Zwart Cavitation Model Research Articles

Numerical study on cavitating flow-induced vibration of liquid rocket engine inducer

The cavitating flow-induced vibrations have become one of the major issues for the operation safety and stability of the liquid rocket engine. The objective of this paper is to numerically investigate the cavitating flow around a four-blade inducer, with focus on the cavitating flow-induced vibration characteristics. In the numerical simulation, the curvature correction turbulence model and the Zwart cavitation model is used for the simulation of the flow field. The loose coupled method is adopted for the prediction of the fluid structure interaction, including the calculation of the fluid forces based on the multiphase fluid dynamics, computation of the structural deformation via the governing equation of the structural motion, and then the update the fluid and structure mesh. The results showed that good agreement has been obtained between the experimental and numerical results. The reverse flow vortex cavitation develops and rotates with the blade, but with a much lower rotational speed than that of the blade. The vibration of the hydrocone is mainly affected by the blade rotation of the inducer, and the blade vibration is mainly affected by the reverse flow vortex cavitation

Numerical investigation into cavitating flow around a NACA66 hydrofoil with DCM models

Unsteady cavitating flow is difficult to be predicted accurately with traditional RANS turbulence model, especially cavities shedding and evolution from sheet cavity to cloud cavity. In order to determine an appropriate numerical setup for accurate and reliable simulations of cavitating flow, the unsteady-state cavitating flow simulations are performed with the Zwart cavitation model accompanying with the DCM(Density correction model) model based on the RNG k-ε turbulence model after grid convergence test. The details about pressure distribution and cavities evolution around the hydrofoil show that the used models predict the cavities shedding frequency well, the pressure distribution along chord is quasi-periodic. Due to the dynamic of the shed cavities, periodic lift and drag coefficient are pretty clear with both positive and negative values. The cavities formation, breakup, shedding and collapse in a cycle are also presented.

Experimental and numerical investigation of cavitating vortical patterns around a Tulin hydrofoil

The objective of this paper is to investigate the cavitating flow patterns around a specific hydrofoil (Tulin hydrofoil) via combined experimental and numerical studies, and to better understand the vortex-cavitation interactions in transient cavitating flows. The experimental studies were carried out in the closed-loop cavitation tunnel, and a high-speed digital camera is applied to document the cavitation patterns. The numerical investigations are performed using a large-eddy simulation method and the Zwart cavitation model. The results showed that the predicted cavity formation and evolution agree well with the experimental observation. With decreasing of the cavitation number, different cavitating flow patterns occur around the hydrofoil, namely inception cavitation (σ = 1.57), vortex cavitation (σ = 1.27), cavitating vortex street (σ = 1.07), cloud cavitation (σ = 0.87), mixture supercavitation (σ = 0.67), and developed supercavitation (σ = 0.54). Especially, the flow structures of vortex cavitation, cavitating vortex street and cloud cavitation were further investigated with the Euler and Lagrangian method. For vortex cavitation, the cavitating vortex forms and sheds at the leading and trailing edge of the foil alternatively, with a pair of asymmetric vortex structures observed. The trailing edge cavitating vortex has a regular vortex shape and a clear boundary between the vortex structures. For cavitating vortex street, vortex shedding process is not independent, instead, the vortex braid between the trailing edge cavitating vortexes and the so called “cat's eye” vortex row can be obviously observed. The center of circulation region is corresponding to low finite-time Lyapunov exponent (FTLE) value, and the bridges of the FTLE is concentrated in the boundary of the vortex structure and curling in the dynamic surrounding of the circulation region. The trajectory of the points well presents the dynamic flow pattern. For cloud cavitation pattern, the cavity develops to cover the entire suction surface, and the cloud cavity sheds downstream periodically.

