Numerical Analysis of 2-D and 3-D Cavitating Hydrofoils Under a Free Surface

2001 ◽  
Vol 45 (01) ◽  
pp. 34-49 ◽  
Author(s):  
Sakir Bal ◽  
Spyros A. Kinnas ◽  
Hanseong Lee
Keyword(s):  
Integral Equation ◽  
Free Surface ◽  
Three Dimensional ◽  
Radiation Condition ◽  
Flow Conditions ◽  
Surface Conditions ◽  
Constant Strength ◽  
Cavitating Hydrofoil ◽  
Upstream Waves ◽  
Transverse Boundary

A method which models two- or three-dimensional cavitating hydrofoils moving with constant speed under a free surface is described. An integral equation is obtained by applying Green's theorem on all surfaces of the fluid domain. This integral equation is divided into two parts:the cavitating hydrofoil problem, andthe free-surface problem. These two problems are solved separately, with the effects of one on the other being accounted for in an iterative manner. The cavitating hydrofoil surface and the free surface are modeled with constant strength dipole and source panels. The source strengths on the free surface are expressed in terms of the second derivative of the potential with respect to the horizontal axis by applying the linearized free-surface conditions. The induced potential by the cavitating hydrofoil on the free surface and by the free surface on the hydrofoil are determined in an iterative sense. In order to prevent upstream waves the source strengths from some distance in front of the hydrofoil to the end of the truncated upstream boundary are enforced to be equal to zero. No radiation condition is enforced at the downstream boundary or at the transverse boundary. The method is applied to 2-D and 3-D hydrofoil geometries in fully wetted or cavitating flow conditions and the predictions are compared with those of other methods in the literature.

A numerical method for the prediction of wave pattern of surface piercing cavitating hydrofoils

2007 ◽  
Vol 221 (12) ◽  
pp. 1623-1633 ◽  
Author(s):  
S Bal
Keyword(s):  
Free Surface ◽  
Numerical Method ◽  
Radiation Condition ◽  
Wave Pattern ◽  
The Body ◽  
Constant Strength ◽  
Lift And Drag ◽  
Yaw Angle ◽  
Cavitating Hydrofoil ◽  
Iterative Boundary Element Method

The iterative boundary-element method, which is originally developed before for submerged cavitating hydrofoils is extended and modified to predict the wave pattern and lift and drag values of surface piercing cavitating hydrofoils (vertical struts) moving with a constant speed on the free surface. The iterative numerical method, which is based on the Green's theorem, allows the separation of surface piercing cavitating hydrofoil (or vertical strut) problem and the free surface problem. Those problems are solved separately, with the effects of one on the other being accounted for in an iterative manner. The wetted surface of the body (hydrofoil or strut) and the free surface are modelled with constant strength dipole and constant strength source panels. In order to prevent upstream waves the source strengths from some distance in front of the body to the end of the truncated upstream boundary are enforced to be zero. No radiation condition is enforced for downstream and transverse boundaries on the free surface. The method is applied to a rectangular non-cavitating hydrofoil with a yaw angle to compare the results with those of experiments and other numerical methods given in the literature. Then, the method is applied to a rectangular cavitating vertical strut and the effects of Froude number on wave pattern and lift and drag values of vertical strut are discussed.

Three-Dimensional Large Amplitude Body Motions in Waves

2007 ◽  
Author(s):  
Xinshu Zhang ◽  
Robert F. Beck
Keyword(s):  
Free Surface ◽  
Three Dimensional ◽  
Surface Boundary ◽  
Forward Speed ◽  
Time Step ◽  
Surface Boundary Conditions ◽  
Submerged Body ◽  
Calm Water ◽  
Wigley Hull ◽  
Constant Strength

