Fluid Flow and Transfer Processes; Mechanics of Materials; Computational Mechanics; Mechanical Engineering; Fluid Flow Instabilities; Linear Stability Analysis
Abstract :
[en] Linear stability analyses are performed to study the dynamics of linear convective instability mechanisms in a laminar shock-wave/boundary-layer interaction at Mach 1.7. In order to account for all two-dimensional gradients elliptically, we introduce perturbations into an initial-value problem that are found as solutions to an eigenvalue problem formulated in a moving frame of reference. We demonstrate that this methodology provides results that are independent of the numerical setup, frame speed, and type of eigensolutions used as initial conditions. The obtained time-integrated wave packets are then Fourier-transformed to recover individual-frequency amplification curves. This allows us to determine the dominant spanwise wavenumber and frequency yielding the largest amplification of perturbations in the shock-induced recirculation bubble. By decomposing the temporal wave-packet growth rate into the physical energy-production processes, we provide an in-depth characterization of the convective instability mechanisms in the shock-wave/boundary-layer interaction. For the particular case studied, the largest growth rate is achieved in the near-vicinity of the bubble apex due to the wall-normal (productive) and streamwise (destructive) Reynolds-stress energy-production terms. We also observe that the Reynolds heat-flux effects are similar but contribute to a smaller extent.
Disciplines :
Aerospace & aeronautics engineering
Author, co-author :
Niessen, Sébastien ; Université de Liège - ULiège > Aérospatiale et Mécanique (A&M)
Groot, Koen J. ; Department of Aerospace Engineering, Texas A&M University, College Station, Texas 77843, USA
Hickel, Stefan ; Faculty of Aerospace Engineering, Delft University of Technology, Delft 2629HS, The Netherlands
Terrapon, Vincent ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Modélisation et contrôle des écoulements turbulents
Language :
English
Title :
Convective instabilities in a laminar shock-wave/boundary-layer interaction
Publication date :
February 2023
Journal title :
Physics of Fluids
ISSN :
1070-6631
eISSN :
1089-7666
Publisher :
AIP Publishing
Volume :
35
Issue :
2
Pages :
024101
Peer reviewed :
Peer Reviewed verified by ORBi
Tags :
CÉCI : Consortium des Équipements de Calcul Intensif
J. Délery and J.-P. Dussauge, "Some physical aspects of shock wave/boundary layer interactions," Shock Waves 19, 453-468 (2009). 10.1007/s00193-009-0220-z
A. Ferri, "Experimental results with airfoils tested in the high-speed tunnel at Guidonia," Report No. NACA-TM-946 (National Advisory Committee for Aeronautics, 1939).
C. d. Donaldson, "Effects of interaction between normal shock and boundary layer," Report No. NACA-CB-4A27 (National Advisory Committee for Aeronautics, 1944).
H. W. Liepmann, "The interaction between boundary layer and shock waves in transonic flow," J. Aeronaut. Sci. 13, 623-637 (1946). 10.2514/8.11473
J. Ackeret, F. Feldmann, and N. Rott, "Investigations of compression shocks and boundary layers in gases moving at high speed," Report No. NACA-TM-1113 (National Advisory Committee for Aeronautics, 1947).
A. Fage and R. F. Sargent, "Shock-wave and boundary-layer phenomena near a flat surface," Proc. R. Soc. London, Ser. A 190, 1-20 (1947). 10.1098/rspa.1947.0058
J. Délery, J. G. Marvin, and E. Reshotko, "Shock-wave boundary layer interactions," Report No. ADA171302 (Advisory Group for Aerospace Research and Development, 1986).
