Detached Eddy Simulation - 2

ANRV365-FL41-11 ARI 12 November 2008 14:57

Detached-Eddy SimulationPhilippe R. SpalartBoeing Commercial Airplanes, Seattle, Washington 98124; email: [email protected]

Annu. Rev. Fluid Mech. 2009. 41:181202

First published online as a Review in Advance onAugust 4, 2008

The Annual Review of Fluid Mechanics is online atfluid.annualreviews.org

This articles doi:10.1146/annurev.fluid.010908.165130

Copyright c 2009 by Annual Reviews.All rights reserved

0066-4189/09/0115-0181$20.00

Key Words

turbulence, separation, boundary layer, modeling

AbstractDetached-eddy simulation (DES) was first proposed in 1997 and first used in1999, so its full history can be surveyed. A DES community has formed, withadepts and critics, as well as new branches. The initial motivation of highReynolds number, massively separated flows remains, for which DES is con-vincingly more capable presently than either unsteady Reynolds-averagedNavier-Stokes (RANS) or large-eddy simulation (LES). This review dis-cusses compelling examples, noting the visual and quantitative success ofDES. Its principal weakness is its response to ambiguous grids, in which thewall-parallel grid spacing is of the order of the boundary-layer thickness. Insome situations, DES on a given grid is then less accurate than RANS on thesame grid or DES on a coarser grid. Partial remedies have been found, yetdealing with thickening boundary layers and shallow separation bubbles is acentral challenge. The nonmonotonic response of DES to grid refinementis disturbing to most observers, as is the absence of a theoretical order ofaccuracy. These issues also affect LES in any nontrivial flow. This reviewalso covers the numerical needs of DES, gridding practices, coupling withdifferent RANS models, derivative uses such as wall modeling in LES, andextensions such as zonal DES and delayed DES.

181

Ann

u. R

ev. F

luid

Mec

h. 2

009.

41:1

81-2

02. D

ownl

oade

d fr

om w

ww

.ann

ualr

evie

ws.

org

Acc

ess

prov

ided

by

Uni

vers

ity o

f A

berd

een

on 0

7/25

/15.

For

per

sona

l use

onl

y.


a b

Figure 1(a) Vorticity isosurfaces colored with pressure over an F-15 jet at a 65 angle of attack (Forsythe et al. 2004). Figure courtesy ofJ. Forsythe. (b) Acoustic-source isosurface around a Ford Ka automobile (es turbo 3.1) (Mendonca et al. 2002). Figure courtesy of F.Mendonca and Ford Motor Co.

1. BASICS

Figure 1 illustrates the nature of detached-eddy simulation (DES). The aircraft geometry iscomplete (except for detailed surface and propulsion effects); the simulation is at flight Reynoldsnumber; the large-eddy simulation (LES) content (resolved turbulence) in the separated regionis rich; and the Reynolds-averaged Navier-Stokes (RANS) function plays a role on the aircraftsnose. Furthermore, the forces and moments are accurate to within 6% (Forsythe et al. 2004).This approach must still be considered experimental as a prediction method, and the accuracybenefits from the thin edges on the wing; there is no marginal separation to challenge the model.In addition, grid refinement does not indicate grid independence on the smaller components, suchas the tail surfaces.

The automobile geometry is also complete, a feat of the grid generator and solver ratherthan of DES (Mendonca et al. 2002). The two regions of the DES are especially well visualized:steady attached boundary layers and striking LES content around the wheels and the important Apillar and outside mirror. The drag is dependent on the separation line near the end of the roof,and the accuracy of the RANS model matters. At the same time, the LES function is indispensableto predict the aerodynamic noise and in fact the drag. These two studies reflect the broad diffusionof DES.

1.1. Conceptual History

DES was created to address the challenge of highReynolds number, massively separated flows,which must be addressed in such fields as aerospace and ground transportation, as well as inatmospheric studies. It combined LES and RANS, spurred by the belief that each alone waspowerless to solve the problem at hand (Spalart et al. 1997). This complaint can be revisitedpresently, assuming a working knowledge of LES and RANS (Rogallo & Moin 1984, Wilcox 1998).

The objection to pure LES is simple and centers on computational cost. A pure LES of anairborne or ground vehicle would use well over 1011 grid points and close to 107 time steps, whichis estimated to be possible in approximately 2045 (Spalart 2000). The boundary layer dominatesthis expense, which is necessary even if investigators solve the problem of wall modeling in LES.Regardless, the resolution needs in the outer region of the boundary layer are firm, with at theleast 20 points per thickness in each direction. No unforeseen breakthrough has occurred in

182 Spalart

Ann

u. R

ev. F

luid

Mec

h. 2

009.

41:1

81-2

02. D

ownl

oade

d fr

om w

ww

.ann

ualr

evie

ws.

org

Acc

ess

prov

ided

by

Uni

vers

ity o

f A

berd

een

on 0

7/25

/15.

For

per

sona

l use

onl

y.


LES since 1997, and RANS is simply necessary for the large extent of thin boundary layers (thethicker parts are discussed below).

The objection to pure RANS is not as limpid because it arises from a negative assessment ofmodels and the relentless attempts to build into them first-principle content and rational ideas. Inthis view, RANS models can be adjusted to predict boundary layers and their separation well, butnot large separation regions, whether behind a sphere or past buildings, vehicles, in cavities, andso on. Observers are hopeful for a new perspective that could erase this objection soon. However,since 1997, researchers have tended to shift their effort from RANS to LES and hybrid methods.A second motivation for DES over RANS appears in situations that, even if RANS were accurate,would need unsteady information for engineering purposes (e.g., vibration and noise).

The original reasons to believe in DES can also be revisited. The original version of DES, whichwe refer to as DES97 here, was defined as a three-dimensional unsteady numerical solution usinga single turbulence model, which functions as a subgrid-scale model in regions where the griddensity is fine enough for a large-eddy simulation, and as a Reynolds-averaged model in regionswhere it is not (Travin et al. 2000a). A working definition is that the boundary layer is treatedby RANS, and regions of massive separation are treated with LES; the space between these areas,known as the gray area, may be problematic unless the separation is abrupt, often fixed by thegeometry. A single model, with a RANS origin but sensitized to grid spacing via a DES limiter,provides the desired function in both the RANS and LES limits. The mixing length then can belimited by two constraints: the wall distance and the grid spacing. When neither constraint is felt,the model follows its own natural RANS history; this is the case for free shear flows when theyhave a grid too coarse to use LES for that particular layer.

The capability of LES in free shear flows is not in question, which does not imply that anygeometry has allowed grid convergence. Few groups have conducted grid refinement, with atbest a factor of 2 in each direction, except in homogeneous turbulence. There is only consensusthat finer grids improve the physics and that grid refinement, away from walls, has not createdbad surprises. Refinement reduces the eddy viscosity, and a plausible view of LES is that the eddyviscosity is an error, of order 4/3 in the Kolmogorov situation. Reducing also reduces numericalerrors because the cutoff is further down the spectrum, and velocity scales like 1/3.

RANS development has been static, as almost all the models used in DES date back to 1992.In a natural DES, with RANS function extending to the separation line, perfection cannot bereached, and grid refinement brings no improvement beyond the accuracy barrier of the model.The computing cost of the RANS region is easily manageable, as expected, and the principaldifficulty may be to generate grids that cover all of the boundary layer well in terms of thickness.Initially, the Spalart-Allmaras model was used, but DES now draws on several other models(Strelets 2001) (see Section 4.1).

The gray area drew complaints as soon as 2000 in an application to an overexpanded nozzle,although there were none for DESs first application, which was to a thin airfoil, in 1999 (Shuret al. 1999). Surprisingly, users quickly encountered grid spacings that disturbed the RANS model(see Section 3.2). This motivated a relatively deep change in its formulation with shielded DESand delayed DES (Menter & Kuntz 2002, Spalart et al. 2006) as the DES length-scale limiter nowdepends on the solution, rather than on the grid only. Nonetheless, these methods are aimed atbetter fulfilling the original mission of DES.

1.2. Types of Simulation for Massive Separation

Simulation for massive separation is an important field in which the differences in approachare deep and deserve a detailed discussion. Figure 2 illustrates possible contenders for the

www.annualreviews.org Detached-Eddy Simulation 183

Ann

u. R

ev. F

luid

Mec

h. 2

009.

41:1

81-2

02. D

ownl

oade

d fr

om w

ww

.ann

ualr

evie

ws.

org

Acc

ess

prov

ided

by

Uni

vers

ity o

f A

berd

een

on 0

7/25

/15.

For

per

sona

l use

onl

y.


a

b

c

d

e

f

184 Spalart

Ann

u. R

ev. F

luid

Mec

h. 2

009.

41:1

81-2

02. D

ownl

oade

d fr

om w

ww

.ann

ualr

evie

ws.

org

Acc

ess

prov

ided

by

Uni

vers

ity o

f A

berd

een

on 0

7/25

/15.

