Nonlinear Transition Stages in Hypersonic Boundary Layers: Fundamental Physics, Transition Control and Receptivity

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1 Nonlinear Transition Stages in Hypersonic Boundary Layers: Fundamental Physics, Transition Control and Receptivity PI: Hermann F. Fasel Co-PI: Anatoli Tumin Christoph Hader, Leonardo Salemi, Jayahar Sivasubramanian University of Arizona This work was supported by AFOSR Grant FA monitored by Dr. Ivett Leyva. Computer time was provided by the US Army Engineering Research and Development Center (ERDC) under the Department of Defense (DOD) High Performance Computing Modernization Program (HPCMP)

2 Outline Background State of last year New Results Summary Next Steps Publications Remaining technical challenges

3 Transition Regions Schematic Theory/DNS Receptivity Linear/Nonlinear PSE/DNS/ Theory Quiet Tunnels (BAM6QT, TAMU) Linear Growth DNS Nonlinear Growth and Interactions DNS/LES Shock Tube (T5,T9) Breakdown/ Turbulence Roughness Nose Transient Growth Control Bluntness, (small α) Surface Crossflow (larger α) Chemistry Gas Chemistry

4 Outline Background State of last year New Results Summary Next Steps Publications Remaining technical challenges

5 State of last year New start Focus on nonlinear stages of transition regime Fundamental Flow Physics: Nonlinear Stages Understand nonlinear physics of quiet flow before introducing free-stream turbulence Investigate various geometries to understand influence of geometry on nonlinear behavior (Purdue/NASA straight and flared cones) Fundamental Flow Physics: Caltech T5 Conditions hot gas/cold wall T5 conditions: high-enthalpy Flow Control: Modify nonlinear transition regime Use passive and active flow control to delay or even prevent transition and the associated detrimental effects Receptivity Investigations (in collaboration with A. Tumin) Investigate the role of disturbance generator location on receptivity Receptivity studies are crucial for active flow control scenario and optimal actuator placement

6 Outline Background State of last year New Results Summary Next Steps Publications Remaining technical challenges

Motivation/ Goals Hot streaks of limited downstream extent are observed

Investigate underlying physical mechanisms responsible for steak pattern

Focus on nonlinear breakdown CFD (U of A) hot streaks (large local heat

7 Motivation/ Goals Hot streaks of limited downstream extent are observed in both simulation and experiment Qualitatively similar patterns Investigate underlying physical mechanisms responsible for steak pattern Why do streaks appear, disappear and reappear? Focus on nonlinear breakdown CFD (U of A) hot streaks (large local heat fluxes may compromise structural integrity of hypersonic flight vehicle) Experiment (Purdue, BAM6QT, B. Chynoweth)

base flow with higher-order finite difference code (nose of the

8 Simulation Strategy Converge base flow with finite volume code (axisymmetric, steady, nose of the cone included) Re-converge base flow with higher-order finite difference code (nose of the cone excluded) Wave packet simulation after obtaining a converged base flow

9 Controlled breakdown simulations Fundamental Resonance (K-type): 2D wave (n,m): high ampl. 3D wave (n, ±m): low ampl. m (1,1) (1,0) 1 2 (1,-1) n Subharmonic Resonance (H-/N-type): 2D wave (n,m): high ampl. 3D wave (n, ±m): low ampl. m (1,1) 1 2 (1,-1) (2,0) n Oblique Breakdown Pair of oblique waves (n,±m) forced at the same amplitude m high amplitude 2 low amplitude (1,1) 1 2 (1,-1) n

10 New Results Nonlinear transition development for Purdue flared cone experiments Receptivity investigations for flat plate and cone for Purdue conditions Linear/nonlinear stages for high-enthalpy Caltech T5 conditions

