The Status of Detached-Eddy Simulation for
Bluff Bodies
Philippe R. Spalart1 and Kyle D. Squires2
1
2
Boeing Commercial Airplanes, PO Box 3707, Seattle, WA 98052, USA
philippe.r.spalart@boeing.com
MAE Department, Arizona State University, Tempe, AZ 85287, USA
squires@asu.edu
Proposed in 1997, DES was applied to an airfoil beyond stall in 1999, and
then to a range of bluff bodies. Its accuracy has often been far superior to
that of steady or unsteady Reynolds-averaged Navier-Stokes methods, and it
avoids the Reynolds-number limitations that plague Large-Eddy Simulation.
Cases fall into three classes: simple shapes such as cylinders and spheres;
transportation components such as landing gear, simplified; and full airplane
geometries. All are manageable on present computers, some even on personal
computers. Simple shapes now and then yield surprises, but DES appears
sound and reacts well to the type of boundary-layer separation (i.e., laminar
or turbulent), and to grid refinement. However, it is possible to confuse the
method by using a grid density that is both too fine for RANS and too coarse
for LES. Component studies display progress, without reaching an industrial
level of accuracy in predicting all forces. The few full-airplane predictions
have been successful, thanks to high CPU power, and partly thanks to fixed
separation lines.
Progress and a proper dissemination in industry and by CFD vendors
now depends on prudent improvements in numerics and in physical models,
preferably without losing any of the simplicity of DES, and on communication
with non-experts. The experimental database remains weak in some areas.
Numerical issues include grid generation, code performance in unsteady flows,
and numerical dissipation. Codes used for complex configurations stabilize the
calculations via upwinding and/or limiters, and assessing their effects on DES
predictions remains important. Slight improvements to the treatment of the
“RANS region” of DES (essentially comprising the boundary layers up to
separation) are also desired. Good gridding and time-stepping practices are
both costly and crucial; deficiencies have often been traced to the grid. Few
users have experience with LES, let alone with issues specific to DES, which
are clarified here. The prediction of bluff-body flows at application Reynolds
numbers will place heavy demands on the user, as numerous aspects of the
30
P.R. Spalart and K.D. Squires
simulation must all be carefully controlled. Error-proof methods should not
be promised, and the natural robustness of DES should not be abused.
1 Critical History of DES
DES was inspired by estimates initiated in 1997 [1] and completed in 2000
[2], which indicate that Large-Eddy Simulation (LES) is not about to become
practical for industrial flows, such as aircraft or road vehicles. This applies
for about forty years, and is true even if it is assumed that “wall modeling”
has become successful, in other words, that limits on the grid spacing in wall
units such as ∆x+ have been removed within LES. Relevant to these estimates is the assumption that much of the boundary layer is turbulent; an
assumption which is most reasonable in practice. The estimates have yet to
be challenged by LES proponents, and too much work remains mired at unchallenging Reynolds numbers, from which clear conclusions cannot be made.
Empirical evidence that strongly supports the estimates is offered by the LESFOIL workshops [3], for which the Reynolds number was sufficiently large to
expose LES methodologies: current super-computers, even for a single simulation with a “designer grid” optimized by experts given detailed advance
knowledge of the flow, can handle only an airfoil slice of the order of 1% of
the chord, at a moderate Reynolds number and with a laminar stagnation
region [4]. In other words, the real-life problem of a wing is roughly 1,000
times larger, even before the extra difficulties of sweep (giving a thin and
turbulent attachment-line boundary layer) and of a full-size Reynolds number
are included.
When considering near-future industrial CFD methods capable in highReynolds-number bluff-body flows, experience and projections lead to a strong
consensus that Reynolds-averaged Navier-Stokes (RANS) technology is indispensable in the large areas of thin attached boundary layers, and to a weaker
consensus that pure RANS methods cannot provide sufficient accuracy in regions of massive separation. These regions are dominated by large, inviscid,
geometry-specific eddies, which are excellent candidates for LES. As a result,
hybrid methods are receiving wide attention.
