microgravity conditions must be measured. Potential flow boiling applications in HEDS missions include Rankine cycle power generation, heat pumps, life-support systems, and thermal manage- ment. Applications of two-phase technologies for these systems in space vehicles and lunar and Martian habitats promise to significantly increase thermal efficiency and to reduce the hardware mass to be launched. Two-phase systems can provide higher heat transfer rates at uniform temperatures under variations of heat load than single- phase systems. As already discussed, distinct regimes of flow boiling have been identified in which the dominant heat transfer mechanism varies as the two-phase mixture progresses through a heated duct. Current research on the develop- ment of mechanistic models for nucleate boiling under microgravity conditions has been recently reviewed (Dhir and Hassan, 1998) and need not be repeated here. Over 100 references on both pool and forced-flow boiling are cited in that document. For example, the very important problem of forced-flow nucleate boiling under reduced gravity has received only very limited research attention, and there is no known international effort under way to develop mechanistic models for nucleate boiling or to obtain CHF data under low-velocity conditions in micro- gravity. Fundamental research needs are identified for developing a basic understanding of the mechanisms responsible for heat transfer and vapor removal from the vessel wall. In spite of the fact that forced flow boiling is an attractive means of heat transfer in the microgravity space environment owing to its efficient transport of energy, only two series of aircraft trajectory experiments have been performed. Saito et al. (1994) used Japanese experimental aircraft to study the low-gravity, low-velocity (<6.7 cm/s) flow boiling of water on a rod heater placed in a square channel at about 0.01 go for 20 s. The photographs reveal
146 MICROGRAVITY RESEARCH that under Earth gravity, small bubbles are detached from the heater rod surface, whereas under microgravity conditions, the bubbles hardly detach from the heater rod. The bubbles grow as a result of direct heating from the rod and/or coalesce to become much larger and surround the heater rod. Their measurements were limited to low nucleate boiling heat fluxes, and no data for CHF were taken. Tests of pressure drop and CHF aboard a NASA DC-9 aircraft were performed by Abdollachian et al. (1996~. Unfortunately, there were some serious deficiencies in the experiments (i.e., an electrical tape was used to heat a glass tube) and insufficient details were provided in the report, so these test data cannot be used to thoroughly assess a model. Subcooled forced-convection nucleate boiling experiments with R-113 under terrestrial gravity conditions have demonstrated that if buoyancy is significant relative to bulk liquid momentum, then a decrease in the buoyancy normal to and away from the heater surface enhances heat transfer (Kirk et al., 1995~. In addition, it has been shown that the effect of the bulk flow velocity on heat transfer is dependent on surface orientation. Reference is made to recent accounts on flow boiling for the effects of, among others, subcooling, flow velocity, heater surface orientation, and internal vs. external flow, on flow boiling under the influence of gravity (Dhir, 1991, 1998; Brusstar and Merte, 1998; Hewitt, 1998~. Recently, Brusstar and Merte (1998) concluded that the CHF for forced convection in microgravity is comparable to that for vertical upflow under normal gravity for flow velocities exceeding the buoyant terminal velocity of a vapor bubble in pool boiling. However, they argued that for flow velocities lower than this, the CHF in microgravity is expected to be much lower than in the presence of buoyancy, since the forces acting on the vapor are reduced substantially. Yamada and Fujii (1999) have reported on short (~10 s) drop tower two-phase flow and heat transfer experiments under microgravity conditions. They found that in microgravity forced flow boiling (of Fluorinert F-22) heat transfer is less than in Earth gravity and pressure drop greater. Research Issues for Flow Boiling Many questions are still wide open, and to resolve them would require both experimental and theoretical work on forced boiling heat transfer under microgravity conditions. A few specific topics have been identified for research, including innovative experiments to simulate microgravity conditions on Earth that would allow per- forming long-term two-phase flow and heat transfer experiments and experiments to obtain data needed for validating models and for developing design correlations. Experimental results obtained on board an aircraft are difficult to characterize owing to the often unknown influence of transient effects, and the question often arises as to whether true steady-state conditions are present to a great enough degree to draw valid conclusions. Condensation Heat Transfer Condensation in the context of heat transfer is a phase change process that occurs when a saturated vapor comes in contact with a surface at a lower temperature. Condensation processes require that the enthalpy of phase change be removed through the wall. Three distinct modes of condensation are possible: direct contact conden- sation, in which the vapor being condensed and the subcooled liquid that is condensing it are mixed, and film and dropwise condensation, in which the vapor and liquid are separated by a solid surface. Direct contact condensation produces very high rates of phase-change heat transfer (Marto, 1998), but care must be taken to avoid instabilities and condensation-induced loads. Film condensation occurs if the condensate film wets a wall and a complete film of liquid covers it. The film thickness will grow as it flows down, say, along a vertical wall under the action of gravity. Dropwise condensation occurs when the condensate does not wet the wall and instead, droplets of condensate nucleate at small pits and other surface imperfections and these droplets grow rapidly by direct vapor condensation upon them and by coalescence. Many factors influence condensation heat transfer (Marto, 1998~; gravity is only one. Film condensation heat transfer for laminar flow along a vertical wall is known to scale with gi/4 and for turbulent flow with gi/3 (Marto, 1998~. Unfortunately, no film condensation experiments have been performed under low-gravity conditions, and it is uncertain if the scaling relations are valid for g ~ O. There has been relatively little research on the detailed mechanisms operative at the film interface between condensed liquid and
PHENOMENA OF IMPORTANCE IN RED UCED GRA VITY 147 its vapor under low-gravity conditions (Bankoff, 1994; Oron et al., 1997~. Experiments and theoretical analyses are needed to determine the condensate film layer growth and stability, the development of interfacial distur- bances, and the heat transfer rate. In shear-controlled condensers, interfacial stability, the condensation coeffi- cient, and the effects of noncondensable gases on the condensation coefficient are important issues in the design of the components intended for operation under microgravity. Understanding of the phenomena and practical correlations are needed by designers of equipment for life support, thermal management, and power generation systems. An example of a life-support system is the carbon dioxide condenser/evaporator that is required for the closed-cycle regenerator. A recent review of theoretical interphase mass transfer during condensation and evaporation has been pre- pared (Rose, 1999~. The calculated heat transfer coefficients for dropwise condensation of steam have been compared with experimental data. The results are limited to normal gravity conditions, but the results do not reveal any direct dependence on gravity. In a low-gravity environment interfacial forces such as surface and thermocapillary forces can become significant and could affect the interfacial boundary conditions and dropwise condensation heat transfer. The fundamentally different stability characteristics of condensate film and how they differ from those of films of comparable scale in the absence of condensation is not fully understood. Consider- ation of the combined effects of reduced body force and thermocapillary forces suggests the existence of a convective pattern arising in the presence of condensation that can only be revealed under low-gravity conditions. The fundamental fluid physics for condensate film growth, film instability, and the resulting interfacial motion under reduced gravity, and the corresponding implications for heat transfer have been little studied, are poorly understood, and deserve research attention. Recent work has shed light on the thermocapillary mechanisms driving fluid motion and instabilities in liquid layers with nonuniform temperature. The basically different instability and convective behavior of films in reduced gravity will likely lead to a very different relationship between temperature and wall heat flux (i.e., condensation curve) for both laminar and turbulent flow from that on Earth. For HEDS applications and systems, this topic is worthy of both theoretical and experimental research attention. Research Issues Theoretical and experimental research on interfacial transport phenomena involving phase transition under transient and steady-state conditions is suggested. Condensation is influenced by both gravity and interfacial forces. There is a need to identify flow and transport regimes as well as their boundaries by properly scaling the thermal phenomena with gravity. Boundaries, where the physics of the phenomena change with the gravity level, need to be understood and clearly delineated. Fundamental studies of condensation phenomena under reduced and microgravity conditions need to be undertaken. In parallel with experiments, detailed theoretical analyses should be carried out to develop an understanding of the fundamental fluid physics responsible for condensate film growth, film instability, and the resulting interfacial motion under reduced gravity, and the corresponding implica- tions for forced-flow condensation heat transfer. Two-Phase Forced Convection Heat Transfer Gas/liquid mixtures occur in numerous situations relevant to space missions (Swanson et al., 1989~. The application of two-phase flow and heat transfer technology in future power-generation and thermal management systems for space vehicles and for lunar and Martian habitats promises to significantly increase thermal efficiency and reduce the system mass that must be launched. As compared with single-phase systems, two-phase systems can provide larger heat transfer rates at uniform temperature under large variations of heat load. Studies in Earth gravity show that heat transfer rates and frictional pressure drop depend on how the phases are distributed in the duct (i.e., the flow regimes). Since gravity plays a significant role in the development of flow patterns, these flow regimes are expected to change in low gravity and microgravity conditions. Similarly, heat transfer and pressure drop will be altered with variations in gravity. Surface tension is expected to be a dominant force in determining two-phase flow patterns in gas/liquid mixtures in microgravity. However, inclusion of such a force in theoretical
