Numerical simulation of the unsteady behaviour of cavitating flows

A 2D numerical model is proposed to simulate unsteady cavitating flows. The Reynolds‐averaged Navier–Stokes equations are solved for the mixture of liquid and vapour, which is considered as a single fluid with variable density. The vapourization and condensation processes are controlled by a barotropic state law that relates the fluid density to the pressure variations. The numerical resolution is a pressure‐correction method derived from the SIMPLE algorithm, with a finite volume discretization. The standard scheme is slightly modified to take into account the cavitation phenomenon. That numerical model is used to calculate unsteady cavitating flows in two Venturi type sections. The choice of the turbulence model is discussed, and the standard RNG k–εmodel is found to lead to non‐physical stable cavities. A modified k–εmodel is proposed to improve the simulation. The influence of numerical and physical parameters is presented, and the numerical results are compared to previous experimental observations and measurements. The proposed model seems to describe the unsteady cavitation behaviour in 2D geometries well. Copyright © 2003 John Wiley & Sons, Ltd.     

水下高速射弹超空泡运动建模与仿真

建立并简化了水下高速射弹动力学和运动学模型。基于空泡模型假设和空泡截面独立扩张原理,确定了空化数与速度、深度的耦合计算关系;定义了水下射弹尾翼穿刺前的临界空化数;对水下高速射弹弹道特性进行了仿真研究。仿真计算结果表明：水下射弹有效射程受初始入射角影响较大;随着初始入射角的增大,有效射程逐渐减小;提升初速度可以带来有效射程的增大,但增幅效果不显著,在满足预定指标条件下应合理选择初速度;初始攻角对射弹弹道散布影响较大,初始角速度对其影响很小,但较大的初始角速度会带来明显的攻角变化。     

弹塑性变形油藏中多相渗流的数值模拟

基于流固耦合力学理论,建立了弹性变形油藏中多相渗流的数学模型,该模型考虑了渗流与变形的耦合作用,以及注采交变载荷作下油藏多孔介质的弹性变形特征,给出了耦合数值模拟方法和算例。     

Comparison of numerical solvers for cavitating flows

Different computational fluid dynamics (CFD) strategies have been developed to simulate, analyse and better understand cavitating flows. Based on homogeneous models, two numerical approaches using compressible and incompressible codes are applied to capture large density variations and unsteady behaviours of cavitating flows. Simulations are performed on two-dimensional Venturi geometries and compared with experimental data. Local and global analyses are proposed and the necessity to account for compressibility phenomena is discussed.     

Implementation of phase change thermodynamic probability for unsteady simulation of cavitating flows

The aim of this work is to investigate the non‐equilibrium effects of phase change in cavitating flows. For this purpose, the concept of phase change thermodynamic probability is used along with homogeneous model to simulate two‐phase cavitating flows. For simulation of unsteady behaviors of cavitation, which have practical applications, unsteady PISO algorithm based on the non‐conservative approach is utilized. For multi‐phase simulation, single‐fluid Navier–Stokes equations, along with the volume fraction transport equation, are employed. In this paper, phase change thermodynamics probabilities and cavitation model is briefly summarized. Thus, derivation of the cavitation model, starting from the basic thermodynamic equations to the mass and momentum conservation equations at a liquid–vapor two‐phase flow, is presented to explain the numerical model. Unsteady simulations of cavitation around a flat plate normal to flow direction are presented to clarify the accuracy of the model. The accuracy of the numerical results is good, and it is possible to apply this method to more complex geometries. Copyright © 2010 John Wiley & Sons, Ltd.     

