JOURNAL OF

windengineePing
Journal of Wind Engineering
ELSEVIER and Industrial Aerodynamics 69-71 (1997) 55 75

Comparison of LES and RANS calculations

of the flow around bluff bodies
W. R o d i 1
Institute jbr Hydromechanics, University of Karlsruhe, Karlsruhe, German3,

Abstract

The paper compares LES and RANS calculations of vortex-shedding flow past a square
cylinder at Re = 22.000 and of the 3D flow past a surface-mounted cube at Re = 40.000. Results
from the author's group are included as well as results submitted to an LES workshop for which
both flows were test cases. The RANS calculations were obtained with various versions of the
k-t: model and in the square-cylinder case also with Reynold-stress models, The various
calculation results are compared with detailed experimental data and an assessment is given of
the performance, the cost and the potential of the various methods.

1. Introduction

Flows past bluff bodies, which occur in many engineering situations, involve
complex phenomena like separation and reattachment, unsteady vortex shedding and
bimodal behaviour, high turbulence, large-scale turbulent structures as well as curved
shear layers. There is a great need in practice to predict such flows and the loading
imposed on the bodies, but this is a difficult task even for relatively simple geometries.
Turbulence plays an important role in the flow phenomena considered, especially
since the Reynolds numbers are high in practical problems, and the influence of
turbulence must be accounted for in a prediction method in one way or another. Until
recently, it was mainly the Reynolds-averaged Navier-Stokes (RANS) equations that
were used together with statistical turbulence models which simulate the effects of all
contributions to the turbulent motion, i.e. the complete turbulence spectrum; in
vortex-shedding situations, unsteady RANS equations are solved to determine the
periodic shedding motion and only the superimposed stochastic turbulence fluctu-
ations are simulated with a turbulence model. It was mainly the k-e eddy-viscosity
turbulence model that was used in bluff body calculations, and only few calculations

1 E-mail: rodi@ifh.bau-verm.uni-karlsruhe.de.

0167-6105/97/$17.00 ~, 1997 Elsevier Science B.V. All rights reserved.

PI1 S 0 1 6 7 - 6 1 0 5 ( 9 7 ) 0 0 1 4 7 - 5
56 ffK Rodi/J. Wind Eng. Ind. Aerodyn. 69 7l (1997) 55-75

with other models like the Reynolds-stress model (RSM) have been reported (see
reviews by Rodi [1,2]). It has become clear in these calculations that statistical
turbulence models have difficulties with the complex phenomena mentioned above,
especially when large-scale eddy structures dominate the turbulent transport, when
unsteady processes like vortex shedding and bistable behaviour prevail and dynamic
loading is of importance, and when special influences like buoyancy and curvature are
important. Conceptually, the large-eddy simulation (LES) approach is more suitable
in such situations as it resolves the large-scale unsteady motions and requires model-
ling only of the small-scale, unresolvable turbulent motion which is less influenced by
the boundary conditions. Of course, the LES approach is computationally consider-
ably more expensive, but the recent advances in computer performance and numerical
methods have made LES calculations feasible also for flows around bodies of various
shapes. It should be added here that direct numerical simulations (DNS) in which all
scales of the turbulent motion are resolved and no model needs to be introduced are
feasible only for relatively low Reynolds numbers (say below Re = 104) as the number
of grid points required for the resolution of all scales increases approximately as Re ~.
In the author's research group, both the RANS and LES approach have been
applied to calculate two fairly basic bluff body flows for which detailed experimental
results are available. One is the vortex-shedding flow past a long square cylinder
(which is two-dimensional in the mean) at Re = 22.000 as studied experimentally by
Lyn and Rodi [3] and Lyn et al. [4]. The second one is the flow past a surface-
mounted cube placed in developed channel flow at Re = 40.000 (based on cube height
and mean approach-flow velocity), for which detailed experimental results are re-
ported in Refs. [5,6]. In this case the mean flow is fully three-dimensional, and has
complex multiple separations. Both flows were also test cases for an LES Workshop
organised by the author together with Professor J.H. Ferziger of Stanford University
[7,8] and a number of computor groups submitted LES results for the two cases. The
present paper compares the results obtained with the LES and RANS method for the
two flows mentioned and summarises the experiences gained so far.

2. Methods

2.1. RANS with statistical turbulence models"

In the calculations of the cube problem, the steady 3D time-averaged

Navier Stokes equations are solved together with the time-averaged continuity equa-
tion. The former involves the Reynolds stresses u'iu) which have to be determined with
a statistical turbulence model. The overbar indicates time averaging. In the case of the
flow past a long square cylinder, the mean flow is considered to be two-dimensional
and the triple decomposition is used to express the instantaneous quantities, e.g.
U = ~7 + ~ + u', where G is the time-mean value, 0 the periodic vortex-shedding
component and u' the superimposed stochastic turbulent fluctuation. The
ensemble- (or phase-) averaged quantities, e.g. <U> = ~7 + ~, are determined by
solving the phase-averaged 2D Navier-Stokes and continuity equations. In the
 V~ Rodi/J. Wind Eng. Ind. Aerodyn. 6 9 - 7 1 (1997) 55 75 57

former, phase-averaged Reynolds stresses (ulu'j} appear which have again to be

determined by a turbulence model.