For

per

sona

l use

onl

y.


simulation of flow past a circular cylinder and similar cases. The situation is not as simple asit appeared in 1997. It was then considered obvious that unsteady RANS (URANS) solutionssuppressed three-dimensionality over two-dimensional (2D) geometries, and it had been foundthat drag and lift fluctuations were overpredicted by URANS, although the shedding frequencywas accurate. The term URANS here means running an unmodified (grid-insensitive) transport-equation turbulence model, in unsteady mode and with periodic spanwise conditions. Recentfindings have revealed that under fairly general conditions, these simulations in fact sustain three-dimensionality and are more accurate than 2D URANS (Shur et al. 2005a). Figure 2 illustratesthe classic steady RANS (an unstable solution) and 2D URANS and includes the newer 3DURANS. The three-dimensionality is much coarser than in DES and does not become fineron a finer grid, which it does in DES. URANS largely suppresses three-dimensionality, butnot completely. Shur et al. (2005a) also cite and demonstrate a troublesome sensitivity to thespanwise period and to the turbulence model, making 3D URANS with standard models aweak contender for this simulation. There is no evidence that the lateral length scales in the 3DURANS field are physical. Besides the cylinder, these authors treated an airfoil and a roundedsquare.

Nishino et al. (2008) present a thorough URANS and DES study of a cylinder near a wall,which strongly supports the idea that URANS, even if 3D, is less accurate than DES and (whenapplicable) LES. More effective RANS models could be devised. Still, URANS is vulnerable tothe criticism that its partial differential equations are known, but the (Reynolds?) averaging itactually represents is not known, in the absence of a spectral gap. A somewhat similar challengecan be directed at DES, a point to which we return.

In spite of its failings, there are reasons to be familiar with URANS. First, some researchers dobelieve in its capabilities and would dispute our conclusions from Figure 2. Second, in a complexgeometry, sometimes the DES grid and time step only allow, effectively, URANS near the smallercomponents. Examples include the wiper blade on a car and the active-flow-control slot on anaircraft (Spalart et al. 2003). It is desirable for hybrid methods to handle such situations gracefully,even with the knowledge that the geometric detail ideally would be granted LES content on itslength scales and timescales through a finer grid and a shorter time step.

Figure 2 also vividly illustrates the response of DES to grid refinement in its LES region.Finally, it confirms that DES solutions with different base RANS models are not sensitive tomodel choice in the LES region (as opposed to the RANS region, particularly if separation occurs).This has been verified quantitatively in many cases (e.g., a backward-facing step) and is a valuablefeature. The boundary layers being laminar, Figure 2 does not reflect DESs value in treatingturbulent boundary layers in a manner LES cannot, but subsequent figures do.

2. STRENGTHS

This section aims to verify the soundness of DES quantitatively in the important respects ofcomparison with experiment and response to grid refinement.

Figure 2Vorticity isosurfaces by a circular cylinder: ReD = 5 104, laminar separation. Experimental dragcoefficient Cd = 1.151.25. (a) Shear-stress transport (SST) turbulence model steady Reynolds-averagedNavier-Stokes (RANS), Cd = 0.78; (b) SST 2D unsteady RANS, Cd = 1.73; (c) SST 3D unsteady RANS,Cd = 1.24; (d ) Spalart-Allmaras (SA) detached-eddy simulation (DES), coarse grid, Cd = 1.16; (e) SA DES,fine grid, Cd = 1.26; ( f ) SST DES, fine grid, Cd = 1.28. Figure courtesy of A. Travin.


Ann

u. R

ev. F

luid

Mec

h. 2

009.

41:1

81-2

02. D

ownl

oade

d fr

om w

ww

.ann

ualr

evie

ws.

org

Acc

ess

prov

ided

by

Uni

vers

ity o

f A

berd

een

on 0

7/25

/15.

For

per

sona

l use

onl

y.


a b

Reso

lved

TKE

(k/U

2 )

X/c

0.5

0.4

0.3

0.2

0.1

00.250 0.50 0.75 1.00

G1 (1.2 M cells)

G2 (2.7 M cells)

G3 (6.6 M cells)

G4 (10.5 M cells)Experimental peak approximately 0.5

Figure 3(a) Flow visualizations and (b) resolved turbulent kinetic energy (TKE) for a sharp-edged delta wing at a 27 angle of attack, chordReynolds number 1.56 106 (Morton 2003). Figure courtesy of S. Morton.

2.1. Simple Geometries

Above it was mentioned that grid refinement on the jet aircraft had nontrivial effects on the smallercomponents. Grid-refinement effects were more predictable, however, on Mortons (2003) deltawings. The simpler geometry helped, but the phenomenon of vortex breakdown is a subtle one.The results are rewarding, shown visually in Figure 3a and quantitatively in Figure 3b. Finergrids introduce vortex shedding at the trailing edge and much finer structures in the vortex.The front half of the vortex is also quite different: The helical striations switch direction froma coarse to a fine grid. Figure 3b is especially favorable, as it suggests near-grid convergenceof the resolved turbulent kinetic energy to a level that agrees with experiment both for energylevel, approximately 0.5, and location, X/c = 0.65 0.05 (Mitchell et al. 2000). A scale-adaptivesimulation also produced resolved turbulence in this flow (Egorov & Menter 2008).

The study featured in Figure 4a,b also reflects the quantitative success of DES. Constantinescuet al. (2002) simulated the flow past a sphere with approximately 600,000 points in the baselinegrid and controlled the model in the boundary layer so that it produced laminar separation ata diameter of Re = 105 and turbulent separation at Re = 1.1 106. The latter is somewhatsimplistic because in the real flow, transition and separation are not segregated (Travin et al.2000a), but it is far superior to letting an untrained subgrid-scale model handle the boundarylayer, effectively in RANS mode. Quite a few recent cylinder computational fluid dynamics (CFD)studies even failed to select laminar separation at subcritical Reynolds numbers; Travin et al.s(2000a) tripless approach is needed, and Nishino et al. (2008) adopted it successfully. With thisapproach, the prediction of a drag crisis is striking, and the pressure distributions are extremelyfavorable both when compared with experiment and when comparing baseline and fine grids. Atthe lower Reynolds number, DES predicts a drag coefficient of 0.41, compared with 0.400.51in experiments; at the higher Reynolds number, DES gives 0.084 and experiments give 0.12. It istempting to extend this approach to golf balls. The drag crisis caused by dimples can be capturedin a gross sense, simply by imposing turbulent separation with a smooth geometry. However, no

186 Spalart

Ann

u. R

ev. F

luid

Mec

h. 2

009.

41:1

81-2

02. D

ownl

oade

d fr

om w

ww

.ann

ualr

evie

ws.

org

Acc

ess

prov

ided

by

Uni

vers

ity o

f A

berd

een

on 0

7/25

/15.

For

per

sona

l use

onl

y.


C p

0 1 2

0

a

b c1.00

0.50

0.00

0.50

1.00

1.500 30 60 90 120 150 180

0.5

0.5

y/D

x/D

Re = 105 Re = 1.1 106

Re = 1.1 106

Re = 105

Figure 4Simple bluff bodies. (a) Flow visualizations and (b) pressure distributions for a sphere. Re = 105 and 1.1 106. Open circles anddiamonds denote experiments, whereas the dotted and dashed lines denote detached-eddy simulation (DES) on two grids. Panels a andb courtesy of K. Squires. (c) Phase-averaged vorticity contours for a cylinder. Color gradations denote DES conducted by Mockett et al.(2008), and the solid line denotes experiments by the same authors.

RANS model could reproduce the dimple effect accurately, and this will require direct numericalsimulation (DNS), at least of the dimple flow proper.

This is part of a general challenge stemming from the range of scales in fluid mechanics.Compared with DNS, LES addresses the Kolmogorov viscous scale limitation, and wall modelingaddresses the similar viscous-sublayer scale. In its RANS mode, DES in addition addresses theboundary-layer eddies of all sizes. These eddies are numerous and fairly universal. However, ifthey become dependent on geometry, be it on the shape of a wiper blade or that of a dimple, LEStreatment of their scales becomes necessary for high accuracy so that many problems, in particularactive flow control, simply exceed even current grids in excess of 108 points.

Travin et al.s (2000a) circular-cylinder study similarly included laminar- and turbulent-separation cases and a surprise-free grid-refinement study, which added confidence after Shuret al.s (1999) initial thin-airfoil work. Figure 4c compares DES and experiment behind a


Ann

u. R

ev. F

luid

Mec

h. 2

009.

41:1

81-2

02. D

ownl

oade

d fr

om w

ww

.ann

ualr

evie

ws.

org

Acc

ess

prov

ided

by

Uni

vers

ity o

f A

berd

een

on 0

7/25

/15.

For

per

sona

l use

onl

y.


circular cylinder (Mockett & Thiele 2007); the DES visualizations are close to those shown inFigure 2e, f. The agreement on the phase-averaged flow pattern is excellent.

