Numerical Simulations of Subcritical and Supercritical Flows in Shallow Waters

• Main Author: Ghannadi, Shooka Karimpour
• Format: Dissertation
• Language: English
• Published: ProQuest Dissertations & Theses 01-01-2015
• Subjects: Civil engineering; Computational physics; Engineering; Finite volume method; Fluid dynamics; Fluid mechanics; International conferences; Numerical analysis; Simulation
• ISBN: 9798597036953

The formation of shock waves as the currents make transition from supercritical to subcritical flow are common in many environmental science and hydro-technical engineering applications. The numerical challenge for simulation of the supercritical-to-subcritical flow transitions is capturing the depth and velocity discontinuity across the shock waves. Total Variation Diminishing (TVD) methods are one of the most conventional methods to manage the spatial integrations in the vicinity of large gradients. TVD methods however are limited to no more than second or third order of accuracy. There are on the other hand Essentially Non-Oscillatory (ENO) schemes that can be extended to have infinite order of accuracy. ENO compared to the conventional TVD schemes reduces the computational effort with minimum undesirable numerical dissipation. In this thesis a Finite Volume Method (FVM) is developed to simulate subcritical and supercritical flows in shallow waters. The performance of a large numbers of shock capturing strategies is evaluated through grid-refinement studies and comparison with available analytical solutions. The investigation for shock-capturing capability of the numerical scheme in supercritical to subcritical transition has been carried out for (i) The transverse dam-break wave, (ii) the linear development of shear instability and (iii) the non-linear transition to turbulence in shallow water. The first application of the numerical method is the diversion of water from a main channel to the side through a weir. Calculations have been conducted for subcritical to supercritical approaching main flows with Froude numbers ranging from Fro= 0.03 to 2.0. Results are presented in the framework of the classical solution of Ritter's. In the limiting case of supercritical main flow, the results are consistent with Prandtl-Meyer expansion, developed originally for gas dynamics. The results obtained over the entire range of Froude numbers are presented in a unified manner for comparison with available experimental data. Using this numerical method, hydrodynamic instability investigation is conducted without making the assumption of the normal mode. The direct numerical simulation for this problem has been carried out for a base flow with hyperbolic tangent velocity profile, covering a range of convective Froude numbers from 0.1 to 2.0. The results obtained from simulation of the subcritical shallow waters are consistent with the analogous instability studies previously considered in gas dynamics. The supercritical instability on the other hand is associated with entrapment and radiation of waves that are beyond the classical description of the normal mode.The direct numerical simulations allow the continuation of the stability calculation to the non-linear stage of development. The analyses have shown how the presence of shock waves can influence the formation of eddies and shocklets. Reduced mixing layer growth is in agreement with the experimental investigation in gas dynamics. Furthermore in the simulation of the non-linear instability and the study of energy dissipation, shock waves are observed at intermediate convective Froude number of 0.75. Investigation also suggests a drastic drop of lateral to longitudinal velocity fluctuation with rise in Froude number. Grid refinement studies for convergence to analytical solution and the validation of the numerical method using available experimental data are carried out in the implementation of the numerical method to the three fundamental problems considered in this thesis. These convergence studies have shown the numerical calculations across the sharp gradients can be managed to gain the needed computational stability and produce results approaching the accuracy of analytical methods.