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ANALYSIS AND CONTROL OF SUPERSONIC VORTEX BREAKDOWN FLOWS

Osama A. Kandil

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Abstract

Analysis and computation of steady, compressible, quasi-axisymmetric flow of an isolated, slender vortex are considered. The compressible, Navier-Stokes equations are reduced to a simpler set by using the slenderness and quasi-axisymmetry assumptions. The resulting set along with a compatibility equation are transformed from the diverging physical domain to a rectangular computational domain. Solving for a compatible set of initial profiles and specifying a compatible set of boundary conditions, the equations are solved using a type-differencing scheme. Vortex breakdown locations are detected by the failure of the scheme to converge. Computational examples include isolated vortex flows at different Mach numbers, external axial-pressure gradients and swirl ratios.

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Analysis and computation of steady, compressible, quasi-axisymmetric flow of an isolated, slender vortex are considered. The compressible, Navier-Stokes equations are reduced to a simpler set by using the slenderness and quasi-axisymmetry assumptions. The resulting set along with a compatibility equation are transformed from the diverging physical domain to a rectangular computational domain. Solving for a compatible set of initial profiles and specifying a compatible set of boundary conditions, the equations are solved using a type-differencing scheme. Vortex breakdown locations are detected by the failure of the scheme to converge. Computational examples include isolated vortex flows at different Mach numbers, external axial-pressure gradients and swirl ratios.

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Available abstract

Analysis and computation of steady, compressible, quasi-axisymmetric flow of an isolated, slender vortex are considered. The compressible, Navier-Stokes equations are reduced to a simpler set by using the slenderness and quasi-axisymmetry assumptions. The resulting set along with a compatibility equation are transformed from the diverging physical domain to a rectangular computational domain. Solving for a compatible set of initial profiles and specifying a compatible set of boundary conditions, the equations are solved using a type-differencing scheme. Vortex breakdown locations are detected by the failure of the scheme to converge. Computational examples include isolated vortex flows at different Mach numbers, external axial-pressure gradients and swirl ratios.

Key concepts: Mach number, Vortex, Supersonic speed, Compressibility, Compressible flow, Navier–Stokes equations, Mechanics, Rotational symmetry

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