Numerical Comparison for Focused Wave Propagation Between the Fully Nonlinear Potential Flow and the Viscous Fluid Flow Models

Numerical simulations on focused wave propagation are carried out by using three types of numerical models,including the linear potential flow,the nonlinear potential flow and the viscous fluid flow models.The wave-wave interaction of the focused wave group with different frequency bands and input wave amplitudes is examined,by which the influence of free surface nonlinearity and fluid viscosity on the related phenomenon of focused wave is investigated.The significant influence of free surface nonlinearity on the characteristics of focused wave can be observed,including the increased focused wave crest,delayed focused time and downstream shift of focused position with the increase of input amplitude.It can plot the evident difference between the results of the nonlinear potential flow and linear potential flow models.However,only a little discrepancy between the nonlinear potential flow and viscous fluid flow models can be observed,implying the insignificant effect of fluid viscosity on focused wave behavior.Therefore,the nonlinear potential flow model is recommended for simulating the non-breaking focused wave problem in this study.

A fast multipole boundary element method for three-dimensional potential flow problems

A fast multipole methodology (FMM) is developed as a numerical approach to reduce the computational cost andmemory requirements in solving large-scale problems. It is applied to the boundary element method (BEM) for three-dimensional potential flow problems. The algorithm based on mixed multipole expansion and numerical integration isimplemented in combination with an iterative solver. Numerical examinations, on Dirichlet and Neumann problems,are carried out to demonstrate the capability and accuracy of the present method. It has been shown that the methodhas evident advantages in saving memory and computing time when used to solve huge-scale problems which may beprohibitive for the traditional BEM implementation.

Numerical simulation of standing wave with 3D predictor-corrector finite difference method for potential flow equations

A three-dimensional （3D） predictor-corrector finite difference method for standing wave is developed. It is applied to solve the 3D nonlinear potential flow equa- tions with a free surface. The 3D irregular tank is mapped onto a fixed cubic tank through the proper coordinate transform schemes. The cubic tank is distributed by the staggered meshgrid, and the staggered meshgrid is used to denote the variables of the flow field. The predictor-corrector finite difference method is given to develop the difference equa- tions of the dynamic boundary equation and kinematic boundary equation. Experimental results show that, using the finite difference method of the predictor-corrector scheme, the numerical solutions agree well with the published results. The wave profiles of the standing wave with different amplitudes and wave lengths are studied. The numerical solutions are also analyzed and presented graphically.

Dissipative free-surface solver for potential flow around hydrofoil distributed with doublets

A doublet integral equation is formulated for the two-dimensional dissipative potential flow around a hydrofoil submerged below a free-water surface. The free-water surface is assumed to involve energy dissipation, and thus it is the source of damping. A doublet panel method is developed from incorporation of the dissipative Green function approach and the doublet distributions on the hydrofoil surface. Numerical computations are implemented, and the derived numerical results are in good agreement with analytic solutions and experimental measurements.

RELATIVE ENTROPY AND COMPRESSIBLE POTENTIAL FLOW

Compressible （full） potential flow is expressed as an equivalent first-order system of conservation laws for density ρ and velocity v. Energy E is shown to be the only nontrivial entropy for that system in multiple space dimensions, and it is strictly convex in ρ, v if and only if ｜v｜ 〈 c. For motivation some simple variations on the relative entropy theme of Dafer- mos/DiPerna are given, for example that smooth regions of weak entropy solutions shrink at finite speed, and that smooth solutions force solutions of singular entropy-compatible per- turbations to converge to them. We conjecture that entropy weak solutions of compressible potential flow are unique, in contrast to the known counterexamples for the Euler equations.

GENERAL EXACT SOLUTION OF INCOMPRESSIBLE POTENTIAL FLOWS AROUND TWO CIRCLES

Three exact solutions are obtained for 2-D incompressible potential flows around two moving circles in three cases: (i) expansion (or contraction) of themselves, (ii) approaching (or departing from) each other, (iii) moving perpendicularly to the line connecting the centres in opposite directions. Meanwhile, an- other set of two exact solutions is obtained for 2-D incompressible potential flows between two moving eccen- tric circles in two cases: moving parallelly or perpendicularly to the line connecting the centres.

A General Boundary Solution Method for Potential Flow around a 2D Semi-infinite Body

By using Cauchy's integral formula of analytical complex function and the third order complex spline function, a general boundary solution method for solving the complex potential field of the flow field around a 2D semi infinite body is presented in this paper. The pressure coefficients obtained by the present method agree well with those given by Acrivous, showing the validity of our method.

Study on Mooring Design and Calculation Method of Ocean Farm Based on Time-Domain Potential Flow Theory

In order to calculate the mooring force of a new semi-submerged Ocean Farm quickly and accurately,based on the unsteady time-domain potential flow theory and combined the catenary model,the control equation of mooring cable is established,and the mooring force of the platform under the wave spectrum is calculated.First of all,based on the actual situation of the ocean environment and platform,the mooring design of the platform is carried out,and the failure analysis and sensitivity analysis of the single anchor chain by the time domain coupling method are adopted:including different water depth,cycle,pretension size,anchor chain layout direction and wind speed,etc.The analysis results confirm the reliability of anchoring method.Based on this,the mooring point location of the platform is determined,the force of each anchor chain in the anchoring process is calculated,and the mooring force and the number of mooring cables are obtained for each cable that satisfies the specification,the results of this paper can provide theoretical calculation methods for mooring setting and mooring force calculation of similar offshore platforms.

