Velocity field measurements of cavitating flows

A particle Image Velocimetry (PIV) system has been developed to study the microfluid mechanics of cavitating flows. Planar PIV was used to examine the non-cavitating flow in the thin boundary layer near a hydrofoil surface for the cases of a naturally developing boundary layer and a boundary layer stimulated to turbulence by roughness near the foil leading edge. PIV was also used to examine the flow near the surface of individual cavitation bubbles and incipient attached cavitation. A system was devised to create a single nucleus in the flow upstream of a hydrofoil, and planar PIV was used to study the flow around the resulting traveling cavitation bubble. Velocity vectors were determined close to the solid surfaces and the gas/liquid interfaces of the bubbles. Seeding of the flow with particles did not result in the addition of active cavitation nuclei.     

Numerical study of unsteady turbulent cavitating flows

The simulation of cavitating flows is a challenging problem both in terms of modelling the physics and developing robust numerical methodologies. Such flows are characterized by important variations of the local Mach number, compressibility effects on turbulence and involve thermodynamic phase transition. To simulate these flows by applying homogeneous models and Reynolds averaged codes, the turbulence modelling plays a major role in the capture of unsteady behaviours. This paper presents a one-fluid compressible Reynolds-Averaged Navier–Stokes (RANS) solver with a simple equation of state (EOS) for the mixture. A special focus is devoted to the turbulence model influence. Unsteady numerical results are given for Venturi geometries and comparisons are made with experimental data.     

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.     

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.     

High speed digital imaging of cavitating vortices

 Researchers at the Cavitation and Multiphase Flow Laboratory of the University of Michigan worked in conjunction with Princeton Scientific Instruments (PSI) engineers to employ a new digital imaging system in the study of partial attached cavitation. The new high speed solid state system, the Princeton Scientific Ultra Fast Framing Camera (UFFC), was designed for cavitation studies where framing rates of 10⁵–10⁶ frames/s are required to image the detailed mechanisms of cavitating flows. The UFFC, which uses a PSI patented Charge Coupled Device (CCD) array image sensor, was designed to capture 30 frames at a maximum framing rate of 1 million frames/second. In these experiments, a maximum framing rate of 125000 frames per second (8 μs/frame) was used to examine cavitating vortices in the closure region of a partial attached cavity. The vortical structures in the closure region of the attached cavity were imaged, and the evolution and collapse of these flow structures were examined. Relationships between the cavitating vortices size, strength, and collapse time were observed. Received: 15 November 1996/Accepted: 1 December 1997     

PANS模型在空化湍流数值计算中的应用

采用一种基于标准k-ε模型改进的局部时均化模型（Partially-Averaged Navier-Stokes Model,PANS）,并应用于空化流动计算。控制不同的模型参数,分别对绕平头轴对称回转体和Clark-Y型水翼的空化流动进行模拟,并与实验结果进行对比。结果表明：PANS模型中未分解湍动能比率fk的取值对预测空化流动的数值计算精度有重要影响,改变fk的取值可实现对不同滤波尺度范围内的求解;随着fk值的减小PANS的预测精度逐步提高,能在相对较大范围内求解较小尺度的湍流运动过程中,预测到湍流运动中强烈的非定常特性;同时可以比较准确地预测空化流场结构和动力特性。     

Experimental determination of the speed ratio in free-molecular flow of nitrogen

The results are given for measurements of the speed ratio carried out in free-molecular flow of nitrogen. It is shown that hypersonic flow is achieved; the values of the speed ratio are close to theory.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 184–186, July–August, 1973.     

A cavitation model for computations of unsteady cavitating flows

A local vortical cavitation(LVC) model for the computation of unsteady cavitation is proposed.The model is derived from the Rayleigh–Plesset equations,and takes into account the relations between the cavitation bubble radius and local vortical effects.Calculations of unsteady cloud cavitating fows around a Clark-Y hydrofoil are performed to assess the predictive capability of the LVC model using well-documented experimental data.Compared with the conventional Zwart's model,better agreement is observed between the predictions of the LVC model and experimental data,including measurements of time-averaged fl w structures,instantaneous cavity shapes and the frequency of the cloud cavity shedding process.Based on the predictions of the LVC model,it is demonstrated that the evaporation process largely concentrates in the core region of the leading edge vorticity in accordance with the growth in the attached cavity,and the condensation process concentrates in the core region of the trailing edge vorticity,which corresponds to the spread of the rear component of the attached cavity.When the attached cavity breaks up and moves downstream,the condensation area fully transports to the wake region,which is in accordance with the dissipation of the detached cavity.Furthermore,using vorticity transport equations,we also fin that the periodic formation,breakup,and shedding of the sheet/cloud cavities,along with the associated baroclinic torque,are important mechanisms for vorticity production and modification When the attached cavity grows,the liquid–vapour interface that moves towards the trailing edge enhances the vorticity in the attached cav-ity closure region.As the re-entrant jet moves upstream,the wavy/bubbly cavity interface enhances the vorticity near the trailing edge.At the end of the cycle,the break-up of the stable attached cavity is the main reason for the vorticity enhancement near the suction surface.     