148 MICROGRAVITY RESEARCH analysis of slug flow in a pipe, for example, can lead to unexpected results that are inconsistent with experimental data (Taitel and Witte, 1996~. Studies (Bousman et al., 1996; Jayawardena et al., 1997) have identified three distinct flow regimes at reduced gravity conditions: bubbly, slug, and annular, with transitions of bubbly-slug and slug-annular. Very recently, a critical literature survey on two-phase flow in reduced gravity was completed and a model was developed for predicting flow regimes in microgravity (Diev et al., 1998~. The investigators have shown that four flow regimes are sufficient for characterizing two-phase flow in microgravity and for ground testing of thermal control systems: annular, bubbly, plug/slug, and stratified. The stratified flow regime cannot occur in microgravity, but its occur- rence is very probable during ground testing. In annular flow the liquid flows as a thin film along the tube wall and as droplets in a gas/vapor core. The flow regime is relatively simple, occurs over a wide range of gas and liquid flow rates, and has received the most research attention under reduced gravity conditions (Fore et al., 1996~. Pressure drop, film thickness, and heat transfer were measured for annular gas/liquid mixtures at reduced gravity abroad NASA KC-135 aircraft. Air and two liquids, water and 50 percent aqueous glycerin, were used as fluids. Pressure drop measurements agree reasonably well with published correlations. Measured film thicknesses compare well with correlations derived from ground-based vertical annular flow data. Heat transfer coefficient data for each fluid have been compared with established empirical correlations. Hydrodynamic and heat transfer for two-phase slug flows in reduced gravity environment have been measured by the same investigators (Fore et al., 1997~. The measured heat transfer coefficients at reduced gravity were found to be lower than predicted by normal-gravity correlations. For annular flow the pressure drop data agree well with the well-known Lockhart-Martinelli correlation, whereas for the slug flow regime the data do not correlate well either with the Lockhart-Martinelli or the homoge- neous flow correlations. The heat transfer results for the annular two-phase flow are mixed. For some fluid combinations (i.e., air/50 percent aqueous glycerin) the data follow reasonably well the established turbulent flow model, whereas for the air/water system the model overpredicts the Nusselt number. For slug flow, the measured heat transfer coefficients are lower at reduced gravity than predicted by normal-gravity correlations (Fore et al., 1997~. This difference can be attributed to the lower turbulence levels that should exist in reduced gravity, although no turbulence measurements were made. In summary, very limited data exist for annular and slug flow regimes, and there is partial agreement between existing models and experimental data. Liquid sprays are being used widely in many industrial, manufacturing, agriculture, and food production processes and other applications requiring rapid and effective cooling. To overcome the deleterious effects of microgravity on two-phase heat transfer, spray cooling has a potential for use in various thermal management and life support systems in the HEDS context. Experiments on and theoretical analysis of vaporizing droplets and sprays, and on impingement heat transfer to liquid sprays, relevant to HEDS technologies have been very sparse. Experiments with droplets impinging on high-temperature (from 425 to 567 K) surfaces were conducted at 10= gO using a drop shaft (Tokura et al., 1995~. Apparent heat fluxes increased with the collision velocity of the droplet up to about 107 W/m2. The effect of gravity on spray cooling characteristics was investigated by means of parabolic flight maneuvers (Kato et al., 1995; Sone et al., 1995~. Either water or CFC-113 was sprayed from a single nozzle onto a circular chromium-plated surface with wall superheating between 100 and 400 °C. In the experiments the gravity ranged from 2 gO to ~0.01 gO. Spray cooling characteristics (i.e., heat fluxes vs. super- heats) for both water and CFC-113 were measured at low and high volumetric spray fluxes. At high spray fluxes, gravity did not affect the heat transfer characteristics. Since the spray patterns for water and CFC-113 were different, the differences in the experimental findings cannot be attributed to the effects of gravity alone. The experimental results demonstrate that the effects of variable gravity on the two-phase heat transfer in spray cooling can be overcome. Research Issues Some progress has been made in understanding how microgravity affects two-phase flow heat transfer in simple (straight) ducts. Future studies would need to be directed toward bringing experimental and theoretical
PHENOMENA OF IMPORTANCE IN RED UCED GRA VITY 149 closure to simple ducts and focus on more complicated geometries that are expected to arise in practical systems in numerous HEDS technologies. More experimental data under reduced and microgravity conditions would be needed to increase the confi- dence limits in the empirical constants and/or support the development of physically based models for forced- convection two-phase-flow heat transfer mechanisms. For the bubbly flow regime, no heat transfer measurements have been made under reduced or microgravity conditions. In such a flow regime, the capillary-induced migration of the bubbles in the presence of temperature gradients perpendicular to the walls of the conduit may have a significant effect on the phase distribution and convective heat transfer. Additional research on vaporizing droplets, sprays, and spray cooling needs to be performed, because many gravity-related issues, such as the dynamics of evaporating drop deformation, breakup, and coalescence, are not understood in microgravity. The reasons for heat transfer enhancement in the low-heat-flux regime below CHF, the differences in the trends for the CHF for different fluids, the effect of spray patterns and droplet size distribu- tion on heat transfer characteristics, and the effect of gravity on the heat transfer coefficient in the film boiling region: all these, and more, need to be addressed for successful application of the technology in space missions. SolidlLiquid Phase-Change Heat Transfer Solid/liquid phase-change heat transfer phenomena are relevant to HEDS mission-enabling technologies and subsystems. One concern is understanding how altered transport phenomena in microgravity influence the opera- tion of the subsystems. Examples of subsystems or processes include freezing and thawing in stagnant fluid lines, radiators for rejecting waste heat and their start-up (melting) from the frozen or partially frozen state, latent heat thermal energy storage (LHTES) units, start-up (from the frozen state) of liquid cooled nuclear reactors, melting of nuclear reactor core under severe accident conditions, and freezing and start-up of heat pipes under off-design operating conditions, among others. LHTES is needed to ensure a constant heat supply for power generation during the shade period of the orbit. Void formation and void location can impact continuous delivery of heat, but the process has not been studied in microgravity and is not understood. During phase-change heat transfer, such as melting, freezing, and sublimation, there is usually an intrinsic change in density associated with the transition (Ostrach, 1982~. The fluid motion produced by the difference in density between the two phases and buoyancy- induced flow under 1 go conditions is known to affect the local heat transfer rate during melting and solidification and can greatly affect the solid/liquid interface and the solid/melt fraction (Viskanta, 1983~. Solar heat receivers, for example, employing phase-change materials (PCMs) have an advantage over sensible heat receivers: they require less mass because they possess higher energy storage densities. The effects of sedimentation of the denser phase and buoyancy due to expansion or contraction of the phase-change material can combine to induce flows in the melt of the phase-change material, affecting heat transfer. The flows induced by these forces can occur under normal gravity conditions, but their effects are usually masked by convective flow driven by buoyancy. In a low-gravity environment, buoyancy will be absent, but with void formation during solidification or melting, thermocapillary forces will come into play and will affect fluid motions in the melt. The combination of density difference and sedimentation-induced fluid motion and thermocapillary effects could influence the rate of melting/solidification in LHTES units and impact their thermal performance, but fluid motion in the melt has been ignored in predicting the performance of an LHTES unit (Hall et al., 1998~. Some phase- change heat transfer processes are controlled or substantially affected by gravity. The effects of vibration on melting of an unfixed PCM under variable gravity conditions (Shirivanian et al., 1998) and of density change on unfixed rectangular phase-change material in a low-gravity environment (Asako and Faghri, 1999) have been studied theoretically, but experimental data do not exist for validating the predictions. The more critical problem of solidification heat transfer has not been studied either theoretically or experimentally. Research Issues To address the questions related to solid/liquid phase-change heat transfer under reduced or microgravity conditions, it will be necessary to obtain a comprehensive and detailed description of the solid/liquid phase change
150 MICROGRAVITY RESEARCH processes under microgravity conditions. Several critical issues that will have a great impact on the science and technology of melting and solidification could perhaps be studied on Earth instead of in space, by producing artificial low gravity. By imposing an electromagnetic force that opposes Earth's gravity it may be possible to . . . ... . . ~ . . . . ~ . . . .. . simulate the oscillatory gravity environment of space and to damp natural convectlon-llow-lnduced sedimentation. The formation of voids when the PCM used in solar active power generation systems freezes needs to be studied and resolved. Realistic computational models of LUTES capable of simulating relevant physical processes occurring in microgravity need to be developed and validated. Phase-Change Heat Transfer in Porous Media Capillary and porous structures are used widely in two-phase devices such as heat pipes, capillary pumped loops, and loop heat pipes to provide liquid transport and enhanced heat transfer during evaporation and conden- sation in spacecraft fluid and thermal management systems, but neither boiling nor condensation in porous structures has been studied under reduced-gravity or microgravity conditions (Khrustalev and Faghri, 1997~. For example, capillary heterogeneity, induced by variation in permeability, has application in heat pipes operating in a microgravity environment. Phase change (melting or freezing) of the working fluid in the porous (wick) structure of the heat pipes under reduced gravity has not been studied and is not fully understood. Knowledge of the phenomena is necessary for starting up a frozen heat pipe or shutting down a hi~h-temnerature heat nine under emergency conditions. O ., Evaporation of a liquid from porous (wick) structures or micropores under reduced gravity is relevant to the design and efficient operation of heat pipes, micro heat pipes, and capillary-driven devices such as capillary pumped loops (Ku, 1997; Faghri, 1999; Peterson et al., 1998~. During startup of a heat pipe, the vapor flow is in ratified or free molecular flow regimes and lacks continuous flow characteristics. But the transient and often nonequilibrium evaporation processes are not completely understood. Evaporation of a liquid from liquid-vapor menisci attached to a heated, highly curved solid could affect vapor flow (shear) in microfilm and thick films but has not been studied in microgravity. A concrete example of a two-phase heat transfer device that is employed by NASA for spacecraft instrument thermal control is the capillary pumped loop (CPL) (Ku, 1997~. This device is capable of transporting large heat loads over great distances and with very small temperature differences across the system. At the heart of the device is an evaporator, which serves as both a heat-absorbing element and a fluid-circulating pump. A typical evaporator consists of a porous tubular wick that is force-fitted within an axially Grooved aluminum tubing outer shell. the liquid flows axially 1nslde the flow channel and radially through the wick to reach the heating surfaces. As the liquid is heated to the saturation temperature set by the reservoir, vapor bubbles form at the heating surfaces and migrate until vented into the grooves (channels). Surface tension prevents migration of vapor bubbles into the wick structure. At the same time, menisci are formed at the liquid/vapor interfaces resulting in capillary forces that circulate the fluid throughout the loop. There are still technical challenges facing CPLs and loop heat pipes (LHPs). One of the major issues surrounding LHP operation is the temperature hysteresis, i.e., the loop exhibits different operating temperatures under the seemingly same conditions, depending on whether the heat load is increasing or decreasing. The physics leading to hysteresis is not fully understood and has not been addressed in the open literature, and unsteady mathematical models to simulate the behavior of LHP operation are needed (Kaya et al., 1999~. Recent experiments on forced convection nucleate boiling in porous media-filled ducts revealed that when boiling occurs, three zones (liquid, liquid/vapor, and superheated vapor) develop (Miscevic et al., 1998~. A characteristic boiling curve was determined; it revealed that boiling in a porous medium appears at very low wall superheats. The heat flux at small superheats can be considerably greater than for pool boiling in the absence of porous media, and the critical heat flux (CHF) can also be considerably greater than in the case of pool boiling. A mechanistic explanation of the observations is not yet available. Recent experiments on CHF enhancement by porous structures on heat-dissipating surfaces have indicated a significant (twofold) increase in the critical heat flux for one of the modulated porous layer coatings (Liter and Kaviany, 1998~. This suggests that such coatings
