Numerical simulation of the flow around two-dimensional partially cavitating hydrofoils

In the present study, a new approach is applied to the cavity prediction for two-dimensional （2D） hydrofoils by the potential based boundary element method （BEM）. The boundary element method is treated with the source and doublet distributions on the panel surface and cavity surface by usethe of the Dirichlet type boundary conditions. An iterative solution approach is used to determine the cavity shape on partially cavitating hydrofoils. In the case of a specified cavitation number and cavity length, the iterative solution method proceeds by addition or subtraction of a displacement thickness on the cavity surface of the hydrofoil. The appropriate cavity shape is obtained by the dynamic boundary condition of the cavity surface and the kinematic boundary condition of the whole foil surface including the cavity. For a given cavitation number the cavity length of the 2D hydrofoil is determined according to the minimum error criterion among different cavity lengths, which satisfies the dynamic boundary condition on the cavity surface. The NACA 16006, NACA 16012 and NACA 16015 hydrofoil sections are investigated for two angles of attack. The results are compared with other potential based boundary element codes, the PCPAN and a commercial CFD code （FLUENT）. Consequently, it has been shown that the results obtained from the two dimensional approach are consistent with those obtained from the others.     

水下爆炸空化效应作用下全船响应的并行计算(英文)

As well as shock wave and bubble pulse loading, cavitation also has very significant influences on the dynamic response of surface ships and other near-surface marine structures to underwater explosive loadings. In this paper, the acoustic-structure coupling method embedded in ABAQUS is adopted to do numerical analysis of underwater explosion considering cavitation. Both the shape of bulk cavitation region and local cavitation region are obtained, and they are in good agreement with analytical results. The duration of reloading is several times longer than that of a shock wave. In the end, both the single computation and parallel computation of the cavitation effect on the dynamic responses of a full-scale ship are presented, which proved that reloading caused by cavitation is non-ignorable. All these results are helpful in understanding underwater explosion cavitation effects.     

A method based on potential theory for calculating air cavity formation of an air cavity resistance reduction ship

This research is intended to provide academic reference and design guidance for further studies to determine the most effective means to reduce a ship’s resistance through an air-cavity. On the basis of potential theory and on the assumption of an ideal and irrotational fluid, this paper drives a method for calculating air cavity formation using slender ship theory then points out the parameters directly related to the formation of air cavities and their interrelationships. Simulations showed that the formation of an air cavity is affected by cavitation number, velocity, groove geometry and groove size. When the ship’s velocity and groove structure are given, the cavitation number must be within range to form a steady air cavity. The interface between air and water forms a wave shape and could be adjusted by an air injection system.     

A method based on potential theory for calculating air cavity formation of an air cavity resistance reduction ship

This research is intended to provide academic reference and design guidance for further studies to determine the most effective means to reduce a ship’s resistance through an air-cavity. On the basis of potential theory and on the assumption of an ideal and irrotational fluid, this paper drives a method for calculating air cavity formation using slender ship theory then points out the parameters directly related to the formation of air cavities and their interrelationships. Simulations showed that the formation of an air cavity is affected by cavitation number, velocity, groove geometry and groove size. When the ship’s velocity and groove structure are given, the cavitation number must be within range to form a steady air cavity. The interface between air and water forms a wave shape and could be adjusted by an air injection system.     

一种水翼空化的被动控制方法（英文）

This paper introduces a new idea of controlling cavitation around a hydrofoil through a passive cavitation controller called artificial cavitation bubble generator(ACG). Cyclic processes, namely, growth and implosion of bubbles around an immersed body, are the main reasons for the destruction and erosion of the said body. This paper aims to create a condition in which the cavitation bubbles reach a steady-state situation and prevent the occurrence of the cyclic processes. For this purpose, the ACG is placed on the surface of an immersed body, in particular, the suction surface of a 2 D hydrofoil. A simulation was performed with an implicit finite volume scheme based on a SIMPLE algorithm associated with the multiphase and cavitation model. The modified k-ε RNG turbulence model equipped with a modification of the turbulent viscosity was applied to overcome the turbulence closure problem. Numerical simulation of water flow over the hydrofoil equipped with the ACG shows that a low-pressure recirculation area is produced behind the ACG and artificially generates stationary cavitation bubbles. The location, shape, and size of this ACG are the crucial parameters in creating a proper control. Results show that the cavitation bubble is controlled well with a well-designed ACG.     

