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Viscous effects on real gases in quasi-one-dimensional supersonic convergent divergent nozzle flows

Published online by Cambridge University Press:  03 November 2022

Julián Restrepo Open the ORCID record for Julián Restrepo [Opens in a new window]  and
José R. Simões-Moreira Open the ORCID record for José R. Simões-Moreira [Opens in a new window]
Julián Restrepo*
Affiliation:
SISEA – Renewable and alternative Energy Systems Laboratory in the Mechl. Eng. Department at Escola Politécnica, Universidade de São Paulo, Av. Prof. Mello Moraes, 2231, 05508-900 São Paulo, SP, Brazil
José R. Simões-Moreira
Affiliation:
SISEA – Renewable and alternative Energy Systems Laboratory in the Mechl. Eng. Department at Escola Politécnica, Universidade de São Paulo, Av. Prof. Mello Moraes, 2231, 05508-900 São Paulo, SP, Brazil
*
†Email addresses for correspondence: restrepo@usp.br, jcrestrepol@hotmail.com
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Abstract

Viscous effects on an ideal gas flow in a supersonic convergent–divergent nozzle are a well-studied subject in classical gas dynamics. However, the ideal assumption fails on fluids that exhibit complex behaviours such as near-critical-region and non-ideal dense vapours. Under those conditions, a realistic equation of state (EOS) plays a vital role for a precise and realistic computation. This work examines the problem for solving the quasi-one-dimensional viscous compressible flow using a realistic EOS. The governing equations are discretised and solved using the fourth-order Runge–Kutta method coupled with a state-of-the-art EOS to calculate the thermodynamic properties. The role of the Grüneisen parameter along with viscous and real gas effects and their influence on the sonic point formation are discussed. The study shows that the flow may not achieve the supersonic regime for any pressure ratio depending on the combination of that parameter and the normalised friction factor. In addition, the analysis yields the discharge coefficient and the isentropic nozzle efficiency, which may achieve maximum values as a function of the stagnation conditions. Finally, the study also evaluates the formation and intensity of normal shock waves by using the Rankine–Hugoniot relations, which now depend on the real gas and viscous effects in opposition to the inviscid solution. Moreover, the methodology used captures the sonic point and shock wave position by a space marching algorithm using the Brent method for scalar minimisation. Experimental data available in the open literature corroborate the approach.

JFM classification

Compressible Flows: Gas dynamics Compressible Flows: Shock waves Compressible Flows: Supersonic flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 951 , 25 November 2022 , A14
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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