Interfacial dynamics‐based modelling of turbulent cavitating flows,Part‐1: Model development and steady‐state computations

The merits of transport equation‐based models are investigated by adopting an enhanced pressure‐based method for turbulent cavitating flows. An analysis of the mass and normal‐momentum conservation at a liquid–vapour interface is conducted in the context of homogeneous equilibrium flow theory, resulting in a new interfacial dynamics‐based cavitation model. The model offers direct interpretation of the empirical parameters in the existing transport‐equation‐based models adopted in the literature. This and three existing cavitation models are evaluated for flows around an axisymmetric cylindrical body and a planar hydrofoil, and through a convergent–divergent nozzle. Although all models considered provide qualitatively comparable wall pressure distributions in agreement with the experimental data, quantitative differences are observed in the closure region of the cavity, due to different compressibility characteristics of each cavitation model. In particular, the baroclinic effect of the vorticity transport equation plays a noticeable role in the closure region of the cavity, and contributes to the highest level of turbulent kinetic energy there. Copyright © 2004 John Wiley & Sons, Ltd.     

Time‐dependent turbulent cavitating flow computations with interfacial transport and filter‐based models

Turbulent cavitating flow computations need to address both cavitation and turbulence modelling issues. A recently developed interfacial dynamics‐based cavitation model (IDCM) incorporates the interfacial transport into the computational modelling of cavitation dynamics. For time‐dependent flows, it is known that the engineering turbulence closure such as the original k–ε model often over‐predicts the eddy viscosity values reducing the unsteadiness. A recently proposed filter‐based modification has shown that it can effectively modulate the eddy viscosity, rendering better simulation capabilities for time‐dependent flow computations in term of the unsteady characteristics. In the present study, the IDCM along with the filter‐based k–ε turbulence model is adopted to simulate 2‐D cavitating flows over the Clark‐Y airfoil. The chord Reynolds number is Re=7.0 × 10⁵. Two angles‐of‐attack of 5 and 8° associated with several cavitation numbers covering different flow regimes are conducted. The simulation results are assessed with the experimental data including lift, drag and velocity profiles. The interplay between cavitation and turbulence models reveals substantial differences in time‐dependent flow results even though the time‐averaged characteristics are similar. Copyright © 2005 John Wiley & Sons, Ltd.     

An improved progressive preconditioning method for steady non‐cavitating and sheet‐cavitating flows

An improved progressive preconditioning method for analyzing steady inviscid and laminar flows around fully wetted and sheet‐cavitating hydrofoils is presented. The preconditioning matrix is adapted automatically from the pressure and/or velocity flow‐field by a power‐law relation. The cavitating calculations are based on a single fluid approach. In this approach, the liquid/vapour mixture is treated as a homogeneous fluid whose density is controlled by a barotropic state law. This physical model is integrated with a numerical resolution derived from the cell‐centered Jameson's finite volume algorithm. The stabilization is achieved via the second‐and fourth‐order artificial dissipation scheme. Explicit four‐step Runge–Kutta time integration is applied to achieve the steady‐state condition. Results presented in the paper focus on the pressure distribution on hydrofoils wall, velocity profiles, lift and drag forces, length of sheet cavitation, and effect of the power‐law preconditioning method on convergence speed. The results show satisfactory agreement with numerical and experimental works of others. The scheme has a progressive effect on the convergence speed. The results indicate that using the power‐law preconditioner improves the convergence rate, significantly. Copyright © 2010 John Wiley & Sons, Ltd.     

一种修正的低温流体空化流动计算模型

为了更准确地预测低温流体的空化流动特性, 基于Kubota空化模型, 对蒸发和凝结源项进行修正, 建立了一种考虑热力学效应的空化模型. 分别采用原始和修正的Kubota空化模型, 计算了绕对称回转体液氮的空化流动, 通过与实验结果的比较对修正的空化模型进行了评价. 结果表明, 与原Kubota空化模型比较, 修正的空化模型由于考虑了热力学效应, 计算获得的蒸发量减小, 凝结量增大, 空穴长度减小, 空穴界面形态呈模糊状态.计算结果与实验结果更加一致, 说明修正的空化模型能准确的描述低温流体空化过程的质量传输过程, 能够更准确模拟低温流体中的空化流动特性.      