2.2. Applications

DES has been applied often with good results to cavities over a range of Mach numbers (Allen et al.2005, Hamed et al. 2003, Langtry & Spalart 2007, Mendonca et al. 2003, Shieh & Morris 2001),ground vehicles (Kapadia et al. 2003, Maddox et al. 2004, Roy et al. 2004, Spalart & Squires2004, Sreenivas et al. 2006), a simplified landing-gear truck (Hedges et al. 2002), active flowcontrol by suction/blowing (Krishnan et al. 2004, Spalart et al. 2003), space launchers (Deck &Thorigny 2007, Forsythe et al. 2002), vibrating cylinders with strakes (Constantinides & Oakley2006), cavitation in jets (Edge et al. 2006), buildings (Wilson et al. 2006), air inlets (Trapieret al. 2008), aircraft in a spin (Forsythe et al. 2006), high-lift devices (Cummings et al. 2004),jet-fighter tail buffet (Morton et al. 2004), and wing-wall junctions (Fu et al. 2007). Peng &Haase (2008) report on many promising applications at various stages of maturity: wing high-liftsystems, helicopters, combustors, and afterbodies. Chalot et al. (2007) reveal a vigorous line ofwork in another aircraft company, Dassault. Slimon (2003) obtained positive results with (zonal)DES in a turn-around duct; DES did much better than RANS with simple models, however, whichmay not be expected to capture curvature effects. Publications aimed at educating users and codewriters have, appropriately, focused on grid generation (Spalart 2001) and on thorough testing ofthe codes (Bunge et al. 2007, Squires 2004). The terminology Euler region, RANS region, focusregion, and departure region, introduced by Spalart, may be of help. Grid adaptation in DES andLES is a future challenge.

Another promising direction is taken by Mockett et al. (2008) and Greschner et al. (2008):aerodynamic noise. Such studies will contribute both to interior noise in vehicles and aircraftand to community noise (airframe noise to the airline industry). We note above the industrialimportance of the turbulence adjacent to the drivers window (Figure 1b). Mockett et al. (2008)studied the flow in the slat cove of an airfoil in landing configuration; the visualization withdensity gradient in Figure 5a vividly reveals much fine-scale turbulence and sound. Actual soundpredictions are not included.

Greschner et al. (2008) provide sound predictions for the flow past a cylinder, placed aheadof an airfoil so that its turbulent wake impinges on it (see Figure 5b). At low Mach numbers,this impingement, which causes wall-pressure fluctuations, is the dominant noise mechanism.Various Ffowcs-Williams-Hawkings surfaces are used to extract far-field noise. Flow visualizationsresemble those in Figure 2, without as fine a level of resolution. This case is more onerousbecause the turbulence needs to be carried all the way to the airfoil, 10 diameters downstream;the focus region is much larger. Figure 5c compares the sound spectrum with experiment. Anadjustment was made in the vertical direction: In 2D geometries, there is an unsolved problemwhen comparing an experiment of finite length (with some end conditions) to a simulation withperiodic boundary conditions, invariably quite narrow (in contrast, no adjustment was needed forthe spectra inside the turbulence region). Once this correction is accepted, the agreement on theshape of the spectrum, over five octaves, is quite amazing.

Figure 6 (Chauvet et al. 2007) is of interest for two reasons. First, the LES-content developmentin the mixing layer is nearly immediate, which is positive, although it may be excessively 2D (seeSection 3.4). Second, the simulation is simultaneously free enough of numerical dissipation towelcome LES content and robust enough to capture shocks. This result has also been achieved byShur et al. (2006) in jets and by Ziefle & Kleiser (2008) in a supersonic channel with hills. These

188 Spalart

Ann

u. R

ev. F

luid

Mec

h. 2

009.

41:1

81-2

02. D

ownl

oade

d fr

om w

ww

.ann

ualr

evie

ws.

org

Acc

ess

prov

ided

by

Uni

vers

ity o

f A

berd

een

on 0

7/25

/15.

For

per

sona

l use

onl

y.


0

20

40

60

80

Experiment

DES + FWH

= 90

100

PSD

(dB)

St = f D/u

101 100

Y

XZ

|

p'|0.001 0.01 0.1 1 10

a

b

c

Figure 5Complex bluff bodies. (a) Schlieren picture near a slat. Panel a courtesy of C. Mockett. (b) Vorticityisosurfaces for a rod-cylinder case. (c) Far-field spectrum. PSD, power spectral density. Panels b and ccourtesy of B. Greschner.


Ann

u. R

ev. F

luid

Mec

h. 2

009.

41:1

81-2

02. D

ownl

oade

d fr

om w

ww

.ann

ualr

evie

ws.

org

Acc

ess

prov

ided

by

Uni

vers

ity o

f A

berd

een

on 0

7/25

/15.

For

per

sona

l use

onl

y.


X/D X/D

y/D

1

0

1

1

0

11 2 3 1 2 30

a b

Figure 6(a) Experimental schlieren (view through flow) and (b) numerical schlieren (contours in center plane) for asupersonic jet. Figure taken from Chauvet et al. 2007.

studies remove the concern that LES might be barred from supersonic flows, therefore wideningthe range expected for DES, given a powerful numerical method.

3. WEAKNESSES

3.1. Conceptual Issues

The need to predict turbulence numerically is far-reaching. Yet continuing concerns of a con-ceptual nature could categorize DES as a method that is intuitively correct and often successfulbut dissatisfying to the purist. Below we first address these concerns and then delve into practicalissues in the remaining subsections.

The criticism of URANS mentioned above (namely that the approximate PDE that is solvedis known, but the exact PDE it is meant to approximate is not) does not truly apply to DES. Afilter can be linked to the grid cell and to the integration implied by the CFD solver. In LES,systematic studies use filtered versions of DNS fields to steer subgrid-scale model development.This is known as the Clark test or a priori study and could be performed with DES but has not;in LES and DES practice, models are adjusted based on results rather than explicit tests. Thenew difficulty beyond those in LES is that, in the gray area, the model has a strong impact, but aconvincing calibration is simply out of reach: There are far too few degrees of freedom (in DES97,only CDES). A similar problem is present even in simple LES; simply put, one would adjust thesingle Smagorinsky constant to ensure that all six subgrid stresses are correct. The problem ismore severe in wall-modeled LES (WMLES) and more severe again in DES. Clear statementsare much more difficult to make, especially in view of the wide variety of anisotropies possible forthe grid cell and time step, and also because of history effects, which are strong especially in theall-important situation of a separating boundary layer (see Section 3.4). The essential difficulty isthat the model has much more impact on WMLES and DES than it does on the notional LESsituation, namely away from walls and with a grid spacing in the inertial range. In that situation,one can arbitrarily lessen the influence of the Smagorinsky constant and similar constants with gridrefinement. WMLES has been exposed to this issue less than DES, possibly because it sometimesseems unable to escape channel flow.

The literature reflects a desire for an approach that is somehow more justified and mathemati-cally defined than DES. Several hybrid proposals rest on the idea of splitting the turbulent energy ina specified ratio (e.g., 70% resolved and 30% modeled). This is fine in simple flows, but the strengthof DES (and WMLES) is precisely that the split is different in different parts of the same solution.The energy split can be adjusted in different regions, but this increases the decision load for the user.

190 Spalart

Ann

u. R

ev. F

luid

Mec

h. 2

009.

41:1

81-2

02. D

ownl

oade

d fr

om w

ww

.ann

ualr

evie

ws.

org

Acc

ess

prov

ided

by

Uni

vers

ity o

f A

berd

een

on 0

7/25

/15.

For

per

sona

l use

onl

y.


A separate line of critical thought regards the use of the grid spacing in the model. In LES, of course has been standard, although it has been proposed to dissociate the filter size and gridspacing. With RANS-LES hybrids, it has even been proposed to dispose with any length scaleof the nature of a filter width or grid scale. This led to scale-adaptive simulation (SAS). Menteret al. (2003) use an SAS model that appears to have a pure RANS nature but achieves LESbehavior unlike any traditional RANS model. For instance, visualizations over a cylinder look justlike those in Figure 2e, f. Menter et al.s (2003) model differs from traditional ones in its use of ahigher derivative of the velocity field, which is highly active on short scales. Travin et al.s (2004)turbulence-resolving RANS approach has similar features but uses the ratio of strain to vorticityrather than a high derivative.

Besides a philosophical interest in the true nature of turbulence models, the SAS andturbulence-resolving RANS work is motivated by the disruptive effects of in DES with ambigu-ous grids (see Section 3.2). This stimulating controversy is not over. It echoes the one in RANSmodeling over the use of the wall distance [as in the Spalart-Allmaras and shear-stress transport(SST) models]. Wall distance can be expensive to calculate and has unphysical effects (e.g., witha thin wire); however, the sustained wide use of these two models suggests that it is manageableand has a substantial accuracy payoff. Equally active are controversies over the definition of innoncubic grid cells (see Section 4.4). Nonuniqueness issues are most intense with delayed DES(DDES), as discussed in Section 3.2 and Section 4.3, because even the RANS or LES nature ofthe solution is in some cases dependent on initial or inflow conditions.

Finally, the issue of an order of accuracy is clear; careful users are justified in asking for onebecause it is, in principle, a key step in CFD quality control; this is related to the desire formonotonic grid convergence. A typical observation after analyzing a grid-refinement study evenin a simple geometry is the honest but vague statement that the findings are suggesting a certaindegree of grid convergence (Nishino et al. 2008).

