In:
Journal of Fluid Mechanics, Cambridge University Press (CUP), Vol. 76, No. 2 ( 1976-07-28), p. 363-381
Abstract:
The problem of uniform flow past a flat plate whose surface has a constant velocity λ U opposite in direction to that of the mainstream is considered for large values of the Reynolds number R . In a previous communication (Klemp & Acrivos 1972) it was shown that, if the region of reverse flow which is established next to the plate as a consequence of its motion is O ( R −1/2 ) in thickness, the appropriate laminar boundary-layer equations have a solution provided λ ≤ 0·3541. Here the analysis is extended to the range λ 〉 0·3541, which cannot be treated using a conventional boundary-layer approach. Specifically, it is found that for λ 〉 0·3541 the flow consists of three overlapping domains: ( a ) the external uniform flow; ( b ) a conventional boundary layer with reverse flow for x s 〈 x 〈 1, where x s , refers to the point of detachment of the ψ = 0 streamline and x = 1 is the trailing edge of the plate; and ( c ) an inviscid collision region in the neighbourhood of x s , having dimensions O ( R −1/2 ) in both the streamwise and the normal direction, within which the reverse moving stream collides with the uniform flow, turns around and then proceeds downstream. It is established furthermore that x s = 0 for 0 ≤ λ ≤ 1 and that x s 〈 0 for λ 〉 1. Also, detailed streamline patterns were obtained numerically for various λ's in the range of 0 ≤ λ ≤ 2 using a novel computational scheme which was found to be more efficient than that previously reported. Interestingly enough, the drag first decreased with λ, reached a minimum at λ = 0.3541, and then increased monotonically until, at λ = 2, it was found to have attained essentially the value predicted from the asymptotic λ → ∞ similarity solution available in the literature. Thus it is felt that the present numerical results plus the two similarity solutions for λ = 0 and for λ → ∞ fully describe the high- R steady flow for all non-negative values of λ.
Type of Medium:
Online Resource
ISSN:
0022-1120
,
1469-7645
DOI:
10.1017/S0022112076000670
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
1976
detail.hit.zdb_id:
1472346-3
detail.hit.zdb_id:
218334-1
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