Spyros A. Kinnas

A numerical nonlinear analysis of the flow around two- and three-dimensional partially cavitating hydrofoils

The partially cavitating two-dimensional hydrofoil problem is treated using nonlinear theory by employing a low-order potential-based boundary-element method. The cavity shape is determined in the framework of two independent boundary-value problems; in the first, the cavity length is specified and the cavitation number is unknown, and in the second the cavitation number is known and the cavity length is to be determined. In each case, the position of the cavity surface is determined in an iterative manner until both a prescribed pressure condition and a zero normal velocity condition are satisfied on the cavity. An initial approximation to the nonlinear cavity shape, which is determined by satisfying the boundary conditions on the hydrofoil surface rather than on the exact cavity surface, is found to differ only slightly from the converged nonlinear result. The boundary element method is then extended to treat the partially cavitating three-dimensional hydrofoil problem. The three-dimensional kinematic and dynamic boundary conditions are applied on the hydrofoil surface underneath the cavity. The cavity planform at a given cavitation number is determined via an iterative process until the thickness at the end of the cavity at all spanwise locations becomes equal to a prescribed value (in our case, zero). Cavity shapes predicted by the present method for some three-dimensional hydrofoil geometries are shown to satisfy the dynamic boundary condition to within acceptable accuracy. The method is also shown to predict the expected effect of foil thickness on the cavity size. Finally, cavity planforms predicted from the present method are shown to be in good agreement to those measured in a cavitating three-dimensional hydrofoil experiment, performed in MIT’s cavitation tunnel.

A BEM for the Prediction of Unsteady Midchord Face and/or Back Propeller Cavitation

A boundary element method (BEM) is used for the numerical analysis of sheet cavitation on a propeller subjected to the non-axisymmetric wakes of marine vehicles. This method is extended in order to treat mixed partial and supercavity patterns on both the face and back of the blades with searched cavity detachment. The convergence of the method is studied

Modeling of Unsteady Sheet Cavitation on Marine Propeller Blades

Unsteady sheet cavitation is very common on marine propulsor blades. The authors summarize a lifting-surface and a surface-panel model to solve for the unsteady cavitating flow around a propeller that is subject to nonaxisymmetric inflow. The time-dependent extent and thickness of the cavity were determined by using an iterative method. The cavity detachment was determined by applying the smooth detachment criterion in an iterative manner. A nonzeroradius developed vortex cavity model was utilized at the tip of the blade, and the trailing wake geometry was determined using a fully unsteady wake-alignment process. Comparisons of predictions by the two models and measurements from several experiments are given.

A Wake Model for the Prediction of Propeller Performance at Low Advance Ratios

A low order panel method is used to predict the performance of propellers. A wake alignment model based on a pseudounsteady scheme is proposed and implemented. The results from this full wake alignment (FWA) model are correlated with available experimental data, and results from RANS for some propellers at design and low advance ratios. Significant improvements have been found in the predicted integrated forces and pressure distributions.

A numerical nonlinear analysis of two-dimensional ventilating entry of surface-piercing hydrofoils with effects of gravity

The presence of the free surface adds an element of difficulty to the development of numerical and theoretical methods for the performance prediction of surface-piercing hydrofoils. Existing methods of analysis for two-dimensional surface-piercing hydrofoils or blade sections of a surface-piercing propeller solve either a linear problem, assuming a thin section and ventilated surface along with linear free-surface boundary conditions, or a nonlinear problem in a self-similar setting. Both these approaches cannot be used when the effects of gravity are important, which is the case when a craft is operating at low speeds. A two-dimensional boundary-element-method-based numerical scheme is presented here that overcomes these drawbacks by solving the fully ventilated flow past a surface-piercing hydrofoil of finite dimensions and includes the whole gamut of nonlinear free-surface interactions. The unique aspect of the numerical scheme is that fully nonlinear boundary conditions are applied on the free surface which allows for the accurate modelling of the jet generated on the wetted boundary and the ventilated surface formed on the suction side as a result of the passage of the hydrofoil through the free surface. Moreover, the effects of gravity can be considered to take into account the influence of the Froude number. Ventilated-surface shapes predicted by the present scheme are compared with existing experimental results and are shown to be in good agreement.

On the accurate calculation of effective wake/application to ducted propellers

A hybrid method that couples a potential flow solver with a Reynolds-Averaged Navier-Stokes (RANS) solver for calculating the effective wake of a propeller is proposed. Two improvements are addressed in this method: 1) a conservative interpolation scheme that conserves the total forces when passing information from the potential flow solver to the RANS solver; and 2) a novel option that evaluates the effective wake at the control points in the blade zone. The proposed method is first assessed in the case of an open propeller subject to uniform inflow and then applied to predict the performance of the ducted propellers under uniform inflow. The results of the numerical simulation are correlated with available experimental measurements.

Numerical Modeling of a Marine Propeller Undergoing Surge and Heave Motion

A boundary element method (BEM) and a vortex-lattice method (VLM) are extended in order to predict the unsteady performance of propellers subject to rigid body motions. The methods are applied in the case of prescribed surge and heave motions, and the results are compared with those from other methods.

Modeling of cavitating or ventilated flows using BEM

Boundary element method (BEM) techniques for the prediction of cavitating or ventilated flows around hydrofoils and propeller are summarized. Classical, supercavitating, and ventilated blade section geometries are considered. Recent extensions which allow for the modeling of cavities on either or both sides of the blade surface are presented. Numerical validation studies and comparisons with experimental measurements are shown.

Numerical Model of Cavitating Propeller Inside of a Tunnel

The unsteady cavitating flow of a propeller subject to a nonaxisymmetric inflow inside of a tunnel is addressed. A numerical method is developed which solves for the fully unsteady propeller problem and the tunnel problem separately, with the unsteady effects of one on the other being accounted for in an iterative manner. The propeller influence on the tunnel walls is considered via potential while the tunnel walls influence on the propeller is considered via velocity. The iterative process is found to converge very fast, usually within three iterations, even for a heavily loaded propeller. The effect of the tunnel extent and the number of panels on the predicted mean propeller forces is investigated, In the case of uniform inflow the equivalent open water velocity is calculated and then compared to that predicted from Glauerts formula

The local error of a low-order boundary element method at the trailing edge of a hydrofoil and its effect on the global solution

Abstract The performance of a low-order (piecewise constant dipole and source distributions) potential based boundary element method (BEM) is tested when applied for the analysis of the steady flow around two-dimensional hydrofoil geometries. The convergence rate of the results (e.g. the circulation around the foil) with an increasing number of panels N is found to be very slow. The slow convergence is attributed to the O(1/N) local error of the low-order BEM in the vicinity of a sharp trailing edge. To reduce that error an at least linear dipole distribution is shown that must be utilized on each panel. The effect of the difference of the linear from the constant dipole, the so-called “saw-tooth” effect, is accounted for within the low-order BEM in an iterative manner. The inclusion of the “saw-tooth” effect is shown to improve the performance of the low-order BEM substantially.