An order of accuracy has not even been proposed for a simulation using both modes withinDES. In a pure LES, this order exists but depends on the quantity in question, for instance, theresolved or total turbulent kinetic energy or the dissipation. WMLES does not deal with thisproblem much better than DES does. Recent efforts at organizing the quality control of CFD inthe RANS field, in which the differential equation does not depend on the grid, would be defeatedby precisely this dependence in LES and DES.

Whether in DNS, LES, or DES, the difficulty in demonstrating grid convergence is com-pounded by the residual variations owing to finite time samples; some flows have severe modu-lations and drift. Figure 7 uses Travin et al.s (2000a) LS1 cylinder case; the simulation covereda generous 40 cycles of shedding, after an initial transient. The time-averaged drag coefficientis 1.083 over the first half of the sample, but 1.033 over the second half; the lift excursions arealso noticeably less intense over the second half. Although the sample is sufficient to capture themodulations of the lift signal, the drags drift is not mastered to better than several percent andwent unnoticed at the time. There is no theory that would extrapolate to infinite sample length.As a result, searching for grid convergence to 1%, for example, is not possible.

3.2. Modeled-Stress Depletion and Grid-Induced Separation

Modeled-stress depletion (MSD) and grid-induced separation have been the most significantpractical issues and have been worse to deal with than initially anticipated (Spalart et al. 1997).Figure 8a shows the roots of these problems, with three levels of grid density in a boundary layer.The first level matches the initial vision of DES; it is a boundary-layer grid, with the wall-parallelspacing in excess of the boundary-layer thickness , which allows full RANS function. The


Ann

u. R

ev. F

luid

Mec

h. 2

009.

41:1

81-2

02. D

ownl

oade

d fr

om w

ww

.ann

ualr

evie

ws.

org

Acc

ess

prov

ided

by

Uni

vers

ity o

f A

berd

een

on 0

7/25

/15.

For

per

sona

l use

onl

y.


a b0.6

0.4

0.2

0

0.2

0.4

0.6

0 40 80 120 160 200 0 40 80 120 160 200

1.30

1.25

1.20

1.15

1.10

1.05

1.00

0.95

C , C

C d, C

d

tU/D tU/D

Instantaneous

Time-averaged

Instantaneous

Time-averaged

Figure 7Instantaneous (solid line) and time-averaged (dashed line) values of force coefficients on a cylinder: (a) lift and(b) drag. Re = 5 104. Figure courtesy of A. Travin.

third level matches the needs of LES in the outer layer and thus of the extended use of DES asa wall model (see Section 3.3): The grid spacing in all directions is much smaller than . Thesecond level is the troublesome one: small enough for the eddy viscosity to be affected by the DESlimiter but not small enough to support accurate LES content (slow LES development adds tothis difficulty; see Section 3.4). Spalart et al. (2006) coined the term MSD, well after the issue wasdetected by S. Deck (personal communication) and by Menter & Kuntz (2002), who pointed outa consequence of MSD called grid-induced separation (GIS).

Created only one year after Shur et al. (1999) fully defined DES, Figure 8b is an early exampleof gradual grid refinement degrading a solution that was rather good when the RANS model wasfully active (S. Deck, personal communication; see also Caruelle & Ducros 2003). Separation ina nozzle is premature and induces unsteadiness. DES users promptly explored the effects of gridspacing and sought high accuracy, with disturbing outcomes.

Figure 9 is a visualization of GIS, this time on an airfoil (Menter & Kuntz 2002). Whereasthe RANS solution is steady and quite accurate, even in this case of incipient separation, the DESsolution suffers from early separation. It also is unsteady, but in a shedding mode rather than ina sound turbulence-resolving mode. The flow field then obeys the URANS equations, but with amodel that has become grid dependent in an obscure and unintended manner.

Menter & Kuntz (2002) proposed a solution applicable to the SST model called shielding, inwhich the DES limiter is disabled as long as the flow is recognized as a boundary layer, usingthe SST F2 function. Spalart et al. (2006) introduced DDES, which is applicable to most models.Either modification successfully prevents GIS by extending the RANS region, exploiting a historyeffect. Secondary effects are covered in Section 4.3.

3.3. Logarithmic-Layer Mismatch

Simulations with an LES nature in one region and a RANS nature in another were conductedlong before DES; wall modeling near the walls of an LES draws on RANS technology, and earlychannel LES studies even used wall functions. A new feature of DES is that the entire boundarylayer can be handled by RANS. However, DES also naturally provides a simple wall model, which

192 Spalart

Ann

u. R

ev. F

luid

Mec

h. 2

009.

41:1

81-2

02. D

ownl

oade

d fr

om w

ww

.ann

ualr

evie

ws.

org

Acc

ess

prov

ided

by

Uni

vers

ity o

f A

berd

een

on 0

7/25

/15.

For

per

sona

l use

onl

y.


0 10 200

Nor

mal

ized

wal

l pre

ssur

e (P

W/P

C)

0.05

0.04

0.03

0.02

0.01

X/rt

DES computation PR40

SA-URANScomputation PR40

LEA steady experimentaldata PR41.3

1.0

0.5

00 0.5 1.0 1.5 2.0

0 0.5 1.0 1.5 2.0 0 0.5 1.0 1.5 2.0

2.5 3.0 3.5 4.0y/

1.0

0.5

0

1.0

0.5

0

y/

x/

aaa

b

x/ x/

Figure 8(a) Types of grids in boundary layers. The dashed line represents the velocity profile. (b) Pressuredistribution in a supersonic nozzle. Figure courtesy of S. Deck. DES, detached-eddy simulation; LEA,Laboratoire dEtudes Aerodynamiques; SA-URANS, Spalart-Allmaras unsteady RANS.

Nikitin et al. (2000) attempted. The results were not perfect, but the study was successful in keyrespects. The model was robust, with no need for averaging or danger of negative values. LEScontent was sustained even with coarse grids, because = h/10 in most runs, where h is thehalf-width of the channel. Very high Reynolds numbers were reached at little additional cost.

Figure 10a illustrates the response of Nikitin et al.s method to Reynolds number and gridspacing. An increase in Reynolds number on a fixed grid (same but refinement in y to retain afirst y+ near 1) lengthens the modeled part of the profile, which blends into the modeled log layer( y+ roughly from 70 to 700). Grid refinement, conversely, lengthens the resolved-turbulence partof the profile, which blends into the resolved log layer ( y+ roughly from 3000 to 15,000). TheReynolds shear stress comprises modeled stress and resolved stress, which trade places as the gridis varied (Figure 10b).


Ann

u. R

ev. F

luid

Mec

h. 2

009.

41:1

81-2

02. D

ownl

oade

d fr

om w

ww

.ann

ualr

evie

ws.

org

Acc

ess

prov

ided

by

Uni

vers

ity o

f A

berd

een

on 0

7/25

/15.

For

per

sona

l use

onl

y.


Velo

city

0

5.00

10.00

a b

Figure 9Vorticity contours over an airfoil: (a) Reynolds-averaged Navier-Stokes and (b) detached-eddy simulation.Arrows indicate separation. Figure taken from Menter & Kuntz 2002.

The imperfection is that the two log layers are misaligned, by almost three wall units of velocityU+. The probability that this log-layer mismatch would be zero was nil because this study usedthe pure DES97 model, adjusted for other purposes. (The study was also marked by deliberateconstraints, such as equal grid spacing in the wall-parallel directions, to ensure the findings wouldtranslate into practice.) All other wall-modeling approaches have required adjustments to aligntheir log layers. Nikitin et al. (2000) mentioned the ensuing error of the order of 15% for theskin-friction coefficient but did not mention that the slope dU/d y is too high by 65% at y = .Locally, this is highly inaccurate. In addition, grid refinement merely moves the same amount ofmismatch closer to the wall. This is different from MSD in a near-RANS boundary layer, which

40

35

30

25

20

15

10

5101 102 103 104 105

y+

U+

1.0

0.8

0.6

0.4

0.2

00 0.2 0.4 0.6 0.8 1.0

y/h

+

a b

Figure 10Channel-flow, wall-modeled large-eddy simulation. (a) Velocity: Re = 2000 and 20,000. Each profile isshifted by five U+ units. The lower two curves use approximately 140,000 grid points, and the upper curveuses approximately 1,000,000 points. The dashed line represents the log law. (b) Modeled and resolved shearstress: coarser grid (dashed line) and finer grid (solid line). Re = 20,000. Figure adapted from Nikitin et al.2000.

194 Spalart

Ann

u. R

ev. F

luid

Mec

h. 2

009.

41:1

81-2

02. D

ownl

oade

d fr

om w

ww

.ann

ualr

evie

ws.

org

Acc

ess

prov

ided

by

Uni

vers

ity o

f A

berd

een

on 0

7/25

/15.

For

per

sona

l use

onl

y.


