On simulation and analysis of instability and transition in high-speed boundary-layer flows

Abstract The simulation of instabilities and laminar-trubulent transition in high-speed boundary-layer flows represents one of the major computational challenges of the decade. By taking advantage of recent advances in computational science and instability theory for compressible flows, we have formulated an approach to this problem that combines parabolized stability equation (PSE) methodology with spatial direct numerical simulation (DNS). The relatively inexpensive PSE method is used to explore the parameter space, to compute the early (weakly and moderately nonlinear) stages of laminar breakdown, and to provide inflow conditions for the spatial DNS, which is then used to compute the highly nonlinear laminar-breakdown stage. The approach is made feasible by an accurate and efficient DNS algorithm, which has been implemented in parallel on a CRAY C90 supercomputer. The design of the DNS algorithm is discussed in detail, with emphasis on factors that affect both accuracy and efficiency. The method is applied to the investigation of the laminar breakdown of the boundary layer on an axisymmetric sharp cone in Mach 8 flow. Techniques for analysis of the resulting data are also addressed, including novel computational flow imaging procedures.

[1]  George Havener,et al.  Computational flow imaging - Fundamentals and history , 1994 .

[2]  Gordon Erlebacher,et al.  Direct simulation of spatially evolving compressible turbulent boundary layers , 1995 .

[3]  Linda Smith.  Pulsed-laser schlieren visualization of hypersonic boundary-layer instability waves , 1994 .

[4]  Thomas A. Zang,et al.  Direct numerical simulation of laminar breakdown in high-speed, axisymmetric boundary layers , 1992 .

[5]  Sanjiva K. Lele,et al.  Direct numerical simulation of compressible free shear flows , 1989 .

[6]  C. David Pruett,et al.  Spatial direct numerical simulation of high-speed boundary-layer flows part I: Algorithmic considerations and validation , 1995 .

[7]  M. Carpenter,et al.  Fourth-order 2N-storage Runge-Kutta schemes , 1994 .

[8]  F. Hussain,et al.  Three-dimensional numerical simulation of a compressible, spatially evolving mixing layer , 1988 .

[9]  J. Williamson.  Low-storage Runge-Kutta schemes , 1980 .

[10]  T. A. Zang,et al.  Spectral methods for fluid dynamics , 1987 .

[11]  Craig L. Streett,et al.  A SPECTRAL COLLOCATION METHOD FOR COMPRESSIBLE, NON-SIMILAR BOUNDARY LAYERS , 1991 .

[12]  T. Poinsot.  Boundary conditions for direct simulations of compressible viscous flows , 1992 .

[13]  D. Gottlieb,et al.  The Stability of Numerical Boundary Treatments for Compact High-Order Finite-Difference Schemes , 1993 .

[14]  Neil D. Sandham,et al.  Three-dimensional simulations of large eddies in the compressible mixing layer , 1991, Journal of Fluid Mechanics.

[15]  Chau-Lyan Chang,et al.  Non-parallel stability of compressible boundary layers , 1993 .

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

[17]  N. A. Adams,et al.  Direct Numerical Simulation of Transition in A Spatially Growing Compressible Boundary Layer Using A New Fourier Method , 1994 .

[18]  A. Bayliss,et al.  On the interaction between first‐ and second‐mode waves in a supersonic boundary layer , 1991 .

[19]  F. Bertolotti.  Linear and nonlinear stability of boundary layers with streamwise varying properties , 1991 .

[20]  Michael Gaster,et al.  A note on the relation between temporally-increasing and spatially-increasing disturbances in hydrodynamic stability , 1962, Journal of Fluid Mechanics.

[21]  K. Thompson.  Time-dependent boundary conditions for hyperbolic systems, II , 1990 .

[22]  Craig L. Streett,et al.  Spectral multi-domain for large-scale fluid dynamic simulations , 1989 .

[23]  N. A Adams,et al.  Numerical Simulation of Transition in a Compressible Flat Plate Boundary Layer , 1993 .

[24]  Nikolaus A. Adams,et al.  Modeling of nonparallel effects in temporal direct numerical simulations of compressible boundary-layer transition , 1995 .

[25]  C. David Pruett,et al.  Spatial direct numerical simulation of high-speed boundary-layer flows Part II: Transition on a cone in Mach 8 flow , 1995 .

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

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