Статті в журналах: "Cavitating Flows"

1

Wang, Hao, Jian Feng, Keyang Liu, Xi Shen, Bin Xu, Desheng Zhang, and Weibin Zhang. "Experimental Study on Unsteady Cavitating Flow and Its Instability in Liquid Rocket Engine Inducer." Journal of Marine Science and Engineering 10, no. 6 (June 12, 2022): 806. http://dx.doi.org/10.3390/jmse10060806.

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To study instability in the unsteady cavitating flow in a liquid rocket engine inducer, visualization experiments of non-cavitating and cavitating flows inside a model inducer were carried out at different flow conditions. Visual experiments were carried out to capture the evolution of non-cavitating and cavitating flows in a three-bladed inducer by using a high-speed camera. The external characteristic performance, cavitation performance, and pressure pulsation were analyzed based on the observation of non-cavitation and cavitation development and their instabilities. Under non-cavitation conditions, the change of flow rate has a significant impact on the pressure pulsation characteristics in the inducer. The occurrence of cavitation aggravated the instability of the flow and caused the intensity of pressure pulsation at each measuring point to increase. This cavitation structure has strong instability, and the tail region is often accompanied by shedding cavitation clouds perpendicular to the blade surface.

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2

ZHANG, YAO, XIANWU LUO, SHUHONG LIU, and HONGYUAN XU. "A TRANSPORT EQUATION MODEL FOR SIMULATING CAVITATION FLOWS IN MINIATURE MACHINES." Modern Physics Letters B 24, no. 13 (May 30, 2010): 1467–70. http://dx.doi.org/10.1142/s0217984910023888.

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A new transport equation model is proposed for simulating cavitating flows in miniature machines. In the developed model, the surface tension, viscous force, and thermal effect of cavitation are considered to reflect their influence on the cavitation bubble growth. The cavitating flow in a miniature pump is calculated by applying the proposed cavitation model. The comparison between numerical results and experimental data indicates that the new cavitation model is applicable for simulating the cavitating flow in miniature machines.

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3

Ng’aru, Joseph Mwangi, and Sunho Park. "CFD Simulations of the Effect of Equalizing Duct Configurations on Cavitating Flow around a Propeller." Journal of Marine Science and Engineering 10, no. 12 (December 2, 2022): 1865. http://dx.doi.org/10.3390/jmse10121865.

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This study presented the results of a computational study of cavitating flows of a marine propeller with energy saving equalizing ducts. The main purpose of the study was to estimate the cavitating flows around a propeller with a duct, and to investigate the interaction between a duct and a propeller in cavitating flows. The INSEAN E779A propeller was used as a baseline model. Validation studies were conducted for non-cavitating and cavitating flows around a hydrofoil and a propeller. A comparison with the experimental data showed good agreement in terms of sheet cavity patterns and propulsion performances of the propeller. Various duct configurations have been presented, and it was found that a duct in front of the propeller had effects on the propeller’s cavitation and propulsion performance. Higher angles of attack of the duct showed a significant effect on the propeller’s cavitation behavior, especially with a small duct. The small duct lowered the cavitation inception radius with increase in angle of attack of the duct, while the large duct had more effect on the tip cavitation. The propeller with large duct gave higher thrust, however, the higher torque loading affected the propeller efficiency. Overall, it was found that the propeller with small duct provided a higher propeller efficiency

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4

Falcucci, Giacomo, Stefano Ubertini, Gino Bella, and Sauro Succi. "Lattice Boltzmann Simulation of Cavitating Flows." Communications in Computational Physics 13, no. 3 (March 2013): 685–95. http://dx.doi.org/10.4208/cicp.291011.270112s.

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AbstractThe onset of cavitating conditions inside the nozzle of liquid injectors is known to play a major role on spray characteristics, especially on jet penetration and break-up. In this work, we present a Direct Numerical Simulation (DNS) based on the Lattice Boltzmann Method (LBM) to study the fluid dynamic field inside the nozzle of a cavitating injector. The formation of the cavitating region is determined via a multi-phase approach based on the Shan-Chen equation of state. The results obtained by the LBM simulation show satisfactory agreement with both numerical and experimental data. In addition, numerical evidence of bubble break-up, following upon flow-induced cavitation, is also reported.

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5

Zhai, Zhangming, Tairan Chen, and Haiyang Li. "Evaluation of mass transport cavitation models for unsteady cavitating flows." Modern Physics Letters B 34, no. 02 (December 6, 2019): 2050020. http://dx.doi.org/10.1142/s0217984920500207.

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Modeling of unsteady cavitating flow is a critical issue in a lot of practical cases. The objective of this paper is to assess the practical applicability of three widely used mass transport cavitation models under RANS framework, including the Kubota model, Kunz model, and Singhal model, for predicting partial sheet cavitating flow around an axisymmetric body with hemispherical head and unsteady cloud cavitating flow around a Clark-Y hydrofoil. The results show that for the axisymmetric cylindrical body, all three cavitation models could generally predict the pressure distributions. The significant differences are found around the closure region of the attached cavity due to the magnitude and distribution of mass transfer rate. For the unsteady cavitating flow along the hydrofoil, the significant differences with different cavitation model are observed in time-averaged and time-dependent concerning the cavity shapes, multiphase structures and the cloud shedding dynamics. The Singhal model coupling the effect between the vorticity distribution and the cavity dynamics agrees best with the experimental measurements.

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6

Liu, Qian Kun, and Ye Gao. "Numerical Simulation of Natural Cavitating Flow over Axisymmetric Bodies." Applied Mechanics and Materials 226-228 (November 2012): 825–30. http://dx.doi.org/10.4028/www.scientific.net/amm.226-228.825.

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The hydrodynamic characteristics of bodies are greatly affected by cavitation. Coupling with natural cavitaion model, a multiphase CFD method is developed and is employed to simulate supercavitating and partial cavitating flows over axisymmetric bodies using FLUENT 6.2. The results of supercavitation of a disk cavitator agree well with the boundary element method (BEM), the analytical relations and available experimental results. The present computations and the BEM results are compared with experiments for partial cavitating flows over three typical axisymmetric bodies and the results are discussed. Limitations are on the pressure prediction in the cavity closure region for the BEM, although fairly good quantitative agreement is obtained for three axisymmetric bodies at most of cavitation region. The present computational model on cavitating flows are validated, offering references and bases for hydrodynamic researches.

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7

DELALE, C. F., G. H. SCHNERR, and J. SAUER. "Quasi-one-dimensional steady-state cavitating nozzle flows." Journal of Fluid Mechanics 427 (January 25, 2001): 167–204. http://dx.doi.org/10.1017/s0022112000002330.