Numerical investigation of the transient cavitating flow and vortical patterns around a hydrofoil

The objective of this work is to investigate the cavitating flow mechanism of a specific hydrofoil, Tulin hydrofoil, and better understand the vortex-cavitation interactions in transient cavitating flows. The numerical investigations are performed using a large eddy simulation method and the Zwart cavitation model. The predicted cavity formation and evolution agree well with the experimental observation. An asymmetric vortex street has been formed, with the upper one (the trailing edge vortex street) has a regular vortex shape and a clear boundary between vortex structures, while the lower one (the leading edge vortex street) has a larger cavitation area due to the low pressure distribution on the suction side of the foil. The turbulent kinetic energy transport equation has been adopted to examine the balance and contribution of different mechanisms. The formation and evolution of the leading and trailing edge vortex structures are responsible for the generation and modification of the turbulent kinetic energy distributions. The convection term varies significantly in the cavity region during the phase change process, and the boundary of the vortex structures enhance the production term of the turbulent kinetic energy.

Numerical modelling of unsteady cavitation and induced noise around a marine propeller

The objective of this paper is to numerically investigate the cavitating flow around a marine propeller and to explore the intrinsic relationships between the sheet cavitation and its radiation noise. The k-ω SST turbulence model with the turbulence viscosity correction and the Zwart cavitation model are introduced to the simulation of cavitating flow around a propeller in a non-uniform wake. The loading noise and cavitation noise have been predicted based on the theory for acoustic fan source and the sound radiation theory for spherical bubble respectively. The periodic cavitation development has been captured, and the periodic large pressure fluctuation around the blade has been analyzed with the dominant frequencies in accordance to the first order of the blade passing frequency. For the non-cavitation case, the high sound pressure levels mainly concentrate in the low frequency stage and decrease from the low-order to the high-order blade passing frequency. While for the sheet cavitation case, the sound pressure level at the high-order of blade passing frequencies are enhanced. The sound pressure induced by the cavitation development is periodically varied accompanied with the periodic pulsating cavity evolution, and the acoustic energy mainly focus on the low order of blade passing frequencies.

Numerical simulation for the tip leakage vortex cavitation

The tip leakage vortex (TLV) cavitation is investigated by a commercial Reynolds averaged Navier-Stokes (RANS) solver. A referenced test on a NACA0009 hydrofoil is used to validate the numerical simulation. Considering the local rotation characteristics of the vortical flow, a rotation-curvature corrected Shear-Stress-Transport model (SST-CC model) is applied to simulate the time-averaged turbulent flow. Compared to the original SST model, the SST-CC model improves the prediction of the velocity in TLV on the measured sections in downstream, and the vorticity and pressure features along the TLV trajectory are analysed numerically. In order to increase the prediction accuracy for the TLV cavitation, the empirical condensation coefficient (Fc) in Zwart's cavitation model is calibrated based on the referenced experiment. By introducing a vortex identification parameter (f∗) related to the strain rate tensor and the vorticity tensor, a relationship between the Fc and f∗ is built, and the effects of the rotational motion of the vortex on the cavity are embodied in a modified Zwart's cavitation model. Compared to the conventional Zwart's cavitation model, the modified cavitation model significantly improves the prediction of the TLV cavitation and gets a better agreement with the referenced test on different conditions with various gap widths.

Entropy generation analysis for the cavitating head-drop characteristic of a centrifugal pump

Cavitation is a challenging flow abnormality that leads to undesirable effects on the hydraulic behaviour of centrifugal pumps. This study analyses the cavitating flow at a normal flow rate using the shear stress transport k-ω turbulence model and the Zwart cavitation model to capture the cavitation development and spatial distribution of vapour structures within the pump. A general description of the pump head-drop phenomenon was analysed through the study of local and global flow fields. The relationship between vapour distribution and entropy generation fields was mainly investigated through the local flow analysis method. Results show that the tendency of total entropy generation rate within the impeller coincides with the pump head-drop curve. The entropy generation rate changes slightly at the early stage of the cavitation development whereas rapidly increases when the cavitation has fully developed. Cavitation development enhances the hydraulic losses and flow unsteadiness in the impeller. These hydraulic losses are located substantially at the interface of the cavity, especially at the rear portion of the cavity region.

