A NUMERICAL SOLUTION FOR THE LAMINAR WAKE BEHIND A FINITE FLAT PLATE.
STANFORD UNIV CALIF DIV OF ENGINEERING MECHANICS
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A numerical solution is presented for the laminar, two-dimensional viscous, incompressible wake behind a finite flat plate. The plate is infinitely thin and is aligned parallel to a uniform stream. The Reynolds number based on plate length is assumed large enough to allow the formation of boundary layers on the sides of the plate. The upstream influence of the trailing-edge disturbance necessitates solving the complete Navier-Stokes equations in the trailing-edge region. The aim of the investigation is to calculate an improved first approximation to the solution in this region for large values of the Reynolds number. The elliptic equations define a boundary-value problem. A finite-difference solution to equations which closely approximate the Navier-Stokes equations is obtained in a rectangular region which includes the trailing edge. A relaxation-type procedure is used. Weighted differences, which combine backward and central differences in equal proportion, are introduced to provide the upstream influence in the scheme. The nonlinear partial differential equations are replaced by linear difference equations and iteration is used until the solutions converge. Solutions are obtained for Reynolds numbers larger than 100,000. A complete description of the flow field is provided in the rectangle and downstream wake except in a very small region surrounding the trailing edge. Author
- Fluid Mechanics