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UBC Theses and Dissertations

A viscous-inviscid interaction procedure Stropky, Dave


A new viscous-inviscid semi-inverse (VISI) interaction method has been developed for predicting the flow field arising from a combination of inviscid potential flow and viscous flow. The technique involves matching the bounding velocities for each region by iteratively solving for the displacement thickness, δ*(x). The formula used to update δ*(x) after each iteration is generated by linearly perturbing the governing equations. Application of the VISI procedure to predict the unseparated flow past a flat plate gives excellent results, producing numerical solutions essentially indistinguishable from the appropriate analytical solution in less than 0.5 seconds of CPU time on an Amdahl 5850 computer. Application of the technique to external flow over a backward facing step (BFS) indicates that the region of strong interaction between the viscous and inviscid flows is much larger than reported for internal flow. Calculated reattachment lengths, LR, are clearly influenced by the thickness of the boundary layer upstream of the step, thicker boundary layers producing longer reattachment lengths. Good accuracy is achieved for a relatively coarse distribution of control points, and rapid convergence (< 2 seconds on the Amdahl 5850) usually occurs. Finite-difference predictions using an elliptic code (TEACH-T), modified at the outer boundary to simulate external flow, have also been made for the BFS, largely as a basis of comparison for the VISI results. Comparison of results for the two models (VISI and TEACH) gives similar trends in LR as a function of Rh and x₈, (a measure of the displacement thickness at the step). The values of LR obtained with the VISI method, however, are 15-80% longer than those from TEACH. Direct comparison with experiments is difficult because the experimental data does not clearly identify the effects of x₈, in the resulting values of LR. Trends appear to be the same for all computed and observed cases however. Disagreement between the VISI and TEACH results is thought to be due to a combination of neglecting velocities in the recirculation region in the VISI model, and numerical error and inaccurate boundary conditions in the TEACH code.

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