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LARGE EDDY SIMULATION OF SEPARATED FLOW IN

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LARGE EDDY SIMULATION OF SEPARATED FLOW IN Powered By Docstoc
					       LARGE EDDY SIMULATION OF SEPARATED FLOW IN A
        STREAMWISE PERIODIC CHANNEL CONSTRICTION

                          Lionel Temmerman and Michael A. Leschziner
                                      Department of Aeronautics
                        Imperial College of Science, Technology and Medicine
                                         Prince Consort Rd.
                                       London SW7 2BY, UK
                          l.temmerman@ic.ac.uk, mike.leschziner@ic.ac.uk

ABSTRACT                                            and time-averaged. At the high Reynolds num-
   The ability of LES to resolve separation         bers encountered in practical applications, the
from the leeward side of a curved "hill" in a pe-   resource requirements of a wall-resolved sim-
riodically constricted channel is investigated.     ulation quickly become prohibitive, and eco-
The emphasis is on the e ectiveness of di er-       nomical compromises must be sought.
ent combinations of subgrid-scale models and           One such compromise is to bridge the semi-
wall-functions used on relatively coarse grids.     viscous near-wall layer by a "wall-function",
Accuracy is judged by reference to a highly-        based on an assumed shape for the instanta-
resolved simulation on a 4:6 106 nodes grid,        neous velocity between the nodes closest to
allowing Reynolds-stress budgets, realisability     the wall and the wall itself. Variants in-
and structural features to be analysed. It is       clude a power-law pro le (Werner and Wen-
demonstrated that even gross- ow parameters,        gle, 1991) and the log-law pro le (Grotzbach,
such as separation-bubble length, are very sen-     1987). Both are designed to return an es-
sitive to modelling approximations and grid         timate of the instantaneous wall shear stress
quality.                                            for a given velocity at the wall-nearest node,
                                                    which then serves as a wall boundary condi-
                                                    tion for the outer LES domain. While wall-
INTRODUCTION                                        functions have been used extensively in ows
   LES is highly e ective for resolving ows         which are largely una ected by boundary-layer
which are dominated by free shear layers sep-       details, little is known about their e ectiveness
arating at sharp edges and governed, predom-        in attached as well as separated ows in which
inantly, by large-scale structures. In contrast,    near-wall processes are expected to be highly
  ows for which the gross ow features are           in uential. Other, more elaborate approaches
materially a ected by viscous near-wall pro-        rest on matching RANS-type near-wall mod-
cesses pose a major challenge to LES, espe-         els, based on conventional statistical closures,
cially at high Reynolds numbers. Near a wall,       to the outer LES domain. Variants include the
LES is required, in e ect, to approach DNS,         two-layer approach of Balaras et al (1996), re-
as the dynamically important scales dimin-          cently investigated by Cabot and Moin (1999)
ish rapidly towards the dissipative ones, and       for a separated backward-facing-step ow, and
turbulence approaches a two-component state.        the "Detached Eddy Simulation" strategy of
This behaviour has important implications in        Spalart et al (1997).
respect of grid density and quality, resource-         This paper investigates the e ectiveness of
requirements and near-wall representation of        di erent combinations of SGS models and
subgrid-scale transport and dissipation.            wall-functions in simulating separation from
   The above issues are especially pertinent        a curved surface. The geometry, shown in
to ows in which separation is provoked on           Fig. 1, is a streamwise-periodic, spanwise-
a gently curved or sloping wall by the sus-         homogeneous channel segment with one wall
tained action of an adverse pressure gradient       containing hill-shaped constrictions, 9 hill
on the decelerating boundary layer - for exam-      heights apart. The Reynolds number is 10595.
ple, on a highly-loaded aerofoil or blade. The      This is a modi cation of an experimental con-
structure of such a boundary layer will in u-         guration examined by Almeida et al (1993),
ence the separation line, both instantaneous        motivated by a combination of cost consid-
erations and the observation that the experi-                 u+ = A ln(y+) + B if 5 < y+ 30 (4)
mental ow was not fully periodic, that span-
wise con nement provokes spanwise variations,                      u+ = 1 ln(Ey+) if y+ > 30 (5)
and that the short distance between consec-
utive hills did not permit a signi cant post-               with A = ( 1 ln(30E ) 5)=ln(6) and B = 5
                                                                                     ;                       ;
reattachment recovery region to be established              A ln(5).
prior to the acceleration of the ow by the fol-                In the above near-wall approximations, the
lowing hill. The ow o ers the important ad-                 velocity scale in y + is formed with the wall
vantage of not requiring boundary conditions,               shear stress, restricting their validity, in a sta-
except for those at the two walls. The assess-              tistical sense, to the state of turbulence-energy
ment of alternative wall-function implementa-               equilibrium. In RANS computations, the ap-
tions is based on data derived from two highly-             plicability of the log-law may be extended con-
resolved simulations, using the same grid of                siderably by using the turbulent energy to