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Quasi-one-dimensional cavitating nozzle flows are considered by employing a homogeneous bubbly liquid flow model. The nonlinear dynamics of cavitating bubbles is described by a modified Rayleigh–Plesset equation that takes into account bubble/bubble interactions by a local homogeneous mean-field theory and the various damping mechanisms by a damping coefficient, lumping them together in the form of viscous dissipation. The resulting system of quasi-one-dimensional cavitating nozzle flow equations is then uncoupled leading to a nonlinear third-order ordinary differential equation for the flow speed. This equation is then cast into a nonlinear dynamical system of scaled variables which describe deviations of the flow field from its corresponding incompressible single-phase value. The solution of the initial-value problem of this dynamical system can be carried out very accurately, leading to an exact description of the hydrodynamic field for the model considered.A bubbly liquid composed of water vapour–air bubbles in water at 20 °C for two different area variations is considered, and the initial cavitation number is chosen in such a way that cavitation can occur in the nozzle. Results obtained, when bubble/bubble interactions are neglected, show solutions with flow instabilities, similar to the flashing flow solutions found recently by Wang and Brennen. Stable steady-state cavitating nozzle flow solutions, either with continuous growth of bubbles or with growth followed by collapse of bubbles, were obtained when bubble/bubble interactions were considered together with various damping mechanisms.

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8

Luo, Xianwu, Renfang Huang та Bin Ji. "Transient cavitating vortical flows around a hydrofoil using k-ω partially averaged Navier–Stokes model". Modern Physics Letters B 30, № 01 (10 січня 2016): 1550262. http://dx.doi.org/10.1142/s0217984915502620.

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For accurate simulations of wall-bounded turbulent cavitating flows, the present paper proposed a partially averaged Navier–Stokes (PANS) method derived from the [Formula: see text]-[Formula: see text] turbulence model. Transient cavitating vortical flows around a NACA66 hydrofoil were simulated by using the [Formula: see text]-[Formula: see text] PANS model with various filter parameters ([Formula: see text] and [Formula: see text], while [Formula: see text]) and a mass transfer cavitation model based on the Rayleigh–Plesset equation. Compared with the available experimental data, the [Formula: see text]-[Formula: see text] PANS model with [Formula: see text] can accurately reproduce the cavitation evolution with more complicated structures due to the reduction in the predicted eddy viscosity. Further analyses, using the vorticity transport equation, indicate that the transition of cavitation structure from two dimension to three dimension is associated with strong vortex–cavitation interaction, where vortex stretching and dilation may play a major role. Therefore, the [Formula: see text]-[Formula: see text] PANS model with the filter parameter of [Formula: see text] is an effective method to numerically predict the transient cavitating vortical flows around hydrofoils. The results obtained in this paper are helpful to provide a physical insight into the mechanisms of cavitation shedding dynamics.

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9

Gevari, Moein Talebian, Ayhan Parlar, Milad Torabfam, Ali Koşar, Meral Yüce, and Morteza Ghorbani. "Influence of Fluid Properties on Intensity of Hydrodynamic Cavitation and Deactivation of Salmonella typhimurium." Processes 8, no. 3 (March 10, 2020): 326. http://dx.doi.org/10.3390/pr8030326.

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In this study, three microfluidic devices with different geometries are fabricated on silicon and are bonded to glass to withstand high-pressure fluid flows in order to observe bacteria deactivation effects of micro cavitating flows. The general geometry of the devices was a micro orifice with macroscopic wall roughness elements. The width of the microchannel and geometry of the roughness elements were varied in the devices. First, the thermophysical property effect (with deionized water and phosphate-buffered saline (PBS)) on flow behavior was revealed. The results showed a better performance of the device in terms of cavitation generation and intensity with PBS due to its higher density, higher saturation vapor pressure, and lower surface tension in comparison with water. Moreover, the second and third microfluidic devices were tested with water and Salmonella typhimurium bacteria suspension in PBS. Accordingly, the presence of the bacteria intensified cavitating flows. As a result, both devices performed better in terms of the intensity of cavitating flow with the presence of bacteria. Finally, the deactivation performance was assessed. A decrease in the bacteria colonies on the agar plate was detected upon the tenth cycle of cavitating flows, while a complete deactivation was achieved after the fifteenth cycle. Thus, the proposed devices can be considered as reliable hydrodynamic cavitation reactors for “water treatment on chip” applications.

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10

Orekhov, Genrikh. "Cavitation in swirling flows of hydraulic spillways." E3S Web of Conferences 91 (2019): 07022. http://dx.doi.org/10.1051/e3sconf/20199107022.

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During operation of high-head hydraulic spillway systems, cavitation phenomena often occur, leading to destruction of structural elements of their flow conductor portions. The article is devoted to the study of erosion due to cavitation in the circulation flows of eddy hydraulic spillways, including those equipped with counter-vortex flow energy dissipators. Cavitation destructive effects depend on many factors: intensity consisting in the rate of decrease in the volume or mass of a cavitating body per unit of time, the stage of cavitation, geometric configuration of the streamlined body, the content of air in water, the flow rate, the type of material. The objective of the study consisted in determination of cavitation impacts in circulating (swirling) water flows. The studies were conducted by a method of physical modeling using high-head research installations. Distribution of amplitudes of pulses of shock cavitation impact is obtained according to the frequency of their occurrence depending on the flow velocity, the swirl angle, the height of the cavitating drop wall and the stage of cavitation. The impact energy depending on the stage of cavitation and the flow rate is given for different operating modes of the counter-vortex flow energy dissipators of a hydraulic spillway. In the conclusions, it is noted that cavitation impacts in the circulation flows occur mainly inside the flow, which is a fundamental difference from similar processes in axial flows.

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11

Huang, D. G., and Y. Q. Zhuang. "Temperature and cavitation." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 222, no. 2 (February 1, 2008): 207–11. http://dx.doi.org/10.1243/09544062jmes815.

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Pressure, density, and temperature are the fundamental thermodynamic parameters. In a liquid flow field, once the local pressure drops to the saturated pressure, the liquid vapourizes and local cavitation occurs. The cavitation region of the flow is characterized by a mixture of liquid and vapour. Vapourization is an endothermic process. However, in the literature of the past several decades, this vapourization induced thermal effect was sometimes ignored in cavitating flows, and the temperature was always assumed as a constant in the whole flow field. In order to gain a deep insight into the mechanism of cavitation, temperature effects of cavitation are hereby investigated in this paper. An appreciable temperature drop has been found when cavitation occurs, which suggests that thermal effects in cavitating flows from the view of thermodynamics may be of great value to understand the mechanism of cavitation.