Experimental evaluation of numerical simulation of cavitating flow around hydrofoil

Cavitation in hydraulic machines causes different problems that can be related to its unsteady nature. An experimental and numerical study of developed cavitating flow was performed. Until now simulations of cavitating flow were limited to the self developed “in house” CFD codes. The goal of the work was to experimentally evaluate the capabilities of a commercial CFD code (Fluent) for simulation of a developed cavitating flow. Two simple hydrofoils that feature some 3D effects of cavitation were used for the experiments. A relatively new technique where PIV method combined with LIF technique was used to experimentally determine the instantaneous and average velocity and void ratio fields (cavity shapes) around the hydrofoils. Distribution of static pressure on the hydrofoil surface was determined. For the numerical simulation of cavitating flow a bubble dynamics cavitation model was used to describe the generation and evaporation of vapour phase. An unsteady RANS 3D simulation was performed. Comparison between numerical and experimental results shows good correlation. The distribution and size of vapour structures and the velocity fields agree well. The distribution of pressure on the hydrofoil surface is correctly predicted. The numerically predicted shedding frequencies are in fair agreement with the experimental data.     

A numerical method for simulation of attached cavitation flows

A new numerical algorithm for attached cavitation flows is developed. A cavitation model is implemented in a viscous Navier–Stokes solver. The liquid–vapour interface is assumed as a free surface boundary of the computation domain. Its shape is determined with an iterative procedure to match the cavity surface to a constant pressure boundary. The pressure distribution, as well as its gradient along the wall, is taken into account in updating the cavity shape iteratively. A series of computations are performed for the cavitating flows across three kinds of headform/cylinder bodies: conic, ogival and hemispheric heads. A range of cavitation numbers is investigated for each headform/cylinder body. The obtained results are reasonable and the iterative procedure of cavity shape updating is quite stable. The superiority of the developed cavitation model and algorithm is demonstrated. Copyright © 2006 John Wiley & Sons, Ltd.     

Turbulence and cavitation models for time-dependent turbulent cavitating flows

Cavitation typically occurs when the fluid pressure is lower than the vapor pressure at a local thermodynamic state,and the flow is frequently unsteady and turbulent.To assess the state-of-the-art of computational capabilities for unsteady cavitating flows,different cavitation and turbulence model combinations are conducted.The selected cavitation models include several widely-used models including one based on phenomenological argument and the other utilizing interface dynamics.The kε turbulence model with additional implementation of the filter function and density correction function are considered to reduce the eddy viscosity according to the computed turbulence length scale and local fluid density respectively.We have also blended these alternative cavitation and turbulence treatments,to illustrate that the eddy viscosity near the closure region can significantly influence the capture of detached cavity.From the experimental validations regarding the force analysis,frequency,and the cavity visualization,no single model combination performs best in all aspects.Furthermore,the implications of parameters contained in different cavitation models are investigated.The phase change process is more pronounced around the detached cavity,which is better illus-trated by the interfacial dynamics model.Our study provides insight to aid further modeling development.     

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.     

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.     

空化可压缩流动空穴溃灭激波特性研究

为深入研究空化可压缩流动中空泡/空泡团溃灭过程中激波产生、传播及其与空穴相互作用规律,本文采用数值模拟方法对空化可压缩流动空穴溃灭激波特性展开了研究.数值计算基于OpenFOAM开源程序,综合考虑蒸汽相和液相的压缩性,通过在原无相变两相可压缩求解器的控制方程中耦合模拟空化汽液相间质量交换的源项,实现了对空化流动的非定常可压缩计算.利用上述考虑汽/液相可压缩性的空化流动求解器,对周期性云状空化流动进行了数值模拟,并重点研究了空穴溃灭激波特性.结果表明:上述数值计算方法可以准确捕捉到空穴非定常演化过程及大尺度脱落空泡云团溃灭激波现象,大尺度脱落空泡云团溃灭过程分为3个阶段:(1) U型空泡团形成; (2) U型空泡团头部溃灭; (3) U型空泡团腿部溃灭.在U 型空泡团腿部溃灭瞬间,观察到激波产生,并向上游和下游传播,向上游传播的激波与空穴相互作用,导致水翼吸力面新生的附着型片状空穴回缩,直至完全溃灭.并且空穴溃灭激波存在回弹现象, 抑制了下一周期的空化发展.      

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.     

