This slide presentation reviews the use of Detached Eddy Simulation (DES) of hypersonic transistion. The objective of the study was to investigate the feasibility of using CFD in general, DES in particular, for prediction of roughness-induced boundary layer transition to turbulence and the resulting increase in heat transfer

Barnhardt, M.

Candler, G.

Yoon, S.

NASA Technical Reports Server

1 
National Aeronautics and Space Administration 
Detached Eddy Simulations of 
Hypersonic Transition 
S. Yoon and M. Barnhardt 
NASA Ames Research Center 
G. Candler 
Univ. of Minnesota 
The 6th International Conference on Computational Fluid Dynamics 
St. Petersburg, Russia 
July 12-16, 2010 
ICCFD6_yoon  2 
Objective 
• Investigate the feasibility of using CFD in general, DES in 
particular, for prediction of roughness-induced boundary layer 
transition to turbulence and the resulting increase in heat transfer 
STS-114 (July 2005) 
  Threat of overheating the delicate RCC wing leading edges was real. 
https://ntrs.nasa.gov/search.jsp?R=20110011022 2019-08-30T15:29:06+00:00Z
2 
ICCFD6_yoon  3 
Hardware 
• NASA Advanced Supercomputing Facility enables fine-grid 
unsteady turbulent flow simulations. 
Pleiades 
SGI ICE 
56,832 Intel Xeon Cores 
673 TFlops, 75 TB Memory 
ICCFD6_yoon  4 
Software 
•  US3D code – Unstructured, parallel, finite-volume Navier-Stokes 
solver for thermo-chemical non-equilibrium hypersonic flows 
•  Detached Eddy Simulations (or WMLES) – Hybrid RANS/ LES 
approach 
•  Optional low-dissipation numerics 
Wind tunnel model (1 mm high) compared 
with the Shuttle trip (6.35 mm high)                                                
Unstructured hexahedral grid 
near the trip 
3 
ICCFD6_yoon  5 
  
€ 
∂U
∂t + ∇⋅(
r 
F −
r 
F v ) = W
€ 
F = F+ + F− = R−1Λ+RU + R−1Λ−RU
€ 
Fi+1/ 2 = (R−1Λ+R)iUi + (R−1Λ−R)i+1Ui+1
Inviscid Flux Evaluation 
€ 
Fi+1/ 2 = (R−1Λ+R)i+1/ 2Ui + (R−1Λ−R)i+1/ 2Ui+1
Navier-Stokes equations for a 
mixture of species in 
conservation law form 
Steger-Warming Flux Vector Splitting 
At a cell face 
Modified Steger-Warming Flux Vector Splitting 
€ 
Λ± = (Λ± Λ )/ 2
Lower 
dissipation! 
ICCFD6_yoon  6 
€ 
Fi+1/ 2 =
1
2(R
−1ΛR)i+1/ 2(Ui+1+Ui )+
1
2(R
−1Λ R)i+1/ 2(Ui+1−Ui )
€ 
wi+1/ 2 = 1−
1
2
1
(5δp)2 +1
 
 
 
 
 
 
Modified Steger-Warming Flux 
Roe flux form 
Original Steger-Warming Flux 
Roe Flux 
For shock waves 
For smooth flows 
Using a pressure dependent weight 
Baseline 
flux scheme 
High-order fluxes are obtained using the MUSCL approach 
with a weighted least-squares method to compute gradients. 
convection dissipation 
4 
ICCFD6_yoon  7 
€ 
(ρku 'S)f
f
∑ = 12f
∑ (uiui+1+ vivi+1+ wiwi+1)(ρu 'S)f
€ 
di+1/ 2 =α
1
2 (R
−1ΛR)i+1/ 2(Ui+1 −Ui)
Low Dissipation Flux 
•  Existing low-dissipation schemes to predict small turbulent eddies: 
-  Skew-symmetric form to reduce the amplitude of the aliasing errors 
-  Entropy function for secondary conservation law 
•  Present approach: Kinetic energy 
-  Kinetic energy transport eq. derived from density and momentum eqs. 
-  Combined with internal energy:  
Kinetic energy consistent flux 
Dissipative term from the modified Steger-Warming flux 
  
