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Investigation of 3D Shock-Boundary Layer Interaction: A Combined Approach using Experiments, Numerical Simulations and

Stability Analysis Jesse Little and Hermann Fasel

University of Arizona

Andreas Gross New Mexico State University

AFOSR AT and T2 Review July 15, 2015

1

Introduction

• History – Proposal submitted in response to 3D SBLI call in 2013 – 1 year $75k seed grant awarded in July 2014 – Year 1 of full proposal funded TBD

• Presentation Outline – Plans for the full effort – Accomplishments with seed grant funding – Future Work

• Acknowledgements – Post-doc: Jayahar Sivasubramanian – Graduate Students: Robyn Dawson-Ruiz, Jared Hainsworth

(SMART) – Undergraduate Students: Lucio Cota, George Gudgeon,

Clark Pederson

2

Background and Motivation

• Nominally 2D SBLI has been studied extensively in recent years with substantial focus on low frequency unsteadiness. Video

• Arguments for both upstream and downstream mechanisms are compelling and seem to be somewhat reconciled although issues remain (Clemens and Narayanaswamy, 2014). • Questions of if/how the existing understanding for the 2D case

carries over to 3D have never been addressed.

3

Dussauge et al. 2006

Background and Motivation

• Swept SBLIs display cylindrical or conical similarity.

• Unsteadiness observed in nominally 2D SBLI carries over, but freq↑ amp↓.

4

Settles and Teng, 1984

Settles and Kimmel, 1986

Objective

• Understand the relevant hydrodynamic instability mechanisms (or lack thereof) that govern the interaction of a turbulent boundary layer with a swept shock. – Does existing understanding of 2D case carry over? – How does unsteadiness evolve in complex 3-D interactions? – Basic analysis of the underlying physics is missing for 3D SBLI.

5

Schmisseur, 2014

Flow Field

• Swept oblique impinging shock • Removes instabilities

associated with geometric curvature.

• Avoids complexity associated with reattachment of the boundary layer on the shock generator.

• Fundamental physics can be investigated without any geometry bias

• Gap in literature

6

Incoming Flow

Impinging shock location

Tunnel Wall

Previous Research

• Holden (1984) investigated swept impinging SBLIs and compared to swept compression ramp results from Settles (1984)

7

Holden Mach 11, 15o wedge, 0-45o sweep • Only cylindrical similarity • Interaction length (Li) slightly

decreased with sweep (approximately linear)

Settles • Mach 2.95, 16o ramp, 0-40

degree sweep • Cylindrical similarity until critical

sweep angle, then conical • Li asymptotically increases until

transition to conical then decreases

Holden (1984)

Settles and Teng (1984)

Approach

• Experiments: Simultaneous spatially and temporally resolved measurements • Tomo-PIV for select cases

• Computations: Highly accurate numerical simulations • DNS and LES/RANS for low/high

Re select cases respectively • Theory and Analysis: Local and

global stability analyses from experiments and computations • Connect fluid dynamics and

underlying flow instabilities. • Analyze energy fluxes between

the basic flow and the various instability modes

8

Humble et al. 2009

Humble et al. 2009

Approach

• Experiments take the lead in defining “select” cases • Mach 2-4, 12.5-15o wedge, 0-45o sweep • Reϴ≈6400 and 1500 for Mach 2.3

• Select Cases 1. Unswept interaction (reference case) 2. Swept interaction with cylindrical similarity 3. Swept interaction with conical similarity • Turbulent separated cases are a focus, but transitional and

incipient cases may also be examined. • Employ passive and active flow control as diagnostic tools for

identifying/investigating relevant instability mechanisms. • Investigate the use of selective forcing (steady and unsteady)

to control energy fluxes between modes and determine effect on mean flow and large-scale unsteadiness.

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Outcomes

• Fundamental physics-based understanding of the underlying instability mechanisms governing 3D SBLI problems.

• Possibilities for altering the energy fluxes between instability modes such that certain modes are suppressed or enhanced.

• Guidance for ongoing flow control research aimed at, e.g., a suppression or mitigation of the dangerous low-frequency oscillations.

• Guidelines for the design of high-speed atmospheric vehicles with reduced structural fatigue loading and reduced surface heat fluxes.

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1 Year Seed Grant: Setting the Stage

• Establish tools for extracting the relevant flow physics of SBLIs for both experiments and computations.