4:6 106 nodes, in which the SGS viscosity is                scale y , a substitution based on the equivalence
of order of the uid viscosity. The two simu-                u 2 = C 0:5k. This concept may also be ap-
lations were performed with two entirely dif-               plied to LES ( Murakami et al, 1993), with k
ferent codes, one by Mellen et al (2000) and                chosen to be the resolved turbulent energy at
the other by the authors. Here, the simulation              the wall-nearest node. Thus, the universal wall
data are used, in e ect, in lieu of experimental            distance becomes:
data to investigate sensitivity to SGS mod-                                              1
elling, grid density and approximate near-wall
                                                                              y+ =   yC 4 k 1
                                                                                            2
                                                                                                           (6)
treatments.
                                                            Otherwise, the wall-law (LLK) is identical to
                                                            the rst form, eqs. (1) and (2).
                                                               The fourth variant (WW) is a simpli ca-
                                                            tion of the two-layer log-law form proposed
                                                            by Werner and Wengle (1991). This is based
                                                            on an explicit power-law approximation to the
                                                            log-law outside the viscous sublayer, interfaced
                                                            with the linear pro le in the viscous sublayer:
                                                                       u+ = y+ if y+ 11:8                (7)
Figure 1: Constricted channel geometrywith instantanaeous           u+ = 8:3 (y+) 1 if y+ > 11:8
                                                                                  7                        (8)
pressure isosurfaces.
                                                            SUBGRID-SCALE MODELLING
NEAR-WALL TREATMENT                                            SGS models considered here are all based on
   Four di erent formulations have been inves-              the eddy-viscosity concept,
tigated, three utilising di erent forms of the
log-law and the fourth a power-law approxi-                                     ij
mation. The simplest (LL2) is based on the                                ij ; 3 kk = ;2 t S ij          (9)
assumption that the near-wall layer consists                   Simulations have been performed with the
(in an instantaneous sense) of a fully viscous              SGS models given in Table 1. A detailed expo-
sublayer and a fully turbulent layer with the               sition of the above models is not possible here,
interface at y + 11:                                        but a few clarifying comments are given below.
            u+ = y+ if y+ 11               (1)                 The basic Smagorisky model (SMAG) is
                                                            used in conjunction with the van Driest damp-
        u+ = 1 ln(Ey+) if y+ > 11 (2)                       ing functions (WF1, WF2) which ensure that
                                                            the SGS viscosity vanishes as the wall is ap-
   A three-layer generalisation (LL3) of the                proached. The di erence between variants
above form accounts for the bu er region which              WF1 and WF2 lies in the value of A+ .
is described by a modi ed log-function t                       The dynamic Smagorinsky model (DYN) is
(Dahlstrom and Davidson, 2000) as follows:                  that proposed by Germano et al (1991) and
                                                            modi ed by Lilly (1992). Test- ltering is per-
           u+ = y+ if y+ 11                (3)              formed in the streamwise-spanwise grid planes.
 Model Designation          Model Description          Temmerman et al (2000).
      SMAG                Smagorinsky (Cs = 0:1)
  SMAG + WF1              Smagorinsky (Cs = 0:1)
                     wall-damping function (A+ = 5)    CHANNEL-FLOW SIMULATIONS
   SMAG + WF2             Smagorinsky (Cs = 0:1)
                     wall-damping function (A+ = 25)      As a precurser to the main study of sep-
      MSM                   Mixed Scale Model          arated ow, simulations were undertaken for
       DYN            Dynamic Smagorinsky model        fully-developed channel ow, to investigate the
      WALE               WALE Model (Cw = 0:1)
      LDYN                  Localised dynamic          performance of alternative SGS models and ex-
                            Smagorinsky model          amine the ability of the wall laws to return the
                                                       log-law behaviour with coarse near-wall grids
        Table 1: Summary of SGS models used.           for a Reynolds number that is comparable to
Stability is enhanced by spatial averaging over        that of the hill ow. Simulations were per-
any statistically homogeneous direction and by         formed for the case Re = 590 for which DNS
constraining the SGS viscosity to remain posi-         data by Moser et al (1999) are available for
tive.                                                  comparison. Most wall-layer-resolving simula-
    The localized dynamic Smagorinsky model            tions were done on a 96 64 64 grid, covering
(LDYN) by Piomelli and Liu (1995) is a variant         a box of 2 h 2h h and having cell-aspect
of the previous model, wherein the dynamic             ratios ( x+ y + x+ ) = (38 2 42 29), the                               ;

