DESider, July 14-15 2005, Stockholm
THE USES OF DES: NATURAL,
EXTENDED, AND IMPROPER
Philippe Spalart
Boeing Commercial Airplanes
with M. Strelets, M. Shur, A. Travin, A. Garbaruk, & K. Squires
Outline
• Natural uses of DES
–
–
–
–
Initial vision, nice pictures
Problems on “ambiguous grids”, Modeled-Stress Depletion; GIS
Zonal DES by Deck
DDES proposal (as opposed to DES97, the original formula)
• Extended uses of DES
– Wall-Modeled LES
– Methods capable of WMLES, but not of Natural DES
– WMLES in same domain as RANS, “DESFOIL”
• Improper uses of DES
–
–
–
–
Ambiguous grids
2D!!!! And nearly 2D (low Nz)
Coarser grid than LES, in separated region
Improper use of… LES
• Asides:
– Debate over grid length scale in LES
– Edwards modifications to the S-A model
• Outlook
The 1996/1997 Vision:
Natural DES
DES of F-15 Fighter at 65o
by Forsythe, Squires, Wurtzler, in 2000
Re = 13.6 106; lift, drag, moment within 5%
107 cells/side, Cobalt code, US DOD CPU
Delta Wing Vortex Breakdown
DES by S. Morton, USAF Academy
AIAA2003-4217
Grid systematically
refined from 1.2M
cells to 10.7M cells
a)
b)
c)
d)
Turbulent Kinetic Energy in Vortex
over Delta Wing, by S. Morton
0.5
G1 (1.2M Cells)
G2 (2.7M Cells)
G3 (6.6M Cells)
G4 (10.5M Cells)
(Experimental Peak Approx. 0.5)
Resolved TKE (k/U 2∞)
0.4
0.3
0.2
0.1
•Location of Peak
TKE very consistent
•Peak TKE for finest
grid in good agreement
with experiments
0
0
0.25
0.5
X/c
0.75
1
Modeled-Stress Depletion, 1997
• This is not the same as the “grey area,”
– in which the solution has to generate “LES content” after separation
• MSD:
– is inside the boundary layer.
– Starts when ∆x ~ δ, either because ∆x is small, or δ is large.
– The eddy viscosity drops below the RANS level,
and the modeled stress with it,
but there is no LES content to create a “resolved stress”
– This depletion was anticipated, but…
was not given an acronym, and
was not expected on “reasonable” grids.
– It is the root cause of “Grid-Induced Separation” (Menter, 2002 on)
• Tests were shown:
– A strong local refinement causes a crisis in the boundary layer.
• Recommendation:
– Only an “excessively fine” grid (small ∆x and ∆z) will cause real
trouble
– Avoid parasitic refinements in the attached region
Three grid densities in an attached
boundary layer for a DES
Natural
Ambiguous
Assume ∆z ~ ∆x
LES
Modeled-Stress Depletion, 1997
A fine grid (small ∆x) strip near ∆Rx = 0 drops eddy viscosity and skin friction
The simulation is 2D
Zonal DES
• See Deck’s presentation tomorrow
• He was the first to show me the MSD problem in a nonartificial situation (full 3D nozzle)
• The zonal idea:
– Designate RANS and LES zones, usually grid blocks
– Control RANS/SGS function directly, instead of letting the grid
density do that
– Fluid can flow from RANS to LES, and back
– LES may be activated for all separated regions, or only for one of
special interest (see other ONERA work on airframe noise)
• A good idea?
– It will add very much work in truly 3D cases,
and appears even harder in unstructured grids
– The blocks could instead be given widely different ∆z to steer DES
– We (and Menter & Kuntz) prefer a non-zonal method
Delayed DES
• Another solution to MSD
• Submitted to TCFD: Spalart, Deck, Shur, Squires, Strelets,
& Travin
• Other tricks (tried with Forsythe) were not powerful enough:
– Use grid aspect ratio, which “reveals” boundary-layer intent
– Create overshoot in d~ = f ( ∆, d )
• DDES is similar to the F2 fix of Menter & Kuntz
r q
• Essentials:
d
– Now, d~ = f ( ∆, d, νt, Ui,j )
– The model “refuses” LES function,
if it “believes” it is in a boundary layer
• First results:
t + Uij Uij
2 d2
1 ; tanh(8r ]3 )
d~ d ; f max(0 d ; C
)
fd
d
d
– Attached boundary layers are safe from MSD, unless ∆ <<< δ .
