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~ a ~-~r - -- - --- - -- - - - -a- -~ --__ Fukuoka, JAPAN, 8-13 July 2 Computation of Viscous Flow around Fast Ship Superstructures O. E! Moctar (HSVA, currently Germanischer Lloyd, Germany), V. Bertram (HSVA, Germany) There is more control over what to view and what to block out. CFD can capture more flow details. In principle, CFD allows also full-scale simu- lations. The technique is non-intrusive. Abstract A commercial RANSE solver is applied to compute the flow around ship superstructures. The water surface is approximated by a flat surface. For smoke tracing, multi-phase flow can be simulated solving an additional transport equation for the smoke concentration. Similarly, thermic distribu- tions can be traced solving an energy equation. The applications are a surface effect ship and a fast ferry. The surface effect ship is quite simple in geometry and the grid employs only hexahedral elements. Results are shown for various angles of attack. The cruise ship superstructure is more com- plex and tetrahedral elements are used to simulate also smoke propagation. A considerable difficulty for practical applications is the time-consuming creation of the CAD description of the ship super- structure. 1. Introduction Aerodynamic issues are increasingly of interest for ships and offshore platforms. Potential applications include: Smoke and exhaust tracing Operational conditions for take-off and landing of helicopters Wind resistance and drift forces Ventilation of rooms The traditional approach to study aerody- namic flows around ships employs model tests in wind tunnels, Fig.1. These tests are a proven tool supporting design and relatively fast and cheap. Forces are quite easy to measure, but insight into local flow details can be difficult in some spaces. Computational fluid dynamics (CFD) is increasingly used in related fields to investigate aerodynamic flows e.g. around buildings or cars. CFD offers some advantages over wind tunnel tests: The complete flow field can be stored and allowing evaluation at any time in the future. ~ ~ ~ ~ ~ _~w intrusive smoke tracing technique Despite these advantages, CFD has so far rarely been employed for aerodynamic analyses of ships. This is due to a combination of obstacles: The complex geometry of superstructures makes grid generation labor-intensive. Reynolds numbers and domain topology re- quire relatively high cell counts, The flows are turbulent and require often un- steady simulations due to large-scale vortex generation. Recent progress in available hardware and grid generation techniques allows now a re- evaluation of CFD for aerodynamic flows around ship superstructures. Hybrid grids with tetrahedral and prism elements near the ship allow partially automatic grid generation for complex domain boundaries. The resulting higher cell count is acceptable for aerodynamic flows because the Reynolds numbers are lower (typically by a factor 15) than for hydro- dynamic ship flows and thus there are fewer ele- ments needed to resolve the boundary layer.

Our applications here show how to design suitable grids and what type of results can be ob- tained. They also point towards more required validation work and remaining problems in ob- taining suitable electronic descriptions of ship su- perstructure geometries. 2. Literature review Despite the increasing importance of aero- dynamic flows for ships and offshore platforms, there are only few published CFD applications in the field. F0rde et al. (1992) solve the Euler equa- tions for a surface effect ship (SES). The air resis- tance accounts for 25% of the total resistance for this 50 knot ship. The CFD guided improvement of the forebody of the superstructure reduced the wind resistance by Who. F0rde and Gjerde (1999) em- ploy a RANSE code to compute the aerodynamic flow around a 40 knot catamaran. Tai and Carico (1995), Tai (1996) simulate the aerodynamic flow around a destroyer using a RANSE code to determine the flow conditions on deck for landing helicopters. Tai (1995) presents similar applications for another ship. The Danish Maritime Institute conducted extensive aerodynamic CFD investigations for maritime structures. Building