coe cient is allowed to vary during the test-          lowest y + = 2 being that at the wall. Statis-
  ltering operation. This requires the use of a        tical properties were assembled over a period
iterative solver to nd the dynamic coe cient           of 12 ow-through times.
at each time-step. Alternatively, the value of                          <νt>/ν

this coe cient at the previous time-step can
                                                                             1
                                                                        10




be used as an approximation.
                                                                             0
                                                                        10

                                                                             -1




    The mixed-scale model (Sagaut, 1996) is
                                                                        10

                                                                                                                   +3
                                                                         -2
                                                                        10                                        y

based on a weighted geometric average of SGS
                                                                                                                  SMA
                                                                        10
                                                                             -3                                   SMA + wf1

viscosities in which the velocity scale is related,
                                                                                                                  SMA + wf2
                                                                         -4
                                                                        10
                                                                                                                  MSM
                                                                                                                  WALE

respectively, to Sij (as done in the Smagorin-                               -5
                                                                                                                  DYN
                                                                        10                                        LDYN

sky model) and to the SGS turbulence energy                             10
                                                                             -6
                                                                                  1         10     +
                                                                                                   y              100               1000




k, obtained by the application of a test lter          Figure 2: SGS viscosity for channel ow, wall-resolved sim-
analogous to that used for dynamic modelling.          ulation.
    Finally, the WALE model (Nicoud and                   In wall-layer-resolving simulations, the SGS
Ducros, 1999) is speci cally designed to re-           viscosity level in the upper portion of the
turn the correct wall asymptotic y 3 variation         bu er layer and its asymptotic near-wall be-
of the SGS viscosity. It does so by a particu-         haviour were observed to be particularly in u-
lar manipulation of the strain tensors and its         ential. Variations of this viscosity are shown
components within an expression of similar in          in Fig. 2. The only models found to return
structure to the Smagorinsky model.                    the theoretical y +3 decay reasonably well are
                                                       the WALE and the dynamic formulations, al-
COMPUTATIONAL PROCEDURE                                though the latter gives substantially higher vis-
   The LES equations are solved using a                cosity values away from the wall. Table 2 com-
second-order fractional-step method with a             pares errors in centre-line velocity and wall-
multiblock/multigrid non-orthogonal nite-              shear Reynolds numbers, while Fig. 3 shows
volume approach with the variables stored at           the velocity pro les, in wall co-ordinates, and
cell centroids. The time derivative is ap-             turbulence-intensity pro les obtained with the
proximated by a second-order backward Euler            WALE model, judged to give the best overall
scheme. Convection and di usion are approx-            behaviour.
imated by second-order centred interpolation                30                                          0.2

