High-Speed Boundary Layer Transition induced by a Discrete
Roughness element
Prahladh S. Iyer University of Minnesota
Currently at National Institute of Aerospace
Supported by NASA, AFOSR
67th NIA CFD Seminar, Hampton, VA Nov 3 2015
Acknowledgements
• Prof. Krishnan Mahesh, U Minnesota
• Dr. Suman Muppidi (currently at ERC/NASA Ames)
• Dr. Danehy and Dr. Bathel at NASA Langley
• MSI, TACC for computing resources
Roughness Laminar-Turbulent transition
Undesirable increase in heat transfer and drag.
RANS models over predict heat transfer.
Need for DNS/LES capability using unstructured grids.
MacLean et al. AIAA 2008-0641 Gibson et al. AIAA 2010-245
Motivation
Steps, gaps, joints, local/ machining flaws, tripping elements…
Rekk , Reθ/Ma correlations : scatter in data
Need for physics based models.
Berry et al., AIAA-2006-2922
Reda C. D., JSR (2002)
Motivation
Numerical details
• DNS algorithm • Comparison of DNS with LST
DNS of flow past a cylindrical roughness element
• Velocity profile comparisons with experiment DNS of flow past a hemispherical roughness element
• Qualitative Validation with experiment • Transition mechanism • Mean statistics
Effect of boundary layer thickness for Mach 3.37
• Small v/s large boundary layer thickness
Reynolds number correlating transition
Outline of presentation
Numerical Details
Park, N. & Mahesh, K. AIAA-2007-722
Numerical Details
MPCUGLES Solves compressible Navier-Stokes Equations on unstructured grids using a cell centered finite volume methodology.
2nd order accurate in space and time.
Park, N. & Mahesh, K. AIAA-2007-722
Numerical Details
Convective terms face reconstruction : • Green Gauss based gradient computation • Or simple average
Viscous flux splitting : • LSQ based gradient computation for incompressible part
LSQ or Green Gauss based reconstruction has better modified wavenumber properties compared to 4th order central difference
Park, N. & Mahesh, K. AIAA-2007-722
Numerical Details
Predictor-Corrector Time Integration : • 2nd order explicit AB2 time stepping in predictor step
• Characteristic filter based shock capturing in the corrector step based on the algorithm of Yee et al. (JCP, 1999)
• Harten-Yee TVD filter with Ducros sensor which is active only in regions of shocks.
Dynamic Smagorinsky Model and Compressible k-equation model (Chai & Mahesh, JFM 2012)
Applied to a range of complex high speed flows • High speed turbulent jets in crossflow (Chai, Iyer & Mahesh, JFM accepted) • Supersonic transition induced by distributed roughness (Muppidi & Mahesh, JFM 2012), shock-boundary layer interaction (Muppidi & Mahesh, AIAA 2011)
Supersonic boundary layer M = 4.5, Re = 1500
DNS initialized with
Unstable mode for ,
Periodic bcs used in streamwise direction.
100X50, 100X100, 100X200 and 100X300 grids used.
Grid has approximately 60 points within boundary layer. Representative of fine grid used in roughness simulations.
)(~)()( yqyqyq
25.0 002296.02274.0 i
Comparison of DNS with Linear Stability
001.0
DNS of flow past isolated cylindrical roughness element
Bathel, Iyer, Mahesh, Danehy et al. AIAA-2014-236 Iyer, Muppidi & Mahesh AIAA-2011-566
Mach 10 wind tunnel at NASA Langley used by Danehy et al. (2009) and Bathel et al. (2010)
Top surface of wedge simulated as a flat plate.
Wedge placed at various angles to the Mach 10 inflow to give different free-stream Mach numbers for the flat plate.
Mach 10 inflow
Experimental Setup
= 4740, k/δ = 0.64
Conditions match experiments by Bathel et. al. AIAA-2010-4998.
With and without upstream injection slot.
Wall temperature = 300 K, Free-stream temperature = 73.12 K
kukRe
Upstream injection
LU1/D Lu/D LD/D Lz/D H/D
Y 8.85 10.0 22 20 10
N 1.35 17.5 22 20 10
12.8M
Flow past a cylindrical roughness element
480 points around roughness, 30X100 points in injection slot.
13 and 16 million grid points respectively.
Grid Details
Shock produced by roughness element
High speed streaks
Inflectional profile
Flow remains laminar downstream of the roughness.
Density gradient, streamwise velocity and temperature contours shown in the figure.
Instantaneous Snapshot of flowfield
y (c
m)
y (c
m)
u (m/s) u (m/s)
u (m/s) u (m/s) u (m/s) u (m/s)
u (m/s) u (m/s)
x=5.01
x=11.37 x=10.10 x=9.15
x=8.51 x=7.86 x=5.93
y (c
m)
y (c
m)
y (c
m)
y (c
m)
y (c
m)
y (c
m)
Error bars obtained from Bathel et al. (AIAA-2010-4998)
x=12.62
Symmetry plane comparisons
u (m/s) u (m/s) u (m/s) u (m/s)
z (c
m)
z (c
m)
z (c
m)
z (c
m)
x=6.46
X=10.76 x=9.90 x=9.26
x=8.82 x=8.40 x=7.09
x=11.62
u (m/s) u (m/s) u (m/s) u (m/s)
z (c
m)
z (c
m)
z (c
m)
z (c
m)
Profiles taken at 2.1 mm from the wall.
