Wedge flow over a cylinder



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The piecewise local-similarity, or wedge-flow, method is applied to the flow past a two-dimensional or axisymmetric body. The body is represented by a series of wedges when the actual pressure gradient is favorable and by flat plates with a superimposed pressure gradient when the actual pressure gradient is adverse. The formulation is general and application is made to the flow past a circular cylinder. The flow over the series of wedges and flat plates is governed by the Falkner-Skan equation. Each segment (wedge) has a unique solution of the equation which approximates the exact solution for the corresponding portion of the cylinder. Results from the application of the method to the flow over a circular cylinder indicate that it predicts separation at about 100° from the stagnation point (compared to 108.8° by the Blasius-series method) with very slight dependency on step size. Properties, such as displacement thickness, momentum thickness, shape factor and skin friction, can be predicted to within four percent deviation from the Blasius solution by using the optimum equal step size corresponding to eleven equal steps between the stagnation point and 100° along the cylinder. Results also indicated that the predicted boundary-layer velocity profiles are accurate (compared to the Blasius-series profiles) in the forward region of the cylinder up to at least 40°. Farther along the cylinder, the profiles predicted by the wedge-flow method become progressively bad.