PHENOMENA OF IMPORTANCE IN RED UCED GRA VITY 151 may find application in microgravity in cases where it is desirable to enhance heat dissipation from a surface by boiling of a liquid. In spite of the fact that capillary-driven two-phase flow devices can operate in microgravity, a number of technical issues have not been addressed and require testing. Examples include start-up from the frozen state and shutdown, as well as off-design operation such as boiling in the wick due to overheating. The ability of the wick to act as a liquid pump depends on the thermal design of the heat pipe and on the operating conditions. Of critical importance because they affect the capacity and thermal performance of a given heat-pipe design are such factors as wick design and geometry, and interracial stability (Faghri, 1995~. For example, in ordinary heat pipes the liquid and vapor flow in opposite directions within the pipe during operation such as may occur at high heat flux limits, nucleate/film boiling in wick, freezing/thawing of working fluid, and other critical phenomena that will affect andlor limit heat pipe design and performance. Research Issues Among the phenomena relevant to many HEDS mission-enabling technologies are the forced and surface- tension-gradient-driven single- and two-phase flows, evaporation, condensation, and boiling heat transfer that occur in porous media under reduced-gravity or microgravity conditions. Fluid thermal behavior in capillary porous structures at high heat fluxes under microgravity conditions needs to be understood; several areas have been identified for research, including the following: (1) study of the obstruction of the liquid transport to the evaporator by the incipience of nucleate boiling, which can cause evaporator dryout in an axially grooved or other heat pipe; (2) determination of the increase in the overall thermal resistance due to the formation of a vapor zone in the porous structure as a result of boiling in the evaporator, which may finally lead to its dryout; (3) study of the vapor zone in the porous structure of the inverted-meniscus-type evaporator that may cause oscillations in CPL performance; and (4) determination of the conditions for nucleation in a wick structure when bubble nucleation is caused by hot spots on the evaporator wall. Vapor bubbles in the wick of a heat pipe are undesirable because they can obstruct liquid circulation driven by capillary action. References Abdollachian, D., J. Quintal, F. Barez, J. Zahm, and V. Lohr. 1996. Study of Critical Heat Flux and Two-Phase Pressure Drop Under Reduced Gravity. NASA CR-198516. Cleveland, Ohio: NASA Lewis Research Center. Asako, Y., and M. Faghri. 1999. Effect of density change on melting of unfixed rectangular phase-change material under low-gravity environment. Pp. 57-63 in Proceedings of the ASME Heat Transfer Division1998. R.A. Nelson, Jr., et al., eds. HTD-Vol. 361-3. New York: American Society of Mechanical Engineers. Balasubramanian, R., C.E. Lacy, G. Wozniak, and R.S. Subramanian. 1996. Thermocapillary migration of bubbles and drops at moderate values of the Marangoni number in reduced gravity. Phys. Fluids 9(4):872-880. Bankoff, S.G. 1990. Dynamics and stability of thin heated liquid films. J. Heat Transfer 112:538-546. Bankoff, S.G. 1994. Significant questions in thin liquid film heat transfer. J. Heat Transfer 116:10-16. Bousman, W.S., J. McQuillen, and L.C. Witte. 1996. Gas-liquid patterns in microgravity: Effects of tube diameter, liquid viscosity, and surface tension. Int. J. Multiph. Flow 22:1035-1053. Brusstar, M.J., and H. Merte, Jr. 1998. An experimental and analytical approach to modeling the CHF for forced convection boiling in microgravity. Pp. 231-236 in Heat Transfer 1998: Proceedings of the 11th International Heat Transfer Conference 2. Singapore: Hemi- sphere Publishing. Chen, T.S., and B.F. Armally. 1987. Mixed convection in external flow. Handbook of Single-Phase Convective Heat Transfer. S. Kakac, R.K. Shah, and W. Aung, eds. New York: John Wiley & Sons. Dhir, V.K. 1991. Nucleate and transition boiling heat transfer under pool and external flow conditions. Int. J. Heat Fluid Flow 12:290-314. Dhir, V.K. 1998. Boiling heat transfer. Annul Rev. Fluid Mech. 30:365-401. Dhir, V.K., and M.M. Hassan. 1998. Science Requirement Document for a Mechanistic Study of Nucleate Boiling Heat Transfer under Microgravity Conditions. Third draft, July 1998. Cleveland, Ohio: NASA Lewis Research Center. Diev, M.D., A.I. Leontiev, and A.V. Shchetinin. 1998. A software for forecasting the flow patterns in microgravity. Pp. 475-479 in Proceed- ings of the ASME Heat Transfer Division 1998. R.A. Nelson, Jr., T. Chopin, and S.T. Thynell, eds. HTD-Vol. 361-5. New York: American Society of Mechanical Engineers. Dullien, F.A.L. 1998. Capillary effects and multiphase flow in porous media. J. Porous Media 1:1-29. Eckert, E.R.G., and R.M. Drake, Jr. 1972. Analysis of Heat and Mass Transfer. New York: McGraw-Hill.
152 MICROGRAVITY RESEARCH Ehrfeld, W., ed. 1995. Microsystem Technology for Chemical and Biological Microreactors. DECHEMA Monograph, Vol. 132. Frankfurt am Main: DECHEMA. Fa~hri A. 1995. Heat Pine Science and Technolo~v. Washington D.C.: Tavlor and Francis. ~ . ~ ~" ~ . ~ ~ ~ ~ ~ ~ TO . ~ TO · r T T . red r T r ~ ~ ~ T ITS - ~ ~ ~ ~ ~ Faghri, A. 15~ . Recent advances in heat pipe analysis and simulation. Annual Review of Heat Transter, Vol. 8. C.-L. Tien, ed. New York: Begell House. Fahgri, A., and D. Khrustalev. 1997. Advances in modeling enhanced flat miniature heat pipes with capillary grooves. Enhanced Heat Transfer 4:99-109. Fedorov, A., and R. Viskanta. 1999. Heat and mass transfer dynamics in the microchannel adsorption reactor. Microscale Thermophysical Engineering 3: 101 - 139. Fore, L.B., L.C. Witte, and J.B. McQuillen. 1996. Heat transfer to annular gas-liquid mixtures at reduced gravity. J. Thermophys. Heat Transfer 10:633-639. Fore, L.B., L.C. Witte, and J.B. 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Pp. 487-499 in Space Cooperation into the 21st Century (7th ISCOPS), Vol. 96, Advances in the Astronautical Sciences. P.M. Bainum, G.L. May, M. Nagamoto, et al., eds. San Diego, Calif.: American Astronautical Society. Kato, M., Y. Abe, Y.H. Mori, and A. Nagashima. 1995. Spray cooling characteristics under reduced gravity. J. Thermophys. Heat Transfer 9:378-381. Kaya, T., T.T. Hoang, J. Ku, and M.K. Cheung. 1999. Mathematical modeling of loop heat pipes. AIAA Paper No. 99-0477. Reston, Va.: American Institute of Aeronautics and Astronautics. Khrustalev, D., and A. Faghri. 1997. Boiling heat transfer in the miniature axially-grooved discrete heat sources. Enhanced Heat Transfer 4: 163-174. Kim, H., S.G. Bankoff, and M.J. Miksis. 1994. The cylindrical electrostatic liquid film radiator for heat rejection in space. J. Heat Transfer 116:986-992. Kirk, K.M., H. Merte, Jr., and R. Keller. 1995. Low-velocity subcooled flow boiling at various orientations. J. Heat Transfer 117:380-386. Ku, J. 1997. Recent advances in capillary pumped loop technology. AIAA Paper No. 97-3870. Reston, Va.: American Institute of Aeronautics and Astronautics. Lee, H.S., H. Merte, Jr., and F. Chiarmonte. 1997. Pool boiling curve in microgravity. J. Thermophys. Heat Transfer 11:216-222. Lee, H.S., H. Merte, Jr., and F.P. Chiarmonte. 1999. Pool boiling phenomena in microgravity. Pp. 395-400 in Heat Transfer 1998: Proceed- ings of the 11th International Heat Transfer Conference, August 23-28, 1998, Kyongju, Korea, Vol. 2. J.S. Lee, ed. Singapore: Hemi- sphere Publishing. Liter, S.G., and M. Kaviany. 1998. CHF enhancement by modulated porous-layer coating. Pp. 165-173 in Proceedings of the Heat Transfer Division 1998, Vol. 1. R.A. Nelson, Jr., K.S. Ball, and D. Kaminski, eds. New York: American Society of Mechanical Engineers. Lock, G.S.H. 1994. Latent Heat Transfer. Oxford: Oxford University Press. Majumdar, A., and I. Mezic. 1998. Stability regimes of thin liquid films. 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PHENOMENA OF IMPORTANCE IN RED UCED GRA VITY 153 Ohta, H., M. Kawaji, H. Azuma, K. Kawasaki, S. Okada, S. Yoda, and T. Nakamura. 1998. Microgravity pool boiling on a transparent heating surface (4th Report Experiments by TR-1A Rocket). Pp. 443-444 in Proceedings of the 35th National Heat Transfer Symposium of Japan, Nagoya. Tokyo: Heat Transfer Society of Japan. Oron, A., S.H. Davis, and S.G. Bankoff. 1997. Long-scale evolution of thin liquid films. Rev. Mod. Phys. 69:931-980. Ostrach, S. 1982. Low-gravity flows. Annul Rev. Fluid Mech. 14:313-345. Peterson, G.G., L.W. Swanson, and F.M. Gerner. 1998. Micro heat pipes. Pp. 295-337 in Microscale Energy Transport. C.-L. Tien, A. Majumdar, and F.M. Gerner, eds. Washington, D.C.: Taylor and Francis. Raithby, G.D., and K.G.T. Hollands. 1998. Natural convection. Chapter 4 in Handbook of Heat Transfer, 3rd Ed. W.M. Rohsenow, J.P. Hartnett, and Y.I. Cho, eds. New York: McGraw-Hill. Rose, J.W. 1999. Interphase matter transfer, the condensation coefficient and dropwise condensation. Pp. 89-104 in Heat Transfer 1998: Proceedings of the 11th International Heat Transfer Conference, August 23-28, 1998, Kyongju, Korea, Vol. 1. J.S. Lee, ed. Singapore: Hemisphere Publishing. Saito, M., N. Yamaoka, K. Miyazaki, M. Kinoshita, and Y. Abe. 1994. Boiling two phase flow under microgravity. Nucl. Eng. Des. 146:451- 461. Shirvanian, A., M. Faghri, Z. Zhang, and Y. Asako. 1998. Numerical solution of the effect of vibration on melting of unfixed rectangular phase-change material under variable-gravity environment. Numerical Heat Transfer, Part A 34:257-278. Siegel, R. 1967. Effects of reduced gravity on heat transfer. Pp. 143-228 in Advances in Heat Transfer, Vol. 4. J.P. Hartnett and T.F. Irvine, Jr., eds. New York: Academic Press. Sitter, J.S., T.J. Snyder, J.N. Chung, and P.L. Marston. 1998. Terrestrial and microgravity pool boiling heat transfer from a wire in an acoustic field. Int. J. 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Subramanian, R.S. 1992. The motion of bubbles and drops in reduced gravity. Pp. 1-42 in Transport Processes in Bubbles, Drops and Particles. R.P. Chabra and D. Dekee, eds. New York: Hemisphere Publishing. Suzuki, K., H. Kawamura, Y. Koyama, and Y. Aoyaina. 1999. Experiments on subcooled water in microgravity (observation of bubble behavior and burnout). On CD-ROM in Proceedings of the 5th ASME/JSME Joint Thermal Engineering Conference, March 15-19, 1999, San Diego, California. New York: American Society of Mechanical Engineers. Swanson, T.D., A. Juhasz, W.R. Long, and L. Ottenstein, eds. 1989. Workshop on Two-Phase Fluid Behavior in a Space Environment. NASA report CP-3043. Washington, D.C.: NASA Goddard Space Flight Center. Taitel, Y., and L. Witte. 