A New Cavitation Model Based on Evaporation and Condensation Theory

Cavitation of a hydrofoil is observed in detail by using a high speed video camera. A paint removal test is also carried out in order to evaluate cavitation aggressiveness for erosion. 2D hydrofoil profile is Clark Y 11.7% and its angle of attack is seven degrees. Cavitation number is σ = 1.08. The experimental results are compared with cavitation CFD. Numerous features of unsteady cavitation are observed such as cyclic fluctuation of the sheet cavity, existence of the glassy cones on a sheet cavity, generation of the cloud cavitation from the sheet cavity and the isolated bubbles traveling over the suction surface of the blade. The isolated traveling bubbles and their collapses are thought to be one of the main causes of the severe paint removals. The isolated traveling bubbles are derived from the flowing cavitation nucleus or from abrupt onset at the leading edge of the blade. For computing these complicated phenomena, combination of grid scale bubbles (GSB) and sub grid scale bubble model (SGSB) are proposed. GSB shall be computed by using the computational scheme for the free surface with phase change model. SGSB can be computed with conventional cavitation model. The breakup of GSB generates SGSB, and the coalescence of SGSB makes GSB. Upper limit of void fraction of SGSB is estimated in the range of five or ten percent from the simple speculation of the structure of packed spheres. The two types of cavitation bubble inception model are also discussed based on the generation of the isolated bubbles observed in the experiments. To verify the proposed concepts of cavitation model, a traveling air bubble over a hydrofoil is computed by using the free surface flow scheme of Volume of Fluid (VOF) approach. Cavitation on the hydrofoil is also computed by VOF approach with boiling model concerning the heat transfer. Both the computed results show qualitatively similar characteristics of the bubble dynamics to those in experimental results.

Assessment of unsteady cavitating flow around modified NACA4412 hydrofoil

In this work, we investigate the effect of dissolved gas concentration on cavitation inception and cavitation development in a transparent sharp-edged orifice, similar to that previously analyzed by Nurick in the context of liquid injectors. The working liquid is water, and carbon dioxide is employed as a non-condensable dissolved gas. Cavitation inception points are determined for different dissolved gas concentration levels by measuring wall-static pressures just downstream of the orifice contraction and visually observing the onset of a localized (vapor) bubble cloud formation and collapse. Cavitation onset correlates with a plateau in wall-static pressure measurements as a function of a cavitation number. An increase in the amount of dissolved carbon dioxide is found to increase the cavitation number at which the onset of cavitation occurs. The transition from cloud cavitation to extended-sheet or full cavitation along the entire orifice length occurs suddenly and is shifted to higher cavitation numbers with increasing dissolved gas content. Volume flow rate measurements are performed to determine the change in the discharge coefficient with the cavitation number and dissolved gas content for the investigated cases. CFD analyses are carried out based on the cavitation model by Zwart et al. and the model by Yang et al. to account for non-condensable gases. Discharge coefficients obtained from the numerical simulations are in good agreement with experimental values, although they are slightly higher in the cavitating case. The earlier onset of fluid cavitation (i.e., cavitation inception at higher cavitation numbers) with increasing dissolved carbon dioxide content is not predicted using the employed numerical model.

A newly developed cavitation model and algorithm for predicting hydrodynamic performance of a centrifugal pump under cavitating condition is presented. The cavitation model is implemented in a Reynolds-averaged Navier—Stokes flow solver with turbulence model employed. A priori knowledge of the wall detachment point and bubble length is not required, but naturally a part of the solution by this cavitation model. The liquid/vapour interface is tracked and obtained by an iteration procedure between the flow field computation and the interface updating. The capability to capture some important phenomena of cavitation flows in a centrifugal pump impeller is shown by the cavitation prediction. The numerical results also show that the cavity size increases dramatically with the decrease in the cavitation number and so does the loss of the head rise.