– LES function still takes place after massive separation
• Outlook: we hope DDES will be the new standard
DES
DDES corrects
Modeled-Stress Depletion
in attached boundary layer
RANS
DES97
DDES
Flat-plate boundary layer with severe x (and z) grid clustering
DDES does not prevent LES over
backward-facing step
Fd
ω
νt
DES97 and DDES over BFS
Swirl
surfaces
LES content is
not noticeably
damped
Extended uses of DES
• As a wall model in LES, see next slide
• A confusion is possible:
– Much work goes on in WMLES
– DES was used for WMLES
– The boundary has become blurred (notably in
DESider work!)
• Please do not call DES a method that cannot
provide Natural DES
– Specifically, the model must be able to treat an
entire boundary layer with RANS
• Natural DES and WMLES will be used in the
same flow field
– See DESFOIL slide
– This is preliminary
DES as wall model in LES
•
•
Nikitin et al in Phys Fluids, 2000
Study was run “with both hands tied:”
–
–
–
–
•
Pure DES formulas (very simple)
Rather coarse grids
Equal ∆x and ∆z
Systematic ∆y and ∆t refinement
Fine
grid
High Re
Reynolds number: wall and defect laws
Grid refinement from h/10 to h/20
Three codes
Huge ∆x+ and ∆z+!
Coarse grid
Slight disappointment:
– Modeled and resolved log layers do not
quite match in C (but κ is just fine)
– Grid refinement does not improve match
– Near-wall turbulence is weak and
elongated
•
Very
High
Re
Modeled log layer
Expected response to:
–
–
–
–
•
Resolved log layer
Remedies:
– Piomelli et al, random stirring near wall
– By NTS and Squires, highly secret…
DNS
S-A log layer
Visualization of WMLES in a channel
• Near the wall, the WMLES by DES:
– Generates “super-streaks”
– Fails to make a good use of the grid: 80 by 60 above
DESFOIL concept
• Discussed with Squires and Forsythe
– Jim made a preliminary run without stirring.
• Has potential to deploy WMLES in the difficult region
• Comparing to Mary’s LES:
– No DNS of the separation bubble transition
– Much wider domain for similar cost, no Reynolds-number limit
• The “stirring problem” has not been addressed yet!
• This will be an “exercise,” not a new everyday method
Non-challenging TBL
Separationtransition
within RANS
Laminar
Abrupt grid
refinement
and stirring
RANS
RANS
LES
settles
down
RANS
LES in
challenging
adverse
pressure
gradient
Improper uses of DES?
•
•
Anything 2D!
Anything with fewer than ~ 25 points in any direction
– In the LES region, cells far from isotropic are, at least, a waste
•
Anything without visualization of its LES content
– Simulations can well “default to RANS”
•
•
Any Airbus problem
The misuse of the claim that “DES is cheaper than LES”
– Only when boundary layer can be done in RANS instead of LES
• The difference is then very wide
– After separation, it makes no sense to “compare a 483 DES and a 643 LES!”
• The S-A SGS model is no smarter than pure SGS models
•
DES at Reynolds numbers that allow QDNS
– Really an improper interpretation
– DES cannot do better than LES,
and could justifiably do worse, because fv1 is mis-used.
– Doing well in these flows has a low priority (in my book)
•
Deliberate use of ambiguous grids in DES97
– However, grid refinement will reveal this problem
•
•
Combined NDES + WMLES without “stirring”
Combining DES with other RANS models than S-A is just fine
Improper use of LES!
• Run a cylinder at Re = 106, with current
resources.
• You are really doing Natural DES, with
Smagorinsky (or similar) as the RANS model!
• Results will be inaccurate, and very griddependent.
• Don’t start an LES project if you could predict
that doing it well is not possible for 30 years.
