Global input-output analysis of flow instabilities in high-speed compressible flows

University of Minnesota Ph.D. dissertation. August 2020. Major: Aerospace Engineering and Mechanics. Advisor: Graham Candler. 1 computer file (PDF); xiv, 104 pages.

[1]  V. Theofilis Global Linear Instability , 2011 .

[2]  M. Jovanović,et al.  Model-based design of riblets for turbulent drag reduction , 2020, Journal of Fluid Mechanics.

[3]  B. J. McKeon,et al.  A critical-layer framework for turbulent pipe flow , 2010, Journal of Fluid Mechanics.

[4]  Sung-Eun Kim,et al.  A Multi-Dimensional Linear Reconstruction Scheme for Arbitrary Unstructured Mesh , 2003 .

[5]  Ivan E. Beckwith,et al.  Gortler instability and supersonic quiet nozzle design , 1992 .

[6]  Ivett A. Leyva,et al.  The relentless pursuit of hypersonic flight , 2017 .

[7]  G. Candler,et al.  Onset of three-dimensionality in supersonic flow over a slender double wedge , 2018, Physical Review Fluids.

[8]  M. Y. Hussaini,et al.  Stability of time dependent and spatially varying flows; Proceedings of the Symposium, Hampton, VA, Aug. 19-23, 1985 , 1987 .

[9]  Xiaolin Zhong,et al.  Receptivity of a supersonic boundary layer over a flat plate. Part 1. Wave structures and interactions , 2003, Journal of Fluid Mechanics.

[10]  Denis Sipp,et al.  Effect of base-flow variation in noise amplifiers: the flat-plate boundary layer , 2011, Journal of Fluid Mechanics.

[11]  Eli Reshotko Transition Issues for Atmospheric Entry , 2008 .

[12]  Steven P. Schneider,et al.  Developing mechanism-based methods for estimating hypersonic boundary-layer transition in flight: The role of quiet tunnels , 2013 .

[13]  L. Mack,et al.  Review of Linear Compressible Stability Theory , 1987 .

[14]  Philip Hall,et al.  The linear development of Görtler vortices in growing boundary layers , 1983, Journal of Fluid Mechanics.

[15]  T. Herbert PARABOLIZED STABILITY EQUATIONS , 1994 .

[16]  Joseph Brock Development of Modal Analysis for the Study of Global Modes in High Speed Boundary Layer Flows , 2017 .

[17]  N. Parziale,et al.  Amplification and structure of streamwise-velocity fluctuations in compression-corner shock-wave/turbulent boundary-layer interactions , 2019, Journal of Fluid Mechanics.

[18]  Input-Output Analysis of Shock Boundary Layer Interaction , 2018, 2018 Fluid Dynamics Conference.

[19]  C. Cossu,et al.  Maximum Spatial Growth of Görtler Vortices , 2000 .

[20]  M. R. Malik,et al.  Goertler vortices in supersonic and hypersonic boundary layers , 1989 .

[21]  L. Mack Linear Stability Theory and the Problem of Supersonic Boundary- Layer Transition , 1975 .

[22]  Mihailo R. Jovanovic,et al.  Input-output analysis of high-speed axisymmetric isothermal jet noise , 2016 .

[23]  Pramod K. Subbareddy,et al.  Development of the US3D Code for Advanced Compressible and Reacting Flow Simulations , 2015 .

[24]  Gene H. Golub,et al.  Matrix computations (3rd ed.) , 1996 .

[25]  Dan S. Henningson,et al.  Input-Output Analysis and Control Design Applied to a Linear Model of Spatially Developing Flows , 2009 .

[26]  C. Cossu,et al.  Global Measures of Local Convective Instabilities , 1997 .

[27]  S. Mittal,et al.  Flow past a rotating cylinder , 2003, Journal of Fluid Mechanics.

[28]  B. Chu On the energy transfer to small disturbances in fluid flow (Part I) , 1965 .

[29]  N. Sandham,et al.  Direct simulation of breakdown to turbulence following oblique instability waves in a supersonic boundary layer , 1995 .

[30]  D. Arnal,et al.  Linear Stability Theory Applied to Boundary Layers , 1996 .

