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Ideal and non-ideal planar compressible fluid flows in radial equilibrium

Published online by Cambridge University Press:  22 November 2023

Paolo Gajoni Open the ORCID record for Paolo Gajoni [Opens in a new window]  and
Alberto Guardone Open the ORCID record for Alberto Guardone [Opens in a new window]
Paolo Gajoni
Affiliation:
Department of Aerospace Science and Technology, Politecnico di Milano, Via La Masa 34, 20156 Milano, Italy
Alberto Guardone*
Affiliation:
Department of Aerospace Science and Technology, Politecnico di Milano, Via La Masa 34, 20156 Milano, Italy
*
†Email address for correspondence: alberto.guardone@polimi.it
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Abstract

Two-dimensional compressible flows in radial equilibrium are investigated in the ideal dilute-gas regime and the non-ideal single-phase regime close to the liquid–vapour saturation curve and the critical point. Radial equilibrium flows along constant-curvature streamlines are considered. All properties are therefore independent of the tangential streamwise coordinate. A differential relation for the Mach number dependency on the radius is derived for both ideal and non-ideal conditions. For ideal flows, the differential relation is integrated analytically. Assuming a constant specific heat ratio $\gamma$, the Mach number is a monotonically decreasing function of the radius of curvature for ideal flows, with $\gamma$ being the only fluid-dependent parameter. In non-ideal conditions, the Mach number profile also depends on the total thermodynamic conditions of the fluid. For high molecular complexity fluids, such as toluene or hexamethyldisiloxane, a non-monotone Mach number profile is admissible in single-phase supersonic conditions. For Bethe–Zel'dovich–Thompson fluids, non-monotone behaviour is observed in subsonic conditions. Numerical simulations of subsonic and supersonic turning flows are carried out using the streamline curvature method and the computational fluid dynamics software SU2, respectively, both confirming the flow evolution from uniform flow conditions to the radial equilibrium profile predicted by the theory.

JFM classification

Compressible Flows: Gas dynamics Mathematical Foundations: General fluid mechanics Compressible Flows: Supersonic flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 975 , 25 November 2023 , A43
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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