The interaction of elementary waves for nonisentropic flow in a variable cross-section duct

TL;DR

This paper extends the analysis of wave interactions in variable cross-section ducts from isentropic to nonisentropic flows, focusing on contact discontinuities and stationary waves, supported by numerical verification.

Contribution

It introduces a new framework for analyzing wave interactions in nonisentropic flows, expanding previous isentropic results to more complex flow conditions.

Findings

Interaction results can be shifted parallel in nonisentropic flow compared to isentropic flow.

Focus on contact discontinuity and stationary wave interactions.

Numerical results support the theoretical analysis.

Abstract

The interaction of elementary waves for isentropic flow in a variable cross-section duct is obtained (\cite{ShengZhang}). The authors have discussed rarefaction wave or shock wave interacts with stationary wave. In this paper, we extend their results to the nonisentropic flow. It can be proved that if one changes $(u,\rho)$ plane in isentropic flow with $(u,p)$ plane in nonisentropic case, the interaction results of rarefaction wave or shock wave with stationary wave can be moved parallel from the isentropic case when contact discontinuity is involved. Thus we mainly focus on the interactions between contact discontinuity and stationary wave. Some numerical results are given to verify our analysis. The results can apply to the interaction of more complicated wave patterns.