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Journal of Wind Engineering
and Industrial Aerodynamics 89 (2001) 14711485
Comparison of LES and RANS in
bluff-body flows
H. L .ubcke*, St. Schmidt, T. Rung, F. Thiele
Hermann-F.ottinger-Institut f.ur Str .omungsmechanik, TU Berlin, M.uller-Breslau-Strasse 8,
D-10623 Berlin 10589, Germany
Abstract
The turbulent flow around bluff-bodies features a variety of complex phenomena, e.g.
streamline curvature, separation and the formation of large unsteady vortical structures. In
particular, an accurate representation of the interaction between mean transient motion and
residual turbulence poses a challenge to numerical simulation procedures. In virtually all
commercial simulation packages, the representation of turbulence relies on Reynolds-averagedNavierStokes (RANS) equations in conjunction with Boussinesq-viscosity models (BVM).
Various studies have demonstrated the inability of established RANS methodologies to render
the fundamental physics when applied to transient flows. In contrast to this, the
computationally more demanding large eddy simulation (LES) is known to be a viable
approach to simulate unsteady turbulent flows. The present study aims to assess the predictive
prospects of advanced recent RANS practices, i.e. explicit algebraic stress models (EASM), in
unsteady bluff-body flows. Results are reported in comparison to conventional BVM, LES
and measurements. Examples included refer to three different cylinder flows, which indicate
that the predictive accuracy obtained from an EASM is in close proximity to LES
results, whereas the computational surplus remains moderate in comparison with a linear
BVM. r 2001 Published by Elsevier Science Ltd.
1. Introduction
Due to the progress in computer technology, computational fluid dynamics (CFD)
is now able to tackle industrial flow problems at moderate costs and time-to-
solution. The prospect and success of CFD will therefore depend on the accuracy of
the approach, in particular the predictive realms of the employed physical models. A
*Corresponding author. Tel.: +49-30-314-26283; fax: +49-30-314-21101.
E-mail address: [email protected] (H. L .ubcke).
0167-6105/01/$ - see front matter r 2001 Published by Elsevier Science Ltd.
P I I : S 0 1 6 7 - 6 1 0 5 ( 0 1 ) 0 0 1 3 4 - 9
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specifically challenging example of industrial relevance is the simulation of
unsteady turbulent flows around bluff-bodies, e.g. vehicles, buildings or
flame stabilizers. The principal phenomenon of bluff-body flows, i.e. the unsteady
shedding of vortical structures from the obstacle, hinges on the interactionbetween mean-transient motion and residual turbulence. Hence, an appropriate
treatment of turbulence is crucial for the simulation quality. When attention is
drawn to industrial applications, a direct resolution of the turbulent motion is,
however, unfeasible as the associated grid resolution would cause prohibitive
computational expenses. The simulation of engineering turbulent flows is thus
restricted to turbulence-modeling practices based on Reynolds-averaged Navier
Stokes (RANS) equations and large eddy simulation (LES). In the framework of
RANS, all aspects of turbulence are modeled, which enhances the numerical
efficiency at the expense of a strong model dependency. As opposed to the RANS
approach, a major portion of the turbulent scales is numerically resolved within
LES. The primary advantage of LES is the reduced influence of the turbulence
model, which significantly increases the computational effort in comparison to
RANS. Recently developed explicit algebraic stress models revealed remarkable
improvements of the RANS methodology for several steady flows at low
computational costs, which motivates their investigation in unsteady turbulent
bluff-body flows.