• Perform unswept and swept SBLI experiments to provide insight into the open questions in literature.

• Modify/validate an existing high-order accurate DNS code to allow for use in SBLIs.

• Begin process of sorting out the interesting cases for future fully resolved 3D DNS and tomographic PIV.

• Products: 3 AIAA conference papers and 1 MS thesis

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Incoming Flow, U∞

Impinging shock location, Xo

x0*

z0

y0

x1*

z1

y1

x2*

z2

y2

PIV Measurement Planes

Tunnel Wall

3/8”

1.5” 1”

Z = 0.44

Z = 0.22

Z = 0

Incoming Flow, U∞

Impinging shock location, Xo

x0*

z0

y0

x1*

z1

y1

x2*

z2

y2

PIV Measurement Planes

Tunnel Wall

3/8”

1.5” 1”

Z = 0

Z = 0.22

Z = 0.44

Z normalized by span of shock generator

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• Mach 2.3, 15 degree wedge • X* normalized by the interaction length

in each plane: 𝑥𝑥∗𝑛𝑛 ≡ (𝑥𝑥 − 𝑋𝑋0𝑛𝑛) 𝐿𝐿𝑛𝑛⁄

Experiments

Experiments: Mean Flow v/U

• Interaction region shrinks with increasing sweep • Conical similarity in the 40o case • Recirculation region near x*=-0.25 • Intensity of negative v/U increases with Z*, in the 40o case

Unswept 22.5 degree sweep 40 degree sweep

z* =

0.4

4

z*

= 0

.22

z*

= 0

13

Experiments: Mean Flow v/U (mirror) Unswept 40 degree sweep

z* =

0.4

4

z*

= 0

.22

z*

= 0

14

• Confirms trends seen in initial experiment • Interaction region shrinks with increasing sweep • Conical similarity in the 40o case • Intensity of negative v/U increases with Z*, in the 40o case • Conclusion: Conical similarity is observed for incident swept shocks

Summary of 1 Year Seed Grant Results: Experiment

• Cylindrical and conical similarity are present – Cylindrical at 0o and 22.5o, Conical at 40o

– Existence of both similarity types agrees with trends seen in compression ramps

• Interaction lengths decrease with sweep angle for both similarity types – Decrease is at a faster rate for conical similarity – Decreasing interaction length agrees with Holden, but is in

contrast with Settles and other compression ramp studies

• All cases show high probability of separation in mean • Velocity profiles in the separated region show 3D

effects which generally increase with sweep

15

16

• In-house developed high-order accurate compressible Navier Stokes solver

• Solves the Navier Stokes equations in cartesian, conical and cylindrical generalized co-ordinates

• Numerical Method – Time integration: 4th-order Runge-Kutta – Spatial Discretization

• Grid Centered standard finite difference stencils with upwinding for convective fluxes in x and y-direction1

• Convective fluxes are split using van Leer’s splitting2 • High-order Central differences for viscous terms in x and y-

direction • In the z/φ - direction option between:

– Pseudo-Spectral approach using Fourier-modes – High-order Compact Finite Differences

• High-order shock capturing capabilities (5th order WENO)

• Robust and efficient immersed boundary method capabilities

• Validated and applied to investigate several transitional and turbulent compressible flow problems

1 Zhong, X., 1998, “High-Order Finite-Difference Schemes for Numerical Simulation of Hypersonic Boundary-Layer Transition,” J. Comp. Phys. 144, 662-709. 2 van Leer, B., 1982, “Flux--Vector Splitting for the Euler Equations,” In International Conference on Numerical Methods in Fluid Dynamics, vol. 170, pp. 507-512, Springer-Verlag.

Compressible Navier-Stokes Solver Oblique breakdown on a cone at Mach 3.5

Turbulent boundary layer at Mach 6.0

SBLI at Mach 2.0

Streamwise wall pressure distribution

Code Validation: Results • Wall pressure show the rapid

changes near the separation and reattachment region and a pressure plateau in the bubble region

*Sansica, A., Sandham, N. D., and Hu, Z., “Stability and Unsteadiness in a 2D Laminar Shock–Induced Separation Bubble,” AIAA-2013-2982, 2013.