Wall-parallel plane comparisons
DNS of flow past isolated hemispherical roughness element
Iyer & Mahesh J. Fluid Mech. (2013) Iyer, Muppidi & Mahesh AIAA-2011-0566 Iyer, Muppidi & Mahesh AIAA-2010-5015
3.37 9121 0.881 0.394
5.26 14190 1.842 0.481
8.23 16831 4.110 0.840
Simulation parameters match Danehy et al. (AIAA 2009-394).
Wall maintained at a constant temperature of 300 K.
kukRe
(10 D)
(10 D) (35 D)
(8.85 D)
MT
Tw
k
Problem Description
Coarse, medium and fine grids used with 16, 40 and 154 million grid points.
Grid convergence study performed.
Fine grid , Δx+=15, Δy+wall =0.6, Δz+=10 for Mach 3.37 case.
Grid Details
Contours of temperature/ density on bottom(DNS) compared with NO-PLIF images from Danehy et. al.
(AIAA-2009-394).
Qualitative behavior consistent between experiment and computation.
Unsteady structures appear closer to the bump for lowest Ma.
Mach 3.37 Mach 4.2 Mach 5.26
PLIF PLIF PLIF
DNS DNS DNS
Mach 3.37 Mach 5.26 Mach 8.23
DNS DNS PLIF
Qualitative comparison with experiment
Iso-contour of Q colored by u contours for Mach 3.37
Laminar boundary layer
Trains of hairpin vortices
Upstream separation
Turbulent wake
Overview of transition mechanism
Mach ReD ReD,wall D/δ*
3.37 18241 22728 11.507
5.26 28378 9258 6.442
8.23 33662 2208 2.924
Upstream vortex system : function of flow parameters.
Behavior qualitatively consistent with Baker’s results.
.
Baker, C. J., JFM (1979)
DuDRe
wall
wallD
Du
,Re
Upstream separation vortices
M∞ x,SP x,SP’ x,OSP’ z,max
3.37 9.6 -5.4 3.6 -4.5
5.26 5.9 -5.1 1.7 -3.0
8.23 1.7 -1.1 - -1.5
Upstream vortices wrap around to form counter-rotating streamwise vortices downstream.
Strength of streamwise vortices depends on vorticity in the laminar boundary layer.
SP OSP OSP’
Image vortices
Streamwise vortices in x=0 plane
Mach 3.37
Mach 5.26
Mach 8.23
Induced velocity
Image vortices
Induced velocity
Image vortices
Upwash
Downwash
Perturbation of the shear layer
Net upwash perturbs vortex lines => Hairpin vortices.
3 trains of hairpins initially.
Mach 3.37
Mach 5.26
Coherence of hairpin vortices
M∞ Vortex System
Shock Shear layer
3.37 strong weak strong
5.26 weak weak strong
8.23 weak weak Weak
Upstream vortex system, shock system and downstream shear layer : sources of unsteadiness.
Upstream vortex unsteadiness
Downstream shear layer unsteadiness Shock induced unsteadiness
Sources of unsteadiness
Z=0, 3D
Z=0, 2D
Incomp. , 2D
Shedding suppressed at supersonic speeds for the flow conditions under study.
Also observed by Chang & Choudhari (2011)
Shedding of hairpin vortices?
Spanwise inhomogenity in Ch contours..
Mean Wall Heat Flux
Spanwise inhomogenity in Cf contours.
Rise in Cf by a factor of 2 for Mach 3.37 and 5.26.
Mach 8.23 reaches laminar value far downstream.
Mean Skin Friction Coefficient
Mach 3.37
Mach 5.26
Comparison with turbulent boundary layer data
Z=0.5 Z=0
x=-15
No global oscillation.
Dominant frequencies in the upstream separation region.
Wall pressure spectra for Mach 3.37
Tw/Te=0.88 ReD=18241 ReD,wall=22728
Tw/Te=5.0 ReD=18241 ReD,wall=7420
Mach ReD ReD,wall
3.37 18241 22728
5.26 28378 9258
8.23 33662 2208
DuDRe
wall
wallD
Du
,Re
Local Reynolds Number correlating transition
Effect of boundary layer thickness for hemispherical roughness element
Iyer, Muppidi & Mahesh AIAA-2012-1106
M∞ = 3.37, Rek=4560 , T∞=340.48K
Isothermal wall condition: Twall=300K
All four cases appear transitional downstream.
