Proceedings of the Sixth International Conference on Numerical Ship Hydrodynamics (1994) / Chapter Skim
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Session 12- Lifting-Surface Flow: Steady Viscous Methods
Session 12- Lifting-Surface Flow: Steady Viscous Methods
Pages 633-682
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From page 635... ...
p Po Rc constant projected surface area sound speed lift coefficient base chord length Smagorinsky constant damping coefficient lift Mach number normal coordinate of wall pressure reference pressure radius of curvature 635 Re Reynolds number Rex Reynolds number based on x Re Reynolds number based on momentum thickness radius in polar coordinate core radius strain rate tensor Strouhal number time reference velocity resolved velocity components velocity at outer flow unresolved velocity components r rc S t] st U U We Ut _ at tangential velocity UT shear velocity Vt mean tangential velocity x, y, z coordinates 1 - ~ ~ Yw A,Ai r Z/t W Ins p Po distance trom the wall length scales circulation molecular viscosity turbulent viscosity mean vorticity local maximum mean vorticity density reference density momentum thickness 1.
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From page 636... ...
In most unsteady flows, the weak compressibility of the fluid can contribute a great deal to the pressure field, hence the whole flow phenomena. The three dimensional compressible hydrodynamic equations, which previously were called the weakly compressible model, has been established by Song and Yuan t24.
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From page 637... ...
and (3) are called compressible hydrodynamic equations.
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From page 638... ...
The quasi-steady boundary layer calculation provided the information for imposing the partial slip boundary conditions in the outer flow. It is a novel combination of boundary layer computation and outer flow simulation.
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From page 639... ...
Boundary layers along the channel walls are not so interesting for present study; in addition, these boundary layers will not affect the foil wall boundary layer and the wake region. The channel wall has been simply treated with full slip velocity and zero gradient pressure conditions.
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From page 640... ...
e ~ So ~ _e I" i.' ~o ~ ~ ., ~ ~ -~.0 _ CUMULATED DATA; -10.0 -7 5 ~ lXPrRlMZl~TAL DATA ma_ ala' 7 I _ -lo 0.0 Fig.3 Simulated and Measured Mean Boundary Layer Profiles vectors are shown in Figs.4 and 5 for simulated values and experiment values respectively. The agreement between simulated values and experimental data is quite good.
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From page 641... ...
And the Reynolds number of the simulation is 7.0 x 105. However, since the mesh size are not fine enough and the boundary layer on the foil surface is not resolved well in the (b)
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From page 642... ...
It is worth pointing out that the current simulation has not tried to resolve the boundary layers on the foil surface. It is believed that the boundary layer on the foil surface germinates the tip vortex, but the above result seems to imply that the tip vortex trajectory is independent of the boundary layer.
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From page 643... ...
The region affected by the wake becomes larger as the wake spreads wider along the streamwise direction. Measurements engaging the assumption of asymmetric vorticity field could lead to errors in their data since the tangential velocity profiles around the tip vortex core are quite different depending on how the wake affects them.
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From page 644... ...
LEGEND ° X/Co-1.100; simulated ~ TheoreoCal R8IU" vortex Fig. 13 Mean Tangential Velocity around Tip Vortex Core ool ° .
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The independence of the tip vortex trajectory on the Reynolds number, boundary layer where the tip vortex originated, has been observed again from the numerical solution. The simulated tip vortex shows that the ideal Rankine vortex assumption for such case is inapplicable.
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From page 646... ...
14. Cebeci, T., and Bradshaw, P., Momentum Transfer in Boundary Layers, Hemisphere Publishing Corporation, 1977.
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From page 647... ...
The Reynolds number corresponding to the calculations in Figure 11 has not been stated. However, it is interesting to note that our experimenta1 observations for a series of foils of identical planform, but with different cross sections and different boundary layer characteristics, indicate that an almost universal cavitation scaling law exists: t71 = -Cpo = k C12 ReO 4 where 0.045 < k < 0.073 and Re is Reynolds number based on maximum chord length.
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From page 648... ...
Indeed we have simulated flow noise due to boundary layer separation and vortex shedding. The main idea behind the Large Eddy Simulation (LES)
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From page 649... ...
