Numerical simulation unsteady cloud cavitating flow with a filter-based density correction model

We investigated the three-dimensional characteristics in the unsteady cavitating flow over an axisymmetric body with a blunt headform. A high-speed video camera was used to visualize the cavitating flow structures. A modified PANS (Partially-averaged Navier-Stokes) turbulence model coupled with Kubota cavitation model was used to simulate the time-evolution process of the unsteady cavitating flows. The finite-time Lyapunov exponent (FTLE) and Lagrangian coherent structures (LCS) methods are applied to investigate the three-dimensional flow patterns. The results show that the numerical method is capable of simulating the unsteady cavitating flow for capturing the attached cavity with maximum-length, the cavity break-off and U-type shedding, in accordance with the qualitative features observed in the experiment. Three-dimensional characteristics are extremely impressive in the unsteady cavitating flows. The re-entrant flows originate from different circumferential positions at the closure region of the attached cavity, and move upstream at different speeds. Moreover, substantial circumferential motions in the unsteady cavitating flow are found based on Lagrangian trajectories, and it is reasonably deduced that the U-type shedding cavity is primarily induced by the effect of re-entrant flow motions consisting of moving upstream and circumferential flows as well.

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.

Partially Averaged Navier-Stokes method for time-dependent turbulent cavitating flows

In this paper, the cavitation and flow characteristics of the unsteady liquid nitrogen (LN2) cavitating flow in a submersible pump are investigated through both experimental and numerical approaches. The performance curve of the LN2 submersible pump is obtained via experimental measurement. Numerical simulations are performed using a modified shear stress transport k–ω turbulence model, incorporating corrections for rotation and thermal effects as per the Schnerr–Sauer cavitation model. The numerical framework is verified by comparing the cavitation morphology features with previously reported visual data of the LN2 inducer and aligning pump performance data with those obtained from experimental tests of the LN2 submersible pump. The results indicate that cavitation at the designed flow rate predominantly manifests as tip clearance vortex cavitation in the inducer. Increased flow rates exacerbate cavitation, potentially obstructing the flow passage of the impeller. The vortex identification method and the vorticity transport equation are employed to identify the vortex structures and analyze the interaction between cavitation and vortices in the unsteady LN2 cavitating flow. The vortex structures primarily concentrate at the outlet of the impeller flow passage, largely attributed to the vortex dilation term and baroclinic torque. The influence of thermal effects on the cavitation flow of submersible pumps is analyzed. An entropy production analysis model, comprehensively involving various contributing factors, is proposed and utilized to accurately predict the entropy production rate within the pump. This study not only offers an effective numerical approach but also provides valuable insight into the cavitation flow characteristics of the LN2 submersible pump.

Experience using pressure-based CFD methods for Euler–Euler simulations of cavitating flows

Dynamics of unsteady compressible cavitating flows associated with the cavity shedding

Comparative study between turbulence models in unsteady cavitating flow with special emphasis on shock wave propagation

Unsteady cavitating flow usually contains various vapor structures with different length scales and significant fluid compressibility, which poses great challenges to numerical simulation. In this work, we propose a compressible Eulerian–Lagrangian method to investigate cloud cavitation inside a nozzle, with particular emphasis on the effect of compressibility on multiscale structures. The macroscopic cavity evolution is dealt with using large eddy simulation and the volume of fluid method in a compressible Eulerian framework. Microscopic bubble dynamics are described using the equation of bubble motion and the compressible Rayleigh–Plesset equation. A two-way coupling algorithm is established to bridge the two frameworks. The calculated results are validated by comparison with available experimental data. The numerical results show that the compressibility exacerbates the instability of the cavitating flow field, generates more discrete bubbles, and promotes liquid–vapor mass exchange, which further increases the overall cavitation volume. Furthermore, two distinct power laws for bubble size distribution, with exponent −4/3 for small bubbles and −10/3 for large bubbles, are obtained. Owing to the influence of the high flow velocity and high ambient pressure in the nozzle, and the wall effects on bubble dynamics, the number of large-size bubbles calculated by the numerical simulation is greater than that obtained by theoretical analysis. The formation of these bubbles is affected by shear on the liquid–vapor interface, the presence of vortex structures, and turbulence, thus differing significantly from the case of cavitation flow around a hydrofoil.