These considerations leave some leeway in designing a hybrid RANS-LES
method. The first choice is between a method that is explicitly zonal, as opposed to a method that solves a single set of equations. DES reflects a strong
preference for non-zonal systems and simple formulations. It involves a single
grid and a single field for velocity, pressure, and even eddy viscosity, whether
using the Spalart-Allmaras (S-A) model or the SST model as the RANS base
[5]. The choice of model is of course an element of leeway, and a welcome opportunity to test the sensitivity of solutions. Simplicity is favorable in terms
of repeatability between codes and users, and experience-building. The formulation using a single model only leads to a discontinuity in the gradient
of the length scale that enters the destruction term of the turbulence model
DES for Bluff Bodies
31
(this discontinuity would be easily removed by rounding the min function that
determines the lengthscale). In contrast, explicitly-zonal methods often suffer from steep variations near the zonal interface, and much work is expended
controlling these. The change in the lengthscale leads to a model that becomes
region-dependent in nature – in most cases a RANS model in the boundary
layers and a Sub-Grid-Scale (SGS) model within massive separation. Objections have been made to the use of the grid spacing ∆ in the formulation,
but this appears absolutely natural. The foundation of LES is the existence
of a filter width that controls the end of the energy cascade, and is available
for reduction in order to increase the range of scales and therefore improve
the physics of the simulation [2]. As separate issue, present in any LES, is
whether the filter width and the grid spacing should be tied; a recent trend is
to untie them, and seek a grid-converged solution for a fixed filter width. In
all DES studies, they have remained tied; this appears to provide a balance
between numerical and SGS-modeling errors, although this balance has not
been established (which would be difficult to do beyond question, because
in LES the error measures are quite arbitrary). Thus the nature of the SGS
model inside DES is classical, and in particular its scaling is identical to that
of the Smagorinsky model. It was adjusted to extend the inertial range in a
classical Kolmogorov setting as far as possible [18]; this adjustment requires
care when generalizing it to unstructured grids. There is no obvious accuracy
advantage in solving a transport equation for the SGS eddy viscosity, instead
of using a local algebraic formula; it is done for commonality with the RANS
region.
In addition to the formulation, there is also flexibility in the design of a
DES simulation, primarily within the prediction of the boundary layer upstream of separation. In “natural” DES it is handled by the RANS model
but there is a trend, at least in fundamental studies, to predict parts of the
attached boundary layers with LES. The study of Nikitin et al. in a channel was conducted to explore such applications [6] and was quite successful.
Commentators have focused on the imperfection in the skin friction, instead
of the great simplicity of the approach and excellent Reynolds-number scaling
both in terms of computing cost and accuracy. Applied to an airfoil in this
limit, DES then resembles the LESFOIL exercise [3]. Keeping in mind that
the unmanageable cost of LES arises due to the resolution requirements in the
thin regions of the boundary layer, switching from RANS to LES is feasible
only after the boundary layer thickens sufficiently. In this régime, LES treatment within the boundary layer is attractive since it is possible to exploit the
accuracy of the technique and the grid-refinement possibilities inherent to the
method – a proposition that is expensive, but represents an important and
valuable research activity. A key concept underlying such an approach, and
for that matter all applications of DES, is to clearly “steer” the simulation
either to RANS or to LES behavior by means of the grid density. Unfortunately this can become delicate, and normally the detailed characteristics of
a flow are not known in advance as, for example, is the case for LESFOIL.
32
P.R. Spalart and K.D. Squires
Note that “natural” DES of the LESFOIL case, with its shallow separation,
is essentially a RANS, and therefore has similar accuracy. In fact, RANS predictions are more accurate than LES has been to date, presumably because
no LES has had both sufficient grid density and adequate spanwise extent.
This judgment assumes the particular experiments on that airfoil are more
accurate than CFD, which will not be true indefinitely.
