A NURBS-based high-order panel method for three-dimensional radiation and diffraction problems with forward speed

A high-order Rankine panel method based on Non-Uniform Rational B-Spline (NURBS) is developed for solving the three-dimensional radiation and diffraction problems with forward speed. A NURBS surface is used to precisely represent the body geometry. Velocity potential on the body surface is described by B-spline after the source density distribution on the boundary surface is determined. A collocation approach is applied to numerical computation and the integral equations are evaluated by applying Gauss–Legendre quadrature. The m_j-terms are evaluated by a desingularized method which utilizes NURBS technique. In order to verify the method proposed, it is firstly applied to the unbounded flow problem of a sphere and spheroids. The numerical results are found to be in good agreement with analytical solutions. Then the method is used to solve the radiation and diffraction problems of a sphere and the diffraction problem of a spheroid moving with a forward speed beneath the free surface in frequency domain. The numerical results are satisfactory in comparison with the published analytical results and experimental results.     

A B-spline based higher order panel method for analysis of steady flow around marine propellers

A higher order panel method based on B-spline representation for both the geometry and the solution is developed for the analysis of steady flow around marine propellers. The self-influence functions due to the normal dipole and the source are desingularized through the quadratic transformation, and then shown to be evaluated using conventional numerical quadrature. By selecting a proper order for numerical quadrature, the accuracy of the present method can be increased to the machine limit. The far- and near-field influences are shown to be evaluated based on the same far-field approximation, but the near-field solution requires subdividing the panels into smaller subpanels continuously, which can be effectively implemented due to the B-spline representation of the geometry. A null pressure jump Kutta condition at the trailing edge is found to be effective in stabilizing the solution process and in predicting the correct solution. Numerical experiments indicate that the present method is robust and predicts the pressure distribution on the blade surface, including very close to the tip and trailing edge regions, with far fewer panels than existing low-order panel methods.     

NURBS高阶面元法在多体水动力分析中应用

当位于海上的多个浮体距离相近时,它们间将产生显著的水动力相互作用。使用NURBS(非均匀有理B样条)高阶面元法进行多体水动力分析,速度势用任意阶的B样条函数近似,物面用NURBS曲面表示,由于水动力与几何表示相分离,就可以方便地实现计算机辅助设计与水动力分析的集成。对截断圆柱与椭球间的水动力相互作用和半潜式平台与箱型驳船间的水动力相互作用的计算显示此种方法可以对多体间的水动力相互作用给出准确的分析,计算时间和占用内存大幅减少。     

A panel-free method for time-domain analysis of the radiation problem

A panel-free method (PFM), based on the desingularized Green’s formulae proposed by Landweber and Macagno, has been developed to solve the radiation problem of a floating body in the time domain. The velocity potential due to a non-impulsive velocity is obtained by solving the boundary integral equation in terms of source strength distribution. The singularity in the Rankine source term of the time-dependent Green function is removed. The geometry of a body surface is mathematically represented by NURBS surfaces. The integral equation can be globally discretized over the body surface by Gaussian quadratures. No assumption is needed for certain degree of approximation of distributed source strength on the body surface. The accuracy of PFM was demonstrated by its application to a classical problem of uniform flow past a sphere. The response function of a hemisphere at zero speed was then computed by PFM. The computed response function, added-mass and damping coefficients are compared with other published results.     

A potential based panel method for 2-D hydrofoils

A potential based panel method for the hydrodynamic analysis of 2-D hydrofoils moving beneath the free surface with constant speed without considering cavitation is described. By applying Green's theorem and the Green function method, an integral equation for the perturbation velocity potential is obtained under the potential flow theory. Dirichlet type boundary condition is used instead of Neumann type boundary condition. The 2-D hydrofoil is approximated by line panels which have constant source strength and constant doublet strength distributions. The free surface condition is linearized and the method of images is used for satisfying this free surface condition. All the terms in fundamental solution (Green function) of perturbation potential are integrated over a line panel. Pressure distribution, lift, residual drag and free surface deformations are calculated for NACA4412, symmetric Joukowski and van de Vooren profile types of hydrofoil. The results of this method show good agreement with both experimental and numerical methods in the literature for the NACA4412 and symmetric Joukowski profile types. The lift and residual drag values of the van de Vooren profile are also presented. The effect of free surface is examined by a parametric variation of Froude number and depth of submergence.     