The structures of unsteady cavitation shedding flow around an axisymmetric body with a blunt headform

The objective of this paper is to investigate the cavity shedding dynamics in unsteady cavitating flows around an axisymmetric body with a blunt headform. A high-speed video camera is used to record the cavity evolution process. The numerical simulations are performed based on the homogenous method coupled with a modified PANS (Partially-averaged Navier-Stokes) turbulence model and Zwart cavitation model. The results show that the predicted time-evolution process of cavity agree fairly well with the corresponding experimental data for two different cavitation numbers (σ = 0.7 and σ = 0.6 ). Compared to that of σ = 0.6, the cavity shedding behavior of σ = 0.7 presents more fluctuations and instabilities. To elucidate the different shedding structures, the Lagrangian coherent structures (LCS) and particle trajectory methods are also utilized here. It is found that the particle tracers respectively demonstrate the cavity shedding behaviors of conjunction at σ = 0.6 and rolling up at σ = 0.7. Moreover, the LCS distributions vary with the timeevolution of vortex structures. The particle trajectories can illustrate the upstream and downstream vortex structures connect together at σ = 0.6 but separate at σ = 0.7, which highly consistent with the cavity shedding behaviors.

Large eddy simulation and Euler–Lagrangian coupling investigation of the transient cavitating turbulent flow around a twisted hydrofoil

In the present paper, large eddy simulations combined with the Zwart cavitation model are conducted to simulate the transient cavitating turbulent flow around a Delft Twisted hydrofoil. Numerical results show a reasonable agreement with the available experimental data. A three dimensional Lagrangian technology is developed to provide an alternative method for the analyses in cavitating flow, which is based on Lagrangian viewpoint. With this technology, the track lines of re-entrant and side-entrant jets are straightforwardly displayed and clearly indicate that collisions of the mainstream, the re-entrant jet and the side-entrant jet play an important role in the primary and secondary shedding. The evolution of U-type structures and the interactions between cavitation and vortices are well captured and discussed in detail from the Eulerian viewpoint. The numerical results show that during the stage of attached cavity, the topology of the cavity leaves an important influence on the vortex structure. Once the cavity is cut off, the vortex structure evolution will affect significantly the local cavitating flow. Further analysis demonstrates that the lift acting on U-type structures, which is induced by velocity circulation around U-type structures, significantly affects the formation and the development of U-type structures. Lagrangian Coherent Structures (LCSs) obtained with the three dimensional Lagrangian technology are used to reveal the influence of U-type structures on local flow patterns and it shows that there is a close relationship between the local flow separation and vortex structures. Our work provides an insight into the interactions of cavitation-vortex in the cavitating flow around a twisted hydrofoil and demonstrates the potential of 3D LCSs in the analyses of cavitating flow.

Verification and validation of URANS simulations of the turbulent cavitating flow around the hydrofoil

In this paper, we investigate the verification and validation (V&V) procedures for the URANS simulations of the turbulent cavitating flow around a Clark-Y hydrofoil. The main focus is on the feasibility of various Richardson extrapolation-based uncertainty estimators in the cavitating flow simulation. The unsteady cavitating flow is simulated by a density corrected model (DCM) coupled with the Zwart cavitation model. The estimated uncertainty is used to evaluate the applicability of various uncertainty estimation methods for the cavitating flow simulation. It is shown that the preferred uncertainty estimators include the modified Factor of Safety (FS1), the Factor of Safety (FS) and the Grid Convergence Index (GCI). The distribution of the area without achieving the validation at the Vv level shows a strong relationship with the cavitation. Further analysis indicates that the predicted velocity distributions, the transient cavitation patterns and the effects of the vortex stretching are highly influenced by the mesh resolution.