2.1. l. k-e model

Calculations were carried out with various versions of the k e model which relates
the Reynolds stresses to the mean velocity gradients via the eddy viscosity yr. The eddy
viscosity itself is expressed by two parameters characterising the local state of
turbulence, the turbulent kinetic energy k and the rate of its dissipation e,, which
together define the velocity and length (or time) scale of the turbulent motion. The
distribution of k and e, in space and time is determined from model transport
equations for these quantities. Standard values of the empirical constants appearing in
the model [9] have been used. For application to the vortex-shedding flow, the
extension of the widely used steady model [9] is straightforward in that all quantities
appearing are now phase-averaged quantities and a time-dependent term is added in
each of the transport equations.
The standard k e, model based on the isotropic eddy-viscosity concept is
known to lead to unrealistically high production of k in stagnation regions which
are present in both application cases. This is a consequence of the inability
of this kind of model to simulate correctly the difference between normal
stresses governing the production Pk in such regions. Kato and Launder [10]
suggested as an ad hoc measure to replace the original production term
Pk = C~eS 2 by Pk = CueS• where S = k/e, x/l(1 U i,j + Us,i)2 and Q = k/e. x/½(
1 U ;,J - U j,i) 2,
denote, respectively, the strain and vorticity invariants. In simple shear flows, the
behaviour remains unchanged as Q ~ S while in stagnation regions ~ ~ 0 so that the
spurious turbulence production is eliminated. This version of the k-e, model was also
tested for both flow cases.

2.1.2. Reynolds-stress model (RSM)

Eddy-viscosity models do not properly account for history and transport effects on
turbulence and therefore have difficulties in regions of complex separated flows where
these effects are important. For example, Franke et al. [11] have found by evaluation
of data of vortex-shedding flow past a circular cylinder that substantial regions exist
where, due to the dominance of history and transport effects, the eddy viscosity is
negative and hence the eddy-viscosity concept invalid. Reynolds-stress models ac-
count for these history and transport effects by solving model transport equations for
the individual stresses (u'iu~); they do not employ the eddy-viscosity concept. Franke
and Rodi [12] adopted the standard Reynolds-stress model of Launder et al. [13]
with wall corrections to the pressure-strain terms due to Gibson and Launder [14] for
calculating unsteady phase-averaged stresses. They applied the model to the square-
cylinder case.

2.1.3. Near-wall treatment

With the various turbulence models, different approaches were tested for handling
the near-wall region. In most practical calculations today, wall functions are still used
58 W. Rodi/J. Wind Eng. Ind. Aerodyn. 69-71 (1997) 55-75

in which the viscous sublayer is not resolved but the first grid point is located outside
this layer. Basically, the quantities at this grid point are related to the friction velocity
based on the assumption of a logarithmic velocity distribution and of local equilib-
rium of turbulence (production = dissipation). These assumptions are, however, ques-
tionable in separated flow regions. For both flow cases, as alternative the two-layer
approach was also tested in connection with the k ~:model and for the square-cylinder
case also in connection with the RSM. In this approach, the viscous sublayer is
resolved with a simpler one-equation model due to Norris and Reynolds [15]. In this,
the velocity scale of the turbulent motion is also determined from the k-equation, but
the length scale is not determined from an ~:-equation. Rather, the length-scale
distribution very near the wall is prescribed, and in particular a linear distribution is
used which is damped very near the wall as in the van Driest mixing-length model.

2.2. LES methods

In large-eddy simulations, the three-dimensional time-dependent Navier-Stokes

equations are solved numerically. Since at higher Reynolds numbers the small-scale
turbulent motion cannot be resolved in such calculations, it is filtered out and only
motions larger than the filter width, which is in general effectively the mesh size, are
resolved; these include in the square-cylinder case the 2D periodic shedding motions.
The effect of the unresolved small-scale fluctuations on the resolved larger-scale
motion needs to be modelled. The Japanese school following K u w a h a r a (e.g. Ref.
[16]) leaves this simply to the damping effect of their third-order upwind scheme used
for discretizing the convection terms. This "quasi-LES" approach was also used for
the square-cylinder calculations by some contributors to the LES Workshop. The
implications of this approach and in particular the dependence of the results on the
grid employed are not entirely clear.

2.2.1. Subgrid-scale models

In most LES calculations, including those of the author's group, the effect of the
unresolved small-scale motion is simulated with a subgrid-scale model. The 3D
time-dependent Navier-Stokes equations solved represent equations from which the
small-scale motion has been filtered out or, what is generally equivalent, that were
averaged over the control volumes of the numerical grid. The filtering or averaging
introduces correlations between the unresolved fluctuating velocities which act as
stresses on the resolved motions, and these stresses need to be modelled. Two different
models were used in the author's group and also by the workshop participants. One is
the Smagorinsky [17] eddy-viscosity model which relates the subgrid-scale eddy
viscosity to the strain rate of the resolved motion as velocity scale and to the mesh size
as length scale. Near the wall, this length scale is modified by a van Driest damping
function. The model introduces one empirical constant Cs which was, however, found
not to be universal but to depend on the flow considered. In calculations of the
author's group, a value of Cs = 0.1 was chosen.
Because the optimal value of Cs varies from flow to flow and even from point to
point within one flow and because a special near-wall treatment is needed in the
 W Rodi/~ Wind Eng. Ind Aerodyn. 69 71 (1997) 55 75 59

Smagorinsky model, recently the dynamic model proposed by Germano et al. [18]
became popular. In this, the information available from the smallest resolved scales is
used to calculate a local (and time-dependent) value of the "constant" Cs in the
Smagorinsky model. The resulting Cs can have erratic values and even go negative
which in principle could account for backscatter, but this undermines the numerical
stability of the method. Hence, some averaging and possibly clipping is necessary, and
the measures taken in the author's group are described in Ref. [19]. The dynamic
model was used by a number of workshop participants for calculating the square-
cylinder case.

