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Old   July 17, 2000, 13:59
Default Goldstheins Singularity
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Anybody have any idea on the relevance of Goldstheins singularity in relation to BL flow.

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Old   July 18, 2000, 15:14
Default Re: Goldstheins Singularity
John C. Chien
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(1). If you type "goldstein singularity" into a web search site, you will get more information about it. (2). The Prandtl 1904 boundary layer theory provided simplified set of equation for wall boundary layer region. The equation is parabolic and can be solved by marching method (in the downstream direction). (3). The boundary layer equation has the outer boundary condition on the velocity distribution in the streamwise direction (or the pressure distribution in the streamwise direstion) as the input condition. (4). For adverse pressure gradient condition, the boundary layer solution will exhibit singular behavior at the point of separation. (5). In other words, one can not find the solution near, at, and after the point of separation using the boundary layer equation.(due to adverse pressure gradient imposed on the boundary layer equation) (6). Somehow this limitation was related to Goldstein's work in late 40's. (7). If you are solving modern Navier-Stokes equations or Reynolds averaged equations, you don't have this built-in limitation due to simplification of governing equations. (8). It simply says that the simplified boundary layer equation can not handle flow separation, because it is singular at the point of separation. The boundary layer equation is good for "attached flows" only.
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