11 Cone Geometry and Base Flow Geometry: Nose radius : r nose = m Initial half angle : θ = 1.4 Cone flare : r flare = 3 m Cone length : L cone = 0.51 m Flow conditions: Mach number : M = 6 stagnation temperature : T 0 = 420 K Stagnation pressure : p 0 = 140 psi Unit Reynolds number : Re 1 = /m Grid study to ensure grid converged solution Good match between FV, FD and STABL How to choose primary/secondary wave frequency? Axisymmetric pulse simulations How to choose wave number of secondary wave? Low-resolution fundamental resonance onset simulations

12 Fundamental Resonance Breakdown Setup Primary/Secondary wave frequency: Track N-factors in downstream direction Maximum N-factor: f 300 khz Wave number of secondary wave: M = 6 T 0 = 420 K p 0 = 140 psi Largest growth rate after fundamental resonance onset for k c 80

13 Fundamental Breakdown Conditions: p 0 = 140 psi T 0 = 420 K Re 1 = /m Primary wave, mode (1,0) f (1,0) = 300 khz k c, (1,0) = 0 => 2D wave A (1,0) = 10-4 Secondary wave, mode (1,1) f (1,1) = 300 khz k c(1,1) = 80 => 3D wave A (1,1) = xi (i = 1 5) : Data are extracted in wall-normal direction at fixed x-position 80-φi (i = 1,2) : Data are extracted along the wall for fixed azimuthal position 80-pi (i = 1 6) : Data are extracted in wall-normal direction or in time at fixed point on the surface of the cone

φ1 and φ2 collapse Streaks appear: Clearly distinct curves Streaks disappear: curves

14 Fundamental Breakdown Skin-friction coefficient Overshoot in Stanton number much more significant compared to skin-friction coefficient Before streaks appear: curves along φ1 and φ2 collapse Streaks appear: Clearly distinct curves Streaks disappear: curves collapse again Streak development strongly linked to three dimensional effects Stanton number

15 Fundamental Breakdown Streaks appear (80-x1) Streamwise vortices form when streaks begin to appear

16 Fundamental Breakdown Location where Stanton number becomes maximal (80-x2)

17 Fundamental Breakdown Streaks begin to fade (80-x3)

18 Fundamental Breakdown Streaks disappeared (80-x4)

19 Fundamental Breakdown Streaks reappear (80-x5)

20 Fundamental Breakdown Time-averaged skin-friction coefficient and Stanton number in normalized azimuthal direction 80 streaks at position where streaks first appear 160 streaks at position where streaks reappear skin friction coefficient Stanton number

21 Fundamental Breakdown Mode (0,1) becomes dominant when streaks appear ( T max ) Streaks are linked to steady longitudinal vortex modes

22 New Results Nonlinear transition development for Purdue flared cone experiments Receptivity investigations for flat plate and cone for Purdue conditions Linear/nonlinear stages for high-enthalpy Caltech T5 conditions

23 Flat Plate: Disturbance Development Wall pressure disturbance (low amplitude wave packet) u amplitude u phase T amplitude T phase * DNS LST Good match between LST and DNS truly linear wavepacket

Flat Plate: Forcing locations Pulse forcing amplitude: A

004 m Case A: Forcing hole center location: x A * = 0.

24 Flat Plate: Forcing locations Pulse forcing amplitude: A pulse = 10-5 Hole diameter = m Case A: Forcing hole center location: x A * = m R x = 811 Case B: Forcing hole center location: x A * = m R x = 1405 Initial response similar Introducing a broad spectrum of frequencies and wave numbers Case A 1 st mode Case B 2 nd mode

25 Disturbance Development: Early Stage t* = ms t* = ms t* = ms t* = ms Case A Case B Similar development of wave packet in early stages

Disturbance Development: Late Stage Wavepacket spreads in the streamwise

Oblique waves are observed close to the tail of the packet Late stages of

oblique waves are observed for case A (forced close to leading edge) Only

064 ms t* = 0.174 ms t* = 0.291 ms t* = 0.

