Determination of the Minimum Wave Speed for the Modelling of Ventilated Cavitation

Ventilated cavitation plays an important role on the drag reduction of underwater vehicles and surface ships. For the modelling of ventilated cavitation, the minimum speed of the pressure wave is a crucial parameter for the closure of the pressure-density coupling relationship. In this study, the minimum wave speed is determined based on a theoretical model coupling the wave equation and the bubble interface motion equation. The influences of several paramount parameters （e.g., frequency, bubble radius and void fraction） on the minimum wave speed are quantitatively demonstrated and discussed. Compared with the minimum wave speed in the traditional cavitation, values for the ventilated cavitation are much higher. The physical mechanisms for the above difference are briefly discussed with the suggestions on the usage of the present findings.

Numerical analyses of ventilated cavitation over a 2-D NACA0015 hydrofoil using two turbulence modeling methods

The present paper studies the ventilated cavitation over a NACA0015 hydrofoil by numerical methods. The corresponding cavity evolutions are obtained at three ventilation rates by using the level set method. To depict the complicated turbulent flow structure, the filter-based density corrected model（FBDCM） and the modified partially-averaged Navier-Stokes（MPANS） model are applied in the present numerical analyses. It is indicated that the predicted results of the cavitation shedding dynamics by both turbulence models agree fairly well with the experimental data. It is also noted that the shedding frequency and the super cavity length predicted by the MPANS method are closer to the experiment data as compared to that predicted by the FBDCM model. The simulation results show that in the ventilated cavitation, the vapor cavity and the air cavity have the same shedding frequency. As the ventilated rate increases, the vapor cavity is depressed rapidly. The cavitation-vortex interaction in the ventilated cavitation is studied based on the vorticity transport equation（VTE） and the Lagrangian coherent structure（LCS）. Those results demonstrate that the vortex dilatation and baroclinic torque terms are highly dependent on the evolution of the cavitation. In addition, from the LCSs and the tracer particles in the flow field, one may see the process from the attached cavity to the cloud cavity.

Characteristics of Flow Field Around an Underwater Projectile with Natural and Ventilated Cavitation

The present simulation investigates the multiphase cavitating flow around an underwater projectile.Based on the homogeneous equilibrium flow assumption,a mixture model is applied to simulate the multiphase cavitating flow including ventilated cavitation caused by air injection as well as natural cavitation.The transport equation cavitating model and a local linear low-Reynolds-number turbulence model are incorporated to the equation system.The calculations are executed based on a suite of computational fluid dynamics code.The hydrodynamics characteristics of flow field under the interaction of natural cavitation and ventilated cavitation are analyzed.The results indicate that the ventilated cavitation numbers and the drag coefficient are relative to the natural cavitation numbers and gas flow rate in the multiphase cavitating flows.

THE WALL EFFECT ON VENTILATED CAVITATING FLOWS IN CLOSED CAVITATION TUNNELS

For ventilated cavitating flows in a closed water tunnel, the wall effect may exert an important influence on cavity shape and hydrodynamics, An isotropic mixture multiphase model was established to study the wall effect based on the RANS equations, coupled with a natural cavitation model and the RNG k-ε turbulent model. The governing equations were discretized using the finite volume method and solved by the Gauss-Seidel linear equation solver on the basis of a segregation algorithm. The algebraic multigrid approach was carried through to accelerate the convergence of solution. The steady ventilated cavitating flows in water tunnels of different diameter were simulated for a conceptual underwater vehicle model which had a disk cavitator. It is found that the choked cavitation number derived is close to the approximate solution of natural cavitating flow for a 3-D disk. The critical ventilation rate falls with decreasing diameter of the water tunnel. However, the cavity size and drag coeflicient are rising with the decrease in tunnel diameter for the same ventilation rate, and the cavity size will be much different in water tunnels of different diameter even for the same ventilated cavitation number.

NUMERICAL INVESTIGATION OF THE VENTILATED CAVITATING FLOW AROUND AN UNDER-WATER VEHICLE BASED ON A THREE-COMPONENT CAVITATION MODEL

Based on the Reynolds-Averaged Navier-Stokes equations and mass transfer model, an approach, where a three-component cavitation model is proposed, is presented to simulate ventilated cavitating flow as well as natural cavitation. In the proposed cavitation model, the initial content of nucleus in the local flow field is updated instantaneously, and is coupled with the Rayleigh-Plesset equation to capture the cavity development. The proposed model is applied to simulate the cavitating flow around an under-water vehicle in different cavitation conditions. The results indicate that for the natural and ventilated cavitation simulation, the predicted cavitation characteristics including the cavity length, cavity diameter and cavity shape agree satisfactorily with the analytic and experimental results, for the ventilated cavitation, the proposed methods reproduce the special behavior that the axial line of the cavity bends and rises at the tail part. The study concludes that the ventilated flow rate of the non-condensate gas influences the development of natural cavitation as well as ventilated cavitation, and the vapor cavity is suppressed remarkably by the gas cavity with the increase of the gas ventilation.