ABSTRACT The behavior of the boundary layer over a flat plate in a non-uniform incoming flow was simulated using low Reynolds number k-E models of Launder and Sharm a and Chien and a transition model. Mean velocity profiles and skin-frictions on the flat plate wee also measured in the wake generated by a circular cylinder at the upstream.
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From page 650... ...
For Mae detailed assessment of the numerical method, boundary layer measurements on the airfoil ircluding the shear stress on the wall are needed not only with various free stream turbulent intensities but also in non-uniform incoming velocity profiles. Noting that most of the transition model were studied using the measured data on the flat plate in a uniform flow with different level of turbulence intensity, their characteristics of predicting the transition shear layer of general profile were not investigated yet.
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From page 651... ...
. At the inlet boundary x= 0, mean velocity profiles, kinetic energy and rate of di ssipaticn profiles are estimated using the similarity solution of the plane wake described in the text [141.
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From page 652... ...
The uniformity of mean flow is about 1% and the freestream turbulence level is around 0.3% at the speed of 30 m/s. Boundary layer measurements were carried out on a smooth flat plate of 10mm thick and 1.6 m long hat plate, which was installed on a hinge at the center of the tunnel.
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From page 653... ...
The boundary layer over the leading edge is a laminar-lil~ Dow with high turbulence intensity, which is early diffused into the flow near the wall due to the turbulence in the external flow. These results confirm the discussed aspects in the previous studies of the uniform flow of high turbulence intensity [4, 7, 101.
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Fig. 5 Comparison of starting and ending locations of transition on a flat plate in a uniform flow.
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From page 655... ...
At the end of transition turbulent kinesic energy diffuses to the external flow and finally the profile approaches to the typical one of the equilibrium turbulent boundary layer. It is observed that the maximum value of kinetic energy during transition is larger than the peak value in the hilly developed turbulent boundary layer at the downstream.
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From page 656... ...
15. Mean velocity profiles on the flat plate in the uniform free stream.
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From page 657... ...
bee omes typ ical logan thmic pro files of the fully developed turbulent boundary layer at the far downstream location. From this fundamental test in the uniform flow, the CPM technique is verified to be a useful tool to investigate the skin-friction of the transitional boundary layer with reasonable accuracy.
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From page 658... ...
The accuracy of CPM measurement should be fort her invesiigaed. CONCLUSION TO results of the numerical and experimental study of the transitional boundary layer over the flat plate in a non-unifUrm flow are summarized as follows: (1)
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K.H Sohn and E Reshotko, " Experimental Study of Boundary Layer Transition With Elevated Free stream Turbulence on a Heated Flat Plate," NASA CR 187068, 1991.
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The specification of the inlet boundary conditions is also investigated and the use of Neumann boundary conditions is proposed to obtain a smoother solution close to the inlet boundary. A good agreement between the numerical predictions and experimental data is obtained.
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From page 662... ...
. The paper is organized in the following way: The mathematical formulation with the boundary conditions appropriate to this problem and the turbulence model are presented in section 2.
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From page 663... ...
and (4) is to use the Cartesian velocity components, Ui, as the dependent variables.
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From page 664... ...
This means that normal pressure variations, 4, are essentially in viscid in origin and so the present set of equations represents an extension of interacting boundary layer theory. 2.1 Boundary Conditions The flow around the tip of a wing has six boundaries.
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From page 665... ...
be predicted with a boundary-layer method. The inlet boundary is not a natural boundary of the flow and so the choice between Dirichlet and Neu mann boundary conditions is not clear, because in both cases some approximations will be required to specify the boundary conditions.
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From page 666... ...
3 Numerical Solution 3.l Discretized Equations The continuity and contravariant momentum equations written for the Cartesian velocity components, (7)
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From page 667... ...
Namely, the location of the outlet boundary, inner boundary and external boundary. Numerical studies were also performed to evaluate the influence of the type of boundary conditions at the inlet.
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From page 668... ...
4.2 Sensitivity to the Choice of the Size of the Computation Domain In the present zonal approach to the calculation of tip vortex flows, some of the boundaries of the viscous region are artificial boundaries and so the specification of the boundary conditions will include approximations of the local flow. Examples of these boundaries are the inlet and outlet planes, the external boundary and the inner boundary.
