Development of Cartesian grid method for simulation of violent ship-wave interactions

We present a Cartesian grid method for numerical simulation of strongly nonlinear phenomena of ship-wave interactions. The Constraint Interpolation Profile(CIP) method is applied to the flow solver, which can efficiently increase the discretization accuracy on the moving boundaries for the Cartesian grid method. Tangent of Hyperbola for Interface Capturing(THINC) is implemented as an interface capturing scheme for free surface calculation. An improved immersed boundary method is developed to treat moving bodies with complex-shaped geometries. In this paper, the main features and some recent improvements of the Cartesian grid method are described and several numerical simulation results are presented to discuss its performance.     

Large eddy simulation of free-surface flows

This paper introduces and discusses numerical methods for free-surface flow simulations and applies a large eddy simulation(LES) based free-surface-resolved CFD method to a couple of flows of hydraulic engineering interest. The advantages, disadvantages and limitations of the various methods are discussed. The review prioritises interface capturing methods over interface tracking methods, as these have shown themselves to be more generally applicable to viscous flows of practical engineering interest, particularly when complex and rapidly changing surface topologies are encountered. Then, a LES solver that employs the level set method to capture free-surface deformation in 3-D flows is presented, as are results from two example calculations that concern complex low submergence turbulent flows over idealised roughness elements and bluff bodies. The results show that the method is capable of predicting very complex flows that are characterised by strong interactions between the bulk flow and the free-surface, and permits the identification of turbulent events and structures that would be very difficult to measure experimentally.     

NUMERICAL SIMULATION OF TURBULENT FREE SURFACE FLOW OVER OBSTRUCTION

A two-dimensional hybrid numerical model, FEM-LES-VOF, for free surface flows is proposed in this study, which is a combination of three-step Taylor-Galerkin finite element method, large eddy simulation with the Smagorinsky sub-grid model and Computational Lagrangian-Eulerian Advection Remap Volume of Fluid （CLEAR-VOF） method. The present FEM-LES-VOF model allows the fluid flows involving violent free surface and turbulence subject to complex boundary configuration to be simulated in a straightforward manner with unstructured grids in the context of finite element method. Numerical simulation of a benchmark problem of dam breaking is conducted to verify the present model. Comparisons with experimental data show that the proposed model works well and is capable of producing reliable predictions for free surface flows. Using the FEM-LES-VOF model, the free surface flow over a semi-circular obstruction is investigated. The simulation results are compared with available experimental and numerical results. Good performance of the FEM-LES-VOF model is demonstrated again. Moreover, the numerical studies show that the turbulence plays an important role in the evolution of free surface when the reflected wave propagates upstream during the fluid flow passing the submerged obstacle.     

Comparative study of MPS method and level-set method for sloshing flows

This paper presents a comparative study of a meshless level-set method in the simulation of sloshing flows. The numerical moving particle semi-implicit （MPS） method and a grid based schemes of the MPS and level-set methods are outlined and two violent sloshing cases are considered. The computed results are compared with the corresponding experimental data for validation. The impact pressure and the deformations of free surface induced by sloshing are comparatively analyzed, and are in good agreement with experimental ones. Results show that both the MPS and level-set methods are good tools for simulation of violent sloshing flows. However, the second pressure peaks as well as breaking and splashing of free surface by the MPS method are captured better than by the level-set method.     

双圆柱的入水参数对水作用力的影响

为了分析多圆柱入水的各个状态参数对圆柱所受水作用力的影响,本文采用了CFD方法对双圆柱同步常速入水这一物理过程进行了动态数值模拟。采用变密度的不可压缩Euler方程作为控制方程,通过求解密度域的接触间断来追踪自由液面。基于直角切割网格系统,采用Roe型的Upwind格式的有限体积法作数值离散。采用双时间推进法和人工压缩法来进行时域步进。相对单圆柱入水的受力而言,本文对双圆柱相互作用所引起的附加水作用力,采用数值拟合的方法,提出了简单的代数表达式。然后分别以双圆柱的半径、间距和入水速度作为状态参数,定量地分析了这些参数对附加水作用力的影响,综合构造出可用于任意双圆柱同步入水模型的附加水作用力的估算表达式。本文的思想方法也可用在多柱状体的工程结构的入水分析中。     