A numerical method to simulate turbulent cavitating flows

The objective of this paper is to develop a numerical method for simulating multiphase cavitating flows on unstructured grids. The multiphase medium is represented using a homogeneous mixture model that assumes thermal equilibrium between the liquid and vapor phases. We develop a predictor–corrector approach to solve the governing Navier–Stokes equations for the liquid/vapor mixture, together with the transport equation for the vapor mass fraction. While a non-dissipative and symmetric scheme is used in the predictor step, a novel characteristic-based filtering scheme with a second order TVD filter is developed for the corrector step to handle shocks and material discontinuities in non-ideal gases and mixtures. Additionally, a sensor based on vapor volume fraction is proposed to localize dissipation to the vicinity of discontinuities. The scheme is first validated for simple one dimensional canonical problems to verify its accuracy in predicting jump conditions across material discontinuities and shocks. It is then applied to two turbulent cavitating flow problems – over a hydrofoil using RANS and over a wedge using LES. Our results show that the simulations are in good agreement with experimental data for the above tested cases, and that the scheme can be successfully applied to both RANS and LES methodologies.     

High speed cine observations of cavitating flow in a duct

The dynamics of cavities produced in cavitating flow confined in a duct was studied. The ultimate purpose of the work is to develop models of the flow to assist in predicting cavitation erosion and noise. Observations of the cavitating flow using high speed cine photography allowed confirmation to be made of the shedding mechanism originally described by Knapp, and measurements of the cavity dimensions to be determined as a function of time. It was found that the time for a cavity to collapse was found three times greater than expected from Rayleigh's classical theory.     

Experimental determination of three-dimensional finite-time Lyapunov exponents in multi-component flows

We present an experimental approach for estimating finite-time Lyapunov exponent fields (FTLEs) in three-dimensional multi-component or multi-phase flows. From time-resolved sequences of particle images, we directly compute the flow map and coherent structures, while avoiding and outperforming the computationally costly numerical integration. Performing this operation independently on each flow component enables the determination of three-dimensional Lagrangian coherent structures (LCSs) without any bias from the other components. The locations of concurrent LCSs for different flow elements (e.g., passive tracers, inertial particles, bubbles, or active particles) can provide new insight into the interpenetrating FTLE structure in complex flows.     

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.     

An exact multiphase Riemann solver for compressible cavitating flows

This paper presents a new one-fluid method for simulating formation and the collapse of cavitation regions in water during an isothermal process. In this method, the fluid phase changes are included into the wave pattern of an exact Riemann solver. The model behavior is assessed by comparing the numerical results with the other numerical models for several 1D Riemann problems. One-dimensional water hammer problems with vast creation and collapsing of cavitation zones are simulated as well—and the numerical results are compared to experimental results. The new model results are in very good agreement with accepted results reported in the literature. The presented results clearly show that the new model is able to capture the various behaviors of water during the phase change in the saturation dome and the vapor state, which was neglected in previous studies. Finally, the new model is adopted to an ALE method on an adaptive triangular grid to simulate an underwater explosion phenomenon inside a rigid cylinder—and the results are compared with other simulations.     

A thermodynamically consistent model for cavitating flows of compressible fluids

This work presents a logically consistent thermodynamic model to describe the isothermal cavitation phenomenon in compressible fluid flows. The fluid is regarded as a continuum mixture of liquid and vapor phases (both having the same velocity and temperature), which can or cannot coexist at a same material point and time. The volume fraction is considered as an internal variable and its constraint is treated as a material property, being part of the constitutive relations. Dissipative effects associated with the liquid-vapor phase change transformation and with the vapor volume fraction evolution are taken into account in such a way the Second Law of Thermodynamics is always satisfied. It is shown that the dissipative mechanisms are responsible for a cavitation threshold rule that leads to cavity formation under completely different situations from that characterized by the traditional (reversible) theory. The potentiality of the model as well as its basic features are illustrated and highlighted through a simple numerical example. It is demonstrated that the irreversibility associated with the phase change transformation may be seen as an intermediate case between two physically different non-dissipative situations. One in which the phase change takes place at a constant pressure (the saturated vapor pressure) and the other in which the vapor expands and contracts in the mixture without transforming into liquid.     

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.