2.2.2. Near-wall treatment

Ideally, the no-slip conditions should be used at walls in LES calculations, but this
would strictly demand very high resolution near the wall at high Reynolds numbers as
otherwise the scales of motions contributing most to the turbulent momentum
transfer in the viscous sublayer cannot be resolved. Sufficient resolution is usually not
possible, but the no-slip conditions are nevertheless sometimes used. More appropri-
ate at high Reynolds numbers is, however, the employment of a near-wall model
similar to the wall functions used in RANS calculations. Various such models have
been proposed, and the calculations of the square cylinder and cube cases by the
author's group recorded below adopted the approach of Werner and Wengle [20].
This assumes that the instantaneous tangential velocity inside the first cell is in phase
with the instantaneous wall shear stress and that a linear (y+ < 11.81) or + power law
(y+ > 11.81) distribution of the instantaneous velocity can be assumed. It should be
mentioned that all wall models were basically developed for attached flows and their
application in separated flow regions is somewhat questionable.

2.3. Numerical solution methods

The RANS calculations reported (except the ones of Franke and Rodi [12]) were
obtained with a finite-volume code [21] from which the LES code was derived. Hence
the two codes have many common features, which are described first. A finite-volume
method is used for solving the incompressible Navie~Stokes equations on general
(but structured) body-fitted curvilinear grids. A non-staggered, cell-centred grid ar-
rangement is used with Cartesian velocity components. The well-known pressure field
checkerboard problem is avoided by applying the momentum interpolation technique
of Rhie and Chow. The pressure-velocity coupling is achieved with the S I M P L E
algorithm, and the viscous fluxes are approximated by central differences. The
resulting set of linear difference equations is solved by an incomplete LU decomposi-
tion method or in Bosch's [22] calculations by a T D M A algorithm. Both finite-
volume codes are highly vectorised. In the earlier square-cylinder calculations of
Franke and Rodi [12], the older program T E A C H employing rectangular staggered
grids was used.
The differences between the RANS and LES code are now described: The RANS
code is entirely implicit. It is an iterative procedure for the 3D steady calculations and
uses first-order backward time differencing for the unsteady vortex shedding
60 W. Rodi/J. Wind Eng. Ind. Aerodyn. 69 71 (1997) 55 75

calculations. In contrast, the LES method requires at least second-order accuracy in

time and also small time steps to properly resolve the time variation of the fluctua-
tions, which can be obtained more efficiently with an explicit method. Therefore,
a p r e d i c t o r ~ o r r e c t o r scheme is used, where the predictor step is an explicit
Adams Bashforth scheme for the m o m e n t u m equations (second-order in time), and
the corrector step involves the implicit solution of the Poisson equation for the
pressure correction. In the LES code, the convective fluxes are approximated by
central differences. In the RANS method, mostly the H L P A (hybrid linear parabolic
approximation) of Zhu [23] is used, which is low diffusive (mainly second order) and
oscillation-free. It was already found by Franke and Rodi [12] and confirmed by
Bosch [22] that first-order upwind difference schemes cannot be used for vortex-
shedding calculations as they d a m p out the periodic shedding motion.
A variety of other numerical schemes were used in the LES calculations submitted
to the workshop, including Euler, Runge Kutta, Leap-Frog and Crank-Nicholson
schemes for time discretization and Q U I C K and third-order upwind schemes for the
convection terms [7,8].

3. Square-cylinder calculations

Calculations are presented here for the flow past a long square cylinder at
Re = 22.000, for which detailed phase-resolved measurements are available [3,4].
RANS calculations obtained with various turbulence models ranging from the
algebraic Baldwin-Lomax model to an RSM and also a single LES [24] were
reviewed already in Refs. [1,2]. In the meantime, Bosch [22] has recalculated this case
with various versions of the k c model using an extended calculation domain, and
a number of new LES calculations submitted for the LES Workshop (9 groups
submitted 16 different results [7,8]) are available which have the advantage over
the previous LES calculation of Ref. [24] that the extent of the calculation domain in
the spanwise direction is 4D instead of 2D which was considered too short to allow for
the evolution of 3D structures. Here, mainly the new results are compared and
reviewed but the older RSM results of Franke and Rodi [12] are included because
they are the only ones obtained with a model that does not use the eddy-viscosity
concept.
Following Franke and Rodi [12], the calculation domain set for the LES calcu-
lations extended 4.5D upstream of the cylinder, at least 14.5D downstream and 6.5D
on either side of the cylinder (where the tunnel walls were located). Wang and Vanka
[25] used a somewhat different domain their results obtained after the workshop
with a finer grid and a higher-order convection scheme are included here. In all LES
calculations presented, the calculation domain extended 4D in the spanwise direction.
Bosch [22] found that 4.5D was too close to the cylinder to allow the assumption of
uniform inflow velocity, and he extended the calculation domain to - 10D. In the
experiments, a turbulence level of 2% was measured in the oncoming flow. In all the
LES calculations, turbulence at the inflow was neglected while in the RANS calcu-
lations the measured turbulence level was prescribed. There remains, however, an
 W. Rodi/J. Wind Eng. Ind. Aerodyn. 69-71 (1997)55-75 61