船舶螺旋桨尾流场的数值分析

利用基于速度势的低阶面元法计算船舶螺旋桨的尾流场。采用计算较为简捷的关于扰动速度势的基本积分微分方程，并采用双曲面形状的面凶以消除面元间的缝隙。Newton-Raphson迭代过程被用来在桨叶随边满足压力Kutta条件，使桨叶面上表面的压力在随边有良好的一致性。在计算面元的影响系数时，应用了Morino导出的解析计算公式，加快了数值计算的速度。从解面元法的基本积分方程得到的偶极强度和源汇强度，直接求得尾流场的速度分布。     

仿鱼尾潜器推进系统的水动力分析

以开发适用于小型潜器的仿生操纵与推进系统为研究背景 ,对金枪鱼的月牙形尾鳍进行水动力分析。文中将金枪鱼的尾鳍处理为在做横移和摇摆的耦合运动的同时 ,以某一匀速向前运动的月牙形刚性尾翼。计算中应用了双曲面元和压力库塔条件 ,利用面元法计算分析该三维尾翼的非定常水动力性能。探讨了前进速度、横荡和摇首的幅度、频率及其相位差对推进性能的影响     

Design of ship's bow form by potential-based panel method

A surface panel method treating a boundary-value problem of the Dirichlet type with the free surface is presented to design a three-dimensional body corresponding to a prescribed pressure distribution. The free surface boundary condition is linearized with respect to the oncoming flow, and computed by four-point finite difference scheme. Sample designs for submerged spheroids and Wigley hull are carried out to demonstrate the stable convergence, the effectiveness and the robustness of the method. The design of a 5500TEU container carrier is performed with respect to reduction of the wave resistance. To reduce the wave resistance, calculated pressure on the hull surface is modified to have the lower fluctuation, and is applied as a Dirichlet type dynamic boundary condition on the hull surface. The designed hull form is verified to have the lower wave resistance than the initial one not only by computation but also by experiment.     

A B-spline-based method for radiation and diffraction problems

An open uniform B-spline-based panel method is developed for solution of potential flow problems. In this method, both geometry as well as the field variables are represented by the same open uniform B-spline basis function. The method is initially applied for the radiation problem in unbounded fluid. Computed results for a spheroid of different aspect ratio are found to be in excellent agreement with analytical results. The method is then applied for diffraction problem formulated based on the transient (time-domain) Green's function. Computed results for a hemisphere and Wigley hull are compared with published results and the comparison shows good agreement.     

Numerical calculation of free-surface potential flow around a ship using the modified Rankine source panel method

A modified Rankine source panel method is presented for solving a linearized free-surface flow problem with respect to the double-body potential. The method of solution is based on the distribution of Rankine sources on the hull as well as its image and on the free surface. An iterative algorithm is used for determining the free surface and wave resistance using upstream finite difference operator. A verification of numerical modeling is made using the Wigley hull and the validity of the computer program is examined by comparing the details of wave profiles and wave making resistance with Series 60 model.     

An approximation to energy dissipation in time domain simulation of sloshing waves based on linear potential theory

This paper proposes a new approximation to energy dissipation in time domain simulation of sloshing waves by use of a linear potential theory.The boundary value problem is solved by the NURBS(non-uniform rational B-spline) higher-order panel method,in which a time-domain Green function is employed.The energy dissipation is modeled by changing the boundary condition on solid boundaries.Model experiments are carried out in a partially filled rectangular tank with forced horizontal motion.Sloshing-induced internal pressures and horizontal force obtained numerically and experimentally are compared with each other.It is observed that the present energy dissipation approximation can help produce a fair agreement between experimental forces and those of numerical simulations.     

A potential based panel method for 2-D hydrofoils

A potential based panel method for the hydrodynamic analysis of 2-D hydrofoils moving beneath the free surface with constant speed without considering cavitation is described. By applying Green's theorem and the Green function method, an integral equation for the perturbation velocity potential is obtained under the potential flow theory. Dirichlet type boundary condition is used instead of Neumann type boundary condition. The 2-D hydrofoil is approximated by line panels which have constant source strength and constant doublet strength distributions. The free surface condition is linearized and the method of images is used for satisfying this free surface condition. All the terms in fundamental solution (Green function) of perturbation potential are integrated over a line panel. Pressure distribution, lift, residual drag and free surface deformations are calculated for NACA4412, symmetric Joukowski and van de Vooren profile types of hydrofoil. The results of this method show good agreement with both experimental and numerical methods in the literature for the NACA4412 and symmetric Joukowski profile types. The lift and residual drag values of the van de Vooren profile are also presented. The effect of free surface is examined by a parametric variation of Froude number and depth of submergence.     

3D hydrodynamic modelling of fixed oscillating water column wave power plant by a boundary element methods

A three-dimensional (3D) numerical model of fixed Oscillating Water Column system (OWC) is presented and validated. The steady-state potential flow boundary value problem due to regular wave interaction with the OWC is solved by a first order mixed distribution panel method. Ocean response predictions are derived using a deterministic statistical model based on a spectral analysis method. The model validation focusses on diffraction predictions and involves convergence tests and numerical comparisons with independent potential flow computations. Predictions of both regular and irregular wave responses are also compared against experimental results. Sample results including the yearly-averaged power conversion efficiency are presented in the final section to illustrate the method’s suitability to a 3D hydrodynamic design optimisation.     

