A numerical finite difference solution to a jet impinging on a liquid surface
A numerical finite difference solution to the problem of a two dimensional gas jet impinging on a liquid surface at right angles has been obtained in this work. For an idealized situation of flow, the liquid surface profiles and the gas jet free streamlines were determined at several values of the parameter X corresponding to different physical situations, the parameter Y being defined as equal to 2SgVj2/gcSlb. The most recent significant works along this line are the experimental investigations performed by Banks and Chandrasekhara and that of Olmstead , the latter being an analytical solution by methods of conformal mapping. Comparison of the numerical results obtained in this paper with Olmstead's results shows very good agreement for small values of y. However, for larger values of y corresponding to higher jet velocities, the liquid profile obtained numerically has a more complicated shape. Besides a lip, the numerical solution also shows the presence of ripples on the liquid surface. This phenomenon is supported by photographs taken during experimental runs by Banks and Chandrasekhara.
Fagela-Alabastro, Estrella B. "A numerical finite difference solution to a jet impinging on a liquid surface." (1965) Master’s Thesis, Rice University. https://hdl.handle.net/1911/89687.