Ongoing Debate over ∆ (1)
• An LES issue, not only a DES issue
• Consider a structured grid for now: ∆x, ∆y, ∆z
• A “basic” LES, away from walls, has ∆x ~ ∆y ~ ∆z
– All definitions agree
• LES tradition is ∆ = ( ∆x ∆y ∆z )1/3
– This is clearly incorrect if the cells are very anisotropic, but the
small-scale turbulence is (statistically) isotropic (Kolmogorov)
– A definition such as ∆ = min ( ∆x, ∆y, ∆z ) would be absurd
• DES “tradition” is ∆ = max ( ∆x, ∆y, ∆z )
– In a Kolmogorov situation, the smaller of the ∆’s are wasted,
but the accuracy is preserved
• In Wall-Modeled LES,
– The grid becomes anisotropic: ∆y << ∆x ? ∆z
– The SGS model is influenced by ∆’s definition…
and often by many other changes.
– We are “playing” with a modified near-wall ∆
Ongoing Debate over ∆ (2)
• In separated flows,
– Breuer, Jovicic & Mazaev get better shear-layer transition with
( ∆x ∆y ∆z )1/3
– However, they have ∆x ~ ∆y << ∆z,
– and a shear layer aligned with the axes: d/dz << d/dx.
– Combining these two will be difficult in 3D geometries
– Obtaining transition in shear layers with an SGS model is a
notorious problem. It’s the DES Grey Area
– In jets, we have been disabling the SGS model.
• In unstructured grids:
– Both ∆ = ( ∆x ∆y ∆z )1/3 and ∆ = max ( ∆x, ∆y, ∆z ) can be
generalized using cell volume and diameter
– Using the distance between cell centroids is risky
• because the code may not keep track of the “logical” neighbor cell
Definition of ∆ in Unstructured Grids
• 2D example
– Triangular cells
– The logical ∆x is the distance from 0 to 5 (if using centroids)
– Cells 0 and 5 do not share a face, and many codes will pick
0 and 2
– The difference is not drastic, but it worsens MSD
Spalart-Allmaras revised by Edwards & Chandra
• The modifications were made to improve robustness
• No mention was made of changing results!
• The model can’t have ν = 0 any more!
• The modifications amount to a change in fw
• Edwards, 1997: “Yes, in general I did observe a slight lowering
of the Cf with the modified approach”
• The Cf change is around 2%
In SA
In EC
S + 2ed2 fv2 :
Se
Se
"
S
e
+ fv1
#1=6
6
cw3
g
6
cw3
:
1+
6
=
g
=
r
+
c
(
r
;
r ):
w2
6
e
2
2
g +
S d
tanh(r) g = r + c (r6 ; r ):
In EC rEC tanh(1)
EC
w2
EC
EC
In SA
r
e
fw
Spalart-Allmaras revised by Edwards & Chandra
fw function controls
skin friction through
its slope near r = 1
Outlook (1)
• DES stands as a:
– stable,
– simple,
– shared
approach to:
– High-Re separated flows (“natural DES”)
– Wall-Modeled LES.
• Principal “opportunities:”
– Natural DES
• Modeled-Stress Depletion
• Delayed DES appears to be a fair solution
– WMLES
• Log-Layer Mismatch
• Problem has been over-estimated
• Solutions are under study
– Combined NDES and WMLES
• Generation of LES content
• No easy solution in sight
Outlook: Principal “gripes”
• DES is too simple!
–
–
–
–
–
It uses a single velocity field and continuous formulas
Modeled and resolved stresses overlap
Desire to look at RANS-LES hybrids from scratch
“More theory must give more accuracy”
DES uses the two (only?) pillars of turbulence theory:
• Kolmogorov (energy cascade, statistical isotropy)
• Prandtl (law of the wall, l = κ y)
• Not the Reynolds-Stress-Transport equation
• DES does not “chase” a known filtered equation
–
–
–
–
LES region: filter is “about the size of the grid”
RANS region: filter is “much larger than wall distance (eddy size)”
Grey area: “model is evolving fast”, instabilities dominate
This makes “a priori” tests impossible
• However, these tests remain debatable (focus on stresses, or force, or
curl of force?)
– Serious grid refinement IS a relevant test of a DES study
Shear Stresses in Channel WMLES
Fine
Coarse
Modeled stress
• Modeled stress and resolved stress overlap
• This overlap layer shrinks as the grid is refined