Three-dimensional, time-domain, wave-body interactions are studied in this paper for cases with and without forward speed. In the present approach, an exact body boundary condition and linearized free surface boundary conditions are used. By distributing desingularized sources above the calm water surface and using constant-strength panels on the exact submerged body surface, the boundary integral equations are solved numerically at each time step. Once the fluid velocities on the free surface are computed, the free surface elevation and potential are updated by integrating the free surface boundary conditions. After each time step, the body surface and free surface are regrided due to the instantaneous changing submerged body geometry. The desingularized method applied on the free surface produces non-singular kernels in the integral equations by moving the fundamental singularities a small distance outside of the fluid domain. Constant strength panels are used for bodies with any arbitrary shape. Extensive results are presented to validate the efficiency of the present method. These results include the added mass and damping computations for a hemisphere. The calm water wave resistance for a submerged spheroid and a Wigley hull are also presented. All the computations with forward speed are started from rest and proceed until a steady state is reached. Finally, the time-domain forced motion results for a modified Wigley hull with forward speed are shown and compared with the experiments for both linear computations and body-exact computations.

Numerical Study of Forward-Speed Ship Motion and Added Resistance

2017 ◽  
Author(s):  
D. C. Hong ◽  
T. B. Ha ◽  
K. H. Song
Keyword(s):  
Integral Equation ◽  
Free Surface ◽  
Numerical Study ◽  
Three Dimensional ◽  
The Body ◽  
Experimental Results ◽  
Surface Boundary ◽  
Forward Speed ◽  
Added Resistance ◽  
Following Seas

The added resistance of a ship was calculated using Maruo’s formula [1] involving the three-dimensional Kochin function obtained using the source and normal doublet distribution over the wetted surface of the ship. The density of the doublet distribution was obtained as the solution of the three-dimensional frequency-domain forward-speed Green integral equation containing the exact line integral along the waterline. Numerical results of the Wigley ship models II and III in head seas, obtained by making use of the inner-collocation 9-node second-order boundary element method have been compared with the experimental results reported by Journée [2]. The forward-speed hydrodynamic coefficients of the Wigley models have shown no irregular-frequencylike behavior. The steady disturbance potential due to the constant forward speed of the ship has also been calculated using the Green integral equation associated with the steady forward-speed free-surface Green function since the so-called mj-terms [3] appearing in the body boundary conditions contain the first and second derivatives of the steady potential over the wetted surface of the ship. However, the free-surface boundary condition was kept linear in the present study. The added resistances of the Wigley II and III models in head seas obtained using Maruo’s formula showing acceptable comparison with experimental results, have been presented. The added resistances in following seas obtained using Maruo’s formula have also been presented.

Directional Response of a B-Train Vehicle Combination Carrying Liquid Cargo

1993 ◽  
Vol 115 (1) ◽  
pp. 133-139 ◽  
Author(s):  
R. Ranganathan ◽  
S. Rakheja ◽  
S. Sankar
Keyword(s):  
Free Surface ◽  
Three Dimensional ◽  
Lateral Acceleration ◽  
Flow Conditions ◽  
Vehicle Model ◽  
Liquid Motion ◽  
Directional Response ◽  
Response Characteristics ◽  
Weight Density ◽  
Liquid Movement

Directional dynamics of a B-train tank vehicle is investigated by integrating the three-dimensional vehicle model to the dynamics associated with the movement of free surface of liquid within the partially filled tanks. The motion of the free surface of liquid due to instantaneous tank roll and lateral acceleration is computed assuming steady state fluid flow conditions. The influence of liquid motion on the dynamic response of the rearmost trailer is investigated for both constant and transient steer inputs, assuming constant forward speed. Directional response characteristics of the B-train tank vehicle are compared to those of an equivalent rigid cargo vehicle to demonstrate the destabilizing effects of the liquid movement within the tank vehicle. Directional response characteristics are further discussed for variation in weight density of liquid and thus the fill height, while the axle loads are held constant around maximum permissible values.

