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.     

Quasi-static cylindrical cavity expansion in an elastoplastic compressible Mises solid

The self-similar elastoplastic field induced by quasi-static expansion of a pressurized cylindrical cavity is investigated for Mises solids under the assumption of plane-strain. Material behavior is modeled by the elastoplastic J₂ flow theory with the standard hypoelastic version. The theory accounts for elastic-compressibility and allows for arbitrary strain-hardening (or softening) in the plastic range. A formulation of the exact governing equations is presented and analyzed in detail for the remote elastic field and for asymptotic plastic behavior near the cavity wall, along with numerical investigations for the entire deformation zone. An analytical solution was obtained under the axially-hydrostatic assumption (axial stress coincides with hydrostatic stress) within an error of about 2% or less as compared to the exact, numerically evaluated, value of cavitation pressure. Two ad-hoc compressibility approximations for cavitation pressure are suggested. These relations, which give very accurate results, appear to provide tight lower and upper bounds on the exact value of cavitation pressure within an error of less than 0.5%.     

Flow past a plate lattice with developed cavitation

Problems of streamline cavitation flow past a lattice were studied in [1–8] using the Kirchhoff scheme. In this scheme the magnitude of the velocity at the free surface is equal to the stream velocity behind the lattice, and the cavitation number is zero (for a lattice the relative velocity and the cavitation number are defined from the stream velocity behind the lattice). In [4, 7] a solution is given of the problem of flow past a lattice using a scheme with an Efros-Gilbargreturn streamline, which permits considering arbitrary cavitation numbers; however, a unique solution is not given. Some other streamline schemes are mentioned in [8].In the following we consider the cavitational flow of an ideal incompressible inviscid and weightless fluid past an infinite lattice of flat plates, using the streamline wake model previously utilized by Wu [9] in studying cavitational flow past an isolated obstacle. In accordance with this model, the streamlines which separate from the body and bound the cavity behind it pass into two curvilinear infinitely long walls, along which the pressure increases and approaches the pressure in the undisturbed stream.It is further assumed that in the hodograph plane there corresponds to the curvilinear walls a cut along some line and that the complex potential takes the same values at points lying on opposite sides of the cut. In particular, at the points of contact of the streamlines with the curvilinear walls the complex potential is the same. In the Wu scheme the latter condition leads to vanishing of the velocity circulation along the contour CABC₁ (Fig. 1).In conclusion the author wishes to thank N. V. Yurtaeva for the accurately performed numerical work.     

Study of cavitation phenomena based on a technique for visualizing bubbles in a liquid pressurized chamber

In this paper, the influence of nozzle geometry on cavitation and near-nozzle spray behavior under liquid pressurized ambient is studied. For this purpose, eight steel drilled plates, with different diameters and degrees of conicity of their holes, are analyzed. A special near-nozzle field visualization technique, using a test rig pressurized with fuel, is used. Due to the difference in refractive index between liquid and vapor phase, bubbles present at the outlet of the orifice are visualized. The pressure conditions at which bubbles start appearing at the orifice outlet are compared with those at which choked flow appears. The results showed that pressure conditions for inception of cavitation obtained in the visualization tests differs from those seen for choked flow (5–8% in terms of cavitation number). In addition to this, the images taken are analyzed to get the angle of the jet formed by fuel bubbles, showing that it increases significantly for those conditions more prone to cavitate. Furthermore, comparison of bubbles generation when increasing or decreasing backpressure indicates the presence of hysteresis in cavitation inception phenomena.     

Visualisation and les simulation of cavitation cloud formation and collapse in an axisymmetric geometry