2. Mathematical model
The present study is confined to incompressible and isothermal flows, thus the flow
field is fully determined by the conservation of mass and momentum. The influence
of turbulence is either entirely modeled by means of a statistical turbulence model
(RANS), or partially resolved (LES) with only the small, dissipative scales being
closed by a subgrid-scale model. Since only parts of the energy spectrum are
numerically resolved, it is necessary to ensemble average (RANS) or filter (LES) the
governing equations. In both cases the resulting equation system can be cast into a
common form based on a Cartesian coordinates xi
q %ui
qxi 0; 1
D %ui
Dt
1
r
q %p
qxiq %tij %Tij qxj
; 2
where D=Dt; %ui; %p; r denote the material derivative and the mean-average or filteredvelocity, pressure and density. The viscous stresses are given by %tij 2nSij; where
Sij q %ui=qxj q %uj=qxi =2 represents the strain-rate tensor. All unresolved effectsof turbulence are absorbed into %Tij: The closure models %Tij are described in theremainder of this section.
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2.1. Rans
Due to the ensemble averaging process, further unknowns are introduced to the
momentum equations by means of the Reynolds stresses %Tij u0ju0j: In industrialsimulations, two-equation Boussinesq-viscosity models (BVM) for u0ju
0j have gained
the most popularity. Employing the Boussinesq-viscosity hypothesis, the Reynolds
stresses are modeled in analogy to the viscous stresses
u0iu0
j 23kdij 2ntSij: 3
In Eq. (3), k u0iu0i=2 denotes the turbulent kinetic energy, nt marks the turbulent
viscosity and dij is the Kronecker delta. The present study is confined to the standard
k2o model of Wilcox [1], which employs two additional transport equations for k
and the specific dissipation rate o; viz.
nt k
o; with o e= cmk
;
Dk
Dt P cmok
q n nt=2
qk=qxj
qxj; 4
Do
Dt a
o
kP bo2
q n nt=2
qo=qxj
qxj:
Here, P %Tijq %ui=qxj denotes the production of turbulent energy and e is the energydissipation rate. The coefficients a; b and cm employ heir standard values 0.55, 0.075and 0.09, respectively. Despite their numerical advantages, BVM fail to represent the
complex interaction mechanisms between Reynolds-stresses and mean velocity field.
As a well-known example, the conventional BVM (3) fails to mimic effects related to
streamline curvature or secondary motion. Although a general approach would,
arguably, be based on a full differential-stress model for u0iu0
j; such models are hardlyused in industry due to their increased numerical effort and reduced robustness. To
remedy the shortcomings of the linear BVM, Gatski and Speziale [2] derived an
explicit solution for the algebraic stress model of Rodi [3], that features most benefitsof the differential stress model while retaining the numerical advantages
of the BVM. The derivation of the explicit algebraic stress model (EASM) stems
from the transport equation for the Reynolds stress-anisotropy tensor bij
u0iu0
j=2k dij=3 assuming an isotropic representation of the diffusion process, viz.
Dbij
Dt bij P e =k
2
3Sij
1
2kFij bjlSli bilSlj
2
3bmlSmldij
bjlWli bilWlj
: 5
Here, Fij is the pressurestrain correlation and Wij q %ui=qxj q %uj=qxi =2 therotation-rate tensor. Employing the structural equilibrium assumption Dbij=Dt 0;Rung et al. [4] devised an EASM along the route suggested by Gatski and
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Speziale, viz.
u0iu0
j 2
3
kdij 2cnmk
cmo
Sij b2k
e
SikWkj SjkWki b3k
e
SikSkj S2kkdij=3 !
6
with cnm b1= 1 2Z2=3 2x2
and
Z2 b3S 2
=8; x2 b2O 2
=2;
S k=e ffiffiffiffiffiffiffiffi
2S2jj
q; O k=e
ffiffiffiffiffiffiffiffiffiffiffiffiffiffi2W2jj
q;
b1 2=3 C2=2
=g; b2 1 C4=2
=g;
b3 2 C3 =g; g fgC1 1 C ;
C 0:421 0:526S2= 4 1:83ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
0:2S2 0:8O2p
fg 1 0:95 1 tanh 0:465S 2
The coefficients of the employed pressurestrain correlation model are listed in
Table 1. In contrast to the Gatski and Speziale approach, the present model does not
require a regularization, due to an improved representation of the production-to-
dissipation ratio CEP=e within the stressstrain relation. The unregularized EASM
satisfies the positivity requirement for the eddyviscosity and obeys the realizabilityprinciple.
