Shimizu, Takeshi; (1999) Hypersonic planar flow through a nozzle, with upstream influence; A composite approach. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

This thesis consists of a theoretical computational study of flows at high Reynolds number and high Mach number, where upstream influence or non-uniqueness is of concern. Hypersonic flow has the special and important feature of prolonged upstream influence, in the presence of viscous forces, as upstream influence in a compressible boundary layer increases with increasing Mach number. Non-uniqueness is associated with eigenvalues and corresponding eigenfuctions in an expansion in powers of the distance from a reference point. One of the objectives in this thesis is to allow for the presence of upstream influence in an internal flow system, which is accompanied by local non-uniqueness of the solutions. The eigenfunction above is due essentially to the interaction of viscous and inviscid layers, and is analogous to an eigenfunction in hypersonic external flow. This non-uniqueness of the solution is a particular focus in the analysis. The present study is concerned mostly with upstream influence in hypersonic planar flow through a nozzle and the eigenvalue problem is discussed in the context of a composite approach. A single composite system of equations is derived to cover the four separate regions of the nozzle flow identified by asymptotic analysis, the composite system being still a subset of the Navier-Stokes system. Non-uniqueness in the flow, due to upstream influence within the composite partial-differential system, is examined both by numerical treatment of certain similarity solutions and by means of eigenvalue analysis in the flow solution. The presence of upstream influence is also shown by analysis of a limiting pressure equation. Finally, in a preliminary attempt at solving the composite partial-differential system in full, a semi-implicit computational method is introduced to compute the flow solution, incorporating the strong upstream influence present. Further discussion is also presented in brief at the end.

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