Reduced-order modeling of three-dimensional unsteady partial cavity flows

An efficient reduced-order modeling to analyze three-dimensional unsteady partial cavity flows is proposed. The proposed approach is based on the boundary element method along with the potential flow assumption. To this end, a novel non-iterative method based on the flow eigenmodes of three-dimensional partial cavity flows is applied. Eigenanalysis and reduced-order modeling for unsteady flows over a three-dimensional hydrofoil with various sections are performed. The results obtained from the present analysis are compared with those reported in the literature to verify the strength of the proposed approach. In order to examine the performance of the introduced algorithm for unsteady cavitating flows, various simulations for several reduced frequencies, hydrofoil geometries and different cavitation numbers are also investigated. Comparison between the obtained results using the novel and conventional methods indicates that the present algorithm works very well with sufficient accuracy. Moreover, it is shown that the proposed method is computationally more efficient than the conventional ones for unsteady sheet cavitation analysis on three-dimensional hydrofoils.     

可压缩空化流动空穴演化及压力脉动特性实验研究

空化流动具有高度的压缩性,空化流动非定常特性及其流体动力与压缩性密切相关.为研究可压缩空化流动空泡脱落的回射流和激波机制下周期性空穴结构演化及其诱导流体动力特性,本文采用多场同步测试方法对典型云状空化流动进行了实验研究,获得了文丘里管扩张段内部云状空化空穴形态演化及其诱导同步壁面压力脉动信号.并基于数字图像处理技术,对附着型片状空穴和脱落型云状空穴结构演化进行了精细化定量分析.结果表明:可压缩空化流动回射流机制下,空穴演化呈现附着型空穴生长$\!$-$\!$-$\!$回射流产生及发展$\!$-$\!$-$\!$附着型空穴失稳断裂及大尺度空泡云团产生脱落的非定常过程,激波机制下空穴演化具有附着型空穴生长$\!$-$\!$-$\!$激波产生及传播$\!$-$\!$-$\!$附着型空穴失稳断裂及大尺度空泡云团脱落的非定常特征,激波传播时间占空穴脱落周期小于回射流推进.激波与空穴相互作用导致空穴内部含气率瞬间大范围大幅度下降,诱导复杂流体动力.激波传播过程中,空泡内部压力脉动大幅增加,激波前缘诱导压力脉冲,而回射流推进过程中,壁面压力脉动相对平稳,回射流头部存在小幅增加. 不同机制下空穴结构存在显著差异,具有不同的相间质量传输过程.      

Influence of cavitation on the hydroelastic stability of hydrofoils

This work numerically examines the effect of turbulent and cavitating flow on the hydroelastic response and stability of a hydrofoil. A cantilevered, rectangular, chordwise rigid hydrofoil is modeled as a 2-degrees-of-freedom structure for its spanwise bending and torsional flexibilities. The fluid flow is modeled with the incompressible, Unsteady Reynolds Averaged Navier–Stokes equations using an eddy-viscosity turbulence closure model that is corrected for the presence of cavitation, and with a transport equation based cavitation model. The results show that, in general, massive cavitation tends to: (i) reduce the mean lift, (ii) increase the mean drag, (iii) lower the mean deformations, and (iv) delay static divergence, while unsteady sheet/cloud cavitation promotes flow induced vibrations. Such vibrations and load fluctuations could be as large as (and even greater than) the mean values for cases with unsteady cavitation, so dynamic and viscous fluid–structure models are needed to simulate flexible hydrofoils in cavitating flows. In general, the flow induced vibrations, and hence the drag force, are higher with decreasing stiffness. For small leading edge partial cavitation, increasing foil flexibility increases the maximum cavity length and reduces the cavity shedding frequency; however, the influence of foil flexibility is limited for cases where the maximum cavity length is near or beyond the foil trailing edge, because of the relocation of the center of pressure at the elastic axis, near the mid-chord. The results show that the mean deformations are generally limited by stall, and by the quasi-steady linear theory predictions at the fully-wetted and supercavitating limits. Furthermore, frequency focusing can occur when the cavity shedding frequency is near the fundamental system resonance frequencies, and broadening of the frequency spectrum can occur due to excitation of the sub-harmonics and/or modulation induced by the fluctuating cavities, if the cavity shedding frequency is away from the fundamental system resonance frequencies.     

