Very Large Eddy Simulation of Cavitation from Inception to Sheet/Cloud Regimes by A Multiscale Model

The cavitating flow in different regimes has the intricate flow structure with multiple time and space scales. The present work develops a multiscale model by coupling the volume of fluid(VOF) method and a discrete bubble model(DBM), to simulate the cavitating flow in a convergent-divergent test section. The Schnerr-Sauer cavitation model is used to calculate the mass transfer rate to obtain the macroscale phase structure, and the simplified Rayleigh-Plesset equation is applied to simulate the growing and collapsing of discrete bubbles. An algorithm for bridging between the macroscale cavities and microscale bubbles is also developed to achieve the multiscale simulation. For the flow field, the very large eddy simulation(VLES) approach is applied. Conditions from inception to sheet/cloud cavitation regimes are taken into account and simulations are conducted. Compared with the experimental observations, it is shown that the cavitation inception, bubble clouds formation and glass cavity generation are all well represented, indicating that the proposed VOF-DBM model is a promising approach to accurately and comprehensively reveal the multiscale phase field induced by cavitation.     

Numerical analysis of a propeller during heave motion in cavitating flow

In practical maritime conditions, ship hulls experience heave motion due to the action of waves, which can further drive the ship’s propellers to oscillate relative to the surrounding water. In order to investigate the motion of a propeller working behind a surface vessel sailing in waves, a numerical simulation is conducted on a propeller impacted by heave motion in cavitating flow using the Reynolds-averaged Navier-Stokes (RANS) method. The coupling of the propeller’s rotation and translation is fulfilled using equations of motion defined for this purpose. The heave motion is simplified as a periodic motion based on a sinusoidal function. The numerical transmission of information from the unsteady flow field is achieved using the overset grid approach. In this manner, the unsteady thrust coefficient and torque coefficient of propellers in different periods of heave motion are analyzed. A comparative study is implemented on the unsteady cavitation performance and wake characteristics of propeller. With the propeller’s heave motion, the flow field non-uniformity constantly changes the load on the propeller during each revolution period and each heaving period, the propeller load and the wake field are closely related to the variation of heave motion period. The results obtained from the numerical simulation are expected to serve as a useful theoretical reference for the numerical analysis of a propeller in a heave motion.     

A two dimensional hydrodynamic and sediment transport model for dam break based on finite volume method with quadtree grid

This study aims to develop a robust, accurate and computationally efficient hydrodynamic and sediment transport model for dam break flows. The two dimensional shallow water equations are resolved based on the finite volume method with an unstructured quadtree mesh. The sediment transport and bed evolution modules are coupled with hydrodynamic module to predict simultaneously the hydrodynamics, sediment concentrations and morphological changes. The interface flux is computed by the HLL approximate Riemann solver with second order accuracy. The effects of pressure and gravity are included in source term in this model, which can simplify the computation and eliminate numerical imbalance between source and flux terms. For dam break flows occurring in complicated geometries, the quadtree rectangular mesh is used to refine the interesting area and important part. The model is first verified against results from laboratory experiments, existing numerical models and real life case. It is then used to simulate dam break flows over a mobile bed to investigate the bed evolution. The results are compared with experimental data and field data with good agreement. The method is simple, efficient, and conservative. It shows promise for handling hydrodynamic simulation and sediment transport for a wide range of dam break flows.     

A new efficient finite volume modeling of small amplitude free surface flows with unstructured grid

A staggered finite-volume technique for non-hydrostatic, small amplitude free surface flow governed by the incompressible Navier-Stokes equations is presented there is a proper balance between accuracy and computing time. The advection and horizontal diffusion terms in the momentum equation are discretized by an integral interpolation method on the orthogonal unstructured staggered mesh and, while it has the attractive property of being conservative. The pressure-correction algorithm is employed for the non-hydrostatic pressure in order to achieve second-order temporal accuracy. A conservative scalar transport algorithm is also applied to discretize k-ε equations in this model. The eddy viscosity is calculated from the k-ε turbulent model. The resulting model is mass and momentum conservative. The model is verified by two examples to simulate unsteady small amplitude free surface flows where non-hydrostatic pressures have a considerable effect on the velocity field,and then applied to simulate the tidal flow in the Bohai Sea.     

基于高阶边界元的三维数值波浪港池--波浪破碎的模拟

在势流理论的框架内,采用高阶边界元方法和混合欧拉-拉格朗日法,实现了对三维波浪破碎过程的数值模拟.数值模型使用可调节时间步长的基于二阶显式泰勒展开的混合欧拉-拉格郎日时间步进来求解自由表面的演化过程.在所使用的边界元方法中,采用16节点三次滑移四边形单元来表示,这种单元在单元内具有高阶的精度同时在单元之间具有良好的连续性.给出了孤立波的传播和周期性非线性波浪沿缓坡传播的计算结果,表明数值模型具有良好的稳定性.     