Prediction of Hydrodynamic Performance of 3-D WIG by IBEM

2018 ◽  
Vol Vol 160 (A3) ◽  
Author(s):  
S Bal
Keyword(s):  
Free Surface ◽  
Water Surface ◽  
Three Dimensional ◽  
Free Water ◽  
Hydrodynamic Performance ◽  
Ground Vehicle ◽  
Surface Part ◽  
Free Water Surface ◽  
Constant Strength ◽  
Lift And Drag

The hydrodynamic performance of three-dimensional WIG (Wing-In-Ground) vehicle moving with a constant speed above free water surface has been predicted by an Iterative Boundary Element Method (IBEM). IBEM originally developed for 3-D hydrofoils moving under free surface has been modified and extended to 3-D WIGs moving above free water surface. The integral equation based on Green's theorem can be divided into two parts: (1) the wing part, (2) free surface part. These two problems are solved separately, with the effects of one on the other being accounted for in an iterative manner. Both the wing part including the wake surface and the free surface part have been modelled with constant strength dipole and source panels. The effects of Froude number, the height of the hydrofoil from free surface, the sweep, dihedral and anhedral angles on the lift and drag coefficients are discussed for swept and V-type WIGs.

Unsteady Linearized Lifting-Surface Theory in the Presence of a Free Surface

1987 ◽  
Vol 31 (03) ◽  
pp. 151-163
Author(s):  
J. Leclerc ◽  
P. Salaun
Keyword(s):  
Integral Equation ◽  
Free Surface ◽  
Unknown Function ◽  
Pressure Difference ◽  
Angle Of Attack ◽  
Three Dimensional ◽  
Thin Structures ◽  
Surface Theory ◽  
Lifting Surface ◽  
The Right

A new lifting-surface theory is developed for the computation of three-dimensional hydrodynamic pressures on thin structures in the presence of a free surface. Two interesting cases are treated: the steady case and the supercritical unsteady case. The theory is linearized and the problem is reduced to the solution of an integral equation where the unknown function is the pressure difference between the elements of the structure and the right-hand side the angle of attack. Forces and moments are presented in both the steady and unsteady cases. This theory allows the analysis of flutter and the study of steady drag and of the turn of ships.

Numerical Study of the Ship Motion in Waves Using the Three-Dimensional Time-Domain Forward-Speed Free-Surface Green Function and a Second-Order Boundary Element Method

2008 ◽  
Author(s):  
D. C. Hong ◽  
S. Y. Hong ◽  
H. G. Sung
Keyword(s):  
Integral Equation ◽  
Free Surface ◽  
Green Function ◽  
Time Domain ◽  
Time Derivative ◽  
Three Dimensional ◽  
Forward Speed ◽  
Surface Green Function ◽  
The Green Function ◽  
The Time Domain

The radiation and diffraction potentials of a ship advancing in waves are calculated in the time-domain using the three-dimensional time-domain forward-speed free-surface Green function and the Green integral equation on the basis of the Neumann-Kelvin linear wave hypothesis. The Green function approximated by Newman for large time is used together with the Green function by Lamb for small time. The time-domain diffraction problem is solved for the time derivative of the potential by using the time derivative of the impulsive incident wave potential represented by using the complementary complex error function. The integral equation for the potential is discretized according to a second-order boundary element method where the collocation points are located inside the panel. It makes it possible to take account of the line integral along the waterline in a rigorous manner. The six-degree-of-freedom motion and memory functions as well as the diffraction impulse response functions of a hemisphere and the Wigley seakeeping model are presented for various Froude numbers. Comparisons of the wave damping and exciting force and moment coefficients for zero forward speed, calculated by using the Fourier transforms of the time-domain results and the frequency-domain coefficients calculated by using the improved Green integral equation which is free of the irregular frequencies, have been shown to be satisfactory. The wave damping coefficients for non-zero forward speed, calculated by using Fourier transforming of the present time-domain results have also been compared to the experimental results and agreement between them has been shown to be good. A simulation of coupled heave-pitch motion of the Wigley seakeeping model advancing in regular head waves of unit amplitude has been carried out.