D. S. Dolling, "Fifty years of shock-wave/boundary-layer interaction research: What next?," AIAA J. 39, 1517-1531 (2001). 10.2514/2.1476
H. Babinsky and J. Harvey, Shock wave-Boundary-Layer Interactions (Cambridge University Press, Cambridge, 2011).
D. V. Gaitonde, "Progress in shock wave/boundary layer interactions," Prog. Aerosp. Sci. 72, 80-99 (2015). 10.1016/j.paerosci.2014.09.002
S. J. Beresh, N. T. Clemens, and D. S. Dolling, "Relationship between upstream turbulent boundary-layer velocity fluctuations and separation shock unsteadiness," AIAA J. 40, 2412-2422 (2002). 10.2514/2.1609
B. Ganapathisubramani, N. T. Clemens, and D. S. Dolling, "Effects of upstream boundary layer on the unsteadiness of shock-induced separation," J. Fluid Mech. 585, 369-394 (2007). 10.1017/S0022112007006799
B. Ganapathisubramani, N. T. Clemens, and D. S. Dolling, "Low-frequency dynamics of shock-induced separation in a compression ramp interaction," J. Fluid Mech. 636, 397-425 (2009). 10.1017/S0022112009007952
M. Wu and M. P. Martín, "Analysis of shock motion in shockwave and turbulent boundary layer interaction using direct numerical simulation data," J. Fluid Mech. 594, 71-83 (2008). 10.1017/S0022112007009044
B. W. Tester, J. G. Coder, C. S. Combs, and J. D. Schmisseur, "Hybrid RANS/LES simulation of transitional shockwave/boundary-layer interaction," in Fluid Dynamics Conference, 2018.
L. E. Lash, M. Gragston, P. A. Kreth, Z. McDaniel, J. G. Coder, and J. D. Schmisseur, "Upstream influence in shock wave/transitional boundary layer interactions at Mach 1.8," AIAA J. 59, 4842-4857 (2021). 10.2514/1.J059980
N. F. Nutter, J. W. Cobourn, R. B. Bond, P. A. Kreth, J. D. Schmisseur, R. S. Glasby, D. L. Stefanski, E. Hereth, and J. G. Coder, "Simulations of dynamic shock wave/boundary layer interactions using HPCMP CREATETM-AV Kestrel COFFE," in AIAA Scitech 2021 Forum, 2021.
J. J. Sebastian and F. K. Lu, "Upstream-influence scaling of fin-induced laminar shockwave/boundary-layer interactions," AIAA J. 59, 1861-1864 (2021). 10.2514/1.J059354
E. Touber and N. D. Sandham, "Oblique shock impinging on a turbulent boundary layer: Low-frequency mechanisms," in 38th AIAA Fluid Dynamics Conference and Exhibit (University of Southampton, Southampton, UK, 2008).
E. Touber and N. D. Sandham, "Large-eddy simulation of low-frequency unsteadiness in a turbulent shock-induced separation bubble," Theor. Comput. Fluid Dyn. 23, 79-107 (2009). 10.1007/s00162-009-0103-z
S. Pirozzoli and F. Grasso, "Direct numerical simulation of impinging shock wave/turbulent boundary layer interaction at M = 2.25," Phys. Fluids 18, 065113 (2006). 10.1063/1.2216989
J.-P. Dussauge, P. Dupont, and J. F. Debiève, "Unsteadiness in shock wave boundary layer interactions with separation," Aerosp. Sci. Technol. 10, 85-91 (2006). 10.1016/j.ast.2005.09.006
S. Piponniau, J. P. Dussauge, J. F. Debiève, and P. Dupont, "A simple model for low-frequency unsteadiness in shock-induced separation," J. Fluid Mech. 629, 87-108 (2009). 10.1017/S0022112009006417
M. Grilli, P. J. Schmid, S. Hickel, and N. A. Adams, "Analysis of unsteady behaviour in shockwave turbulent boundary layer interaction," J. Fluid Mech. 700, 16-28 (2012). 10.1017/jfm.2012.37
A. Sansica, N. D. Sandham, and Z. Hu, "Instability and low-frequency unsteadiness in a shock-induced laminar separation bubble," J. Fluid Mech. 798, 5-26 (2016). 10.1017/jfm.2016.297
