Boundary Layer Development on a Wedge Impulsively Set into Motion

Authors:
  • IWIii J. C. Williams
    Iii J. C. Williams
  • TRT. B. Rhyne
    T. B. Rhyne
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Abstract
The problem of impulsively set into motion wedge type (Falkner–Skan) flows has been formulated in a new set of scaled coordinates. Both the short time solution and the solution for infinite time, the Falkner–Skan solution, are included in the new formulation of the problem. In addition a new scaling reduces the region of integration from the traditional infinite region to a finite region, thus reducing the time required for numerical computations. The solution for the impulsively started flat plate has been obtained and compared with existing solutions to this special case to verify the method of solution. The agreement between the present solution and existing solutions for the flat plate case is excellent. Solutions have also been obtained for a number of impulsively started Falkner–Skan type flows ranging from the two-dimensional stagnation point flow to the incipient separation flow. Flows which involve an adverse pressure gradient are considered in detail to determine what information can be gained from the present solutions regarding downstream moving unsteady boundary layer separation. Separation does not occur in the present case for pressure gradients less than or equal to that required for incipient separation. For pressure gradients more adverse than that required for incipient separation, separation does not occur in the early phases of the impulsively started flow. It is also shown that if separation does occur in the later phase of flow development, it must move with a velocity lower than the local speed at the edge of the boundary layer.

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