An expansion theorem applicable to problems of wave propagation in an elastic half-space containing a cavity

1967 ◽  
Vol 63 (4) ◽  
pp. 1341-1367 ◽  
Author(s):  
R. D. Gregory
Keyword(s):  
Free Surface ◽  
Half Space ◽  
Radiation Condition ◽  
Elastic Half Space ◽  
Potential Fields ◽  
Governing Equations ◽  
Expansion Theorem ◽  
Surface Conditions ◽  
Harmonic Vibrations ◽  
Time Harmonic

AbstractThis paper is principally concerned with the two-dimensional time harmonic vibrations of an elastic half-space y ≥ 0, containing a submerged cavity in the form of an infinite circular cylinder. Two sequences of line source potentials are obtained which are singular along the axis of the cylinder, satisfy the free surface conditions on y = 0, and represent outgoing waves at infinity. (The radiation condition.) It is proved that any solution of the governing equations which satisfies the free surface conditions and consists of outgoing waves at infinity is expansible as a sum of these fundamental source potentials, with coefficients to be determined from the boundary conditions on the cylinder only.The requirement of outgoing waves is carefully discussed and it is shown that the conditions taken give rise to, and are satisfied by, potential fields which would be regarded intuitively as representing outgoing waves.

Potential flow solution for a yawed surface-piercing plate

1991 ◽  
Vol 226 ◽  
pp. 291-317 ◽  
Author(s):  
Hongbo Xü
Keyword(s):  
Integral Equation ◽  
Free Surface ◽  
Surface Condition ◽  
Leading Edge ◽  
Radiation Condition ◽  
Lateral Force ◽  
Vertical Surface ◽  
Analytical Investigation ◽  
Surface Boundary ◽  
Kutta Condition

This paper presents the results of an analytical investigation of the steady translation of a vertical surface-piercing plate at a small angle of attack. This problem is the antisymmetric equivalent of the symmetric thin-ship problem solved by Michell. The linearized boundary-value problem is transformed into an integral equation of the first kind by the method of Green functions. The Kelvin–Havelock Green function is used to satisfy the linearized free-surface boundary condition and radiation condition. A pressure Kutta condition is imposed at the trailing edge. Effective algorithms are developed to evaluate the hypersingular kernel without recourse to numerical integration. The resulting integral equation is solved by a collocation method with a refined scheme of discretization. After establishing the convergence of the present algorithm, computations are carried out for a surface-piercing rectangular plate of aspect ratio 0.5. The integrated lateral-force and yaw-moment coefficients show good agreement with experimental data. Other parameters of the flow such as pressure distributions, drag, strength of leading-edge singularity and free-surface profiles on the plate are also presented. The incompatibility between the pressure Kutta condition and the linearized free-surface condition does not affect the global solution.

Three-Dimensional Large Amplitude Body Motions in Waves

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Xinshu Zhang ◽  
Robert F. Beck
Keyword(s):  
Free Surface ◽  
Time Domain ◽  
Three Dimensional ◽  
Surface Boundary ◽  
Forward Speed ◽  
Time Step ◽  
Surface Boundary Conditions ◽  
Calm Water ◽  
Wigley Hull ◽  
Constant Strength

Three-dimensional, time-domain, wave-body interactions are studied in this paper for cases with and without forward speed. In the present approach, an exact body boundary condition and linearized free surface boundary conditions are used. By distributing desingularized sources above the calm water surface and using constant-strength flat panels on the exact wetted body surface, the boundary integral equations are numerically solved at each time step. Once the fluid velocities on the free surface are computed, the free surface elevation and potential are updated by integrating the free surface boundary conditions. After each time step, the body surface and free surface are regrided due to the instantaneous wetted body geometry. The desingularized method applied on the free surface produces nonsingular kernels in the integral equations by moving the fundamental singularities a small distance outside of the fluid domain. Constant-strength flat panels are used for bodies with any arbitrary shape. Extensive results are presented to validate the efficiency of the present method. These results include the added mass and damping computations for a hemisphere. The calm water wave resistance for a submerged spheroid and a Wigley hull are also presented. All the computations with forward speed are started from rest and proceeded until a steady state is reached. Finally, the time-domain forced motion results for a modified Wigley hull with forward speed are shown and compared to the experiments for both linear computations and body-exact computations.

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