uncertainty with regard to the value of e at the inflow plane which also needs to be
prescribed. Franke determined this value by assuming the ratio of eddy viscosity to
laminar viscosity to have a value of 100 while Bosch used a value of 10 and argued
that this is more realistic. In Table 1 the numical grids of the various LES and RANS
calculations compared here are given. Only few of the LES calculations submitted to
the workshop can be included and they were selected (as in Ref. [8]) to show the range
of results. Wang and Vanka's 1-25] improved calculations obtained after the workshop
are added. The labelling of the individual contributions to the workshop was taken
over from Refs. [7,8]. UKAHY2 refers to the contribution from the author's group
also published in Ref. [26].
When sufficiently accurate numerical schemes are used and other parameters of the
calculation are chosen carefully, all models produce vortex shedding. Fig. 1 presents
the streamlines at three phases calculated with an RSM RANS model and the
UKAHY2 LES method in comparison with the measurements. Clearly, both model
types give good qualitative agreement with the measurements: the basic shedding
mechanism appears to be well reproduced. There are, however, differences in detail,
which are quite considerable among the various LES calculations. The shedding in the
experiments and also generally in the LES calculations is not very regular as can be
seen from excerpts of pressure and lift signals shown in Fig. 2. Clearly, lower fre-
quency amplitude variations are present, but a clear shedding frequency could still be
determined. In the RANS calculations, which force the resolved motion to be two-
dimensional, the shedding behaviour is generally regular.
Table 1 summarises various global parameters such as the dimensionless shedding
frequency (Strouhal number St =ID/Uo), the time mean drag coefficient (r,, the RMS
values of the fluctuations of drag and lift coefficients c~ and c{, respectively, and the
reattachment length 1R indicating the length of the time-mean separation region

Table 1
Global parameters for flow past square cylinder

Calculation St Co C'o C'L IR Grid

method

LES KAWAMU, No SGS "} 0.15 2.58 0.27 1.33 1.68 125 × 78 x 20
UMIST2, Dyn t 0.09 2.02 -- 1.21 140 x 81 × 13
UKAHY2, Smag [7,8] 0.13 2.30 0.14 1.15 1.46 146× 146× 20
TAMU2, Dyn 0.14 2.77 0.19 1.79 0.94 165×I13x17
Wang and Vanka, Dyn [25] 0.13 2.17 0.18 1.29 1.20 192 × 160 × 48

RANS Std k-t: WF 0.134 1.64 ~ 0 0.305 2.8 100x 76

KL-k-t: WF [22] 0.142 1.79 0.012 0.614 2.04 100x 76
TL k-e, 0.137 1.72 s0 0.426 2.4 170× 170
TL-KI-k e, 0.143 2.0 0.07 1.17 1.25 170x 170
RSM WF [12] 0.136 2.15 0.27 1.49 0.98 70x64
TL-RSM 0.159 2.43 0.06 1.3 1.0 186 x 156

Experiments 0,132 1.9-2.2 1.38

62 W. Rodi/J. Wind Eng. Ind. Aerodyn, 69 71 (1997) 55 75

O.5
o.o
.e.s
- .Lo

-1.5

L~

Fig. 1. Flow past a square cylinder: streamlines ~at 3 ophases[

~ -50 1

~,.o , ~,~.,.,~ . ' ~IVvl/l j~lj

"2
"~
Exp.: pressureon side of cylinder ~[ V ,~
50 20 4O ~0 80

L E S - U K A H Y 2 : lift

Fig. 2. Time variation of pressure and lift in flow past square cylinder.

behind the cylinder. The Strouhal number predicted by RANS models using wall
functions is roughly correct, while the two-layer versions predict St slightly too high
and 20% too high in the case of the RSM. Most LES calculations yielded the correct
value of St ~ 0.13, and it appears that St is not very sensitive to the parameters of the
 W Rodi/J. Wind Eng. Ind. Aerodyn. 69 71 (1997) 55 75 63

simulation; there are however a few deviations from this value. The basic k e model
predicts 6D tOO lOW resulting from a too large base pressure [-2] and being associated
with a too long separation region. Both the introduction of the K a t o - L a u n d e r
modification and the two-layer approach reduces the base pressure and the length of
the separation region and increases gD, and a combination of both approaches yields
roughly the correct values (albeit 1R is now somewhat too small). RSM calculations
with wall functions produce the correct CD while the two-layer version overpredicts
this quantity. Many of the LES calculations yielded CD-values falling in the experi-
mental range, most of them are however on the high side, especially those that do not
use wall functions. In the LES calculations there is not such a clear relation between
6D and the reattachment length IR. RANS calculations yielded generally smaller
cD-ftuctuations than LES calculations and the same can be said about the CL-
fluctuations obtained with the basic k e model. However, RANS calculations with
either combined K L and two-layer approach and RSM yield similar magnitudes to
the LES results.
Fig. 3 displays the distribution of the time-mean velocity ~7 along the centreline.
Experimental data due to Lyn et al. [-4] and Durfio et al. [27] are included. The data
agree fairly well in the near-cylinder region, but the approach to the free-stream
velocity is quite different for reasons that are not entirely clear. In front of the cylinder
where the flow is basically inviscid, all results are more or less the same, while there are
large differences in the wake region. There the results reflect the lR behaviour discussed
already. The standard k e model overpredicts the length of the separation zone
considerably; introducing the K L modification and the two-layer approach improves
the calculations; in fact, the combination of the two approaches gives the best
agreement with the measurements. The approach to the free-stream velocity is
however faster than measured by Lyn et al. [4] but close to Durfio et al.s' [27] data. In
fact these RANS calculations are better than the RSM results which yield too short
a separation region and considerably too small negative velocities. The LES results
exhibit surprisingly large differences both in terms of the length of the separation
region and the recovery behaviour. The recovery is generally predicted faster than
that of Lyn et al.s' data, but there is one calculation which is in fairly good accord
and one even produces a slower recovery. The UKAHY2 results show an unrealistic
slope of U at larger x-values; this is most likely caused by the relatively coarse
grid in the downstream region as it goes away when a finer grid is used
there [28].
Fig. 4 presents the distribution of the total (periodic plus turbulent) fluctuating
kinetic energy along the centreline. Here the various LES results show an even wider
variation with an almost fourfold difference in the peak level of ktot, but the picture is
not entirely consistent. T A M U 2 yields excessive fluctuations which cause under-
prediction in separation length, while K A W A M U produces too small fluctuations
which explain the excessive separation length. Difficult to understand is why the
UMIST2 calculations with an even lower fluctuation level lead to an underprediction
in the separation length. It can generally be observed that the total fluctuations are
predicted too small when the drag coefficient and separation length are reasonable.
Turning to the RANS calculations, it can be seen from Fig. 4 that the standard k e
64 W. Rodi/J. Wind Eng. Ind. Aerodyn. 69-71 (1997) 55 75