The structural equilibrium assumption is at the root of almost any EASM. It is
reasonably accurate in flows which involve only weak streamline curvature. Girimaji
[5] pointed out, that the predictive response of the EASM to strong streamline
curvature can be improved when the structural-equilibrium hypothesis is applied to
the coordinates of the stress-anisotropy tensor in a mean-acceleration system ba
ij
rather than a Cartesian system (cf. Eq. (5)), viz.
Dbij
Dt
D ba
ij%
ea
i%
ea
j
h iDt
E ba
ij
D%
ea
i%
ea
j
Dt
: 7
Restricting our interest to the convective part of Eq. (7), all curvature related
modifications of the EASM can be absorbed into the definition of an effective
vorticity tensor [5]
#Wij Wij 2
2 C4Tri%ul
qTrj
qxl
!; 8
Table 1
Coefficients of the employed EASM
C1 C2 C3 C4
2.5 0.39 1.25 0.45
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which replaces the rotation-rate tensor in Eq. (6). In Eq. (8) Tij denotes the
transformation matrix between the base vectors%
ea
i of the acceleration system
and the Cartesian base%
ei; that is traditionally used for the fully conservative
numerical formulation, i.e.%e a i
%e a j TipTjp
%ep
%eq: The determination of the accelera-
tion system and its derivatives with respect to Cartesian coordinates is a non-trivial
task, particularly when focusing upon general three-dimensional flows. In the
considered two-dimensional mean flows, the acceleration vector is always
perpendicular to the homogeneous direction, which significantly simplifies the
procedure.
2.2. LES
In contrast to the RANS methodology, the spatial filtering of the instantaneousequations employed in LES explicitly considers the three-dimensional,
unsteady character of turbulent motion. Turbulent scales which exceed the
utilized filter width %D are resolved by the numerical procedure. Smaller
scales, which are assumed to behave in a universal-isotropic way, are attributed
to a subgrid-scale (sgs) model. The present study employs the dynamic one-
equation model of Davidson [6] to approximate the unknown subgrid stress
tensor
%Tij tsgs
ij
2C%D ffiffiffiffiffiffiffiffiksgsp %Sij 2nt %Sij: 9Quantities of influence to the modeled stresses are the local grid-resolution quality%D DxDyDz 1=3 and the subgrid turbulent kinetic energy ksgs; which is determinedby its transport equation [6]
Dksgs
Dt Psgs C
nksgs%D
q n nt qksgs=qxj
qxj; 10
where Psgs tsgsij q %ui=qxj denotes the production of subgrid energy. The model
parameters C LijMij=2MijMij and Cn Psts gPsgsPsgs Cngk1:5sgsk1:5sgs= %Dh i *%DK1:5sts are
evaluated in a dynamic procedure, based on an explicit test-filter (sts) which is set
twice the grid size *%D 2 %D: The filtered Leonard-stresses are evaluated via Lij g%ui%uj%ui%uj *%ui*%uj: The kinetic energy of the test-filter level Ksts is computed via Ksts gksgsksgs Lii=2: A scale similarity tensor Mij *%D gffiffiffiffiffiffiffiffiKstspffiffiffiffiffiffiffiffiKstsp *%Sij %D gffiffiffiffiffiffiffiffiffiffiffiffiffiksgsSijpffiffiffiffiffiffiffiffiffiffiffiffiffiksgsSijp supplementsthe basis of the dynamic model.
The model is able to capture different flow phenomena, such as backscattering and
relaminarization, by the adaption of the model parameters Cand C to the local flow
structure. The benefit of David-sons dynamic one-equation approach is itsinsensitivity to the existence of homogeneous directions, which recommends the
model for complex flow geometries.