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12

Zhang, Kai, Zhiyong Dong, and Meixia Shi. "Turbulence Characteristics of Cavitating Flows Downstream of Triangular Multiorifice Plates." Advances in Mathematical Physics 2022 (July 4, 2022): 1–6. http://dx.doi.org/10.1155/2022/8100937.

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Cavitating flow fields downstream of triangular multiorifice plates with different geometrical parameters were measured by PIV technique, and effects of orifice size, orifice number, and orifice layout on turbulence intensity and Reynolds stress were analyzed. The experimental results showed that the turbulence intensity and Reynolds stress downstream of the different multiorifice plates exhibited sawtooth-like profiles. Decrease in orifice size, increase in orifice number, and taking staggered layout could contribute to intensification of turbulence mixing and shear effects of multiple cavitating jets downstream of the multiorifice plates and thus reaching the expected cavitation effects.

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13

Xu, Changhai, Stephen D. Heister, and Robert Field. "Modeling Cavitating Venturi Flows." Journal of Propulsion and Power 18, no. 6 (November 2002): 1227–34. http://dx.doi.org/10.2514/2.6057.

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14

Delale, Can F., Kohei Okita, and Yoichiro Matsumoto. "Steady-State Cavitating Nozzle Flows With Nucleation." Journal of Fluids Engineering 127, no. 4 (April 2, 2005): 770–77. http://dx.doi.org/10.1115/1.1949643.

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Quasi-one-dimensional steady-state cavitating nozzle flows with homogeneous bubble nucleation and nonlinear bubble dynamics are considered using a continuum bubbly liquid flow model. The onset of cavitation is modeled using an improved version of the classical theory of homogeneous nucleation, and the nonlinear dynamics of cavitating bubbles is described by the classical Rayleigh-Plesset equation. Using a polytropic law for the partial gas pressure within the bubble and accounting for the classical damping mechanisms, in a crude manner, by an effective viscosity, stable steady-state solutions with stationary shock waves as well as unstable flashing flow solutions were obtained, similar to the homogeneous bubbly flow solutions given by Wang and Brennen [J. Fluids Eng., 120, 166–170, 1998] and by Delale, Schnerr, and Sauer [J. Fluid Mech., 427, 167–204, 2001]. In particular, reductions in the maximum bubble radius and bubble collapse periods are observed for stable nucleating nozzle flows as compared to the nonnucleating stable solution of Wang and Brennen under similar conditions.

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15

Tian, Chunlai, Tairan Chen, and Tian Zou. "Numerical study of unsteady cavitating flows with RANS and DES models." Modern Physics Letters B 33, no. 20 (July 18, 2019): 1950228. http://dx.doi.org/10.1142/s0217984919502282.

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Unsteady cavitating flow with high Reynolds number and significant instability commonly exists in fluid machinery and engineering system. The high-resolution approaches, such as direct numerical simulation and large eddy simulation, are not practical for engineering issues due to the significant cost in the computational resource. The objective of this paper is to provide the approach with Detached-Eddy Simulation (DES) model based on the Reynolds-averaged Navier–Stokes (RANS) equations for predicting unsteady cavitating flows. The credibility of the approach is validated by a set of numerical examples of its application: the unsteady cavitating flows around the two-dimensional (2D) Clark-Y hydrofoil and the three-dimensional (3D) blunt body. It is found that the calculated cavity shapes, cavity lengths and unsteady characteristics by DES model agree well with the experimental measurements and observations. Further analysis indicates that the turbulent eddy viscosity around the cavity and wake region is well predicted by the DES model, which results in the development of large-scale vortexes, and further cavitation instability. The DES model, which exhibits a significantly unsteady 3D behavior, is a more comprehensive turbulence model for unsteady cavitating flows.

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16

Coutier-Delgosha, O., P. Morel, R. Fortes-Patella, and JL Reboud. "Numerical Simulation of Turbopump Inducer Cavitating Behavior." International Journal of Rotating Machinery 2005, no. 2 (2005): 135–42. http://dx.doi.org/10.1155/ijrm.2005.135.

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In the present study a numerical model of 3D cavitating flows is proposed. It is applied to investigate the behavior of a spatial turbopump inducer in noncavitating and cavitating conditions. Experimental and numerical results concerning inducer characteristics and performance breakdown are compared at different flow conditions. The cavitation development and the spatial distribution of vapor structures within the inducer are also analyzed. The results show the ability of the code to simulate the quasi-steady cavitating behavior of such a complex geometry. Discrepancies concerning the breakdown prediction are also discussed.

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17

Nouri, N. M., S. M. H. Mirsaeedi, and M. Moghimi. "Large eddy simulation of natural cavitating flows in Venturi-type sections." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 225, no. 2 (June 23, 2010): 369–81. http://dx.doi.org/10.1243/09544062jmes2036.

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Large eddy simulation (LES) is used here to model the cavitating flow at a Venturi-type section. Cavitating flows can occur in a wide range of applications. The flow is represented here by means of LES, which compared to Reynolds-averaged Navier—Stokes (RANS) has the advantage that in it the large, energy-containing structures are resolved directly, whereas most of these structures are modelled in RANS. This gives LES an improved fidelity over RANS, although, due to the time averaging, the required computational time is considerably lower for RANS than for LES. The conclusion of this work shows that the qualitative comparisons with earlier preliminary data and the simulated general cavitation behaviour correlate reasonably well with experimental observations and that the simulations have the ability to predict cavitation cycle in more detail.

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18

Zhao, Yu, Guoyu Wang, and Biao Huang. "A cavitation model for computations of unsteady cavitating flows." Acta Mechanica Sinica 32, no. 2 (August 14, 2015): 273–83. http://dx.doi.org/10.1007/s10409-015-0455-0.

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19

Zhao, Yu, Yutong Jiang, Xiaolong Cao, and Guoyu Wang. "Study on tip leakage vortex cavitating flows using a visualization method." Modern Physics Letters B 32, no. 01 (January 10, 2018): 1850003. http://dx.doi.org/10.1142/s0217984918500033.

