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On an analogy to the area–velocity relation of gasdynamics in slender vortices

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Abstract

Inviscid compressible flow in a slender longitudinal vortex with the axis parallel to the main flow direction is discussed. The Euler equations for steady, axially symmetric flow are simplified for the neighbourhood of the axis of the vortex. The resulting relations, expressing the angular velocity in terms of the axial mass flow, when recast and integrated, represent an analogy to the area–velocity and the area-Mach number relation of one-dimensional gasdynamics. By restricting the analysis to the flow in a Rankine vortex with constant stagnation enthalpy, the static pressure on the axis can be related to the free-stream pressure far away from the axis and the maximum value of the azimuthal velocity. The influence of a radial wake-like distribution of the axial velocity component on the axial pressure is discussed. Its dependence on variable external boundary conditions is given. A condition is formulated, which has to be satisfied for the formation of a free stagnation point on the axis.

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  1. Aerodynamisches Institut, RWTH Aachen, Wüllnerstr.5a, 52062, Aachen, Germany

    Egon Krause

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  1. Egon Krause
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Correspondence to Egon Krause.

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Dedicated to Professor Wilhelm Schneider on the occasion of his 70th birthday

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Krause, E. On an analogy to the area–velocity relation of gasdynamics in slender vortices. Acta Mech 201, 23–30 (2008). https://doi.org/10.1007/s00707-008-0069-8

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  • DOI: https://doi.org/10.1007/s00707-008-0069-8

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