Proceedings of the Sixth International Conference on Numerical Ship Hydrodynamics (1994) / Chapter Skim
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Session 7- Viscous Flow: Numerical Methods
Session 7- Viscous Flow: Numerical Methods
Pages 365-406
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From page 367... ...
INTRODUCTION k turbulent kinetic energy ~rate of turbulence dissipation Advances in numerical solution I Identity tensor methodology along with increased computer storage VT eddy viscosity and speed have made it possible to seek numerical C C solutions of the three-dimensional Reynolds A' £1, k-£ coefficients Averaged Navier Stokes Equations (RANSE) for Ce2,~k,<~e moderately complex ship hulls.
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From page 368... ...
This small region is characterized by a nearly uniform U component, a linear variation of the vertical component W preceding a maximum and again an "hook" shape of the pressure contours. These features confirm the existence of an intense longitudinal bilge vortex emanating from the hull and leads us to classify the HSVA tanker as an U-shaped hull rather than a Vshaped hull for which the longitudinal vortex is far more intense and does not create this very characteristic hook shape of the longitudinal velocity contours.
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From page 369... ...
The resulting turbulent closure problem is solved by means of the classical k-£ turbulence model in which the Reynolds stress is linearly related to the mean rate of strain tensor through an isotropic eddy viscosity as follows: uu = 3 kI - vT(VU + VTU)
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From page 370... ...
oc~=o~pUi -- (bjVT~ +b~vTll +b~v SO = 2(gl2Q;~ + glad If; + g23~ ~ - s (2.14) The additional source terms contain classically the pressure gradients and the turbulence contributions: SU1 = J Abe (p + 3 kanji .
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From page 371... ...
This strategy simplifies coding and leads to significant savings in computational time and storage. Even if a steady solution is looked for, a local time step ensuring a fixed amount of diagonal dominance with respect to the momentum equations, is devised to accelerate the convergence towards the steady state.
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From page 372... ...
3.2 Method 2 The Cone ection Diffusion Scheme The major drawback of the previous discretisaiion schemes comes from the fact that the local variations of the convection or diffusion coefficients as well as the source term are not accounted for in the influence coefficients.The CPI (Consistent Physical Interpolation) scheme, based on a fully conservative formulation of the momentum equations, was proposed recently by the authors to remedy this weakness t93.
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From page 373... ...
The calculated skin friction lines go up from the keel line and cross this region without any distortion. The axial velocity contours at the propeller plane (x/L=0.976)
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From page 374... ...
However, the simulated flow seems more regular than the experimental one and some very specific details, such as the low speed region in the vicinity of the propeller disk associated to the hook-shaped velocity contours, appear filtered by the simulation. Actually, the computed flow looks like the flow around a slender hull, which makes questionable the use of the results of simulations to improve the geometry via an interactive design process.
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From page 375... ...
This numerical experiment indicates clearly that the turbulent eddy viscosity is the key parameter which controls the near wake of the tiow. The classical turbulence models seem to produce a too high level of eddy viscosity in the central part of the wake which hides the characteristics of discretisation schemes.
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From page 376... ...
~ 1' Figure 2c- HSVA Tanker- Axial velocity contoursxiL=1.005 (from [11~.
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From page 377... ...
X/L Figure Sa- Cp distribution along the keel line.
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From page 378... ...
1 .~.................. ~ 7 Figure 8a- Axial velocity contours- 7 points Multi exponential scheme- x/L=0.976.
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From page 381... ...
5.o 50 ~ _ tI.0 `'l.~} 1.5 I.0 ~, ~ 11 _ r,.~ 2,0 ~[ff=~ r'°~" ~_ ~0 U~ ~ ~ a ~`.
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From page 382... ...
Figure 17- Axial velocity contours- CPI schemex/I,=0.976-Grid I
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From page 383... ...
x/L=0.978-Grid I Figure 20- Wall flow- Computations with a reduction of eddy viscosity-Grid I
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From page 384... ...
I would, thus, like to ask the authors how can we improve the available turbulence models in order to accurately predict the wake distributions? Author's Reply We believe that it is time to implement new turbulence models which are not based on the eddy viscosity concept if the simulation of complex three-dimensional flows is aimed.
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From page 385... ...
, published in the wake of the 1990 Gothenburg Workshop, indicated that future CFD validation studies should avoid attempts at improving the accuracy of discretization schemes and recommended instead "(that) a comprehensive assessment of different wall treatments and turbulence models (should be undertaken)
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From page 386... ...
With our numerical study (see our paper in the present conference) , we found that the distortional wake pattern in the propeller plane is produced by the flow separation in which phenomenon the Reynolds stress intensity is observed, in many experiment, lower than those in thin turbulent boundary layer.
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From page 387... ...
A grid independent numerical solution has been obtained from the present RANS computer code when the average value Of Y1+ is less than 7, and the rate of solution convergence is controlled by avoiding the use of grid cells with an excessively large aspect ratio and extreme grid stretching. Comparisons with experiment are presented for axial velocity and turbulent shear stress profiles in the stern regions of four axisymmetric bodies are used to evaluate and validate various turbulence models.
