Vortex Simulation of Separated Flows in Two and Three Dimensions

Citation

Chua, Kiat (1990) Vortex Simulation of Separated Flows in Two and Three Dimensions. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/9ENS-EP36. https://resolver.caltech.edu/CaltechETD:etd-08092005-142847

Abstract

This thesis is concerned with the applications of vortex methods to the problem of unsteady, separated flows in two and three dimensions, and can be divided into three parts. In the first part, an improved method for satisfying the boundary conditions on a flat plate is developed and applied to the two-dimensional separated flow problem. In this method, boundary layers on both side of the plate are represented by stacks of multiple vortex panels, the strength of which are determined by enforcing both the no-through flow and no-slip boundary conditions at the plate. Vortex shedding at the sharp edge of the plate is represented as the separation of the boundary vortex elements. Both forced and unforced flows are studied and comparisons to experiments are carried out. For the case without forcing, large discrepancy between calculations and experiments, which is also reported by other workers using a different vortex method or Navier-Stokes calculations, is observed. In the case with forcing, the discrepancy is reduced with lateral forcing at low amplitude; and eliminated, regardless of amplitude, with streamwise forcing (acceleration). In the second part, an improved three-dimensional vortex particle method is developed. In this method, vortex elements of vorticity that move with the local velocity and are stretched and rotated according to the local strain field, are used. To mimic the effects of vorticity cancellations, close pairs of opposite sign vortex elements are replaced by high order dipoles. The method is designed to handle complex high Reynolds number vortical flows and a non-linear viscosity model is included to treat small-scale effects in such flows. Applications to two problems involving strong interactions of vortex tubes are carried out and core deformation with complex internal strucures and induced axial flow within vortex tubes are observed. Qualitative comparison to experiments are encouraging. In the third part, the two-dimensional method developed in the first part is modified and extended to three dimensions. Here, solenoidal condition for vorticity is considered and closed vortex loops are used to represent the boundary layer vorticity and the vorticity at shedding. For the evolution of the vortex wake, the vortex particle method developed in the second part is used. Applications to the flow past a normal square plate is carried out and the early stages of the flow are studied.

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