0 2 4 6 8

1

0

1

x

y

0 2 4 6 8

1

0

1

x

y

a b

Figure 11Vorticity in a jet: (a) standard detached-eddy simulation and (b) implicit large-eddy simulation, eddy viscosity disabled. Figure courtesyof M. Shur.

becomes more severe as the grid is refined. Follow-on work by Piomelli and his group also showedthat the near-wall solution has poor LES content. The practical advantages of wall modeling byDES, and the understanding that in practice thick wall-bounded layers lead to LES grids in thesense of Figure 8a, motivate efforts to resolve log-layer mismatch (Piomelli & Balaras 2002,Travin et al. 2006).

3.4. Slow Large-Eddy Simulation Development in Mixing Layers

Separation is the essential flow feature motivating DES, with the expectation that the boundarylayer is treated with RANS and is quasi-steady, but the free shear layer it feeds develops LEScontent. By consensus, the sooner this takes place, the better. Unfortunately, standard DES ontypical grids does not achieve this switch very fast at all (Figure 11); a zonal approach that disablesthe model in the mixing layer and activates implicit LES is visually far more successful (Shuret al. 2005b,c). This is the case with the book-shaped grid cells typical of such regions, with onedimension much smaller than the other two, and may be a perverse effect of the careful adaptationof the grid to the shear layer. The DES model fails to sense the opportunity because the lateralgrid spacing is loose (here, 10% of the diameter D, with 64 points around) and the standarddefinition of is used (see Section 4.4). The model defaults to RANS until the layer thicknessreaches approximately 40% of D because the mixing length in a RANS-treated mixing layer isapproximately one-tenth the vorticity thickness, much smaller than the lateral grid spacing, mak-ing the DES limiter inoperative. Other definitions are then more successful (see Section 4.4),but in a manner dependent on the alignment and shape (book or pencil) of the grid cells. Thisproblem has received and deserved attention, but unlike the two problems discussed in the pre-ceding subsections, it is remediable with grid refinement.

4. RECENT PROPOSALS

4.1. Alternate Reynolds-Averaged Navier-Stokes Models

The original formulation of DES rested on the simple Spalart-Allmaras model, and no CFDsystem should ever be confined to one model. Travin et al. (2000b) pioneered the adaptationto two-equation models, in particular the SST model, which has been smooth. Recent work in-cludes, for instance, Greschner et al.s (2008) cubic explicit algebraic stress models. The motivationfor complex models is debated because the RANS region normally comprises thin shear layers;relatively thick and curved boundary layers could make using complex models worthwhile.


Ann

u. R

ev. F

luid

Mec

h. 2

009.

41:1

81-2

02. D

ownl

oade

d fr

om w

ww

.ann

ualr

evie

ws.

org

Acc

ess

prov

ided

by

Uni

vers

ity o

f A

berd

een

on 0

7/25

/15.

For

per

sona

l use

onl

y.


4.2. Zonal Detached-Eddy Simulation

In zonal DES, the user explicitly marks different regions as RANS or as DES (Deck 2005). Ineffect, in RANS regions, is made infinite (as opposed to zero in implicit LES). This is probablythe strongest departure from the original concept of DES, in which the use of a single but versatileequation set is central, and creates most of the conceptual and practical challenges. The motivationis to be fully safe from MSD and GIS (see Section 3.2) and to clarify the role of each region. ZonalDES worked well for Brunet & Deck (2008) in the important problem of wing buffet, Chauvetet al. (2007) in jets, Simon et al. (2007) for a base flow, and Slimon (2003) in a duct.

The geometries in these studies were simple, such as the jet featured in Figure 11. A fairquestion to propose to zonal DES proponents concerns complex flows, in which decisions areneeded for numerous regions (including the thickness of regions meant to contain RANS boundarylayers). This is similar to issues with zonal control of laminar-turbulent transition. Which modewill be the default, and which will be the exception? S. Deck (personal communication) is in favorof RANS as the default mode; the author may disagree, and, more importantly, there is the concernthat smooth-wall separation is normally not known at the time the zones are set. Compared withDES, ZDES appears simultaneously more powerful and less self-sufficient.

4.3. Delayed Detached-Eddy Simulation and Improved DelayedDetached-Eddy Simulation

A key motivation here is precisely to avoid zonal measures, thus leaving it to the solution processto determine separation, while addressing the MSD issue that affects DES97 (see Section 3.2).Following Menter & Kuntz (2002), DDES detects boundary layers and prolongs the full RANSmode, even if the wall-parallel grid spacing would normally activate the DES limiter. This detectiondevice depends on the eddy viscosity, so that the limiter now depends on the solution (Spalartet al. 2006). This is a formal deviation from DES97 but not a different mission. DDES wasshown to resolve GIS, without impeding LES function after separation. For instance, it handleda backward-facing-step flow well, even with grids that would cause severe MSD both upstreamof the step and all along the opposite wall. DDES is likely to be the new standard version ofDES.

Improved delayed DES (IDDES) is more ambitious yet (Shur et al. 2008). The approach isalso nonzonal and aims at resolving log-layer mismatch in addition to MSD. One basis is a newdefinition of , which includes the wall distance and not only the local characteristics of the grid.The modification tends to depress near the wall and give it a steep variation, which stimulatesinstabilities, boosting the resolved Reynolds stress. Other components of IDDES include newempirical functions, some involving the cell Reynolds number, which address log-layer mismatchand the bridge between wall-resolved and wall-modeled DES (grids with moderate values of thespacing in wall units, + ). These functions make the formulation less readable than that of DES97.Yet many groups have had success with IDDES in practice (Mockett & Thiele 2007).

The history effect introduced by shielding or by DDES has consequences in terms of theuniqueness of solutions. For instance, in a channel flow with periodicity and a grid and timestep capable of LES (as in Nikitin et al. 2000 and Figure 10), the solution has two branches,depending on the initial condition. If the flow is in a RANS state, with high eddy viscosity andweak perturbations, it remains in that mode and finds a steady state. If the flow starts in anLES state with low eddy viscosity and sufficient LES content, it settles into a statistically steadyLES. Both solutions are valid, but this situation perplexes some observers (Frolich & von Terzi2008).

196 Spalart

Ann

u. R

ev. F

luid

Mec

h. 2

009.

41:1

81-2

02. D

ownl

oade

d fr

om w

ww

.ann

ualr

evie

ws.

org

Acc

ess

prov

ided

by

Uni

vers

ity o

f A

berd

een

on 0

7/25

/15.

For

per

sona

l use

onl

y.


Nonuniqueness, however, is not unknown in RANS practice. Some flows, such as airfoilsnear maximum lift, have hysteresis both in real-world situations and in CFD. More striking isthe behavior of models in the tripless mode (Travin et al. 2000a), which is an essential tool forcapturing the drag crisis of smooth bluff bodies. The mature solution depends on the level of theturbulence variables in the initial field.

4.4. Modified Length Scales

The IDDES length scales principal motivation is in a fully turbulent wall layer in the LES mode.Other proposals relate instead to transition, more precisely the growth of LES content. Severalgroups (Breuer et al. 2003, Chauvet et al. 2007, Yan et al. 2007) have tested with some successdefinitions radically different from the standard one in DES, namely the maximum dimension ofthe grid cell; if it is aligned with the axes, then = max(x, y, z). In contrast with the DDESmodification (which raises eddy viscosity in specific situations), all these definitions tend to reduceit, therefore worsening the MSD tendencies. They all appear to be responses to the problem ofLES development in mixing layers (see Section 3.4) with the purpose of allowing the Kelvin-Helmholtz instability to grow. Some use the time-honored definition in LES = (xyz)1/3,which of course reduces , but its physical justification is thin. Chauvet et al.s (2007) length scale

N 2x yz + N 2y xz + N 2z xy , where N is the unit vector aligned with vorticity, is

aimed at the situation in which the vorticity is closely aligned with one of the grid lines.The debate is whether promoting the 2D Kelvin-Helmholtz instability, knowing that the true

switch to 3D turbulence occurs only once the mixing-layer thickness has caught up with the lateralgrid spacing, is far superior to letting the mixing layer thicken in the RANS mode. For instance, theRANS mode creates no sound, but the near-2D LES mode could create too much. The reducedlength scales have an advantage over the implicit LES approach shown in Figure 11 as they arenot zonal and can reverse to the normal scale when the grid is not strongly anisotropic.

5. NUMERICAL REQUIREMENTS

DES codes need qualities that are absent in many RANS codes and others that are absent in manyLES codes. Considering the filiation of the model, it is more common to start from a RANS code.These codes often have placed a high priority on convergence to a steady state, complex-geometrycompatibility, and shock capturing. The unsteady capability, with resolution of high frequenciesand short waves, has been neglected, and the other demands all benefit from numerical dissipation.As a result, an extensive testing campaign and modifications to reduce dispersion, dissipation, andtime-integration errors are key (Caruelle & Ducros 2003, Mockett & Thiele 2007, Strelets 2001,Temmerman & Hirsch 2008). The most effective schemes are structured and hybrid, not onlyin their treatment of turbulence, but also in their numerics. The differencing scheme is centered(nondissipative) or nearly so in the LES region and is more strongly upwind in the Euler and RANSregions. This hybridization was introduced by Travin et al. (2000b) and is now widely used (e.g.,Mockett & Thiele 2007). Conversely, the code used in Figure 1a is unstructured and uniformlybased on second-order upwind differencing, but it displays generous LES content. Therefore, itis best to avoid blanket statements.

