טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentRegev Amir
SubjectAnalysis of Density Jumps
DepartmentDepartment of Civil and Environmental Engineering
Supervisor Professor Samuel Hassid


Abstract

A density jump is a steep change in flow height and density, occurring when a stream of heavier fluid flows under a lighter fluid, or vice-versa.  In a density jump, ambient fluid from the surroundings is entrained into the fluid in motion and thus the mass flux and the density change. A uni-directional analysis based on conservation equations for mass, momentum, and an additional scalar (salinity or heat) is developed.   A simple expression is derived from these equations relating the heights before and after the hydraulic jump with the Froude number and the entrainment. An additional boundary condition is required, which, in the case of a downstream weir or a downstream width contraction, is the conservation of energy after the jump up to a control section. For a downstream contraction, an exact expression is obtained for the entrainment and downstream flow height, whereas for a weir-controlled jump, the expression is approximate. The results are verified by numerical simulation using the CFD program "FLUENT", and are further supported by experiments with smoke entraining into air. In addition, an analytical method for calculating the length of the jump is developed. From the numerical simulation, it is shown that the distance to the weir has a large effect on the entrainment, and accordingly, an expression for the entrainment as a function of distance is derived for the cases where the distance to the weir is shorter than the full jump length. The results are confirmed by numerical simulations and experiments.