BOUNDARY LAYER THEORY

Co-ordinators:Prof. P.W. Duck, Mathematics Department, OWENS, (Maths Blg 5.09 x 55895)

Dr D D Apsley, Civil and Construction Engineering, UMIST (P/B11, x 3732)


 
Assessment
Credits
Contact hours
% Exam
% Coursework
Level
10
24h lectures, 6h tutorials
80
20
M

General Description

The course examines the basis of boundary-layer theory, and the predictions provided by that theory. Laminar, translational and turbulent boundary layers are considered. Illustrative examples are chosen from a range of problems, including a number with practical applications

Aims 

The aim of the module is to introduce students to the fundamental mathematical theory of viscous flows, in particular that relating to laminar and turbulent boundary layers.

Objectives

Upon successful completion of the module, students will:

1.be able to calculate by approximate methods the overall behaviour of two-dimensional low speed boundary layers and analyse the self-similar cases.

2.be able to calculate the detailedbehaviour for high speed laminar boundary layers on flat plates and insulated surfaces.

3.be able to apply averaging methods to derive various transport equations for turbulent flow.

4.understand the closure problem and be able to apply suitable turbulence models to achieve a specified level of closure.

5.be ableto analyse a turbulent boundary layer and calculate the drag taking transition into an account.

6.to become aquainted with key experimental data and recent findings from direct numerical simulation.

Course content

(i)Laminar Boundary Layers 12 Lectures + 3Classes

(a)Introductory remarks.

Review of the connection between the boundary layer and form drag, vorticity, circulation, lift and induced drag.

(b)Basic equations for viscous laminar flow Cartesian tensors. The Navier-Stokes equations and the energy equation.

(c)Laminar boundary-layer equations for incompressible flows.

Physical description of boundary-layer/inviscid flow. Derivation of boundary layer equations for two-dimensional flow: the (Reynolds number) transformation and rules for skin friction and laminar flow drag.Blasius and Falkner-Skan classes of solution, unsteady boundary layers. The influence of pressure gradient on separation and transition.

(d)Laminar compressible boundary layers.

Non-dimensional forms of the compressible boundary-layer equations; heat transfer and the Stewartson-Illingworth transformation. 

(ii)Turbulent Boundary Layers 12 Lectures + 3Classes

(e)Stability of laminar flow; transition to turbulence. Reynolds equations of turbulent flow; boundary-layer equations. Displacement and momentum thickness; integral analysis. 

(f) Velocity profiles; inner, outer and overlap layers; law of the wall. The flat-plate boundary layer; turbulent flow in pipes and channels; rough-wall flows; Colebrook-White formula and Moody chart. Effects of pressure gradients. 

(g) Compressible boundary layers. Heat transport; temperature law of the wall; Reynolds analogy.

(h) Modelling; mixing-length models. Experimental data and results from direct numerical simulation.

Assessment

Coursework 20% and end of module two-hour closed book examination 80%.

Suggested reading

White, F.M., Viscous Fluid Flow (Second Edition), McGraw-Hill, 1991.
Pope, S.B., Turbulent Flows, Cambridge, 2000.

Schlichting, H.and Gersten, K. 'Boundary Layer Theory' 8th. Edition, 2000, Springer (£60.00).

Rosenhead, L. 'Laminar Boundary Layers' Dover Paperback - but out of print at present.

Young, A.D. 'Boundary Layers' 1st. Edition, 1989, BSP Professional (£23.50).