                                                                                                                                           DNS - u’rms/Ub

and are advanced in time using the Adams-                   25
                                                                                                       0.15
                                                                                                                                           WALE - u’rms/Ub
                                                                                                                                           DNS - v’rms/Ub

Bashforth scheme. Pressure is obtained by
                                                            20
                                                                 DNS                                                                       WALE - v’rms/Ub
                                                                 WALE
                                                                                                                                           DNS - w’rms/Ub

solving the pressure-Poisson equation using
                                                         + 15                                           0.1
                                                        u                                                                                  WALE - w’rms/Ub



partial diagonalisation in conjunction with a
                                                            10
                                                                                                       0.05
                                                             5



V-cycle multigrid scheme and LSOR relax-                     0                                           0



ation. The code is fully parallelised. Details
                                                                  1                   100   1000              0         0.2   0.4           0.6     0.8      1
                                                                                  +
                                                                                  y                                                 y/h



of the parallel implementation on various ar-          Figure 3: Velocity and turbulence intensities for channel
chitectures and its e ciency can be found in            ow, wall-resolved simulation.
        SGS Model Re                                Error               uc =Ub                 Error             number is 10595. The mesh is close to orthog-
           DNS    584                                 -                 1.1418                    -              onal, of low aspect ratio over most of the ow
          SMAG    617                             +5.6 %                1.1533                +1.00 %
           MSM    578                              -1.0 %               1.1424                +0.05 %            domain and mesh expansion ratio below 1:05.
       SMAG & wf1 595                             +1.8 %                1.1444                +0.23 %            The y + -value at the nodes closest to the lower
       SMAG & wf2 538
           DYN    529
                                                   -7.8 %
                                                   -9.3 %
                                                                        1.1319
                                                                        1.1298
                                                                                              -0.86 %
                                                                                              -1.05 %            wall is around 0:5. SGS e ects are represented
          WALE    542                              -7.1 %               1.1440                +0.20 %            by the WALE model, giving viscosity values
          LDYN    520                             -10.9 %               1.1221                -1.73 %            below that of the uid viscosity over most of
                                                                                                                 the ow domain. A similar simulation was also
Table 2: Wall shear stress and centreline velocity for channel                                                   performed by Mellen et al (2000), and this gave
 ow, wall-resolved simulation.
    SGS Model         Re       Error uc =Ub Error
                                                                                                                 results in close agreement to the present ones.
        DNS            584       -      1.1418         -                                                         A few statistical results, derived by integra-
   WALE + LL2 558.5 -4.4 % 1.12 -1.91 %                                                                          tion over 55 through- ow periods, are shown
   WALE + LL3 557.8 -4.5 % 1.118 -2.08 %
   WALE + LLK 537.6 -7.9 % 1.13 -1.03 %
                                                                                                                 in Figs. 5-8.
  WALE + WW 598.4 2.5 % 1.133 -0.08 %
Table 3: Wall shear stress and centreline velocity for channel
 ow, wall-function simulation.
   Simulations were then performed with the
four wall-laws and the WALE model for Re =
590 over a deliberately coarser grid of 64                                                                        Figure 5: Streamlines for the highly-resolved simulation.
32 32 nodes giving cell-aspect ratios ratios                                                                        Fig. 5 gives the the time-averaged stream-
( x+ y + x+ ) (58 37 58). Table 3 com-                                                                           function eld. The ow separates at x = 0:22h
pares errors in centre-line velocity and wall-                                                                   and reattaches at x = 4:72h. Velocity and
shear Reynolds numbers, while Fig. 4 gives ve-                                                                   normal-stress pro les are included in compar-
locity and turbulence-intensity pro les for the                                                                  isons to follow in the next section. Adherence
four wall-law formulations. The results illus-                                                                   to realisability constraints is demonstrated in
trate that, despite the evidently serious resolu-                                                                Fig. 6 which gives 3 cross- ow pro les relating
tion limitations which arise when coarse grids                                                                   the second and third stress invariants on Lum-
are used, the simulations are able to resolve the                                                                ley's realisability map. The simulation was
essential features of the statistical elds.                                                                      also used to extract stress budgets, currently
                                                                                                                 employed to examine second-moment closures.
      30                                                      30




