Chapter 7 Conclusions
Contents
7.1 Summary . . . 147 7.2 Future Research . . . 149
7.1 Summary
In chapter 1, extensive overview of turbulence modeling and its application to wave impact flows, and interface capturing methods and their advantages and disadvantages has been given. Additionally, a literature review of experimental and numerical studies conducted on dam break flow has been presented as a model problem for wave impact flows.
In chapter 2, A mathematical model for the time dependent turbulent incompressible multi-fluid flow have been presented.
In chapter 3, the finite volume discretization of the mathematical model outlined in Chapter2has been presented. The cell-centered topology was used for the discretiza-tion. Spatial and temporal discretization of the equations and boundary conditions have
147
been given. Detailed description of the pressure velocity coupling has been provided.
In chapter 4, a detailed description of the UMTHINC method has been presented.
An error analysis of the method revealed the following: The source of the nonphysi-cal values in the UMTHINC method was extensively investigated by adhering to the similarities with PLIC VOF method. It was found that the accuracy of the interface placement parameterdenot only affects the accuracy of solution but also it has major ef-fect on the boundedness of the volume fraction field. Although improving its accuracy doesn’t completely eliminate over/undershoots but it substantially reduces the nonphys-ical values so much that it can be corrected using a suitable redistribution algorithm. A revised method was successfully compared to geometric VOF methods as well as the most recent version of THINC and the results were very satisfactory.
In chapter 5, an experimental study of the dam-break impact on a vertical cylinder, placed over a dry horizontal bed, has been performed. The gate motion was studied and a novel gate motion formula was proposed which provides a better statistical fit for the new experimental data. The time of impact with cylindrical obstacle was found to be directly correlated the parameters of the proposed motion profile thus demonstrating its importance in the study of dam-break flows. The pressure loads on the vertical cylinders and the downstream vertical wall were investigated for the square and circular cross-section. The pressure on the vertical wall was compared with the no-obstacle case to highlight the cross-section effect on the pressure on the downstream wall. Examining the free surface profile showed higher turbulence and circulation downstream of the square cylinder than the circular cylinder. This was also reflected in the variance of the pressure measurement of the downstream vertical wall.
In chapter 6, numerical solutions of the dam break flow over a vertical wall and ver-tical cylinder have been presented. A novel simplified gate model has been described and validate using experimental data. The numerical solutions were compared with the newly conducted experiments and very good agreement was observed in free surface
149 7.2. FUTURE RESEARCH comparison. As expected, the square cylinder experiences higher force for smaller du-ration while the circular cylinder experiences nearly half as much force for more than twice the duration. This is owing to the different nature of separation for the two differ-ent cross-sections. The effect of turbulence models was investigated for the case circu-lar cylinder. The force and pressure predictions by the RANS models were very simicircu-lar while the LES model presented very different predictions. The pressure prediction on the downstream vertical wall were qualitatively similar but quantitatively different. This shows that a proper choice of turbulent model has very important effect in obtaining ac-curate predictions for separated flows and thus requires further investigation.
7.2 Future Research
Further investigation are needed for the turbulence modeling of impact flows. Investi-gation of higher order turbulence models such as Menter k−ω SST model, dynamic sub-grid scale LES model and Detached Eddy Simulation models. Studying turbulence transition is also necessary in order to obtain more accurate predictions of wave prop-agation over solid surfaces. The air compressibility and cavitation is a phenomenon present in many impact flows, thus, it requires more study and investigation. Improve the quality of surface tension approximation by coupling the present method with the level-set method to obtain more accurate curvature .
Regarding the UMTHINC method:
• Extending the method to arbitrary polyhedral mesh by employing barycentric co-ordinates
• Explore function approximation such as Neural Networks approximations, Re-sponsive surface methodology, and other reduced order models to provide a com-putationally cheaper approximation for the interface placement parameterde
CHAPTER 7. CONCLUSIONS
• Invetigate conservative flux correction methods as means to correct small values nonphysical values of the volume fraction field.
• Considering higher sharpness parameter(β) values (i.eβ >6): Preliminary stud-ies not reported here showed that it would require much more quadrature points.
In fact,β values higher than 10 showed difficulty obtaining a convergent solution during the computation ofdebecause of machine precision issues when comput-ing hyperbolic functions at such highβ. This can be fixed by lowering the VOF cutoff value to 10−6or 10−4instead of the currently implemented 10−8.
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