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3. Numerical method
To preclude the effects of different numerical algorithms, all simulations were
performed with the same implicit finite-volume NavierStokes procedure of Xue [7].The general accuracy of the procedure is of second-order in time and space. The
algorithm is based on the strong conservation form within general body-fitted
coordinates, and employs a fully co-located storage arrangement for all transport
properties. Diffusion terms are approximated using either second or fourth-order
accurate central differences, whereas advective fluxes are approximated by central
differencing or third-order bounded (monotonic) upwind-biased schemes. The odd
even decoupling problem of the cell-centered formulation is suppressed with a
fourth-order artificial pressure term in the continuity equation as introduced by Rhie
and Chow [8]. The solution is iterated to convergence using a SIMPLE pressure-
correction scheme. The procedure is parallelized by means of domain decomposition
technique. All RANS simulations were performed on a PC-cluster, whereas the LES
were carried out on the CRAY T3E of Berlins supercomputing center.
4. Results
To assess the influence of the turbulence-representation practice, three different
cylinder flows have been investigated in the present study. The selected test cases
refer to the flow around a square (Re=22 000) and a circular cylinder (Re=3900,Re=140 000), which feature geometry-fixed and pressure-induced separation,
impinging flow and streamline curvature.
4.1. Square cylinder at Re=22 000
The experimental study of the flow around a square cylinder at Re=22 000
conducted by Lyn et al. [9], is a well-known example for the validation of numerical
simulation techniques (see e.g. [10] or [11]). A comprehensive overview of this case
related to LES is given by Voke [12]. The computational grid employed in the LES
mode consists of 32 grid nodes in the homogeneous (z-) direction and 32 304 gridnodes in the main-flow (xy-) plane. The physical domain covers 20 diameters in
streamwise direction (5ox/Do15), 14 diameters in normal direction (7oy/
Do7) and four diameters in the homogeneous direction. RANS computations were
restricted to two-dimensional flow conditions, which were carried out on the xy-
portion of grid. The resolution of the cylinder edges in the xy-plane was based on 30
grid nodes. Approximately 125 70 grid nodes were used to resolve the wake regime
aft of the cylinder. A uniform velocity profile with a turbulence level of 2% and an
eddyviscosity ratio of nt=n or L=D{1 was prescribed at the inlet, which is in linewith recommendations of former studies [11]. Fig. 1 depicts the phase-averaged
streamlines for four selected phases, where each period was split into 20 phases. Thestrong influence of the turbulence-modeling practice is evident at first glance. Both,
the EASM and LES simulations return approximately the same topological features.
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The overprediction of the recirculation length Lr=D; as indicated by Table 2, revealsthat the EASM slightly underpredicts the intensity of the transient motion in
comparison to the experiments (cf. CL; rms). In contrast to this, the LES, returns anaugmented intensity of the transient motion, which is confirmed by an under-
estimation of the recirculation length. When attention is drawn to the BVM,
Fig. 1. Phase-averaged streamlines.
Table 2
Global parameters for square cylinder
CD Lr=D CL;rms St
Exp. 2.1 1.38 F 0.13
LES 2.178 1.06 1.47 0.13
BVM 1.68 2.12 0.03 0.12
EASM 2.206 1.64 0.95 0.15
LESa 2.3 1.46 1.15 0.13
BVMb 2.11 F F 0.15
aLES is taken from Breuer [10].bBVM from [11].
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however, a completely different picture emerges. The recirculation zone becomes
larger and the wake is much more stretched, which is in line with a significant
damping of the transient motion. The BVM fails to mimic the dynamics of the flow,
which is indicated by the reduced root-mean-square value of the lift coefficient
(CL; rms).
In conclusion, the EASM offers a reasonable predictive response to unsteady flow
conditions, which is in close proximity to LES results and the traditional BVM fails
to capture the transient phenomenon. Fig. 2 provides an explanation for the poorperformance of the BVM. Distinct from the EASM and LES simulations, the BVM
model predicts almost no resolved kinetic energy kres 0:5 uiui uiui : In contrastto this, the level of total kinetic energy predicted by the EASM is much higher, still,
the LES is closer to the measured data. The recirculation length is resolved with a
comparable error by both EASM and LES; however, the EASM shows a faster
recovery and consequently overpredicts the downstream velocity.