Streamwise skin friction distribution

• As expected the results show the rapid changes near the separation and reattachment region

17

density

Code Validation: Results

• Shock wave impinges on the laminar boundary layer, causes the flow to separate • Oblique shocks, compression waves in the separation and reattachment regions and

an expansion fan emanating from the top of the bubble are visible

pressure

density with sonic line density with streamlines

`Asymmetric bubble`

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Linear Stability Investigations: 2D Disturbances

Without SBLI

With SBLI

• Low amplitude pulse disturbances with a broad spectrum introduced into the boundary layer

• Streamwise distribution of wall pressure amplitude indicates that the 2D disturbances are strongly amplified in the presence of SBLI

Solid line: without SBLI Dashed line: with SBLI

F = 6.3837E − 5

F = 7.4476E − 5

F = 8.5116E − 5

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Linear Stability Investigations: 3D Disturbances

F = 5.3197E − 5

F = 6.3837E − 5

F = 7.4476E − 5

Solid line: without SBLI Dashed line: with SBLI

Without SBLI

With SBLI

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• Pulse for spanwise wave number β*=0.9/mm (most amplified wavenumber at impingement location)

• Streamwise distribution of wall pressure amplitude indicates that the 3D/oblique disturbances are strongly amplified in the presence of SBLI

wall-normal velocity

Effect of Shock Angle: Increased to 6 degrees (Re=200k)

Wall pressure Frequency Spectra

• The time history of wall pressure data indicates the vortex shedding

• Frequency spectra show distinct peaks at higher frequencies that correspond to the vortex shedding (Kelvin-Helmholtz instability)

• A stronger shock produced a stronger pressure jump and larger separated flow region

• Separated flow region becomes unsteady and starts to shed vortices

21

Effect of Reynolds Number: Increased to 500,000 (6 deg)


• Time history of wall pressure indicates the vortex shedding and the low frequency ``breathing’’ of bubble.

• The ``breathing’’ of the bubble manifests itself as a distinct low frequency peak in the spectra.

• Bubble starts to shed vortices even more strongly

• Boundary layer thickness near the separation is reduced and hence the length of the bubble is also reduced

22

Wall pressure Frequency Spectra

3D Simulations 23

• Vortex shedding that results from the shear layer instability is clearly visible and downstream of the reattachment location the flow transitions to turbulence


Flow visualization using the Q-criterion

• Contours of streamwise velocity in x-z plane show remarkable streamwise structures

• These streamwise

structures (streaks) may be a consequence of a dominant physical mechanism playing a role in the natural transition process

3D Simulations: Contours of Streamwise Velocity in x-z plane 24

Summary of 1 Year Seed Grant Results: Simulation

• Modified the in-house developed compressible Navier-Stokes solver to compute SBLI

• Implemented high-order accurate shock capturing schemes and characteristics based boundary conditions to generate impinging shocks

• Validated the code by comparing the results with the experimental and numerical results available in the literature

• Implemented methodologies to generate a turbulent boundary layer at the inflow (currently being tested and validated)

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Future Work

• Experiment – Turbulence characteristics, oil flow vis – Instantaneous velocity data analysis, schlieren – Proper orthogonal decomposition (POD) to investigate dynamics – Tunnel modifications and pressure spectra

• Simulation – Finalize validation cases, move to turbulent interactions and 3D – DNS (UA) and LES (NMSU) – Support with stability theory and similar data analysis as

experiment • Outstanding Challenges/Plans

– Swept impinging shocks vs. swept ramps (and others)—why different mean flow behavior?

– Understand the relevant instability mechanisms – More closely link experiments and computations

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Publications

• Hainsworth J., Dawson, R. and Little, J., “Experimental Study of Unswept and Swept Oblique Shock-Turbulent Boundary Layer Interactions,” AIAA Paper 2014-2738.

• Hainsworth, J. “Experimental Study of Unswept and Swept Oblique Shock-Turbulent Boundary Layer Interactions,” MS Thesis, 2014.

• Dawson-Ruiz, R., Pederson, C. and Little, J., “Effects of Sweep on Impinging Oblique Shock-Turbulent Boundary Layer Interaction,” AIAA Paper 2015-2933.

• Sivasubramanian, J. and Fasel, H., “Numerical Investigation of Shock-induced Laminar Separation Bubble in Supersonic Flows,” AIAA Paper 2015-2641.

