Quantitative Water Surface Flow Visualization by the Hydraulic Analogy

Abstract

A qualitative and quantitative study of the hydraulic analogy; that is the analogy between flow with a free surface and two dimensional compressible gas flow, is described. The experimentation was done using a water table, and results are compared with Computational Fluid Dynamic (CFD) results for actual free surface flow models, and a fictitious gas model. Different test cases are considered (i) a wedge moving at steady supersonic/supercritical speeds of Froude or Mach number equal to 2.38, 3.12 and 4.31 (ii)unsteady motion of a wedge accelerating to supersonic speeds and then decelerating. Quantitative results for the experimental case are achieved by using a colour encoding slope detection technique. Qualitatively, with respect to wave angles, the fictitious gas case shows the best agreement to the experimental case, but at higher Froude/Mach numbers the free surface models also show good agreement. Quantitatively, with respect to wave location and depth profile, the free surface models show better agreement to the experimental case. For the unsteady case the resulting flow patterns are quite similar for the two cases considered, namely the experimental and free surface CFD cases.