The objection to incorporating the grid spacing into the turbulence model
in DES has one root in the inaccuracies encountered by careful users, as they
gradually refine the grid starting from a natural DES [7, 8, 9]. This threat was
illustrated in the initial DES paper [1]. Once the grid spacing in both directions parallel to the wall becomes smaller than about half of the boundarylayer thickness, the DES limiter reduces the eddy viscosity, thus “corrupting”
it compared with its RANS level, but without allowing LES behavior. The
resulting solution creates insufficient total Reynolds stresses (modeled + resolved stress [6]). There is no solution ready for release at present, and this
adds to the burden on the DES user of checking that the RANS/LES interface
is not deep inside the boundary layer. It also conflicts with the tendency to
refine the grid at shock-boundary-layer interactions, either manually or automatically. However, the only true need is to refine in the direction normal to
the shock, and therefore in a typical situation the shock-parallel spacing will
keep ∆ large enough to avoid unintentional eddy-viscosity limiting. Some adjustments may be introduced, but removing the grid spacing altogether from
the DES formulation is out of the question.
Nearly all other hybrid methods currently under consideration sensitize
the model to the grid in order to achieve LES behavior [10, 11, 12, 13]. As
the exception, the SAS hybrid is free of grid spacing and has demonstrated,
visually, LES-like behavior past a circular cylinder and a wall-mounted cube
[14]. This gives much food for thought. On the other hand, it is still extremely
new with only one conference paper, has not yet demonstrated LES behavior
during grid refinement, and has simply failed to function as LES in a channel
flow. New findings may appear rapidly.
Another issue addressed in [1] is the “grey area” in which a shear layer,
after separation, needs to generate “LES content” (random eddies) which
it did not possess as a boundary layer upstream. The process of generating
LES content is most easily achieved by a thin shear layer that is rapidly
departing from the wall, typically thanks to a thin edge or sharp corner;
greater uncertainty was anticipated over smooth-wall separations. Similarly,
LES is widely expected to be more successful for bodies with sharp edges than
smooth ones (even with laminar boundary layers; for turbulent separation LES
poses a bigger challenge, and SGS models are sometimes naively used as RANS
models in the entire thickness of the boundary layers). These considerations
motivated the circular-cylinder study, which was quite re-assuring, see §2. A
more extreme case is a shallow separation, either unclosed or a bubble. There,
depending on the grid, the DES may not create any LES content. This is
not incompatible with the original motivation for the method to achieve LES
DES for Bluff Bodies
33
behavior only in massive separation, but shallow separation and especially
reattachment also activate finite errors in any RANS model. In some cases
it is desirable to explore the performance of LES in such flows, as already
mentioned.
An separate source of ambiguity exists in vortex-dominated flows, because
the effect of the DES limiter and that of rotation/curvature (RC) corrections
to RANS models on the eddy viscosity are similar. Consider a typical RANS
model such as k-% or S-A. In a vortex, it produces much too high an eddy
viscosity, rapidly smearing the vortex. This is well mitigated by RC corrections
[15], which drastically reduce the eddy viscosity. Unfortunately, this is also
what occurs in DES, relative to RANS, leading to the very real possibility of
improving results by activating DES but for the wrong reason. The grid may
be still much too coarse for robust LES content (especially considering the
stabilizing effect of rotation), but the vortices will become more coherent and
their low-pressure signature on the wall deeper, the effects expected from a
good rotation term (see §2). Naturally, grid refinement by a large ratio would
exhibit the problem, but that is very difficult in 3D. In general, extensive flow
visualization is a much more practical step; the user needs to ask “does the
solution really have LES behavior in the intended LES region?”.
A discussion and manual to generating DES grids was funded by NASA,
and can be downloaded [16]. At the time, it did not emphasize the issue of grid
refinement parallel to the wall, outlined above; however many other concepts
and examples can be found, and the report constitutes a fair starting point
for a new DES user.
We now turn to examples drawn from recent studies.
2 Simple Objects
The circular cylinder remains a major challenge to bluff-body CFD methods
of any type, and gives an excellent arena in which to make DES succeed,
or fail. Even shapes reputed to be less challenging such as square cylinders
cannot be considered as “solved” even with over 106 grid points [17]; however
it is plausible that a simple increase in resolution past 107 points will be
quite helpful (the workshop [17] took place in 1995). Ensuring a good balance
between the three directions of the grid and the time step will also help. It
is not clear why the thin-airfoil or thin-plate problem appeared under good
control, at several angles of attack, already with only about 2 × 105 points
[18]. In contrast to these cases, the separation off the smooth surface of the
cylinder, a textbook case well-known to strongly depend on transition, tests
CFD approaches and codes in many areas.