If the starting code is an LES code, common obstacles include the limitation to simple geome-tries, without implicit time integration or multiblock capabilities, let alone unstructured grids.The addition of a transport-equation turbulence model is not trivial, and few codes have shock-capturing capability (Hou & Mahesh 2004). The priority was given to high orders of accuracy.


Ann

u. R

ev. F

luid

Mec

h. 2

009.

41:1

81-2

02. D

ownl

oade

d fr

om w

ww

.ann

ualr

evie

ws.

org

Acc

ess

prov

ided

by

Uni

vers

ity o

f A

berd

een

on 0

7/25

/15.

For

per

sona

l use

onl

y.


An advantage of DES is the ease of programming and application. Potentially, it is activateddirectly from the menu of turbulence models in many of the vendor CFD codes. This is a double-edged advantage, as users not invested in turbulence and/or too trusting of the experts could acceptresults without verifying LES content, grid resolution, time step, time sample, and so on. An earlyexample of this was an entry in the LESfoil workshop (Mellen et al. 2003). The simulation wasformally a DES, and the results were fine. However, there is every indication from the grid thatthe simulation was actually in RANS mode, even in the key region. In contrast, the genuine LESstudies struggled with all the issues of lateral domain size, resolution, and initiation of LES contentin attached flows.

6. OUTLOOK

It is certain that DES has a future and therefore deserves a critique. Greschner et al. (2008)deem that DES is still in its infancy and undergoes continuing improvements. Under one nameor another, a form of a RANS-LES hybrid that is capable of full RANS function in boundarylayers will be in use for the foreseeable future in many industries. It will also remain conceptuallydifficult, and efforts toward more predictable behavior under grid variations and better wall-modeling performance will continue. LES-content creation in attached flows will flourish, andthe numerical quality of the codes will receive sustained attention. A clear need in practice is toorganize and facilitate grid generation and to set guidelines for systematic refinement. Programssuch as DESider and focused workshops will be most beneficial to the progress of DES and otherhybrids (Peng & Haase 2008).

An unfortunate trend is that models have moved away from the simplicity of DES97 in termsof the equations and nonuniqueness of solutions (in DDES and IDDES) and in terms of the userdecision load and need to mark regions (in ZDES). Users by now have identified situations inwhich DES gives too little eddy viscosity and others in which it gives too much. Even in DES97,large steps in the grid spacing can be used to steer the solution toward one mode or the other,so that grid design can become involved, especially now that the dangers of ambiguous grids areknown. What may be an ideal of CFD, namely that grid refinement will do no harm (in otherwords, be monotonic) and follow a known power of the grid size, will remain elusive in DES andLES (without explicit filtering), except in the simplest of flows.

There are signs that a productive DES user community has formed. We must recognize,however, a school of thought that considers DES to be a somewhat unsafe activity.

Owing to space limitations, this review does not discuss hybrid RANS-LES methods besidesDES and SAS (e.g., limited numerical scales, very large eddy simulation, flow simulation method-ology, nonlinear disturbance equations, extra-large eddy simulation, lattice Boltzmann method,transient RANS, partially averaged Navier-Stokes, semideterministic method, organized eddysimulation, partially integrated transport model, and the self-adapting model) (some are found inSagaut et al. 2006; Frolich & von Terzi 2008). I do not believe that any of these methods providesa clear remedy to the difficulties discussed here, but this could change in the future. The principalconcerns are GIS and in general the potentially poor knowledge of the nature of the simulation ineach region of a complex flow: driven URANS, spontaneous URANS, or LES. This nature canchange under grid refinement and become ambiguous, and therefore it is not the case that anygrid refinement improves the solution. The nominally universal character of DES makes theseobservers justifiably dubious that a sufficiently error-proof approach results, or that the user com-munity is being properly informed. Such comments are encountered more often in conversationsand anonymous reviews than in publications. It does not detract from their value, and the taskof resolving them is an inspiring one. Locally ambiguous grids may be a permanent feature of

198 Spalart

Ann

u. R

ev. F

luid

Mec

h. 2

009.

41:1

81-2

02. D

ownl

oade

d fr

om w

ww

.ann

ualr

evie

ws.

org

Acc

ess

prov

ided

by

Uni

vers

ity o

f A

berd

een

on 0

7/25

/15.

For

per

sona

l use

onl

y.


practical DES. One might ask, is it justified to simulate the flow past a car, when the wiper anddoor handle are not well resolved? The answer depends on the purpose of the simulation.

FUTURE ISSUES

1. The numerical resolution over relevant geometries needs improvement, ultimately withgrid adaptation.

2. The link between the DES flow field and the exact or DNS flow field should be estab-lished.

3. The choice between zonal and nonzonal treatments of the turbulence needs to be ad-dressed.

4. The generation of resolved turbulence in attached boundary layers needs to becomeroutine and efficient.

DISCLOSURE STATEMENT

The author is not aware of any biases that might be perceived as affecting the objectivity of thisreview.

ACKNOWLEDGMENTS

I am grateful to Drs. Allmaras, Deck, Mockett, Strelets, Shur, and Travin for their comments onthis manuscript and their partnership over the years.

LITERATURE CITED

Allen R, Mendonca F, Kirkham D. 2005. RANS and DES turbulence model predictions of noise on the M219cavity at M = 0.85. Int. J. Aeroacoust. 4:13551

Breuer M, Jovicic N, Mazaev K. 2003. Comparison of DES, RANS and LES for the separated flow around aflat plate at high incidence. Int. J. Numer. Methods Fluids 41:35788

Brunet V, Deck SF. 2008. Zonal-detached eddy simulation of transonic buffet on a civil aircraft type config-uration. See Peng & Haase 2008, pp. 18291

Bunge U, Mockett C, Thiele F. 2007. Guidelines for implementing detached-eddy simulation using differentmodels. Aerosp. Sci. Technol. 11:37685

Caruelle B, Ducros F. 2003. Detached-eddy simulations of attached and detached boundary layers. Int. J. CFD17:43351

Chalot F, Levasseur V, Mallet M, Petit G, Reau N. 2007. LES and DES simulations for aircraft design. Presentedat AIAA Aerosp. Sci. Meet. Exhib., 45th, Reno, Pap. No. AIAA-2007-0723

Chauvet N, Deck S, Jacquin L. 2007. Zonal detached eddy simulation of a controlled propulsive jet. AIAA J.45:245873

Constantinescu GS, Pacheco R, Squires KD. 2002. Detached-eddy simulation of flow over a sphere. Presented atAIAA Aerosp. Sci. Meet. Exhib., 40th, Reno, Pap. No. AIAA-2002-0425

Constantinides Y, Oakley OH. 2006. Numerical prediction of bare and straked cylinder VIV. Proc. 25th Int.Conf. Offshore Mech. Artic Eng., Pap. No. OMAE2006-92334. New York: ASME Int.

Cummings RM, Morton SA, Forsythe JR. 2004. Detached-eddy simulation of slat and flap aerodynamics for ahigh-lift wing. Presented at AIAA Aerosp. Sci. Meet. Exhib., 42nd, Reno, Pap. No. AIAA-2004-1233

Deck S. 2005. Zonal detached-eddy simulation of the flow around a high-lift configuration with deployed slatand flap. AIAA J. 43:237284


Ann

u. R

ev. F

luid

Mec

h. 2

009.

41:1

81-2

02. D

ownl

oade

d fr

om w

ww

.ann

ualr

evie

ws.

org

Acc

ess

prov

ided

by

Uni

vers

ity o

f A

berd

een

on 0

7/25

/15.

For

per

sona

l use

onl

y.


Deck S, Thorigny P. 2007. Unsteadiness of an axisymmetric separating-reattaching flow. Phys. Fluids 19:065103Edge BA, Trujillo MF, Paterson EG. 2006. Modeling of cavitation inception in high-Reynolds number circular

jets using detached-eddy simulation. Proc. 26th Symp. Naval Hydrodyn., RomeEgorov Y, Menter F. 2008. Development and application of SST-SAS turbulence model in the DESider

project. See Peng & Haase 2008, pp. 26170Forsythe JR, Hoffmann KA, Squires KD. 2002. Detached-eddy simulation with compressibility corrections applied

to a supersonic axisymmetric base flow. Presented at AIAA Aerosp. Sci. Meet. Exhib., 40th, Reno, Pap. No.AIAA-2002-0586

Forsythe JR, Strang WZ, Squires KD. 2006. Six degree of freedom computation of the F-15E entering a spin.Presented at AIAA Aerosp. Sci. Meet. Exhib., 44th, Reno, Pap. No. AIAA-2006-0858

First application to a fullaircraft in a stall, withgood agreement.