The misrepresentation of the velocity profile attached to the wall (x 0:0), inparticular the boundary-layer thickness, suggests that the defect of the BVM is
related to an insufficient modeling of the quasi-steady flow regime upstream of the
separation. The failure is attributed to the models tendency towards a prematuretransition to turbulence when the flow is exposed to irrotational strain in the vicinity
of the impingement zone [11].
-0.5 0 0.5 1 1.5
U
0
0.5
1
1.5
2
2.5
3
3.5
4
y
x=0.0
0 0.5 1
U
0
0.5
1
1.5
2
2.5
3
3.5
4
y
EXP
LES
WILCOX
EASM
x=2.0
0 0.5 1
U
0
0.5
1
1.5
2
2.5
3
3.5
4
y
x=4.0
0 0.5 1
U
0
0.5
1
1.5
2
2.5
3
3.5
4
y
x=6.0
0 0.5 1
U
0
0.5
1
1.5
2
2.5
3
3.5
4
y
x=8.0
0 0.2
k
0
0.5
1
1.5
2
2.5
3
3.5
4
y
x=0.0
0 0.2 0.4
k
0
0.5
1
1.5
2
2.5
3
3.5
4
y
EXP
LES
WILCOX
EASM
x=2.0
0 0.2 0.4
k
0
0.5
1
1.5
2
2.5
3
3.5
4
y
x=4.0
0 0.2 0.4
k
0
0.5
1
1.5
2
2.5
3
3.5
4
y
x=6.0
0 0.2 0.4
k
0
0.5
1
1.5
2
2.5
3
3.5
4
y
x=8.0
EXP
LES
EASM
BVM
EXP
LES
BVM
EASM
EXP
EXP
LES
BVM
EASM
LES
EASM
BVM
Fig. 2. Time-averaged resolved kinetic energy and mean streamwise velocity in the wake.
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4.2. Circular cylinder at Re=3900
In cases where the flow exhibits sharp corners, such as the square-cylinder
example, the separation is fixed and the solution is less sensitive to the impact ofcurvature and near-wall modeling. In contrast to this, the separation of the pressure
driven boundary layer from the continuous surface of a circular cylinder is a much
more delicate task. The location of the separation depends on the details of the
attached boundary layer. Moreover, impingement issues are less severe than in the
square-cylinder case, due to the streamlined shape of the obstacle.
The first round-cylinder example refers to subcritical conditions at Re=3900,
where experiments are reported by Lourenco and Shih [13] and Ong and Wallace
[14]. For comparison, the LES results of Beaudan and Moin [15] are included in the
figures. In the present LES, the velocity at the inflow is constant with no turbulence
superimposed, whereas in the RANS a uniform profile with a low turbulence level of
0.12% and nt 0:02n was prescribed. The boundary layer along the cylinder remainslaminar, and transition to turbulence occurs in the separated shear-layer,
approximately one diameter aft of the cylinder. The computational mesh employed
in the (2D) RANS mode consists of approximately 15 000 grid points, covering 32
diameters in streamwise direction (8ox/Do24) and 16 diameters in normal
direction (8oy/Do8). The LES grid extends in spanwise direction to pD and 19D
in streamwise direction and covers 14 diameters in normal direction (-7oy/Do7)
with approximately 900 000 cells.
Fig. 3 displays the time-averaged streamlines obtained from the LES. Thetopology involves two small counter-rotating vortices attached to the rear of the
obstacle, followed by two larger vortices in the near-wake region. In conjunction
with the linear BVM, the counter-rotating vortices are completely suppressed. The
X
Y
_1 0 1 2 3
_1.5
_1
_0.5
0
0.5
1
Fig. 3. Time-averaged streamlines (LES).
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EASM, however, is able to capture the flow topology due to the application of thecurvature correction described in Eq. (8).