on previous work by Leer-Andersen and Hughes (1996) at DTU, Aage et al. (1997), Hvid et al. (1997) describe RANSE applications for a ferry and an offshore platform with focus on wind forces and smoke tracing. Jen- sen et al. (1997) describe the capabilities of CFD for cruise vessels and others maritime structures, but conclude that the grid generation effort is still too large to see CFD as commercially viable alter- native to wind tunnel testing: "The comparison of CFD, wind-tunnel tests, and full-scale measure- ments show an overall good agreement, even if large discrepancies are indeed seen at some wind directions. The differences between CFD and model-test results are not generally larger than between full-scale and model-scale results. Actu- ally, the differences are not much larger than often found when the same vessel is tested in different wind tunnels. Therefore, it is concluded that de- termination of wind loads on ships and offshore structures by CFD is a realistic computational al- ternative to the experimental methods. However, due to the time involved in generating the compu- tational mesh and in computing the solution, the CFD method is not at the moment economically competitive to routine wind-tunnel model testing." SIREHNA in France has simulated aero- dynamic flow for smoke tracing at a combatant (www.ec-nantes.fr/sirehna). Details are not pub- lished. Stanford University has conducted aero- dynamic studies for US Navy landing ships, cro- magnon.stanford.edu/jship. This study compared data for full-scale measurements, wind tunnel tests, and CFD simulations. The CFD grids employed 650,000 cells for the commercial RANSE code FLUENT. Jin et al. (2001) employ FLUENT to simulate smoke tracing for various alternatives of a tanker superstructure design. The computations use exclusively tetraeder grids with 500,000 cells slightly simplifying the computational model for the bow geometry and omitting details like on-deck pipes and radar masts. E1 Moctar et al. (2001 a,b) presented re- sults of aerodynamic RANSE simulations for a cruise vessel with a rather detailed geometric model. The simulations included also smoke trac- ing and thermodynamic analysis of the exhaust of funnels. 3. RANSE Code We employed the code Comet, ICCM (2001~. The fundamental theory and main em- ployed options are described below. The aerodynamic flows around ship super- structures are slow enough to be considered incom- pressible. The fundamental field equations describe conservation of mass (continuity equation) and conservation of momentum (Reynolds-averaged Navier-Stokes equations = RANSE). The time averaging is an ensemble averaging, i.e. the aver- age is considered to be taken over a time span large compared to the turbulent fluctuations, but small compared to the large vortex shedding. In the fol- lowing, all equations are to be understood as time averaged in this way. The RANSE equations are given in inte- gral form as the code is based on the f~nite-volume method approach: J. pdV +J. p~v-vs) ds= 0 (1) v s

J. pvdV +) pv(v-vs)ds= | (S-pI-pv'v') dS + | f dV (2) s v Bold symbols denote vectors and Tensors. p is the fluid density, V the volume, S the surface area of a control volume (CV), ds the outward normal on the surface. v is the (time averaged) velocity vector of the fluid, vs the velocity vector of the CV surface, p the pressure, v' the turbulent fluctuation of the velocity, f a resultant body force per unit volume, t the time, I the unit tensor, and S the viscous part of the stress tensor. For incom- pressible (Newtonian) fluids the components of S are proportional to the fluid's rate of deformation: S = ,u (grad v + (grad v)T) (3) ,u is the dynamic viscosity. The Reynolds stress tensor pvi'vj' is expressed as a function of time-averaged quantities using a turbulence model following the eddy-viscosity hypothesis of Boussi- nesq: -p Vi'Vj'= At (3vi/3xj+Ovj/3xi) - (2/3) p djj k (4) ~ = Cad, p k2/e is eddy viscosity which is a function of the local turbulence, Cam, an empirical constant, dij the components of the unit tensor. We solve corresponding transport equations for the turbulent kinetic energy k=0.5 v' v' and its dissipa- tion rate £ = (pit) (grad v': (grad