Studies On Numerical Wave Flume And Its Application

Water wave is one of the most important dynamic factors, which threaten the safety of offshore and coastal structures, influence the layout and design of engineering structures as well as production operations at nearshore region. Therefore, the interaction between water wave and offshore structure becomes a hot topic in the field of hydrodynamics. The objective of present study is to develop a computational program which can be applied to two phase flows, and then set up an efficient numerical wave flume. Taken the home-made code, interactions between wave and structure as well as overtopping characteristics are systematically investigated.Firstly, the mathematical model for two phase flows with free surface is studied. To solve the multiphase compressible flows, numerical algorithms are investigated systematically and profoundly. The governing equations include filtered NS equations, filtered continuity equation, transpotation equation for free surface and the additional equations to close system of equations. Particularly, the free surface is tracked by VOF method, and Smagorinsky model for turbulence flow.The studies on numerical algorithms for two phase flows are followed as: (1) both phases are treated and a single set of equations is solved simultaneously, a systematic investigation on space discretzations for momentum equation is carried out. It is found that treatments for density are sensitive to numerical diffusion and instability. Hence, TVD scheme with flux limiter is adopted for density interpolation. (2) An efficient, stable and accurate solver is necessary for violent free surface flow related to deformation, breaking, air entrapment as well as long time propagation of irregular waves. A detailed study on solving NS equation is conducted, a temporal second-order algorithm is presented, in which both velocity and pressure are second-order accurate. (3) The accuracy of free surface tracking is another one of the most important parts for two phase flows. According to the characters of concerned problems, the free surface reconstruction algorithm and transportation algorithm involved in VOF method are investigated. To eliminate the mass imbalance problem, a mass redistribution technique is presented. (4) Considering the nature of simplicity and convenience of Cartesian grid, the immerse boundary method is used to treat solid boundary. This implicit treatment for solid boundary condition can not only alleviate the difficulties to deal with complex geometric boundaries, but also intrinsically match with VOF method. (5) In order to study the influences of air compressibility during wave impacting processes, the algorithm for incompressible two phase flow is extended and air compressibility is taken into account. The detailed derivation is presented. (6) Free surface tracking needs high resolutions, a preliminary investigation on adaptive local refinement of Cartesian grid is carried out. This kind of grid can refine local mesh based on the characters of flow field, which is beneficial to the complicated problems.Based on the developed numerical solver, validations for the numerical methods and techniques are conducted through different test cases. In this respect, three aspects are considered: the algorithm of solving NS equations, VOF method and the two phase compressible flow solver. It is indicated from the test cases that the developed numerical solver is very efficient and stable to solve complex flows with free surface.To validate the importance of air compressibility on predicting impacting force on the structure during sloshing, both incompressible and compressible two phase flow model are adopted to simulate violent sloshing. It is found that the influences of entrapped air can't be reflected by incompressible two phase flow model. Violent sloshing at high fillings is simulated and compared with experimental data. The importance of air compressibility on accurate impacting forces is validated.A numerical wave flume is set up with the developed NS solver and efficient wave maker and absorber boundaries. The relaxation method is introduced to the flow filed through solving NS equations. Coupled wave maker and absorption is realized in numerical wave flume and wave reflection from work zone can be eliminated efficiently. Then, regular wave and standing wave are simulated to validate the correct set-up of wave maker and absorption layer. To further validate the capability of numerical wave flume, a series of regular wave and irregular wave with different wave parameters are simulated. Comparing with analytical results, the fundamental grid resolutions for the propagation of regular wave and irregular wave are established through numerical experiments, therefore grid convergence validation is conducted.Systematic investigations on wave overtopping over simple slope are carried out. For regular wave overtopping, a series of test cases combined different crest heights and wave parameters are carried out. These results are compared with experimental results and numerical results available. The relationship between overtopping discharges and maximum horizontal velocities over the top of the dike is fitted. For the erosion problem on the inner slope, overtopping flow pattern and maximum velocity are studied quantitatively. Furthermore, the varying tendency of layer thickness and maximum velocity along dike crest is analyzed for both non-breaking and breaking waves. It is indicated that layer thicknesses along dike crest decay at exponential rule, while maximum velocities along dike crest have an increasing tendency.For irregular wave overtopping, multiple runs with different random seeds are carried out for each specified irregular wave spectrum to model stationary ergodic stochastic processes. It turns out that the statistical mean overtopping rates show good agreement with empirical formulas, other numerical results and experimental data. Hence, this feasible and relative cheap method is proposed to predict the average overtopping discharge with numerical simulation when a specified irregular wave spectrum is provided.