                                                                                                                 Fig. 7 gives the turbulence-energy budget at
      25                                                      25
                                                                              DNS
                                                                              WALE + LL2


                                                                                                                 the location x = 2h, midway along the sepa-
      20                                                      20              WALE + WW
                      DNS
                      WALE + LL3
  + 15                WALE + LLK                         + 15
 u                                                       u

      10                                                      10
                                                                                                                 ration bubble. Dissipation was obtained from
       5                                                       5
                                                                                                                 the balance of other processes. The behaviour
       0
       0.01                1
                                 +
                                            100   1000
                                                               0
                                                               0.01                1
                                                                                         +
                                                                                                    100   1000
                                                                                                                 across the shear-layer is observed to be qualita-
                                                                                                                 tively close to that reported by Le et al (1997)
                                 y                                                      y

  u’rms/Ub                                               v’rms/Ub

                                                                                                                 in their DNS of a backward-facing-step ow,
      0.2




                                                                                                                 while the near-wall behaviour is quite similar
                                                             0.06

     0.15
                               DNS

                                                                                                                 to that in an ordinary channel ow (Mansour
                               WALE + WW
                               WALE + LL3                    0.04
                               WALE + LL2

                                                                                                                 et al, 1988).
      0.1
                               WALE + LLK                                     DNS
                                                                              WALE + WW
                                                                              WALE + LL3
     0.05
                                                             0.02             WALE + LL2
                                                                              WALE + LLK
                                                                                                                                  0.2      Axisymmetric contraction
                                                                                                                                           Axisymmetric expansion
       0
            0   0.2       0.4         0.6   0.8    1
                                                               0
                                                                    0   0.2       0.4         0.6   0.8    1                               2D Turbulence
                                y/h                                                     y/h                                                x/h = 0.05
                                                                                                                                 0.15      x/h = 2.0
                                                                                                                                           x/h = 8.0

Figure 4: Velocity and turbulence intensities for channel
 ow, wall-function simulations.                                                                                               -II 0.1


                                                                                                                                 0.05




HIGHLY-RESOLVED SIMULATION OF
SEPARATED CHANNEL FLOW
                                                                                                                                    0
                                                                                                                                   -0.01             0                0.01   0.02
                                                                                                                                                             III



   To enable the accuracy of coarse-grid/wall-                                                                     Figure 6: Realisability map for 3 cross- ow traverses.
functions simulations to be assessed for the                                                                        The simulation allowed a-priory testing of
separated ow shown in Fig. 1, a highly-                                                                          the wall-functions to be undertaken. Fig. 8
resolved reference simulation was performed                                                                      gives an example in which the Werner-Wengle
over a grid of 4:6 106 (196 128 186) cells.                                                                      approximation was used to extract the instan-
The channel is 9h long, 3:036h high and 4:5h                                                                     taneous wall-shear stress from the velocity re-
deep, h being the hill height. The Reynolds                                                                      solved at di erent distances (grid lines) from
                                                                 x/h = 2.0                   Balance
                                                                                             Viscous diffusion                             Grid                           SGS &                  ( h )sep:
                                                                                                                                                                                                   x
                                                                                                                                                                                                                         ( x )reat:
                                                                                                                                                                                                                           h
                                                                                                                            Nx             Ny            Nz             Wall Model
                                                                                             Turbulent transport
                   0.06
                                                                                             Dissipation


                                                                                                                           196             128           186            WALE + NS                  0.22                    4.72
                                                                                             Production
                                                                                             Pressure diffusion
                                                                                             Convection

