Abstract
Shock wave propagation in a variable cross-section channel is a recurrent issue in the literature. Seminal work regarding this flow configuration has been proposed by Whitham (1958) through the derivation of a one-dimensional approach connecting the shock Mach number and the area channel: the A-M relation. It is based on strong theoretical restrictions: (i) shock equations applied on a , (ii) omission of the postshock influence, and (iii) initial conditions at rest. It has been the focus of many studies aimed at generalizing it. However, very little attention has been paid to the study of the shock motion outside the varying cross-sectional region since Russell (1967). The objective of the current work is to describe and to explain the shock wave behavior in a constant area channel behind a convergent or divergent channel. It is found that the shock propagation in the downstream uniform area region is influenced by the postshock flow unsteadinesses. Therefore, the Whitham model is not suited to the shock motion study in a constant area region downstream of a convergent or divergent area region. A detailed flow description is provided and a quasisteady model for determining the waves intensity at large times is proposed. This model gives accurate results without any assumptions on the shock strength, area variation or the shock upstream state. Finally, this study points out the limits of the use of Whitham's theory in a variable area channel with increasing section variation rate (where ).
- Received 10 November 2020
- Accepted 1 April 2021
DOI:https://doi.org/10.1103/PhysRevFluids.6.044802
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