Unsteady pressure fluctuation characteristics in the process of breakup and shedding of sheet/cloud cavitation

The objective of this paper is to investigate the unsteady pressure fluctuation characteristics in the process of breakup and shedding of unsteady sheet/cloud cavitating flows via combined experimental and computational methods. Experiments are conducted in the divergent section of a convergent-divergent channel using a simultaneous sampling technique to synchronize the transient cavitation behaviors and wall-pressure signals. In the numerical simulations, the Zwart cavitation model and the modified RNG k-ε turbulence model are solved, with the compressibility effects of both water and vapor considered. In addition, one-dimensional bubbly shock wave relationship is applied to analyze the process of the vapor fraction discontinuity propagation. Two different types of cavity breakup and shedding existing in the unsteady sheet/cloud cavitating flows are observed, which is induced by re-entrant flow and vapor fraction discontinuity propagation mechanism, respectively. The re-entrant flow generates at the rear of the cavity, moving forward along the wall. When it arrives at the throat, it breaks up the attached cavity, resulting in the cloud cavity shedding. During the process, the wall pressure fluctuation is relatively small. The vapor fraction discontinuity propagation is resulted from the bubbly shock in water/vapor mixture of the sheet/cloud cavity. There is a significant difference of vapor fraction between the pre- and post of the discontinuity. The pre-discontinuity area is almost pure vapor, and the post-discontinuity area consists of water/vapor mixtures with relatively low vapor fraction. During the discontinuity propagation, the pressure peak exists at shock wave front. When the discontinuity arrives at the throat, the void fraction will suddenly decrease, which indicates the low vapor generation rate. Under the convection of the main flow, the attached cavity will be separated from the newly generated vapor, resulting in the attached cavity breaking up and the cavity cloud shedding.

Application of the semi-analytical cavitation model to flows in a centrifugal pump

Visualization experiments are carried out to investigate the cavitating flows in a centrifugal pump at different flow rates. The cavity lengths under different pump inlet pressure are obtained. The semi-analytical cavitation model is improved since it is not suitable for predicting large cavities full of vapor. The improved cavitation model is used to numerically study the steady and rotating cavitation in the centrifugal pump. Compared with the Zwart cavitation model, the numerical results predicted by the semi-analytical model agree much better with the experiments, especially for large cavities. The cavity lengths at the suction side are overestimated during the simulations, especially by using the Zwart model. At low flow rates, the prediction of the rotating cavitation effect is weaker and the cloud shedding frequency is smaller than those in the experiments.

Numerical study on the cavitating flow in liquid hydrogen through elbow pipes with a simplified cavitation model

Cavitation is usually caused by the pressure difference between the static pressure and the saturated vapor pressure under the local temperature and may result in huge damage to the pipelines. This paper developed a simplified cavitation model based on Rayleigh–Plesset bubble equation and Zwart cavitation model, and conducted a series of numerical simulations with the process of phase change and latent heat added to the solver by UDFs (User Defined Functions). The aim of the paper is to study the affecting factors on the cavitation process of liquid hydrogen in elbow pipes. The results show that the thermal effect can suppress the occurrence and development of cavitation. As the process of cavitation goes on, the suppression of thermal effect is more remarkable. Before the cavitating flow reaches its steady state, cavitation process is very sensitive to the changes of inlet velocity and outlet pressure. Increasing the inlet velocity or decreasing the outlet pressure can both strengthen the cavitation process. The turbulent viscosity ratio has little effects on cavitation process of liquid hydrogen, but the increase of turbulent viscosity ratio can enhance the thermal effect and lower the temperature gradient in the cavity. In addition, the structure of the cavity is found to be related to the bend angles. The cavitation process is enhanced with the decrease of the angles since the duration of centrifugal force is longer.

Physical and numerical investigation of the flow induced vibration of the hydrofoil