Considering that large eddy simulation (LES) often requires more computational resources to capture small-scale flow characteristics, while the Reynolds-Averaged Navier–Stokes (RANS) methods offers better computational efficiency at the expense of accuracy. The traditional Zwart–Gerber–Belamri cavitation model (Z–G–B) has good universality but insufficiently considers the influencing factors of cavitation. This article proposes a method combining very large eddy simulation (VLES) with the Z–G–B cavitation model (VLES_Z–G–B). However, there remains a certain discrepancies between the predictions and experimental results. To address this, on the basis of the Z–G–B cavitation model, the unsteady cavitation computation method (VLES_Water_Non) is developed, considering the weak compressibility effect of the fluid and incorporating three components: the liquid, vapor, and non-condensable gas. The results indicate that the VLES_Water_Non method compensates for the deficiencies of the VLES_Z–G–B approach, and clarifying that the combined effect of re-entrant flow, side-incident reverse flow, and mainstream are the primary causes of cavity shedding. Using a robust Ω-criterion, multiscale flow features during the cavity evolution process were identified. Additionally, it was found that the vortex stretching and dilation terms are the main reason for the flow separation and formation of complex structures around the hydrofoil. The baroclinic torque term has an significant impact on the generation of vorticity during the shedding process of the cavity. This study is expected to provide a more precise scale resolution method and predictive accuracy for analyzing the internal flow mechanisms of complex fluid machinery.

Multi-phase flow simulations of E779A and DTMB5168 propellers' tip vortex flow field are conducted to qualify the improved Sauer cavitation model in propeller tip vortex local flows prediction, under non-cavitation and initial inception conditions. Mesh refinement strategies pointing to blocking-structured and stream-adaptive grid for vortex flow are concluded in this process. The models account for the effects of mass and volume fraction of the noncondensable gas (NCG) and the turbulence on both cavitation inception and bubble growth by means of mixture density formula and phase-changing threshold pressure formula explicitly. With comparison to the experiments, open water performances of two propellers are both predicted satisfactory with cavitation model un-activated. The simulated propeller cavity pattern and cavitating area under moderately cavitation level are very close to the measurements after cavitation model activated. The circumferentially averaged axial, circumferential and radial velocity components on wake cross plane correspond very well with the measurements outer 0.9R radius. The predicted peaks of three velocity component variation with circumferential theta show a discrepancy to the tests up to about 5%, 40% and 20% respectively at 0.92R, and a maximum prediction error smaller than 10% at 0.7R. The predicted trajectories of tip vortex core are very close to the experiment at front of the downstream 0.3R wake plane, wherein a bigger predicted core radius than the tests further away. Results above show that the mesh strategies introduced in conjunction with the adopted numerical models are positive and beneficial to the vortex-dominated flow of propeller.

The unsteady cavitating flow and pressure fluctuation around the 3-D NACA66 hydrofoil were simulated and validated based on detached eddy simulation turbulence model and a homogeneous cavitation model. Numerical results show that detached eddy simulation can predict the evolution of cavity inception, sheet cavitation growth, cloud cavitation shedding, and breakup, as well as the pressure fluctuation on the surface of hydrofoil. The sheet cavitation growth, detachment, cloud cavitation shedding are responsible for the features of the pressure fluctuation.

Hydraulic torque converter is widely used in transmission units as it is able to provide variable speed and torque ratio, isolate vibration, and absorb shock. The pursuit of a highly packed power unit requires a high capacity/speed torque converter, consequently resulting in a higher risk for cavitation and severe performance degradation, noise, vibration, and even failure. Existing cavitation models generally focus on water, and the empirical parameters are not suitable for the cavitation prediction of torque converter which utilizes high viscosity oil as its working medium. This paper focused on the influence of parameters on the performance and cavitation characteristics of torque converter. A full flow passage geometry and different computational fluid dynamics (CFD) models with cavitation were developed to predict torque converter fluid behavior by resolving Reynolds-averaged Navier–Stokes equations using finite volume method (FVM). The numerical results indicated that nuclei volume fraction, vaporization coefficient, mean nucleation site radius, and maximum density ratio have great influences on the cavitation behavior. These parameters altered the degree of cavitation and the pressure distribution on the surface of stator blades, and affected the stall performance such as stall capacity factor and torque ratio. The cavitation model was then modified to improve calculation accuracy. The test results showed that the prediction error under stall operating condition was decreased from 6.7% to 2%. This study provides insight on the influences of the empirical parameters on both internal cavitation behavior as well as overall hydrodynamic performance.

