Incompressible flow along a corner

Abstract

The incompressible viscous flow along a right-angle corner, formed by the intersection of two semi-infinite flat plates, is considered. The effect of the three-dimensional geometry on the second-order ‘boundary layer’ flow away from the corner is determined and an interesting secondary flow is deduced. It is observed that this cross-flow prescribes the necessary asymptotic boundary conditions for the equations governing the flow inside the ‘corner layer’. A systematic matching scheme is specified and the corner flow problem is reformulated in terms of the ‘corner layer-boundary layer’ matching conditions.

Laminar flow in rectangular channels. Part I: Entry analysis. Part II: Numerical solution for a square channel?

“…9b) for the secondary velocity ~~ is identical wit h that derived in earlier studies of the flow along an unbounded corne r [10] . An interesting secondary flow reversal is predic t ed , and this be havior is shown qualitatively on FI g. 6.…”

“…i. e ., in the as ymptotic entry flow described in Part I. In view of the parabolic character of the vi scous c h a n n e l e q u at i o n s , the only remaining infl u e n ce of the initial values will be reflected in the mass Conservation integral ( 10). This behavior has previously been verified for two-dimensional channels L4-6 ) wh ere the asymptotic entry behavior is closely approximated by the numerical boundary layer solutions [7][8][9] .…”

“…2. Thin boundary layers grow along the walls fl ow has bee n st udied extensively for a n Infinite corner, see refe rences [10,11] , and can be neg lecte d to lowest-order i n the boundary laye r analysis.~~~~~ LImES c 7…”

Theoretical solutions to three-dimensional asymmetrical shock/shock interaction

“…The shock/shock interaction induced by two intersecting wedges has been studied, and remarkable progress has been made via several experimental and computational investigations [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Charwat, Cresci, Watson, and West et al [1][2][3][4] conducted the earliest experimental research on the distribution of the surface pressure and the wave structure in the corner region for both symmetrical corner and asymmetrical models.…”

“…Cresci, Stainback, Korkegi, and Venkateswaran et al [2,[5][6][7] performed experimental studies on aerodynamic heating in the vicinity of corners. With the rapid development of computer technology and computational fluid dynamics, numerical methods are used to investigate the corner flows conveniently and economically [8][9][10][11][12][13][14][15][16][17]. Rubin, Kutler, Shang, and Marconi et al [8][9][10][11] did the earliest numerical studies on characteristics of corner flows using a low-order numerical scheme and a rough mesh resolution.…”