旋转射弹高速倾斜入水多相流场与弹道数值模拟

基于VOF多相流模型和有限体积法求解水、汽、气多相流动的RANS方程,结合重叠网格技术和six DOF算法对某一型号舰载射弹倾斜入水过程进行数值模拟研究。首先基于该方法研究了射弹旋转效应对射弹运动特性及流体动力特性的影响,然后对不同入水角下倾斜入水过程进行分析,得到不同倾角下旋转射弹入水空泡形态发展规律、弹体运动特征及流体动力特性变化规律。研究结果表明：射弹的旋转有利于弹体在初始对称面内的弹道稳定性,但会降低弹体侧向稳定性,使射弹受到的阻力系数、俯仰力矩系数变小;入水角越小,形成的空泡越不对称,由射弹运动状态的改变引起的空泡形态变化越明显,在超空泡航行阶段,弹体运动较稳定,不同角度下流体动力系数差别很小,当弹体下表面刺破空泡壁沾湿时,弹体运动状态发生较大变化,流体动力系数迅速增大,此时入水角度过小,弹体容易失稳;弹体的沾湿对空泡形态、弹体运动稳定性和流体动力特性有着重要的影响。

     

翼型空泡周期性流动的数值模拟及机理分析

采用基于正压关系的均质平衡流空化模型和低雷诺数修正的k-ε湍流模式,自行开发了空泡流数值模拟方法和计算软件,对绕翼型空泡的周期性流动现象进行了数值模拟.计算结果与实验数据的对比表明,空泡的宏观特征、流动特性、周期性脱落的斯坦顿数St等与试验结果接近,验证了计算结果的可靠性.空泡在大约一个周期的2/3时间段内成长,并在大约1/3周期时刻发生断裂脱落.这两个特征时间与高速摄像实验结果一致.所取工况对应的组合参数σ/2α=2.865,以翼弦长计算可得St=0.217,与文献的最新试验结果吻合.空泡周期性运动过程中升阻系数也周期性振荡,时均值C<,1>=0.41,C<,d>=0.097,振荡频率与空泡脱落频率一致.对空泡运动过程中流场结构的变化进行了分析,结果表明在大攻角条件下,空泡闭合区后的逆压梯度导致涡的形成及回射流的发展,沿壁面逆向流动的混合介质射流是引起空泡断裂的原因,回射流发展、涡结构变化与空泡非稳态演化过程存在密切的联系,探讨了翼型空泡发生周期性脱落的一些机理.     

Recent advances in studies on multiphase and reacting flows in China

The recent developments and advances of studies on multiphase and reacting flows, including gas-solid, gas-liquid, liquid-solid and reacting flows, in China are reviewed. Special emphasis is laid on the fundamental studies and numerical models. Some important experimental results are also reported. But measurement techniques are not covered.     

Numerical simulation of cavitating flow in 2D and 3D inducer geometries

A computational method is proposed to simulate 3D unsteady cavitating flows in spatial turbopump inducers. It is based on the code FineTurbo, adapted to take into account two‐phase flow phenomena. The initial model is a time‐marching algorithm devoted to compressible flow, associated with a low‐speed preconditioner to treat low Mach number flows. The presented work covers the 3D implementation of a physical model developed in LEGI for several years to simulate 2D unsteady cavitating flows. It is based on a barotropic state law that relates the fluid density to the pressure variations. A modification of the preconditioner is proposed to treat efficiently as well highly compressible two‐phase flow areas as weakly compressible single‐phase flow conditions. The numerical model is applied to time‐accurate simulations of cavitating flow in spatial turbopump inducers. The first geometry is a 2D Venturi type section designed to simulate an inducer blade suction side. Results obtained with this simple test case, including the study of its general cavitating behaviour, numerical tests, and precise comparisons with previous experimental measurements inside the cavity, lead to a satisfactory validation of the model. A complete three‐dimensional rotating inducer geometry is then considered, and its quasi‐static behaviour in cavitating conditions is investigated. Numerical results are compared to experimental measurements and visualizations, and a promising agreement is obtained. Copyright © 2004 John Wiley & Sons, Ltd.     