At Reynolds numbers that produce laminar separation (LS), DES is not
very different from LES, except that a simple LES method is not equipped to
disable the SGS model, as must be done in the boundary layers. A DES based
on the S-A model functions quite well in “tripless” mode, and the model
34
P.R. Spalart and K.D. Squires
Fig. 1. Pressure distribution on circular cylinder. Left, laminar separation; right,
turbulent separation. Left: ◦, #, exp.; - - -, —, – – –, DES with improving resolution.
Right: same lines, and - – - RC correction.
is indeed disabled up to separation without the user imposing a transition
line [19]. In the régime of turbulent separation (TS), the usual cost increase of
LES rapidly outruns the capacity of any computer today, and serious attempts
must use a hybrid method. The study of Travin et al used DES in its standard
form, with the user only specifying whether the boundary layers would be
laminar or turbulent ahead of separation [19]. The study included variations
in the spanwise periodicity length, and grid refinement by a factor of 2 in all
directions. The finest grid had about 106 points, which is moderate by current
standards.
Figure 1 suggests both real progress, and room for improvement. The LS
results indicate grid convergence (which is elusive in methods containing LES)
at least for the pressure distributions: the three curves approach the experimental results, which are themselves in excellent agreement. Admittedly, even
that case showed much scatter for velocity profiles and Reynolds stresses in
the wake. The TS cases have scatter even in the most basic of result: the
pressure. The DES results, which are quite consistent on different grids and
with(out) RC, fall between two experiments which both appear reliable, but
nevertheless are far apart. Therefore, the cylinder with Reynolds number past
106 remains an excellent candidate for experiments, with special care to improve and document two-dimensionality. It would facilitate CFD validation to
include cases with trips well upstream of the separation line. This is because
skin-friction distributions shown in [19] reveal that making the boundary layers turbulent ahead of separation is simplistic, relative to the true transition
process on a smooth surface, even at Reynolds number as high as 3.6 × 106 .
Separation and transition are concurrent, which RANS models (at least, S-A)
are unable to render. In its tripless mode, S-A produces laminar separation,
at any Reynolds number. Unfortunately, the next level of fidelity in numerical simulation appears to involve a DNS of the transition, presumably with
DES for Bluff Bodies
35
realistic imperfections of both the surface and the incoming flow. Whether
differences in these imperfections were sufficient to cause the differences in
experimental pressures is an intriguing conjecture.
Travin et al also found that very long time samples are essential to converge
the statistics, as the vortex shedding has strong modulations in DES, just
as occurs in the experiment [20]. Although this could be a “pathology” of
2D-geometry separated flows, it is a warning for any study of a flow with
large-scale shedding: simulating only a few cycles of such shedding is unsafe.
Constantinescu & Squires presented the equivalent study for a sphere [22].
0.008
Measurements
DES - Fine Grid
DES - Medium Grid
DES - Coarse Grid
RANS
a = 20o
x/L = 0.77
0.006
Cf
0.004
0.002
0
0
30
60
90
f
120
150
180
Fig. 2. Skin-friction distribution around a prolate spheroid.
The prolate spheroid at angle of attack provides an opportunity for assessing turbulence treatments in a flow exhibiting complex three-dimensional
separation. Analogous to the circular cylinder, separation is not fixed by a geometric feature and challenges predictive models. Unlike other simple objects
such as cylinders and spheres, however, the flow structure in the leeward/wake
region is strongly influenced by a pair of longitudinal vortices.
A proto-typical example is the 6:1 prolate spheroid for which there are
extensive experimental measurements of surface quantities such as the pressure and skin friction distributions as well as profiles of the mean velocity and
second-order statistics [21]. A prediction of the azimuthal distribution of the
skin friction magnitude is shown in Figure 2. In the figure, φ = 0◦ defines
the windward coordinate of the symmetry plane, and φ = 180◦ coincides with
36
P.R. Spalart and K.D. Squires
leeward coordinate of the symmetry plane. The distributions shown are in the
aft region, at x/L = 0.77 for which measurements show well-developed primary and secondary separation. The computations are for a freestream at 20
degrees angle of attack and at a Reynolds number of 4.2 × 106 (based on the
freestream speed and spheroid length, L). The flow parameters of the computation match the experimental measurements reported by [21], including
a boundary layer trip at x/L = 0.2 which is activated in the computations
using the trip terms of the S-A model.