δ/k = 0.4 δ/k = 1
δ/k = 4 δ/k = 8
Effect of boundary layer thickness
primary vortex
secondary vortex
Length scale of primary vortex roughly the same for all cases. Strength of secondary vortex decreases with increasing δ. Upstream separation length decreases with increasing δ:
δ/k=0.4
δ/k=1
ω z contours Streamlines upstream
δ/k=4
δ/k=8
δ/k du/dy|w
0.4 10.79
1.0 4.35
4.0 1.09
8.0 0.54
Upstream separation
Streamwise vortices perturb shear layer. Weak Off-symmetry plane (OSP) vortices for larger δ cases. Center of symmetry plane (SP) vortices moves away from wall with increasing δ.
δ/k=0.4
δ/k=1
ω z contours Streamlines
δ/k=4
δ/k=8
SP vortices OSP vortices
Streamwise cut 2D downstream of roughness
δ/k=0.4
Single train of hairpins for larger δ cases while multiple for lower δ.
Length scale of symmetry plane hairpins increases with increasing δ.
δ/k=1
δ/k=4 δ/k=8
Freestream
(M∞ = 3.37)
δ/k=0.4
Iso-contour of Q colored by u contours
δ/k=1
δ/k=4 δ/k=8
Hairpin vortices downstream of roughness
Dynamic/Koopman Mode Decomposition (Rowley et al. JFM 2009, Schmid JFM 2010)
],.........,,[ 0
1
0
2
00 xAxAAxxK m
• Consider m snapshots of data, {x0, x1, x2 …..xm}
Kcxcxcxcxcx mmm 11221100 ........• Express the last snapshot as a linear combination of previous snapshots,
• Compute the companion matrix C by minizing r and diagonalize it
aCa
• Eigenvalues of C, approximate those of A. The spatial eigenvector is given by v
],.........,,[ 1210 mxxxxK
)( n
kx
)........,,( 1210 mcccccm )1,....0,0( , TT ereKCAK
1
2
1
0
1000
.......1..
...........10
..........01
0000
mc
c
c
c
C
1 1 where j
iijTKTKav
Re St (DNS, CL) St (Koopman)
60 0.1465 0.1467
100 0.1701 0.1697
200 0.1856 0.1856
DMD: 2D Cylinder validation
Re=60 Re=100 Re=200
mode 1
mode 2
• DMD agrees well with the St measured from DNS. • Grid contains 20k points. 50 snapshots used with Δt=0.4 for all the cases
Dynamic Mode Decomposition(DMD) : δ/k=8
• Dominant frequency of St=0.088 from DMD matches observed frequency of the hairpin vortices. • 160 snapshots with dt=0.25.
St=0.088
4560 5682 175.1
4560 5682 111.2
1915 2386 55.9
1067 1330 39.3
9121 11364 247.6
9121 3710 105.5
kukkRe
Transition Strength of vortices Wall shear of unperturbed boundary layer
Friction velocity : wall shear of unperturbed boundary layer.
accounts for effect of boundary layer thickness and wall temperature.
wall
kwallk
ku
,Re
wall
k
ku
,Re
,Re k
37.3M
88.0/ TTw
5/ TTw
4.0/ k
1/ k
8/ k
4/ k
Reynolds number based on friction velocity
wall
wally
uu
DNS solver agrees well with Linear Stability Theory (LST). Flow past cylindrical roughness element at Mach 8.12
Velocity profile comparisons showed good agreement. Quantified uncertainties with measurement technique.
Flow past hemispherical roughness at Mach 3.37, 5.26 and 8.23
Qualitative comparisons agree with experiments. Proposed physical mechanism for transition: Roughness 3D Separation Perturbation of shear layer Hairpins Transition. Upwash v/s Downwash of vortices. Mechanism at high speeds differ from low speed shedding.
Effect of boundary layer thickness for Mach 3.37 Single train of hairpins for larger δ cases while multiple trains for lower δ. Koopman/Dynamic mode decomposition identified hairpin vortices with dominant frequency. Reynolds number based on friction velocity and wall viscosity correlates effect of
boundary layer thickness.
Summary
Current projects at NIA/NASA
1. Wall-modeled LES of separated flows using CharLES (Cascade Tech)
2. DNS of crossflow transition using high order spectral element code Nek5000 (Argonne National Lab)
Thank You
Effect of grid resolution (z=0 plane)
ρ
u
TKE
y
y
y
• Coarse, Medium and Fine grids
• Profiles at x=5, 15 and 25 downstream of the roughness element.
Effect of grid resolution
Grid convergence observed.
Smaller scales captured by the fine grid.
y+
uVD+
uVD+
z=0
z=0.5
x=30
u (m/s) u (m/s)
u (m/s)
z (c
m)
u (m/s)
x=8.51
y (c
m)
PLIF could give erroneous data near wall because of laser scatter (could use transparent wall)
Slightly Different Locations? z
(cm
)
x=6.46
Discrepancy caused by comparing wrong spatial locations and spatial resolution issue
• Comparing at wrong spatial location. Uncertainty in position ~ velocity*300ns(0.39 mm)
• Laser sheet position (+/- 0.5 mm)
• Effect of upstream injection of NO.
x=6.46
x=6.46
z (c
m)
Figure illustrating MTV technique
* Suggested by Dr. Danehy, NASA Langley
Uncertainties associated with experiment*