Numerical simulation for formed projectile of depleted uranium alloy

IntroductionThecharactersoftheprocessesofformedprojectilebydetonationarelargestrainandhighstrainrate .InanalysisoftheprocesseswithLagrangianfinite_elementorfinite_differenceapproachestherearemajorproblemsthatsomemeshesalwaysbecomeseverelydistortiontocauselargecomputationalerrors .Toovercomethesedifficulties,themeshrezoningtechniquewasused[1] butrezoningnumberwaslimited .Smoothedparticlehydrodynamics (SPH)isuniqueincomputationalcontinuumdynamicsinthatitusesnospatialmesh .ItisapureLagrangianp…     

冲击起爆弹丸内装药延迟起爆数值模拟

对穿爆燃弹的穿靶及释能过程进行数值模拟,解释了SPH-FEM耦合方法在模拟冲击起爆过程的优越性。通过对不同弹芯头部形状、直径及材料的对比分析,得到了不同工况下装药热点成长的压力-时间曲线,计算结果表明:在弹芯直径不变的情况下,弹芯头部直角尖刺越短,装药的热点成长时间越短;在头部尖刺长度不变的情况下,减小弹芯直径,热点生成时间也缩短;选用钢弹芯比钨合金弹芯有一定靶后释能优势。模拟穿靶效果与真实穿靶效果符合较好,这种方法可以为穿爆类弹丸设计提供依据。     

Dynamic mode decomposition and reconstruction of transient cavitating flows around a Clark-Y hydrofoil

The transient cavitating flow around the Clark-Y hydrofoil is numerically investigated by the dynamic mode decomposition with criterion. Based on the ranking dominant modes, frequencies of the first four modes are in good accordance with those obtained by fast Fourier transform. Furthermore, the cavitating flow field is reconstructed by the first four modes, and the dominant flow features are well captured with the reconstructed error below 12% when compared to the simulated flow field. This paper offers a reference for observing and reconstructing the flow fields, and gives a novel insight into the transient cavitating flow features.     

Towards multi-fidelity simulation of flows around an underwater vehicle with appendages and propeller

Flow around a real-life underwater vehicle often happens at a high Reynolds number with flow structures at different scales from the boundary layer around a blade to that around the hull. This poses a great challenge for large-eddy simulation of an underwater vehicle aiming at resolving all relevant flow scales. In this work, we propose to model the hull with appendages using the immersed boundary method, and model the propeller using the actuator disk model without resolving the geometry of the blade. The proposed method is then applied to simulate the flow around Defense Advanced Research Projects Agency(DARPA) suboff. An overall acceptable agreement is obtained for the pressure and friction coefficients. Complex flow features are observed in the near wake of suboff. In the far wake, the core region is featured by a jet because of the actuator disk, surrounded by an annular region with velocity deficit due to the body of suboff.     

Comparative study of two corrective gradient models in the simulation of multiphase flows using moving particle semi-implicit method

In this study, two corrective gradient models (CGMs) are compared in the simulation of multiphase flows. Linear consistency of the gradient model of moving particle semi-implicit (MPS) method has been recovered by introducing corrective matrix. However, it is found that particles tend to disperse along the streamline while using the CGM proposed in a previous study. Particle shifting (PS) schemes are necessary to reduce the irregularity of particle distribution to stabilize the calculation. To enhance the accuracy and stability, another CGM with dummy particle (CGMD) was proposed in our previous study. This enhanced CGM is featured by linear consistency and purely repulsive pressure gradient force. In this study, this enhanced CGM is modified and applied to multiphase flow simulation. Comparative study suggests that the modified CGM with PS scheme is capable of calculating various multiphase flows and predicting the interface evolution both clearly and accurately.     

