Cavitation Number As a Function of Disk Cavitator Radius: A Numerical Analysis of Natural Supercavitation

Due to the greater viscosity and density of water compared to air, the maximum speed of underwater travel is severely limited compared to other methods of transportation. However, a technology called supercavitation — which uses a disk-shaped cavitator to envelop a vehicle in a bubble of steam — promises to greatly decrease skin friction drag. While a large cavitator enables the occurrence of supercavitation at low velocities, it adds substantial drag at higher speeds. Based on CFD results, we propose a new relationship between drag coefficient and disk cavitator radius, and we predict the optimum cavitator radius for a particular torpedo design.

Drag and Cavity Development of Two Slender Bodies: A Numerical Study

In the present study, an unsteady three-dimensional flow simulation based on the RANS (Reynolds Average Navier-Stokes) equations with k-ε turbulence model and Singhal et al.’s cavitation model is conducted to study the cavity development behavior of two slender bodies, that is, a flat-headed cylinder and a step-headed cylinder of 50 mm in length and 10 mm in diameter. Using so called VOF method to track the liquid-vapor phase interface, time dependent solutions with varying approach speed range from 10 m/s to 55 m/s are obtained and analyzed to provide key information such as cavity initiation speed, drag coefficient and the cavity shape and size (max. length and diameter). The implemented numerical model is validated for flows over a flat disk cavitator against the experimental correlation. According to the present simulation results, slender bodies with two different head shapes, that is, a flat cylinder and a stepped one, respectively, showed very close behavior in their cavity initiation speed, maximum developed cavity diameter and length, but consistently lower drag coefficient with the step-headed cylinder case, which suggests the possible advantage of seeking optimized cavitator shape.

Model and Control Validation of High Speed Supercavitating Vehicles

This article presents a hybrid validation technique to test mathematical models and control systems for a High Speed Supercavitating Vehicle HSSV. The test method combines simulation of the vehicle motion, real-time experimental measurements of hydrodynamic forces acting at the vehicle wetted areas, and vehicle flight computer to evaluate the HSSV performance subject to steady and unsteady flows. The proposed validation platform is deployed in the high speed water tunnel located at the University of Minnesota Saint Anthony Falls Laboratory SAFL. The supercavitating test vehicle, operated with ventilation, consists of an actuated disk cavitator and two actuated lateral wedge fins. The model of the vehicle motion, used to develop the validation platform and design HSSV controllers, is derived through experimental data obtained in the high speed water tunnel. An illustration is given on how the control system is able to track pitch angle reference commands and reject flow perturbations produced by an oscillating foil gust generator.

The Optimum Design of a Cavitator for High-Speed Axisymmetric Bodies in Partially Cavitating Flows

In this paper, the partially cavitating flow over an axisymmetric projectile is studied in order to obtain the optimum cavitator such that, at a given cavitation number, the total drag coefficient of the projectile is minimum. For this purpose, the boundary element method and numerical simulations are used. A large number of cavitator profiles are produced using a parabolic expression with three geometric parameters. The potential flow around these cavitators is then solved using the boundary element method. In order to examine the optimization results, several cavitators with a total drag coefficient close to that of the optimum cavitators are also numerically simulated. Eventually, the optimum cavitator is selected using both the boundary element method and numerical simulations. The effects of the body radius and the length of the conical section of the projectile on the shape of the optimized cavitator are also investigated. The results show that for all cavitation numbers, the cavitator that creates a cavity covering the entire conical section of the projectile with a minimum total drag coefficient is optimal. It can be seen that increasing the cavitation number causes the optimum cavitator to approach the disk cavitator. The results also show that at a fixed cavitation number, the increase in both the radius and length of the conical section causes the cavitator shape to approach that of the disk cavitator.

Application of Non-Linear Turbulence Models on the Numerical Simulation of Cavitating Flows

Quadratic and cubic non-linear eddy-viscosity turbulence Models (NLEVM) with low Reynolds number correction were employed to provide better treatment about the anisotropic turbulence stresses in cavitating flows, in which large density ratio and swirling structures consist. These models were carried out through a self-developed computer code, and were validated by the case of the cavity over disk cavitator. It was proven that, the nonlinear models could effectively eliminate the non-physical numerical oscillation of the cavity profile which was usually caused by linear models. It had also been experimentally proved that the computed cavity shapes and pressure inside the cavity were accurately captured by these nonlinear models. One of such nonlinear models was further applied on the simulation of the cavitating flows around submerged vehicles. The numerical results were compared with experiment data to investigate the influence of the vehicle’s head and the after-body on the characteristics of the cavity. Ultimately, the cavitating flows around an especially designed complex underwater vehicle were predicted using the cubic k–ε turbulence model. The corresponding cavitation behaviors were studied to provide a beneficial experience for the research in future.

Numerical Simulation of Natural Cavitating Flow over Axisymmetric Bodies

The hydrodynamic characteristics of bodies are greatly affected by cavitation. Coupling with natural cavitaion model, a multiphase CFD method is developed and is employed to simulate supercavitating and partial cavitating flows over axisymmetric bodies using FLUENT 6.2. The results of supercavitation of a disk cavitator agree well with the boundary element method (BEM), the analytical relations and available experimental results. The present computations and the BEM results are compared with experiments for partial cavitating flows over three typical axisymmetric bodies and the results are discussed. Limitations are on the pressure prediction in the cavity closure region for the BEM, although fairly good quantitative agreement is obtained for three axisymmetric bodies at most of cavitation region. The present computational model on cavitating flows are validated, offering references and bases for hydrodynamic researches.