The objective of this paper is to investigate the flow induced vibration of a flexible hydrofoil in cavitating flows via combined experimental and numerical studies. The experiments are presented for the modified NACA66 hydrofoil made of POM Polyacetate in the closed-loop cavitation tunnel at Beijing Institute of Technology. The high-speed camera and the single point Laser Doppler Vibrometer are applied to analyze the transient flow structures and the corresponding structural vibration characteristics. The hybrid coupled fluid structure interaction model is conducted to couple the incompressible and unsteady Reynolds Averaged Navier-Stokes solver with a simplified two-degree-of-freedom structural model. The k-ω SST turbulence model with the turbulence viscosity correction and the Zwart cavitation model are introduced to the present simulations. The results showed that with the decreasing of the cavitation number, the cavitating flows display incipient cavitation, sheet cavitation, cloud cavitation and supercavitation. The vibration magnitude increases dramatically for the cloud cavitation and decline for the supercavitation. The cloud cavitation development strongly affects the vibration response, which is corresponding to the periodically developing and shedding of the large-scale cloud cavity. The main frequency of the vibration amplitude is accordance with the cavity shedding frequency and other two frequencies of the vibration amplitude are corresponding to the natural frequencies of the bending and twisting modes.

A hybrid RANS/LES model for simulating time-dependent cloud cavitating flow around a NACA66 hydrofoil

Cloud cavitating flow is highly turbulent and dominated by coherent large-scale anisotropic vortical structures. For the numerical investigation of such a class of flow, large eddy simulation (LES) is a reliable method but it is computationally extremely costly in engineering applications. An efficient approach to reduce the computational cost is to combine Reynolds-averaged Navier–Stokes (RANS) equations with LES used only in the parts of interest, such as massively separated flow regions. A new hybrid RANS/LES model, the modified filter-based method (FBM), is proposed in the present study which can perform RANS or LES depending on the numerical resolution. Compared to the original FBM, the new method has three modifications: the state-of-the-art shear stress transport (SST) model replaces the k-e model as a baseline RANS model. A shielding function is introduced to obviate the switch from RANS to LES occurring inside the boundary layer. An appropriate threshold controlling the switch from RANS to LES is added to achieve an optimal predictive accuracy. The new model is assessed for its predictive capability of highly unsteady cavitating flows in a typical case of cloud cavitation around a NACA66 hydrofoil. The new model results are compared with data obtained from the Smagorinsky LES and SST model based on the same homogeneous Zwart cavitation model. It is found that the modified FBM method has significant advantages over SST model in all aspects of predicted instantaneous and mean flow field, and its predictive accuracy is comparable to the Smagorinsky LES model even using a much coarser grid in the simulations.

Computational modeling of cavitating flows in liquid nitrogen by an extended transport-based cavitation model

Developing a robust computational strategy to address the rich physical characteristic involved in the thermodynamic effects on the cryogenic cavitation remains a challenge in research. The objective of the present study is to focus on developing modelling strategy to simulate cavitating flows in liquid nitrogen. For this purpose, numerical simulation over a 2D quarter caliber hydrofoil is investigated by calibrating cavitation model parameters and implementing the thermodynamic effects to the Zwart cavitation model. Experimental measurements of pressure and temperature are utilized to validate the extensional Zwart cavitation model. The results show that the cavitation dynamics characteristic under the cryogenic environment are different from that under the isothermal conditions: the cryogenic case yields a substantially shorter cavity around the hydrofoil, and the predicted pressure and temperature inside the cavity are steeper under the cryogenic conditions. Compared with the experimental data, the computational predictions with the modified evaporation and condensation parameters display better results than the default parameters from the room temperature liquids. Based on a wide range of computations and comparisons, the extensional Zwart cavitation model may predict more accurately the quasi-steady cavitation over a hydrofoil in liquid nitrogen by primarily altering the evaporation rate near the leading edge and the condensation rate in the cavity closure region.

Numerical simulation of cavitation erosion on a NACA0015 hydrofoil based on bubble collapse strength

The prediction of erosion under unsteady cavitation is crucial to prevent damage in hydraulic machinery. The present investigation deals with the numerical simulation of erosive partial cavitation around a NACA0015 hydrofoil. The study presents the calculation of the bubble collapse strength, Sb, based on the bubble potential energy to identify the surface areas with highest risk of damage. The results are obtained with a numerical scheme assuming homogeneous mixture flow, implicit LES and Zwart cavitation model. The 3D unsteady flow simulation has been solved using OpenFOAM. Python language and OpenFOAM calculator (foamCalcEx) have been used to obtain and represent Sb. The obtained results clearly show the instants of erosive bubble collapse and the affected surface areas.