Numerical solution of potential flow equations with a predictor-corrector finite difference method

We develop a numerical solution algorithm of the nonlinear potential flow equations with the nonlinear free surface boundary condition.A finite difference method with a predictor-corrector method is applied to solve the nonlinear potential flow equations in a two-dimensional (2D) tank.The irregular tank is mapped onto a fixed square domain with rectangular cells through a proper mapping function.A staggered mesh system is adopted in a 2D tank to capture the wave elevation of the transient fluid.The finite difference method with a predictor-corrector scheme is applied to discretize the nonlinear dynamic boundary condition and nonlinear kinematic boundary condition.We present the numerical results of wave elevations from small to large amplitude waves with free oscillation motion,and the numerical solutions of wave elevation with horizontal excited motion.The beating period and the nonlinear phenomenon are very clear.The numerical solutions agree well with the analytical solutions and previously published results.

Real-time solution of nonlinear potential flow equations for lifting rotors

Analysis of rotorcraft dynamics requires solution of the rotor induced flow field.Often,the appropriate model to be used for induced flow is nonlinear potential flow theory（which is the basis of vortex-lattice methods）.These nonlinear potential flow equations sometimes must be solved in real time––such as for real-time flight simulation,when observers are needed for controllers,or in preliminary design computations.In this paper,the major effects of nonlinearities on induced flow are studied for lifting rotors in low-speed flight and hover.The approach is to use a nonlinear statespace model of the induced flow based on a Galerkin treatment of the potential flow equations.

A BOUNDARY INTEGRAL EQUATION AND ITS NUMERICAL SOLUTION OF POTENTIAL FLOW AROUND SURFACE-IRREGULA-RITIES

In this paper,using complex functional theory,the authors turn the potential flow around the surface irregularities in a pressure conduit and semi-infinite platforms into Dirichlet problem.Based on Schwarz formula and by the application of Plemelj's formula,the authors change the problem into the integration of a Cauchy boundary integral equation in the flow plane through the substitution of variables.Using numerical integration,the authors obtain the velocity distribution and pressure coefficient along surface irregularities and platforms.The physical concept of this method is clear,the convergent speed is rapid and the computative effi- ciency is high.The calculated values agree well with the measured results.It is an effective and simple method in solving potential flow.

Reduced Basis Approximation and Error Bounds for Potential Flows in Parametrized Geometries

In this paper we consider(hierarchical,Lagrange)reduced basis approximation and a posteriori error estimation for potential flows in affinely parametrized geometries.We review the essential ingredients:i)a Galerkin projection onto a lowdimensional space associated with a smooth“parametric manifold”in order to get a dimension reduction;ii)an efficient and effective greedy sampling method for identification of optimal and numerically stable approximations to have a rapid convergence;iii)an a posteriori error estimation procedure:rigorous and sharp bounds for the linearfunctional outputs of interest and over the potential solution or related quantities of interest like velocity and/or pressure;iv)an Offline-Online computational decomposition strategies to achieve a minimum marginal computational cost for high performance in the real-time and many-query(e.g.,design and optimization)contexts.We present three illustrative results for inviscid potential flows in parametrized geometries representing a Venturi channel,a circular bend and an added mass problem.

THE VERIFICATION OF THE CURRENT TRANSIENT EQUATION AT TUBULAR ELECTRODES IN A FLOWING FLUID UNDER POTENTIAL STEP

The equation derived for the response of the current transients in the flowing fluid is verified experimentally.

Momentum-Dependent Symmetry Potential from Nuclear Collective Flows in Heavy Ion Collisions at Intermediate Energies

Within the isospin-dependent quantum molecular dynamics model, we investigate the nuclear collective flows produced in semi-central 197 Au＋197 Au collisions at intermediate energies. The neutron proton differential flows and difference of neutron proton collective flows are sensitive to the momentum-dependent symmetry potential. This sensitivity is less affected by both the isoscalar part of nuclear equation of state and in-medium nucleon- nucleon cross sections. Moreover, this sensitivity becomes pronounced with increasing the rapidity cut.

Comparisons of Wave Force Model Effects on the Structural Responses and Fatigue Loads of a Semi-Submersible Floating Wind Turbine

The selection of wave force models will significantly impact the structural responses of floating wind turbines.In this study,comparisons of wave force model effects on the structural responses and fatigue loads of a semi-submersible floating wind turbine(SFWT)were conducted.Simulations were performed by employing the Morison equation(ME)with linear or second-order wave kinematics and potential flow theory(PFT)with first-or second-order wave forces.A comparison of regular waves,irregular waves,and coupled wind/waves analyses with the experimental data showed that many of the simulation results and experimental data are relatively consistent.However,notable discrepancies are found in the response amplitude operators for platform heave,tower base bending moment,and tension in mooring lines.PFT models give more satisfactory results of heave but more significant discrepan-cies in tower base bending moment than the ME models.In irregular wave analyses,low-frequency resonances were captured by PFT models with second-order difference-frequency terms,and high-frequency resonances were captured by the ME models or PFT models with second-order sum-frequency terms.These force models capture the response frequencies but do not reasonably predict the response amplitudes.The coupled wind/waves analyses showed more satisfactory results than the wave-only analyses.However,an important detail to note is that this satisfactory result is based on the overprediction of wind-induced responses.