1.2 , | ,

KAWAMU
1 '-",:"
.-~,,~.. UMIST2 ........
~ UKAHY2 ......... ...................... . .....
0.8 " r ~ a u 2 .............. ......... . ...........................
, , ~ ~ x p ..... / ' S I ~ : ~ : ~ _ ~ Z
0.6

0.4

0.2
/i;"
0

-0.2
~' Wang & Vanka [26]
-0.4 . . | i i i i

(a) -4 -2 0 2 4 6 8 l0
x

/too
0.8
/..'5..:- ....... ~....'~ .......... ~i.........
0.6 /.* 4 . .f. .
//,'. .'.. ,,,
0.4
/ ." ,. . . . . . . Std. k-e W F
,.'• ~ .." ,,' ............... KL-k-~ W F [25
." t :' / ........ TL-KL-k-E
0.2
m t3 Exp. Durao [27]
Exp. Lyn [4]
0 *,.J / :: ,
~-?.::..~ ... ...-"
-0,2
i I I I I I I

0 1 2 3 4 5 6
(b) x/D

F i g . 3. T i m e - m e a n velocity U along centreline of square cylinder.

model with wall functions predicts the peak of the fluctuations considerably too far
downstream and yields a much too small fluctuation level behind the cylinder. Using
the two-layer model (not shown in the figure) moves the peak a little to the left, and it
should be mentioned that there are considerable differences to the calculations of
Franke and Rodi [2], who, with the same model, obtain a much lower level of kto~.
This indicates that the results are sensitive to the details of the simulation parameters
chosen. Switching to the K L modification moves the peak closer to the cylinder and
raises its value to roughly the correct levels and, when the combination of KL
modification and two-layer approach is used, the location of the peak is roughly
correct, but the fluctuation level is now overpredicted. Franke and Rodi's RSM
calculations are not included here because they did not present ktot itself but only the
 I4~ Rodi/J. Wind Eng. Ind. Aerodyn. 69-71 (1997) 55-75 65

i I i i

KAWAMU --
UMIST2 ......
0.8 UKAHY2 ....
...,."~... TAMU2 .......
EXP o
/ ....... Wang & Vanka [26] ....
0.6
...../ °°°°%,
f.z\ ~.
: <~ :." . . . <>~
0.4 " ~/ "''" ~O

::- 8 /o.~" / - - - - - - "'.'....

. ~ . ' - . % .......
o ~.......................
0.2

0 I I I I f I I

(a) } 2 3 4 5 6

! l l l

k_/ ....... TL-KL-k-~

u~ ............. KL-ke-WF [22]
....... Std. ke-WF
x Exp. [4]
0.8 I-.,,
.,. .,.
:,
i ",.
0.6 i

0.4

1[7 ," /°" x x'"~,,, ....... "........

0.2

_. : ....................
i i i

0 I 2 3 4 5 6
(b) x/D

Fig. 4. Total kinetic energy of fluctuations (periodic + turbulent) along the centreline of square cylinder.

sum of the s t r e a m w i s e a n d lateral fluctuations. This agrees quite well with the
c o r r e s p o n d i n g data, the t w o - l a y e r version being s o m e w h a t on the high side.
Fig. 5 shows the c o r r e s p o n d i n g d i s t r i b u t i o n of the t u r b u l e n t k i n e t i c - e n e r g y c o m -
p o n e n t of the fluctuations. H e r e only the U K A H Y 2 - L E S results are available. All
R A N S c a l c u l a t i o n s are c o n s i d e r a b l y t o o low while the L E S results a v a i l a b l e are
r o u g h l y in a c c o r d with the m e a s u r e m e n t s . This m e a n s that in the R A N S c a l c u l a t i o n s
where the t o t a l fluctuations are realistic o r t o o high, the p e r i o d i c fluctuations are
o v e r p r e d i c t e d . The very different b e h a v i o u r of R A N S a n d L E S c a l c u l a t i o n s is m o s t
likely to be due to the fact that the fairly high t u r b u l e n t kinetic energy stems from
c o n t r i b u t i o n s of low-frequency fluctuations as i n d i c a t e d in Fig. 2. In the e x p e r i m e n t s
these o r i g i n a t e from the 3D n a t u r e of the large-scale structures, also o b s e r v e d in the
66 W. Rodi/'J. Wind Eng. Ind. Aerodyn. 69 71 (1997) 55 75

experiments, and to some extent from low-frequency unsteadiness of the oncoming

flow. The LES results can capture the 3D nature and count any low-frequency
fluctuations originating from these as turbulence, while of course the 2D RANS
calculations cannot; they determine k from solving the turbulence model equations.
The overall behaviour of the vortex-shedding flow is determined largely by the
prediction of the evolution of the separated shear layers on the sides of the cylinder.
Hence, it is interesting to consider the U-velocity profile at the location of the rear face
of the cylinder, and this is done in Fig. 6 for the ensemble-averaged velocity at phase 1.

0.45
0.4 LES UKAHY2 [271
u~ TL-RSM [12] * -~
0.35 TL-KL-k-• [22] ..............
Std. k-E [22] ..........
0.3
Exp. [41 ta
0.25
0.2
0.15 r ,,
0.1 I 1::1 ~. rn m E I O m
DOQfn

0.05
0
/ ! , I I I I I I
-0.05
0 1 2 3 4 5 6 7
x/D

Fig. 5. Turbulent component of kinetic energy along the centreline of square cylinder.