Forsythe JR, Squires KD, Wurtzler E, Spalart PR. 2004. Detached-eddy simulation of the F-15E athigh alpha. J. Aircraft 41:193200

Frolich J, von Terzi D. 2008. Hybrid LES/RANS methods for the simulation of turbulent flows. Prog. Aerosp.Sci. 44:34977

Fu S, Xiao Z, Chen H, Zhang Y, Huang J. 2007. Simulation of wing-body junction flows with hybridRANS/LES methods. Int. J. Heat Fluid Flow 28:137990

Greschner B, Jacob MC, Casalino D, Thiele F. 2008. Prediction of sound generated by a rod-airfoil configu-ration using EASM DES and the generalised Lighthill/FW-H analogy. Comp. Fluids 37:40213

Hamed A, Basu D, Das K. 2003. Detached eddy simulation of supersonic flow over cavity. Presented at AIAA Aerosp.Sci. Meet. Exhib., 41st, Reno, Pap. No. AIAA-2003-0549

Hedges LS, Travin A, Spalart PR. 2002. Detached-eddy simulations over a simplified landing gear. J. FluidsEng. 124:41323

Hou Y, Mahesh K. 2004. A robust, colocated, implicit algorithm for direct numerical simulation of compress-ible, turbulent flows. J. Comp. Phys. 205:20521

Kapadia S, Roy S, Wurtzler K. 2003. Detached-eddy simulation over a reference Ahmed car model. Presented atThermophys. Conf., 36th, Orlando, Pap. No. AIAA-2003-0857

Krishnan V, Squires KD, Forsythe JR. 2004. Prediction of separated flow characteristics over a hump using RANSand DES. Presented at AIAA Flow Control Conf., 2nd, Portland, Pap. No. AIAA-2004-2224

Langtry RB, Spalart PR. 2007. Detached-eddy simulation of a nose landing-gear cavity. Presented at. IUTAMSymp. Unsteady Separated Flows and Their Control, Corfu, Greece

Maddox S, Squires KD, Wurtzler KE, Forsythe JR. 2004. Detached-eddy simulation of the ground trans-portation system. See McCallen et al. 2004, pp. 89104

McCallen R, Browand F, Ross J, eds. 2004. The Aerodynamics of Heavy Vehicles: Trucks, Buses, and Trains. NewYork: Springer

Mellen CP, Frolich J, Rodi W. 2003. Lessons from LESFOIL project on large-eddy simulation of flow aroundan airfoil. AIAA J. 41:57381

Mendonca F, Allen R, de Charentenay J, Kirkham D. 2003. CFD prediction of narrowband and broadband cavityacoustics at M = 0.85. Presented at AIAA/CEAS Aeroacoust. Conf. Exhib., Hilton Head, South Carolina,Pap. No. AIAA-2003-3303

Mendonca F, Allen R, de Charentenay J, Lewis M. 2002. Towards understanding LES and DES for industrialaeroacoustic predictions. Presented at Int. Workshop LES Acoust., Gottingen

Clearest critique ofgrid-inducedseparation. Menter FR, Kuntz M. 2002. Adaptation of eddy-viscosity turbulence models to unsteady separated

flow behind vehicles. See McCallen et al. 2004, pp. 33952

Presents SAS, thebest-known alternativeto DES for hybridRANS-LES.

Menter FR, Kuntz M, Bender R. 2003. A scale-adaptive simulation model for turbulent flow predictions.Presented at AIAA Aerosp. Sci. Meet. Exhib., 41st, Reno, Pap. No. AIAA-2003-0767

Mitchell AM, Molton P, Berberis D, Delery J. 2000. Oscillation of vortex breakdown location and control ofthe time-averaged location by blowing. AIAA J. 38:793803

Mockett C, Greschner B, Knacke T, Perrin R, Yan J, Thiele F. 2008. Demonstration of improved DESmethods for generic and industrial applications. See Peng & Haase 2008, pp. 22231

Mockett C, Thiele F. 2007. Overview of detached-eddy simulation for external and internal turbulent flow applications.Presented at Int. Conf. Fluid Mech., 5th, Shanghai, China

Morton SA. 2003. High Reynolds number DES simulations of vortex breakdown over a 70 degree delta wing. Presentedat Appl. Aerodyn. Conf., 21st, Orlando, Pap. No. AIAA-2003-4217

200 Spalart

Ann

u. R

ev. F

luid

Mec

h. 2

009.

41:1

81-2

02. D

ownl

oade

d fr

om w

ww

.ann

ualr

evie

ws.

org

Acc

ess

prov

ided

by

Uni

vers

ity o

f A

berd

een

on 0

7/25

/15.

For

per

sona

l use

onl

y.


Morton SA, Cummings RM, Kholodar DB. 2004. High resolution turbulence treatment of F/A-18 tail buffet.Presented at AIAA/ASME/ASCE/AHS/ASC Struct. Struct. Dyn. Mater. Conf., 45th, Palm Springs,Calif., Pap. No. AIAA-2004-1676

Concise exploration ofDES for wall modelinginside LES.

Nikitin NV, Nicoud F, Wasistho B, Squires KD, Spalart PR. 2000. An approach to wall modeling inlarge-eddy simulations. Phys Fluids 12:162932

Nishino T, Roberts GT, Zhang X. 2008. Unsteady RANS and detached-eddy simulations of flow around acircular cylinder in ground effect. J. Fluids Struct. 24:1833

Presents a widecollection of recentwork on DES and otherhybrid approaches (butnot all).

Peng SH, Haase W, eds. 2008. Advances in Hybrid RANS-LES Modelling. Berlin: SpringerPiomelli U, Balaras E. 2002. Wall-layer models for large-eddy simulations. Annu. Rev. Fluid Mech. 34:34974Rogallo R, Moin P. 1984. Numerical simulation of turbulent flows. Annu. Rev. Fluid Mech. 16:99137Roy CJ, Brown JC, DeChant LJ, Barone MF. 2004. Unsteady turbulent flow simulations of the base of a generic

tractor/trailer. Presented at AIAA Fluid Dyn. Conf. Exhib., 34th, Portland, Pap. No. AIAA-2004-2255Sagaut P, Deck S, Terracol M. 2006. Multiscale and Multiresolution Approaches to Turbulence. London: Imp. Coll.

PressShieh CM, Morris PJ. 2001. Comparison of two- and three-dimensional cavity flows. Presented at AIAA Aerosp.

Sci. Meet. Exhib., 39th, Reno, Pap. No. AIAA-2001-0511Shur ML, Spalart PR, Squires KD, Strelets M, Travin A. 2005a. Three-dimensionality in unsteady Reynolds-

averaged Navier-Stokes simulations of two-dimensional geometries. AIAA J. 43:123042Shur ML, Spalart PR, Strelets MKh. 2005b. Noise prediction for increasingly complex jets. Part I: methods

and tests. Int J. Aeroacoust. 4:21346Shur ML, Spalart PR, Strelets MKh. 2005c. Noise prediction for increasingly complex jets. Part II: applications.

Int J. Aeroacoust. 4:24766

First true 3Dapplication, calibrationof CDES , and successfulprediction of airfoilforces at all angles.

Shur ML, Spalart PR, Strelets M, Travin A. 1999. Detached-eddy simulation of an airfoil at highangle of attack. In Engineering Turbulence Modelling and Experiments 4, ed W Rodi, D Laurence,pp. 66978. Oxford, UK: Elsevier Sci.

Shur ML, Spalart PR, Strelets MKh, Garbaruk AV. 2006. Further steps in LES-based noise prediction for complexjets. Presented at AIAA Aerosp. Sci. Meet. Exhib., 44th, Reno, Pap. No AIAA-2006-0485

Shur ML, Spalart PR, Strelets MKh, Travin A. 2008. A hybrid RANS-LES model with delayed DES andwall-modeled LES capabilities. Int. J. Heat Fluid Flow. In press

Simon F, Deck S, Guillen P, Sagaut P, Merlen A. 2007. Numerical simulation of the compressible mixinglayer past an axisymmetric trailing edge. J. Fluid Mech. 591:21553

Slimon S. 2003. Computation of internal separated flows using a zonal detached eddy simulation approach.Proc. ASME Int. Mech. Eng. Congr., Pap. No. IMECE2003-43881. New York: ASME Int.

Spalart PR. 2000. Strategies for turbulence modelling and simulations. Int. J. Heat Fluid Flow 21:25263Spalart PR. 2001. Young persons guide to detached-eddy simulation grids. Tech. Rep. NASA CR-2001-211032.

Langley Res. Center, Hampton, Va. http://techreports.larc.nasa.gov/ltrs/PDF/2001/cr/NASA-2001-cr211032.pdf Introduced delayed

DES to combatgrid-inducedseparation.

Spalart PR, Deck S, Shur ML, Squires KD, Strelets MKh, Travin A. 2006. A new version of detached-eddy simulation, resistant to ambiguous grid densities. Theor. Comp. Fluid Dyn. 20:18195

Spalart PR, Hedges L, Shur M, Travin A. 2003. Simulation of active flow control on a stalled airfoil. FlowTurbul. Combust. 71:36173

Motivation for DES,basic equations (withCDES constantundetermined), andtwo-dimensionalexamples.