                                                                                                                            176             64           92             WALE + NS                  0.38                    3.45
                                                                                             Turbulence energy ( * 2/3)
                   0.04



                                                                                                                            176             64           92            WALE + WW                   0.32                    4.56
                                                                                                                            176             64           92            WALE + LL3                  0.34                    4.32
            Gain
                   0.02



                                                                                                                            112             64           92             WALE + NS                  1.12                    2.17
                                                                                                                            112             64           92            WALE + WW                   0.46                    4.00
            -
                     0



                                                                                                                            112             64           92            WALE + LL2                  0.54                    2.95
            Loss


               -0.02
                                                                                                                            112             64           92            WALE + LL3                  0.53                    2.98
                          0                             0.5
                                                                         y/h
                                                                               1                          1.5
                                                                                                                            112             64           92            WALE + LLK                  0.49                    3.38
                                                                 x/h = 2.0                                                  112             64           92            SMA & WF2                   0.50                    3.59
                                                                                             Balance
                                                                                             Viscous diffusion                                                            + WW
                                                                                                                            112             64           92            MSM + WW                    0.45                    4.18
                                                                                             Turbulent transport
                                                                                             Dissipation


                                                                                                                            112             64           92             DYN + WW                   0.46                    3.56
                                                                                             Production
                   0.02                                                                      Pressure diffusion


                                                                                                                            112             64           92            LDYN + WW                   0.47                    3.56
                                                                                             Convection
            Gain




                                                                                             Turbulence energy ( * 2/3)




                                                                                                                          Table 4: Separation and reattachement locations for
            -




                     0



                                                                                                                          constricted-channel simulations.
            Loss




                                                                                                                          SGS modelling and wall-law approximations -
                                                                                                                          to permit an appreciation of the relative im-
               -0.02


                          0                   0.1              0.2                 0.3              0.4            0.5



                                                                                                                          portance of the three issues in relation to pre-
                                                                         y/h


Figure 7: Turbulent-energy budget at x=h = 2:0 left: across
the shear layer right: zoom on the lower wall region, highly-
                                                                                                                          dictive accuracy.
resolved simulation.                                                                                                         Table 4 provides a comparison of pre-
the wall in the mid-span plane. This test                                                                                 dicted separation and reattachment positions
illustrates the smoothing e ect of the wall-                                                                              obtained with di erent SGS models, wall-
function treatment and its tendency to seri-                                                                              functions and grid densities (NS indicates "no-
ously underestimate the peak wall-shear stress.                                                                           slip" conditions). As seen, both positions are
These defects re ect , in parts, the fact that                                                                            materialy sensitive to all three parameters. Es-
the near-wall velocity pro les, shown in Fig. 9                                                                           pecially poor results are obtained when the
at 3 streamwise locations, do not adher, ei-                                                                              streamwise grid density is low in the vicinity of
ther statistically or instantaneously, to the                                                                             the separation point (112 64 92 grid) and
velocity-pro le assumptions underpinning the                                                                              when the no-slip condition is applied. Reason-
wall laws.                                                                                                                ably good results are returned by the combina-
                                                                                                                          tion of WALE model and the Werner-Wengle
                                                                                                                          or 3-layer wall law approximation, provided
                          0.03




                          0.02
                                                          Dense grid
                                                          Distance to the wall = 0.0151 h                                 adequate resolution around the separation lo-
                                                                                                                          cation.
                                                          Distance to the wall = 0.0511 h
                                                          Distance to the wall = 0.0854 h
                      τw
                          0.01                                                                                                                          x/h = 2.0                                       x/h = 6.0

                                                                                                                            3                                                      3

                                                                                                                                           Dense grid
                                  0                                                                                                        LL                                              Dense grid
                                                                                                                                           LL3                                             LL
                                                                                                                            2              LLK                                     2       LL3
                                      0             2                4                   6                 8                               WW                                              LLK
                                                                         x/h                                              y/h              NS                                    y/h       WW
                                                                                                                                                                                           NS