EXPERIMENTAL RESEARCH ON THE SHAPE CHARACTERS OF NATURAL AND VENTILATED SUPERCAVITATION

A series of projectile and water-tunnel experiments were conducted to investigate the shape characters of natural and ventilated supercavitation. It was found that the shape and dimensions of both the natural supercavitation and the ventilated supercavitation are similar through the comparison of them when the cavitation number is small and equal, and the contour of both the natural supercavitation and the ventilated supercavitation can be calculated effectively with the Savchenko formula. The gravity effect can induce the asymmetry of ventilated supercavitation, and the asymmetry is more apparent as the Froude number is smaller. The empirical formula for calculating the axial deformation of ventilated supercavitation was corrected and expanded based on experiment data. The evolution rules of both the natural supercavitation and the ventilated supercavitation were described, and the vortex frequency of natural cavitation was obtained. In addition, the hysteretic aspect was observed between the development and the fall process of ventilated cavitation.

Numerical simulation of multiphase cavitating flows around an underwater projectile

The present simulation investigates the multiphase cavitating flow around an underwater projectile.Based on the Homogeneous Equilibrium Flow assumption,a mixture model is applied to simulate the multiphase cavitating flow including ventilated cavitation caused by air injection as well as natural cavitation that forms in a region where the pressure of liquid falls below its vapor pressure. The transport equation cavitating model is applied.The calculations are executed based on a suite of CFD code.The hydrodynamics characteristics of flow field under the interaction of natural cavitation and ventilated cavitation is analyzed.The results indicate that the ventilated cavitation number is under a combined effect of the natural cavitation number and gas flow rate in the multiphase cavitating flows.

EXPERIMENTAL STUDY OF VENTILATED SUPERCAVITIES WITH A DYNAMIC PITCHING MODEL

An investigation of the ventilated supercavitation for a supercavitating vehicle pitching up and down in the supercavity was carded out in a high-speed water tunnel. The emphasis is laid on the understanding of the interaction of the vehicle aft body with the cavity boundary. The flow characteristics were measured and the stability of supercaviting flow with different pitching frequencies and amplitudes was analyzed. In particular, the objectives of this study are to understand the effect of the impact upon the cavity distortion, and to quantify the impact process by investigating the evolution of the pressure inside the cavity and then the loads on the vehicle during the pitching motion. It is also shown that the evolution of the pressure detected in different,as inside the supercavity, is coherent and uniform during the periods of the pitching motion. This study is of direct relevance to reliable and accurate prediction of hydrodynamic loads associated with the slamming and impact on supercavitating vehicles.

Numerical Investigation of Characteristics of Water-Exit Ventilated Cavity Collapse

The collapse of the ventilated cavitation occurring on a cylindrical vehicle during the water-exit is numerically researched. The numerical model employs the finite volume method to solve the multiphase Reynoldsaveraged Navier-Stokes(RNNS) equations and uses the volume of fluid(VOF) method to capture the free surface.A practical water wave environment that the vehicle usually encounters is reproduced in a numerical wave flume,so that the water wave's effect on the cavity collapse flow regime is investigated. The main feature of the waterexit collapse of a ventilated cavity is studied under the wave-free condition. The result indicates that a collapsing ventilated cavity experiences two stages, in which the pattern of cavity evolution is different. In the early stage,the cavity undergoes a rapid shrinkage as a closed body. In the late stage, the cavity releases gas from the front due to the increase of the cavity pressure. The water wave effect is investigated at three typical wave phases: the wave crest, the wave trough and the wave node. Results show that when the vehicle is launched under the wave node, the cavity collapse regime remains fairly axisymmetric and is similar to the wave-free case. However, when the vehicle is launched under the wave crest and trough, the cavity evolution presents highly three-dimensional(3D) features. The results of predicted cavity size, pressure distributions and hydrodynamic forces at different wave phases show that the wave effect is relatively weak at the wave node but becomes apparent at the wave crest and trough.