Compressible potential flows around round bodies: Janzen-Rayleigh expansion inferences

Idan S. Wallerstein, Uri Keshet

Research output: Working paper/PreprintPreprint

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The subsonic, compressible, potential flow around a hypersphere can be derived using the Janzen-Rayleigh expansion (JRE) of the flow potential in even powers of the incident Mach number M∞. JREs were carried out with terms polynomial in the inverse radius r−1to high orders in two dimensions (2D), but were limited to order M4 in three dimensions (3D). We derive general JRE formulae to arbitrary order, adiabatic index, and dimension. We find that powers of ln(r) can creep into the expansion, and are essential in 3D beyond order M4. Such terms are apparently absent in the 2D disk, as we confirm up to order M100 ∞ ,although they do show in other dimensions (e.g. at order M2 in 4D) and in non-circular 2D bodies. This suggests that the disk, which was extensively used to study basic flow properties, has additional symmetry. Our results are used to improve the hodograph-based approximation for the flow in front of a sphere. The
symmetry-axis velocity profiles of axisymmetric flows around different prolate spheroids are approximately related to each other by a simple, Mach-independent scaling
Original languageEnglish
StatePublished - 26 Nov 2020


  • physics.flu-dyn


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