V. Pasquariello, S. Hickel, and N. A. Adams, "Unsteady effects of strong shock-wave/boundary-layer interaction at high Reynolds number," J. Fluid Mech. 823, 617-657 (2017). 10.1017/jfm.2017.308
M. C. Adler and D. V. Gaitonde, "Dynamic linear response of a shock/turbulent-boundary-layer interaction using constrained perturbations," J. Fluid Mech. 840, 291-341 (2018). 10.1017/jfm.2018.70
K. Sasaki, D. C. Barros, A. V. G. Cavalieri, and L. Larchevêque, "Causality in the shock wave/turbulent boundary layer interaction," Phys. Rev. Fluid 6, 064609 (2021). 10.1103/PhysRevFluids.6.064609
N. T. Clemens and V. Narayanaswamy, "Low-frequency unsteadiness of shock wave/turbulent boundary layer interactions," Annu. Rev. Fluid Mech. 46, 469-492 (2014). 10.1146/annurev-fluid-010313-141346
A. Dwivedi, N. Hildebrand, J. W. Nichols, G. V. Candler, and M. R. Jovanović, "Transient growth analysis of oblique shock-wave/boundary-layer interactions at Mach 5.92," Phys. Rev. Fluids 5, 063904 (2020). 10.1103/PhysRevFluids.5.063904
N. Bonne, V. Brion, E. Garnier, R. Bur, P. Molton, D. Sipp, and L. Jacquin, "Analysis of the two-dimensional dynamics of a Mach 1.6 shock wave/transitional boundary layer interaction using a RANS based resolvent approach," J. Fluid Mech. 862, 1166-1202 (2019). 10.1017/jfm.2018.932
B. Bugeat, J.-C. Robinet, J.-C. Chassaing, and P. Sagaut, "Low-frequency resolvent analysis of the laminar oblique shock wave/boundary layer interaction," J. Fluid Mech. 942, A43 (2022). 10.1017/jfm.2022.390
J. W. Nichols, J. Larsson, M. Bernardini, and S. Pirozzoli, "Stability and modal analysis of shock/boundary layer interactions," Theor. Comput. Fluid Dyn. 31, 33-50 (2017). 10.1007/s00162-016-0397-6
S. Pirozzoli, J. Larsson, J. Nichols, M. Bernardini, B. Morgan, and S. Lele, "Analysis of unsteady effects in shock/boundary layer interactions," in Proceedings of the Summer Program (Center for Turbulence Research, 2010), pp. 153-164.
J. C. Robinet, "Bifurcations in shock-wave/laminar-boundary-layer interaction: Global instability approach," J. Fluid Mech. 579, 85-112 (2007). 10.1017/S0022112007005095
N. J. Hildebrand, A. Dwivedi, J. W. Nichols, M. R. Jovanović, and G. V. Candler, "Simulation and stability analysis of oblique shock-wave/boundary-layer interactions at Mach 5.92," Phys. Rev. Fluids 3, 013906 (2018). 10.1103/PhysRevFluids.3.013906
D. Rodríguez, E. M. Gennaro, and L. F. Souza, "Self-excited primary and secondary instability of laminar separation bubbles," J. Fluid Mech. 906, A13 (2020). 10.1017/jfm.2020.767
F. Guiho, F. Alizard, and J. C. Robinet, "Instabilities in oblique shock wave/laminar boundary-layer interactions," J. Fluid Mech. 789, 1-35 (2016). 10.1017/jfm.2015.729
Y. Yao, L. Krishnan, N. D. Sandham, and G. T. Roberts, "The effect of Mach number on unstable disturbances in shock/boundary-layer interactions," Phys. Fluids 19, 054104 (2007). 10.1063/1.2720831
A. Sansica, N. D. Sandham, and Z. Hu, "Forced response of a laminar shock-induced separation bubble," Phys. Fluids 26, 093601 (2014). 10.1063/1.4894427
V. Theofilis, "Advances in global linear instability analysis of nonparallel and three-dimensional flows," Prog. Aerosp. Sci. 39, 249-315 (2003). 10.1016/S0376-0421(02)00030-1
K. J. Groot, "BiGlobal stability of shear flows spanwise & streamwise analyses," Ph.D. thesis (TU Delft and Von Karman Institute for Fluid Dynamics, 2018).