• 3 abstracts for AIAA SciTech 2016 • J. Little---AFOSR YIP 2012, ARO YIP 2014, AIAA FDTC

27

Business Update

• One year seed grant spent down on-time (7/14/15).

• Final report to follow • Parallel SBLI funded effort with Raytheon

Missile Systems currently in progress.

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References (1)

• Degrez, G., Boccadoro, C.H., and Wendt, J.F., “The interaction of an oblique shock wave with a laminar boundary layer revisited. An experimental and numerical study,” J. Fluid Mech., Vol. 177, 1987, pp. 247-263

• Dussauge, J.P., Dupont, P., and Debiève, J.F., 2006, “Unsteadiness in shock wave boundary layer interactions with separation,” Aerosp. Sci. Technol. 10: 85–91

• Settles, G.S. and Teng, H.Y. 1984. “Cylindrical and conical upstream influence regimes of three-dimensional shock/turbulent boundary layer interactions.” AIAA Journal, 22, 194–200.

• Settles, G., and Kimmel, R., 1986 “Similarity of Quasiconical Shock-Wave/Turbulent Boundary-Layer Interactions,” AIAA Journal, 24, pp. 47-53.

• Schmisseur, J., “Aerothermodynamics: Transforming the Present, Inventing the Future,” March 2014.

• Holden, M.S., 1972, “Shock Wave-Turbulent Boundary Layer Interaction in Hypersonic Flow,” AIAA-72-74

• Holden, M.S., 1984, “Experimental Studies of Quasi-Two-Dimensional and Three-Dimensional Viscous Interaction Regions Induced by Skewed-Shock and Swept-Shock Boundary Layer Interactions,” AFOSR Technical Report 84-1228.

29

References (2)

• Humble, R., Elsinga, G., Scarano, F. and Oudheusden, B. v., "Three-Dimensional Instantaneous Structure of a Shock Wave/Turbulent Boundary Layer Interaction," Journal of Fluid Mechanics, Vol. 622, 2009, pp. 33-62.

• Gross, A., 2002, “Numerische Untersuchung abgelöster Düsenströmungen,” PhD dissertation, University of Aachen, Germany

• Mayer, C.S.J., Wernz, S., and Fasel, H.F., 2010a, “Numerical investigation of the nonlinear transition regime in a Mach 2 boundary layer,” J. Fluid Mech. 668: 113-149

• Mayer, C.S.J., von Terzi, D.A., and Fasel, H.F., 2010b, “Direct numerical simulation of complete transition to turbulence via oblique breakdown at Mach 3,” J. Fluid Mech. 674: 5-42

• Bookey, P. B., Wyckham, C., and Smits, A. J., 2005, “Experimental Investigations of Mach 3 Shock-Wave Turbulent Boundary Layer Interactions,” AIAA Paper 2005-4899

• Fasel, H.F., Balzer, W., and Gross, A., 2008, “Investigation of Separation Control for Low-Pressure Turbines Using CFD,” ICAS 2008, 26th International Congress of the Aeronautical Sciences

• Jacobi, R., Wernz, S., and Fasel, H., 2008, “Numerical Investigation of Localized Separation Induced by a Three-Dimensional Pressure Gradient, AIAA-2008-4056

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EXTRA Slides

31

Approach

• Experiments: Simultaneous spatially and temporally resolved measurements • Establish some “select” cases of interesting using surface flow

visualizations, schlieren imaging, stereoscopic PIV and high bandwidth pressure measurements

• Tomographic PIV for “select” cases • Computations: Highly accurate numerical simulations

• DNS and LES/RANS for low and high Re “select” cases respectively • Theory and Analysis: Local and global stability analyses from

experiments and computations • Fourier transforms, POD, DMD, pressure-velocity correlations,

vortex-ID techniques, etc. • Connect fluid dynamics and underlying flow instabilities. • Analyze energy fluxes between the basic flow and the various

instability modes

32

Approach Highlights: Experiments

• Simultaneous tomographic PIV and high bandwidth pressure measurements.

• If we want to do this: • We need to start taking measurements like this:

33

Humble et al. 2009

• 3D SBLI is excellent tomo-PIV candidate.

• Data analysis possibilities enhanced significantly

• Treat CFD and experiments and with same techniques

Schmisseur, 2014

Approach Highlights: Simulations

• DNS Code (low Re case): Developed with funding from AFOSR and NASA for the Hypersonic Transition Center. • First ever simulation of the entire transition process for a

supersonic boundary layer (Mayer and Fasel, 2010a/b).