DES predictions on three grids are shown together with a S-A RANS result. Experiments on the spheroid have shown that minima in Cf are well
correlated with the separation locations indicated by wall streamlines, the
measured skin friction then indicating primary separation at φ ≈ 115◦ and
secondary separation at φ ≈ 145◦ . The S-A RANS result predicts primary
separation at a slightly more leeward location. Figure 2 shows that the minimum in Cf is around 125◦ and that the magnitude is slightly greater than the
measured minimum. The variation in Cf around 145◦ in the RANS prediction
is indicative of the influence of a secondary separation, though its influence
is very weak and an outcome of the S-A model devoid of rotation correction,
with its large eddy viscosity in the core of the vortices, overly diffusing these
structures.
For the DES, with grid refinement the skin friction magnitude shows an
increasingly well-defined secondary separation, as evidenced by the Cf distribution around φ = 145◦. Increases in grid resolution results in lower eddy
viscosity, an effect that is similar to that which could be obtained using a
RANS model with R/C corrections. Nevertheless, the more sharply defined
separated structures, in this case the coherent longitudinal vortices, experience
less diffusion with increases in mesh resolution, in turn resulting in pronounced
signatures in the skin friction and (not shown here) surface pressures.
Figure 2 also shows that the influence of grid resolution on the minima
corresponding to primary separation is not weak. On progressively finer grids
the minimum shifts windward and the magnitude decreases. For the unstructured grids used for the DES predictions shown in the figure, the RANS-LES
interface is within the boundary layer upstream of separation. As discussed
in §1, this could lower the total Reynolds stress and shift the separation location “upstream” (in this case, towards the windward direction). This is under
intense investigation.
3 Components
The distinction between “simple objects” and “vehicle components” can be
blurry. Forsythe, Hoffmann and Dieteker simulated a circular base flow at
Mach 2.46 [23] with the Cobalt code, second-order upwind on unstructured
grids. The DES results were far superior to RANS results, even qualitatively,
and quite close to the experiment. Simulations were run with various values
DES for Bluff Bodies
37
of the CDES adjustable constant. Even simulations without any turbulence
model worked quite well, suggesting that the numerical stabilization of the
simulation comes close to playing the role of an SGS model away from walls
(so that low values of CDES have little effect); however, its boundary-layer
velocity profiles were incorrect, confirming that such methods are inadequate
when the boundary layers need to be reproduced accurately.
Deck, Garnier and Guillen simulated more complex geometries, namely
an under-expanded rocket nozzle and an after-body with conical base and
emerging nozzle with jet [24]. The nozzle flow DES exceeds Mach 5 at the Mach
disk, sustains three-dimensional flow structures, and is in excellent agreement
with experiment both on the separation location and the post-shock pressures.
The afterbody study is directed at buffeting. Reconciling shock-capturing and
LES content with a numerical scheme is a challenge. The FLU3M code of
ONERA uses structured grids and a second-order upwind scheme. In this
flow as in the nozzles, RANS based on the S-A model reaches steady state.
Here, RANS and DES give rather different mean flows, particularly in terms of
reattachment location, and the experimental result appears to be in-between
the two. The three-dimensional unsteady activity is obvious. The unsteady
forces are shown, but not compared with experimental measurements, which
may well be proprietary. This study comes very close to flow phenomena of
extreme industrial importance, considering recent failures of space launchers.
Fig. 3. Vorticity contours in six axial planes along the leeward side of the GTS (10◦
yaw). Surface colored by pressure.
38
P.R. Spalart and K.D. Squires
The Ground Transportation System tested by NASA is classified as a
component, because its geometry is very simplified. In return, very detailed
measurements are available, at several conditions, and allow a thorough examination of CFD results [25]. Vorticity contours at six axial stations along
the leeward side of the GTS are shown in Figure 3 from DES predictions of
the flow at 10◦ yaw. The findings are that DES is justified over RANS already
for mean quantities, since the drag error is 12% instead of 49% without sidewind, and of course even more if unsteady information is needed. DES can
be clearly faulted only for the size of the separation region near the front end
with side-wind, which is much too large, although other aspects of that solution are good, including the skin friction under the roof vortex, for instance.