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Experimental investigations of unsteady cavitating flows in a hydrofoil tip leakage region with different gap sizes are conducted to highlight the development of gap cavitation. The experiments were taken in a closed cavitation tunnel, during which high-speed camera had been used to capture the cavitation patterns. A new visualization method based on image processing was developed to capture time-dependent cavitation patterns. The results show that the visualization method can effectively capture the cavitation patterns in the tip region, including both the attached cavity in the gap and the tip leakage vortex (TLV) cavity near the trailing edge. Moreover, with the decrease of cavitation number, the TLV cavity develops from a rapid onset-growth-collapse process to a continuous process, and extends both upstream and downstream. The attached cavity in the gap develops gradually stretching beyond the gap and combines with the vortex cavity to form the triangle cavitating region. Furthermore, the influences of gap size on the cavitation are also discussed. The gap size has a great influence on the loss across the gap, and hence the locations of the inception attached cavity. Besides, inception locations and extending direction of the TLV cavity with different gap sizes also differ. The TLV in the case with [Formula: see text] = 0.061 is more likely to be jet-like compared with that in the case with [Formula: see text] = 0.024, and the gap size has a great influence on the TLV strength.

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20

Bunnell, R. A., and S. D. Heister. "Three-Dimensional Unsteady Simulation of Cavitating Flows in Injector Passages." Journal of Fluids Engineering 122, no. 4 (July 11, 1999): 791–97. http://dx.doi.org/10.1115/1.1315590.

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Fully 3-D, unsteady, viscous simulations are performed on a plain-orifice pressure atomizer being fed by a manifold with a crossflow. This geometry replicates features present in both liquid rocket and diesel engine injectors. Both noncavitating and cavitating conditions are considered to determine the role of cavitation on the orifice discharge characteristics. The presence of cavitation is shown to affect both the mean and unsteady components of the orifice discharge coefficient. The presence of a significant cavitation zone can inhibit vorticity transport causing nearly all the fluid to be ejected through a crescent-shaped sector of the orifice exit plane. [S0098-2202(00)01604-7]

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21

Wang, Yi-Chun. "Stability Analysis of One-Dimensional Steady Cavitating Nozzle Flows With Bubble Size Distribution." Journal of Fluids Engineering 122, no. 2 (December 20, 1999): 425–30. http://dx.doi.org/10.1115/1.483273.

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A continuum bubbly mixture model coupled to the Rayleigh-Plesset equation for the bubble dynamics is employed to study one-dimensional steady bubbly cavitating flows through a converging-diverging nozzle. A distribution of nuclei sizes is specified upstream of the nozzle, and the upstream cavitation number and nozzle contraction are chosen so that cavitation occurs in the flow. The computational results show very strong interactions between cavitating bubbles and the flow. The bubble size distribution may have significant effects on the flow; it is shown that it reduces the level of fluctuations and therefore reduces the “cavitation loss” compared to a monodisperse distribution. Another interesting interaction effect is that flashing instability occurs as the flow reaches a critical state downstream of the nozzle. A stability analysis is proposed to predict the critical flow variables. Excellent agreement is obtained between the analytical and numerical results for flows of both equal bubble size and multiple bubble sizes. [S0098-2202(00)00702-1]

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22

LEGER, A. TASSIN, and S. L. CECCIO. "Examination of the flow near the leading edge of attached cavitation. Part 1. Detachment of two-dimensional and axisymmetric cavities." Journal of Fluid Mechanics 376 (December 10, 1998): 61–90. http://dx.doi.org/10.1017/s0022112098002766.

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The flow near the cavity detachment region of stable attached cavitation was examined using qualitative and quantitative flow visualization. The non-cavitating and cavitating flows around a hydrophilic brass and hydrophobic Teflon sphere and cylinder were examined. The location of non-cavitating boundary layer separation and cavity detachment was related to the free-stream Reynolds and cavitation numbers. The shape of the cavity near the detachment was greatly affected by the material of the cavitating object. The cavity interface on the hydrophilic test objects curved downstream to form a forward facing step. A region of recirculating fluid existed upstream of the cavity interface. The cavity detachment on the hydrophobic test objects was much closer to the location of boundary layer separation. The forward facing step and the recirculating region were nearly absent.The measured flow field near the surface of the brass sphere, cylinder, and hydrofoils under cavitating and non-cavitating conditions was used to calculate the position of two-dimensional laminar boundary layer separation. Thwaites' and Stratford's methods were used to predict the location of boundary layer separation upstream of the cavity detachment. The predictions compared well with the observed position of separation.

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23

Han, Chengzao, Yun Long, Mohan Xu, and Bin Ji. "Verification and Validation of Large Eddy Simulation for Tip Clearance Vortex Cavitating Flow in a Waterjet Pump." Energies 14, no. 22 (November 15, 2021): 7635. http://dx.doi.org/10.3390/en14227635.

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In this paper, large eddy simulation (LES) was adopted to simulate the cavitating flow in a waterjet pump with emphasis on the tip clearance flow. The numerical results agree well with the experimental observations, which indicates that the LES method can make good predictions of the unsteady cavitating flows around a rotor blade. The LES verification and validation (LES V&V) analysis was used to reveal the influence of cavitation on the flow structures. It can be found that the LES errors in cavitating region are larger than those in the non-cavitating area, which is mainly caused by more complicated cavitating and tip clearance flow structures. Further analysis of the interaction between the cavitating and vortex flow by the relative vorticity transport equation shows that the stretching, dilatation and baroclinic torque terms have major effects on the generation and transport of vortex structure. Meanwhile the Coriolis force term and viscosity term also exacerbate the vorticity transport in the cavitating region. In addition, the flow loss characteristics of this pump are also revealed by the entropy production theory. It is indicated that the tip clearance flow and trailing edge wake flow cause the viscous dissipation and turbulent dissipation, and the cavitation can further enhance the instability of the flow field in the tip clearance.

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24

Coutier-Delgosha, O., R. Fortes-Patella, J. L. Reboud, M. Hofmann, and B. Stoffel. "Experimental and Numerical Studies in a Centrifugal Pump With Two-Dimensional Curved Blades in Cavitating Condition." Journal of Fluids Engineering 125, no. 6 (November 1, 2003): 970–78. http://dx.doi.org/10.1115/1.1596238.

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In the presented study a special test pump with two-dimensional curvature blade geometry was investigated in cavitating and noncavitating conditions using different experimental techniques and a three-dimensional numerical model implemented to study cavitating flows. Experimental and numerical results concerning pump characteristics and performance breakdown were compared at different flow conditions. Appearing types of cavitation and the spatial distribution of vapor structures within the impeller were also analyzed. These results show the ability of the model to simulate the complex three-dimensional development of cavitation in a rotating machinery, and the associated effects on the performance.