通气空化中反向射流与双涡流型转换的数值研究（英文）

Contrary to natural cavitation, ventilated cavitation is controllable and is not harmful. It is particularly used to reduce the drag of the hydraulic vehicles. The ventilated cavitation is characterized by various gas regimes. The mechanisms of ventilated cavitation are investigated in the present work with CFD based on a 2D solver. The attention is especially focused on the transition between the reentrant jet and twin vortex regimes. The results confirm that the product of ventilated cavitation number and Froude number is lower than 1(σcFr 1) in the twin vortex regime, while it is higher than 1(σ_cFr 1) in the reentrant jet regime, as reported in the literature. Further analysis shows that ventilated cavitation is significantly influenced by the natural cavitation number.     

空泡闭合区压力特性试验研究(英文)

The most complicated component in cavitating flow and pressure distribution is the flow in the cavity closure line. The cavitating flow and pressure distribution provide critical aspects of flow field details in the region. The integral of pressure results of the hydrodynamic forces, indicate domination in the design of a supercavitating vehicle. An experiment was performed in a water tunnel to investigate the pressure characteristics of the cavity closure region. Ventilation methods were employed to generate artificial cavity, and the ventilation rate was adjusted accordingly to obtain the desired cavity length. An array of pressure transducers was laid down the cavity closure line to capture pressure distribution in this region. The experimental results show that there is a pressure peak in the cavity closure region, and the rise rate of pressure in space tends to be higher in the upwind side when the flow is non-axisymmetric. The transient pressure variations during the cavity formation procedure were also present. The method of measurement in this paper can be referenced by engineers. The result helps to study the flow pattern of cavity closure region, and it can also be used to analyze the formation of supercavitating vehicle hydrodynamics.     

3D numerical modeling of wave forces on tandem fixed cylinders using the BEM

In this paper a 3D numerical model was developed to study the complicated interaction between waves and a set of tandem fixed cylinders.The fluid was considered to be inviscid and irrotational.Therefore,the Helmholtz equation was used as a governing equation.The boundary element method（BEM） was adopted to discretize the relevant equations.Open boundaries were used in far fields of the study domain.Linear waves were generated and propagated towards tandem fixed cylinders to estimate the forces applied on them.Special attention was paid to consideration of the effect on varying non-dimensional cylinder radius and distance between cylinders,ka and kd on forces and trapped modes.The middle cylinder wave forces and trapped modes in a set of nine tandem cylinders were validated utilizing analytical data.The comparisons confirm the accuracy of the model.The results of the inline wave force estimation on n tandem cylinders show that the critical cylinder in the row is the middle one for odd numbers of cylinders.Furthermore the results show that the critical trapped mode effect occurs for normalized cylinder radiuses close to 0.5 and 1.0.Finally the force estimation for n tandem cylinders confirms that force amplitude of the middle cylinder versus normalized separation distance fluctuates about that of a single cylinder.     

A new source number estimation method based on the beam eigenvalue

Most source number estimation methods based on the eigenvalues are decomposed by covariance matrix in MUSIC algorithm. To develop the source number estimation method which has lower signal to noise ratio and is suitable to both correlated and uncorrelated impinging signals, a new source number estimation method called beam eigenvalue method (BEM) is proposed in this paper. Through analyzing the space power spectrum and the correlation of the line array, the covariance matrix is constructed in a new way, which is decided by the line array shape when the signal frequency is given. Both of the theory analysis and the simulation results show that the BEM method can estimate the source number for correlated signals and can be more effective at lower signal to noise ratios than the normal source number estimation methods.     

Control of Vortex Shedding and Drag Reduction through Dual Splitter Plates Attached to a Square Cylinder

In this paper we have made a numerical study on the control of vortex shedding and drag reduction of a cylinder by attaching thin splitter plates. The wake structure of the cylinder of square cross-section with attached splitter plates is analyzed for a range of Reynolds number, based on the incident stream and height of the cylinder, in the laminar range. The Navier-Stokes equations governing the flow are solved by the control volume method over a staggered grid arrangement. We have used the semi-implicit method for pressure-linked equation(SIMPLE) algorithm for computation. Our results show that the presence of a splitter plate upstream of the cylinder reduces the drag, but it has a small impact on the vortex shedding frequency when the plate length is beyond 1.5 time the height of the cylinder. The presence of a downstream splitter plate dampens the vortex shedding frequency. The entrainment of fluid into the inner side of the separated shear layers is obstructed by the downstream splitter plate. Our results suggest that by attaching in-line splitter plates both upstream and downstream of the cylinder, the vortex shedding can be suppressed, as well as a reduction in drag be obtained. We made a parametric study to determine the optimal length of these splitter plates so as to achieve low drag and low vortex shedding frequency.     