26 Disturbance Development: Late Stage Wavepacket spreads in the streamwise direction as it propagate downstream Front region is predominantly 2D, Oblique waves are observed close to the tail of the packet Late stages of wavepacket development show distinct differences Stronger first mode oblique waves are observed for case A (forced close to leading edge) Only weaker first mode oblique waves are observed for case B t* = ms t* = ms t* = ms t* = ms Case A acoustic waves First mode oblique waves Case B Front region is predominantly 2D, Oblique waves are observed in the tail region

27 Flat Plate: Disturbance Development Comparison of centerline traces (wall pressure disturbance) Signal of case B (forced further downstream) is picked up earlier at a fixed location compared to case A Envelope of wave packet indicate case A has reached larger amplitudes compared to case B Case A Case B x = 0.50 m x = 0.45 m x = 0.40 m CASE B CASE A x = 0.35 m x = 0.30 m x = 0.50 m CASE B CASE A x = 0.25 m x = 0.20 m

28 Flat Plate: Linear growth rate Theory, Case A Theory, Case A DNS, Case A (x = 0.25 m) Theory, Case B Theory, Case B DNS, Case B (x = 0.25 m)

Sharp Cone: Geometry and Flow Cond. Geometry (Purdue sharp cone): Half opening angle: Θ c = 7 Length of the cone: L c = 0.517 m Nose radius: r Nose = 0.

29 Sharp Cone: Geometry and Flow Cond. Geometry (Purdue sharp cone): Half opening angle: Θ c = 7 Length of the cone: L c = m Nose radius: r Nose = 0.05 mm Domain length: 0.1 m Domain height: m ( 65 δ at outflow) Flow Conditions (BAM6QT): Mach number: M = 6.0 Reynolds number: Re 1 = /m Freestream Temp.: T = 52.8 K

30 Comparison: Flat Plate - Cone Comparison of wall pressure disturbance (p ) between flat plate and straight cone Forcing location of wavepacket at R x = 811 Similar development of wavepacket for both geometries Flat plate Shallow oblique waves 2D wave fronts Straight cone Highly oblique waves

31 New Results Nonlinear transition development for Purdue flared cone experiments Receptivity investigations for flat plate and cone for Purdue conditions Linear/nonlinear stages for high-enthalpy Caltech T5 conditions

32 Caltech T5 Supersonic 2 nd mode waves Tumin & Fedorov, 1983, Spatial growth of disturbances in a compressible boundary layer, J. Appl. Mech. Tech. Phys. 24

33 Caltech T5: Axisym. Lin. Wavepacket 2 nd mode wave is supersonic in relation to freestream Synch. of 2 nd mode wave and slow acoustic mode 2 nd mode instability driven by the presence of relative supersonic regions 2 nd mode dominated wavepacket emits (radiates) sound

179 Modulation/flattening of p wall due to emission of sound in synchronization

34 Caltech T5 Emission of sound 2D 2D Linear Axisymmetric Wavepacket 4703x464 5deg Straight Cone Caltech T5 - T w /T e =0.179 Modulation/flattening of p wall due to emission of sound in synchronization region Salemi, Fasel, Wernz & Marquart AIAA & AIAA Fedorov & Chuvakhov AIAA Flat plate M e =6 - T w /T e =0.5

35 Caltech T5 Emission of sound 3D 3D Nonlinear Wavepacket 4703x464x201 5deg Straight Cone Caltech T5 - T w /T e =0.179 Modulation of p wall due to emission of sound in synchronization region Fedorov & Chuvakhov AIAA Flat plate M e =6 - T w /T e =0.5

36 Caltech T5 3D Nonlinear Wavepacket High-resolution 3D Wavepacket 4703x464x201 Complex interactions between 2 nd mode instability and acoustic waves X-Z plane (unrolled) Isometric view Decaying low freq. mode 2 nd mode dominated wavepacket Fast acoustic waves

37 Flow visualization x-locations Hot (Caltech T5 5 deg cone) Fundamental Breakdown investigations Visualization x-locations C f departure is located at 0.24 m

38 Flow visualization x-location 1 Hot (Caltech T5 5 deg cone) Fundamental Breakdown investigations Temperature- - x*= [m] Profile extraction locations First structures inside sonic layer

