Viscous-inviscid interaction on moving walls
File(s)
Author(s)
Kirsten, Julius
Type
Thesis
Abstract
This thesis consists of two parts. In part I, the viscous-inviscid interaction in su- personic flows over down- and upstream moving walls is analysed. The separation is assumed to be provoked by an impinging shock or expansion wave. For large val- ues of the Reynolds number and under the assumption that the speed of the wall is [Mathematical equation appears here. To view, please open pdf attachment], the interaction is described by the classical triple deck theory. For the case [Mathematical equation appears here. To view, please open pdf attachment], the Navier-Stokes equations are analysed in a vicinity of the separation point using the method of matched asymptotic expansions.
In chapter 2, the linearised interaction problem for a downstream moving wall is stud- ied and the upstream influence of small perturbations is shown to be exponentially decaying. Moreover, it is found that small perturbations to the skin friction decay alge- braically downstream. The focus then shifts towards the fully non-linear problem, when the strength of the impinging shock wave is of [Symbol appears here. To view, please open pdf attachment], and it is shown numerically that a singularity, indicative of separation, develops at the outer edge of the viscous sublayer.
In chapter 3, supersonic flow over an upstream moving wall is considered for which the development of a singularity is observable in the non-linear problem, when the imping- ing shock wave is replaced by an expansion wave.
Part II consists of chapter 4, in which hypersonic flows are investigated. In this case the viscous-inviscid interaction extends over the entire body surface and is described by a two-layer model. On motionless and downstream moving walls, the solution to the interaction problem near the leading edge is not unique and there exists an alge- braic upstream influence of perturbations. The associated eigenvalue problem near the leading edge is solved numerically using an iterative procedure and it is shown that the upstream influence becomes smaller as the speed of the wall is increased.
In chapter 2, the linearised interaction problem for a downstream moving wall is stud- ied and the upstream influence of small perturbations is shown to be exponentially decaying. Moreover, it is found that small perturbations to the skin friction decay alge- braically downstream. The focus then shifts towards the fully non-linear problem, when the strength of the impinging shock wave is of [Symbol appears here. To view, please open pdf attachment], and it is shown numerically that a singularity, indicative of separation, develops at the outer edge of the viscous sublayer.
In chapter 3, supersonic flow over an upstream moving wall is considered for which the development of a singularity is observable in the non-linear problem, when the imping- ing shock wave is replaced by an expansion wave.
Part II consists of chapter 4, in which hypersonic flows are investigated. In this case the viscous-inviscid interaction extends over the entire body surface and is described by a two-layer model. On motionless and downstream moving walls, the solution to the interaction problem near the leading edge is not unique and there exists an alge- braic upstream influence of perturbations. The associated eigenvalue problem near the leading edge is solved numerically using an iterative procedure and it is shown that the upstream influence becomes smaller as the speed of the wall is increased.
Version
Open Access
Date Issued
2017-11
Date Awarded
2018-06
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
Advisor
Ruban, Anatoly
Sponsor
Engineering and Physical Sciences Research Council
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)