水翼部分空化流动二维数值仿真研究（英文）

In the present study, a new approach is applied to the cavity prediction for two-dimensional(2D) hydrofoils by the potential based boundary element method(BEM). The boundary element method is treated with the source and doublet distributions on the panel surface and cavity surface by the use of the Dirichlet type boundary conditions. An iterative solution approach is used to determine the cavity shape on partially cavitating hydrofoils. In the case of a specified cavitation number and cavity length, the iterative solution method proceeds by addition or subtraction of a displacement thickness on the cavity surface of the hydrofoil. The appropriate cavity shape is obtained by the dynamic boundary condition of the cavity surface and the kinematic boundary condition of the whole foil surface including the cavity. For a given cavitation number the cavity length of the 2D hydrofoil is determined according to the minimum error criterion among different cavity lengths, which satisfies the dynamic boundary condition on the cavity surface. The NACA 16006, NACA 16012 and NACA 16015 hydrofoil sections are investigated for two angles of attack. The results are compared with other potential based boundary element codes, the PCPAN and a commercial CFD code(FLUENT). Consequently, it has been shown that the results obtained from the two dimensional approach are consistent with those obtained from the others.     

二维水翼型空化流的数值计算(英文)

In order to predict the effects of cavitation on a hydrofoil, the state equations of the cavitation model were combined with a linear viscous turbulent method for mixed fluids in the computational fluid dynamics (CFD) software FLUENT to simulate steady cavitating flow. At a fixed attack angle, pressure distributions and volume fractions of vapor at different cavitation numbers were simulated, and the results on foil sections agreed well with experimental data. In addition, at the various cavitation numbers, the vapor fractions at different attack angles were also predicted. The vapor region moved towards the front of the airfoil and the length of the cavity grew with increased attack angle. The results show that this method of applying FLUENT to simulate cavitation is reliable.     

涂层对空化流动特性影响的实验研究

利用实验的方法研究了涂层对绕水翼空化流动特性的影响。分别针对喷涂环氧涂层和氟碳涂层的 Clark-Y 型水翼,采用高速摄像装置观察了不同空化阶段的空化流动形态。研究结果表明：（1）在初生空化阶段,当σ=1.82时,沿环氧涂层水翼表面展向排列着初生空泡,而氟碳涂层水翼还处于无空化状态,说明相对于环氧涂层,氟碳涂层对空化现象的产生有一定的抑制作用,氟碳涂层水翼初生空化数为1.50;（2）在片状附着型阶段,当σ小于1.63时,绕环氧涂层水翼的空化先于氟碳涂层水翼发展至片状空化,绕水翼空化流动产生大量分散空泡,沿水翼表面向后运动过程中逐渐长大,在高压区溃灭后形成小空泡并以马蹄涡形式继续运动。同一空化数下,绕环氧涂层水翼空化流动的空泡长度大于氟碳涂层水翼。但随空化数降低,两者空泡长度逐渐接近,说明环氧涂层在片状空化阶段对空化的抑制作用逐渐增强;（3）σ=0.87时空化发展至云状空化阶段,空化流动伴随周期性的云状空泡的脱落,绕环氧涂层水翼的空化流动周期及无量纲空化面积均小于氟碳涂层水翼,说明涂层对空化的非定常变化也有一定的抑制作用,且环氧涂层强于氟碳涂层。     

基于均相流输运模型的二维水翼空化模拟

基于均相流输运模型对NACA661-012型水翼进行了空化数值模拟,计算了不同空化数K和不同攻角α下的升力系数与阻力系数.从流场、压力场和边界层的变化分析了空化的产生发展对水翼升力和阻力的影响.当攻角α大于8°以后,空化流动的不稳定性增强,空泡呈现出周期性的生长溃灭,并伴有升力系数和阻力系数的周期性波动.计算结果与实验进行了对比,结果吻合较好.     

水翼叶顶间隙漩涡空化流动特性研究

采用试验的方法研究了不同空化数下水翼叶顶间隙区域漩涡空化流动的发展变化。试验在闭式空化水洞中进行,采用高速全流场显示技术对空化流场进行观测,并采用图像处理技术对试验结果进行处理,提出空化涡模型,阐述了涡空化的发展规律。研究结果表明:随着空化数的降低,叶顶间隙漩涡空化的发展主要经历如下三个阶段:(I)泄露涡内部空化初生阶段:在水翼中部附近产生游离状空化,向下游运动并迅速溃灭消失。(II)叶顶间隙内部附着空化发展阶段:涡空化逐渐发展并向水翼尾缘延伸,空化涡带呈螺旋状非轴对称旋转;叶顶位置压力面中部附近开始出现片状附着型空化,并体现出强烈的非定常特性。(III)射流剪切层内部空化形成阶段:涡空化延伸至水翼下游;叶顶附着空化充分发展,充满间隙并形成射流剪切层空化,和空化涡带共同形成三角状空化结构。     