[31]  Michael T. Semper,et al.  Calibration of an Actively Controlled Expansion Hypersonic Wind Tunnel , 2010 .

[32]  P. Dimotakis,et al.  Baroclinic Torque and Implications for Subgrid-Scale Modeling , 2014 .

[33]  V. C. Patel,et al.  Equations of Laminar and Turbulent Flows in General Curvilinear Coordinates. , 1986 .

[34]  Mihailo R. Jovanovi'c From bypass transition to flow control and data-driven turbulence modeling: An input-output viewpoint , 2020, ArXiv.

[35]  J. Chomaz,et al.  GLOBAL INSTABILITIES IN SPATIALLY DEVELOPING FLOWS: Non-Normality and Nonlinearity , 2005 .

[36]  James Demmel,et al.  SuperLU_DIST: A scalable distributed-memory sparse direct solver for unsymmetric linear systems , 2003, TOMS.

[37]  Scott A. Berry,et al.  Streamwise Vortex Instability and Transition on the Hyper-2000 Scramjet Forebody , 2005 .

[38]  Acoustic-wave-induced cooling in onset of hypersonic turbulence , 2020 .

[39]  P. Schmid,et al.  A new mechanism for rapid transition involving a pair of oblique waves , 1992 .

[40]  E. Kansa Local, Point-Wise Rotational Transformations of the Conservation Equations into Stream-Wise Coordinates , 2002 .

[41]  Eiji Shima,et al.  Green–Gauss/Weighted-Least-Squares Hybrid Gradient Reconstruction for Arbitrary Polyhedra Unstructured Grids , 2013 .

[42]  L. Mack,et al.  Transition prediction and linear stability theory , 1977 .

[43]  D. Henningson,et al.  SPATIAL SIMULATIONS OF OBLIQUE TRANSITION IN A BOUNDARY LAYER , 1994 .

[45]  I. E. Beckwith,et al.  Effects of nozzle design parameters on the extent of quiet test flow at Mach 3.5 , 1985 .

[46]  W. Saric GORTLER VORTICES , 2007 .

[47]  Graham V. Candler,et al.  Simulation and stability analysis of oblique shock wave/boundary layer interactions at Mach 5.92 , 2017, 1712.08239.

[48]  M. Landahl A note on an algebraic instability of inviscid parallel shear flows , 1980, Journal of Fluid Mechanics.

[49]  Joël Piraux,et al.  A new interface method for hyperbolic problems with discontinuous coefficients: one-dimensional acoustic example , 2001 .

[50]  M. Jovanović,et al.  Optimal spatial growth of streaks in oblique shock/boundary layer interaction , 2017 .

[51]  T. Ellingsen,et al.  Stability of linear flow , 1975 .

[52]  Vassilis Theofilis,et al.  Structural changes of laminar separation bubbles induced by global linear instability , 2010, Journal of Fluid Mechanics.

[53]  W. Haase,et al.  Experimental and computational investigations of hypersonic flow about compression ramps , 1995, Journal of Fluid Mechanics.

[54]  H. Olivier,et al.  Effect of Small Bluntness on Formation of Görtler Vortices in a Supersonic Compression Corner Flow , 2017 .

[55]  Denis Sipp,et al.  Characterization of noise amplifiers with global singular modes: the case of the leading-edge flat-plate boundary layer , 2013 .

[56]  P. Schmid,et al.  Transient growth in compressible boundary layer flow , 1996 .

[57]  Salvador Navarro-Martinez,et al.  Numerical simulation of Görtler vortices in hypersonic compression ramps , 2005 .

[58]  Bassam Bamieh,et al.  Componentwise energy amplification in channel flows , 2005, Journal of Fluid Mechanics.

[59]  D. Henningson,et al.  Optimal disturbances and bypass transition in boundary layers , 1999 .

[60]  P. Bradshaw Effects of Streamline Curvature on Turbulent Flow. , 1973 .

[61]  H. Olivier,et al.  Experimental investigation of Görtler vortices in hypersonic ramp flows , 2017 .

[62]  G. Inger,et al.  Three-Dimensional Heat-and Mass-Transfer Effects across High-Speed Reattaching Flows , 1976 .