• LES, hybrid RANS/LES and URANS (high Re case) • In-house developed compressible Navier-Stokes code (Gross and

Fasel, 2008c, 2010e).

34

Experiments by Holden, 1972 Simulations by Gross, 2002

Approach Highlights: Theory and Analysis

• Local and global stability analysis: Developed with funding from AFOSR and ONR for 2D and 3D low speed separation bubbles – Low-frequency and a high-frequency oscillations, indications

of global instability. Carry over to SBLI?

35

• The uncontrolled flow was found to be absolutely unstable. • Controlled flow was absolutely stable (with respect to the 3D

secondary instability), but still convectively unstable with respect to the primary mode--competing instability modes--insight for control

• 3D case had horn vortices and foci in the wall skin friction lines similar to those observed by, e.g., Bookey et al. (2005) for SBLIs.

Experiments: Incoming Flow Characterization 36

Plane M∞ U∞ (m/s) uτ (m/s) Po (kPa) To (k) δ (mm) δ*(mm) θ(mm) H Reθ z*=0.00 2.3 550 32 93.1 298 7.8 2.4,1.2 0.60,0.88 4.0,1.4 5880,8630 z*=0.22 2.3 540 28 93.1 298 8.4 2.5,1.3 0.67,0.93 3.8,1.4 6400,8880 z*=0.44 2.3 550 31 93.1 298 7.7 2.7,1.3 0.70,0.96 3.8,1.4 6870,9420

Interaction Lengths

• 40 degree sweep has conical similarity • 22.5 degree and unswept are cylindrical • Interaction length decreases with sweep angle

• The slope of this decrease is higher for conical similarity • Mirrored experiment confirms trends seen in initial experiment

37

z*-0.1 0 0.1 0.2 0.3 0.4 0.5

L/

2.5

3

3.5

4

4.5

5

5.5

6

6.5

7

0 Degree Sweep

22.5 Degree Sweep

40 Degree Sweep

0 Degree Mirrored

40 Degree Mirrored

z*

-0.1 0 0.1 0.2 0.3 0.4 0.5

L/

2.5

3

3.5

4

4.5

5

5.5

6

6.5

7

0 Degree Sweep

22.5 Degree Sweep

40 Degree Sweep

0 Degree Mirrored

40 Degree Mirrored

Experiments: Comparison with Literature

• Holden (1984) – Mach 11 – 15o shock generator – Similarity: cylindrical

• Settles (1984) – Mach 2.95 – 16o compression ramp – Similarity: cylindrical

(conical at higher sweep) • Current study

– Mach 2.3 – 15o shock generator – Similarity: both

• Interaction length decreases with almost the same slope as Holden while cylindrical

• Rate of decay increases sharply with transition to conical flow • Ramp data also decays upon transition to conical

0.0

0.2

0.4

0.6

0.8

1.0

0 10 20 30 40

L /δ

Sweep Angle (degrees)

z*=0z*=0.22z*=0.44HoldenSettles

38

Boundary Layer Profiles (𝑈𝑈 𝑈𝑈∞⁄ vs. 𝑦𝑦 𝛿𝛿⁄ at x*=-0.75-0 ): 0o Sweep Initial Experiment

General Observations • At x*

0,1,2 =-0.25 there is separation for all cases except for 40o swept plane 0

• At x*0,1,2 =-0.25 there is an

inflection point, more at x*0,1,2

=-0.5, 0 → consistent with presence of a shear layer

• Majority of 3-D behavior x*

0,1,2 =-0.5 to -0.25 • Three dimensionality shows a

significant increase between 22.5 and 40o sweep

• Small increase in fullness with increasing sweep

x*0,1,2=-0.50 x*

0,1,2=-0.75

x*0,1,2=0 x*

0,1,2=-0.25

39

• Still some 3-D behavior although nominally 2-D • At x*

0,1,2 =-0.5 the beginning of the expansion wave does not match exactly • Strongest SBLI • Spreading is organized (spanwise trend) but some deviation is present