V')T): d | pkdV +| pk(v-vs)ds= dt V s | qk-dS + | (P-p£) dV s v dt l P £ dV + ,( p £ (v-vs) ds = J. qua ds + 1 (ClPe/k- C2pe2/k-C4p £ div v) dV (6) v qk and q£ are the diffusion fluxes for k and £: qk = (~l+~k/6k) grad k (7) qua = (`U+Lk/Ce) grad £ (8) P is the production of turbulent energy by shear: P= -p v'v': grad v (9) Cl, C2, C4, Ok, G~ IT, 6cj are empirical constants. We employed the RNG-k-£ model of Speziale und Thangam (1992), which differs from the standard k-£ model in two aspects: 1. An additional source term in the transport equation for £, which is associated with the ef- fect of the rate of mean flow distortion on tur- bulence dissipation rate. This extra term is be- lieved to be important when the nondimen- sional shear is large compared to unity. 2. Other empirical constants are chosen: Cu 0.085 c6 0.012 The above described transport equations are discretized in a finite-volume method (FVM). The domain is discretized by control volumes. We employed tetraeder, prism, and hexaeder elements in our grids. The variables are stored at the cell center (colocated variable arrangement). The field equa- tions are discretized employing assorted interpola- tion and differencing schemes. The resulting alge- braic system of equations is solved numerically. Volume and surface integrals are determined using a second-order midpoint rule. The convective flux of the variable 0 through cell side j is approximated as follows: J. p ~ (v-vs) dS ~ oj J. p (v-vs) dS ~ ojp(v-vs~j S sj s =oj my (10) <5' The mass flux my through the cell face is taken from the previous iteration following a sim- ple Picard iteration approach. The remaining un- known oj at the center of the cell face j is deter- mined combining a central difference scheme (CDS) with an upwind differencing scheme (UDS). The CDS employed a correction to ensure second order accuracy for arbitrary cell, Demirdzic and Muzaferija (1995~. Second-order CDS can lead to unphysical oscillations if the Peclet number ex- ceeds 2 and large gradients are involved. UDS on the other hand are unconditionally stable, but lead to higher unphysical diffusion. To obtain a good compromise between accuracy and stability, the schemes were blended as follows: tj = 0jUDS +\j (ojCDS ~ UDS'

The blending factor ~ was chosen be- tween 0.9 and 0.95 near the hull and 0.8 further away. This choice is motivated by the higher cell density near the hull. Unphysical oscillations ap- pear often at the begin of the simulation for grids involving tetraedal and prism cells. These oscilla- tions are smoothed by a higher UDS contribution in the beginning which is reduced in the course of the iteration. The stability and computational efficiency is further increased in Comet following the de- ferred correction approach of Kohsla and Rubin (19741. Only the first-order approximation contrib- utes to the coefficient matrix, while the correction term is calculated explicitly using values from the previous iteration and is added to the source term. In the converged solution, explicit and implicit contributions of the UDS cancel each other and only CDS remains. The diffusive fluxes through cell faces are ap- proximated using a second-order midpoint rule. The Euler implicit method was used to integrate in time. This first-order fully-implicit approximation is unconditionally stable. Pressure and velocity are coupled by a variant of the SIMPLE algorithm as derived in Ferziger and Peric (19961. The system of equations are under-relaxed to dampen changes between iterations. All equa- tions except the pressure correction equations were under-relaxed using a relaxation factor 0.6. The pressure correction equations were under-relaxed using a relaxation factor 0.04 for steady flow simulation, 0.1 to 0.5 for unsteady simulations finding in each case a suitable compromise be- tween stability and convergence speed. v, k, and ~ are initialized at all cell centers. For parameter studies (e.g. wind direction or speed), the values of the previous parameter are taken which typically saves 20% CPU time. At the inlet, v, k, and ~ are specified. At the outlet all gradients in flow direction are set to zero. At sym- metry boundaries (rigid water surface) normal velocities and