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From page 669... ...
This reduction of crossbow at Z = 1.600, caused by the imposed boundary conditions, produces a non smooth behaviour of the transverse velocity field close to the external boundary on the upper surface. We recall that at the external boundary the tangential velocity components are imposed.
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From page 670... ...
The results obtained with the approximate boundary conditions suggest that the present approach is more efficient in the calculation of the tip vortex, than placing the inner boundary at the symmetry plane of the wing to obtain exact boundary conditions. 4.2.3 External Boundary At the external boundary the tangential velocity components and the pressure are prescribed by a potential flow solution.
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From page 671... ...
The nonsmooth behaviour of the transverse velocity field close to the external boundary on the upper surface is not present in the solution obtained with the external boundary moved outwards, because in the wider computation domain the local crossflow components are determined by the boundary condition at the inner boundary without a conflict with the conditions imposed on the ex Reference Case -- - Boundary moved outwards 12.55to c x = 0.939 Cp lines ~-0.35 < Cp < 0.05, ACp = 0.05 \ \ / 1.55 2.00 z - - 0.37 ~ Cp < 0.10 C _ 0.41 < Cp < 0.10 Xc = 1.065 Cp lines ~-0.30 < Cp < 0.10, ACp = 0.05 0.45 1.55 2.45 2.00 2.45 z -- 0.35 < Cp < 0.14 -- - 0.38 < Cp < 0.15 Figure 8: Comparison of the pressure fields at two different stations for solutions obtained with different locations of the external boundary. ternal boundary (compare the earlier discussion in section 4.2.2~.
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From page 672... ...
4.3 Specification of the initial velocity profiles At the inlet station two types of boundary conditions were tested: prescribed velocity profiles and prescribed streamwise velocity gradients. It should be mentioned the the Neumann condition was applied as a Dirichlet condition, updated in the course of the solution process.
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From page 673... ...
1 1.55 2.00 2.45 z c -0.80 < Cp ~ 0.10 Figure 10: Comparison of the pressure fields at the first streamwise station for solutions obtained with different inlet boundary conditions. for the streamwise stations at tic = 0.939 and c = 1.065.
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From page 674... ...
With this type of boundary conditions it is possible to obtain a converged pressure field in the whole computation domain. The imposition of a weaker boundary condition at the inlet boundary removed the jumps of (~\Cp~ma~ at the inlet boundary obtained with specified velocity profiles.
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From page 675... ...
This suggests that innaccuracies in the specification of the streamwise velocity gradient are less damaging to the solution process than inaccuracies in the specification of inlet velocity profiles. However, with Neumann boundary conditions at the inlet boundary the method becomes more time consuming than with specified velocity profiles.
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From page 676... ...
The inlet boundary is 15% of the chord downstream of the leading edge. Like in the calculations of Govidan et al., the inlet boundary conditions of the present calculations consist of specified velocity profiles.
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From page 677... ...
Angle of attack 6.5 degrees and Reynolds number of 8.5 x 105. results with the experimental data the velocity components at the experimental measuring plane are obtained from the values at the grid nodes using linear interpolation along the ~ lines.
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From page 678... ...
However, this type of boundary condition reduces the convergence rate of the method, making it more time consuming. The comparison between the solutions obtained with the two types of boundary conditions suggests that the influence of small inaccuracies in the inlet velocity profiles is restricted to a small region close to the inlet boundary.
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From page 679... ...
A good correlation between numerical predictions and experimental results was obtained for the calculation of the flow at the tip of a rectangular wing with a squared tip. However, the size of the tip vortex core is overpredicted in the present calculations.
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From page 680... ...
- Gerleratiorl of Initial Velocity Profiles for Boundary Layer Calculatiorls. Marin Report N° 50028-1-SR, March 1980.
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From page 681... ...
In our present approach, see section 2.1, the boundary conditions in the inner part of the span imply that cross-stream derivatives,-, of the Cartesian veloca; ity components and of the pressure are set equal to zero. A potential flow solution is used to specify boundary conditions at the external bounty, without viscous-inviscid interaction.
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