1996. The role of surface tension in microgravity slug flow. Chem. Eng. Sci. 51:695-700. Tokura, I., Y. Hanaoka, and H. Saito. 1995. Droplet impingement on a heat transfer surface in microgravity. Pp. 549-550 in Proceedings of 32nd National Heat Transfer Symposium of Japan, 1995, Yamaguchi, Japan, Vol. II. Tokyo: Heat Transfer Society of Japan. Tonkovich, A.L.Y., D.M. Jimenez, J.L. Zilka, M.J. LaMont, Y. Wang, and R.S. Wegeng. 1998. Microchannel chemical reactors for fuel processing. Technical Report. Richland, Wash.: Pacific Northwest National Laboratory. Tuckerman, D.B., and R.F.W. Pease. 1981. High-performance heat sinking for VLSI. IEEE Electron Device Lett. EDL-2:126-129. Verkin, B.I., and Y.A. Kirichenko. 1976. Heat transfer under reduced gravity conditions. Acta Astronautica 3:471-480. Viskanta, R. 1983. Phase-change heat transfer. Pp. 153-222 in Solar Heat Storage: Latent Heat Materials, Vol. I. G.A. Lane, ed. Boca Raton, Fla.: CRC Press. Wayner, P.C., Jr. 1998. Interfacial forces and phase change in thin liquid films. Pp. 187-224 in Microscale Energy Transport. C.-L. Tien, A. Majumdar, and F.M. Gerner, eds. New York: Taylor and Francis. Wegeng, R.S., C.J. Call, and M.K. Drost. 1996. Chemical system miniaturization. Proceedings of the AIChE Spring National Meeting, New Orleans, La., February 25-29. New York: American Institute of Chemical Engineers. Weinzierl, A., and J. Straub. 1982. Nucleate pool boiling in microgravity environment. Pp. 21-27 in Proceedings of the Seventh International Heat Transfer Conference, Vol. 4. U. Grigull et al., eds. Washington, D.C.: Hemisphere Publishing. Yamada, H., and T. Fujii. 1999. Convective heat transfer of the two-phase flow under microgravity. Proceedings of the 5th ASME/JSME Joint Thermal Engineering Conference, March 15-19, San Diego, Calif. Paper No. AJTE99-6416. New York: American Society of Mechani- cal Engineers. IV.E SOLIDIFICATION Solidification is a phase change initiated by the nucleation of one or more crystallites in the liquid and proceeding by the growth of these nuclei as latent heat is removed from the solidification front. The impingement
154 MICROGRAVITY RESEARCH of two growing nuclei of different orientation results in a grain (crystal) boundary in the solid. Nucleation occurs by a statistical fluctuation and is either homogeneous in the liquid or heterogeneous on foreign particles or surfaces. In a pure substance, the liquid and solid coexist in equilibrium at a single melting/freezing temperature TM (for fixed pressure); it is generally possible, however, for the liquid to persist in an undercoated state below TM provided care is taken to suppress heterogeneous nucleation. In a multicomponent system, there is a range of temperatures at each of which solid and liquid of different composition coexist in equilibrium. Nucleation is the ultimate amplification process in which an event on an atomic scale is amplified by growth to the macroscopic scale. Indeed, this is the reason for the use of cloud and bubble chambers to reveal atomic/ nuclear events via nucleation in a metastable phase. In a solidification context, heterogeneous nucleation is sensitive to minute concentrations of foreign particles or the detailed condition of container surfaces. The driving forces for both nucleation and growth (freezing) increases with undercooling, but the kinetic response to the driving forces decreases with undercooling. Rapid cooling generally favors nucleation relative to growth and results in a fine-grained material. For growth or solidification to proceed, the latent heat released at the solid/liquid interface must be transported away. In multicomponent systems, components must also be transported to or from the interface to adjust any composition differences between the liquid and solid. This energy and mass transport that accompanies solidifi- cation influences the shape evolution of the moving interface and the associated mode of solidification. The influence arises from two usually competing effects: the so-called point effect of diffusion or heat flow, in which local projections of the solid into the liquid facilitate the transport of energy and matter to/from the interface, and the capillary effect, which favors a minimum interface area (more precisely, free energy); the scale and extent of the projections are determined by the balance between these two effects. For example, the point effect of heat flow accounts for the breakdown of a planar into a dendritic shape of a liquid/solid interface advancing into a pure undercoated liquid. In general, the two effects lead to local kinetic equations that determine the time-dependent differential geometry of the evolving interface. Mathematically, the problems described above belong to a class of free-boundary problems in which the configuration of the boundary (liquid/solid interface), on which conditions of temperature and composition fields hold, is not specified in advance but emerges as part of the solution. The configuration of the advancing liquid/solid interface affects the microstructure of the solid left in its wake. For example, in the dendritic mode, solute may be rejected from the dendritic tips and arms; it then accumulates in the liquid interstices between these features. The result is a segregation pattern in the solid that reflects the dendritic configurations. It is this coupling between microstructure of the frozen solid and the morphological details of the evolving interface shape as related to the temperature and composition fields in the liquid that makes the evolving interface morphology of practical importance. Solidification occurs in many of the enabling technologies for HEDS, as is indicated in Table III.G. 1. Specific subsystems where solidification (freezing) occurs include latent heat-of-fusion thermal energy storage systems and off-design freezing of liquid lines, space radiators, and heat pipes. In addition to the obvious cases of traditional casting methods and unidirectional solidification (Larson and Pirich, 1982; Coriell and McFadden, 1990), it occurs in joining methods such as soldering and welding, in liquid-phase sintering (German et al., 1995), in direct manufacturing processes that depend on rapid solidification of metal powder deposited layer by layer and melted by laser scanning, and in crystal growth from the melt (Hurle et al., 1987; Alexander and Rosenberger, 1990~. The effect of gravity levels on solidification stems from the magnitude of buoyancy-induced convection in the liquid. This affects the distribution of temperature and composition in the liquid near the liquid/solid interface and accounts for the segregation pattern in the solid, as explained above. In addition, buoyancy-driven convection affects the distribution of foreign particles and gas bubbles in the liquid and hence exerts an influence on nucle- ation rate and on porosity and inclusions in the solid. For example, castings made in microgravity are observed to have more porosity than corresponding castings at 1 g, perhaps because gas bubbles do not rise to the surface in microgravity (Abbaschian et al., 1996~. It should be emphasized that convection may be driven by nonbuoyancy forces such as the Marangoni effect at a fluid/fluid interface. Discussions of gravity effects in solidification are given by Tabeling (1995), Hurle (1995), and Curreri and Stefanescu (1988~. Research on solidification has focused on fundamental scientific questions using both theoretical and experi-
PHENOMENA OF IMPORTANCE IN RED UCED GRA VITY 155 mental methods. Research on nucleation has focused more on control than on understanding. Suppression of nucleation allows large undercoating and the preparation of potentially interesting metastable solid materials. Nucleation control has been studied experimentally by the use of containerless solidification (Herlach et al.,1993; Shong et al., 1987; Hofmeister et al., 1987; Naumann and Elleman, 1986~. Theoretical research on growth has focused on the following generic question: Given some interface configu- ration with specified initial conditions of temperature and composition throughout the phases and specified conditions on an external boundary (e.g., a closed system), how will the system evolve? To make the problem complete, boundary conditions for the temperature and composition fields on the moving interface must be specified. These are often taken to be given by the phase diagram adjusted for the effects of capillarity (i.e., surface tension and local curvature), the so-called local equilibrium boundary conditions. To make the problem tractable, capillary effects are often assumed to be isotropic and convection is neglected. With all the preceding assumptions, the problem becomes a well-posed standard free-boundary problem (Antar and Nuotio-Antar, 1993~. Several computational methods have been developed to obtain solutions, but they do not apply to all ranges of parameters of interest (Wang and Sekerka,1996~. Therefore, the problem is often further simplified by developing steady-state solutions involving the simple geometries of an advancing planar or cellular interface or a growing dendrite tip (Billie and Trivedi, 1993), which are then analyzed for stability of shape. One usually finds that a range of steady state stable solutions are possible; the problem then becomes one of finding an additional Principle (em.. marginal stability) that selects the operating noint of the system (see Wang and Sekerka, 1996; Langer, 1980~. Experimental tests of theory are based on the control of experimental conditions to realize as much as possible the assumptions underlying the theories. Thus, controlled experiments in microgravity are carried out to minimize convection, and materials are chosen that conform closely to such assumptions as isotropy. The elegant work of Glicksman et al. (1987), Glicksman et al. (1995a-c), Abbaschian (1996), and Bassler et al. (1995) exemplifies these experiments. Additional theoretical and experimental work has explored the effect of crystal anisotropy, including the appearance of facets, the breakdown of the local equilibrium assumption at high growth speeds and its replacement by kinetic assumptions, and the effects of convection (Sekerka, 1986; Coriell and McFadden, 1993~. In some cases, the appropriate physics is not yet fully understood. Research Issues Although considerable progress has been made in understanding the principles that determine pattern forma- tion (e.g., cells, dendrites, spatial variation of composition) during solidification, it is still not possible to predict the microstructure of a casting except under very special controlled conditions. Research to address this lack of understanding would include (1) extension of the theoretical, computer modeling, and experimental work sup- ported by NASA to advance the predictive capabilities of solidification theory by including the many complica- tions of crystalline anisotropy, interface kinetics, convection, and the effects of suspended particles and bubble formation and (2) research at the technical level of casting and other practical solidification processes under different gravity conditions to determine the ellect of gravity on such casting parameters as grain size, porosity, inclusion distributions, and segregation. The research at the technical level is needed to supplement the theoretical models, which do not yet have sufficient predictive capabilities. . . _ References Abbaschian, R. 1996. In-situ monitoring of crystal growth using MEPHISTO. Pp. 45-87 in Second United States Microgravity Payload: One Year Report. P.A. Curreri and D.E. McCauley, eds. Huntsville, Ala.: NASA Marshall Space Flight Center. Alexander, J.I.D., and F. Rosenberger. 1990. Bridgeman crystal growth in low gravity: A scaling analysis. P. 87 in Low-Gravity Fluid Dynamics and Transport Phenomena. J.N. Koster and R.L. Sani, eds. New York: American Institute of Aeronautics and Astronautics. Antar, B.N., and V.S. Nuotio-Antar. 1993. Materials processing. Fundamentals of Low Gravity Fluid Dynamics and Heat Transfer. Boca Raton, Fla.: CRC Press.
