Comparison Les Rans Bluff-body

8/3/2019 Comparison Les Rans Bluff-body

1/15

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


2/15

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.

H. L .ubcke et al. / J. Wind Eng. Ind. Aerodyn. 89 (2001) 147114851472


3/15

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

H. L .ubcke et al. / J. Wind Eng. Ind. Aerodyn. 89 (2001) 14711485 1473


4/15

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



5/15

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.



6/15

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.



7/15

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].



8/15

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.



9/15

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).



10/15

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



11/15

[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).



12/15

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



13/15

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).



14/15

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.

References

[1] D.C. Wilcox, Reassessment of the scaledetermining equation for advanced turbulence models,

AIAA J. 26 (11) (1988) 1299.

[2] T.B. Gatski, C.G. Speziale, On explicit algebraic stress models for complex turbulent flows, J. Fluid

Mech. 254 (1993) 59.

[3] W. Rodi, A new algebraic relation for calculating the Reynolds stresses, Z. Angew. Math. Mech. 54

(1976) T219.



15/15

[4] T. Rung, H. L .ubcke, M. Franke, L. Xue, F. Thiele, S. Fu, Assessment of explicit algebraic stress

models in transonic flows, Engineering Turbulence Modelling and Experiments 4, Ajaccio, 1999,

p. 659.

[5] S.S. Girimaji, A Galilean invariant explicit algebraic Reynolds stress model for turbulent curvedflows, Phys. Fluids A 9 (4) (1997) 1067.

[6] L. Davidson, A dynamic one-equation subgrid model for three dimensional flow, 11th International

Symposium on Turbulent Shear Flow, Vol. 3, Grenoble, 1997, p. 26.1.

[7] L. Xue, Entwicklung eines effizienten parallelen L.osungsalgorithmus zur 3d Simulation komplexer

turbulenter Str.omungen, Dissertation, TU Berlin, 1998.

[8] C. Rhie, W. Chow, Numerical study of the turbulent flow past an airfoil with trailing edge separation,

AIAA J. 21 (11) (1983) 1525.

[9] D.A. Lyn, S. Einav, W. Rodi, J.H. Park, A laser-Doppler velocimetry study of ensemble-averaged

characteristics of the turbulent near wake of a square cylinder, J. Fluid. Mech. 304 (1995) 285.

[10] W. Rodi, J.H. Ferziger, M. Breuer, M. Pourqui!e, Status of large eddy simulation: results of a

workshop, J. Fluids Eng. 119 (1997) 248.

[11] G. Bosch, W. Rodi, Simulation of vortex shedding past a square cylinder, Proceedings of the tenthSymposium on Turbulent Shear Flows, Pennsylvania State University, USA, 1995, p. 4.13.

[12] P.R. Voke, Flow past a square cylinder: test case LES2, in: J.P. Chollet, P.R. Voke, L. Kleiser (Eds.),

Direct and Large-Eddy Simulation II, ERCOFTAC Series, Vol. 5, Kluwer Academic Press,

Dordrecht, 1997, p. 355.

[13] L.M. Lourenco, C. Shih, Characteristics of the plane wake of a circular cylinder, A particle image

velocimetry. From Kravchenko & Moin Report TF-73, 1998, Stanford University, California, 1993.

[14] L. Ong, J. Wallace, The velocity field of the turbulent very near wake of a circular cylinder, Exp.

Fluids 20 (1996) 441.

[15] B. Beaudan, P. Moin, Numerical experiments on the flow past a circular cylinder at sub-critical

Reynolds-number, Report TF-62, Center for Trubulence Research, Stanford University, 1994.

[16] A.G. Kravchenko, P. Moin, Numerical studies of flow over circular cylinder at Re=3900, Phys.

Fluids A 12 (2000) 403.[17] B. Cantwell, D. Coles, An experimental study of entrainment and transport in the turbulent wake of a

circular cylinder, J. Fluid Mech. 136 (1983) 321.

[18] M. Breuer, A challenging test case for large eddy simulation: high Reynolds number circular cylinder,

in: Banerjee, et al., (Eds.), Proceedings of the first Turbulence and Shear Flow Phenomena,

Begelhouse Inc., New York, 1999, p. 735.

[19] F.R. Menter, Two-equation eddyviscosity turbulence models for engineering applications, AIAA J.

32 (8) (1994) 1598.


Comparison Les Rans Bluff-body

Documents

Transcript of Comparison Les Rans Bluff-body