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25

Kang, Wenzhe, Lingjiu Zhou, Dianhai Liu, and Zhengwei Wang. "Backflow effects on mass flow gain factor in a centrifugal pump." Science Progress 104, no. 2 (April 2021): 003685042199886. http://dx.doi.org/10.1177/0036850421998865.

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Previous researches has shown that inlet backflow may occur in a centrifugal pump when running at low-flow-rate conditions and have nonnegligible effects on cavitation behaviors (e.g. mass flow gain factor) and cavitation stability (e.g. cavitation surge). To analyze the influences of backflow in impeller inlet, comparative studies of cavitating flows are carried out for two typical centrifugal pumps. A series of computational fluid dynamics (CFD) simulations were carried out for the cavitating flows in two pumps, based on the RANS (Reynolds-Averaged Naiver-Stokes) solver with the turbulence model of k- ω shear stress transport and homogeneous multiphase model. The cavity volume in Pump A (with less reversed flow in impeller inlet) decreases with the decreasing of flow rate, while the cavity volume in Pump B (with obvious inlet backflow) reach the minimum values at δ = 0.1285 and then increase as the flow rate decreases. For Pump A, the mass flow gain factors are negative and the absolute values increase with the decrease of cavitation number for all calculation conditions. For Pump B, the mass flow gain factors are negative for most conditions but positive for some conditions with low flow rate coefficients and low cavitation numbers, reaching the minimum value at condition of σ = 0.151 for most cases. The development of backflow in impeller inlet is found to be the essential reason for the great differences. For Pump B, the strong shearing between backflow and main flow lead to the cavitation in inlet tube. The cavity volume in the impeller decreases while that in the inlet tube increases with the decreasing of flow rate, which make the total cavity volume reaches the minimum value at δ = 0.1285 and then the mass flow gain factor become positive. Through the transient calculations for cavitating flows in two pumps, low-frequency fluctuations of pressure and flow rate are found in Pump B at some off-designed conditions (e.g. δ = 0.107, σ = 0.195). The relations among inlet pressure, inlet flow rate, cavity volume, and backflow are analyzed in detail to understand the periodic evolution of low-frequency fluctuations. Backflow is found to be the main reason which cause the positive value of mass flow gain factor at low-flow-rate conditions. Through the transient simulations of cavitating flow, backflow is considered as an important aspect closely related to the hydraulic stability of cavitating pumping system.

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26

Vaidyanathan, Rajkumar, Inanc Senocak, Jiongyang Wu, and Wei Shyy. "Sensitivity Evaluation of a Transport-Based Turbulent Cavitation Model." Journal of Fluids Engineering 125, no. 3 (May 1, 2003): 447–58. http://dx.doi.org/10.1115/1.1566048.

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A sensitivity analysis is done for turbulent cavitating flows using a pressure-based Navier-Stokes solver coupled with a phase volume fraction transport model and nonequilibrium k-ε turbulence closure. Four modeling parameters are assessed, namely, Cε1 and Cε2, which directly influence the production and destruction of the dissipation of turbulence kinetic energy, and Cdest and Cprod, which regulate the evaporation and condensation of the phases. Response surface methodology along with design of experiments is used for the sensitivity studies. The difference between the computational and experimental results is used to judge the model fidelity. Under noncavitating conditions, the best selections of Cε1 and Cε2 exhibit a linear combination with multiple optima. Using this information, cavitating flows around an axisymmetric geometry with a hemispherical fore-body and the NACA66(MOD) foil section are assessed. Analysis of the cavitating model has identified favorable combinations of Cdest and Cprod. The selected model parameters are found to work well for different geometries with different cavitation numbers for attached cavity. It is also confirmed that the cavitation model parameters employed in the literature are within the range identified in the present study.

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27

WANG, GUOYU, BIAO HUANG та BO ZHANG. "k-ε-BASED TURBULENCE MODELS FOR SIMULATION OF CLOUD CAVITATING FLOWS". Modern Physics Letters B 24, № 13 (30 травня 2010): 1357–60. http://dx.doi.org/10.1142/s021798491002361x.

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Cavitating flows around a hydrofoil are simulated in this work by using a transport equation-based model. It is shown that the original Launder-Spalding k-ε model significantly over-predicts the viscosities. The viscosity-corrected models can simulate better the cavitation characteristics including the shedding process.

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28

Bałdyga, Jerzy, Łukasz Makowski, Wojciech Orciuch, Caroline Sauter, and Heike P. Schuchmann. "Agglomerate dispersion in cavitating flows." Chemical Engineering Research and Design 87, no. 4 (April 2009): 474–84. http://dx.doi.org/10.1016/j.cherd.2008.12.015.

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29

Zhao, Yu, Guoyu Wang, and Biao Huang. "A curvature correction turbulent model for computations of cloud cavitating flows." Engineering Computations 33, no. 1 (March 7, 2016): 202–16. http://dx.doi.org/10.1108/ec-01-2015-0026.

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Purpose – The purpose of this paper is to assess the predictive capability of the streamline curvature correction model (CCM) and investigate the unsteady vortex behavior of the cloud cavitating flows around a hydrofoil. Design/methodology/approach – The design of the paper is based on introducing the curvature correction method to the original k-ε model. Calculations of unsteady cloud cavitating flows around a Clark-Y hydrofoil are performed using both the CCM and the baseline model. Findings – Compared with the baseline model, better agreements are observed between the predictions of the CCM model and experimental data, especially the cavity shedding process. Based on the computations, it is demonstrated that streamline curvature correction of the CCM model can effectively decrease predicted turbulence kinetic energy and eddy viscosity in cavity shedding region. This leads to the better prediction for the recirculation zone located downstream of the attached cavity, and dynamics of this recirculation zone contribute to the formation and development of the re-entrant jet. Originality/value – The authors apply streamline curvature correction to the calculations of unsteady cloud cavitating flows and discuss the interactions between the cavitation unsteadiness and vortex structures to get an insight of the correction mechanics.

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30

Kumar, Aishvarya, Ali Ghobadian, and Jamshid M. Nouri. "Assessment of Cavitation Models for Compressible Flows Inside a Nozzle." Fluids 5, no. 3 (August 13, 2020): 134. http://dx.doi.org/10.3390/fluids5030134.