1 v

0.8
0.6 ~.~_~
UKAHY2-LES [7]
0.4 - - ' - - UMIST2-LES [7]
............ 2L-RSM [12]
0.2 t~ Exp.-2 comp. [4]
Exp.-1 comp. [3]
0
-0.2
-0.4
-0.6 ' ~ - - ~
-0.8
-1
-1 -0.5 0 0.5 1 1.5 2

Fig. 6. Profiles of ( U ) at x location of rear cylinder wall for phase 1.

 VK Rodi/.~ Wind Eng. Ind. Aerodyn. 69 71 (1997) 55 75 67

In the experiments it was found that the separated shear layers do not reattach at any
phase. F r o m Fig. 6 it can be seen that on the upper side the RANS calculations
predict unrealistically reattachment while on the lower side the shear layer remains
detached in the calculations. Here all LES calculations definitely are in closer
agreement with the experiments; for two of them the predicted velocity distributions
with the actual grid points are shown. This gives an impression of the resolution in
this region: In the U K A H Y 2 calculations (with height of near-wall cell Ay~/D = 0.01)
at least a few grid points are located in the region with reverse flow while in the
U M I S T 2 calculations the first grid point is at the peak of the negative velocity. This
points to a clear resolution problem in this area which is one of the main reasons for
the disagreement with experiments and also a m o n g the various LES calculations. On
the other hand, the T L - R S M calculations give poor results in spite of the much better
resolution (AyjO = 0.00125).

4. Surface-mounted-cube calculations

The flow considered is that over a cube mounted on the lower wall of a plane
channel; the cube height H is half of that of the channel. For this geometry and
Re = U~H/v = 40 000, flow visualisation studies and detailed LDA measurements are
available [5,6]. The entry section of the channel was long enough to have developed
channel flow. F r o m the visualisation studies and the detailed measurements, Mar-
tinuzzi [-5] devised the flow picture given in Fig. 7 which clearly shows the very
complex nature of the flow in spite of the simple geometry. The flow separates in front
of the cube; in the mean there is a primary separation vortex and also a secondary one,
while instantaneously up to four separation vortices were detected. The main vortex is
bent as horseshoe vortex around the cube into the wake where it has a typical
converging-diverging behaviour. The flow separates at the front corners of the cube
on the roof and side walls. In the mean it does not reattach on the roof. A large
separation region develops behind the cube which interacts with the horsehoe vortex.
Originating from the ground plate, an arch vortex develops behind the cube. Predomi-
nant fluctuation frequencies were detected sideways behind the cube, which were

Fig. 7. Flow around a surface m o u n t e d cube according to Ref. [5].

68 W. Rodi/'J. Wind Eng. hM. Aerodvn. 69 71 (1997) 55 75

traced to some vortex shedding of the flow past the side walls. Further, bimodal
behaviour of the flow separation, and in particular of the vortices in front and on the
roof were observed.
For the LES Workshop, 4 results were submitted by 3 groups, but one set of results
showed clearly insufficient averaging and is hence not included here. Information on
the remaining submissions is provided in Table 2 and the U K A H Y methods and
results are described in Ref. [19]. RANS calculations for this flow were performed by
Lakehal and Rodi [29] with various versions of the k ~:model as listed in Table 2. The
calculation domain extended 3.0H and 3.5H upstream of the cylinder, 6H and
10H downstream and 7H and 9H laterally for the LES and RANS calculations,
respectively. With each method, developed channel flow was calculated first and
the results were then used as inflow conditions. Periodic or no-slip conditions were
used on the lateral boundaries, and in the two-layer (TL) RANS calculations, the
two-layer approach was used only on the cube walls and on the bottom wall. The
grids employed are listed in Table 2; they are generally non-uniform with finer
resolution near the walls. The height of the near-wall cells was 0.01H in the RANS
calculations with wall functions, 0.001H in the two-layer calculations and 0.0125 in
the U K A H Y - L E S calculations from the author's group. In these, about 160000 time
steps were necessary to obtain reasonably reliable statistics.
Fig. 8 compares the streamlines in the plane of symmetry (left) and near the channel
floor (right) for some of the calculations, while Table 2 compares various lengths of
separation regions defined in Fig. 7. There is now much closer agreement among the
various LES calculations than in the case of the square cylinder. Similar conclusions
were drawn for a lower Reynolds number case (Re = 3000) for which more entries
were submitted to the workshop; it was also found that the effect of Reynolds number
is small as the results obtained are very similar to those for the high Reynolds number
case. The streamline picture in Fig. 8 shows that on the whole LES is able to simulate
this complex flow very well. With the dynamic model, the separation in front of
the cube is predicted correctly while k c models using wall functions predict late

Table 2
G l o b a l p a r a m e t e r s for c u b e c a l c u l a t i o n

Calculation Key -~| 1 -'( i -'(R 1 G rid

method

LES UKAHY3, Smag 1.29 1.70 165 x 65 × 97

[7,8,26] UKAHY4, Dyn LES-D 1.00 - 1.43 165 x 65 x 97
UBWM2, Smag 0.81 0.837 1.72 144 x 58 × 88

RANS Std. k ~: W F KE 0.65 0.43 2.18 110×32x32

[29] KL-k e-WF KL 0.64 - 2.73 110x32×32
TL-k-~ TLK 0.95 - 2.68 1 4 2 x 8 4 × 64
T L - K L - k ~: TLKK 0.95 3.40 142 x 84 x 64

E x p e r i m e n t [5,6] 1.04 1.61

 Rodi/~ Wind Eng. Ind. Aerodyn. 69 71 (1997) 55 75 69

2.0 l - - , , , ~ ,. ,~ - i ~ r

1.5 ~

1.0

0.5
EXP
0.0
-2 -1 0 I 2 3

1.5

1.0 LES-D.~
0.5

0.0
-2 0 2 4
-2 0 2 4

2.0

1.5 °l

1.o KE
0.5

0.0 .

