Computation of free-surface flow by using depth-averaged k hat-epsilon hat turbulence model
[Thesis]
M. Younus
M. H. Chaudhry
Washington State University
1993
176
Ph.D.
Washington State University
1993
This dissertation presents a numerical model to compute the free-surface flow by solving the depth-averaged, two-dimensional, unsteady flow equations. The turbulence stresses are closed by using a depth-averaged usd\ k\\epsilonusd model. However, viscous stresses and momentum dispersion stresses are neglected. The governing equations are first transformed into a general curvilinear coordinate system and then solved by the Beam and Warming Alternating Direction Implicit (ADI) scheme. Two type of computer codes are developed. In the first case, all the equations are solved simultaneously, whereas in the second case the flow equations are decoupled from the turbulence transport equations. The model is applied to a number of test cases including: (i) flow in a straight rectangular channel, (ii) flow in open channel transitions, and (iii) free-surface radial flow. The numerical model is verified by comparing the computed results with the available measured data. The comparison of results with and without effective stresses shows that in many cases the effective stresses do not significantly affect the solution. However, it was observed that the computation of supercritical flow in a diverging channel and the simulation of radial hydraulic jump was improved when the depth-averaged usd\ k\\epsilonusd model was applied. The effect of artificial viscosity coefficients on the final converged solution is also studied and it is observed that they do not significantly affect the results in the absence of a shock. However, for the flows with shocks (hydraulic jump), the solution is very sensitive to these coefficients. An increase in the values of these coefficients smears the shock front, thus overpredicting the jump length. By decreasing the values of these coefficients, a sharper shock wave front is obtained.