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This study assessed two cavitation models for compressible cavitating flows within a single hole nozzle. The models evaluated were SS (Schnerr and Sauer) and ZGB (Zwart-Gerber-Belamri) using realizable k-epsilon turbulent model, which was found to be the most appropriate model to use for this flow. The liquid compressibility was modeled using the Tait equation, and the vapor compressibility was modeled using the ideal gas law. Compressible flow simulation results showed that the SS model failed to capture the flow physics with a weak agreement with experimental data, while the ZGB model predicted the flow much better. Modeling vapor compressibility improved the distribution of the cavitating vapor across the nozzle with an increase in vapor volume compared to that of the incompressible assumption, particularly in the core region which resulted in a much better quantitative and qualitative agreement with the experimental data. The results also showed the prediction of a normal shockwave downstream of the cavitation region where the local flow transforms from supersonic to subsonic because of an increase in the local pressure.

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31

KANFOUDI, HATEM, and RIDHA ZGOLLI. "A NUMERICAL MODEL TO SIMULATE THE CAVITATING FLOWS." International Journal of Modeling, Simulation, and Scientific Computing 02, no. 03 (September 2011): 277–97. http://dx.doi.org/10.1142/s1793962311000505.

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The object of this paper is to propose a model to simulate steady and unsteady cavitating flows. In the engineering practice, cavitation flow is often modeled as a single-phase flow (mixture), where the cavitation area is handled as an area with the pressure lower than the vapor pressure. This approach always leads to the result, and the requirement of computer time is many times lower in comparison with multiphase flow models. The Reynolds-averaged Navier–Stokes equations are solved for the mixture of liquid and vapor, which is considered as a single-phase with variable density. The vaporization and condensation processes are controlled by barocline low. A transport equation with source terms is implanted in the code Computational Fluid Dynamics (CFD) to compute the volume fraction of the vapor. The CFD code used is ANSYS CFX. The influence of numerical and the physical parameters are presented. The numerical results are compared to previous experimental measures. For steady flow, a SST turbulence model is adopted and LES for the unsteady flow.

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32

Hong, Feng, Jianping Yuan, Banglun Zhou, and Zhong Li. "Modeling of unsteady structure of sheet/cloud cavitation around a two-dimensional stationary hydrofoil." Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering 231, no. 3 (October 7, 2015): 455–69. http://dx.doi.org/10.1177/0954408915607390.

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Compared to non-cavitating flow, cavitating flow is much complex owing to the numerical difficulties caused by cavity generation and collapse. In the present work, cavitating flow around a two-dimensional Clark-Y hydrofoil is studied numerically with particular emphasis on understanding the cavitation structures and the shedding dynamics. A cavitation model, coupled with the mixture multi-phase approach, and the modified shear stress transport k-ω turbulence model has been developed and implemented in this study to calculate the pressure, velocity, and vapor volume fraction of the hydrofoil. The cavitation model has been implemented in ANSYS FLUENT platform. The hydrofoil has a fixed angle of attack of α = 8° with a Reynolds number of Re = 7.5 × 105. Simulations have been carried out for various cavitation numbers ranging from non-cavitating flows to the cloud cavitation regime. In particular, we compared the lift and drag coefficients, the cavitation dynamics, and the time-averaged velocity with available experimental data. The comparisons between the numerical and experimental results show that the present numerical method is capable to predict the formation, breakup, shedding, and collapse of the sheet/cloud cavity. The periodical formation, shedding, and collapse of sheet/cloud cavity lead to substantial increase in turbulent velocity fluctuations in the cavitation regimes around the hydrofoil and in the wake flow.

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33

Niedźwiedzka, Agnieszka, Günter H. Schnerr, and Wojciech Sobieski. "Review of numerical models of cavitating flows with the use of the homogeneous approach." Archives of Thermodynamics 37, no. 2 (June 1, 2016): 71–88. http://dx.doi.org/10.1515/aoter-2016-0013.

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Abstract The focus of research works on cavitation has changed since the 1960s; the behaviour of a single bubble is no more the area of interest for most scientists. Its place was taken by the cavitating flow considered as a whole. Many numerical models of cavitating flows came into being within the space of the last fifty years. They can be divided into two groups: multi-fluid and homogeneous (i.e., single-fluid) models. The group of homogenous models contains two subgroups: models based on transport equation and pressure based models. Several works tried to order particular approaches and presented short reviews of selected studies. However, these classifications are too rough to be treated as sufficiently accurate. The aim of this paper is to present the development paths of numerical investigations of cavitating flows with the use of homogeneous approach in order of publication year and with relatively detailed description. Each of the presented model is accompanied by examples of the application area. This review focuses not only on the list of the most significant existing models to predict sheet and cloud cavitation, but also on presenting their advantages and disadvantages. Moreover, it shows the reasons which inspired present authors to look for new ways of more accurate numerical predictions and dimensions of cavitation. The article includes also the division of source terms of presented models based on the transport equation with the use of standardized symbols.

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34

Nouroozi, M., M. Pasandidehfard, and M. H. Djavareshkian. "Simulation of Partial and Supercavitating Flows around Axisymmetric and Quasi-3D Bodies by Boundary Element Method Using Simple and Reentrant Jet Models at the Closure Zone of Cavity." Mathematical Problems in Engineering 2016 (2016): 1–13. http://dx.doi.org/10.1155/2016/1593849.

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A fixed-length Boundary Element Method (BEM) is used to investigate the super- and partial cavitating flows around various axisymmetric bodies using simple and reentrant jet models at the closure zone of cavity. Also, a simple algorithm is proposed to model the quasi-3D cavitating flows over elliptical-head bodies using the axisymmetric method. Cavity and reentrant jet lengths are the inputs of the problem and the cavity shape and cavitation number are some of the outputs of this simulation. A numerical modeling based on Navier-Stokes equations using commercial CFD code (Fluent) is performed to evaluate the BEM results (in 2D and 3D cases). The cavitation properties approximated by the present research study (especially with the reentrant jet model) are very close to the results of other experimental and numerical solutions. The need for a very short time (only a few minutes) to reach the desirable convergence and relatively good accuracy are the main advantages of this method.

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35

Wei, Ying-Jie, Chien-Chou Tseng, and Guo-Yu Wang. "Turbulence and cavitation models for time-dependent turbulent cavitating flows." Acta Mechanica Sinica 27, no. 4 (July 20, 2011): 473–87. http://dx.doi.org/10.1007/s10409-011-0475-3.

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36

Coutier-Delgosha, O., R. Fortes-Patella, and J. L. Reboud. "Evaluation of the Turbulence Model Influence on the Numerical Simulations of Unsteady Cavitation." Journal of Fluids Engineering 125, no. 1 (January 1, 2003): 38–45. http://dx.doi.org/10.1115/1.1524584.