1.5
2.0 i
l.o KL

0.5

~)'0-2 -1 0 1 2 3 4
-2 .I q~ t ~ 3 4

1.5

l.o TLK ,,
0.5

0"0-2 -1 0 1 2 3 4
-2 -I 0 t 2 3 4

Fig. 8. Streamlines in the symmetry plane (left) and near the channel floor (right) for flow a r o u n d cube.
70 W. Rodi/J. Wind Eng. Ind. Aeroclvn. 69. 71 (1997) 55- 75

separation. On the other hand, the two-layer versions also predict the separation
location correctly and only they as well as the LES calculations produce a small
secondary separation in the corner.
On the roof, the U K A H Y - L E S calculations do not predict reattachment in the
mean, as was also found in the experiment, and the location and extent of
the separation region are well reproduced. The only other LES result included
here yielded reattachment. The k e, models using wall functions also lead to reattach-
ment on the roof and predict much too small and thin a separation region. When
the K L modification is switched on, this region becomes much longer and in fact there
is now no reattachment, but the separation bubble is still too thin. The improvement
is brought about by the significant reduction of the turbulent kinetic energy produced
in front of the obstacle, as can be seen from the k-contours given in Fig. 9. As
a consequence, in the K L version there is less turbulence swept around the front
corner so that the eddy viscosity over the roof is smaller, leading to a longer
separation region. The excessive kinetic energy in front of the cube is also absent in the
LES results which indicate strong turbulence generation in the separated shear layer.
Switching from wall functions to the two-layer approach also improves the prediction
over the roof; this is due to better resolution of the relatively thin bubble and the more
realistic treatment of the near-wall region and is in line with previous observations
made in 2D separated-flow calculations. As far as the flow over the roof is concerned,
combining the two-layer approach with the K L modification yields the best RANS
prediction.
All RANS models tested overpredict the extent of the separation region behind the
cube (XR1). The standard k-t: model with wall functions already predicts this quantity
35% too long, and both the introduction of the KL modification and the two-layer
approach increase XR1 further; a combination of both approaches gives the most
excessive length (see Table 1). in the calculations with the K L modification, less
turbulence is swept around the front corners and over the roof into the downstream

2.0 2.0
1.5 !
1.0 1.0
0.5 0.5
O0 0"0-2 -1 0 1 2 3 4
-i 0 I 2 3
Std. ke-WF KL-ke-WF
2.0 , ~.
1.5 ~ ~

0.5
00
UKAHY4-LES
Fig. 9. k-contours in symmetry plane of cube.
 I~ R o d i / Z Wind Eng. Ind. Aerodyn. 69 71 (1997) 5 5 - 7 5 71

region leading to lower eddy viscosity there which explains the longer separation zone
vis-a-vis the standard model calculations. Moving from W F to T L calculations, the
resulting larger separation zone on the roof also increases the separation zone behind
the cube. LES clearly does a better job in the lee of the cube and predicts the

Mean velocity profile U: x =0.5 Mean velocity profile U: x = 2.5 Mean velocity profile U: x = 4.0
2 . 2
1.8 6.'~, 1.8
~v
1.6 1.6 )~i 1.6
1.4 1.4 1.4
1.2 1.2 ~ * 1.2
// o
;~ 1
0.8 K-E--
;~ 1

0.8
! ,f, g*o
i ft.
,,.6" ~ oo° ;'" I
0.8
i
,,£/
/// 4
0.6 TLK - - - 0.6 t " ~ * 0.6
: // q
0,4 LES-D ...... 0.4
Exp.(u-v) o 0.4 I~.~,S,/ioo,,," , ,
0.2 Exp.(u-w) + 0.2 .7 ' :' 0.2
I!
0 i i 0 :1 0
-0.5 0.5 I 1.5 -0.5 0 0.5 1 0 0.5 I
U U U
Shear stress profile u'v': x = 0.5 Shear stress profile u'v': x = 2.5 Shear stress profile u'v': x = 4.0
2
1.8
1.6
1.4
1.2 ~. ~ :
. .:-d.SC"o /
1.8
1.6
1.4
1.2 .,..
,-'~"
2
1.8
1.6
1.4
1.2
1
/
~" 1
o,"
0.8 K-E - - o '; . I 0.8
08 o., \!t~
KL---
0.6 TLK - . - 0.6 , ~ 0.6 !
0.4 LES-D ...... 0.4 ~ 0.4
Exp.(u-v) o
0.2 0.2 0.2
0 0 L i 0
-0.1 -0.05 0 0.05 -0.05 -0.025 0 0.025 0.05 -0.05 -0.025 0 0,025 0.05
u'v' u'v' u'v'
Turbulence Kinetic Energy: x = 0.5 Turbulence Kinetic Energy: x = 1.0 Turbulence Kinetic Energy: x = 2.0

1.8 1.8 ~ 1.8

1.6 ~ , 1.6 1.6
1.4 ~.':-~ 1,4 [,4
1.2 - 1.2 ~ ~ - ' ~ " " ~-g o 1.2
~ I ~ 1 :~ 1
0.8 0.8 0.8 '~+ , o
+'.o
0,6 0.6 0.6 + o'
0.4 Exp.(u-v) 0.4 0.4 +~.
0.2 Exp.fu-w) + 0.2 0.2
0 ' 0 ' ~ 0
-0.05 0 0.05 0.1 0.15 0.2 025 -0.05 0 0.05 0.1 0.15 0,2 0.25 -0.05 0 0.05 0.1 0.15 0.2 0.25
k k k

Fig. 10. P r o f i l e s o f U, u'v' a n d k in s y m m e t r y p l a n e o f c u b e .