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From page 388... ...
Performance of the turbulence model can then be assessed by comparisons of measured and computed results. In this paper the measured pressures, skin friction, turbulence shear stress and axial velocity profiles of turbulent axisymmetric stern flows are used to evaluate computed results using various grid resolutions.
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From page 389... ...
The rate of solution convergence is monitored during the F= computation to identify the presence of grid cells with excessively large aspect ratios. Computation of body drag at high values of Reynolds number is a major challenge for any CFD code.
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From page 390... ...
Numerical experiments with the revised artificial dissipation terms with carefully devised boundary conditions for the dissipation terms have demonstrated that the revised dissipation models are robust and accurate in the calculation of the flow problems which include high aspect ratio grid cells. The multigrid method developed by Jameson [9]
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From page 391... ...
The modification of the Baldwin-Lomax model made by Degani and Schiff is implemented in the IFLOW code for an axisymmetric body at angle of attack. The differentiation between the vorticity within the attached boundary layers from the vorticity on the surfaces of separated vortices is made to select a length scale based on the thickness of the attached boundary layers rather than one based on the radial distance between the body surface and the surfaces of separated vortices.
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From page 392... ...
The effects of grid distribution on the computed pressure and skin friction coefficients on the body, the axial velocity and turbulent shear stress profiles at two axial locations of x/L=0.904 and 0.978 on the Suboff Axisymmetric Body have been shown in Reference 3. The computed RMS differences of the flow variables as a function of the average values Of Y1+ for the Suboff model are shown in Fig.
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From page 393... ...
It is seen that satisfactorily computed results for axial velocity and turbulent shear stress profiles were obtained for an average value Of Y1+=4~4. The computed axial velocity profiles at RL=6.6x106 and 2.5x107, and the computed profiles of the difference in axial velocity at the two RL's for the DTNSRDC Axisymmetric Body 1 are shown Fig.
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From page 394... ...
differences between the measured and computed flow variables are summarized. It was found that when the average values of Y1+ for the first grid center from the wall was smaller than 7, the RMS differences between all the measured and computed flow variables were within the measurement uncertainties, and the computed total skin friction coefficients were approaching ~e values of the standard ship-model correlation line of the 1957 International Towing Tank Conference.
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From page 395... ...
, multigrid~for fast solution) , local refinement (for efficient use of grid cells)
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From page 396... ...
19. Sung, C.H.," A Multiblock Multi~rid Local Refinement Method for Incompressible Reynolds-averaged Navier-Stokes Equations", 6th Copper Mountain Conference on Mul~grid Methods, Copper Mountain, Colorado, April 4-9, 1993.
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From page 397... ...
...1 0 0.2 0.4 0.6 u/UOO FIGURE 3. THE EFFECT OF TURBULENCE MODEL ON THE COMPUTED AXIAL VELOCITY PROFILES Grid 112x32x64, Measurement Uncertainty of UU : +0.025 397 0.8 0.1
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From page 398... ...
. DTNSRDC Axisymmetric Body 2 X/L = 0.977, RL = 6.8 X 106 1 1 TURBULENCE MODEL ~~ BL - ~ BL-G BL-PG O Measured (r~rO)
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From page 399... ...
O ,0.4 0.2 O FIGURE 5. COMPARISON OF COMPUTED AND MEASURED AXIAL VELOCITY PROFILES Suboff Axisym metric Body, RL = 1.2 x 107, Grid 128 x32 x88 Turbulence Model: BL-GP, Measurement Uncertainty of u/UOO: + 0.025 399 1 1 ~ ~ Computed (RANS)
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From page 400... ...
COMPARISON OF COMPUTED AND MEASURED TURBULENT SHEAR STRESS PROFILES Suboff Axisymmetric Body, RL = 1.2 x 107, Grid 128x32x88 Turbulence Model: BL-GP, Measurement Uncertainty of 100~-u'v')
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From page 401... ...
~ l l l 0.8 1 FIGURE 7. COMPUTED AXIAL VELOCITY PROFILE AT X/L = 0.97S, DTNSRDC AXISYMMETRIC BODY 1 RL= 6.6x106 and 2.5x107 Measurement Uncertaintv of u/U~ = ~ 0.025 f~4~ -z LoglO Residuals _3 -4j i~` Multigrid Only Refinement Levels 1 2 & 3 Number of Cycles Convergence History n 32 V~V ~;~7 LeV~
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From page 403... ...
EFFECT OF TURBULENCE MODELS ON THE RMS DIFFERENCES BETWEEN MEASURED AND COMPUTED FLOW VARIABLES Grid 112X32X64 403
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From page 405... ...
" Author's Reply In our paper the value of Y1+ at the first grid point around 7 to 10 is meant to say that the maximum value of Y1+ is 10 and the arithmetic mean value is 7. When one value of Y1+ is given that is the arithmetic mean value of Y1+ for all the grid cells on the body.
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