normal derivatives of parallel veloc- ity components and scalar quantities are set to zero. On the hull, we enforce the no-slip condition via a standard wall function (following capacity restric- tions rather than physical insight) and set the ki- netic energy to zero. The dissipation rate ~ is fixed at the first point near the wall to a value corre- sponding to the computed kinetic energy following the assumption of local balance of turbulence. Filigree elements like railings can be treated as porous surfaces (baffle elements) avoid- ing geometrical modelling with excessive cell counts. The basic transport equations retain their form then, with ds in the surface integral being replaced by P dS, and if the source terms are up- dated to account for interaction between fluid and solid parts of the porous medium. The surface po- rosity P relates the area available to flow Sf to the total control surface vector s: =Ps (12) P is a symmetric matrix. There are, how- ever, many situations where it is neither necessary nor practical to define the surface porosity in this degree of generality. In those cases the actual ve- locity v (which is discontinuous at discontinuity in porosity) is combined with the surface porosity to give a continuous averaged velocity vsup = P v called superficial velocity ( m = v Sf = vsup s). This approach is adopted in Comet. (13) 4. Applications 4.1. Surface effect ship Surface effect ships (SES) reach often speeds in excess of 40 knots. Aerodynamic resis- tance plays a bigger role for these ships than for conventional ships. We selected for our application the French SES "AGNES 200", Guezou (1993), Table I. Table I: Main data "AGNES 200" Dispi. 250 t Cushion length 41.4 m L a 51 m Cushion width 8.0 m O L 45 m T (on cushion) 1.1 m PIP Boa 13 m Speed V 40 kn As a first step, a CAD description of the SES was generated in ICEM-CFD, which served as basis for further grid generation. The f~nite-volume grid used an inner cylindrical domain surrounded by an outer block-shaped domain, Fig.2. The grid extended from 1 ship length L=Lpp ahead of the forward perpendicular to 1.5 L behind aft perpen- dicular, 1.5 L in vertical direction, and 1.5 L to each side from the plane of symmetry. The inner cylindrical domain was designed such that a for

each rotation by 5° cell nodes would again coincide with cell nodes in the outer domain, i.e. for each 5° increase in relative wind angle we could again work with matching interfaces in the code. The relatively simple geometry of the SES superstruc- ture allowed to use hexahedral elements for the whole domain. Results shown here were obtained with a grid using 2.9 million cells. . _ . _ it_ Ad. Fig.2: Grid detail for SES with inner cylindrical domain foredeck, there are corresponding low pressure zones. Fig.4 shows streamlines starting after the cabin. There are large recirculation regions above the helicopter deck and behind the stern. Between the funnels there are strong vortices as visualized by "cork screw" streamlines. Figs.S and 6 show streamlines starting in the foreship. The two layers differ by O.Sm in height of the starting points. The starting height yields here totally different streamline characteristics which is an indication of the strong three-dimensionality of the flow. ~~:~ . ~: --- Fig.3: Pressure distribution for,u=180° For wind coming from relative wind angle ,u=180° (e.g. pure wind resistance due to the mov- ing ship), the computed pressure distribution looks as expected, Fig.3. At the skirt front, the flow is retarded to almost stagnation resulting in high pres- sures. Smaller high-pressure regions appear on the funnels in areas not in the wind shade of the cabin and on the forward inclined front of the cabin. At the edges and particularly on the cabin top and . ~- : ~~ - Fig.4: Streamlines behind cabin for ,u=180°; side view (top) and detail between funnels (bottom) For the lower layer, Fig.S, the outer streamlines are sucked into the recess between foreship and cabin. Afterwards the follow largely the side of the ship. The center lines hit the lower edge of the cabin, and are then diverted to the sides where the speed is reduced to such an extent that the streamline tracing breaks down.

