St Andrews Research Repository

St Andrews University Home
View Item 
  •   St Andrews Research Repository
  • Mathematics & Statistics (School of)
  • Mathematics & Statistics Theses
  • View Item
  •   St Andrews Research Repository
  • Mathematics & Statistics (School of)
  • Mathematics & Statistics Theses
  • View Item
  •   St Andrews Research Repository
  • Mathematics & Statistics (School of)
  • Mathematics & Statistics Theses
  • View Item
  • Login
JavaScript is disabled for your browser. Some features of this site may not work without it.

Compressible boundary layers with sharp pressure gradients

Thumbnail
View/Open
MichaelReader-HarrisPhDThesis.pdf (22.73Mb)
Date
1981
Author
Reader-Harris, Michael John
Supervisor
Curle, S. N.
Funder
Science Research Council (Great Britain)
Rolls-Royce Ltd.
Metadata
Show full item record
Altmetrics Handle Statistics
Abstract
The work of this thesis was undertaken as a C.A.S.E. award project in collaboration with Rolls-Royce to examine compressible laminar boundary layers with sharp adverse pressure-gradients. Much of the work is devoted to the solution of two important particular problems. The first flow considered is that along a semi-infinite flat plate with uniform pressure when X < X₀ and with the pressure for X > X₀ being so chosen that the boundary layer is just on the point of separation for all X > X₀. Immediately downstream of X₀ there is a sharp pressure rise to which the flow reacts mainly in a thin inner sublayer; so inner and outer asymptotic expansions are derived and matched for the stream function and a function of the temperature. Throughout the thesis the ratio of the viscosity to the absolute temperature is taken to be a function of x, the distance along the wall, alone, and the Illingworth-Stewartson transformation is applied. The Prandtl number, σ, is taken to be of order unity and detailed results are presented for σ= 1 and 0.72. The second flow considered is that along a finite flat plate where the transformed external velocity U₁(X) is chosen such that U₁(X) = u₀(-X/L)[super]ε, where O< ε <<1, is the transformed length of the plate and X represents transformed distance downstream from the trailing edge. The skin friction, position of separation and heat transfer right up to separation are determined. On the basis of these two solutions, another solution which is not presented in detail, and a solution (due to Curie) to a fourth sharp pressure gradient problem, a general Stratford-type method for computing compressible boundary layers is derived, which may be used to predict the position of separation, skin friction, heat transfer, displacement and momentum thicknesses for a compressible boundary layer with an unfavourable pressure gradient. In all this work techniques of series analysis are used to good effect. This led us to look at another boundary-layer problem in which such techniques could be used, one in which two parallel infinite disks are initially rotating with angular velocity Ω about a common axis in incompressible fluid, the appropriate Reynolds number being very large. Suddenly the angular velocity of one of the disks is reversed. A new examination of this problem is presented in the appendix to the thesis.
Type
Thesis, PhD Doctor of Philosophy
Collections
  • Mathematics & Statistics Theses
URI
http://hdl.handle.net/10023/13795

Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.

Advanced Search

Browse

All of RepositoryCommunities & CollectionsBy Issue DateNamesTitlesSubjectsClassificationTypeFunderThis CollectionBy Issue DateNamesTitlesSubjectsClassificationTypeFunder

My Account

Login

Open Access

To find out how you can benefit from open access to research, see our library web pages and Open Access blog. For open access help contact: openaccess@st-andrews.ac.uk.

Accessibility

Read our Accessibility statement.

How to submit research papers

The full text of research papers can be submitted to the repository via Pure, the University's research information system. For help see our guide: How to deposit in Pure.

Electronic thesis deposit

Help with deposit.

Repository help

For repository help contact: Digital-Repository@st-andrews.ac.uk.

Give Feedback

Cookie policy

This site may use cookies. Please see Terms and Conditions.

Usage statistics

COUNTER-compliant statistics on downloads from the repository are available from the IRUS-UK Service. Contact us for information.

© University of St Andrews Library

University of St Andrews is a charity registered in Scotland, No SC013532.

  • Facebook
  • Twitter