| Natural cavitation is a kind of phenomenon that vapor bubble or vapor cavity appears in liquid phase at some specific conditions. The general hydrodynamic mechanism of natural cavitation is high-speed flow, where local pressure in liquid falls down under the saturating vapor pressure of liquid, thus the liquid vaporizes to form cavity.Cavitation has extremely important influence on erosion and noise of hydraulic instruments, hydrodynamic characteristics and stability control of high-speed body. With the great raise of navigating velocity of water-surface or under-water vehicles, cavitation phenomenon becomes unavoidable to appear.Researches on the property and mechanism of cavitating flow are still one of the leading fields in current studies of hydrodynamics. Therefore, it's not only of great theoretical significance but also of wide application values on engineering and national defence to develop reasonable cavitation models and numerical methods adaptable for three-dimensional unsteady cavitating flows.This dissertation is aimed at exploring more sound cavitation models, developing efficient and accurate numerical methods, and creating computer software with independent intellectual property rights, for the simulation of three-dimensional multi-phase unsteady natural cavitating flows, and utilizing them to analyze actual engineering cavitation problems.The primary researching contents and innovations are as follows:1. The mathematical model of multi-phase flow for simulating complex natural cavitating flows was researched systematically and profoundly. Five types of Homogenous Equilibrium cavitation Models (HEM) based on barotropic relation or transportation equation of phase fraction were introduced, combining with five kinds of linear or nonlinear eddy viscosity turbulence models, to develop the simulation method for turbulent natural cavitating flows based on solving three-dimensional RANS equations system. By improving these models'form and arithmetic achievement, the flows of cavitation number smaller than 0.01 and complicated unsteady cavitating flows were successfully simulated. A new high-speed cavitation model taking into account the compressibility of incoming flow was also proposed, to simulate high-subsonic cavitating flows.2. Unique works about the numerical methods suitable for the computation of cavitating flows were carried out. Because of the speciality in the solving of cavitation problems, non-cavitating single phase flow field was used as the initial condition for cavitating flow computation. The pressure below the saturated vapor pressure was reset before computation starts, then the pressure range inside the whole flow field was limited during computation. In the pressure-velocity-density coupling correction method, the compressibility of mixture was artificially restrained to make the reset pressure to diffuse rapidly after computation begins, which guarantees the cavitation model to continuously keep phase transformation potential, so as to grow up reasonable cavity shape. A compressibility parameter emplaced on computational nodes was set according to local phase fraction, to choose different pressure correction modes for the incompressible incoming flow and compressible cavitating region respectively. The cavity interface capturing method by TVD limited High-Order-Convection scheme was studied.3. A computer code for the numerical simulation of three dimensional natural cavitating flows was developed. This code was developed using Finite-Volume-Method, and is applicable for arbitrarily complicated computational domain divided into multi-block structured grid. A segregated implicit solver based on the pressure-velocity-density coupling correction method was adopted. The equation system includes RANS equation, pressure correction equation, energy equation, turbulence model equations, and phase fraction equation, etc. The cavitation models improved or proposed in this dissertation, combining with over ten kinds of linear or nonlinear turbulence models, were utilized in the software. One-order to two-order upwind scheme with deferred correction and some types of TVD High-Order-Convection schemes were adopted in the convection terms of controlling equations. This software was verified to be applicable to wide ranges of cavitation number and Reynolds number.4. Calculations and comparisons were carried out for some classic problems which have classical analytic solution or reliable experimental results, to verify the accuracy of the present numerical simulation method in forecasting natural cavitation and the wide applicability for working conditions. Some basic factors for the computation, such as mesh density, convection scheme, model parameter, and Reynolds number's influence were analyzed, and their effects on computational results were investigated. Stable and smooth cavity profiles were obtained in wide range of cavitation number. The cavity shape, cavity dimensions, pressure distribution and drag-force coefficient agree well with analytic solutions and experimental data.The compressible subsonic high-speed cavitating flows were simulated based on the model proposed in this dissertation. The present results proved the conclusion derived in the subsonic compressible theory of potential flow that, cavity length and drag-force increase along with the increment of Mach number at fixing cavitation number. This indicates the need to account for the compressibility effect in high-speed flows.The combinations of cavitation models and turbulence models were compared and reviewed in the aspects of computational stability, grid reliability, cavity profile, cavity size, flow structure inside cavity, hydrodynamic characteristics, etc., to provide valuable references for further numerical simulation works.5. The phenomenon and mechanism of natural cavitating flows in realistic engineering application, including the cavitating flows in venturi tubes, around hydrofoils, and over an underwater vehicle with large angle of attack, were studied by using the numerical methods established in the dissertation. For the cavitating flows inside the venture tubes at different convergence-divergence degrees, steady cavity shape and unsteady cavity evolution were obtained respectively. The cavity presents periodic growth, breaking, shedding, cascading and collapse during the process, which accords with experimental phenomena. Cavity length, shedding frequency, velocity distribution and phase fraction distribution inside cavity are close to experimental ones. The fluctuation frequency of incoming pressure corresponds with that of cavity shedding, which means the influence of cavity motion on the structure of flow field.As to the unsteady cavitating flows around hydrofoils, the cavity shedding phenomenon simulated accords with the large cloud cavities observed experimentally, and the shedding frequency was in accordance with the oscillation frequency of lift and drag, and the Strouhal numbers agree well with theoretical and experimental ones. The structure, characters and mechanism of the unstable cavitating flow were analyzed in detail finding that, there are close relations between the periodic cavity shedding process and the development of reentrant jet flow, the adverse pressure near cavity closure, and the vortex structure evolution. The unsteady cavitating flows in turbulent condition and laminar condition were simulated and compared, and obvious distinctions exist in the two cases at the aspects of cavity break position, shedding pattern and flow confusion level.For the cavitating flows over underwater vehicle with large angle of attack, three-dimensional cavity profiles and pressure distributions calculated are consistent with experiment ones. The cavity shape distribution on the body surface was studied. The dependences of some cavity dimensions on cavitation number and angle of attack were investigated, and also the variation relations of lift and drag coefficients in reference to cavitation number and angle of attack were computed. Quantitative analysis shows that the asymmetry of cavity will cause the nonuniform stress along body, and result in the great hydrodynamic load of vehicle navigating at large angle of attack.
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