Numerical investigation of cavitation vortex dynamics in unsteady cavitating flow with shock wave propagation

To accurately capture the behaviors of cavitation and reveal the unsteady cavitating flow mechanism, a condensate pump inducer is numerically analyzed in a separate numerical experiment with large eddy simulation (LES) at critical cavitation number σind,c under the design point. Based on the new Omega vortex identification method, the correlation between the flow structures and cavities is clearly illustrated. Besides, the pressure fluctuations around the inducer are analyzed. Special emphasis is put on the analysis of the interactions between the cavities, turbulent fluctuations, and vortical flow structures. The Omega vortex identification method could give an overall picture of the whole cavitating flow structures to present a clear correlation between the vortices and cavities. The results show that the shear cavitation dominates the cavitation characteristics under the design point. The pure rigid rotation region mainly concentrates at the edge of the cavities while the other sheet-like cavities near the casing walls are characterized by strong turbulence fluctuations. Besides, based on the analysis of the correlation between the cavities and flow structures, the rotating cavitation under the design point may mainly be attributed to the interaction between the tip leakage vortex cavitation and the next blade.

A compressible 3D finite volume approach for the simulation of unsteady viscoelastic cavitating flows

In the present work, a cavitation model based on a new truncated form of the full Rayleigh-Plesset (R-P) equation for the source terms controlling vapor generation and destruction has been developed and implemented in the ANSYS FLUENT platform. Coupled with a Filter-based density corrected model (FBDCM), the cavitating flow over a 2-D Clark-Y hydrofoil is investigated numerically with particular emphasis on understanding the effect of cavitation structures and the shedding dynamics on the hydrodynamics coefficients and surrounding flow velocity structures. The hydrofoil has a fixed angle of attack of α = 8° with a moderate Reynolds number of Re = 7.0×105. Simulations have been carried out for various cavitation numbers ranging from non-cavitating flows to the cloud cavitation regime (σ = 0.80). In particular, we compared the lift and drag coefficients, the cavitation dynamics and the time-averaged velocity with available experimental data for two cavitation models, i.e. the proposed model and Schnerr-Sauer model. The comparisons between the numerical and experimental results show that the proposed model has a better capability than Schnerr-Sauer model to capture the characteristics of lift and drag coefficients under cavitation conditions. Meanwhile, the proposed model is sufficiently robust to predict the initiation of the sheet/cloud cavity, growth towards the trailing edge, and subsequent shedding downstream, which is in accordance with the experimental quantitative features in literature.

Numerical study of unsteady turbulent cavitating flows

Large eddy simulations were used to investigate unsteady tip-leakage cavitating flow over a National Advisory Committee for Aeronautics 0009 hydrofoil. The proper orthogonal decomposition (POD) was combined with fast Fourier transforms to help better understand the deformation dynamics of the vortex and cavity. The results show three typical vortices, i.e., the tip-leakage vortex (TLV), tip-separation vortex (TSV), and shedding–trailing vortex (STV) with their own helical core lines in the averaged cavitating flows. Upstream of x/C = 1.8, the mean TLV core carries the breathing mode waves through the vortex dilatation effect, while the TSV core generates the dilatation, shrinkage, and bending distortions near the cavity interface by vortex stretching and deflection effects. Further downstream, the TLV starts to intertwine with the TSV, and the STV gradually diffuses. The TLV wandering encourages large cavity deformations dominated by the breathing and bending modes. However, in the lower-order POD modes, the contribution of bending modes to the cavity fluctuation energy is greatly weakened due to the variation of the relative cavity radius, r*, which indicates that the breathing mode and the double helix mode play major roles in the cavity interfacial waves. The results also show that the cavity interfacial oscillations are highly correlated with the surrounding velocity fluctuations. Moreover, a modified theoretical dispersion equation can well reproduce the quantitative relation between the vibration frequencies and the axial wavenumbers of the TLV cavity, especially for the wave dynamics of the breathing modes and the double helix modes.

With the increasing demand of higher performance and efficiencies for marine propulsion and hydropower system, structures became more flexible and were subjected to high flow rates. Cavitation-structure interaction has become one of the major issues for most engineering applications. In order to analyze the characteristics of unsteady cavitating flow induced vibration, the cloud cavitation flow over three dimensional NACA66 hydrofoil is studied by numerical simulation in this paper. The cavitating flow is modeled by large eddy simulation method and Zwart cavitation model, and the structural vibration model of three dimensional hydrofoil is established. The numerical calculation of fluid-solid coupling is realized based on ANSYS Workbench. The main dimensionless parameters of three-dimensional hydrofoil cavitation flow-induced vibration are obtained by means of dimensional analysis, including density ratio, cavitation number, Reynolds number, and the frequency ratio of flow to structure. The changes of cavity morphology during the cloud cavitation development of flexible hydrofoil and the flow-induced vibration characteristics under cloud cavitation flow of flexible hydrofoil are analyzed. The results showed that the periodic development of cavitation can be divided into three stages: the growth of attached cavity, the development of re-entrant jet and the shedding of cavity in cloud cavitaion stage. The centroid displacement of the free end of the flexible hydrofoil varies periodically with time at the stage of cloud cavitation. The hydrofoil vibration is affected by the development of cloud cavitation, and the vibration frequency corresponds to the shedding frequency of cloud cavitation.