Figure 8: Instantaneous wall-shear stress derived from the
                                                                                                                                1                                                      1




Werner-Wengle wall-treatment at 3 grid lines progressively
removed from the wall.
                                                                                                                            0                                                      0
                                                                                                                                    -0.2   0     0.2     0.4     0.6   0.8   1         0   0.2      0.4            0.6      0.8       1
                                                                                                                                                        <u>/Ub                                            <u>/Ub



                                                                                                                          Figure 10: Distribution of streamwise velocity with the
                              20
                                                          log-law                                                         WALE model and 4 wall-treatments on the coarsest grid.
                                                          x/h = 0.5

                                                                                                                             Comparisons of streamwise velocity and
                                                          x/h = 2.0
                                                          x/h = 6.0


                                                                                                                          streamwise stress at two locations, one in
                              +
                      u
                              10




                                                                                                                          the recirculation zone and the other in the
                                                                                                                          post-reattachment recovery region, are given
                                                                                                                          in Figs. 10-12. The velocity pro les (Fig. 10
                                  0
                                          1                               +                   100
                                                                         y


Figure 9: Near-wall velocity pro les at 3 streamwise loca-                                                                and 11) were obtained using the coarse and
tions derived from highly-resolved simulation.                                                                            medium grids and the WALE model. Fig. 12
                                                                                                                          shows the streamwise stresses obtained with
                                                                                                                          the medium grid (176 64 92), the WALE
WALL-FUNCTION SIMULATIONS OF                                                                                              model and three wall-treatments.
SEPARATED CHANNEL FLOW                                                                                                       The results reinforce the observation that
   Coarse-grid simulations were performed                                                                                 substantial errors can arise especially from
along three parametric 'axes' - grid density,                                                                             insu cient resolution around the separation
                       x/h = 2.0                                                           x/h = 6.0
                                                                                                                                         ACKNOWLEDGMENTS
                                                                                                                                            This work is part of the "LESFOIL" EU-
  3                                                          3

          Dense grid


                                                                                                                                         project (No. BRPR-CT97-0565), nanced
          LL3                                                               Dense grid
          WW                                                                WW
  2       NS                                                 2              LL3


                                                                                                                                         through the Brite-Euram programme.
                                                                            NS
y/h                                                        y/h

      1                                                          1




  0
           0                 0.5
                          <u>/Ub
                                                 1
                                                             0
                                                                 0          0.2          0.4
                                                                                               <u>/Ub
                                                                                                        0.6          0.8           1     REFERENCES
                                                                                                                                                                 a
                                                                                                                                            Almeida, G.P., Dur~o, D.F.G., and Heitor,
Figure 11: Distribution of streamwise velocity with the                                                                                  M.V., 1993, Experimental Thermal and Fluid
WALE model for 3 wall-treatments and the medium grid.
                                                                                                                                         Science, Vol. 7, pp. 87-101.
point, in which case, sensitivy to SGS and                                                                                                  Balaras, E., Benocci, C., and Piomelli, U.,
near-wall modelling is very high. As reso-                                                                                               1996, AIAA Journal, Vol. 34, pp. 1111-1119.
lution improves, this sensitivity declines and                                                                                              Cabot, W., and Moin, P., 1999, Flow, Tur-
resonable agreement with the highly-resolved                                                                                             bulence and Combustion, Vol. 63, pp. 269-291.
solution is obtained. Although none of the                                                                                                  Dahlstrom, S., and Davidson, L., 2000, Pro-
simulations is satisfactory, those using Werner-                                                                                         ceedings, ECCOMAS 2000.
Wengle wall-law and the WALE model models                                                                                                   Germano, M., Piomelli, U., Moin, P., and
are found to give results closest to the highly-                                                                                         Cabot, W.H., 1991, Physics of Fluids A, Vol.
resolved simulation.                                                                                                                     3 , pp. 1760-1765.
                       x/h = 2.0                                                           x/h = 6.0
                                                                                                                                            Grotzbach, G., 1987, Encyclopedia of Fluid
                                                                                                                                         Mechanics, Vol. 6, pp. 1337-1391.
  3                                                          3

