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  • Electronic Resource  (4)
  • 1990-1994  (4)
  • 1
    Electronic Resource
    Electronic Resource
    On the nonlinear stability of a high-speed, axisymmetric boundary layer (1991)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 3 (1991), S. 2910-2926 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The stability of a high-speed, axisymmetric boundary-layer flow is investigated by means of secondary instability theory and direct numerical simulation. Parametric studies based on temporal secondary instability theory identify subharmonic secondary instability as a likely path to transition on a hollow cylinder at Mach 4.5. The theoretical predictions are validated by direct numerical solution of the compressible Navier–Stokes equations. Initial perturbations for the temporal direct numerical simulation consist of an axisymmetric "second-mode'' primary disturbance and a subharmonic secondary disturbance comprised of four oblique wave components. At small initial amplitudes of the secondary disturbance, growth rates obtained from the spectrally accurate numerical simulation agree to several significant digits with linear growth rates predicted by secondary instability theory. Qualitative agreement persists to relatively large amplitudes of the secondary disturbance. Moderate transverse curvature is shown to significantly affect the growth rate of axisymmetric "second-mode'' disturbances, the likely candidates of primary instability. The influence of curvature on secondary instability is largely indirect, but most probably significant, through modulation of the primary disturbance amplitude. Subharmonic secondary instability is shown to be predominantly inviscid in nature, and to account for peaks in the Reynolds stress components near the critical layer.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.857834
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Direct numerical simulation and data analysis of a Mach 4.5 transitional boundary-layer flow (1994)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 6 (1994), S. 1323-1330 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: This paper describes the creation by temporal direct numerical simulation and the analysis based on the Reynolds stress transport equations of a high quality data set that represents the laminar–turbulent transition of a high-speed boundary-layer flow. Following Pruett and Zang [Theoret. Comput. Fluid Dyn. 3, 345 (1992)], and with the help of algorithmic refinements, the evolution of an axial, Mach 4.5 boundary-layer flow along the exterior of a hollow cylinder is simulated numerically. From a perturbed laminar initial state, the well-resolved simulation proceeds through laminar breakdown to the beginning of a turbulent flow regime. Favre-averaged Reynolds stress transport equations are derived in generalized curvilinear coordinates and are then specialized to the cylindrical geometry at hand. Reynolds stresses and various turbulence quantities, such as turbulent kinetic energy and turbulent Mach number, are calculated from the numerical data at various stages of the transition process. The kinetic energy "budgets'' are also constructed from the transport equations. Various contributing terms for the evolution of kinetic energy, like the rates of production, dissipation, transport, and diffusion, are presented. The compressible dissipation rate is small in comparison with the solenoidal dissipation rate for all times. The pressure–dilatation term is of the same order of magnitude as the compressible dissipation rate. The authors hope that both the data set and the analysis presented will benefit those who attempt to model high-speed transitional flow.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.868300
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    A spectral collocation method for compressible, non-similar boundary layers (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 13 (1991), S. 713-737 
    Details
    ISSN: 0271-2091
    Keywords: Spectral collocation methods ; Compressible flow ; Boundary layer equations ; Stability theory ; Transverse curvature ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An efficient and highly accurate algorithm based on a spectral collocation method is developed for numerical solution of the compressible, two-dimensional and axisymmetric boundary layer equations. The numerical method incorporates a fifth-order, fully implicit marching scheme in the streamwise (timelike) dimension and a spectral collocation method based on Chebyshev polynomial expansions in the wall-normal (spacelike) dimension. The discrete governing equations are cast in residual form and the residuals are minimized at each marching step by a preconditioned Richardson iteration scheme which fully couples energy, momentum and continuity equations. Preconditioning on the basis of the finite difference analogues of the governing equations results in a computationally efficient iteration with acceptable convergence properties. A practical application of the algorithm arises in the area of compressible linear stability theory, in the investigation of the effects of transverse curvature on the stability of flows over axisymmetric bodies. The spectral collocation algorithm is used to derive the non-similar mean velocity and temperature profiles in the boundary layer of a ‘fuselage’ (cylinder) in a high-speed (Mach 5) flow parallel to its axis. The stability of the flow is shown to be sensitive to the gradual streamwise evolution of the mean flow and it is concluded that the effects of transverse curvature on stability should not be ignored routinely.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650130605
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    On the accurate prediction of the wall-normal velocity in compressible boundary-layer flowResearch funded by the Theoretical Flow Physics Branch of the Fluid Mechanics Division, NASA Langley Research Center, under contract NASI-18599. (1993)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 16 (1993), S. 133-152 
    Details
    ISSN: 0271-2091
    Keywords: Boundary-layer equations ; Spectral collocation methods ; Compressible flow ; Wall-normal velocity ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: We consider a problem which arises in the numerical solution of the compressible two-dimensional or axisymmetric boundary-layer equations. Numerical methods for the compressible boundary-layer equations are facilitated by transformation from the physical (x, y) plane to a computational (ξ, η) plane in which the evolution of the flow is ‘slow’ in the time-like ξ direction. The commonly used Levy-Lees transformation results in a computationally well-behaved problem, but it complicates interpretation of the solution in physical space. Specifically, the transformation is inherently non-linear, and the physical wall-normal velocity is transformed out of the problem and is not readily recovered. 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 satisfies the continuity equation nearly to machine precision. As demonstration of the utility of the method, the boundary layers of three prototypical high-speed flows are investigated and compared: the flat plate, the hollow cylinder, and the cone. An important implication for classical linear stability theory is also briefly discussed.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650160204
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    Paper (German National Licenses)
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