P' Spalart

1
Turbulence Are We Getting Smarter?

• P. Spalart
• Boeing Commercial Airplanes
• Training by NASA
• Many CFD runs by and discussions with
• M. Strelets, M. Shur, K. Squires

2
If were not smarter, in what sense?

• RANS models appear frozen at their 1992 level
• S-A and SST rule in Aerospace, with minor
  tweaks
• We lost the Karman constant!
• Experiments challenge its accepted values and
  each others
• Direct Numerical Simulation fails to find the
  log law
• Models are rebellious around laminar regions
• S-A can refuse to wash away eddy viscosity
• SST can refuse to transition
• Setting inflow values of turbulence quantities is
  delicate
• Turbulence theories come and go
• Examples Power laws RNG Lie groups
• LES is coming strong but is it smart?

3
RANS models frozen at their 1992 level

• This is meant in practical CFD
• Research Community spent much effort on
• Reynolds-Stress Transport models
• Algebraic Reynolds-Stress models
• Realizable, two-component limit, elliptic effect,
  etc.
• Some propagated in vendor CFD codes, but none
  won workshops
• Separation prediction is paramount
• The elaborate models still do not win at that
  game
• They win in some vortex flows, e.g. the spheroid,
  but SARC is not bad
• Extra CPU power is going into finer grids and
  complexity
• Recent drag workshop (courtesy E. Tinoco)
• We are far from grid overkill, even for simple
  wing-body case
• Grid differences exceed model differences
• The worst flaw in each model is still not clear
  (unlike for k-e)
• Did Menter and Spalart stop working?

4
F6 WB w/wo FX2 Total Drag Convergence
Tinoco Charts at the Drag-Prediction Workshop
(FX2 is a fairing at the
wing root)
SST and SA have very different trends for drag
vs. grid count
5
F6 WB w/wo FX2 Skin Friction Drag Convergence
6
F6 WB Separation Bubble on Wing Turbulence
Modeling
Overlay of Computed Streamlines, SST Turbulence
Model, Re5M
Edge of Separation Bubble on Wing
It would be fun to test the nonlinear
constitutive relation, for the corner flow (or a
Reynolds-Stress model)
Wind Tunnel Oil Flow Photo, Re3M
7
Did Menter and Spalart stop working?

• No.
• Turbulence research is like nicotine
• Both worked on
• Curvature and rotation corrections
• RANS-LES hybrids DES and SAS
• There is also work on
• Wall roughness
• Compressibility
• Nonlinear constitutive relation
• Over-tripping
• More general wall functions
• R. Langtry with Menter created a
  transition-prediction method by transport
  equations that looks like dynamite

8
If we are not smarter, in what sense?

• RANS models appear frozen at their 1992 level
• S-A and SST rule in Aerospace, with minor
  tweaks

• We lost the Karman constant!
• Experiments challenge its accepted values
• Direct Numerical Simulation fails to find the
  log law

9
We Lost the Karman Constant in Experiments

• In the Good Old Days
• The accepted values were 0.40 to 0.41
• Probably dominated by the Stanford Olympics
• Although k-e gave 0.433 all along!
• Direct Numerical Simulation (DNS) seemed to
  agree (more on this)
• The Superpipe experiments gave 0.436
• And later 0.42 (smaller Pitot tube, rethink of
  corrections, etc)
• The NDF and KTH boundary-layer experiments gave
  0.385 or 0.38
• The two teams are talking
• Still, they dont use the same instrumentation
• The variation of Cf with Reynolds number is more
  conclusive than
• U profiles

If k is different in these two flows, Ill quit!
10
We Lost the Karman Constant in Experiments

• k controls the trend of Cf versus Re
• Experiments, even ancient,
• disagree with 0.40,0.41 when Cf is
  examined over a wide range
• Inject 0.436 into a model, and Cf goes the wrong
  way in boundary layer
• The rule used by Boeing since 1961
• agrees with the latest data and 0.38!
• The 2 difference in Cf means about
• 1 airplane drag
• S-A model
• matches the NDF-KTH log law with k 0.38 and C
  4.1, and also the CTTM point,
• by adjusting to k 0.38,
• cv1 6.08, cw2 0.58
• -- A better fv1 is in the works practical
  impact will be slight

(Collaborative Testing of Turbulence
Models, Bradshaw-Launder-Lumley)
Wings, bodies
10
11
Effect of k 0.38 on RAE2822 Flow is Minimal
Case 10, M0.75, arecom2.57

Note, Cf is higher with 0.38 because the Reynolds
number is not very high about 4 106 to the shock
12
Guidance for a new fv1 in S-A model

• fv1 is reverse-engineered from velocity profiles
• Agreement between DNS and experiment is
  compelling up to y 200
• Very near the wall, trust DNS
• For high Reynolds number, trust experiment
• Including k 0.38
• Skin-friction was strongest argument in favor
• Its still a big jump!