U. Ehrenstein and F. Gallaire, "On two-dimensional temporal modes in spatially evolving open flows: The flat-plate boundary layer," J. Fluid Mech. 536, 209-218 (2005). 10.1017/S0022112005005112
F. Alizard and J.-C. Robinet, "Spatially convective global modes in a boundary layer," Phys. Fluids 19, 114105 (2007). 10.1063/1.2804958
D. A. Rodríguez, A. Tumin, and V. Theofilis, "Towards the foundation of a global modes concept," in 6th AIAA Theoretical Fluid Mechanics Conference (American Institute of Aeronautics and Astronautics, Honolulu, HI (AIAA, 2011), pp. 1-18.
K. J. Groot and H. M. Schuttelaars, "Accurate numerical approximation of the absolute stability of unbounded flows," Physica D 402, 132224 (2020). 10.1016/j.physd.2019.132224
S. Mittal and B. Kumar, "A stabilized finite element method for global analysis of convective instabilities in nonparallel flows," Phys. Fluids 19, 088105 (2007). 10.1063/1.2759977
S. Mittal, J. J. Kottaram, and B. Kumar, "Onset of shear layer instability in flow past a cylinder," Phys. Fluids 20, 054102 (2008). 10.1063/1.2909587
B. Kumar and S. Mittal, "On the origin of the secondary vortex street," J. Fluid Mech. 711, 641-666 (2012). 10.1017/jfm.2012.421
R. H. M. Giepman, "Flow control for oblique shock wave reflections," Ph.D. thesis (Delft University of Technology, 2016).
S. Hickel, C. P. Egerer, and J. Larsson, "Subgrid-scale modeling for implicit large eddy simulation of compressible flows and shock-turbulence interaction," Phys. Fluids 26, 106101 (2014). 10.1063/1.4898641
S. Niessen, "BiGlobal stability analysis: Laminar shock-wave/boundary-layer interactions," Master's thesis (Faculty of Applied Sciences, University of Liège, 2017).
E. Åkervik, L. Brandt, D. S. Henningson, J. Hœpffner, O. Marxen, and P. Schlatter, "Steady solutions of the Navier-Stokes equations by selective frequency damping," Phys. Fluids 18, 068102 (2006). 10.1063/1.2211705
B. E. Jordi, C. J. Cotter, and S. J. Sherwin, "Encapsulated formulation of the selective frequency damping method," Phys. Fluids 26, 034101 (2014). 10.1063/1.4867482
J. Casacuberta, K. J. Groot, H. J. Tol, and S. Hickel, "Effectivity and efficiency of selective frequency damping for the computation of unstable steady-state solutions," J. Comput. Phys. 375, 481-497 (2018). 10.1016/j.jcp.2018.08.056
N. Cerulus, H. Quintanilha, and V. Theofilis, "Global linear stability analysis of the supersonic flows over a hollow cylinder flare model," in AIAA Scitech Forum, Reston, VA (American Institute of Aeronautics and Astronautics, 2021), p. 247.
D. Chapman, D. Kuehn, and H. Larson, "Investigation of separated flow in supersonic and subsonic streams with emphasis of the effect of transition," Report No. 1356 (National Advisory Committee for Aeronautics, Ames Aeronautical Lab, Moffett Field, CA, 1958).