Flow around circular and noncircular cylinders by a low-order panel method

Time-dependent cross-flow was studied around cylinders with circular and noncircular cross-sections. The numerical approach for the analysis was a low-order panel method based on constant source and dipole values along each panel. The method was previously used successfully for several applications, such as calculation of the added mass and damping coefficients. In simulating the viscous time-dependent flow around the cylinder, the time-dependent wake feature of the code was used. For the circular and D-cylinders, the results agreed well with the experiments. Suggestions for improving the results for T-cylinders with angle of attack are included.     

Prediction of non-cavitation propeller noise in time domain

The blade frequency noise of non-cavitation propeller in a uniform flow is analyzed in time domain. The unsteady loading (dipole source) on the blade surface is calculated by a potential-based surface panel method. Then the time- dependent pressure data is used as the input for Ffowcs Williams-Hawkings formulation to predict the acoustics pressure. The integration of noise source is performed over the true blade surface rather than the nothickness blade surface, and the effect of hub can be considered. The noise characteristics of the non-cavitation propeller and the numerical discretization forms are discussed.     

Prediction of Non-Cavitation Propeller Noise in Time Domain

The blade frequency noise of non-cavitation propeller in a uniform flow is analyzed in time domain. The unsteady loading (dipole source) on the blade surface is calculated by a potential-based surface panel method. Then the time- dependent pressure data is used as the input for Ffowcs Williams-Hawkings formulation to predict the acoustics pressure. The integration of noise source is performed over the true blade surface rather than the nothickness blade surface, and the effect of hub can be considered. The ...     

Prediction of added resistance of ships in waves

The prediction of the added resistance of ships in waves is a demanding, quasi-second-order seakeeping problem of high practical interest. In the present paper, a well established frequency domain 3D panel method and a new hybrid time domain Rankine source-Green function method of NTUA-SDL are used to solve the basic seakeeping problem and to calculate first order velocity potentials and the Kochin functions, as necessary for the calculation of the added resistance by Maruo's far-field method. A wide range of case studies for different hull forms (slender and bulky) was used to validate the applicability and accuracy of the implemented methods in practice and important conclusions regarding the efficiency of the investigated methods are drawn.     

基于非定常面元法的海上浮式风机气动性能研究

对于海上浮式风机而言,由于受到剪切风、塔影效应、浮式基础运动等因素的共同影响,其气动载荷会更加复杂,因此如何准确快速地对海上风力机的气动性能进行预估显得尤为重要。基于速度势的非定常面元法理论,研究海上浮式风机气动载荷特性,编制了相关的计算程序。以NREL 5 MW风机为例,建立了叶片和尾流的三维数值模型,计算得到了不同风速下风机的输出功率以及叶片表面的压力分布,对比数据结果分析了该方法的可靠性。针对非定常流动,模拟了剪切风和塔影效应的作用,并重点分析了浮式基础运动对风机气动载荷的影响。研究表明,浮式基础的纵荡和纵摇会增加输出功率的波动幅值,艏摇运动会导致单个叶片上的气动载荷产生较大的波动,为浮式风机叶片控制提供了参考。     

柔性仿金枪鱼月牙形尾鳍水动力分析

为研究鱼类高速游动机理,以金枪鱼月牙形尾鳍为对象,采用面元法计算分析了其非定常水动力性能。假设尾鳍在横移和摇摆的同时,以某一匀速向前运动,并假设其在弦向和展向以某一给定规律发生变形,以模仿柔性变形。探讨了前进速度、横移和摇摆的幅度、频率及其相位差对柔性尾鳍推进性能的影响,并与做相应运动的刚性尾鳍进行了对比。     

Finite-element computation of wave impact load due to a violent sloshing

A nonlinear sloshing problem is numerically simulated. During excessive sloshing, the sloshing-induced impact load can cause a critical damage on the tank structure. Recently the problem becomes an important research topic in LNG (Liquefied Natural Gas) Tanker and FPSO (Floating Production Storage Offloading) design. In this study, the wave impact load on the structure is obtained numerically by imposing the exact nonlinear free surface conditions and compared with that predicted by Morison's formula. As a theoretical model, a three-dimensional free surface flow in a tank is formulated in the scope of potential flow theory with the exact nonlinear free-surface conditions. A finite-element method based on Hamilton's principle is employed as a numerical method. The problem is treated as an initial-value problem. The nonlinear problem is numerically solved through an iterative scheme at each time step.