Numerical Solutions of the Navier-Stokes Equations for the Supersonic Laminar Flow Over a Two-dimensional Compression Corner PDF Download
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Author: James Edward Carter
Publisher:
ISBN:
Category : Aerodynamics, Supersonic
Languages : en
Pages : 90
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Book Description
Numerical solutions have been obtained for the supersonic, laminar flow over a two-dimensional compression corner. These solutions were obtained as steady-state solutions to the unsteady Navier-Stokes equations using the finite-difference method of Brailovskaya, which has the second-order accuracy in the spatial coordinates. Good agreement was obtained between the computed results and the wall pressure distributions measured experimentally by Lewis, Kubota, and Lees for Mach numbers of 4 and 6.06, and respective Reynolds numbers, based on free-stream conditions and the distance from the leading edge to the corner, of 6.8 x 104 and 1.5 x 105. In those calculations, as well as in others, sufficient resolution was obtained to show the streamline pattern in the separation bubble. Upstream boundary conditions to the compression-corner flow were provided by numerically solving the unsteady Navier-Stokes equations for the flat-plate flow field, beginning at the leading edge. The compression-corner flow field was enclosed by a computational boundary with the unknown boundary conditions supplied by extrapolation from internally computed points. Numerical tests were performed to deduce that the magnitude of the errors introduced by the extrapolation was small. Calculations were made to show the effect of ramp angle and wall suction on the interaction flow field. The pressure distributions obtained in the present calculations, including a case of incipient separation, were plotted together by using the free-interaction scaling of Stewartson and Williams. A good correlation of the numerical results was found, but only fair agreement was found between this correlation and the universal pressure distribution found numerically by Stewartson and Williams.
Author: James Edward Carter
Publisher:
ISBN:
Category : Aerodynamics, Supersonic
Languages : en
Pages : 90
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Book Description
Numerical solutions have been obtained for the supersonic, laminar flow over a two-dimensional compression corner. These solutions were obtained as steady-state solutions to the unsteady Navier-Stokes equations using the finite-difference method of Brailovskaya, which has the second-order accuracy in the spatial coordinates. Good agreement was obtained between the computed results and the wall pressure distributions measured experimentally by Lewis, Kubota, and Lees for Mach numbers of 4 and 6.06, and respective Reynolds numbers, based on free-stream conditions and the distance from the leading edge to the corner, of 6.8 x 104 and 1.5 x 105. In those calculations, as well as in others, sufficient resolution was obtained to show the streamline pattern in the separation bubble. Upstream boundary conditions to the compression-corner flow were provided by numerically solving the unsteady Navier-Stokes equations for the flat-plate flow field, beginning at the leading edge. The compression-corner flow field was enclosed by a computational boundary with the unknown boundary conditions supplied by extrapolation from internally computed points. Numerical tests were performed to deduce that the magnitude of the errors introduced by the extrapolation was small. Calculations were made to show the effect of ramp angle and wall suction on the interaction flow field. The pressure distributions obtained in the present calculations, including a case of incipient separation, were plotted together by using the free-interaction scaling of Stewartson and Williams. A good correlation of the numerical results was found, but only fair agreement was found between this correlation and the universal pressure distribution found numerically by Stewartson and Williams.
Author: James Edward Carter
Publisher:
ISBN:
Category :
Languages : en
Pages : 384
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Author: Peter A. Gnoffo
Publisher:
ISBN:
Category : Aerodynamics, Supersonic
Languages : en
Pages : 100
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Author:
Publisher:
ISBN:
Category : Aerodynamics
Languages : en
Pages : 808
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Author: Richard G. Hindman
Publisher:
ISBN:
Category : Axial flow compressors
Languages : en
Pages : 60
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A computer code for solving the two-dimensional compressible Navier-Stokes equations governing the supersonic/hypersonic flow over a compression ramp as developed by MacCormack was extended to apply to axisymmetric flows over cylinder-flare shapes. Two new operators were developed for this extension, one of which was found to produce an upper stability bound on the step size. This bound is proportional to the Prandtl number and inversely proportional to the ratio of thermal capacities of the fluid times the maximum value over all grid points of the kinematic viscosity scaled by the radial coordinate value. Additionally, the computer code was modified to allow for the option of wall mass transfer. This required reformulation of the hyperbolic fine mesh operator because of an assumption in the development of the original operator that the wall-normal velocity in the fine mesh is much less than the sound speed. Numerical results are presented for a particular hollow cylinder-flare configuration, and comparisons are made with the experimental data of Roshko and Thomke and with the results of a boundary-layer code attributable to Patankar and Spalding. (Author).
Author: James Edward Carter
Publisher:
ISBN:
Category : Boundary layer
Languages : en
Pages : 72
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Numerical solutions of the laminar, incompressible boundary-layer equations are presented for flows involving separation and reattachment. Regular solutions are obtained with an inverse approach in which either the displacement thickness or the skin friction is specified; the pressure is deduced from the solution. A vorticity--stream-function formulation of the boundary-layer equations is used to eliminate the unknown pressure. Solutions of the resulting finite-difference equations, in which the flow direction is taken into account, are obtained by several global iteration schemes which are stable and have unconditional diagonal dominance. Results are compared with Klineberg and Steger's separated boundary-layer calculations, and with Briley's solution of the Navier-Stokes equations for a separated region. In addition, an approximate technique is presented in which the streamwise convection of vorticity is set equal to zero in the reversed flow region; such a technique results in a quick forward-marching procedure for separated flows.
Author:
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ISBN:
Category : Aeronautics
Languages : en
Pages : 584
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Author:
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ISBN:
Category : Aeronautics
Languages : en
Pages : 724
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Author: Anthony W. Fiore
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ISBN:
Category : Turbulent boundary layer
Languages : en
Pages : 962
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In 1975 the U.S. Air Force and the Federal Republic of Germany signed a Data Exchange Agreement numbered AF-75-G-7440 entitled 'Viscous and Interacting Flow Fields.' The purpose was to exchange data in the area of boundary layer research. It includes both experimental and theoretical boundary layer research at speeds from subsonic to hypersonic Mach numbers in the presence of laminar, transitional, and turbulent boundary layers. The main effort in recent years has been on turbulent boundary layers, both attached and separated in the presence of such parameters as pressure gradients, wall temperature, surface roughness, etc. In the United States the research was conducted in various Department of Defense, NASA, aircraft corporations, and various university laboratories. In the Federal Republic of Germany it was carried out within the various DFVLR, industrial, and university research centers.
Author: Y. Kronzon
Publisher:
ISBN:
Category :
Languages : en
Pages : 102
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