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

Cavitation is a typical and unavoidable phenomenon for small waterline ships and high-speed vehicles. It creates a highly complex multiphase flow near the free surface and is primarily represented by the free surface-cavitation interaction. In this paper, the large-eddy method and Schnerr-Sauer cavitation model are combined to address the effects of a free surface on the cavitation dynamics of a NACA66 hydrofoil. The numerical method is validated by comparing the cavitation morphology and pressure with available experimental data. The results show that the presence of a free surface affects the cavitation evolution and hydrodynamic load characteristics. Compared with the non-free surface case for the same cavitation number, the free surface suppresses the cavitation intensity and increases the frequency of cavitation shedding. Furthermore, an improved dynamic mode decomposition method is applied to investigate the unsteady cavitation flow features. The results show a correlation between the characteristic mode and the flow state. Meanwhile, the presence of a free surface is found to reduce the energy content in each order mode and results in smaller scale of the coherent structure in higher-order modes. Moreover, with increasing distance from the hydrofoil to the free surface, the cavitation intensity increases, as well as the average lift and drag coefficients. In particular, significant free-surface unsteady fluctuations are observed in the wake region.

A series of numerical investigations was carried out to study the behavior of cavitating turbulent flows in an orifice. In the present work, two different cavitation models were used for the simulation. In the first model, flow was modeled as two interpenetrating fluids (liquid and vapor), and in the second model, the working fluid was assumed to be a mixture of three fluids (liquid, vapor and non-condensable gas). In both cases, we used a finite volume method to discretize the equations and SIMPLEC algorithm to link the pressure and velocity fields. An upwind scheme was used to model convective fluxes and other transport equations. Turbulence effects were considered using the k-ε model. Computations were performed at various inlet pressures and a fixed outlet pressure. The values of discharge coefficient obtained from the simulations were compared with published experimental data. Better agreement was found with the second model. This revealed the importance of non-condensable gases on cavitation. Furthermore, the distributions of vapor volume fraction and velocity magnitude were investigated with using both models. The results showed considerable differences between two models in description of inception of cavitation, distributions of vapor volume fraction and velocity magnitude.

The swirling flow developing in Francis turbine draft tube under part load operation leads to pressure fluctuations usually in the range of 0.2 to 0.4 times the runner rotational frequency resulting from the so-called vortex breakdown. For low cavitation number, the flow features a cavitation vortex rope animated with precession motion. Under given conditions, these pressure fluctuations may lead to undesirable pressure fluctuations in the entire hydraulic system and also produce active power oscillations. For the upper part load range, between 0.7 and 0.85 times the best efficiency discharge, pressure fluctuations may appear in a higher frequency range of 2 to 4 times the runner rotational speed and feature modulations with vortex rope precession. It has been pointed out that for this particular operating point, the vortex rope features elliptical cross section and is animated of a self-rotation. This paper presents an experimental investigation focusing on this peculiar phenomenon, defined as the upper part load vortex rope. The experimental investigation is carried out on a high specific speed Francis turbine scale model installed on a test rig of the EPFL Laboratory for Hydraulic Machines. The selected operating point corresponds to a discharge of 0.83 times the best efficiency discharge. Observations of the cavitation vortex carried out with high speed camera have been recorded and synchronized with pressure fluctuations measurements at the draft tube cone. First, the vortex rope self rotation frequency is evidenced and the related frequency is deduced. Then, the influence of the sigma cavitation number on vortex rope shape and pressure fluctuations is presented. The waterfall diagram of the pressure fluctuations evidences resonance effects with the hydraulic circuit. The influence of outlet bubble cavitation and air injection is also investigated for low cavitation number. The time evolution of the vortex rope volume is compared with pressure fluctuations time evolution using image processing. Finally, the influence of the Froude number on the vortex rope shape and the associated pressure fluctuations is analyzed by varying the rotational speed.

