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Transonic flows of single-phase supercritical fluids over thin airfoils

Published online by Cambridge University Press:  17 March 2021

Zvi Rusak Open the ORCID record for Zvi Rusak [Opens in a new window]  and
Akashdeep Singh Virk Open the ORCID record for Akashdeep Singh Virk [Opens in a new window]
Zvi Rusak
Affiliation:
Department of Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY 12180 USA
Akashdeep Singh Virk*
Affiliation:
Department of Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY 12180 USA
*
†Email address for correspondence: asvirk@vt.edu
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Abstract

A small-disturbance model for a steady, two-dimensional, inviscid and transonic flow of a single-phase real gas around a thin airfoil is presented. The approach explores the nonlinear interactions among near-sonic speed of the flow, small thickness ratio of the airfoil and upstream properties of the fluid. The gas thermodynamic properties are related by a general equation of state. Information about thermodynamic modelling of the gas is lumped into one similarity parameter, $K_G$, related to the fundamental derivative of gas dynamics. The flow field is described by a modified transonic small-disturbance problem. The theory applies to any working fluid of interest. Model problems are derived for steam flows described by the perfect, van der Waals, virial and Redlich–Kwong gas equations of state. Predictions are compared according to the various gas models under various free-stream operating conditions from low subcritical to high supercritical thermodynamic states to gain insights into the sensitivity of the small-disturbance problem solution to thermodynamic modelling of the gas. Results show that transonic flows are independent of gas modelling at low subcritical thermodynamic conditions. However, at near-critical and supercritical thermodynamic conditions, transonic flow behaviour is significantly sensitive to gas modelling and variations of $K_G$. The upstream flow critical Mach number increases as the flow approaches thermodynamic critical state and a wider range of upstream Mach numbers can be found where pressure drag is zero. However, at supercritical conditions, $K_G$ increases, resulting in lower critical Mach numbers and higher pressure drags.

JFM classification

Compressible Flows: Shock waves Compressible Flows: Gas dynamics

Information

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 915 , 25 May 2021 , A61
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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