Numerical simulation of multiphase cavitating flows around an underwater projectile

The present simulation investigates the multiphase cavitating flow around an underwater projectile. Based on the Homogeneous Equilibrium Flow assumption, a mixture model is applied to simulate the multiphase cavitating flow including ventilated cavitation caused by air injection as well as natural cavitation that forms in a region where the pressure of liquid falls below its vapor pressure. The transport equation cavitating model is applied. The calculations are executed based on a suite of CFD code. The hydrodynamics characteristics of flow field under the interaction of natural cavitation and ventilated cavitation is analyzed. The results indicate that the ventilated cavitation number is under a combined effect of the natural cavitation number and gas flow rate in the multiphase cavitating flows.     

A compressible single‐temperature conservative two‐phase model with phase transitions

A model for multidimensional compressible two‐phase flow with pressure and velocity relaxations based on the theory of thermodynamically compatible system is extended to study liquid–gas flows with cavitation. The model assumes for each phase its own pressure and velocity, while a common temperature is considered. The governing equations form a hyperbolic system in conservative form and are derived through the theory of a thermodynamically compatible system. The phase pressure‐equalizing process and the interfacial friction are taken into account in the balance laws for the volume fractions of one phase and for the relative velocity by adding two relaxation source terms, while the phase transition is introduced into the model considering in the balance equation for the mass of one phase the relaxation of the Gibbs free energies of the two phases. A modification of the central finite‐volume Kurganov–Noelle–Petrova method is adopted in this work to solve the homogeneous hyperbolic part, while the relaxation source terms are treated implicitly. In order to investigate the effect of the mass transfer in the solution, a 1D cavitation tube problem is presented. In addition, two 2D numerical simulations regarding cavitation problem are also studied: a cavitating Richtmyer–Meshkov instability and a laser‐induced cavitation problem. Copyright © 2014 John Wiley & Sons, Ltd.     

Dynamics of cavitation–structure interaction

Cavitation–structure interaction has become one of the major issues for most engineering applications. The present work reviews recent progress made toward developing experimental and numerical investigation for unsteady turbulent cavitating flow and cavitation–structure interaction. The goal of our overall efforts is to(1) summarize the progress made in the experimental and numerical modeling and approaches for unsteady cavitating flow and cavitation–structure interaction,(2) discuss the global multiphase structures for different cavitation regimes, with special emphasis on the unsteady development of cloud cavitation and corresponding cavitating flow-induced vibrations,with a high-speed visualization system and a structural vibration measurement system, as well as a simultaneous sampling system,(3) improve the understanding of the hydroelastic response in cavitating flows via combined physical and numerical analysis, with particular emphasis on the interaction between unsteady cavitation development and structural deformations. Issues including unsteady cavitating flow structures and cavitation–structure interaction mechanism are discussed.     

A finite volume unstructured multigrid method for efficient computation of unsteady incompressible viscous flows

An unstructured non‐nested multigrid method is presented for efficient simulation of unsteady incompressible Navier–Stokes flows. The Navier–Stokes solver is based on the artificial compressibility approach and a higher‐order characteristics‐based finite‐volume scheme on unstructured grids. Unsteady flow is calculated with an implicit dual time stepping scheme. For efficient computation of unsteady viscous flows over complex geometries, an unstructured multigrid method is developed to speed up the convergence rate of the dual time stepping calculation. The multigrid method is used to simulate the steady and unsteady incompressible viscous flows over a circular cylinder for validation and performance evaluation purposes. It is found that the multigrid method with three levels of grids results in a 75% reduction in CPU time for the steady flow calculation and 55% reduction for the unsteady flow calculation, compared with its single grid counterparts. The results obtained are compared with numerical solutions obtained by other researchers as well as experimental measurements wherever available and good agreements are obtained. Copyright © 2004 John Wiley & Sons, Ltd.     

深埋隧道地震动力响应的复反应分析

采用高速摄影技术对定常来流中ＮＡＣＡ４４１２翼的不稳定的空泡流形态特征进行了水洞试验研究．试验结果揭示了由于空泡形态断裂而产生的低频脉动现象．这一现象在跨空泡流（Ｔｒａｎｓ－ｃａｖｉｔａｔｉｎｇｆｌｏｗ）情况下尤为明显，常使空泡长度和厚度在大幅范围内拟周期地变动，其频率特性比较稳定，有别于空泡末端局部泡团脱落而产生的脉动