39 Flow visualization x-location 2 Hot (Caltech T5 5 deg cone) Fundamental Breakdown investigations Temperature- - x*= [m] Structures develop between sonic line and critical layer Profile extraction locations Several conter-rotating structures inside sonic layer

40 Flow visualization x-location 3 Hot (Caltech T5 5 deg cone) Fundamental Breakdown investigations Temperature- - x*= [m] Structures lift-up to critical layer Structures inside sonic layer lift-up Highly inflectional profile at z-location 3

Flow visualization x-location 4 Hot (Caltech T5 5 deg cone) Fundamental Breakdown investigations Temperature- - x*=0.

41 Flow visualization x-location 4 Hot (Caltech T5 5 deg cone) Fundamental Breakdown investigations Temperature- - x*= [m] Structures lift-up past critical layer Profile extraction locations Structures inside sonic layer lift-up further and skew Profile at z-location 3 gets severely inflected!

Comparison: BAM6QT T5 Conditions Comparison

(Caltech T5: 5º straight cone) freestream

10-6 Large gradient at the wall for T5 conditions

42 Comparison: BAM6QT T5 Conditions Comparison between cold (BAM6QT: 7º straight cone) and hot (Caltech T5: 5º straight cone) freestream conditions Fundamental resonance scenario BAM6QT case: Re e =13.6e6, M e =5.35 T =52.43K, T w =300K A (1,0) = 10-3, A (1,1) = 10-5 Caltech T5 case: Re e =6.67e6, M e =5.05 T =1530K, T w =297K A (1,0) = 10-2, A (1,1) = 10-6 Large gradient at the wall for T5 conditions Maximum amplitude of density close to the wall due to density gradient in the basic flow for T5 conditions

43 Comparison: BAM6QT T5 Conditions Resonance onset for BAM6QT conditions when primary wave reaches large amplitudes Resonance onset for T5 conditions before primary wave saturates Larger growth of secondary wave after resonance onset for T5 conditions

44 Comparison: BAM6QT T5 Conditions x*=0.58 m Purdue BAM6QT: 7º straight cone x*=0.37 m Higher harmonic Caltech T5: 5º straight cone 2 nd mode Steady, streamwise vortex modes Oblique waves Predominantly 2D wave fronts

45 Outline Background State of last year New Results Summary Next Steps Publications Remaining technical challenges

46 Summary Flared Cone Purdue Fundamental Breakdown: Determined primary wave frequency and wave number that led to largest growth rate of secondary wave ( Carried out high-resolution DNS for fundamental breakdown Number of streaks in circumferential direction corresponds to azimuthal wave number of dominant secondary wave Streak formation leads to significant overshoot in skin friction and Stanton number Streaks are strongly linked to streamwise vortical modes, in particular mode (0,1) Receptivity investigations (flat plate and straight cone) Investigated receptivity of a hypersonic boundary layer to a localized disturbance using DNS and Theory. Effect of Reynolds number on the receptivity was investigated by by using several forcing locations from the leading edge. We found that the structure of the resulting wave packet and its spectral contents depend on the forcing location. When forced close to the leading edge, in addition to the dominant 2D second mode disturbances, 3D waves dvelop at the lateral sides of wave packet: Due the 3D first mode waves which are more receptive to the forcing location close to the leading edge.

47 Summary Caltech T5 (high-enthalpy) cone experiments Highly cooled wall(i.e. T w /T e =0.179) yields supersonic 2 nd mode waves components, which synchronize with the slow acoustic continuous modes The synchronization 2 nd mode waves with slow acoustic waves results in the emission of acoustic disturturbances into the freestream for both axisymmetric and 3D wavepackets Strongly nonlinear 3D wavepackets therefore presents intricate interactions between 2 nd mode instability waves, fast acoustic waves and sound emission Due to the extreme temperature gradient at the wall, Caltech T5 case wave packets include only fast growing 2 nd mode waves much faster growth rates than for Purdue conditions) Wave-packet investigations demonstrate that 2 nd mode fundamental breakdown is a viable route to transition for T5 conditions For fundamental breakdown the first streaks appear between the sonic line and the wall, and and further downstream near the critical layer High-enthalpy cooled wall conditions result not only larger secondary growth rates (compared to low-enthalpy case), but also in a much wider azimuthal wavenumber range of secondary unstable waves (compared to Purdue conditions)