NDF-KTH B-layer
Hoyas-Jimenez channel
13
We Lost the Karman Constant in U

• Define a local k
• as d ( log y ) / d U
• it is constant in a log layer
• in theory, this plateau stretches with Reynolds
  number
• Experiments show this, but have noise in k
• NDF and KTH Experiments also have an overshoot
  near y 80
• Which is nothing to worry about
• It can be erased by inserting ( y 10 ) instead
  of y , which is entirely justified, as the
  virtual origin does not have to be y 0
• DNS
• Hoyas Jimenez 2006 reached Ret 2000 in
  channel, but
• overshoot to 0.43, and have no plateau at
  all!
• Spalart 1988 thought he had just reached plateau
  (_at_ 0.406) in a BL
• Johnstone Coleman 2006 also have overshoot in
  the Ekman layer
• RANS models
• S-A behaves as expected (while settling a bit too
  late near y 80)
• SST does not, at relevant Reynolds numbers

14
Local Karman Constant

• Expected qualitative behavior
• Channel flow

Increasing Re
15
Velocity Profile Overshoots the Log Law

Courtesy Prof. Nagib and Mr. Kapil
16
We Lost the Karman Constant in DNS

• Expected qualitative behavior
  High-Reynolds-number DNS

Disaster struck
Increasing Re
17
We Lost the Karman Constant in DNS

• If not the Law of the Wall! We seem secure only
  to y 200

BL-channel and DNS-expt agreement
Rq 1410, 1988
18
We Lost the Karman Constant in SST (k-w)

• S-A model closer to DNS and experiment than SST
  (k-w) (in which k 0.406)
• Not having an fv1 does not pay off. This
  presentation magnifies differences

19
If we are not smarter, in what sense?

• RANS models appear frozen at their 1992 level
• S-A and SST rule in Aerospace, with minor
  tweaks
• We lost the Karman constant!
• Experiments challenge its accepted values
• Direct Numerical Simulation fails to find the
  log law

• Models are rebellious around laminar regions
• S-A can refuse to wash away eddy viscosity
• Transition Creep
• SST can refuse to transition
• Setting inflow values of turbulence quantities
  is delicate

20
Rebellious Models S-A Transition Creep

• S-A is supposed to go turbulent from either
• A turbulent inflow value, n 3 n or more, FT
  mode (more soon)
• A trip
• Separation Trip-Less mode
• I am not fond of production blanking
• A forward creep is seen
• In attached boundary layers
• When eddy viscosity is supposed to wash away
  because
• run was started in FT mode, and then switched to
  laminar inflow
• trip creates eddy viscosity where desired
• Causes, remedies, actions
• Eddy viscosity dynamic range is huge
• No conclusive remedy known yet, other than very
  fine x grid spacing, and details of
  discretization
• Users need to plot S-A Turbulence Index (0
  laminar, 1 turbulent)

21
Rebellious Models S-A Transition Creep

• This is a tripped case
• Eddy viscosity rises by more than a factor of 10
  within one cell, twice
• Any averaging between values lt 1 and values O(10)
  defeats the ft2 term, and production starts. The
  cb2 term is also a threat.

22
Rebellious Models Refusing to Transition

• First, S-A
• Rumsey reports trouble at this meeting
  (AIAA-2006-3906)
• Both balking and non-uniqueness
• It is with n / n 1.341946
• a NASA value derived from nt / n 0.009
• itself derived from RT 0.1 in Baldwin-Barth
• The trouble goes away with inflow n 3 to 5 n
  (as recommended)
• FT behavior is easily obtained
• Rumsey also advocates setting ct3 to 0, which is
  OK if FT
• Two-equation models
• Again, Rumsey has issues with balking
• He wanted FT behavior
• Again, baseline has inflow nt / n 0.009
• Inflow nt / n 1.294 helps a little
• k, e and nt decay considerably during the
  approach (more soon)
• Finer grids make the problem worse

23
Rebellious Models Setting Inflow Values

• First issue desirable ambient values (near the
  wing)
• Laminar regions
• nt needs to be well below n (but Official SST
  has no trip term)
• No laminar regions, FT
• nt may be well above n!
• Only the Reynolds number based on flap gap or
  leading-edge radius and nt needs to be large
• The eddy viscosity must be smaller outside the
  boundary
• layer than inside, so that its value does
  not control the BL
• This is not satisfied by the inflow values
  recommended by some
• CFD vendors
• This implies k cannot have a realistic
  ambient value, such as
• 10-4 U2, giving 1 FST (time scale has
  grown too much)
• Second issue reverse-engineer inflow values
• With S-A, there is no distinction between inflow
  and ambient values

24
Rebellious Models Setting Ambient Values

• Courtesy S. Allmaras
• McDonnell-Douglas three-element airfoil
• Boeing GGNS adaptive code, S-A model
• Chord Reynolds number 9 x106
• FT mode requesting transition in all B-layers
• Inflow n /n 5, 500, and 5000!
• Gap Reynolds number 40,000, 400, and 40
• Only highest value has high impact