156 MICROGRAVITY RESEARCH Bassler, B.T., W.H. Hofmeister, and R.J. Bayuzick. 1995. Examination of solidification velocity determination in bulk undercooled nickel. Materials Research Society Fall Meeting, Boston, Mass. Warrendale, Penn.: Materials Research Society. Billia, B., and R. Trivedi. 1993. Pattern formation in crystal growth. Pp. 899-1073 in Handbook of Crystal Growth, Vol. IB. D.T.J. Hurle, ed. Amsterdam: North-Holland. Coriell, S.R., and G.B. McFadden. 1990. Instability during directional solidification: Gravitational effects. P. 369 in Low-Gravity Fluid Dynamics and Transport Phenomena. J.N. Koster and R.L. Sani, eds. New York: American Institute of Aeronautics and Astronautics. Coriell, S.R., and G.B. McFadden. 1993. Morphological stability. P. 785 in Handbook of Crystal Growth, Vol. 1B. D.T.J. Hurle, ed. New York: Elsevier. Curreri, P.A., and D.M. Stefanescu. 1988. Low-Gravity Effects During Solidification. P. 147 in Metals Handbook, 9th Ed., Vol. 15. Metals Park, Ohio.: ASM International. German, R.M., R.G. Iacocca, J.L. Johnson, Y. Liu, and A. Upa&yaya. 1995. Liquid-phase sintering under microgravity conditions. J. Met. 47(8):46-48. Glicksman, M.E., and S.P. Marsh. 1993. The dendrite. Pp. 1075-1122 in Handbook of Crystal Growth, Vol. IB. D.T.J. Hurle, ed. Amsterdam: North-Holland. Glicksman, M.E., E. Winsa, R.C. Hahn, T.A. Lograsso, R. Rubinstein, and M.E. Sellick. 1987. Isothermal dendritic growth. P. 37 in Materials Processing in the Reduced Gravity Environment of Space. R.H. Doremus and P.C. Nordine, eds. Materials Research Society (MRS) Symposia Proceedings, Vol. 87. Warrendale, Pa.: Materials Research Society. Glicksman, M.E., M.B. Koss, L.T. Bushnell, and J.C. LaCombe. 1995a. The isothermal dendritic growth experiment: Implications for theory. P. 663 in Modeling of Casting, Welding, and Advanced Solidification Processes VII. M. Cross and J. Campbell, eds. Warrendale, Pa.: Minerals, Metals, and Materials Society. Glicksman, M.E., M.B. Koss, L.T. Bushnell, J.C. LaCombe, and E.A. Winsa. 1995b. Dendritic growth of succinontrile in terrestrial and microgravity conditions as a test of theory. ISIJ International 35(6):1216. Glicksman, M.E., M.B. Koss, L.T. Bushnell, J.C. LaCombe, and E.A. Winsa. 1995c. Dendritic growth in terrestrial and microgravity condi- tions. P. 13 in Fractal Aspects of Materials: Proceedings of Materials Research Society (MRS) Fall 1994 Symposium, Vol. 367. F. Family, P. Meakin, B. Sapoval, and R. Wool, eds. Warrendale, Pa.: Materials Research Society. Herlach, D.M., R.F. Cochrane, I. Egry, H.J.Fecht, and A.L. Greer. 1993. Containerless processing in the study of metallic melts and their solidification. Int. Mat. Rev. 38:273-347. Hofmeister, W., M.B. Robinson, and R.J. Bayuzick. 1987. Undercooling of bulk high temperature metals in the 100 meter drop tube. P. 149 in Materials Processing in the Reduced Gravity Environment of Space: Proceedings of the Materials Research Society (MRS) Symposium, Vol. 87. R.H. Doremus and P.C. Nordine, eds. Warrendale, Pa.: Materials Research Society. Hurle, D.T.J. 1995. Crystallization processes. European Low-Gravity Physical Sciences in Retrospect and in Prospect. ELGRA Report. Paris: European Low Gravity Research Association (ELGRA). Hurle, D.T.J., G. Muller, and R. Nitsche. 1987. Crystal growth from the melt. P. 313 in Fluid Sciences and Materials Science in Space. H.U. Walter, ed. New York: Springer-Verlag. Langer, J.D. 1980. Instabilities and pattern formation in crystal growth. Rev. Mod. Phys. 52: 1-28 Larson, D.J., and R.G. Pirich. 1982. Influence of gravity driven convection on the directional solidification of Bi/MnBi eutectic composites. P. 523 in Materials Processing in the Reduced Gravity Environment of Space: Proceedings of the Materials Research Society (MRS) Symposium. G.E. Rindone, ed. Warrendale, Pa.: Materials Research Society. Naumann, R.J., and D.D. Elleman. 1986. Containerless processing technology. P. 294 in Material Science in Space. B. Feuerbacher, H. Hamacher, and R.J. Naumann, eds. New York: Springer-Verlag. Sekerka, R.F. 1986. Phase interfaces: Morphological stability. P. 3486 in Encyclopedia of Materials Science and Engineering. M.B. Bever, ed. New York: Pergamon. Shong, D.S., J.A. Graves, Y. Ujiie, and J.H. Perepezko. 1987. Containerless processing of undercooled melts. P. 17 in Materials Processing in the Reduced Gravity Environment of Space: Proceedings of the Materials Research Society (MRS) Symposium, Vol. 87. R.H. Doremus and P.C. Nordine, eds. Warrendale, Pa.: Matenals Research Society. Tabeling, P. 1995. Solidification and nucleation. European Low-Gravity Physical Sciences in Retrospect and in Prospect. ELGRA Report. Pans: European Low Gravity Research Association (ELGRA). Wang, S.-L., and R.F. Sekerka. 1996. Computation of the dendntic operating state at large supercoolings by the phase field model. Phys. Rev. E 53(4):3760. IV.F CHEMICAL TRANSFORMATION Combustion Behavior of Combustion Phenomena in Microgravity Gravitational acceleration influences combustion phenomena because of the large density differences that appear as a consequence of the large temperature differences that result from the exothermic chemical reactions
PHENOMENA OF IMPORTANCE IN RED UCED GRA VITY 157 that characterize combustion processes. Density changes of nearly a factor of ten in combustion gases are not uncommon. That buoyancy forces are important in many combustion phenomena on Earth is evident through examination of the Grashof number, the ratio of buoyancy to viscous forces. For Earth gravity and a density ratio of about 10, this force ratio is not small for physical scales of the size of about 0.1 m or more. Because the Grashof number increases as the cube of the physical scale, the influence of buoyancy increases rapidly compared to viscous effects as the scale approaches the usual laboratory scales of experimental investigation. Consequently, "quiescent" combustion experiments in earthbound laboratories are nearly impossible to conduct unless some element of free fall is present. Drop towers, for example, are earthbound laboratories in which quiescent experiments can be conducted, but they are limited to experimental times of approximately 10 s and less, generally between 2 and 5 s. For forced flows to overwhelm buoyancy and eliminate its influence, i.e., for the Reynolds number to be much larger than the square of the Grashof number, forced-flow velocities on the order of a meter per second or more are needed to suppress the influence of buoyancy. Slow-flow combustion phenomena are therefore difficult to investigate on Earth without interference from buoyancy. While some combustion phenomena are not influenced by buoyancy, several important ones are: mixture flammability, instability, gas diffusion flames, droplet combustion, particle cloud combustion, smoldering, and flame spread (Law, 1990; Sacksteder, 1990; NRC, 1995~. The importance of these phenomena to HEDS and the associated reduced-gravity environments stems either from their role in fire safety for space travel and the habitation of distant planets or from their use in processes such as materials production or construction during space missions. Each of these combustion phenomena is addressed separately below. Because those aspects of the phenomena that are of HEDS interest are interrelated, the research recommendations are grouped together at the end of the section rather than listed under each phenomenon. Mixture Flammability Whether a premixed mixture of fuel and oxidizer is flammable following a sufficient input of ignition energy is a question of importance to fire safety. Mixtures exhibit both lean and rich flammability limits on Earth, with the limits for upward-propagating flames being wider than those for downward-propagating flames. For down- ward-propagating flames the burnt gases are above the unburnt gas, while for upward-propagating flames the opposite is true, which leads to a curvature in flame shape as the burnt gases tend to rise under buoyancy into the unburnt gases to enhance flammability. This curvature produces flame stretch, which influences the flame temperature and hence flame propagation. Depending on the magnitude and sign of the product of the strain rate with the transit time through the flame and the Lewis number (the ratio of the thermal diffusivity to the mass diffusivity of the less abundant reactant), flame stretch can widen or narrow the flammability limits (Law, 1990~. At reduced gravity and reduced flame stretch, it is possible for the limits to be outside the normal-gravity limits (Law, 1990; Sacksteder, 1990~. At one time, because flammability limits were thought to exist only as a result of the influence of gravity, it was thought that there would be no flammability limits at zero gravity. However, flammability limits at reduced gravity have been found, and they are hypothesized to exist because of the relatively enhanced influence of radiative losses at reduced gravity and/or the effects of chemical kinetics; as such, they would be fundamental limits (Law, 1990~. Near-limit premixed flames at reduced gravity exhibit unusual behavior not observed at normal gravity. For Lewis numbers less than unity, spherically expanding flames propagate and then extinguish. The extinction occurs as a result of enhanced radiative loss and the reduced effects of flame stretch as the flame radius increases. Under certain circumstances, "stationary" spherical flames, or flame balls, have been observed (Ronney et al., 1998~. Because these flame balls, which require radiative heat losses for their stability, are "convectionless," they cannot exist at normal gravity, where there is convective flow through buoyancy (Law, 1990; Sacksteder, 1990~.
