Vorticity and its rate of change just downstream of a curved shock |
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Authors: | G Emanuel H Hekiri |
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Institution: | (1) Department of Mechanical and Aerospace Engineering, University of Texas at Arlington, Arlington, TX 76019-0018, USA |
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Abstract: | A theory is developed for the vorticity and its substantial derivative just downstream of a curved shock wave, the resulting
formulas are exact, algebraic, and explicit. Analysis is for a cylinder-wedge or sphere-cone body, at zero incidence, whose
downstream half-angle is θb. Derived formulas directly depend only on the ratio of specific heats, γ, the freestream Mach number, M
1, the local slope and curvature of the shock, and the dimensionality parameter, σ, which is zero for a two-dimensional shock
and unity for an axisymmetric shock. In turn, the slope and curvature depend on γ, M
1, and θb. Numerical results are provided for a bow shock in which θb is 5°, 10°, or 15°, M
1 is 2, 4, or 6, and γ = 1.4. There is little dependence on the half angle but a strong dependence on the freestream Mach number
and on dimensionality. For vorticity and its substantial derivative, the dimensionality dependence gradually decreases with
increasing Mach number. In comparison to the two-dimensional case, an axisymmetric shock generates considerable vorticity
in a region relatively close to the symmetry axis. Moreover, the magnitude of the vorticity, in this region, is further enhanced
in the flow downstream of the shock. This dimensionality difference in vorticity and its substantial derivative is attributed
to the three-dimensional relief effect in an axisymmetric flow.
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Keywords: | Bow shock wave Vorticity Substantial derivative of vorticity |
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