Hydrodynamic response of a passive shape-adaptive composite hydrofoil

The primary objective of this paper is to present cavitation tunnel tests performed on an optimised shape-adaptive composite hydrofoil and compare the results to other composite hydrofoils. The optimised composite hydrofoil was designed based on prior literature and was manufactured using an optimised ply orientation schedule and a pre-twist. In the same experiment schedule a composite hydrofoil that has a ply orientation that is opposite to the optimised hydrofoil was also tested. In addition to the cavitation tunnel experiments, the paper also presents results predicted from FEA and CFD simulations for the optimised hydrofoil and compares the results from numerical methods to experiments. The results show that the optimised hydrofoil has an improved L/D ratio and a delayed stall phenomenon compared to other hydrofoils. Furthermore, due to the pre-twisted optimised geometry, the hydrofoil does not suffer from loss of lift at low angles of attack. The experimental results demonstrated the importance of characterising the performance of flexible shape-adaptive hydrofoils based on the actual velocity of the flow in addition to the conventional characterisation based on Reynold's number. Additional numerical simulations were performed to investigate the hydrofoils observed load dependant deformation behaviour. These results clearly show that for the same Reynold's number, the hydrofoil can have an appreciably different response if the flow velocity is different.     

大攻角水下航行体自然空泡流的数值模拟研究

基于相分数输运方程型的均质平衡流空化模型,采用有限体积法研制了大型空泡流计算程序,对大攻角下运行的水下航行体三维空泡流进行了数值模拟,并与实验结果进行了对比.首次将非线性涡粘湍流模式与基于Rayleigh-Pies-set方程的TEM型空化模型相结合,建立了自然空泡流的数学模型.采用基于SIMPLE的压力-速度-密度耦合修正算法、二阶精度三时间层格式以及基于延迟修正的高阶对流TVD格式.计算模拟了0.2～0.6空化数、4°～20°攻角的不同工况,得到的三维空泡形状及压力分布与实验结果相符.研究了大攻角下航行体周向上的空泡形态分布特征,给出了多种空泡尺度和升阻系数与空化数和攻角之间的关系.通过定量分析发现,空泡的不对称性导致航行体某些部位受力集中,表明高速带空泡运动的航行体在大攻角运动中其结构将受到巨大的水动力载荷.计算还发现,大攻角下的阻力系数与空化数之间的关系和零攻角条件下刚好相反,并根据空泡的不对称性从形状阻力与粘性阻力的关系上对这种现象作出了解释.     

基于求解速度势通量的指定压力分布二维翼型设计方法

为了提升翼型的水动力和空泡等性能,指定压力分布的翼型剖面设计的方法多数集中在给定攻角下的翼型剖面的设计,该方法存在计算量较大,收敛性不理想,特别是推广到三维问题时,上述问题尤为突出,限制了翼型设计的进一步发展。文章以势流理论面元方法为基础,通过求解指定压力分布条件下翼型表面的速度势通量,获得翼型表面形状的修正量,并将修正量分解为攻角的变化以及剖面自身的变化两部分,从而得到了翼型唯一的设计攻角和翼型剖面几何（厚度分布、拱度分布）。文中采用上述方法对二维翼型问题进行了设计验证,表明该方法可以设计任意指定压力分布的翼型剖面,理论上该方法可以用于全三维翼型的设计问题。     

Investigation of cavitation inception characteristics of hydrofoil sections via a viscous approach

Unlike traditional approaches based on potential theory, this work investigated the cavitation inception characteristics of hydrofoil sections by solving Reynolds-averaged Navier–Stokes (RANS) equations. The viscous effects at high Reynolds numbers were taken into account through calculation of the eddy viscosity using a k- model. This viscous approach delivers the lift and drag forces in a more self-contained way, which cannot be obtained directly from the potential theory. A comparison with smooth surface measurements validates the proposed numerical method. Two approaches to include the roughness effects are also described. The predictions of cavitation bucket characteristics based on potential theory are more conservative than those reached by the proposed viscous computations. Hydrofoil sections with different camber ratios, foil thicknesses, and Reynolds numbers were studied numerically. A decrease in the Reynolds number tends to increase the cavitation-free region without changing the shape of the steep region. An increase in foil thickness gives a range increase in the angle of attack where no cavitation is expected. An increase in the camber ratio moves the cavitation-free location of the angle of attack, and slightly increases its range.