Visualisation and Large Eddy Simulations (LES) of cavitation inside the apparatus previously developed by Franc (2011) for surface erosion acceleration tests and material response monitoring are presented. The experimental flow configuration is a steady-state closed loop flow circuit where pressurised water, flowing through a cylindrical feed nozzle, is forced to turn 90° and then, move radially between two flat plates towards the exit of the device. High speed images show that cavitation is forming at the round exit of the feed nozzle. The cavitation cloud then grows in the radial direction until it reaches a maximum distance where it collapses. Due to the complexity of the flow field, direct observation of the flow structures was not possible, however vortex shedding is inferred from relevant simulations performed for the same conditions. Despite the axisymmetric geometry utilized, instantaneous pictures of cavitation indicate variations in the circumferential direction. Image post-processing has been used to characterize in more detail the phenomenon. In particular, the mean cavitation appearance and the cavity length have been estimated, showing good correlation with the erosion zone. This also coincides with the locations of the maximum values of the standard deviation of cavitation presence. The dominant frequency of the ‘large-scale’ cavitation clouds has been estimated through FFT. Cloud collapse frequencies vary almost linearly between 200 and 2000 Hz as function of the cavitation number and the downstream pressure. It seems that the increase of the Reynolds number leads to a reduction of the collapse frequency; it is believed that this effect is due to the agglomeration of vortex cavities, which causes a decrease of the apparent frequency. The results presented here can be utilized for validation of relevant cavitation erosion models which are currently under development.     

Numerical simulation of cavitation effects behind obstacles and in an automotive fuel jet pump

By means of computational fluid dynamics (CFD) this study examines cavitation effects behind obstacles and within an automotive fuel jet pump. Especially with regard to gasoline such effects are serious issues for applications of jet pumps in automotive fuel systems. The cavitation phenomena are captured by a model based on a void region approach within the volume-of-fluid method (VOF) including the k--model of turbulence. A first-order and a second-order scheme are compared, and the potential of the numerical method is evaluated by considering benchmark cases.     

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.     

Time resolved PIV and flow visualization of 3D sheet cavitation

Time-resolved PIV was applied to study fully developed sheet cavitation on a hydrofoil with a spanwise varying angle of attack. The hydrofoil was designed to have a three-dimensional cavitation pattern closely related to propeller cavitation, studied for its adverse effects as vibration, noise, and erosion production. For the PIV measurements, fluorescent tracer particles were applied in combination with an optical filter, in order to remove the reflections of the laser lightsheet by the cavitation. An adaptive mask was developed to find the interface between the vapor and liquid phase. The velocity at the interface of the cavity was found to be very close to the velocity predicted by a simple streamline model. For a visualization of the global flow dynamics, the laser beam was expanded and used to illuminate the entire hydrofoil and cavitation structure. The time-resolved recordings reveal the growth of the attached cavity and the cloud shedding. Our investigation proves the viability of accurate PIV measurements around developed sheet cavitation. The presented results will further be made available as a benchmark for the validation of numerical simulations of this complicated flow.     

Comparison of mass transfer models for the numerical prediction of sheet cavitation around a hydrofoil

Cavitating flows, which can occur in a variety of practical cases, can be modelled with a wide range of methods. One strategy consists of using the RANS (Reynolds Averaged Navier Stokes) equations and an additional transport equation for the liquid volume fraction, where mass transfer rate due to cavitation is modelled by a mass transfer model. In this study, we compare three widespread mass transfer models available in literature for the prediction of sheet cavitation around a hydrofoil. These models share the common feature of employing empirical coefficients, to tune the models of condensation and evaporation processes, that can influence the accuracy and stability of the numerical predictions. In order to compare the different mass transfer models fairly and congruently, the empirical coefficients of the different models are first well tuned using an optimization strategy. The resulting well tuned mass transfer models are then compared considering the flow around the NACA66(MOD) and NACA009 hydrofoils. The numerical predictions based on the three different tuned mass transfer models are very close to each other and in agreement with the experimental data. Moreover, the optimization strategy seems to be stable and accurate, and could be extended to additional mass transfer models and further flow problems.     

An adaptive ALE method for underwater explosion simulations including cavitation

The aim of this paper is to develop a numerical procedure for simulating a simplified mathematical model of underwater explosion phenomena. The Euler set of equations is selected as the governing equations and the ideal gas and Tammann equations of state (EOS) are used to obtain pressure in the gas bubble and the surrounding water zone, respectively. The modified Schmidt EOS is used to simulate the cavitation regions. An arbitrary Lagrangian–Eulerian method is used to integrate the governing equations over an unstructured moving grid. A mesh adapting technique is applied to increase the accuracy as well as for better capturing of flow physics. Moreover, a least-square smoother is employed to moderate the undesirable effects of gas–water interface irregularities. The numerical results verify that the proposed method is capable of predicting complex physics involved in a spherical underwater explosion. The method also shows a very good performance in smoothing the interface while minimizing the loss of mass and momentum in two-dimensional problems.     