人工神经网络与遗传算法预测液体晃荡参数的比较

This paper develops a numerical code for modelling liquid sloshing.The coupled boundary element-finite element method was used to solve the Laplace equation for inviscid fluid and nonlinear free surface boundary conditions.Using Nakayama and Washizu’s results,the code performance was validated.Using the developed numerical mode,we proposed artificial neural network(ANN)and genetic algorithm(GA)methods for evaluating sloshing loads and comparing them.To compare the efficiency of the suggested methods,the maximum free surface displacement and the maximum horizontal force exerted on a rectangular tank’s perimeter are examined.It can be seen from the results that both ANNs and GAs can accurately predict η_(max) and F_(max).

Hodograph method of flow on two-dimensional manifold

For some special flows, especially the potential flow in a plane, using the hodograph method has obvious advantages. Realistic flows have a stream surface, namely, a two-dimensional manifold, on which the velocity vector of the flow lies on its tangent space. By introducing a stream function and a potential function, we establish the hodo- graph method for potential flows on a surface using the tensor analysis. For the derived hodograph equation, we obtain a characteristic equation and its characteristic roots, from which we can classify the type of the second-order hodograph equation. Moreover, we give some examples for special surfaces.

New P3D Hydraulic Fracturing Model Based on the Radial Flow

Pseudo three-dimension (P3D) hydraulic fracturing models often overpredict the fracture height for a poorly contained fracture. To solve this problem, a new method is presented in shaping the P3D fracture geometry on the basis of the fundamental theory and the original 1D fluid flow is replaced with a more representatively radial flow. The distribution of the fluid in the modified fluid field is analyzed and a sound explanation to the problem is given. Due to the consideration of the fluid flow in the vertical direction, the modified model can predict the fracture height much better. To validate the rationality of the radial fluid flow assumption, the distribution of the fluid in the modified fluid field is simulated with the plane potential flow by using finite element method. And the results agree effectively with those from the assumption. Through comparing with the full 3D model, the results show that this new P3D model can be used to aid the fracturing design and predict the fracture height under poorly contained situation.

Low-Speed Aerodynamic Characteristics of Supercritical Airfoil with Small High-Lift Devices from Flow Pattern Measurements

In this paper, the lift coefficients of SC-0414 airfoil are estimated by applying modified Yamana’s method to the flow visualization results, which are obtained by utilizing the smoke tunnel. The application of the modified Yamana’s method is evaluated with two calculation methods. Additionally, the lift estimation, wake measurements, and numerical simulations are performed to clarify the low-speed aerodynamic characteristics of the SC airfoil with flaps. The angle of attack was varied from −5° to 8°. The flow velocity was 12 m/s and the Reynolds number was 1.6 × 105. As a result, the estimated lift coefficients show a good agreement with the results from reference data and numerical simulations. In clean condition, the lift coefficients calculated from the two methods show quantitative agreement, and no significant difference could be confirmed. However, the slope of the lifts calculated from ys is higher and closer to the reference data than those obtained from sc, where ys denotes the height where the distance from the streamline to the reference line is the largest, and sc denotes the displacement of the center of pressure from the origin of the coordinate, respectively. In the case of flaps, the GFs have an observable effect on the aerodynamic performance of the SC-0414 airfoil. When the height of the flap was increased, the lift and drag coefficients increased. The installation of a GF with a height equal to 1% of the chord length of the airfoil significantly improved the low-speed aerodynamic performance of SC airfoils.

半潜船波浪诱导运动与载荷预报数值方法比较研究

Numerical simulation tools based on potential-flow theory and/or Morison’s equation are widely used for predicting the hydrodynamic responses of floating offshore wind platforms.In general,these simplified approaches are used for the analysis under operational conditions,albeit with a carefully selected approach to account for viscous effects.Nevertheless,due to the limit hydrodynamic modelling to linear and weakly nonlinear models,these approaches severely underpredict the low-frequency nonlinear wave loads and dynamic responses of a semisubmersible.They may not capture important nonlinearities in severe sea states.For the prediction of wave-induced motions and loads on a semisubmersible,this work systematically compares a fully nonlinear viscous-flow solver and a hybrid model combining the potential-flow theory with Morison-drag loads in steep waves.Results show that when nonlinear phenomena are not dominant,the results obtained by the hybrid model and the high-fidelity method show reasonable agreement,while larger discrepancies occur for highly nonlinear regular waves.Specifically,regular waves with various steepness over different frequencies are focused in the present study,which supplements the understanding in applicability of these two groups of method.