Page 222 - Computational Fluid Dynamics for Engineers

II
Boundary-Layer Equations

7.1 Introduction

The solution of the boundary-layer equations of subsection 2.4.3 can be obtained
for boundary conditions that include a priori specification of the external pres-
sure or velocity distributions either from experimental data or from inviscid
flow theory (called the standard problem). The solution of the boundary-layer
equations can also be obtained for boundary conditions that include a priori
specification of an alternative boundary condition which may be the longitudi-
nal variation of the cross-sectional area of a duct or of a displacement thickness
(called the inverse problem) or the determination of the freestream boundary
condition by iteration between solutions of inviscid and boundary-layer equa-
tions (called the interaction problem).
Section 7.2 describes the standard and inverse problems for two-dimensional
laminar and turbulent flows. It also discusses a brief description of the interac-
tion problem. This section is followed by a description of the numerical proce-
dures used to solve the boundary-layer equations in standard mode. Section 7.4
presents and describes a computer program for two-dimensional incompressible
external flows. Applications of this program for boundary conditions of relevance
to engineering for a sample of flows are discussed in Section 7.5.
In the solution of the boundary-layer equations for turbulent flows, we make
use of the eddy-viscosity concept discussed in Section 3.1 so that the momentum
equation given by Eq. (2.4.34) can be written as
du du I dp d ( hdu\
dx dy gdx dy \ dyj

where
b = l + e+, e+ = 6 -^ (7.1.2)