Boundary Integral Formulation for Asymmetric Impinging Wall Jets with Arbitrary Nozzles

초록

We present an efficient boundary integral formulation for solving two-dimensional impinging wall jets which has arbitrary nozzles. We assume that the jet emanating from an arbitrary nozzle impinges to a straight wall, and the flow is incompressible, irrotational, and inviscid. The point of this problem is to find the free boundary, the contacting surface between the flow and the surrounding air. The solution can be represented as the stream function and we can use a layer potential over the nozzle and free boundary. The free boundary is not known a priori and it is a part of the solution in this jet problem, which makes this problem highly nonlinear, and therefore hard to solve. For this reason, it is inevitable to devise an iterative algorithm. If a prescribed free boundary is given, then our formulation gives the direction toward the solution in a systematic way. We show the convergence of our method, provide examples for the reliability of numerical results, and finally illustrate the calculated solutions of the jets with arbitrary nozzles.