~~ ~ i: :~ ~~ ::~ U: ~ Hi: : ~ :~:: :~:: :: :::: ~ :~::: ~~ ~~ : :::~: i: : ~ ~~ ::~:: :: ~ : : : ~ Id ~ d ~::o ;~:~~ ~:~:::~::~:::~:: :~ ::: ::::: :: ::: ::~ : ::::: ~ - Fig.5: Streamlines starting in foreship, lower layer For the upper layer, Fig.6, the center streamlines are diverted upwards over the cabin forming recirculation areas behind the cabin. The streamlines at the side are no longer sucked into the recess between cabin and foreship, but follow on the upper deck sideways around the cabin. A moderate oblique flow direction of 170° changes the flow noticeably. The high-pressure region at the forward cabin incline is increased, Fig.7. On the luff side, the low-pressure regions disappear almost, on lee the low-pressure regions are more pronounced. The flow is partially by- passing the superstructure, but the cork-screw streamlines indicating strong vortices behind the superstructure are still dominant, Fig.8. The flow changes observed for 170° be- come more pronounced with increasing angle as demonstrated for 150°, Figs.9 and 10. There is a distinct blockage effect of the superstructure ex- pressed in the pressures on the lee side. The flow is now predominantly in transverse direction and less complicated as there are hardly any superstructure elements downstream of other superstructure ele- ments. The flow resembles the flow around a foil. Fig.6: Streamlines starting in foreship, upper layer Fig.7: Pressure distribution for '170°

=~:~:~s 'I ~ - ~ A ~~ :~ ~~ ~~ Ail: ~~ ~~ ~~ it. I. .~. .: ~~.j A. ~ ~ ! Fig.8: Streamlines starting in foreship, ,u=170° _ ~ .,_ ~~ as_ [ ~~ ~~ ~ ~ L- : ~ ~~ ~ ~~ ~~ ~ ~ ~ ~ ..~. : : : Fig.10: Streamlines starting in foreship, ~150° Fig.9: Pressure distribution for p=150° Fig. 11: Streamlines further away in foreship, ,u=150° On the downwind side, the flow is sucked partially along the ship sides before it detaches approaching its original flow direction again, as becomes appar- ent when zooming out to a larger perspective, Fig. 1 1. Results for the SES including a helicopter on deck are intended to be presented in Lindenau et al. (2002~.

4.2. Two-phase flow for funnel A reference application for a typical ge- neric cruise vessel was produced from published deck plans of actual modern cruise vessels. Several grids of increasing fineness were created with the largest having approximately 5 million cells, Figs.12 and 13. The grid consists of 10 layers of prism cells at the ship surface with the residual space of the computational domain being automati- cally meshed with tetrahedral elements. Ongoing research focuses on determining proper grid reso- lution, and we expect that 1-2 million cells may suffice for most applications in practice. The aero- dynamic CFD analysis showed extensive recircula- tion regions at the upper deck of the cruise vessel. One of these recirculation areas appears directly behind the funnel structure, Fig.14. Fig. 12: Grid for cruise vessel , . .. . . . . . . . . . . . . . . . . . . Fig. 13: Grid detail for cruise vessel For exhaust propagation we modeled the flow as two-phase flow in Comet. We specified the exhaust temperature and velocity and then traced the development in an externally specified wind distribution, Fig.15. We used a uniform wind speed over height at the domain inlet. We tested this pro- cedure first for a funnel on a flat plate, Fig.16. This initial test gave plausible results. There were no validation data. We then performed a similar study for the cruise ship in wind direction coming from 150° (oblique head wind), Fig.17. The results look again plausible. Current research performs similar computations for a "Superfast" ferry, Mechsner (2001), where there are also wind tunnel experi- ments for comparison. These will be presented in Schmode et al. (2001~. Fig. 14: Streamlines behind funnel Fig.15: Exhaust temperature at funnel .. . . . . . . . . . At. ~ ~ ~ . . ~ ~ ....... , ~ , ~ .; . Fig.16: Funnel on plate with smoke contours