48 Outline Background State of last year New Results Summary Next Steps Publications Remaining technical challenges

49 Next Steps Flared Cone Purdue Investigate streak development for breakdown scenarios initiated with wave numbers that did not lead to maximum growth of the secondary wave Investigate influence of roughness elements on the development of the streaks Quantitative comparison of the DNS results to the experiments carried out at the BAM6QT facility (in collaboration with Professor S. Schneider) Receptivity investigations (flat plate and straight cone) Additional forcing locations closer to the leading edge Multi-mode decomposition to better understand the role played by the different modes Investigate the effect of receptivity on the forcing location on the nonlinear development Caltech T5 (high-enthalpy) cone experiments Investigate the influence of T w /T e for high-enthalpy flow conditions utilizing axisymmetric wavepackets Perform fundamental breakdown controlled transition investigation for the Caltech T5 highenthalpy flow Investigate emission of sound in the high-cooled wall Caltech T5 case utilizing wavetrains

50 Outline Background State of last year New Results Summary Next Steps Publications Remaining technical challenges

51 Publications Brehm, C., Hader, C., and Fasel, H.F., A locally stabilized immersed boundary method for the compressible Navier Stokes equations, Journal of Computational Physics, Vol. 295, 2015, pp Sivasubramanian, J., and Fasel, H.F., Direct numerical simulation of transition in a sharp cone boundary layer at Mach 6: fundamental breakdown, Journal of Fluid Mechanics, Vol. 768, 2015, pp Sivasubramanian, J., and Fasel, H.F., Direct Numerical Simulation of Laminar-Turbulent Transition in a Flared Cone Boundary Layer at Mach 6, AIAA , 54th AIAA Aerospace Sciences Meeting, 4 8 January 2016, San Diego, CA Hader, C., and Fasel, H.F., Laminar-Turbulent Transition on a Flared Cone at Mach 6, AIAA , 46th AIAA Fluid Dynamics Conference, June 2016, Washington, D.C. Sivasubramanian, J., Tumin, A., and Fasel, H.F., The Reynolds Number Effect on Receptivity to a Localized Disturbance in a Hypersonic Boundary Layer, AIAA , 46th AIAA Fluid Dynamics Conference, June 2016, Washington, D.C.

52 Outline Background State of last year New Results Summary Next Steps Publications Remaining technical challenges

53 Remaining technical challenges DNS are computationally very expensive Data storage and processing: Statistical analysis of the laminar-turbulent transition process requires data sampling at a high rate very large data sets Efficient execution of very large parallel simulations ( cores) Parallel input/output Flow visualization of large volume data (TBs of data) DNS of transition for high enthalpy flows is very challenging, due to the large gradients at the wall: Thus the resolution requirements increase drastically compared to the quiet tunnel conditions

54 Budget Reports all current, next technical due 8/31/16 Vouchers to date (all paid): 176, Yr 1 Budget: 337,423 Expenditures to date: 183, Balance: 154,045 Encumbrances through 8/31/16: $74, Balance after encumbrances: $79, Parallel SBLI funded effort with Raytheon Missile Systems

Numerical Study of Boundary-Layer Receptivity on Blunt Compression-Cones in Mach-6 Flow with Localized Freestream Hot-Spot Perturbations

Numerical Study of Boundary-Layer Receptivity on Blunt Compression-Cones in Mach-6 Flow with Localized Freestream Hot-Spot Perturbations Blunt Compression-Cones in Mach-6 Flow with Localized Freestream Hot-Spot Perturbations Yuet Huang 1 and Xiaolin Zhong 2 Mechanical and Aerospace Engineering Department, University of California, Los Angeles,