A study on propeller noise source localization in a cavitation tunnel

Localizing noise sources in cavitation experiments is an important research subject along with predicting noise levels. A cavitation tunnel propeller noise localization method is presented. Propeller noise measurement experiments were performed in the MOERI cavitation tunnel. To create cavitating conditions, a wake-generating dummy body was devised. In addition, 10 hydrophones were put inside a wing-shaped casing to minimize the unexpected flow inducing noise around the hydrophones. After measuring both of the noises of the rotating propeller behind the dummy body and acoustic signals transmitted by a virtual source, the data were processed via three objective functions based on the ideas of matched field processing and source strength estimation to localize noises on the propeller plane. In this paper, the measured noise analysis and the localization results are presented. Through the experiments and the analysis, it was found that the source localization methods that have been used in shallow water applications could be successfully adapted to the cavitation tunnel experiments.     

基于大涡模拟的波状前缘水翼空化抑制研究

为了降低空化造成的水动力性能损失,基于仿生学原理,参考座头鲸鳍肢剖面形状,将前缘波浪构型引入到水翼设计中,研究波状前缘水翼的非定常空化特性,并探究前缘参数改变对空化控制的效果和规律。选用NACA63₄-021水翼为基准模型,进行前缘参数化重构,设计出3种不同的波状水翼进行对比研究。采用大涡模拟（LES）方法对空化流场进行精细化数值模拟,针对基准水翼和不同波幅与波长参数下的波状水翼开展了空化周期、升阻力系数、压力脉动以及流向涡结构的对比分析。结果发现,波状水翼在抑制空化和降低压力脉动方面都取得了显著效果。其中,3种不同的波状水翼空化抑制率分别为15.7%、18.6%和27.9%,压力脉动幅值分别降低了55.3%、67.3%和74.6%。分析表明,波浪前缘的引入使得空化的分区效应更加凸显,空化从波谷处初生,增大波幅或减小波长都可以加强对空化的抑制效果,并可以提高升力系数以及显著降低水翼表面的压力脉动。前缘波浪构型还将诱发向下游发展的对转涡结构,不同前缘参数的波状水翼涡结构的演化是相似的,空泡发展与溃灭的整个过程对涡结构的发展也具有显著影响。     

Test method of cavitation erosion for marine coatings with low hardness

Rudders of large container ships are easily affected by cavitation, which is well known to be induced by significant axial flows behind a propeller and discontinuities in the rudder. Among several methods to prevent or reduce the cavitation erosion occurred in the rudder, painting is gaining a lot of attention because it can be employed easily and cheaply. To conduct erosion tests properly, the simulation of heavily erosive cavitation is necessary. This can be generated using an inclined propeller dynamometer in the medium-size cavitation tunnel of MOERI (Maritime & Ocean Engineering Research Institute). The inclined shaft of the propeller creates strong cavitation, which occurs around the root of the propeller blade. This cavitation creates impacts through the collapsing process that are very severe, and are useful for realistic and efficient cavitation erosion tests. In the present study, the newly developed cavitation erosion test method is successfully employed to evaluate marine coatings that is mainly composed of epoxy elastomer or silicone polymer material. Silicone polymer-type paint B was found to have three times larger endurance than epoxy elastomer-type paint A.     

Numerical simulation of viscous cavitating flow around a ship propeller

In the present study, cavitation and a ship propeller wake are reported by computed fluid dynamics based on viscous multiphase flow theory. Some recent validation results with a hybrid grid based on unsteady Navier-Stokes (N-S) and bubble dynamics equations are presented to predict velocity, pressure and vapor volume fraction in propeller wake in a uniform inflow. Numerical predictions of sheet cavitation, tip vortex cavitation and hub vortex cavitation are in agreement with the experimental data, same as numerical predictions of longitudinal and transversal evolution of the axial velocity. Blade and shaft rate frequency of propeller is well predicted by the computed results of pressure, and tip vortex is the most important to generate the pressure field within the near wake. The overall results indicate that the present approach is reliable for prediction of cavitation and propeller wake on the condition of uniform inflow.     