Boundary Layer Profiles (𝑈𝑈 𝑈𝑈∞⁄ vs. 𝑦𝑦 𝛿𝛿⁄ at x*=-0.75-0 ): 22.5o Sweep Initial Experiment

x*0,1,2=-0.50 x*

0,1,2=-0.75

x*0,1,2=0 x*

0,1,2=-0.25

40



• At x*0,1,2 =-0.25 there is an

inflection point, more at x*

0,1,2 =-0.5, 0 → consistent with presence of a shear layer





• Good collapse for expansion wave location at x*0,1,2 =-0.5

• At x*0,1,2 =-0.25 organized spreading, fuller at z*=0

• Weak three dimensionality as the profiles collapse again at x*0,1,2 =0

Boundary Layer Profiles (𝑈𝑈 𝑈𝑈∞⁄ vs. 𝑦𝑦 𝛿𝛿⁄ at x*=-0.75-0 ): 40o Sweep Initial Experiment

x*0,1,2=-0.50 x*

0,1,2=-0.75

x*0,1,2=0 x*

0,1,2=-0.25

41



• At x*0,1,2 =-0.25 there is an




0,1,2 =-0.5 to -0.25 • Three dimensionality shows

a significant increase between 22.5 and 40o sweep


• Significantly smaller and weaker interaction region, but most 3-D behavior • Three dimensionality still dies out by x*

0,1,2 =0 • At x*

0,1,2 =-0.25, organized spreading with fullness decreasing with increasing sweep. • Note: collapse occurs at X* = 0 because of coordinates 𝑥𝑥∗𝑛𝑛 ≡ (𝑥𝑥 − 𝑋𝑋0𝑛𝑛) 𝐿𝐿𝑛𝑛⁄

Boundary Layer Profiles (𝑈𝑈 𝑈𝑈∞⁄ vs. 𝑦𝑦 𝛿𝛿⁄ at x*=-0.75-0 ): 0o Sweep Mirrored Experiment



• At x*0,1,2 =-0.25 there is an







42

• Still some 3-D behavior although nominally 2-D • At x*

0,1,2 =-0.5 the beginning of the expansion wave does not match exactly • Strongest SBLI • Three dimensionality is strongest at X* = -0.25 and symmetric around Z* = 0.22

y/

0

0.5

1

1.5

2

U/U0 0.2 0.4 0.6 0.8 1

a) x* = -0.75

z* = 0

z* = .22

z* = .44

y/

0

0.5

1

1.5

2

U/U0 0.2 0.4 0.6 0.8 1

b) x* = -0.5

z* = 0

z* = .22

z* = .44

y/

0

0.5

1

1.5

2

U/U0 0.2 0.4 0.6 0.8 1

c) x* = -0.25

z* = 0

z* = .22

z* = .44

y/

0

0.5

1

1.5

2

U/U0 0.2 0.4 0.6 0.8 1

d) x* = 0

z* = 0

z* = .22

z* = .44

Boundary Layer Profiles (𝑈𝑈 𝑈𝑈∞⁄ vs. 𝑦𝑦 𝛿𝛿⁄ at x*=-0.75-0 ): 40o Sweep Mirrored Experiment

43



• At x*0,1,2 =-0.25 there is an







• Significantly smaller and weaker interaction region, but most 3-D behavior • Three dimensionality still dies out by x*

0,1,2 =0 • At x*

0,1,2 =-0.25, organized spreading with fullness decreasing with increasing sweep. • Note: collapse occurs at X* = 0 because of coordinates 𝑥𝑥∗𝑛𝑛 ≡ (𝑥𝑥 − 𝑋𝑋0𝑛𝑛) 𝐿𝐿𝑛𝑛⁄

y/

0

0.5

1

1.5

2

U/U0 0.2 0.4 0.6 0.8 1

a) x* = -0.75

z* = 0

z* = .22

z* = .44

y/

0

0.5

1

1.5

2

U/U0 0.2 0.4 0.6 0.8 1

b) x* = -0.5

z* = 0

z* = .22

z* = .44

y/

0

0.5

1

1.5

2

U/U0 0.2 0.4 0.6 0.8 1

c) x* = -0.25

z* = 0

z* = .22

z* = .44

y/

0

0.5

1

1.5

2

U/U0 0.2 0.4 0.6 0.8 1

d) x* = 0

z* = 0

z* = .22

z* = .44

Vorticity

• Region of high vorticity forms upstream and lifts off at x* ~= -0.75 • Vorticity lifts off highest for unswept case, where reverse flow is

most likely

Unswept 22.5 degree sweep 40 degree sweep

z* =

0.4

4

z*

= 0

.22

z*

= 0

44

Interaction of an oblique shock with a laminar boundary layer

Flow parameters match the conditions in the experiments by Hakkinen et al.*

*‘The interaction of an oblique shock wave with a laminar boundary layer’, Hakkinen et al., 1959, NASA Technical Report.