[63]  V. Theofilis,et al.  On the origins of unsteadiness and three-dimensionality in a laminar separation bubble , 2000, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[64]  Michael B. Giles,et al.  Validity of Linearized Unsteady Euler Equations with Shock Capturing , 1994 .

[65]  Valeria Simoncini,et al.  Computational Methods for Linear Matrix Equations , 2016, SIAM Rev..

[66]  Dan S. Henningson,et al.  Matrix-Free Methods for the Stability and Control of Boundary Layers , 2009 .

[67]  Anne E. Trefethen,et al.  Hydrodynamic Stability Without Eigenvalues , 1993, Science.

[68]  V. C. Patel,et al.  Longitudinal curvature effects in turbulent boundary layers , 1997 .

[69]  Meelan Choudhari,et al.  Görtler Instability and Its Control via Surface Suction Over an Axisymmetric Cone at Mach 6 , 2018, 2018 Fluid Dynamics Conference.

[70]  Chao Yang,et al.  ARPACK users' guide - solution of large-scale eigenvalue problems with implicitly restarted Arnoldi methods , 1998, Software, environments, tools.

[71]  G. Candler,et al.  Input-output analysis for Görtler-type instability in axisymmetric hypersonic boundary-layers , 2020, AIAA AVIATION 2020 FORUM.

[72]  Michael T. Semper,et al.  Freestream Turbulence Measurements in a Continuously Variable Hypersonic Wind Tunnel , 2012 .

[73]  Graham V. Candler,et al.  Effect of Vibrational Nonequilibrium on Hypersonic Double-Cone Experiments , 2003 .

[74]  R. LeVeque,et al.  The immersed interface method for acoustic wave equations with discontinuous coefficients , 1997 .

[75]  Boris Laschka,et al.  Small Disturbance Euler Equations: Efficient and Accurate Tool for Unsteady Load Prediction , 2000 .

[76]  C. B. Lee,et al.  Hypersonic boundary layer transition on a concave wall: stationary Görtler vortices , 2019, Journal of Fluid Mechanics.

[77]  A. Fedorov Transition and Stability of High-Speed Boundary Layers , 2011 .

[78]  Michael T. Semper,et al.  On the Design and Calibration of an Actively Controlled Expansion Hypersonic Wind Tunnel , 2009 .

[79]  Armin Zare,et al.  Modeling mode interactions in boundary layer flows via the parabolized Floquet equations , 2017, Physical Review Fluids.

[80]  Chau-Lyan Chang,et al.  Oblique-mode breakdown and secondary instability in supersonic boundary layers , 1994, Journal of Fluid Mechanics.

[81]  Randall J. LeVeque,et al.  High-resolution finite-volume methods for acoustic waves in periodic and random media , 1999 .

[82]  G. Candler,et al.  Subgrid-scale effects in compressible variable-density decaying turbulence , 2018, Journal of Fluid Mechanics.

[83]  Pramod K. Subbareddy,et al.  A fully discrete, kinetic energy consistent finite-volume scheme for compressible flows , 2009, J. Comput. Phys..

[84]  M. Malik Numerical methods for hypersonic boundary layer stability , 1990 .

[85]  Peter J. Schmid,et al.  A preconditioned Krylov technique for global hydrodynamic stability analysis of large-scale compressible flows , 2010, J. Comput. Phys..

[86]  T. Colonius,et al.  Spectral analysis of jet turbulence , 2017, Journal of Fluid Mechanics.

[87]  E. Reshotko,et al.  Optimal Disturbances in Compressible Boundary Layers { Complete Energy Norm Analysis , 2005 .

[88]  Graham V. Candler,et al.  The solution of the Navier-Stokes equations using Gauss-Seidel line relaxation , 1989 .

[89]  E. Reshotko Transient growth: A factor in bypass transition , 2001 .

[90]  L. Mack Boundary-Layer Linear Stability Theory , 1984 .

[91]  M. Y. Hussaini,et al.  Compressible stability of growing boundary layers using parabolized stability equations , 1991 .

[92]  G. Candler,et al.  Görtler instability analysis of Mach 6 flow on a flared axisymmetric cone with and without suction , 2019, AIAA Aviation 2019 Forum.

