A Method for Computing Three-Dimensional Viscous Flows over an Ogival Body at Angle of Attack
Final rept. 19 Sep 1974-18 Oct 1975
UNITED TECHNOLOGIES RESEARCH CENTER EAST HARTFORD CT
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A method for computing three-dimensional flow over an ogival body at an angle of attack is described. An approximate set of governing equations is derived for viscous flows which have a primary flow direction. The derivation is done in a coordinate independent manner, and the resulting equations are expressed in terms of tensors. In keeping with the inherent generality of the tensor formulation, a two-level second-order accurate marching procedure is derived for general tensor-like equations. With this procedure, a three- dimensional turbulent flow can be solved in any coordinate system by marching along the assumed primary flow direction. General tube-like coordinates are developed for a class of geometries applicable to flows between tubular surfaces. The coordinates are then particularized to the flow field bounded between an ogival body at angle of attack and its bow shock. Unlike the ogival body surface, the bow shock surface is not known in advance of the solution but instead must be computed as the solution develops. One marching step of the solution process is broken down into several steps. First, the bow shock surface is discretely extended by an iteration of explicit local inviscid solutions. The bow shock surface is then smoothly extended to provide a best fit to the discrete shock data. Tube-like coordinates are generated and finally the second order numerical scheme is applied to advance the fully viscous solution to the next station.
- Numerical Mathematics
- Fluid Mechanics