NUMERICAL SIMULATIONS OF HIGHLY NONLINEAR STEADY AND UNSTEADY FREE SURFACE FLOWS

A numerical simulation model based on an open source Computational Fluid Dynamics (CFD) package-Open Field Operation and Manipulation (OpenFOAM) has been developed to study highly nonlinear steady and unsteady free surface flows. A two-fluid formulation is used in this model and the free surface is captured using the classical Volume Of Fluid (VOF) method. The incompressible Euler/Navier-Stokes equations are solved using a finite volume method on unstructured polyhedral cells. Both steady and unsteady free surface flows are simulated, which include: (1) a submerged NACA0012 2-D hydrofoil moving at a constant speed, (2) the Wigley hull moving at a constant speed, (3) numerical wave tank, (4) green water overtopping a fixed 2-D deck, (5) green water impact on a fixed 3-D body without or with a vertical wall on the deck. The numerical results obtained have been compared with the experimental measurements and other CFD results, and the agreements are satisfactory. The present numerical model can thus be used to simulate highly nonlinear steady and unsteady free surface flows.     

SPH方法在自由面问题中的应用

作为无网格粒子法,SPH法在处理大变形、自由面流动问题时具有显著的优势.介绍了SPH法的基本数值方法,并基于SPH法数值模拟了2个二维溃坝问题,将计算结果与试验数据进行了比较,结果表明:SPH法在处理自由面时具有很强的适应性.尽管水面发生了翻卷、破碎等剧烈的变化,但SPH法仍然能够较好地捕捉到这些流动现象,同时数值模拟得到的水头位置和自由面形状均能与试验结果相吻合,表明SPH法在处理自由面问题时具有较高的准确性及可靠性.     

NUMERICAL SIMULATION OF SLOSHING IN RECTANGULAR TANK WITH VOF BASED ON UNSTRUCTURED GRIDS

A new method for sloshing simulation in a sway tank is present, in which the two phase interface is treated as a physical discontinuity, which can be captured by a well-designed high order scheme. Based on Normalized Variable Diagram (NVD), a high order discretization scheme with unstructured grids is realized, together with a numerical method for free surface flow with a fixed grid. This method is implemented in an in-house code General Transport Equation Analyzer (GTEA) which is an unstructured grids finite volume solver. The present method is first validated by available analytical solutions. A simulation for a 2-D rectangular tank at different excitation frequencies of the sway is carried out. A comparison with experimental data in literature and results obtained by commercial software CFX shows that the sloshing load on the monitor points agrees well with the experimental data, with the same grids, and the present method gives better results on the secondary peak. It is shown that the present method can simulate the free surface overturning and breakup phenomena.     

Pressure-balanced Saint–Venant equations for improved asymptotic modelling of pipe flow

In urban drainage networks, steady free surface flows in circular-shaped pipes are commonly observed given low inflow discharges. Therefore, accurate computation of such steady states is of great practical significance, especially considering bent pipes. This requires numerical schemes to be capable of achieving a delicate balance between slope source terms and fluxes in the discrete framework. To this end, in the current study, a new method using pressure balanced Saint–Venant equations and positivity preserving Godunov-type finite volume scheme, is developed for 1D flow simulation in bent circular pipes. Using pressure balancing, a set of pre-balanced Saint–Venant equations is derived. The numerical discretization method uses an approximate Riemann solver and is capable of dealing with wetting–drying process stably in frictional pipes. As verified by several test cases, the proposed method shows better performances than existing methods in modelling the asymptotic flow behavior and preserving steady states in bent circular pipes.     