Again, the BVM returns an excessively overestimated recirculation, which is
obvious from the evolution of the wake centerline velocity shown in Fig. 4 and the
flow global parameters listed in Table 3. As opposed to this, both the LES and
EASM return a fair agreement with the experimental data. However, the necessity of
the curvature correction in conjunction with the EASM is quite evident from the
global parameters in Table 3. A standard (std.) EASM without the modification,
Eq. (8), returns almost the same result as the BVM.
The EASM exhibits the most pronounced recovery due to the augmented intensity
of the flow reversal. A more complete picture of the simulation quality emerges fromthe streamwise evolution of the wake-velocity profiles displayed in Fig. 5. All
simulations give v-shaped profiles inline with the experiments, whereas Kravchenko
U
_0.4
_0.3
_0.2
_0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
EXP [LS93]EXP [OW96]LESBVMEASMLES [BM94]Std EASM
X
_1 0 1 2 3 4 5 6 7 8
Fig. 4. Mean centerline velocity (Re=3900).
Table 3
Global parameters for circular cylinder (Re=3900)
CD Lr=D St
Exp. 0.99 1.181.33 0.215
LES 1.314 1.00 0.216
BVM 0.88 2.1 0.198
EASM 0.98 1.2 0.203
Std. EASM 0.89 1.9 0.200
LES [14] 1.00 1.3 0.203
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[16] reported an alteration to u-shaped profiles when increasing the spanwise
resolution. The application of the EASM clearly improves the predictive
performance. The curvature correction facilitates an enhanced sensitivity to a
curvature-induced attenuation of turbulence, which is obvious from the reducedshear-stress levels returned by the EASM (cf. Fig. 6).
4.3. Circular cylinder at Re=140 000
The final example refers to the flow around a circular cylinder at Re=140 000,
where experiments were reported by Cantwell and Coles [17]. Both grids cover the
same area as in the former case, but feature an increased resolution of the boundary
layer region (3D-LES: 2 600 000 points; 2D-RANS: 18 000 points). The resolution of
the LES grid in spanwise direction is 64 nodes and the wall distance of the first grid
point is Dn=D=0.0001. Results obtained from the three modeling approachesconsidered in the present study confirm the above-mentioned findings, thus reported
details are confined to the global flow parameters listed in Table 4 and the evolution
U
y
0 0.5 1
_2
_1
0
1
2
x=1.06
U
y
0 0.5 1
_2
_1
0
1
2
EXP [LS93]
LESBVMEASMLES [BM94]
StdEASM
x=1.54
U
y
0 0.5 1
_2
_1
0
1
2
x=2.02
U
y
0.4 0.6 0.8 1
_2
_1
0
1
2
x=3.00
U
y
0.6 0.8 1
_2
_1
0
1
2EXP [OW96]EXP [LS93]LESBVMEASMStdEASM
x=4.00
U
y
0.6 0.8 1
_2
_1
0
1
2
x=5.00
Fig. 5. Evolution of the %u-velocity in the wake (Re=3900).
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of the wake centerline depicted in Fig. 7. With the LES the drag coefficient is
underpredicted by E50% compared to the experiment and the reference LES of
Breuer [18]. This great discrepancy is caused by an earlier separation at Y 921
against Breuers LES with Y 961: This leads to a wrong pressure distributionaround the cylinder, wherein the pressure coefficient on the back cpb=0.649 is only
uv
y
_0.4 _0.2 0 0.2 0.4
_2
_1
0
1
2
x=1.06
uv
y
_0.8 _0.4 0 0.4 0.8
_2
_1
0
1
EXP [LS93]
LESBVM
EASM
Std EASM
x=1.54
uv
y
_0.4 _0.2 0 0.2 0.4
_2
_1
0
1
2
x=2.02
uv
y
_0.1 0 0.1
_2
_1
0
1
2
x=3.00
uv
y
_0.1 _0.05 0 0.05 0.1
_2
_1
0
1
2
EXP [OW96]
EXP [LS93]LES
BVMEASM
Std EASM
x=4.00
uv
y
_0.1 _0.05 0 0.05 0.1
_2
_1
0
1
2
x=5.00
Fig. 6. Evolution of the shear stress in the wake (Re=3900).