Spalart PR, Jou W-H, Strelets M, Allmaras SR. 1997. Comments on the feasibility of LES for wings,and on a hybrid RANS/LES approach. In Advances in DNS/LES, ed. C Liu, Z Liu, pp. 13747.Columbus, OH: Greyden Press

Spalart PR, Squires KD. 2004. The status of detached-eddy simulation for bluff bodies. See McCallen et al.2004, pp. 2945

Squires KD. 2004. Detached-eddy simulation: current status and perspectives. In Direct and Large-Eddy Sim-ulation V, ed R Friedrich, BJ Geurts, O Metais, pp. 46580. Dordrecht: Kluwer

Sreenivas K, Pankajakshan R, Nichols DS, Mitchell BCJ, Taylor LK, Whitfield DL. 2006. Aerodynamic simu-lation of heavy trucks with rotating wheels. Presented at AIAA Aerosp. Sci. Meet. Exhib., 44th, Reno, Pap.No. AIAA-2006-1394 Presents a wide range of

applications, includingmodels other thanSpalart-Allmaras.

Strelets M. 2001. Detached eddy simulation of massively separated flows. Presented at AIAA Aerosp. Sci.Meet. Exhib., 39th, Reno, Pap. No. AIAA-2001-0879


Ann

u. R

ev. F

luid

Mec

h. 2

009.

41:1

81-2

02. D

ownl

oade

d fr

om w

ww

.ann

ualr

evie

ws.

org

Acc

ess

prov

ided

by

Uni

vers

ity o

f A

berd

een

on 0

7/25

/15.

For

per

sona

l use

onl

y.


Temmerman L, Hirsch Ch. 2008. Towards a successful implementation of DES strategies in industrial RANSsolvers. See Peng & Haase 2008, pp. 23241

Trapier S, Deck S, Duveau P. 2008. Delayed detached-eddy simulation and analysis of supersonic inlet buzz.AIAA J. 46:11831

First DES with gridrefinement, fairagreement on the dragcrisis, and refineddefinition of DES inappendix.

Travin A, Shur M, Strelets M, Spalart PR. 2000a. Detached-eddy simulations past a circular cylinder.Flow Turbul. Combust. 63:293313

Travin A, Shur M, Strelets M, Spalart PR. 2000b. Physical and numerical upgrades in the detached-eddysimulation of complex turbulent flows. In Advances in LES of Complex Flows, ed. R Friedrich, W Rodi,pp. 23954. New York: Kluwer Acad.

Travin AK, Shur ML, Spalart PR, Strelets MKh. 2004. On URANS solutions with LES-like behaviour. Presentedat Eur. Cong. Comput. Methods Appl. Sci. Eng., Jyvaskyla, Finland

Travin AK, Shur ML, Spalart PR, Strelets MKh. 2006. Improvement of Delayed Detached-Eddy Simulation forLES with wall modelling. Presented at Eur. Conf. CFD, ECCOMAS CDF 2006. Delft, Neth.

Wilcox DC. 1998. Turbulence Modeling for CFD. La Canada, CA: DCW Ind.Wilson RP, Haupt SE, Peltier LJ, Kunz RF. 2006. Detached Eddy Simulation of a surface mounted cube at

high Reynolds number. Proc. ASME Joint U.S. Eur. Fluids Eng. Summer Meet. New York: ASME Int.Yan J, Tawackolian K, Michel U, Thiele F. 2007. Computation of jet noise using a hybrid approach. Presented at

AIAA/CEAS Aeroacoust. Conf., 13th, Pap. No. AIAA-2007-3621Ziefle J, Kleiser L. 2008. Compressibility effects on turbulent separated flow in streamwise-periodic hill

channel, part 2. See Peng & Haase 2008, pp. 31625

202 Spalart

Ann

u. R

ev. F

luid

Mec

h. 2

009.

41:1

81-2

02. D

ownl

oade

d fr

om w

ww

.ann

ualr

evie

ws.

org

Acc

ess

prov

ided

by

Uni

vers

ity o

f A

berd

een

on 0

7/25

/15.

For

per

sona

l use

onl

y.

AR365-FM ARI 12 November 2008 17:57

Annual Review ofFluid Mechanics

Volume 41, 2009Contents

Von Karmans Work: The Later Years (1952 to 1963) and LegacyS.S. Penner, F.A. Williams, P.A. Libby, and S. Nemat-Nasser 1

Optimal Vortex Formation as a Unifying Principlein Biological PropulsionJohn O. Dabiri 17

Uncertainty Quantification and Polynomial Chaos Techniquesin Computational Fluid DynamicsHabib N. Najm 35

Fluid Dynamic Mechanism Responsible for Breaking the Left-RightSymmetry of the Human Body: The Nodal FlowNobutaka Hirokawa, Yasushi Okada, and Yosuke Tanaka 53

The Hydrodynamics of Chemical Cues Among Aquatic OrganismsD.R. Webster and M.J. Weissburg 73

Hemodynamics of Cerebral AneurysmsDaniel M. Sforza, Christopher M. Putman, and Juan Raul Cebral 91

The 3D Navier-Stokes ProblemCharles R. Doering 109

Boger FluidsDavid F. James 129

Laboratory Modeling of Geophysical VorticesG.J.F. van Heijst and H.J.H. Clercx 143

Study of HighReynolds Number Isotropic Turbulence by DirectNumerical SimulationTakashi Ishihara, Toshiyuki Gotoh, and Yukio Kaneda 165

Detached-Eddy SimulationPhilippe R. Spalart 181

Morphodynamics of Tidal Inlet SystemsH.E. de Swart and J.T.F. Zimmerman 203

v

Ann

u. R

ev. F

luid

Mec

h. 2

009.

41:1

81-2

02. D

ownl

oade

d fr

om w

ww

.ann

ualr

evie

ws.

org

Acc

ess

prov

ided

by

Uni

vers

ity o

f A

berd

een

on 0

7/25

/15.

For

per

sona

l use

onl

y.

AR365-FM ARI 12 November 2008 17:57

Microelectromechanical SystemsBased Feedback Controlof Turbulence for Skin Friction ReductionNobuhide Kasagi, Yuji Suzuki, and Koji Fukagata 231

Ocean Circulation Kinetic Energy: Reservoirs, Sources, and SinksRaffaele Ferrari and Carl Wunsch 253

Fluid Mechanics in Disks Around Young StarsKarim Shariff 283

Turbulence, Magnetism, and Shear in Stellar InteriorsMark S. Miesch and Juri Toomre 317

Fluid and Solute Transport in Bone: Flow-InducedMechanotransductionSusannah P. Fritton and Sheldon Weinbaum 347

Lagrangian Properties of Particles in TurbulenceFederico Toschi and Eberhard Bodenschatz 375

Two-Particle Dispersion in Isotropic Turbulent FlowsJuan P.L.C. Salazar and Lance R. Collins 405

Rheology of the CytoskeletonMohammad R.K. Mofrad 433

Indexes

Cumulative Index of Contributing Authors, Volumes 141 455

Cumulative Index of Chapter Titles, Volumes 141 463

Errata

An online log of corrections to Annual Review of Fluid Mechanics articles may be foundat http://fluid.annualreviews.org/errata.shtml

vi Contents

Ann

u. R

ev. F

luid

Mec

h. 2

009.

41:1

81-2

02. D

ownl

oade

d fr

om w

ww

.ann

ualr

evie

ws.

org

Acc

ess

prov

ided

by

Uni

vers

ity o

f A

berd

een

on 0

7/25

/15.

For

per

sona

l use

onl

y.
Annual Reviews OnlineSearch Annual ReviewsAnnual Review of Fluid Mechanics OnlineMost Downloaded Fluid Mechanics ReviewsMost Cited Fluid Mechanics ReviewsAnnual Review of Fluid Mechanics ErrataView Current Editorial CommitteeAll Articles in the Annual Review of Fluid Mechanics Vol. 41Von Karmans Work: The Later Years (1952 to 1963) and LegacyOptimal Vortex Formation as a Unifying Principlein Biological PropulsionUncertainty Quantification and Polynomial Chaos Techniquesin Computational Fluid DynamicsFluid Dynamic Mechanism Responsible for Breaking the Left-RightSymmetry of the Human Body: The Nodal FlowThe Hydrodynamics of Chemical Cues Among Aquatic OrganismsHemodynamics of Cerebral AneurysmsThe 3D Navier-Stokes ProblemBoger FluidsLaboratory Modeling of Geophysical VorticesStudy of HighReynolds Number Isotropic Turbulence by DirectNumerical SimulationDetached-Eddy SimulationMorphodynamics of Tidal Inlet SystemsMicroelectromechanical SystemsBased Feedback Controlof Turbulence for Skin Friction ReductionOcean Circulation Kinetic Energy: Reservoirs, Sources, and SinksFluid Mechanics in Disks Around Young StarsTurbulence, Magnetism, and Shear in Stellar InteriorsFluid and Solute Transport in Bone: Flow-InducedMechanotransductionLagrangian Properties of Particles in TurbulenceTwo-Particle Dispersion in Isotropic Turbulent FlowsRheology of the Cytoskeletonar: logo:

Documents

Detached Eddy Simulation - 2