3-D numerical simulations of violent sloshing by CIP-based method

The violent sloshing flow inside a rectangular tank is computed by the CIP (Constrained Interpolation Profile) ^[1] based Cartesian grid method. Two kinds of CIP scheme, the original CIP scheme and the RCIP scheme, have been applied to the flow solver. 2-D and 3-D computations using the two CIP schemes are carried out and their performances are discussed by comparing the results of the impact pressures on the wall and the free surface profiles to the experimental measurements.

     

基于CIP方法的入水过程模拟

入水问题涉及到军事、航空等领域,如子弹入水、船舶砰击等,具有很强的应用背景。物体入水的过程涉及到固、液、气三相流动和相互作用,并伴随水花飞溅、空泡形成等复杂的物理现象。该文基于紧致插值CIP(constrained interpolation profile)数学模型,分步求解Navier-Stokes(N-S)方程,并通过多相流理论描述固-液-气之间的相互作用,采用Volume of Fluid(VOF)类型的高精度紧致tangent of hyperbola for interface capturing(THINC)方法重构自由面。模拟了刚性圆柱和方柱的入水过程,结果与实验数据吻合较好。     

Unstructured finite volume method for water impact on a rigid body

A new method is presented for the water impact simulation, in which the air-water two phase flow is solved using the pressure-based computational fluid dynamics method. Theoretically, the air effects can be taken into account in the water structure interaction. The key point of this method is the air-water interface capture, which is treated as a physical discontinuity and can be captured by a well-designed high order scheme. According to a normalized variable diagram, a high order discrete scheme on unstructured grids is realised, so a numerical method for the free surface flow on a fixed grid can be established. This method is implemented using an in-house code, the General Transport Equation Analyzer, which is an unstructured grid finite volume solver. The method is verified with the wedge water and structure interaction problem.     

CALCULATION OF NONLINEAR FREE－SURFACE FLOWS RESULTING FROM LARGE￣AMPLITUDE FORCED OSCILLATION OF A TWO－DIMENSIONAL BODY

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The effect of free surface on cloud cavitating flow around a blunt body

In this study, the effect of the free surface on the cloud cavitating flow around a blunt body is investigated based on the water tank experiment and the CFD method. Numerical results are in good agreement with experimental data, and the mesh independence of the methods is verified. The cavity evolution process includes the cavity growth, the re-entrant jet, the cavity shedding, and the collapse, which can all be observed from the water tank experiment. The effects of the free surface on the cavity length, the thickness, and the cavity evolution period are analyzed by comparing the difference between the cavitating flows on the upper and lower sides of the body. This study also examines the effect of the distance between the free surface and the model through a series of water tank experiments and numerical simulations. The cavity stability and asymmetry, as well as the thickness and the velocity of the re-entrant jet inside the cavity, which varies with the submerged depth, are discussed with consideration of the effect of the free surface. The effect of the free surface on the cavitating flow around the blunt body is enhanced with the decrease of the submerged depth.     

A hybrid DEM/CFD approach for solid-liquid flows简

A hybrid scheme coupling the discrete element method(DEM)with the computational fluid dynamics(CFD)is developed to model solid-liquid flows.Instead of solving the pressure Poisson equation,we use the compressible volume-averaged continuity and momentum equations with an isothermal stiff equation of state for the liquid phase in our CFD scheme.The motion of the solid phase is obtained by using the DEM,in which the particle-particle and particle-wall interactions are modelled by using the theoretical contact mechanics.The two phases are coupled through the Newton’s third law of motion.To verify the proposed method,the sedimentation of a single spherical particle is simulated in water,and the results are compared with experimental results reported in the literature.In addition,the drafting,kissing,and tumbling(DKT)phenomenon between two particles in a liquid is modelled and reasonable results are obtained.Finally,the numerical simulation of the density-driven segregation of a binary particulate suspension involving 10 000 particles in a closed container is conducted to show that the presented method is potentially powerful to simulate real particulate flows with large number of moving particles.     