A large eddy simulation of flows around an underwater vehicle model using an immersed boundary method

A large eddy simulation(LES) of the flows around an underwater vehicle model at intermediate Reynolds numbers is performed. The underwater vehicle model is taken as the DARPA SUBOFF with full appendages,where the Reynolds number based on the hull length is 1.0×105. An immersed boundary method based on the moving-least-squares reconstruction is used to handle the complex geometric boundaries. The adaptive mesh refinement is utilized to resolve the flows near the hull. The parallel scalabilities of the flow solver are tested on meshes with the number of cells varying from 50 million to 3.2 billion. The parallel solver reaches nearly linear scalability for the flows around the underwater vehicle model. The present simulation captures the essential features of the vortex structures near the hull and in the wake.Both of the time-averaged pressure coefficients and streamwise velocity profiles obtained from the LES are consistent with the characteristics of the flows pass an appended axisymmetric body. The code efficiency and its correct predictions on flow features allow us to perform the full-scale simulations on tens of thousands of cores with billions of grid points for higher-Reynolds-number flows around the underwater vehicles.     

Passive control of cavitating flow around an axisymmetric projectile by using a trip bar

Quasi-periodical evolutions such as shedding and collapsing of unsteady cloud cavitating flow, induce strong pressure fluctuations, what may deteriorate maneuvering stability and corrode surfaces of underwater vehicles. This paper analyzed effects on cavitation stability of a trip bar arranged on high-speed underwater projectile. Small scale water tank experiment and large eddy simulation using the open source software Open FOAM were used, and the results agree well with each other. Results also indicate that trip bar can obstruct downstream re-entrant jet and pressure wave propagation caused by collapse, resulting in a relatively stable sheet cavity between trip bar and shoulder of projectiles.     

Numerical simulation of wall roughness effects in cavitating flow

Hydrodynamic cavitation has an important effect on the performance of Diesel injectors. It influences the nature of the fuel spray and the efficiency of the combustion process. In the present study, we investigate numerically the effect of wall roughness in the cavitating and turbulent flow developing inside a Diesel injector. The mixture model based on a single fluid is adopted and the commercial Fluent software is used to solve the transport equations.The discharge coefficient C_d is computed for different cavitation numbers and wall roughness heights. Profiles of density mixture, vapor volume fraction, mean velocity and turbulent kinetic energy are reported. The effects of wall roughness and injection pressure are analyzed.     

Multiphase fluid dynamics and transport processes of low capillary number cavitating flows

To better understand the multiphase fluid dynamics and associated transport processes of cavitating flows at the capillary number of 0.74 and 0.54, and to validate the numerical results, a combined computational and experimental investigation of flows around a hydrofoil is studied based on flow visualizations and time-resolved interface movement. The computational model is based on a modified RNG k-ε model as turbulence closure, along with a vapor-liquid mass transfer model for treating the cavitation process. Overall, favorable agreement between the numerical and experimental results is observed. It is shown that the cavi- tation structure depends on the interaction of the water-vapor mixture and the vapor among the whole cavitation stage, the interface between the vapor and the two-phase mixture exhibits substantial unsteadiness. And, the adverse motion of the interface relates to pressure and velocity fluctuations inside the cavity. In particular, the velocity in the vapor region is lower than that in the two-phase region.     

An improved diffuse interface method for three-dimensional multiphase flows with complex interface deformation

An improved diffuse interface (DI) method is proposed for accurately capturing complex interface deformation in simulations of three-dimensional (3D) multiphase flows. In original DI methods, the unphysical phenomenon of interface thickening or blurring can affect the accuracy of numerical simulations, especially for flows with large density ratio and high Reynolds number. To remove this drawback, in this article, an interface-compression term is introduced into the Cahn-Hilliard equation to suppress the interface dispersion. The additional term only takes effect in the interface region and works normal to the interface. The difference of the current method from the previous work is that the compression rate can be adjusted synchronously according to the magnitude of local vorticity, which is strongly correlated to the interface dispersion and changes with the computational time and interface position. Numerical validations of the proposed method are implemented by simulating problems of Laplace law, Rayleigh-Taylor instability, bubble rising in a channel, and binary droplet collision. The obtained results agree well with the analytical solutions and published data. The numerical results show that the phenomenon of interface dispersion is suppressed effectively and the tiny interfacial structures in flow field can be captured accurately.