M. P. Avanci, D. Rodríguez, and L. S. d. B. Alves, "A geometrical criterion for absolute instability in separated boundary layers," Phys. Fluids 31, 014103 (2019). 10.1063/1.5079536
E. B. White, "Transient growth of stationary disturbances in a flat plate boundary layer," Phys. Fluids 14, 4429-4439 (2002). 10.1063/1.1521124
Z. Huang and X. Wu, "A local scattering approach for the effects of abrupt changes on boundary-layer instability and transition: A finite-Reynolds-number formulation for isolated distortions," J. Fluid Mech. 822, 444-483 (2017). 10.1017/jfm.2017.287
L. Zhao, M. Dong, and Y. Yang, "Harmonic linearized Navier-Stokes equation on describing the effect of surface roughness on hypersonic boundary-layer transition," Phys. Fluids 31, 034108 (2019). 10.1063/1.5086912
N. Hildebrand, M. M. Choudhari, and P. Paredes, "Predicting boundary-layer transition over backward-facing steps via linear stability analysis," AIAA J. 58, 3728-3734 (2020). 10.2514/1.J059713
T. Appel, "Boundary layer instabilities due to surface irregularities: A harmonic Navier-Stokes approach," Ph.D. thesis (Imperial College London, 2020).
M. M. Peck, K. J. Groot, and H. L. Reed, "Boundary-layer instability on a highly swept fin on a hypersonic cone," in AIAA AVIATION 2022 Forum (AIAA, 2022), p. 3555.
K. J. Groot, "Derivation of and simulations with BiGlobal stability equations," Master's thesis (Delft University of Technology, 2013).
W. S. Saric and A. H. Nayfeh, "Nonparallel stability of boundary-layer flows," Phys. Fluids 18, 945-952 (1975). 10.1063/1.861266
P. Huerre and P. A. Monkewitz, "Local and global instabilities in spatially developing flows," Annu. Rev. Fluid Mech. 22, 473-537 (1990). 10.1146/annurev.fl.22.010190.002353
F. P. Bertolotti, T. Herbert, and P. Spalart, "Linear and nonlinear stability of the Blasius boundary layer," J. Fluid Mech. 242, 441-474 (1992). 10.1017/S0022112092002453
P. A. Monkewitz, P. Huerre, and J.-M. Chomaz, "Global linear stability analysis of weakly non-parallel shear flows," J. Fluid Mech. 251, 1-20 (1993). 10.1017/S0022112093003313
C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang, Spectral Methods, Fundamentals in Single Domains (Springer, 2006).
M. Malik, "Numerical methods for hypersonic boundary layer stability," J. Comput. Phys. 86, 376-413 (1990). 10.1016/0021-9991(90)90106-B
K. J. Groot, J. Serpieri, F. Pinna, and M. Kotsonis, "Secondary crossflow instability through global analysis of measured base flows," J. Fluid Mech. 846, 605-653 (2018). 10.1017/jfm.2018.253
B. T. Chu, "On the energy transfer to small disturbances in fluid flow (Part I)," Acta Mech. 1, 215-234 (1965). 10.1007/BF01387235
L. Larchevêque, "Low-and medium-frequency unsteadinesses in a transitional shock-boundary reflection with separation," in 54th AIAA Aerospace Sciences Meeting, San Diego, CA (American Institute of Aeronautics and Astronautics (AIAA 2016-1833), 2016), pp. 1-14.
O. M. F. Browne, A. P. Haas, H. F. Fasel, and C. Brehm, "An efficient linear wavepacket tracking method for hypersonic boundary-layer stability prediction," J. Comput. Phys. 380, 243-268 (2019). 10.1016/j.jcp.2018.11.028
P. J. Schmid and D. S. Henningson, Stability and Transition in Shear Flows (Springer, 2001).
I. P. Montero and F. Pinna, "Analysis of the instabilities induced by an isolated roughness element in a laminar high-speed boundary layer," J. Fluid Mech. 915, A90 (2021). 10.1017/jfm.2021.70