The drag error jumps from 12% to 39%, which is far from industrial accuracy;
in other words, CFD is not a practical tool yet. This problem may eventually
be traced to a difference in the laminar/turbulent state of the boundary layer,
and suggest that the corner radius chosen is unfortunate since it challenges
the RANS region and transition prediction so much (another putative symptom is the hysteresis versus Reynolds number in the test). In that case, actual
geometries which are less rounded could be easier from a flow-physics point
of view, although much harder to grid. Another conclusion is that grid generation on such a geometry is onerous even with an unstructured-grid code,
and can always be re-visited to improve accuracy and reduce waste. This is
intensified by the desire to compare at least two grids and make the refinement strong enough to be meaningful, as well as systematic enough to feel
that the error is reduced everywhere in the domain. The case with boat-tail
plates, designed to reduce drag, has not been calculated yet, and the Reynolds
number was kept out of the hysteresis range. Thus, much more work could be
done.
The DES study of Active Flow Control (AFC) on the airfoil of the V-22 tiltrotor aircraft was partly successful [26]. The flow is driven by the downwash
of the rotors in hover, leading to an airfoil flow at roughly −90◦ angle of
attack, with a highly-deflected flap. The AFC relies on alternating suction and
blowing through a narrow slot at the flap shoulder, designed to enhance mixing
and make the flow more nearly follow the flap. With the AFC off, accurate
predictions could be expected, similar to those on the NACA 0012 airfoil [18].
Initial results with the RANS model active in the boundary layers, leading
to turbulent separation, were disappointing in terms of drag and pressure
pattern at the leading edge. The leading edge is much more rounded than
on the 12%-thick airfoil, allowing the separation line more freedom. Indeed,
simulations with the model inactive in the boundary layers, and therefore
laminar separation, were within experimental error. This flow is sensitive to
transition and an internal controversy with the authors of the experiment,
who had tripped their boundary layers, was unfortunately never resolved [27].
However, arguments were made to the effect that the trips failed because
of Reynolds number and acceleration [26]. This case illustrated the strong
DES for Bluff Bodies
39
residual influence of the model, and the value of being able to routinely control
transition in CFD as provided by the S-A model.
Active Flow Control was a new arena, and proved highly challenging. The
slot was so narrow that it covered only two to three grid points, even with
very strong clustering. Thus, the slot treatment was crude. With a grid of
the order of 600,000 points, the crucial region containing the manipulated
separated shear layer was treated in URANS mode inside the DES; for an
LES treatment, orders of magnitude more grid points would be needed. Thus
the shear-layer treatment fell back on the RANS model; no data were available
to validate the model in such a flow, and the accessible grid refinement would
have been inconclusive. The model may not matter to leading order, since the
roll-up of the shear layer is nearly inviscid, but this is not proven. For the rest
of the wake, the level of confidence was fairly good, based on the agreement
with AFC off.
The pressure distribution responded to AFC, but only qualitatively. The
drag reduction was not very consistent with experiment, and in some ranges,
increasing the level of forcing caused an increase in the predicted drag. The
time samples were adequate, but not all were long enough to rule out hysteresis
or very slow modulations. Repeating the study with larger computer resources
would close some of these issues. However, the very nature of AFC creates
CFD problems containing a huge range of scales (here, from the slot width
at 0.2% of chord to the wake length at 100 chords), which are barely possible
in three dimensions even with thorough grid design. Turbulence is the realm
of wide ranges of scales, but the premise of LES is that the small eddies only
absorb information from the large eddies; here, phenomena in the tiny slot
control the entire flow. As a result, CFD will lag experiments for years in the
field of AFC for lack of CPU power, provided the experiments are done with
care and attention to scale effects.
Other component flows are the simplified landing-gear truck of Hedges et
al. [28] and the jet-fighter forebody of Squires et al. [29].