158 Flame Instabilities MICROGRAVITY RESEARCH Flame front instability, which results in flames whose surfaces are not smooth but instead contain cellular structures, is due to effects associated with heat and mass diffusional processes and hydrodynamic effects that give rise to the curved shape of upward-propagating flames. Buoyancy is stabilizing for downward propagation, and its removal makes the remaining effects dominant, thus allowing for the near-limit phenomena observed in reduced gravity such as the flame balls mentioned above (Law, 1990~. Gas Diffusion Flames in gas jet diffusion flames, in which the flame is formed from a jet of gaseous fuel issuing from a burner tube into an oxidizer, buoyancy is generally important. The flame stabilizes as a premixed flame near the burner rim, where the flow speed and flame speed match. Because buoyancy affects the flow speed near the burner rim, removal of buoyancy affects the stabilization mechanism. Additionally, laminar flames are longer and wider in reduced gravity than in normal gravity and generate more soot. Radiation losses increase, and flame temperatures decrease (Sacksteder, 1990~. Droplet Combustion Diffusion flames surrounding liquid fuel droplets become spherical in the absence of gravity, mirroring the configuration employed in classical droplet-burning theory in which the square of the droplet diameter decreases nearly linearly with time and the flame diameter decreases as the droplet diameter decreases. At reduced gravity, however, unsteady effects are observed in which burning rates and flame diameters initially increase slowly with time. Additionally, soot production is enhanced, and a soot shell may form at the location where the thermophoretic transport of soot back toward the droplet surface is balanced by the outward drag on the soot particles from the outward fuel flow (Law, 1990; Nayagam et al., 1998~. At normal gravity, the soot mantle is swept away from the lower, windward side of a droplet and consumed in the upper reaches of the flame plume above the droplet. Cloud Combustion Arrays or clouds of droplets or combustible particles may exhibit different flame propagation characteristics at normal and reduced gravity. With settling at normal gravity, upward-propagating flames propagate through an initially richer mixture while downward-propagating flames propagate through an initially leaner mixture. Clouds that may not be flammable because of such settling (they are either initially too rich or too lean) may sustain propagation when uniformly dispersed under reduced gravity (Sacksteder, 1990~. Smoldering Smoldering combustion, i.e., the slow surface oxidation of a combustible solid, has practical ramifications for safety. In normal gravity, buoyancy enhances oxygen transport to and product removal from the reacting surface. In reduced gravity, this transport mechanism is absent. Results to date show that carbon monoxide production in smoldering combustion is enhanced substantially in reduced gravity (NRC, 1995; Stocker et al., 1996), but the prevalence of this effect is unknown. Flame Spread Flame spreading over solid and liquid surfaces has direct implications for fire safety and materials selection. Generally, it is classified as either opposed flow or concurrent flow (with respect to the oxidizer flow). Upward spread in normal gravity is concurrent and tends to be acceleratory. Opposed flow spread tends to allow steady
PHENOMENA OF IMPORTANCE IN RED UCED GRA VITY 159 spread to develop. In the absence of a wind, flame spread at reduced gravity is of the opposed flow type, with the opposing flow with respect to the flame equal to the flame propagation speed (West et al., 1996~. In opposed-flow flame spread, the spread rate is determined by the upstream transfer to the unburnt fuel of the heat needed to vaporize it and how this heat transfer is affected by chemical kinetics. Flame extinction occurs at high velocities as a result of kinetic effects and flame blowoff. Flame extinction has also been found to occur at reduced gravity in quiescent environments as a result of radiation loss effects that reduce the flame temperature and propagation speed (this effect is suppressed in normal gravity because of the necessary presence of the induced flow). The reduced speed makes it difficult for oxygen to be transported to the flame, and extinction occurs (Altenkirch et al., 1998~. For thin fuels, the limiting oxygen concentration below which propagation will not occur is higher in reduced Gravity than in normal Gravity. However a low-speed opposing flow enhances flammability for thin fuels at . . . . . . .. . . . . . . . ~ . . . . reduced gravity, such that the limiting oxygen concentration Is below that for normal-grav~ty downward spread (Law, 1990; Olson, 1991~. Consequently, there appears to be a minimum oxygen concentration below which spread does not occur, approximately 15 percent for cellulosic materials (Olson, l991~. The limiting concentration is higher in normal gravity, which indicates that flammability at reduced gravity may be greater, although flame spread rates are lower, under certain circumstances, than at normal gravity. For spread over thick fuels, there appears to be no steady state at reduced gravity. The increased in-depth conduction needed to raise the temperature of the heated layer in the solid causes the flame to spread more slowly than for thin fuels, which enhances heat loss by flame radiation. The enhanced radiation causes a reduction in flame size such that the flame shrinks into a region of continually decreasing oxygen concentration. Eventually, the decreased oxygen transport results in flame extinction. Apparently, the higher spread rates for thin fuels prevent this phenomenon, and so thin fuels exhibit steady spread (Altenkirch et al., 1998~. For liquid fuels, surface tension gradients cause hot liquid fuel to be drawn out from under the flame and brought in front of it to establish the spread rate. For shallow pools, in which buoyancy would be absent even at normal gravity, when the flame spreads at a uniform rate, normal and reduced gravity give the same result. Numerical modeling predicts that pulsation will occur in microgravity with forced convection (Schiller and Sirignano, 1996), although experimental results seem not to indicate such pulsation (Ross and Miller, 1996, 1998~. A tentative explanation for this discrepancy is that modeling is two-dimensional while the scale of the experiments implies three-dimensionality, and expansion normal to the propagating flame is thought to be responsible for dampening the pulsation. Implications of the Behavior of Combustion Phenomena in Microgravity for Spacecraft Design and Operations Differences in combustion phenomena at normal and reduced gravity have implications for fire safety, spacecraft materials selection and utilization, especially interior materials, environment selection, interior environ- ment exchange and ventilation, fire detection and suppression, propulsion, and (potentially) manufacturing/mate- rials synthesis that relies on the maintenance of exothermic chemical reactions (NASA 1992a,b). Flammability of materials is an issue of signal importance to spacecraft fire safety. Because spacecraft inhabitants are virtually captive within the spacecraft, it is imperative that construction materials be selected so that the threat of fire is minimized, and care should be taken to ensure that the spacecraft breathable environment also minimizes fire risk. Methods of installation, for example, that preclude electrical overheating, smoldering, and flaming, are necessary . . . ^. . to minimize fire ns a. While the respiratory system responds to the partial pressure of oxygen, fires respond to the concentration of oxygen. Consequently, judicious selection of breathable environments, whether they be in the spacecraft per se or within inhabitant's space suits. should maintain suitable partial pressures of oven while minimizing, insofar as ~ 1 ~ ~7 possible, oxygen concentration. Detection systems designed with the assumption of buoyancy in mind (e.g., smoke detectors) need rethinking. Technologies different from those usually used on Earth (e.g., radiation sensors) or different applications of
160 MICROGRAVITY RESEARCH existing technologies (e.g., the use of forced ventilation for environment throughput, as opposed to reliance on buoyancy-driven flow for smoke detectors, as is done on Earth) may be necessary. Fire suppression systems must not produce end products toxic to humans (e.g., Halon extinguishers), and they must not produce situations that could pose additional fire safety concerns (e.g., liquid invasion of electrical systems). Fire suppression requires transport of the suppressant to the fire, and this transport often is affected by reduced gravity. It is, for example, beneficial to deliver water or carbon dioxide to the base of a fire, a process that can be aided by buoyant inflow at normal gravity. While it is unlikely that any combustion process in combustion-based propulsion systems will be affected per se by reduced gravity, because of the relatively high velocities developed compared to buoyancy-generated velocities, care should be taken to ensure that the overall system is not adversely affected by reduced gravity without some compensation for that environment. For example, fluid transport of combustibles is affected by reduced gravity, and that should be taken into account in propulsion systems design. There may be a potential for combustion to be used in necessary manufacturing processes. Consequently, depending on the process, reduced gravity may play a role, e.g., in the transfer of heat from flames for processing and in direct, high-temperature materials synthesis. Affected Technologies As discussed in Chapter III, the technologies affected in the presence of reduced gravity that relate to combustion include fire detection and suppression technologies, as mentioned above; electrical/electronic packag- ing to minimize the potential for overheating and smoldering combustion; ventilation control in the presence of a fire; and fluid distribution systems associated with propulsion. In addition, there is the potential, though as yet undetermined, influence on technology for materials synthesis during exothermic reaction. Research Issues The main issue surrounding combustion as it relates to HEDS activities is safety, which has implications for materials selection, environment selection, fire detection, fire management, and fire suppression. Further work on materials and environment selection is needed, but the emphasis should be on robust fire detection and suppression in reduced gravity. As discussed previously, a number of areas of reduced-gravity combustion research are particularly relevant to improving fire detection and suppression in a reduced gravity environment, including flammability and flame behavior (such as flame instabilities and dynamics under different gravity conditions); diffusion-flame structure and behavior for gaseous, liquid, and solid fuels, especially the production of soot and toxic products in such flames and conditions necessary for their extinction; smoldering rates at reduced gravity, with special emphasis on conditions for initiation and termination of smoldering and on products of smoldering combustion; and, finally, flame spread phenomena for various types of fuels. Besides safety-related issues such as these, there is a need, albeit a less pressing one, for reduced-gravity research on materials synthesis and materials processing through combustion. Without practical, agreed-upon means for detection and suppression, fire looms as a potential cause of mission failure. Fluid distribution in propulsion systems and the potential for materials synthesis are combustion areas in which implications for successful HEDS activity may reside, and which also deserve attention, though certainly not to the same extent as fire safety. Pyrolysis As described in Chapter III, pyrolysis is the mechanism by which chemical transformations are brought about by application of heat. Only a small number of the many pyrolysis processes that could be of interest for HEDS are described in Chapter III. The large temperature changes in practical pyrolysis imply appreciable gravity
