Unsteady laminar boundary layers in a compressible stagnation flow

Abstract

The unsteady laminar compressible boundary-layer flow in the immediate vicinity of a two-dimensional stagnation point due to an incident stream whose velocity varies arbitrarily with time is considered. The governing partial differential equations, involving both time and the independent similarity variable, are transformed into new co-ordinates with finite ranges by means of a transformation which maps an infinite interval into a finite one. The resulting equations are solved by converting them into a matrix equation through the application of implicit finite-difference formulae. Computations have been carried out for two particular unsteady free-stream velocity distributions: (i) a constantly accelerating stream and (ii) a fluctuating stream. The results show that in the former case both the skin-friction and the heat-transfer parameter increase steadily with time after a certain instant, while in the latter they oscillate, thus responding to the fluctuations in the free-stream velocity.

Unsteady laminar compressible boundary-layer flow at a three-dimensional stagnation point

“…The skin-friction and heat-transfer results for the steady-state case (t* = 0) have been compared with those of Libby (1967) and Nath & Muthanna (1977) and found to be in excellent agreement. Furthermore, we have also compared the skin-friction and heat-transfer results for the unsteady case (t* > 0) for c = 0 (two-dimensional case), w = 1 and gw = 0.5 with those of Vimala & Nath (1975) and found excellent agreement. It may be remarked that the present analysis is more general than those performed so far.…”

“…These steady-state equations are the same as those obtained by Libby (1967). I n (2.4), c = 0 corresponds to two-dimensional stagnation-point flow, which has been studied by Vimala & Nath (1975) for N = 1, while c = 1 represents axisymmetric stagnation-point flow. The aim of the present study is to obtain solutions for both nodal (0 < c < 1) and saddle ( -1 < c < 0) points of attachment taking into account the variation of N across the boundary layer.…”

“…The unsteadiness in the present case is due to arbitrary variations in the velocity of the incident stream with time. The problem has been solved as an initial-value problem, starting from a steady solution (Vimala & Nath 1975). The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme after transformation to new co-ordinates with a finite domain (Marvin & Sheaffer 1969;Vimala & Nath 1975).…”

“…The problem has been solved as an initial-value problem, starting from a steady solution (Vimala & Nath 1975). The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme after transformation to new co-ordinates with a finite domain (Marvin & Sheaffer 1969;Vimala & Nath 1975). Computations have been carried out for the following free-stream velocity distributions: (i) a stream moving with constant acceleration and (ii) a stream fluctuating about a steady mean.…”

Heat transfer in squish gaps

“…For nonvanishing h Q /s, the flow is nonsimilar and, in general, must be computed solely by numerical methods 8. But since H 0 /s is small, we assume that the actual flow goes through a sequence of unsteady flows with the "local" value of a/a 2 at time /.…”