25
Setting Ambient Values. Eddy Viscosity

• nt / n 5
  nt / n 5000

26
Setting Ambient Values. Velocity

• nt / n 5
  nt / n 5000

27
Setting Ambient Values. Eddy Viscosity

• nt / n 5
  nt / n 5000

28
Setting Ambient Values Lift

• Lift is seriously affected only once ambient nt /
  n is 5000
• Re based on chord and ambient nt is then 2000

29
Rebellious Models Setting Inflow Values

• Reverse-engineer inflow values with two equations
• Use the desired ambient values, and the decay
  laws
• 
  linear growth
• 
  rapid decay
• 
  slower decay
• where x is the distance since the inflow
• These place limits on the achievable ambient
  values, most notably for the time scale k / e
  
• This is work in progress
• Hoping to pursue with Rumsey
• Strelets and Menter groups do not have severe
  problems
• CFD code manuals often not steering users too well

30
If we are not smarter, in what sense?

• RANS models appear frozen at their 1992 level
• S-A and SST rule in Aerospace, with minor
  tweaks
• We lost the Karman constant!
• Experiments challenge its accepted values
• Direct Numerical Simulation fails to find the log
  law
• Models are rebellious around laminar regions
• S-A can refuse to wash away eddy viscosity
• SST can refuse to transition
• Setting inflow values of turbulence quantities is
  delicate

• Turbulence theories come and go
• Examples Power laws High-Order log laws RNG
  Lie groups

31
Turbulence Theories Come and Go

• Power laws for the velocity profile
• Nostalgia value the U y1/7 law of the 1930s
• Physical view of outer layer is not
  Galilean-invariant
• Incompatible with classical thinking (inner and
  outer layer)
• Incompatible with all prevailing
  transport-equation turbulence models
• Rapidly defeated by roughness, sliding walls,
  etc.
• Not supported by data
• Experimental, or DNS
• as a layer that expands with increasing Reynolds
  number
• Higher-Order concepts than the wall-and-defect
  law
• No rigorous basis, or prospects outside the
  simplest of cases
• We are not producing Matched Asymptotic
  Expansions of a known equation. We only have a
  large parameter the Reynolds number
• Re-Normalization Group Lie Groups
• Ostensibly, pure theory
• Very hard to follow, for me
• Not supported by expanding layers either e.g.,
  the exponential profile
• Does RNG k-e model amount to more than
  dimensional analysis?

32
If we are not smarter, in what sense?

• RANS models appear frozen at their 1992 level
• S-A and SST rule in Aerospace, with minor
  tweaks
• We lost the Karman constant!
• Experiments challenge its accepted values
• Direct Numerical Simulation fails to find the
  log law
• Models are rebellious around laminar regions
• S-A can refuse to wash away eddy viscosity
• SST can refuse to transition
• Setting inflow values of turbulence quantities
  is delicate
• Turbulence theories come and go
• Examples Power laws Lie groups

• LES is coming strong but is it smart?
• And what about DNS?

33
LES is Coming Strong, but is it Smart?

• LES is coming to real-life CFD
• Largely as a component of hybrid RANS-LES
  approaches, such as DES
• Pure LES of a wing remains scheduled for 2045
• Only LES can compute large-scale unsteadiness
  well
• Its excellent for jet noise, bluff bodies, and
  cavity flows
• 3D URANS is
• not powerless
• not very predictable
• not responsive to grid refinement. VLES is not
  a sound concept
• LES should have been called Large-and-Medium-Eddy
  Simulation
• LES conflicts with shock-capturing
• Not in the right hands!

34
LES is Coming what about Shocks?

• Shock capturing requires some dissipation
• In the NTS code, run by Shur, it works!

• LES requires low enough numerical dissipation
• This has slight upwind bias and van Albada
  limiters
• The shocks are rather weak

35
DNS is Stronger now, but Smarter?

• Hoyas Jimenez, 2006 Phys Fluids
• Some of the fluctuation intensities do not
  scale well in wall units.
• Spalart, 1987 JFM
• The scaling of turbulent quantities is compared
  with accepted laws, and the significant
  deviations are documented.
• Not referenced by HJ

u
w
v
36
Back to Work?

• RANS models frozen in time
• Having two is much better than one
• Offer version with modern k, primarily for skin
  friction at very high Re
• Offer early separation and late separation
  versions?
• Shock-induced and low-Mach separation may have
  different preferences
• Avoid proliferation of versions
• DES removes some of the burden from RANS
• Look for great new players, and help them
• Karman constant
• Firming up would be so, so nice!
• Im leaning towards 0.38, based on Boundary-Layer
  Cf
• DNS is stronger and less naïve in 2006 than 1986,
  but the goal has moved
• RANS models rebellious
• Confirm two-equation approach decay behavior in
  practice
• Establish consensus on actual requirements for
  ambient values
• Combat Transition Creep, spread transition
  control in Navier-Stokes CFD
• LES