Compressible Boundary Layer Stability Analyzed with the PSE Equations PDF Download
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Author: Fabio P. Bertolotti
Publisher:
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Category :
Languages : en
Pages :
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Author: Fabio P. Bertolotti
Publisher:
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Category :
Languages : en
Pages :
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Author: National Aeronautics and Space Administration (NASA)
Publisher: Createspace Independent Publishing Platform
ISBN: 9781722340674
Category :
Languages : en
Pages : 50
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Compressible stability of growing boundary layers is studied by numerically solving the partial differential equations under a parabolizing approximation. The resulting parabolized stability equations (PSE) account for nonparallel as well as nonlinear effects. Evolution of disturbances in compressible flat-plate boundary layers are studied for freestream Mach numbers ranging from 0 to 4.5. Results indicate that the effect of boundary-layer growth is important for linear disturbances. Nonlinear calculations are performed for various Mach numbers. Two-dimensional nonlinear results using the PSE approach agree well with those from direct numerical simulations using the full Navier-Stokes equations while the required computational time is less by an order of magnitude. Spatial simulation using PSE were carried out for both the fundamental and subharmonic type breakdown for a Mach 1.6 boundary layer. The promising results obtained show that the PSE method is a powerful tool for studying boundary-layer instabilities and for predicting transition over a wide range of Mach numbers. Chang, Chau-Lyan and Malik, Mujeeb R. and Erlebacher, Gordon and Hussaini, M. Yousuff Unspecified Center NAS1-18605; NAS1-19480; NAS1-18240; RTOP 505-90-52-01...
Author: Sean H. Hu
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Category :
Languages : en
Pages :
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Author: National Aeronautics and Space Administration (NASA)
Publisher: Createspace Independent Publishing Platform
ISBN: 9781722458843
Category :
Languages : en
Pages : 46
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Numerical methods for the compressible boundary-layer equations are facilitated by transformation from the physical (x, y) plane to a computational (xi, eta) plane in which the evolution of the flow is 'slow' in the time-like xi direction. The commonly used Levy-Lees transformation results in a computationally well-behaved problem for a wide class of non-similar boundary-layer flows, but it complicates interpretation of the solution in physical space. Specifically, the transformation is inherently nonlinear, and the physical wall-normal velocity is transformed out of the problem and is not readily recovered. In light of recent research which shows mean-flow non-parallelism to significantly influence the stability of high-speed compressible flows, the contribution of the wall-normal velocity in the analysis of stability should not be routinely neglected. Conventional methods extract the wall-normal velocity in physical space from the continuity equation, using finite-difference techniques and interpolation procedures. The present spectrally-accurate method extracts the wall-normal velocity directly from the transformation itself, without interpolation, leaving the continuity equation free as a check on the quality of the solution. The present method for recovering wall-normal velocity, when used in conjunction with a highly-accurate spectral collocation method for solving the compressible boundary-layer equations, results in a discrete solution which is extraordinarily smooth and accurate, and which satisfies the continuity equation nearly to machine precision. These qualities make the method well suited to the computation of the non-parallel mean flows needed by spatial direct numerical simulations (DNS) and parabolized stability equation (PSE) approaches to the analysis of stability. Pruett, C. David Unspecified Center NAS1-18599; RTOP 505-59-53-02.
Author: Institute for Computer Applications in Science and Engineering
Publisher:
ISBN:
Category :
Languages : en
Pages : 52
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Author: Guy Métivier
Publisher: Springer Science & Business Media
ISBN: 9780817633905
Category : Mathematics
Languages : en
Pages : 224
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* Metivier is an expert in the field of pdes/math physics, with a particular emphasis on shock waves. * New monograph focuses on mathematical methods, models, and applications of boundary layers, present in many problems of physics, engineering, fluid mechanics. * Metivier has good Birkhauser track record: one of the main authors of "Advances in the Theory of Shock Waves" (Freistuehler/Szepessy, eds, 4187-4). * Manuscript endorsed by N. Bellomo, MSSET series editor...should be a good sell to members of MSSET community, who by-in-large are based in Europe. * Included are self-contained introductions to different topics such as hyperbolic boundary value problems, parabolic systems, WKB methods, construction of profiles, introduction to the theory of Evans’ functions, and energy methods with Kreiss’ symmetrizers.
Author: Eli Reshotko
Publisher:
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Category : Aerodynamics
Languages : en
Pages : 48
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Author: Nabil M. El- Hady
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Category :
Languages : en
Pages : 44
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Author: J. S. B. Gajjar
Publisher:
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Category :
Languages : en
Pages : 42
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Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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In a previous report the authors analyzed the stability of the lower branch solutions of the incompressible (M sub infinity = O) Falkner-Skan boundary layers. There a perturbation analysis to these boundary layers was performed resulting in the Rayleigh stability equation. Eigen value solutions were obtained for the Rayleigh equation for different adverse pressure gradient (beta) values. All retarded flows were found to be unstable for a small range of frequencies with the amplification factor increasing as the extent of reversed flow increased. In this report they have entended that work by including the effect of Mach number M sub infinity on the stability of adiabatic (S sub W = O) Falker-Skan equations for beta = -.04, -.08, -.12, -.16 and -.19884. We found out that in all these cases as the Mach number M sub infinity increases the instability of flow decreases. In most of the cases the instability almost completely disappeared at M sub infinity = 3.