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Unsteady cavitation in a Venturi-type section was simulated by two-dimensional computations of viscous, compressible, and turbulent cavitating flows. The numerical model used an implicit finite volume scheme (based on the SIMPLE algorithm) to solve Reynolds-averaged Navier-Stokes equations, associated with a barotropic vapor/liquid state law that strongly links the density variations to the pressure evolution. To simulate turbulence effects on cavitating flows, four different models were implemented (standard k-ε RNG; modified k-ε RNG; k-ω with and without compressibility effects), and numerical results obtained were compared to experimental ones. The standard models k-ε RNG and k-ω without compressibility effects lead to a poor description of the self-oscillation behavior of the cavitating flow. To improve numerical simulations by taking into account the influence of the compressibility of the two-phase medium on turbulence, two other models were implemented in the numerical code: a modified k-ε model and the k-ω model including compressibility effects. Results obtained concerning void ratio, velocity fields, and cavitation unsteady behavior were found in good agreement with experimental ones. The role of the compressibility effects on turbulent two-phase flow modeling was analyzed, and it seemed to be of primary importance in numerical simulations.

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37

Fan, D., and A. Tijsseling. "Fluid-Structure Interaction With Cavitation in Transient Pipe Flows." Journal of Fluids Engineering 114, no. 2 (June 1, 1992): 268–74. http://dx.doi.org/10.1115/1.2910026.

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The interactions between axial wave propagation and transient cavitation in a closed pipe are studied. Definitive experimental results of the phenomenon are produced in a novel apparatus. The apparatus is characterized by its simplicity and its capability of studying transient phenomena in a predictable sequence. The influence due to friction is small and the representations of the boundary conditions are straightforward. Measurements with different severity of cavitation are provided to enable other researchers in the area to compare with their theoretical models. A new cavitating fluid/structure interaction cavitation model is proposed. The measurements are compared with the column separation model of Tijsseling and Lavooij (1989) and the new model to validate the experimental results.

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38

Goncalves, Eric, and Dia Zeidan. "Numerical study of turbulent cavitating flows in thermal regime." International Journal of Numerical Methods for Heat & Fluid Flow 27, no. 7 (July 3, 2017): 1487–503. http://dx.doi.org/10.1108/hff-05-2016-0202.

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Purpose The aim of this work is to quantify the relative importance of the turbulence modelling for cavitating flows in thermal regime. A comparison of various transport-equation turbulence models and a study of the influence of the turbulent Prandtl number appearing in the formulation of the turbulent heat flux are proposed. Numerical simulations are performed on a cavitating Venturi flow for which the running fluid is freon R-114 and results are compared with experimental data. Design/methodology/approach A compressible, two-phase, one-fluid Navier–Stokes solver has been developed to investigate the behaviour of cavitation models including thermodynamic effects. The code is composed by three conservation laws for mixture variables (mass, momentum and total energy) and a supplementary transport equation for the volume fraction of gas. The mass transfer between phases is closed assuming its proportionality to the mixture velocity divergence. Findings The influence of turbulence model as regard to the cooling effect due to the vaporization is weak. Only the k – ε Jones–Launder model under-estimates the temperature drop. The amplitude of the wall temperature drop near the Venturi throat increases with the augmentation of the turbulent Prandtl number. Originality/value The interaction between Reynolds-averaged Navier–Stokes turbulence closure and non-isothermal phase transition is rarely studied. It is the first time such a study on the turbulent Prandtl number effect is reported in cavitating flows.

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39

Park, Ilryong, Jein Kim, Bugeun Paik, and Hanshin Seol. "Numerical Study on Tip Vortex Cavitation Inception on a Foil." Applied Sciences 11, no. 16 (August 9, 2021): 7332. http://dx.doi.org/10.3390/app11167332.

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In this paper, the inception of tip vortex cavitation in weak water has been predicted using a numerical simulation, and a new scaling concept with variable exponent has also been suggested for cavitation inception index. The numerical simulations of the cavitating flows over an elliptic planform hydrofoil were performed by using the RANS approach with a Eulerian cavitation model. To ensure the accuracy of the present simulations, the effects of the turbulence model and grid resolution on the tip vortex flows were investigated. The turbulence models behaved differently in the boundary layer of the tip region where the tip vortex is developed, which resulted in different pressure and velocity fields in the vortex region. Furthermore, the Reynolds stress model for the finest grid showed a better agreement with the experimental data. The tip vortex cavitation inception numbers for the foil, predicted by using both wetted and cavitating flow simulation approaches, were compared with the measured cavitation index values, showing a good correlation. The current cavitation scaling study also suggested new empirical relations as a function of the Reynolds number substitutable for the two classic constant scaling exponents. This scaling concept showed how the scaling law changes with the Reynolds number and provided a proper scaling value for any given Reynolds numbers under turbulent flow conditions.

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40

Ducoin, Antoine, Biao Huang, and Yin Lu Young. "Numerical Modeling of Unsteady Cavitating Flows around a Stationary Hydrofoil." International Journal of Rotating Machinery 2012 (2012): 1–17. http://dx.doi.org/10.1155/2012/215678.

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The objective of this paper is to evaluate the predictive capability of three popular transport equation-based cavitation models for the simulations of partial sheet cavitation and unsteady sheet/cloud cavitating flows around a stationary NACA66 hydrofoil. The 2D calculations are performed by solving the Reynolds-averaged Navier-Stokes equation using the CFD solver CFX with thek-ωSST turbulence model. The local compressibility effect is considered using a local density correction for the turbulent eddy viscosity. The calculations are validated with experiments conducted in a cavitation tunnel at the French Naval Academy. The hydrofoil has a fixed angle of attack ofα=6° with a Reynolds number of Re = 750,000 at different cavitation numbersσ. Without the density modification, over-prediction of the turbulent viscosity near the cavity closure reduces the cavity length and modifies the cavity shedding characteristics. The results show that it is important to capture both the mean and fluctuating values of the hydrodynamic coefficients because (1) the high amplitude of the fluctuations is critical to capturing the extremes of the loads to ensure structural safety and (2) the need to capture the frequency of the fluctuations, to avoid unwanted noise, vibrations, and accelerated fatigue issues.

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41

Brandner, Paul A., James A. Venning, and Bryce W. Pearce. "Wavelet analysis techniques in cavitating flows." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2126 (July 9, 2018): 20170242. http://dx.doi.org/10.1098/rsta.2017.0242.