72 W. Rodi/J. Wind Eng. Ind. Aero(tvn. 69 71 (1997) 55 75

separation length fairly well, even though the dynamic model is on the low side. In
the experiments, some shedding from the side walls was observed which enhances the
momentum exchange in the wake and can reduce significantly the length of the
separation region behind obstacles. Even though there was no clear shedding detected
in the LES results, the resolution of large-scale unsteady motions in these calculations
seems to produce the correct effect, while RANS calculations can of course not
account for such effects, explaining possibly the overprediction of the separation
region.
The complex bebaviour of the surface streamlines near the channel floor as
observed in the experimental oil flow pictures is well reproduced by the LES calcu-
lations, including such details as the convergent divergent behaviour of the horseshoe
vortex, the primary and secondary separation in front of the cube, the arch vortices
behind the cube and the reattachment line bordering the reverse flow region. In the
RANS approach only the two-layer model can reproduce these details (but with
a significantly too long reverse-flow region); calculations obtained with wall functions
yield a much simpler picture as the converging diverging behaviour of the horseshoe
vortex is absent and the whole separation region is basically filled by the arch vortices,
which is in contrast to the experimental observation.
Finally, Fig. 10 compares profiles of streamwise velocity U, shear stress u'v'
and turbulent kinetic energy k at various downstream locations in the symmetry
plane. It is evident that LES produces superior results to the RANS calculations,
both on the roof and also in the separation and redevelopment regions. Of course,
in the latter regions the relatively poor RANS predictions are closely linked with
the prediction of late reattachment discussed already. As was to be expected from
the streamlines, the KL version and the TL approach improve the [7-predictions
over the roof, but increase the disagreement in the wake. At the rear face of the
cylinder, LES predicts the peak location ofk somewhat too high above the roof. In the
near wake (x ~ 2), the RANS models severely underpredict the level of k
and also of the shear stress u'v'. The relatively large levels may again be caused largely
by unsteady effects which seem to be responsible also for the fairly short sepa-
ration region and cannot be accounted for in RANS models but apparantly in LES
calculations.

5. Conclusions

Calculations obtained with a variety of LES and RANS methods have been
presented for two basic bluff body flows with relatively simple body geometries albeit
complex flow behaviour. The comparison with detailed measurements has shown that
the main features of these complex flows can be predicted reasonably well, at least
with some of the methods. The square cylinder results are not entirely satisfactory and
do not provide a uniform picture. It is clear, however, that for this flow the standard
k r. model produces rather poor results because the periodic motion is strongly
underpredicted. This is to a large extent due to the excessive turbulence production in
the stagnation flow resulting from the use of this model. The K a t o - L a u n d e r modifica-
 ~K Rodi/~L Wind Eng. Ind. Aerodyn. 69-71 (1997) 55-75 73

tion removes this problem and yields improved results; a further considerable
improvement can be obtained when this model is combined with the two-layer
approach resolving the near-wall region. The excessive turbulence production prob-
lem is also absent when a Reynolds-stress model is used which, however, tends to
overpredict the periodic motion. In all RANS calculations, the turbulence fluctuations
are severely underpredicted; the fairly high value of these fluctuations in the experi-
ment may stem from low frequency variations of the shedding motion due to 3D
effects which cannot be accounted for in 2D RANS calculations. LES seems to pick up
these motions and in general gives a better simulation of the details of the flow. The
price to be paid for this is a large increase in computing time: the UKAHY2 LES
calculations took 73 h on a SNI $600/20 vector computer while the RANS calcu-
lations using wall functions took 2 h and the ones using the two-layer approach
8 h on the same computer. Further, it was found that none of the LES results are
uniformly good and entirely satisfactory and there were large differences between
the individual calculations which are difficult to explain. Reasons for the lack of
agreement with the experiments include insufficient resolution near the side walls of
the cylinder where the separated shear layer undergoes transition and a thin reverse-
flow region is present, neglect of the turbulence in the incoming stream, numerical
diffusion and insufficient domain extent and number of grid points in the spanwise
direction. Hence, this flow was selected once more as a test case for a LES workshop
held in Grenoble in September 1996 (2nd E R C O F T A C Workshop on Direct and
Large-Eddy Simulation).
For the cube flow, the same problem with the excessive k-production in the
stagnation region exists when the standard form of the k e. model is employed, and
this leads to poor predictions of the flow over the roof. These are significantly
improved by introducing the Kato Launder modification and also when the two-
layer approach is used, and only with the latter can the complex structure of the
near-wall streamlines be simulated. However, both modifications increase even fur-
ther the length of the separation region behind the cube which is too large already for
the standard model. It would be interesting to see whether RSM models would
improve the calculations in this respect. Overall significantly better predictions have
been obtained with LES methods which simulate basically all of the complex features
of this 3D flow fairly well, even quantitatively. The difference between various LES
calculations is much smaller than in the square-cylinder case, probably because the
flow is fully turbulent. The better predictions cost, however, a high price: on the SNI
$600/20 vector computer the LES calculations (UKAHY4) took 160 h while the
RANS two-layer model calculations took 6 h and the RANS calculations using wall
functions only 15 min.
RANS methods with statistical turbulence models will be needed and used for
many years to come in engineering calculations of the flow past bluff bodies. However,
inaccuracies must be accepted, and this comparative study has demonstrated that
LES is clearly more suited and has great potential for calculating these complex
flows. Further development and testing is certainly necessary, but with the recent
advances in computing power LES will soon be ready and feasible for practical
applications.
74 W. Rodi/J. Wind Eng. Incl. Aerodyn. 69 71 (1997) 55 75

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