PHENOMENA OF IMPORTANCE IN RED UCED GRA VITY 161 effects by virtue of the associated changes in density. It may therefore be expected that reduced-gravity issues arise in pyrolysis. The effects would involve influences of gravity on the transport of reactants and products to and from regions of pyrolysis, and so pyrolysis processes that may be of use, such as oxygen-production processes, will need study to determine these effects. Many pyrolysis processes that occur during combustion are discussed in the preceding section. For example, soot production in diffusion flames involves pyrolysis of the gaseous fuels in fuel-rich regions of the flow. These pyrolysis processes are of importance in fire protection aboard spacecraft, for example. Research Issues There are many different kinds of pyrolysis processes, with reactants and products in different phases and with very different temperature thresholds and time scales. For this reason, microgravity studies of pyrolysis would need to be pursued on individual bases, separate for each process. One potentially relevant process is the high- temperature recovery of oxygen from silica in lunar regolith. Another is soot production from hydrocarbon fuels. A third is gaseous fuel production from cellulosic fuels. Each process proceeds at successively lower tempera- tures. Many other pyrolysis processes with potential relevance to HEDS can be identified, but each would need to be evaluated separately with respect to its HEDS relevance and its sensitivity to microgravity. However, it can be noted that general categories of processes affected by gravity include gas production from solids and gas-phase chemical transformations in a flow field. Solution Chemistry While the interaction of individual molecules in a solution is not expected to be directly affected by gravity levels (except possibly in the case of very large molecules such as proteins), there are numerous ways in which the effects of gravity on bulk fluid flow might either inhibit or enhance the efficiency of the chemical reactions carried out on a HEDS mission. Incomplete mixing of reactants is possibly the chief area of concern for solution reactions in reduced gravity. On Earth, density-driven convection, particularly in reactions requiring heating, is relied upon as the default method of mixing reactant solutions. While this driving force would be absent or reduced in low gravity, complete mixing could still be accomplished in most cases by the use of mechanical stirrers and by paying careful attention to the design of reaction chambers. On the other hand, for a multiphase mixture of immiscible phases with different densities, the surface area at which a reaction could take place might be greatly enhanced in microgravity. After mixing, density differences would rapidly separate such a solution into layers on Earth, whereas in reduced gravity the dispersed droplets, with their greater surface area, could remain suspended for a longer period of time, allowing reactants in the two phases to interact at a higher rate. Surface tension would still be present, however, as a driving force for coalescence of the phases and thus a reduction in the surface area of reaction. A better understanding of phase distribution and separation in low gravity is cited as a need in a number of sections in this report and so is not discussed in detail here, except to note that such an understanding might also be applied to enhancing the efficiencies of some types of chemical reactions, such as those involving immiscible phases, in low gravity. References Altenkirch, R.A., L. Tang, K. Sacksteder, S. Bhattacharjee, and M.A. Delichatsios. 1998. Inherently unsteady flame spread to extinction over thick fuels in microgravity. Pp. 2515-2524 in Twenty-Seventh Symposium (International) on Combustion. Pittsburgh: Combustion Institute. Law, C.K. 1990. Combustion in microgravity: Opportunities, challenges, and progress. AIAA-90-0120. New York: American Institute of Aeronautics and Astronautics. National Aeronautics and Space Administration (NASA). 1992a. 1991 Integrated Technology Plan for the Civil Space Program. NASA TM- 107988. Washington, D.C.: NASA.
162 MICROGRAVITY RESEARCH National Aeronautics and Space Administration (NASA). 1992b. Review of NASA's Integrated Technology Plan for the Civil Space Pro- gram. NASA TM-107966. Washington, D.C.: NASA. National Research Council (NRC), Space Studies Board. 1995. Microgravity Research Opportunities for the 1990s. Washington, D.C.: National Academy Press. Nayagam, V., J.B. Haggard, Jr., R.O. Colantonio, A.J. Marchese, F.L. Dryer, B.L. rehang, and F.A. Williams. 1998. Microgravity n-heptane droplet combustion in oxygen-helium mixtures at atmospheric pressure. AIAA J. 36(8):1369-1534. Olson, S.L. 1991. Mechanisms of Microgravity flame spread over a thin solid fuel: Oxygen and opposed flow effects. Combust. Sci. Technol. 76(4-6):233-249. Ronney, P.D., M.-S. Wu, H.G. Pearl mar, and K.J. Weilar~d. 1998. Expenmental study of flame balls in space: Preliminary results from STS- 83. AIAA J. 36(8):1361-1368. Ross, H.D., and F.J. Miller. 1996. Detailed experiments of flame spread across deep butanol pools. Pp. 1327-1334 in Proceedings of the Twenty-Sixth Symposium (International) on Combustion. Pitttsburgh: Combustion Institute. Ross, H.D., and F.J. Miller. 1998. Flame spread across liquid pools with very low-speed opposed or concurrent airflow. Pp. 2723-2729 in Proceedings of the Twenty-Seventh Symposium (International) on Combustion. Pitttsburgh: Combustion Institute. Sacksteder, K.R. 1990. The implications of experimentally controlled gravitational accelerations for combustion science. Pp. 1589-1596 in the Proceedings of the Twenty-Third Symposium (International) on Combustion. Pittsburgh: Combustion Institute. Schiller, D.N, and W.A. Singnano. 1996. Opposed-flow flame spread across n-propar~ol pools. Pp. 1319-1325 in Proceedings of the Twenty- Sixth Symposium (International) on Combustion. Pittsburgh: Combustion Institute. c7 Stocker, D.P., S.L. Olson, D.L. Urban, J.L. Torero, D.C. Walther, arid A.C. Fernar~dez-Pello. 1996. Small-scale smoldering combustion experiments in Microgravity Pp. 1361-1368 in Proceedings of the Twenty-Sixth Symposium (International) on Combustion. Pittsburgh: Combustion Institute. West, J., L. Tang, R.A. Altenkirch, S. Bhattacharjee, K. Sacksteder, and M.A. Delichatsios. 1996. Quiescent flame spread over thick fuels in Microgravity Proceedings of the Twenty-Sixth Symposium (International) on Combustion. Pittsburgh: Combustion Institute. IV.G BEHAVIOR OF GRANULAR MATERIALS Lunar and Martian Regolith Characterizing and understanding the behavior of granular materials in different gravitational fields are of critical importance to the HEDS program. In order to carry out tasks ranging from determination of the energy requirements for excavation operations and estimation of the load-carrying capacity of extraterrestrial surfaces, through the handling of granular materials in conveying systems and the prediction of local surface properties of planetary bodies under various gravitational conditions, the influence of gravity on the behavior of granular materials must be better understood. Jaeger, Nagel, and Behringer (1996), in their useful overview of many aspects of granular material behavior, discuss the conditions under which these material systems behave like solids, liquids, or gases, depending on environmental conditions. Granular materials of interest in this discussion are soils, regoliths, and other similar resources that can exhibit cohesion and are arrangements of rigid particles in frictional contact. Because gravity contributes to the normal stress force of interaction between particle surfaces and frictional forces are typically proportional to the normal (hence gravitational ~ forces, the elastic behavior of granular soils, which has both axial and radial force components, is strongly dependent on gravity. In fact, when granular particle assemblies are produced in terrestrial environments with particle density levels that are sufficient to maintain continuous contact between adjacent particles, gravity creates internal stress distributions that are highly nonhomogeneous and anisotropic. Many experiments have shown that the internal stress distributions produced even in highly simplified (identical particle) granular assemblies are distinctly different when test conditions are repeated using the same apparatus. Great care thus will be required to isolate gravitational effects from effects produced by random assembly variations. It is also extremely difficult to conduct terrestrial experi- ments on the behavior of granular systems (other than angle-of-repose experiments) that are not controlled by container boundaries. The ability to construct stable structures and roadways that can carry loaded vehicles on planetary surfaces (geotechnical engineering) is a critical element in designing equipment for testing, processing, and transporting these soils. The soil properties depend strongly on the shape of the individual particles, which can vary from very angular to well rounded. Specifically, it is known that owing to the thermal and mechanical bombardment events undergone by the Moon, its surface materials include nearly spherical glass particles and very irregular fine
PHENOMENA OF IMPORTANCE IN RED UCED GRA VITY 163 particles. In contrast, because of the apparent hydrologic epoch that characterized some portion of Mars's geologic history and because Mars continues to possess an atmosphere that sustains aeolian erosion, it is likely that Mars regolith is composed of less-abrasive granular materials and therefore has a mechanical behavior different from that of the lunar regolith. It is already known that the lunar surface is characterized by the extreme density of its soil only a few centimeters beneath its surface (Carrier and Mitchell, 1990), compaction that exceeds that produced by even heavy compaction equipment on Earth. Hence, even though it will be extremely difficult to excavate material or even drill holes in the lunar surface without employing such techniques as vibratory excava- tion (Klosky, 1997), undisturbed lunar soil should be able to carry heavy loads. The behavior of dust in reduced gravity is also an important consideration. While the composition, particle shape, and atmospheric loading of Mars dust is neither fully known nor understood at this time, their potential impact on future HEDS missions must be considered. Lunar dust, whose characteristics were briefly described above, presents a different set of problems. It is considered to be one of the most difficult design constraints for lunar base construction since the lunar fines are abrasive minerals that, in the desiccated lunar environment, are electrostatically sticky and adhere very tenaciously to most surfaces. Furthermore, there are still questions about what types of attractive forces cause the dust to cling to surfaces and therefore about the cleaning methods that can be used to manage lunar dust (Perko, 1998~. The soil's void ratio (the ratio of void to solids), characteristic particle dimensions, and relative density (the ratio of soil density to that of solid soil without voids) all bear directly on the soil strength. The presence of smooth inclusions even at a level of a few percent can cause a significant decrease in soil strength (Klosky, 1997~. Granular materials under self-weight are used terrestrially to construct structures such as dams, road embank- ments, mine waste dumps, and ore stockpiles. The edges of such piles cannot be steeper than the angle of repose. If more material is added and the maximum stability angle is exceeded, avalanches occur. Well-established failure criteria have been discussed in the literature, but the dominant design criteria for frictional, granular material continue to be Mohr-Coulomb (M-C) failure measurements (Wood, 1990; Craig, 1992~. These measure- ments of granular shearing usually focus on the mean properties of the system and use techniques such as conventional biaxial compression (Klosky, 1997~. Shear stress is applied to a sample under normal load, and the grains respond elastically up to the yield point, where shear displacement occurs. When this failure occurs, the measured shear force decreases. Simultaneous measurement of shear stress and normal stress define M-C failure envelopes. A linear connection through the maxima of these plots has a slope that can be interpreted as the friction angle. The intercept where the normal stress is zero gives c, the apparent cohesion (the shear stress necessary to overcome the cohesion), which is the force that enables the soil to cling together in opposition to the forces tending to separate it into parts. Cohesion implies a surface-surface particle interaction such that as cohesion decreases, particles move more readily and pack more densely under a given set of stress conditions. The interaction forces between grain particles include hard-body interactions, friction, and inelasticity, as char- acterized by a coefficient of restitution less than unity. The dissipative nature of these interactions causes even an energetic (possessing random motion) collection of grains to coalesce into a dense, compact state. Such a compact state is usually very inhomogeneous with regard to the forces acting on individual grains, and large fluctuations in the local forces have been observed (Behringer et al., 1999), with recent studies beginning to provide new insight into their characteristics. Research Issues The continued measurement and characterization of lunar and Martian regolith would have a high priority in any attempt to establish the groundwork needed for the exploration activities that would support the development of extraterrestrial base stations. While important characteristics of the mean properties of the regolith are mea- sured by such techniques as Mohr-Coulomb failure criteria, other aspects are much less well understood: the kinetics of Coulomb friction, the internal variables and energy fluctuations, and the effects of agitation on particle size separation.