Experimental and numerical investigation of hydroelastic response of a flexible hydrofoil in cavitating flow

The objective of this paper is to investigate the hydroelastic response of a flexible NACA66 hydrofoil in cavitating flows by combined experimental and numerical studies. Experimental results are presented for rigid/flexible NACA66 hydrofoils fixed at α0=8° for subcavitating (σ=8.0) and cavitating flows (σ=1.4). The high-speed video camera and Laser Doppler Vibrometer are applied to investigate the flow patterns and vibration characteristics. The multiphase flow is modeled with the incompressible and unsteady Reynolds Averaged Navier–Stokes (URANS) equations. The k−ω SST turbulence model with the turbulence viscosity correction and the Zwart cavitation model are introduced to the present simulations. The results showed that the cavitation has significant effect on the foil deformation and the unsteady characteristics of the hydroelastic response. The bending deformation is enhanced when the cavitation occurred. Meanwhile, the hydroelastic response has also affected the cavitation development and the vortex structure interactions. The cavity shedding frequency and vortex shedding and interacting frequency for the flexible hydrofoil are higher than that for the rigid hydrofoil. Compared to the periodic development of the hydrodynamic coefficients for the rigid hydrofoil, the hydrodynamic load coefficients of the flexible hydrofoil fluctuate more significantly, and the chaotic response of the flexible hydrofoil is mainly attributed to the disturbance caused by the flow-induced flutter and deformation of the foil. The evolution of the transient cavity shape and the corresponding hydrodynamic response can be divided into three stages: During the development of the attached cavity, the partial sheet cavity is formed and develops with the lift and drag coefficients increasing, while the maximum attached cavity formed on the suction side of the flexible hydrofoil is larger than that of the rigid hydrofoil, which is caused by the increase of the effective angle of attack due to the twist deformation. During the vortex structure interaction and cavity shedding process, the hydrodynamic loads for the flexible hydrofoil fluctuate because of the foil deformation, leading to a more complex cavitation pattern. During the residual cavity shedding and partial sheet cavity formation process, the cavities, together with the counter-rotational vortex structures, shed downstream totally and are followed by the formation of partial sheet cavities in next period, which is in advance for the flexible hydrofoil due to the larger effective angle of attack.

Numerical investigation of dynamics of unsteady sheet/cloud cavitating flow using a compressible fluid model

In this paper, a compressible fluid model is proposed to investigate dynamics of the turbulent cavitating flow over a Clark-Y hydrofoil. The numerical simulation is based on the homogeneous mixture approach coupled with filter-based density correction model (FBDCM) turbulence model and Zwart cavitation model. Considering the compressibility effect, the equation of state of each phase is introduced into the numerical model. The results show that the predicted results agree well with experimental data concerning the time-averaged lift/drag coefficient and shedding frequency. The quasi-periodic evolution of sheet/cloud cavitation and the resulting lift and drag are discussed in detail. Especially, the present compressible-mixture numerical model is capable of simulating the shock waves in the final stage of cavity collapse. It is found that the shock waves may cause the transient significant increase and decrease in lift and drag if the cavity collapses near the foil surface.

Numerical analysis of the interactions of sheet cavitation and cloud cavitation around a hydrofoil

Partial cavitation and cloud cavitation on NACA66(MOD) was studied based on PANS turbulence model combined with the Zwart cavitation model. The results agree well with the data from the experimental results. The existence of a kind of unsteady characteristics of cloud cavitation is analysed in details. The reasons for the inhibition mechanism of the sheet cavitation are discussed. Pressure shock wave occurs near the tailing edge of the hydrofoil when the collapse of cloud is so large leading to great influence on the cavity closed to the leading edge. The evolution of the pressure peak and its propagation toward the leading edge were investigated through the study of the time domain signal of the monitor points along the streamline of flow. Finally, the propagation of the pressure wave on the suction side was further investigated through analysing the spatial-time history of wall pressure.