                          QMW - fine grid                                                          QMW - fine grid

                                                                                                                                            Le, H., Moin, P., and Kim, J., 1997, Journal
                          WW                                                                       WW
                          LL3                                                                      LL3
  2                       NS                                 2                                     NS
y/h                                                        y/h
                                                                                                                                         of Fluid Mechanics, Vol. 330, pp. 349-374.
      1                                                          1

                                                                                                                                            Lilly, D.K., 1992, Physics of Fluids A, Vol.
                                                                                                                                         4, pp. 633-635.
                                                                                                                                            Mansour, N.N., Kim, J., and Moin, P., 1988,
  0                                                          0
      0   0.02     0.04            0.06   0.08       0.1         0   0.01         0.02    0.03     0.04       0.05         0.06   0.07
                                    2                                                                   2
                    <u’u’>/Ub                                                            <u’u’>/Ub



Figure 12: Distribution of streamwise stress with the WALE                                                                               Journal of Fluid Mechanics, Vol. 194, pp. 15-
model for 3 wall-treatments and the medium grid.                                                                                         44.
                                                                                                                                            Mellen, C.P., Frohlich, J., and Rodi,
                                                                                                                                         W., 2000, Proceedings, 16th IMACS World
CONCLUSIONS                                                                                                                              Congress.
   The study has demonstrated that the sim-                                                                                                 Moser, R.D, Kim, J and Mansour, N.N,
ulation of separation from curved surfaces can                                                                                           1999, Physics of Fluids, Vol. 11, pp. 943-945.
be very sensitive to the grid density, the de-                                                                                              Murakami, S., Mochida, A., Rodi, W., and
tails of the near-wall treatment and the nature                                                                                          Sakamoto, S., 1993, ASME FED, Engineer-
of the SGS model. This sensitivity appears to                                                                                            ing applications of large eddy simulations, Vol.
be rooted, principally, in variations of the pre-                                                                                        162, pp. 113-120.
dicted separation point: a small downstream                                                                                                 Nicoud, F., and Ducros, F., 1999,Flow, Tur-
shift of this point leads to a major shortening                                                                                          bulence and Combustion, Vol. 62, pp. 183-200.
of the recirculation region and major changes                                                                                               Piomelli, U., and Liu, J., 1995, Physics of
in gross ow features. In the present ow,                                                                                                 Fluids, Vol. 7, pp. 839-848.
sensitivity seems to be especially pronounced                                                                                               Sagaut, P., 1996, La Recherche Aerospatiale,
because of the periodic nature of the ow and                                                                                             Vol. 1, pp. 51-63.
because the boundary layer is subjected, prior                                                                                              Smagorinsky, J., 1963, Monthly Weather
separation, to large rates of streamwise strain-                                                                                         Review, Vol. 91, pp. 99-163.
ing, and thus structural changes.                                                                                                           Spalart, P.R., Jou, W-H., Strelets, M., and
   Of the practices examined, the combination                                                                                            Allmaras, S.R., 1997, Proceedings, Advances in
of the WALE SGS model, giving low levels of                                                                                              DNS/LES.
SGS viscosity, and Werner-Wengle near-wall                                                                                                  Temmerman, L., Leschziner, M.A., Ash-
approximation is the most e ective in return-                                                                                            worth, and Emerson, D.R., 2000, ,Proceedings,
ing the closest delity to the highly-resolved                                                                                            Parallel CFD 2000.
solution. A-priori tests show that the true                                                                                                 Werner,H., and Wengle, H., 1991, Pro-
near-wall ow does not adhere well to the as-                                                                                             ceedings, 8th Symposium on Turbulent Shear
sumptions underpinning any of the wall-laws                                                                                              Flows, pp. 155-168.
used. Thus, better near-wall treatments are
imperative if the physical realism of coarse-grid
simulations is to be improved.

				
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