Table 4
Global parameters
CD Lr=D St
Exp. 1.237 0.50 0.2
LES 0.68 0.40 0.2
BVM 0.41 1.19 0.3
EASM 1.16 0.59 0.22
LES [14] 1.239 0.572 0.204
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half the value of Breuers LES (cpb=1.398). Moreover, the experiment is
subcritical, i.e. the boundary stays laminar and the transition take place in the
separated shear layer. In the present LES, small laminar separation zones cause a
reattachment of a turbulent boundary layer premature to the experimental observed
transition. Despite this, the LES give a fair representation of the recirculation length
and the centerline velocity.
It should be noted, thatFalthough not elaborated in great detail hereFthe merits
of the EASM are, in this case, to a large extent related to a non-equilibrium
modification of the production term in the o-equation as outlined by Menter [19],
who introduced the reciprocal value of the turbulent viscosity in the equation. In an
analogy to Menter, the ratio cm=cn
m appears in the present approach.
DoDt
a cmo
cnmkP bo2 q n n
t=2 qo=qxj qxj
: 11
The modification, which was exclusively used in this testcase, aims to suppress the
EASM related linearization ofP in the generation term ofo and thus adds to the
models predictive benefits in non-equilibrium flows cnmocm
:
5. Conclusion
Generally, unsteady statistical modeling approaches (URANS) rely on the formalexistence of a spectral gap between the time scales of the mean transient flow and the
residual turbulence. This gap does not almost exist in bluff-body flows. Particularly
X
U
_1 0
_0.4
_0.3
_0.2
_0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
EXP [CC83]
LES
BVM
EASM
LES [Br99]
1 2 3 4 5 6 7 8
Fig. 7. Mean centerline velocity (Re=140 000).
H. L .ubcke et al. / J. Wind Eng. Ind. Aerodyn. 89 (2001) 14711485 1483
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in the wake regime, the duration of the flow distortion due to unsteady effects is
much smaller than the intrinsic time scale of the turbulence and the assumption of a
spectral gap is excessively violated. This, however, does not undermine the
defensibility of the URANS approach in engineering computational fluid dynamics.It is important to note, that under such circumstances there is insufficient time for the
turbulence to effect the mean flow, which significantly reduces the impact of an
inaccurate modeling approach. In contrast to this, the attached shear layers close to
the wall are governed by turbulent time scales which are much smaller than the time
scale of the transient distortion. In such situations, the turbulence model operates in
quasi-steady mode, and there are no more reasons to distrust the model than in
steady flow conditions. In conclusion, the predictive failures of a turbulence closure
often pertain to an inaccurate representation of steady phenomena, e.g. flow-
impingement, streamline curvature or massive straining. The RANS approaches
adopted in the present research effort confirm, that deficits inherent to the baseline
turbulence model tend to foster a deterioration of the overall performance in
unsteady flows.
The investigated explicit algebraic stress model, aims to return improved modeling
capabilities for complex engineering shear flows by means of an efficient non-linear
stressstrain relations and related modifications to the background model. The
methodology is seen to enhance the predictive accuracy in unsteady flow conditions
and significantly outperforms the linear BVM. Superficially, results obtained from
the present EASM show many features of the LES. The EASM, however, does not
reproduce the same level of agreement with experimental data as achieved by theLES. Taking into account that the EASM needs only 5% of the LES computing
time, the capability of the EASM to capture the important flow feature makes
EASM attractive in engineering calculations.
Acknowledgements
The authors greatly acknowledge the financial support by the Deutsche
Forschungsgemeinschaft under the umbrella of the SFB 557 Beeinflussung
komplexer turbulenter Scherstr.omungen. Supercomputer access on the CRAY
T3E was provided by the Zentrum f.ur Informationstechnik Berlin.
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