基于IDDES方法的模型尺度和实尺度VLCC阻力预报与流场分析

随着CFD技术的发展和计算机运算能力的提高,CFD在船舶设计中发挥着越来越重要的作用。目前CFD对于船舶阻力的计算基本集中在模型尺度,一方面因为实尺度缺乏相关的实验数据,导致缺乏对实尺度高雷诺数下近壁面湍流模型和壁面函数的探索;另一方面也是因为在实尺度计算中,非定常特征更加明显,数值计算的复杂性会大大增加,传统的RANS方法处理起来较为困难。该文应用基于OpenFOAM开发的船舶与海洋工程水动力求解器naoe-FOAMSJTU,应用改进的DES模型—IDDES,采用CFD方法同时对模型尺度和实尺度的32万吨VLCC进行阻力预报,并分别与RANS的计算结果、实验结果/三因次换算结果进行比较分析。在实尺度计算中考虑到表面粗糙度的影响,采用带粗糙度补贴的壁面函数进行近壁面处理。该文探讨了采用IDDES方法在船模和实船阻力预报中的可行性,同时也对实尺度和模型尺度下的流场进行了讨论与对比分析。     

Numerical prediction of hydrodynamic forces on a ship passing through a lock with different configurations简

A CFD method is used to numerically predict the hydrodynamic forces and moments acting on a ship passing through a lock with a constant speed. By solving the RANS equations in combination with the RNG k-e turbulence model, the unsteady viscous flow around the ship is simulated and the hydrodynamic forces and moments acting on the ship are calculated. UDF is com-piled to define the ship motion. Meanwhile, grid regeneration is dealt with by using the dynamic mesh method and sliding interface technique. Under the assumption of low ship speed, the effects of free surface elevation are neglected in the numerical simulation. A bulk carrier ship model is taken as an example for the numerical study. The numerical results are presented and compared with the available experimental results. By analyzing the numerical results obtained for locks with different configurations, the influences of approach wall configuration, lock configuration symmetry and lock chamber breadth on the hydrodynamic forces and moments are demonstrated. The numerical method applied in this paper can qualitatively predict the ship-lock hydrodynamic interaction and pro-vide certain guidance on lock design.     

RESEARCH OF INNER FLOW IN A DOUBLE BLADES PUMP BASED ON OPENFOAM

The inner flow analysis of centrifugal pumps has gradually become an important issue for the hydraulic design and performance improvement.Nowadays,CFD simulation toolbox of pump inner flow mainly contains commercial tools and open source tools.There are some defects for commercial CFD software for the numerical simulation of 3-D turbulent internal flow in pump,especially in capturing the flow characteristics under the off-design operating conditions.Additionally,it is difficult for researchers to do further investigation because of the undeclared source.Therefore,an open source software like Open Field Operation and Manipulation (OpenFOAM) is increasingly popular with researchers from all over the world.In this paper,a new computational study was implemented based on the original solver and was used to directly simulate the steady-state inner flow in a double blades pump,with the specific speed is 111.In order to disclose the characteristics deeply,three research schemes were conducted.The ratios () of the flow rate are 0.8,1.0 and 1.2,respectively.The simulation results were verified with the Particle Imaging Velocimetry (PIV) experimental results,and the numerical calculation results agree well with the experimental data.Meanwhile,the phenomena of flow separation under the off-design operating conditions are well captured by OpenFOAM.The results indicate that OpenFOAM possesses obvious strong predominance in computing the internal flow field of pump.The analysis results can also be used as the basis for the further research and the improvement of centrifugal pump.     

用密度函数法对自由表面进行数值模拟

本文从二维非定常N-S方程出发，提出了一种处理自由表面问题的数值方法。引入密度函数法(density-function method)追踪自由表面，在密度函数的传输方程中采用TVD格式达到了二阶精度。对均匀来流中的非定常不可压方柱绕流进行了数值模拟。数值结果成功地捕捉了自由表面波动以及漩涡的生成、分离的时间发展历程。同时验证了本方法的有效性。     

Numerical simulation of hydro-elastic problems with smoothed particle hydrodynamics method

Violent free surface flows with strong fluid-solid interactions can produce a tremendous pressure load on structures, resu-lting in elastic and even plastic deformations. Modeling hydro-elastic problem...