Computational and Empirical Investigation of Propeller Tip Vortex Cavitation Noise

In this study, non-cavitating and cavitating flow around the benchmark DTMB 4119 model propeller are solved using both viscous and potential based solvers. Cavitating and non-cavitating propeller radiated noises are then predicted by using a hybrid method in which RANS(Reynolds-averaged Navier-Stokes) and FWH(Ffowcs Williams Hawkings) equations are solved together in open water conditions. Sheet cavitation on the propeller blades is modelled by using a VOF(Volume of Fiuld) method equipped with Schnerr-Sauer cavitation model.Nevertheless, tip vortex cavitation noise is estimated by using two different semi-empirical techniques, namely Tip Vortex Index(TVI, based on potential flow theory) and Tip Vortex Contribution(TVC). As the reference distance between noise source and receiver is not defined in open water case for TVI technique, one of the outputs of this study is to propose a reference distance for TVI technique by coupling two semi-empirical techniques and ITTC distance normalization. At the defined distance, the starting point of the tip vortex cavitation is determined for different advance ratios and cavitation numbers using potential flow solver. Also, it is examined that whether the hybrid method and potential flow solver give the same noise results at the inception point of tip vortex cavitation.Results show that TVI method based on potential flow theory is reliable and can practically be used to replace the hybrid method(RANS with FWH approach) when tip vortex cavitation starts.     

Ships with ventilated cavitation in seaways and active flow control

Bottom ventilated cavitation has been proven as a very effective drag reduction technology for river ships and planning boats. The ability of this technology to withstand the sea wave impact usual for seagoing ships depends on the ship bottom shape and could be enhanced by some active flow control devices. Therefore, there is the need in numerical tools to estimate the effects of bottom changes and to design such devices. The fundamentals of active flow control for the ship bottom ventilated cavitation are considered here on the basis of a special model of cavitating flows. This model takes into account the air compressibility in the cavity, as well as the multi-frequency nature of the incoming flow in wavy seas and of the cavity response on perturbations by incoming flow. The numerical method corresponding to this model was developed and widely manifested with an example of a ship model tested in a towing tank at Froude numbers between 0.4 and 0.7.The impact of waves in head seas and following seas on cavities has been studied in the range of wavelengths from 0.45 to 1.2 of the model (or ship) length. An oscillating cavitator-spoiler was considered as the flow controlling devices in this study. The oscillation magnitude and the phase shift between cavitator oscillation and the incoming waves have been varied to determine the best flow control parameters. The main results of the provided computational analysis include oscillations of cavity surface, of the pressure in cavity and of the moment of hydrodynamic load on the cavitator. The major part of computations has been carried out for the flap oscillating at the frequency coinciding with the wave frequency, but the effect of a frequency shift is also analyzed.     

后台阶下游床面冲刷过程数值模拟研究

以床面瞬时剪应力作为泥沙起动及输运的水动力机制,建立了结构物周围复杂流场下床面局部冲刷的数学模型。并应用大涡模拟方法对后台阶下游三维湍流流动进行数值模拟,得到台阶下游床面瞬时剪应力的分布规律。为了确定床面瞬时剪应力与泥沙上扬通量的关系,先应用数学模型对不同模型参数下,冲刷开始后5分钟时台阶下游床面形状进行试算。通过试算与实验结果的比较,确定床面瞬时剪应力与泥沙上扬通量关系中需要的模型参数。进一步对冲刷开始后30分钟内台阶下游床面演化规律进行模拟,模拟结果与实验结果相符合。     

Incompressible SPH flow model for wave interactions with porous media

The paper presents an Incompressible Smoothed Particle Hydrodynamics (ISPH) method to simulate wave interactions with a porous medium. The SPH method is a mesh free particle modeling approach that is capable of tracking the large deformation of free surfaces in an easy and accurate manner. The ISPH method employs a strict incompressible hydrodynamic formulation to solve the fluid pressure and the numerical solution is obtained by using a two-step semi-implicit scheme. The ISPH flow model solves the unsteady 2D Navier–Stokes (NS) equations for the flows outside the porous media and the NS type model equations for the flows inside the porous media. The presence of porous media is considered by including additional friction forces into the equations. The developed ISPH model is first validated by the solitary and regular waves damping over a porous bed and the solitary wave interacting with a submerged porous breakwater. The convergence of the method and the sensitivity of relevant model parameters are discussed. Then the model is applied to the breaking wave interacting with a breakwater covered with a layer of porous materials. The computational results demonstrate that the ISPH flow model could provide a promising simulation tool in coastal hydrodynamic applications.     