164 MICROGRAVITY RESEARCH Kinetics of Granular Flow The spontaneous flow of granular materials out of the base of a silo or hopper requires the presence of a driving force such as gravity. At reduced gravity, such as lunar or Martian gravity, the flow will likely change, but in ways that are not now obvious; for instance, unlike a true fluid, the hydrostatic pressure is apparently insensitive to the depth of the granular material in containers. The contact forces between the grains, and the static friction with the sides of the container, allow the sand in the hourglass to flow through the orifice at a nearly constant rate. Thus, when granular material is held in a silo, no height-dependent static pressure head occurs, as it would with a liquid. The pressure reaches a maximum value independent of height, and these flows will require further investigation of gravitational effects (Jaeger et al., 1996~. Because many factors contribute to the soil properties, the analysis of these flows is not trivial. Gravity could be replaced by using another driving force such as electrical or magnetic. The former would require imparting a charge to the particles and then subjecting them to an electric field. If the particles were ferromagnetic, such as the agglutinates in an Apollo 11 sample, then a magnet could drive the flow (Agosto, 1985) While the Mohr-Coulomb failure criteria for granular material has permitted the measurement of important mean properties of granular material subjected to shear, the measurements are in a three-dimensional system, so that the normal stress is not separated from the shear. It would be useful to complement this information with direct measurements of the forces and displacements of individual grains in a shearing experiment. Studies of three-dimensional systems show that in systems with 10 to 100 grains, fluctuations in stress are enormous, often more than an order of magnitude greater than the mean stress; this factor is usually ignored in modeling, impairing the ability to predict the state of such granular materials (Miller et al., 1996~. Stresses developed in static piles of cohesionless granular material have received considerable attention (Savage, 1997~. Dense, slow flows and rapid, gaslike flows (Schafer et al., 1996) are useful idealizations for the development of models (Jaeger et al., 1996), and real systems often display both flows simultaneously in different spatial domains. As discussed above, particles coalesce into a dense, packed state, so that to maintain granular material flow at low density, energy must be continuously supplied, for instance, by shaking. To achieve a flow of dense material, enough shear stress must be applied to exceed some yield point, where grains begin to slide past each other. Applied stress (including gravity) is therefore an important parameter, but other important effects include convection, size separation, and mixing. Using a two-dimensional system, where the effects of gravity are effectively removed, some recent experi- ments have shown that the packing density of grains subjected to shear undergo a novel kind of phase transition at a critical packing density (Behringer et al., 1999; Veje et al., l999~. In these experiments the grains are simulated by the use of photoelastic disks that are birefringent under stress/strain so that cross polarizers show light/dark regions. The axially emitted light shows bright and dark bands in the polariscope, and from this observation, it is possible to determine the applied shear forces. The disks, which are on a smooth slippery sheet, are confined at their inner and outer radii by roughened surfaces that apply shear stresses when rotated. The width of the characteristic shear band that forms near the inner wheel depends slightly on the packing fraction and is about six disks in radial direction. Virtually all azimuthal motion of the disks occurs in this band, and the remaining outer disks remain nearly frozen. The disks in the shear band dilate, compacting the disks in the outer region of the experiment. Rearrangements of this type can also occur at dense packings and influence the statistical and mean properties of the flow over relatively long times. In studies of shear from the inner radius, it is observed that there is a critical packing fraction of the grains, Ec, of 0.77, at which point the system undergoes a change from complete slipping, where the disks can remain indefinitely at rest without shear, to a state of nonslipping dynamics, with closely packed grains subject to some shear stress at all times. This transition has some resemblance to a phase transition. Just above Fc, fluctuations are temporally intermittent, and the resulting stress chains tend to be long. As F is increased further, the system becomes more homogeneous, because strong contacts now deform enough to allow other contacts to take up the load. The strong dependence of the dynamic behavior on grain packing density gives new insight into the properties of granular materials. When granular materials are agitated in Earth gravity, size segregation of grains can occur by several mecha- nisms, causing preferential filling of the space beneath large particles by smaller particles (Jenkins and Louge, 1997~. Gravity imparts buoyant forces that separate grains of different sizes. These forces compete with gradients
PHENOMENA OF IMPORTANCE IN RED UCED GRA VITY 165 in concentration and energy and can result in convection cells in which particles with different properties separate (Knight et al., 1993~. In the absence of gravity, only the simpler balance between gradients in concentration and in fluctuation energy remains; important studies in this area are in progress (Jenkins and Louge, 1997~. It would appear that vibrating containers can be designed for operation in microgravity that will be capable of separating particles by their size (Rosato et al., 1987; Williams, 1976~. An area receiving considerable attention in the physics community is the stirring of granular materials by means of paddles to provide mixing without segrega- tion; the design principles have been discussed by Khakhar et al. (1997) and Ottino (1990~. While these systems would likely be used in pressurized environments other than the vacuum of space, it is important to note that the process for separating particles by size has not been validated in environments that are at pressures below 10 torr (Pak et al., 1995~. Research Issues Modeling and predicting the behaviour of granular materials is an important activity that has been the subject of renewed interest. The classical descriptions of dense granular material use static arrays of grains with typically undetermined Coulomb friction forces. Recent studies, described above, show that local forces have large fluctua- tions and are very sensitive to small perturbations in packing density, and such effects must be included in statistical descriptions and models of granular materials. The modeling of granular materials under applied stress is important to a number of HEDS activities, such as construction, surface transport, and materials processing at low pressure. Studies that separate or counter the effects of gravity while examining the effects of shearing on granular behavior in three dimensions would help in understanding the phase transition observed at a critical packing density of granular material. References Agosto, W.N. 1985. Electrostatic concentration of lunar soil minerals. Pp. 453-464 in Lunar Bases and Space Activities of the 21st Century. W.W. Mendell, ed. Houston: Lunar and Planetary Institute. Behringer, R.P., D. Howell, L. Kondic, S. Tennakoon, and C. Veje. 1999. Predictability and granular materials. Physica D: Nonlinear Phenomena 130(1-2): 1-17. Carrier, W.D., III, and J.K. Mitchell. 1990. Geotechnical engineering on the moon. Pp. 51-58 in de Mello Volume: A Tribute to Prof. Dr. Victor F.B. de Mello. E. Blucher, ed. Sao Paulo, Brazil: Editora Edgard Blucher. Craig, R.F. 1992. Soil Mechanics. London: Chapman and Hall. Jaeger, H.M., S.R. Nagel, and R.P. Behringer. 1996. RMP colloquium: Granular solids, liquids, and gases. Rev. Mod. Phys. 68:1259. Jenkins, J.T., and M.Y. Louge. 1997. Pp. 539-542 in Powder and Grains 97: Proceedings of the 3rd International Conference. R.P. Behringer and J.T. Jenkins, eds. Brookfield, Vt.: A.A. Balkema. Khakhar, D.V., J.J. McCarthy, and J.M. Ottino. 1997. Radial segregation of granular mixtures in rotating cylinders. Phys. Fluids 9:3600-3614. Klosky, J.L. 1997. Behaviour of composite granular materials and vibratory helical anchors. Ph.D. dissertation. University of Colorado. Knight, J.B., H.M. Jaeger, and S.R. Nagel. 1993. Phys. Rev. Lett. 70:3728. Miller, B., C. O'Hern, and R.P. Behringer. 1996. Stress fluctuations and continuously sheared granular materials. Phys. Rev. Lett. 77:3110. Ottino, J.M. 1990. The Kinematics of Mixing: Stretching, Chaos and Transport. Cambridge: Cambridge University Press. Pak. H.K.. E. van Doom. and R.P. Behrinaer. 1995. PhYs. Rev. Lett. 74:4643. . . . ~ ~ Perko, H.A. 1998. Surface cleanliness-based dust a&esion model. Pp. 495-505 in Space 98: Proceedings of the Sixth International Confer- ence on Engineering, Construction, and Operations in Space. R.G. Galloway and S. Lokaj, eds. Reston, Va.: American Society of Civil Engineers. Rosato, A., K.J. Shandburg, F. Prinz, and R.H. Swendson. 1987. Why brazil nuts are on top: Size segregation of particulate matter by shaking. Phys. Rev. Lett. 58:1038-1040. Savage, S.B. 1997. Pp. 185-194 in Powder and Grains 97: Proceedings of the 3rd International Conference. R.P. Behringer and J.T. Jenkins, eds. Brookfield, Vt.: A.A. Balkema. Schafer, J.J., J.S. Dippel, and D.E. Wolf. 1996. Force schemes in simulations of granular materials. J. Physique 1(6):1751-1776. Veje, C.T., W. Daniel, W. Howell, and R.P. Behringer. 1999. Kinematics of a two-dimensional granular Couette experiment at the transition to shearing. Phys. Rev. E. 59(1):739-745. Williams, J.C. 1976. The segregation of particulate materials: A review. Powder Tech. 15:245-254. Wood, D.M. 1990. Soil Behavior and Critical State Soil Mechanics. Cambridge: Cambridge University Press.