€ 
α =
∇⋅
r u ( )2
∇⋅
r u ( )2 + r ω 2
€ 
ρE = ρCvT +
ρ
2 u
2
ICCFD6_yoon  8 
€ 
(I + Ai+1/ 2, j+ − Ai−1/ 2, j− + Bi, j+1/ 2+ − Bi, j−1/ 2− )δUi, j = Hi, j
€ 
+Ai−1/ 2, j+ δUi−1, j − Ai+1/ 2, j− δUi+1, j + Bi, j−1/ 2+ δUi, j−1− Bi, j+1/ 2− δUi, j+1
Implicit Time Integration 
Point Relaxation 
For laminar sublayers only 
(Modified Steger-Warming flux) 
Line Relaxation 
Data-Parallel Relaxation 
Baseline Scheme 
€ 
Bi, j+1/ 2− δUi, j+1+ (I + Ai+1/ 2, j+ − Ai−1/ 2, j− + Bi, j+1/ 2+ − Bi, j−1/ 2− )δUi, j − Bi, j−1/ 2+ δUi, j−1 = Hi, j
€ 
−Ai+1/ 2, j− δUi+1, j + Ai−1/ 2, j+ δUi−1, j
€ 
(An
~
− Cn
~
) δUk = H n− Cn
~
δUk−1
€ 
δUn+1 = δUk max
•  Original Gauss-Seidel not parallelizable 
•  Replace the G-S sweeps with a series of 
point Jacobi-like iterations or a series of line 
relaxations. 
•  Second order dual time stepping (KEC flux) 
5 
ICCFD6_yoon  9 
€ 
Dρ ˜ ν
Dt = ∇⋅(
1
σ
µ∇ ˜ ν )+∇⋅( 1
σ
ρ ˜ ν∇ ρ ˜ ν )+ cb2
σ
∇ ρ ˜ ν ⋅ ∇ ρ ˜ ν + cb1 ˜ S ρ ˜ ν − cw1 fwρ(
˜ ν
d )
2
Detached Eddy Simulation 
Spalart-Allmaras 1-eq. model with compressibility correction 
diffusive transport production 
destruction 
•  RANS approach over-predicts the turbulent dissipation levels in separated 
flow regions. 
•  DES introduces a new length scale 
-  Model behaves like a subgrid scale model for LES away from the wall. 
-  Wall-Modeled LES 
€ 
˜ d = min(d ,CDESΔ)
ICCFD6_yoon  10 
Test Case 
NASA LaRC Mach 10 wind tunnel experiment by Danehy et al. 
Flow conditions: Minf = 9.93, Rek ~ 6,000, Tinf = 51.3K, Tw = 308K 
Laminar 
Flow 
BLT Trip Streak 
Instabilities 
Transition Turbulent 
Flow 
6 
ICCFD6_yoon  11 
Grid Refinement Study 
Coarse grid (15 M cells) 
solution using the modified 
S-W flux 
Medium grid (40 M cells) 
solution using the modified 
S-W flux 
Fine grid (44 M cells) 
solution using the modified 
S-W flux (temperature 
contours) 
Grid points redistributed 
(grid density 2x) 
Grid requirements for DNS: 
1B cells to resolve Kolmogorov dissipative scales  
ICCFD6_yoon  Your Title Here 12 
Thank You. 
Laminar Flow 
BLT Trip 
Formation of Vortices 
Transition 
Vortex Breakdown/ 
Turbulence 
Te
m
pe
ra
tu
re
 C
on
to
ur
s:
 B
lu
e 
Pl
an
es
 (a
t 3
0h
, 6
0h
, a
nd
 8
5h
 fr
om
 th
e 
tr
ip
) a
re
 
pe
rp
en
di
cu
la
r t
o 
th
e 
ho
riz
on
ta
l p
la
ne
 (a
t 0
.5
h 
fr
om
 th
e 
w
al
l; 
h 
= 
tr
ip
 h
ei
gh
t) 
 
Fl
ow
 
Fine grid solution using the KEC flux 
7 
ICCFD6_yoon  13 
KEC Flux Solutions 
Fine grid solution using KEC flux with 
DES turbulence model 
Fine grid solution using KEC flux without a 
turbulence model (ILES?) 
  The accuracy of the turbulent flow solutions is driven primarily 
by the grid resolution. 
ICCFD6_yoon  14 
Side Views 
Temperature 
Turbulent Viscosity 
8 
ICCFD6_yoon  15 
Top Views 
1.0 mm above 
the wall 
0.75 mm above 
the wall 
0.5 mm above 
the wall 
ICCFD6_yoon  16 
Top Views (continued) 
0.05 mm above 
the wall 
0.25 mm above 
the wall 
0.1 mm above 
the wall 
9 
ICCFD6_yoon  17 
Comparison 
0.5 mm above the wall 
Experiment 
Computation 
ICCFD6_yoon  18 
Formation of Upstream Vortices 
At the center of 
the trip 
3 mm from the 
center of the trip 
4 mm from the 
center of the trip 
(near the leading 
edge) 
10 
ICCFD6_yoon  19 
Conclusions 
•  DES/ WMLES/ Hybrid RANS-LES can be a useful tool for 
predictions of hypersonic boundary layer transition to 
turbulence triggered by an isolated roughness element. 
•  It is necessary to use the low-dissipation kinetic energy 
consistent scheme on a sufficiently fine grid for an accurate 
simulation of transition. 
•  Accuracy of the turbulent flow solutions is driven primarily by 
the grid resolution. 
•  Interaction of vortices leads to vortex breakdown and hence 
turbulent flow. 
•  Computational results agree well qualitatively with the 
experimental observations. 
ICCFD6_yoon  20 
Acknowledgments 
•  Research supported by NASA Fundamental Aeronautics Program 
•  US3D developed under joint support of AFOSR and NASA NRA 
•  Computing resources provided by NASA Advanced 
Supercomputing Division 


Detached Eddy Simulations of Hypersonic Transition

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