The swirling flow developing in Francis turbine draft tube under part load operation leads to pressure fluctuations usually in the range of 0.2 to 0.4 times the runner rotational frequency resulting from the so-called vortex breakdown. For low cavitation number, the flow features a cavitation vortex rope animated with precession motion. Under given conditions, these pressure fluctuations may lead to undesirable pressure fluctuations in the entire hydraulic system and also produce active power oscillations. For the upper part load range, between 0.7 and 0.85 times the best efficiency discharge, pressure fluctuations may appear in a higher frequency range of 2 to 4 times the runner rotational speed and feature modulations with vortex rope precession. It has been pointed out that for this particular operating point, the vortex rope features elliptical cross section and is animated of a self-rotation. This paper presents an experimental investigation focusing on this peculiar phenomenon, defined as the upper part load vortex rope. The experimental investigation is carried out on a high specific speed Francis turbine scale model installed on a test rig of the EPFL Laboratory for Hydraulic Machines. The selected operating point corresponds to a discharge of 0.83 times the best efficiency discharge. Observations of the cavitation vortex carried out with high speed camera have been recorded and synchronized with pressure fluctuations measurements at the draft tube cone. First, the vortex rope self rotation frequency is evidenced and the related frequency is deduced. Then, the influence of the sigma cavitation number on vortex rope shape and pressure fluctuations is presented. The waterfall diagram of the pressure fluctuations evidences resonance effects with the hydraulic circuit. The time evolution of the vortex rope volume is compared with pressure fluctuations time evolution using image processing. Finally, the influence of the Froude number on the vortex rope shape and the associated pressure fluctuations is analyzed by varying the rotational speed.

PurposeThe purpose of this study is the characterization of the dramatic variation in the flow scenario occurring at incipient stall conditions on a NACA0015 hydrofoil at moderate Reynolds numbers via the experimental analysis of time- and space-resolved skin-friction maps. The examined flow conditions are relevant for a variety of applications, including renewable energy production and unmanned and micro-aerial vehicles.Design/methodology/approachGrounding on the global temperature data acquired via temperature-sensitive paint, the proposed methodology adopts two approaches: one to obtain time-resolved, relative skin-friction vector fields by means of an optical-flow-based algorithm and the other one to extract quantitative, time-averaged skin-friction maps after minimization of the dissimilarity between the observed passive transport of temperature fluctuations and that suggested by the Taylor hypothesis.FindingsThrough the synergistic application of the proposed methods, the time-dependent evolution of the incipient stall over the hydrofoil suction side is globally described by firstly identifying the trailing edge separation at an angle of attack (AoA) AoA = 11.5°, and then by capturing the onset of upstream oriented, mushroom-like structures at AoA = 13°. The concomitant occurrence of both scenarios is found at the intermediate incidence AoA = 12.2°.Originality/valueThe qualitative, time-resolved skin-friction topology, combined with the quantitative, time-averaged distribution of the streamwise friction velocity, enables to establish a portrait of the complex, three-dimensional, unsteady scenario occurring at the examined flow conditions, thus providing new, fundamental information for a deeper understanding of the incipient stall development and for its control.

iew Video Presentation: https://doi-org.tudelft.idm.oclc.org/10.2514/6.2021-2179.vid The unsteady surface pressure fluctuations over trailing-edge serrations retrofitted to the benchmark NACA 633-018 profile are experimentally measured. Miniaturized unsteady pressure transducers installed on the serration surface are used to describe the temporal and spatial distribution of the wall pressure fluctuations over the trailing-edge add-on. The measured spectra, convection velocity, and correlation lengths of the surface pressure fluctuations are presented for the most upstream sensor and compared against the data at different locations along the serration surface. Different angles of attack are tested in a Reynolds number of 2,000,000 (based on the airfoil chord) in order to describe the properties of the wall pressure fluctuations at a range of representative conditions for wind turbine applications. The study details the characteristics of the wall-pressure fluctuations on the serration surface. In particular, the distribution of the wall-pressure fluctuations with and without aerodynamic loading caused by the variation of the airfoil angle of attack is shown, highlighting the impact of the vortex pairs formed around the edges of the serrations under loading on the wall-pressure fluctuations. The experimental results focus on the modifications of the wall-pressure fluctuations over the serration surface. Results show that, at small angles of attack, the amplitude of the wall-pressure fluctuations is higher at the serration root for low frequencies and at the serration tip for high frequencies. As the angle of attack increases, the aerodynamic loading over the serrations causes an increase in the wall pressure fluctuations around the edges of the serrations. This increase depends on the incoming fluctuations from the boundary layer and is related to the degradation of serration acoustic performance at angle. Furthermore, the experimental results corroborate to the benchmark activities for trailing-edge serration noise carried out in collaboration with DTU and DLR, providing information about the pressure fluctuations measured near the edges of the serration.