4 Full Configurations
The series of DES over the F-15 and F-16 fighter aircraft has been the most
noticed work on quite complete configurations [31] (although the engine modeling remains very simple). In particular, agreement with experiment within
5% for lift and drag at 65◦ angle of attack is an excellent result, even once
it is recognized that the extreme angle of attack and thin wing edges mean
that the DES depended almost only on its LES mode, except for the nose
of the airplane. The forebody “component” study [29] gives confidence and
was very favorable to DES over RANS, but accommodating a grid and a time
step capable of LES behavior on the nose while including the entire aircraft
remains very challenging.
40
P.R. Spalart and K.D. Squires
Today’s super-computers are capable of DES on a smooth full configuration; the equivalent simulation on an airliner may suffer as much from the
uncertainty over the shape of the wing, which is much more flexible, as it does
from CFD weaknesses. All simulations would also be more difficult closer to
the stall angle of various components, especially with more rounded leading
edges, because separation prediction would have more leverage. Therefore, a
long validation process needs to take place. However, there is no reason CFD
should shy away from problems such as airplane spin, which is already being
addressed [32] or the possibility of “tumbling” for a blended-wing-body airplane. In terms of fluid mechanics, it is not clear that they are more difficult
than the circular cylinder.
Fig. 4. Truck simulation of Wurtzler. Vorticity surface and wall pressure.
The tractor-trailer truck simulated by Wurtzler with the Cobalt unstructuredgrid code is rather complete, but does not correspond to a geometry that was
tested [33]. In Fig. 4, note the presence of wheels and mirrors, the gap between the cab and trailer, and the side-wind. The grid had about six million
points. Wheel rotation and radiator flow will be added sooner or later, as will
even smaller features such as shafts and brakes, as well as surface roughness
on the trailer sides and tires. The vorticity reveals convincing LES content in
this solution, and a simulation of the buffeting effect on a car appears within
reach, as do noise calculations for low frequencies, or calculations of soiling.
DES for Bluff Bodies
41
Fine effects such as drag reduction by detail shape modifications have not
been demonstrated yet.
5 Algorithm Issues
The application of eddy-resolving techniques to the prediction of turbulent
flows places high demands on the numerical approaches used in DES (as well
as LES). At full-scale Reynolds numbers and when applied to complex configurations, the discretized system of equations is extremely stiff and requires
the application of implicit schemes for efficient integration of the governing
equations. Since many production codes in use today have been developed for
very efficient integration to steady-state, the extension to time-accurate computation is obviously an important step for these codes in order to perform
DES.
In addition, in the absence of kinetic-energy conservation by the numerics, discretizations of the Navier-Stokes equations require some form of artificial dissipation to maintain stability. Two common approaches are the use
of upwind-biased differences and the use of limiting. Strelets, for example,
employs fifth-order accurate upwinding on convection in their numerical approach to solution of the incompressible Navier-Stokes equations [5]. An interesting aspect of that method being the application of upwind-biased differences only within the RANS region and use of centered difference approximations in the LES region. A reasonably wide range of DES predictions have
also been obtained using Cobalt, a cell-centered finite volume approach applicable to arbitrary cell topologies (e.g, hexahedrons, prisms, tetrahedrons)
[30]. There, the stability to the underlying numerical approach is established
using TVD flux limiters.
Regardless the details of the approach, any scheme that requires the introduction of artificial dissipation in order to maintain stability should be
carefully assessed when used in DES. Dissipation from the numerical discretizations are often comparable to that provided by the turbulence model.
Even centered schemes, that do not introduce artificial dissipation, often suffer
from strong dispersive error, an effect that can require great care in controlling aspects such as the grid stretching. The primary approach to assessing
these effects remains variation in the grid density (and time step). Unsteady
content with sufficient statistical sampling increases the computational cost
of DES. Obtaining predictions on more than a single grid further raises the
cost, though such exercises have been invaluable in understanding the method
and contributing to its experience base [19]. As the range of flows amenable
to accurate prediction using DES continues to expand, parallel computation
will represent an even more important tool.