Code Validation

The oblique shock is introduced using the Rankine-Hugoniot jump relation in the top (freestream) boundary

45

46

• To initialize the turbulent flow, mean flow variables and their turbulent fluctuations are prescribed at the inflow1 (currently being tested and validated)

• The incident shock is generated by imposing the Rankine-Hugoniot jump conditions at the top boundary of the computational domain

1 Martin, P., 2007, “Direct numerical simulation of hypersonic turbulent boundary layers. Part 1. Initialization and comparison with experiments,” J. Fluid. Mech. 570, 347-364. 2 Clemens, N.T. and Narayanaswamy, V., 2014, “Low-Frequency Unsteadiness of Shock Wave/Turbulent Boundary Layer Interactions,” Annual Review of Fluid Mechanics, 46, No. 1, pp. 469-492.

Schematic of Turbulent SBLI2

Experiment Test Section Computation domain

DNS Set-up for SBLI (UA experimental conditions)

CFD Effort at NMSU

• Versatile up to ninth-order-accurate (WENO based) compressible finite volume CFD code with one- and two-equation turbulence models (complex geometries)

• Code has been (and currently is) successfully employed for AFOSR/ONR funded subsonic research.

• Validation of code: Preliminary simulation of 2-D SBLI by Degrez at al., 1987 (Re=100,000, M=2.15, ϑ=3.81deg)

47

CFD Effort at NMSU: Turbulence Modeling

• Scale-resolving methods, such as direct numerical simulations (DNS), and large-eddy simulations (LES) are required for accurate simulations that capture essential flow physics.

• DNS of high-Reynolds number problems are very expensive. LES requires high near-wall resolution and becomes less accurate as resolution is reduced.

• RANS models built on equilibrium assumption fail for SBLI problems where turbulence is in strong non-equilibrium; RANS by definition cannot capture flow unsteadiness and is not adequate for stability investigations.

Possible solutions to dilemma: • LES with sub-grid stress (SGS) model. • Implicit LES (truncation error of numerical scheme or explicit filters to

remove energy at grid scale). • Hybrid RANS/LES model that blend between RANS and LES (i.e. hybrid

models) promise to combine versatility of LES with efficiency of RANS.

48

Edwards, J.R., “Numerical simulations of shock/boundary layer interactions using time-dependent modeling techniques: A survey of recent results,” Progress in Aerospace Sciences, Vol. 44, 2008, pp. 447–465

CFD Effort at NMSU: Large Eddy Simulation

• Martin et al., 2000: A priori investigation of subgrid-scale (SGS) models for unclosed terms in Navier-Stokes equations (with focus on energy equation): – For the momentum equations, mixed models (scale similarity and

eddy viscosity) perform better than pure eddy-viscosity models. – Turbulent diffusion term in total energy equation is significant. Model

proposed by Knight et al. (1998) and new scale-similarity model performed well.

• ILES of turbulent SBLI problem by Grilli et al. (2012) – Implicit LES (ILES) model (Hickel et al., 2014); Truncation error acts as a

physically consistent SGS model.

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Grilli, M., Schmid, P.J., Hickel, S., and Adams, N.A., “Analysis of unsteady behaviour in shockwave turbulent boundary layer interaction,” J. Fluid Mech., Vol. 700, 2012, pp. 16-28 Hickel, S., and Egerer, C.P., “Subgrid-scale modeling for implicit Large Eddy Simulation of compressible flows and shock turbulence interaction,” Physics of Fluids, Vol. 26, 2014 Knight, D., Zhou, G., Okong’o, N., and Shukla, V., “Compressible large eddy simulation using unstructured grids,” AIAA Paper AIAA-98-535, 1998 Martin, M.P.., Piomelli, U., and Candler, G.V., “Subgrid-Scale Models for Compressible Large-Eddy Simulations,” Theoret. Comput. Fluid Dynamics, Vol. 13, 2000, pp. 361–376

little fasel gross update - apan community• sivasubramanian, j. and fasel, h., “numerical...

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