Fig.17: Cruise ship in ,u=170° with smoke contours 5. Conclusion The progress in hardware and grid genera- tion capabilities allows now aerodynamic analyses of ship superstructures that are in some aspects superior and in some aspects inferior to wind tunnel tests. Grid generation remains a key issue in such computations. The level of detail achieved by CFD is by now comparable to that of model tests. Acknowledgement The research presented here was partially funded by the German ministry of education and research BMBF. Olaf Lindenau and Scott Gatchell supported us in the pre- and post-processing. References Aage, C.; Hvid, S.L.; Hughes, P.H.; Leer- Andersen, M. "Wind loads on ships and offshore structures estimated by CFD," 8th Int. Conf. Be- haviour of Offshore Structures BOSS'97, Delft, 1997, pp.237-251 Demirdzic, I.; Muzaferija, S., "Numerical method for coupled fluid flow, heat transfer and stress . . analysts using unstructured moving meshes with cells of arbitrary topology", Computer Methods in Applied Mechanics and End. Vol.125, 1995 E1 Moctar, O.; Gatchell, S.; Bertram, V. "RANSE simulations for aerodynamic flows around ship superstructures," 4th Num. Towing Tank SYmp., Hamburg, 2001 El Moctar, O.; Gatchell, S.; Bertram, V., "Aerodynamische Stromungssimulation fur Schif- fe " Hansa 138/9 2001 pp.20-21 , , , Ferziger, J.; Peric, M., Computational methods for fluid dynamics, 1996, Springer-Verlag F0rde, M.; 0rbekk, E.; Kubberud, N. "Reduction of aerodynamic drag of a high speed catamaran by using advanced CFD calculations," IS' Int. Conf. Appl. CFD, Basel, 1992 F0rde, M.; Gjerde, K. "High speed catamaran aerodynamics," CFD'99, Ulsteinvik, 1999 Guezou, J.P. "AGNES 200: Up-to-date technical information and potential use for commercial and military applications," FAST'93, Yokohama, 1993, pp.21-34 Hvid, S.L.; Leer-Andersen, M.; Hughes, P.H. "Wind load prediction on offshore structures using CFD," Conf. Application of Fluid Dynamics in the Safe Design of Topsides and Superstructures, Inst. Of Marine Eng., London, 1997 Jensen, A.G.; S0ndergaard, T.; Livesey, F. "Wind comfort for cruise/passenger vessels," Cruise & Ferry, 1997 Jin, E.; Yoon, J.; Kim, Y. "A CFD-based paramet- ric study on the smoke behaviour of a typical mer- chant ship," PRADS'01, Shanghai, 2001, pp.459- 465 Kohsla, P.K.; Rubin, S.G., "A diagonally dominant second-order accurate implicit scheme," Computers & Fluids Vol.2, 1974 Launder, B.E.; Spalding, D.B., "The numerical computation of turbulent flows," Computer Me- thods in Applied Mechanics and Eng. Vol.3, 1974 Leer-Andersen, M.; Hughes, P.H., "Computations of wind loads on ships and offshore structures," Dept. Naval Arch. & Ofshore Eng., Danish Techni- cal Univ., 1996 Lindenau, O.; Bertram, V.; El Moctar, O.M.; Gatchell, S. "Aerodynamic simulations for an SES employing virtual reality post-processing tech- niques", 3r~ High-Performance Marine Vehicles Conf. HIPER'02, Bergen, 2002 Mechsner, A., "Zwei RoPax-Fahren der Superlative von HDW" Schiff&Hafen 3 2001 pp.31-33 , , ,

Patankar, S.V.; Spalding, D.B., "A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows," Int. J. Heat Transfer Vol. 15, 1972 Schmode, D.; Bertram, V.; E1 Moctar, O.M. "Aerodynamic flow computations for a Superfast ferry", 3r~ High-Performance Marine Vehicles Conf. HIPER'02, Bergen, 2002 Speziale, C.G.; Thangham, S., "Analysis of an RNG based turbulence model for separated flows," Int. J. Eng. Science Vol.30, 1992 Tai, T.C. "Effect of ship motion on DD-963 ship airwake simulated by multizone Navier-Stokes solution" 21St SYmp. Naval HYdrodyn. Trond- , , helm, 1996 Tai, T.C. "Simulation of LED ship airwake by Navier-Stokes method," 6th Asian Congr. Fluid Mechanics, Singapore, 1995 Tai, T.C.; Caric, D., "Simulation of DD-963 ship airwake by Navier-Stokes method," J. of Aircraft 32/6, 1995, pp.1399-1401