On the possibility of shock-induced cavitation in submerged cylindrical shell systems

A circular cylindrical shell loaded by one or two fluids and responding to an external shock wave is analyzed in the context of the possible inception of shock-induced cavitation. Several scenarios of fluid contact are considered including a submerged evacuated shell and a submerged fluid-filled shell for three different combinations of the parameters of the internal and external fluids. A semi-analytical shell-shock interaction model is employed in order to predict the regions of the fluids where cavitation is likely to occur, and the respective cavitation development is hypothesized about. The most interesting and practically important finding is that when fluid is present both inside and outside the shell, there exist conditions when cavitation is expected to occur in both the internal and external fluid, resulting in a particularly complex and violent structural re-loading occurring upon the collapse of the respective cavitation regions. The inception of cavitation in the internal fluid alone and in the external fluid alone is also possible. The findings are summarized in a manner that is suitable for use at the pre-design stage as a guide for preliminary assessment of the possibility of shock-induced cavitation in fluid-interacting industrial systems.     

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.     

基于相变松弛法则的水下爆炸空化模型研究

水下爆炸过程中存在着大量的空化现象,空化的产生、演化及其溃灭过程对于水下冲击波传播、爆炸气泡运动以及水下结构物冲击损伤都会产生重要影响。本文基于多相可压缩流体理论模型,考虑空化发生过程中汽-液两相流体亚平衡状态下两相之间发生的热力学-化学平衡机制,分析汽-液两相介质之间的质量和热量交换,从而实现对相变过程的自动捕捉。该系统的控制方程采用分步法处理,首先利用二阶MUSCL-Hancock格式和HLLC黎曼求解器来求解齐次双曲型方程,再采用牛顿迭代法求解相变方程。数值测试结果表明,本文的计算模型对于空化相变过程具有较好的捕捉能力。最后将该模型应用到水下近水面爆炸空化的数值模拟当中,研究发现空泡的溃灭压力峰值约为冲击波压力峰值的15%,有效作用时间是冲击波载荷有效作用时间的2倍以上。本文的空化相变模型能够为水下爆炸空化现象的机理研究提供重要支撑。     

Capillary cavity flow past a circular cylinder

Cavity flow past a circular cylinder is considered accounting for the surface tension on the cavity boundary. The fluid is assumed to be inviscid and incompressible, and the flow is assumed to be irrotational. The solution is based on two derived governing expressions, which are the complex velocity and the derivative of the complex potential defined in an auxiliary parameter region. An integral equation in the velocity magnitude along the free surface is derived from the dynamic boundary condition. The Brillouin–Villat criterion is employed to determine the location of the point of flow separation. The cases of zero surface tension and zero cavitation number are obtained as limiting cases of the solution. Numerical results concerning the effects of surface tension and cavitation development on the cavity detachment, the drag force and the geometry of the free boundaries are presented over a wide range of the Weber and the cavitation numbers.     

Cavity induced vibration of flexible hydrofoils

The objective of this work is to investigate the influence of cavity-induced vibrations on the dynamic response and stability of a NACA66 hydrofoil at 8° angle of attack at Re=750 000 via combined experimental measurements and numerical simulations. The rectangular, cantilevered hydrofoil is assumed to be rigid in the chordwise direction, while the spanwise bending and twisting deformations are represented using a two-degrees-of-freedom structural model. The multiphase flow is modeled with an incompressible, unsteady Reynolds Averaged Navier–Stokes solver with the k–ω Shear Stress Transport (SST) turbulence closure model, while the phase evolutions are modeled with a mass-transport equation based cavitation model. The numerical predictions are compared with experimental measurements across a range of cavitation numbers for a rigid and a flexible hydrofoil with the same undeformed geometries. The results showed that foil flexibility can lead to: (1) focusing – locking – of the frequency content of the vibrations to the nearest sub-harmonics of the foil׳s wetted natural frequencies, and (2) broadening of the frequency content of the vibrations in the unstable cavitation regime, where amplifications are observed in the sub-harmonics of the foil natural frequencies. Cavitation was also observed to cause frequency modulation, as the fluid density, and hence fluid induced (inertial, damping, and disturbing) forces fluctuated with unsteady cavitation.     