[93]  Hans G. Hornung,et al.  Experiments on passive hypervelocity boundary-layer control using an ultrasonically absorptive surface , 2002 .

[94]  P. Schmid,et al.  Stability and Transition in Shear Flows. By P. J. SCHMID & D. S. HENNINGSON. Springer, 2001. 556 pp. ISBN 0-387-98985-4. £ 59.50 or $79.95 , 2000, Journal of Fluid Mechanics.

[95]  Steven P. Schneider,et al.  Development of Hypersonic Quiet Tunnels , 2008 .

[96]  Armin Zare,et al.  Stochastic receptivity analysis of boundary layer flow , 2018, Physical Review Fluids.

[97]  M. Gaster On the effects of boundary-layer growth on flow stability , 1974, Journal of Fluid Mechanics.

[98]  J. Finnigan,et al.  A streamline coordinate system for distorted two-dimensional shear flows , 1983, Journal of Fluid Mechanics.

[99]  Pramod K. Subbareddy,et al.  Direct numerical simulation of high-speed transition due to an isolated roughness element , 2014, Journal of Fluid Mechanics.

[100]  E. Erdem,et al.  Investigation of the double ramp in hypersonic flow using luminescent measurement systems , 2012 .

[101]  H. Olivier,et al.  Experimental investigation of Görtler vortices in hypersonic ramp flows , 2017, Experiments in Fluids.

[102]  Vassilis Theofilis,et al.  Three-Dimensional Instabilities of Compressible Flow over Open Cavities: Direct Solution of hte BiGlobal Eivenvalue Problem , 2004 .

[103]  S. Cherubini,et al.  The effects of non-normality and nonlinearity of the Navier–Stokes operator on the dynamics of a large laminar separation bubble , 2010 .

[104]  S. Di Sabatino,et al.  A Method of Analysis for Turbulent Flows Using the Streamline Coordinate System , 1997 .

[105]  Hermann F. Fasel,et al.  Direct numerical simulation of transition in supersonic boundary layers: oblique breakdown , 1993 .

[106]  I. Gluzman,et al.  Input-output framework for actuated boundary layers , 2020, Physical Review Fluids.

[107]  Tryphon T. Georgiou,et al.  Colour of turbulence , 2016, Journal of Fluid Mechanics.

[108]  L. Trefethen,et al.  Spectra and Pseudospectra , 2020 .

[109]  J. Spurk Boundary Layer Theory , 2019, Fluid Mechanics.

[110]  J. Robinet,et al.  Bifurcations in shock-wave/laminar-boundary-layer interaction: global instability approach , 2007, Journal of Fluid Mechanics.

[111]  M. Dahleh,et al.  Energy amplification in channel flows with stochastic excitation , 2001 .

[112]  T. Colonius,et al.  Three-dimensional instabilities in compressible flow over open cavities , 2008, Journal of Fluid Mechanics.

[113]  Raman Sujith,et al.  On Chu's disturbance energy , 2011 .

[114]  P. Schmid,et al.  Optimal frequency-response sensitivity of compressible flow over roughness elements* , 2015 .

[115]  F. P. Bertolotti,et al.  Analysis of the linear stability of compressible boundary layers using the PSE , 1991 .

[116]  J. Steelant,et al.  Transitional shock-wave/boundary-layer interactions in hypersonic flow , 2014, Journal of Fluid Mechanics.

[117]  H. Gortler On the three-dimensional instability of laminar boundary layers on concave walls , 1954 .

[118]  P. Schmid Nonmodal Stability Theory , 2007 .

[119]  P. Schmid,et al.  Analysis of Fluid Systems: Stability, Receptivity, SensitivityLecture notes from the FLOW-NORDITA Summer School on Advanced Instability Methods for Complex Flows, Stockholm, Sweden, 2013 , 2014 .

[120]  Eli Reshotko,et al.  Transition Issues at Hypersonic Speeds , 2006 .

[121]  S. Mittal Stability of flow past a cylinder: Energy budget of eigenmodes , 2009 .

[122]  J. Schmisseur,et al.  Influence of Perturbations on 3-D Hypersonic Shock Laminar Boundary Interactions , 2017 .