The incompressible boundary layer in the corner formed by two intersecting, semi-infinite planes is investigated, when the free-stream flow, aligned with the corner,
is taken to be of the form U∞F(x), x
representing the non-dimensional streamwise
distance from the leading edge. In Dhanak & Duck (1997) similarity solutions for
F(x) = xn were considered, and it was found that solutions exist for only a range
of values of n, whilst for ∞ > n > −0.018, approximately, two
solutions exist. In this paper, we extend the work of Dhanak & Duck to the case
of non-90° corner angles and allow for streamwise development of solutions. In addition,
the effect of transpiration at the walls of the corner is investigated. The governing equations
are of boundary-layer type and as such are parabolic in nature. Crucially, although the
leading-order pressure term is known a priori, the third-order pressure term is not,
but this is nonetheless present in the leading-order governing equations, together with
the transverse and crossflow viscous terms.
Particular attention is paid to flows which develop spatially from similarity solutions.
It turns out that two scenarios are possible. In some cases the problem may
be treated in the usual parabolic sense, with standard numerical marching procedures
being entirely appropriate. In other cases standard marching procedures lead
to numerically inconsistent solutions. The source of this difficulty is linked to the
existence of eigensolutions emanating from the leading edge (which are not present in
flows appropriate to the first scenario), analogous to those found in the computation
of some two-dimensional hypersonic boundary layers (Neiland 1970; Mikhailov et
al. 1971; Brown & Stewartson 1975). In order to circumvent this difficulty, a different
numerical solution strategy is adopted, based on a global Newton iteration
A number of numerical solutions for the entire corner flow region are presented.