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Cavitating and bubbly flows involve a host of physical phenomena and processes ranging from nucleation, surface and interfacial effects, mass transfer via diffusion and phase change to macroscopic flow physics involving bubble dynamics, turbulent flow interactions and two-phase compressible effects. The complex physics that result from these phenomena and their interactions make for flows that are difficult to investigate and analyse. From an experimental perspective, evolving sensing technology and data processing provide opportunities for gaining new insight and understanding of these complex flows, and the continuous wavelet transform (CWT) is a powerful tool to aid in their elucidation. Five case studies are presented involving many of these phenomena in which the CWT was key to data analysis and interpretation. A diverse set of experiments are presented involving a range of physical and temporal scales and experimental techniques. Bubble turbulent break-up is investigated using hydroacoustics, bubble dynamics and high-speed imaging; microbubbles are sized using light scattering and ultrasonic sensing, and large-scale coherent shedding driven by various mechanisms are analysed using simultaneous high-speed imaging and physical measurement techniques. The experimental set-up, aspect of cavitation being addressed, how the wavelets were applied, their advantages over other techniques and key findings are presented for each case study. This paper is part of the theme issue ‘Redundancy rules: the continuous wavelet transform comes of age’.

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42

De Giorgi, M. G., A. Ficarella, and M. Tarantino. "A Data Acquisition System to Detect Bubble Collapse Time and Pressure Losses in Water Cavitation." International Journal of Measurement Technologies and Instrumentation Engineering 1, no. 1 (January 2011): 38–54. http://dx.doi.org/10.4018/ijmtie.2011010104.

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This paper presents a data acquisition system oriented to detect bubble collapse time and pressure losses in water cavitation in an internal orifice. An experimental campaign on a cavitating flow of water through an orifice has been performed to analyze the flow behavior at different pressures and temperatures. The experiments were based on visual observations and pressure fluctuations frequency analysis. Comparing the visual observations and the spectral analysis of the pressure signals, it is evident that the behavior of the different cavitating flows can be correlated to the frequency spectrum of the upstream, downstream and differential pressure fluctuations. The further reduction of the cavitation number and the consequent increase in the width of the cavitating area are related to a corresponding significant increase of the amplitude of typical frequency components. The spectrogram analysis of the pressure signals leads to the evaluation of the bubble collapse time, also compared with the numerical results calculated by the Rayleigh–Plesset equation.

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43

Delale, Can F. "Thermal Damping in Cavitating Nozzle Flows." Journal of Fluids Engineering 124, no. 4 (December 1, 2002): 969–76. http://dx.doi.org/10.1115/1.1511163.

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Recent investigations of bubbly cavitating nozzle flows using the polytropic law for the partial gas pressure have shown flow instabilities that lead to flashing flow solutions. Here, we investigate the stabilizing effect of thermal damping on these instabilities. For this reason we consider the energy equation within the bubble, assumed to be composed of vapor and gas, in the uniform pressure approximation with low vapor concentration. The partial vapor pressure is fixed by the vapor saturation pressure corresponding to the interface temperature, which is evaluated by assuming the thin boundary layer approximation within the liquid. Consequently, the partial gas pressure is evaluated by its relation to the heat flux through the interface in the uniform pressure approximation. The model is then coupled to the steady-state cavitating nozzle flow equations replacing the polytropic law for the partial gas pressure. The instabilities found in steady cavitating nozzle flows are seen to be stabilized by thermal damping with or without the occurrence of bubbly shock waves.

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44

Rowe, A., and O. Blottiaux. "Aspects of Modeling Partially Cavitating Flows." Journal of Ship Research 37, no. 01 (March 1, 1993): 34–48. http://dx.doi.org/10.5957/jsr.1993.37.1.34.

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A method for calculating partially cavitating flows is presented. This method respects the impermeability condition on the profile in the vicinity of the cavity. The difficulties inherent in a scheme which gives a solution depending on the internal field organization, when the cavity is open, are analyzed. Several closure models are compared with the experimental results. This comparison shows the great variety of models that would have to be considered in order to give a proper account of the t(ac) law for three types of geometry. The pressure recovery study for one of the three geometries shows that pressure recovery can be simulated by a distribution of sinks distributed immediately downstream of the cavity, followed by a positive flux zone farther downstream. Validated by means of a finite-element calculation, the method proves its capability to take into account the effect of nonparallel confining walls placed very close around a foil of very small relative thickness.

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45

Chen, Yongliang, and Stephen D. Heister. "MODELING CAVITATING FLOWS IN DIESEL INJECTORS." Atomization and Sprays 6, no. 6 (1996): 709–26. http://dx.doi.org/10.1615/atomizspr.v6.i6.50.

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46

ARNDT, Roger Edward Anthony, Gary John BALAS, and Martin WOSNIK. "Control of Cavitating Flows: A Perspective." JSME International Journal Series B 48, no. 2 (2005): 334–41. http://dx.doi.org/10.1299/jsmeb.48.334.

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47

Hosangadi, A., V. Ahuja, and R. J. Ungewitter. "Simulations of Cavitating Flows in Turbopumps." Journal of Propulsion and Power 20, no. 4 (July 2004): 604–11. http://dx.doi.org/10.2514/1.2162.

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48

Kim, Hyunji, Hyeongjun Kim, Daeho Min, and Chongam Kim. "Numerical simulations of cryogenic cavitating flows." Journal of Physics: Conference Series 656 (December 3, 2015): 012131. http://dx.doi.org/10.1088/1742-6596/656/1/012131.

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49

Chen, Yongliang, and S. D. Heister. "Modeling Hydrodynamic Nonequilibrium in Cavitating Flows." Journal of Fluids Engineering 118, no. 1 (March 1, 1996): 172–78. http://dx.doi.org/10.1115/1.2817497.

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A nonlinear numerical model has been developed to assess nonequilibrium effects in cavitating flows. The numerical implementation involves a two-phase treatment with the use of a pseudo-density which varies between the liquid and gas/vapor extremes. A new constitutive equation for the pseudo-density is derived based on the bubble response described by a modified form of the Rayleigh-Plesset equation. Use of this constitutive equation in a numerical procedure permits the assessment of nonequilibrium effects. This scheme provides a quantitative description of scaling effects in cavitated flows. With minimal modifications, the model can also be used for bubbly two-phase flows.

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50

Wang, Guoyu, Inanc Senocak, Wei Shyy, Toshiaki Ikohagi, and Shuliang Cao. "Dynamics of attached turbulent cavitating flows." Progress in Aerospace Sciences 37, no. 6 (August 2001): 551–81. http://dx.doi.org/10.1016/s0376-0421(01)00014-8.

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