42
P.R. Spalart and K.D. Squires
6 Design of a DES
The basis of DES is that the relationship between the grid spacing and the
natural length scales of the turbulence in a given region makes the selection
between RANS and LES behavior [19]. Here, we are assuming that the time
step is short enough to allow LES behavior; since the time step is global to
the simulation, its value can present a difficult compromise. As a result of this
option, and considering the permanent need for economy of grid points, DES
grid design is not simple. The “young person’s guide” (YPG) [16] introduces
terminology and guidelines, many of which also apply to RANS calculations,
even if they have not been named. Focusing on external flows, the YPG distinguishes the Euler Region, into which no turbulence will intrude, the LES
Region, and the RANS region. The latter two also contain viscous layers at
the walls. The wall regions resemble those in RANS: shallow cells with the
usual rules for first wall-normal spacing or “y + ” and stretching ratio. In contrast, the LES and Euler regions have isotropic cells, and the LES region little
stretching. There is also necessarily a “Departure Region” in which eddies that
will never return into the LES region and impinge on the body safely become
dissipated.
Grid refinement tends to concern the LES region and the wall-parallel
spacings of the wall region, which tend to follow the LES-region spacing. For
the wall-normal distribution, there is little point in starting with y + = 10
or a stretching ratio of 2 (as compared with the guidelines y + ≈ 1 − 2 and
ratio ≈ 1.2 − 1.3), say, unless this is explicitly a disposable simulation used to
prime an automatic grid adaptation (it would make much more sense to do
a precursor simulation at a reduced Reynolds number than with an excessive
y + ). The Euler region does not contain a large share of the points, giving
little incentive to save points and have to re-visit it. The LES region leaves
the most leeway, as it is very difficult to predict how many points are needed
to be accurate in a new case. Grid convergence is very elusive, and the order
of convergence is not simple at all. Only the circular cylinder has strongly
suggested grid convergence [19]. In addition, reaching a good accuracy level
can well happen at different levels of resolution in different parts of the flow.
The smaller features of the geometry require finer resolution, which is not a
natural tendency when generating the LES-region grid; in addition, again, the
time step is uniform. There are clear conflicts.
The recommendation is to count many weeks of work for any new case,
several cases to form a new DES user, and to pool experience both by detailed
and critical publications and within the networks of the CFD vendors.
7 Closing comments
For treating bluff bodies at useful Reynolds numbers, the consensus behind
hybrid RANS-LES methods has grown very strong, and DES is at present the
DES for Bluff Bodies
43
most recognized of such methods. It has been stable and has active communities outside the original core, particularly in Germany and France, so that
meaningful critiques have been made (as have a few mistakes, such as grid
refinement that is not consistent in the three directions). The users have been
generally quite satisfied, while recognizing the heavy challenge of designing a
DES. However, the challenge is no surprise to those familiar with LES, with
the possible exception of the issues of corrupting the eddy viscosity in a RANS
boundary layer or accidentally approximating the turbulence depletion by rotation. Abuses have been committed, typically leading to essentially RANS
behavior because of a very insufficient number of grid points; no LES can
develop with 10 points in any of the directions. On a related matter, some
users expect DES to require less resolution than LES everywhere, but this
is true only in the boundary layers. For a region of massive separation, the
size of the numerical task is dictated by a “number of large eddies” which is
no different between an LES and a DES. The recent dissemination in vendor
CFD codes is welcome, but will lead to much more use by non-experts. To
help them, it is desirable for many detailed publications to appear, and again
for the approach to remain stable, simple, and clearly defined; they are urged
to visualize their solutions extensively, and to produce at least two grids.
The warnings made in this paper over the design and interpretation of a
DES, from the simplest to the most complex geometries, make it clear that it
is not a “push-button” technique; DES requires a commitment to numerical
quality, and a working knowledge of turbulence. However, the wait for a pushbutton technique will be very lengthy. Many of the warnings simply reflect
the physics of this new class of flows, which is still widely considered to be out
of reach of CFD. It is out of reach of casual CFD use. Competing methods
do not appear simpler to implement or understand, and since all problems
are three-dimensional, “over-kill” grid resolution is not about to become an
option. Fortunately, we are seeing the beginning of grid adaptation, based
on precursor solutions, which makes grid refinement more rapid and more
systematic.
8 Acknowledgments
Prof. Strelets made comments on the manuscript.
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