基于物理造波和主动消波的黏性数值波浪水槽开发

基于推板造波理论和摇板造波理论,在Open FOAM平台上采用重叠网格技术建立黏性数值波浪水槽,并使用一种结合SIMPLE算法和PISO算法的PIMPLE算法对数值模型进行求解。利用开发的数值模型通过数值收敛性测试和网格独立性测试分别重点研究了时间步长、库朗数和网格尺寸对数值精度和计算效率的影响。并对比研究了此数值模型分别嵌入层流模型和湍流模型的计算精度和计算效率。实现的规则波和二阶有限振幅波与理论结果和试验结果吻合,验证了此黏性数值波浪水槽的造波和主动消波功能。基于二维数值波浪水槽,进一步研究了三维数值造波,数值计算结果与理论结果吻合良好。研究结果不仅验证了重叠网格在二维和三维两相流体域中求解运动物体与流场交互的可靠性和正确性,而且为使用此黏性数值波浪水槽解决更复杂的海洋工程问题提供了依据。     

On the limiting parameters of artificial cavitation

Artificial cavitation, or ventilation, is produced by releasing gas into the liquid flow. One of the objectives of creating this multiphase flow is to reduce frictional and sometimes wave resistance of a marine vehicle completely or partially immersed in the water. Flows around surface ships moving along the water–air boundary are considered in this paper. It is favorable to achieve a negative cavitation number in the developed cavitating flow under the vessel’s bottom in order to generate additional lift. Cavities, formed in the flow, have limiting parameters that are affected by propulsion and lift-enhancing devices. Methods for calculating these influences and the results of a parametric study are reported.     

洞庭湖地区水系水动力耦合数值模型

针对洞庭湖地区复杂水系和复杂水情下的实际水流运动特征,建立了完全基于水力学方法的洞庭湖地区水系的一、二维耦合的全局水动力学模型,实现了不同水体数值模拟的自动有机衔接。模型包括湖泊、河网水系两部分。对长江干流荆江段、湘资沅澧四水、三口分流河道,运用能够反映河道主槽和边滩不同行洪特征的扩展一维水量模型进行模拟;对于洞庭湖湖区部分,采用二维非结构的有限体积法建立水动力模型;应用重叠投影法实现模型的耦合。模型具有动边界的自动处理,河道分区计算,分洪、溃堤过程实时模拟等功能。剖分的网格较为细致地刻画了湖区的地形,使模型能够模拟"高水湖相、低水河相"的湖流特征。运用1996年7月的实际洪水过程,进行了模型的验证,较为准确地模拟了实际水流特征。     

A two-fluid model of turbulent two-phase flow for simulating turbulent stratified flows

In this paper, a two-fluid model of turbulent two-phase flow is used to simulate turbulent stratified flows. This is a unified multi-fluid model for the motion of each phase in the flow, whose turbulent transport is closed by a two-phase k– model. The exchanges of mass, momentum and energy between the two phases are fully accounted for in the simulation. For illustration, a case of turbulent stratified flow with strong buoyancy effects, for which extensive experimental data are available, is selected for examination. It is shown that the numerical results agree well with the experimental data.     

Simulation of Random Waves and Associated Laminar Bottom Shear Stresses

This work presents a new approach for simulating the random waves in viscous fluids and the associated bottom shear stresses. By generating the incident random waves in a numerical wave flume and solving the unsteady two-dimensional Navier-Stokes equations and the fully nonlinear free surface boundaiy conditions for the fluid flows in the flume, the viscous flows and laminar bottom shear stresses induced by random waves axe determined. The deterministic spectral amplitude method implemented by use of the fast Fourier transform algorithm was adopted to generate the incident random waves. The accuracy of the numerical scheme is confirmed by comparing the predicted wave spectrum with the target spectrum and by comparing the nanlerical transfer function between the shear stress and the surface elevation with the theoretical transfer function. The maximum bottom shear stress caused by random waves, computed by this wave model, is compared with that obtained by Myrhaug＇ s model （1995）. The transfer function method is also employed to determine the maximum shear stress, and is proved accurate.     

A higher-efficient three-dimensional numerical model for small amplitude free surface flows

A higher-efficient three-dimensional non-hydrostatic model is developed to simulate small amplitude free surface flows based on a staggered unstructured grid. In this model, a fractional step algorithm is adopted to solve the Navier-Stokes equations in two major steps. A top-layer pressure method is proposed to minimize the number of vertical layers and subsequently the computational cost. Three classical examples of small amplitude free surface flows are used to demonstrate the capability and efficiency of the model. The satisfactory results demonstrated the capability and efficiency of modelling a range of small amplitude free surface flows with only a small number of vertical layers.     

基于格子Boltzmann方法的斜坡堤越浪数值模拟研究

准确确定越浪量对于斜坡堤设计有重要意义。利用格子Boltzmann方法(LBM),并采用主动吸收式速度入口造波、出流边界消波、VOF方法追踪自由表面以及静态Smagorinsky模型模拟紊流运动,建立二维数值波浪水槽,对光滑斜坡堤上规则波与不规则波越浪进行数值模拟。模拟结果与试验值及其他数值模型结果比较表明,二维LBM数值波浪水槽具有模拟斜坡堤越浪的能力,但对于破碎较为剧烈的越浪过程模拟,该模型还存在一定的不足,未来可从提高自由表面模型精度等方面进一步改善其性能。