Modeling and computation of cavitation in vortical flow

The paper presents an investigation of Euler–Lagrangian methods for cavitating two-phase flows. The Euler–Euler methods, widely used for simulations of cavitating flows in ship technology, perform well in regions of moderate flow changes but fail in zones of strong, vortical flow. Reasons are the strong approximations of cavitation models in the Euler concept. Alternatively, Euler–Lagrangian concepts enable more detailed formulations for transport, dynamics and acoustic of discrete vapor bubbles. Test calculations are performed to study the influence of different parameters in the equations of motion and in the Rayleigh–Plesset equation for bubble dynamics. Results confirm that only Lagrangian models are able to describe correctly the bubble behavior in vortices, while Eulerian results deviate strongly. Lagrangian formulations enable additionally the determination of acoustic pressure of cavitation noise. Two-way coupling between the phases is required for large regions of the vapor phase. A new coupling concept between continuous fluid flow and discrete bubble phase is developed and demonstrated for flow through a nozzle. However, the iterative coupling between the phases via volume fractions is computationally expensive and should therefore be applied only in regions where Eulerian treatment fails. A corresponding local concept for combination with an Euler–Euler method is outlined and is in progress.     

Method of approximate account for the wall effect in cavitation flow around bodies in water tunnels

One of the basic questions in the study of advanced cavitation in water tunnels of the closed-circuit type is the establishment of the correspondence between the flow patterns observed in the channel and in an unbounded stream. The objective of the study of the wall effect must be the determination of a connection between the basic characteristics of the phenomenon, i. e., the cavitation numbers, the cavity dimensions, the drag coefficients, etc., for the unbounded flow and the channel flow. A large number of works devoted to this question are known [1–7], but in the majority of them only two-dimensional flows are considered. These studies contain either exact solutions obtained with the aid of the apparatus of functions of a complex variable or solutions in the linearized formulation.At the present time there is urgent need to obtain at least approximate solutions for axisymmetric cavitation flows in a tunnel.In several studies [1, 2, 4] it has been shown that in the case of two-dimensional flows the presence of solid boundaries influences the drag coefficient only through the mechanism of a change of the magnitude of the cavitation number, while the variation of the drag coefficient itself with the cavitation number is not changed in comparison with the unbounded flow. It may be assumed that an analogous situation obtains for the axisymmetric case as well. Then the question of the wall effect may be reduced to establishing the connection between the corresponding cavitation numbers.The present paper makes an attempt to establish the correspondence between the cavitation numbers in the unbounded flow and in the tunnel for which the cavities behind the same body have the same areas of the maximal cross section.     

Modeling of turbulent, isothermal and cryogenic cavitation under attached conditions

Cavitation is often triggered when the fluid pres- sure is lower than the vapor pressure at a local thermo- dynamic state. The present article reviews recent progress made toward developing modeling and computational strat- egies for cavitation predictions under both isothermal and cryogenic conditions, with an emphasis on the attached cav- ity. The review considers alternative cavitation models along Reynolds-averaged Navier-Stokes and very lager eddy simu- lation turbulence approaches to ensure that the computational tools can handle flows of engineering interests. Observing the substantial uncertainties associated with both modeling and experimental information, surrogate modeling strategies are reviewed to assess the implications and relative impor- tance of the various modeling and materials parameters. The exchange between static and dynamic pressures under the influence of the viscous effects can have a noticeable impact on the effective shape of a solid object, which can impact the cavitation structure. The thermal effect with respect to evaporation and condensation dynamics is examined to shed light on the fluid physics associated with cryogenic cav- itation. The surrogate modeling techniques are highlighted in the context of modeling sensitivity assessment. Keywords