Determining Critical Submergence in Tanks by Means of Reynolds & Weber Numbers

Critical submergence in pumping systems can be determined using a number of calculations, all of which result from heterogeneous geometries based on water. The most widely spread critical submergence formula is that of the Hydraulic Institute. A study, carried out in Germany, looked at eight different formulations used to calculate critical submergence, comparing their results with those of a hydraulic model test. The conclusion is that the simplest models, overestimate the critical submergence. Similarly, a study of submergence in water intake structures concluded that predicted values were much higher than real values. A detailed analysis has been done to detect the origin of the off-set between the measured submergence and the calculated value. The main aspects selected from the analysis were the fluid properties involved in the surface deformation and the dynamic behavior outlet flow, so two a-dimensional numbers have been selected, Weber and Reynolds. To build an equation, to calculate the critical submergence, based on the mentioned a-dimensional numbers, a mixed technique (numerical and testing) has been used. The first step was driving a test in a hydraulic model to verify the critical submergence level. Then, a numerical model was built to simulate the same phenomenon and calibrate it, to be used in the future. After that, the second step is to simulate and calculate the critical submergence with other boundary condition (fluid, flow rate, pipe diameter). Once the critical submergence is calculated, a non-linear least squared approach has been developed to build the equation to calculate the critical submergence based on the Reynolds and Weber number. The numerical method used in this paper is a finite element model with a fluid volume scheme, used normally in the fluid simulation activities.