Homogeneous Mixture Model Research Articles

Numerical predictions of the turbulent cavitating flow around a marine propeller and an axial turbine

The numerical predictions of cavitating flow around a marine propeller working in non-uniform inflow and an axial turbine are presented. The cavitating flow is modelled using the homogeneous (mixture) model. Time-dependent simulations are performed for the marine propeller case using OpenFOAM. Three calibrated mass transfer models are alternatively used to model the mass transfer rate due to cavitation and the two-equation SST (Shear Stress Transport) turbulence model is employed to close the system of the governing equations. The predictions of the cavitating flow in an axial turbine are carried out with ANSYS-CFX, where only the native mass transfer model with tuned parameters is used. Steady-state simulations are performed in combination with the SST turbulence model, while time-dependent results are obtained with the more advanced SAS (Scale Adaptive Simulation) SST model. The numerical results agree well with the available experimental measurements, and the simulations performed with the three different calibrated mass transfer models are close to each other for the propeller flow. Regarding the axial turbine the effect of the cavitation on the machine efficiency is well reproduced only by the time dependent simulations.

Evaluation of finite rate homogenous mixture model in cavitation bubble collapse

The objective of this study is to evaluate the performance of finite rate homogeneous mixture models in three key aspects: (a) the ability of the model to predict the dynamics of resolved small scale vapor regions, (b) the importance of finite rate mass transfer and (c) the impact of assuming 2D flow as is done in RANS simulations with a statistically homogeneous direction. We consider a bubble collapse problem to evaluate all these effects.

Large Eddy Simulation of diesel injector opening with a two phase cavitation model

In the current paper, indicative results of the flow simulation during the opening phase of a Diesel injector are presented. In order to capture the complex flow field and cavitation structures forming in the injector, Large Eddy Simulation has been employed, whereas compressibility of the liquid was included. For taking into account cavitation effects, a two phase homogenous mixture model was employed. The mass transfer rate of the mixture model was adjusted to limit as much as possible the occurrence of negative pressures. During the simulation, pressure peaks have been found in areas of vapour collapse, with magnitude beyond 4000bar, which is higher that the yield stress of common materials. The locations of such pressure peaks corresponds well with the actual erosion location as found from X ray scans.

Numerical investigation of shedding partial cavities over a sharp wedge

In this contribution, we examine transient dynamics and cavitation patterns of periodically shedding partial cavities by numerical simulations. The investigation reproduces reference experiments of the cavitating flow over a sharp wedge. Utilizing a homogeneous mixture model, full compressibility of the two-phase flow of water and water vapor is taken into account by the numerical method. We focus on inertia-dominated mechanisms, thus modeling the flow as inviscid. Based on the assumptions of thermodynamic equilibrium and barotropic flow, the thermodynamic properties are computed from closed-form analytical relations. Emphasis is put on a validation of the employed numerical approach. We demonstrate that computed shedding dynamics are in agreement with the references. Complex flow features observed in the experiments, including cavitating hairpin and horse-shoe vortices, are also predicted by the simulations. Furthermore, a condensation discontinuity occurring during the collapse phase at the trailing portion of the partial cavity is equally obtained.

Feasibility and accuracy of quantification of fat content using iterative decomposition of water and fat with asymmetry and least squares estimation-quantitative fat imaging: a phantom study

Objective To validate the feasibility and accuracy of iterative decomposition of water and fat with asymmetry and least squares estimation-quantitative fat imaging (IDEAL-IQ) in fat quantification using fat-water model. Methods A homogeneous fat-water mixture model consisting of various known fat-fractions were described, and the fat fraction was 0.00, 0.01, 0.02, 0.04, 0.06, 0.08, 0.10, 0.14, 0.18, 0.22, 0.26, 0.30 g/ml respectively. A water-vaseline separated model was also described. IDEAL-IQ was performed. Thin slices were acquired for fat-water mixture model and repeated 3 days later. Nineteen slices of 14 mm-thick parallel to the water-vaseline boundary in 1 mm steps from vaseline to water were acquired. The fat-fractions in 11 slices of fat-water mixture model were measured on FatFrac images. Accuracy was assessed through single sample t test or Kolmogorov-Sirmov test. Measured fat-fractions of the same known fat-fraction were assessed through independent samples t test between two scan times. Linear regression was used to assess the relationship between known fat-fractions and measured fat-fractions. Slices containing the water-vaseline boundary were measured with ROI in the middle of the FatFrac images. The relationship between measured fat-fractions and locations of scanning was exploded using curve fitting. Results (1) Fat-water mixture model: no significant difference(P>0.05) was found between measured fat-fractions and known fat-fractions when it was 0.00, 0.02, 0.06 and 0.08 g/ml with the measured fat-fractions 0.60%, (2.30±0.60)%, (5.76±1.40)%, (7.62±1.40)% respectively for the first time. No significant difference(P>0.05) was found between measured fat-fractions and known fat-fractions when it was 0.00, 0.02, 0.10 g/ml with the measured fat-fractions 0.04%, (2.32±0.60)%, (9.41±1.00)% respectively for the second time. Measured fat-fraction was inlinear relation with known fat-fraction: Y=0.898X+0.224, r2=0.993, P<0.01, F=36 129.548.(2) Water-vaseline separated model: measured fat-fraction increased as scanning location changed, Y=0.045X2-0.499X-4.474, r2=0.978, P<0.05, F=350.623. Conclusions IDEAL-IQ can be used to quantify fat content with good repeatability and can accurately assess the actual fat content from the linearrelationship. Key words: Lipids; Magnetic resonance imaging; Comparative study

Two phase flow pressure drop in multiport mini-channel tubes using R134a and R32 as working fluids

In this study, two-phase flow pressure drop was experimentally measured in condensation and evaporation fluid flow. Refrigerants R134a and R32 were tested in a multiport extruded aluminium tube (MPEs) with hydraulic diameters of 0.715 and 1.16 mm. Experimental conditions were in a range: mass velocity 200–1229 kg/m2s, heat flux 2.55–70 kW/m2, saturated temperatures (5,7.5,12.5,30,35,40,45,50,55) °C. To do so, two installations have been used. They were constructed at the Technical University of Cartagena Spain, for the study of boiling and condensation in tubes. They are briefly described in this paper jointly with the experiments performed. The experimental data are compared with some well-known correlations which were developed for macro/mini-channel tubes. The homogeneous mixture model slightly underestimates the experimental boiling data. Classic macro-channel correlations: Friedel and Müller-Steinhagen and Heck predict satisfactorily well our experimental pressure drop data. Some of the new correlations specially developed for mini/micro-channels have been tested, finding that Cavallini et al. and Zhang and Webb predict with reasonable accuracy the experimental two-phase flow pressure drop data.

Characterization and simulation of optical absorption in Si nanocrystals

AbstractThe application of silicon quantum dot (Si QD) based material is regarded as a promising approach for the realization of high efficiency solar cells. When silicon nanocrystals are made very small (within the vicinity of the exciton Bohr radius of bulk Si), they behave as quantum dots due to the three‐dimensional quantum confinement, which could cause the material's effective optical band gap to increase. The optical band gap can be deduced from the absorption coefficient. In this paper, we analyze optical absorption and emission processes in Si QD and attempt to simulate the band‐edge absorption features based on the photoluminescence spectrum. We also investigate the application of ellipsometry in the study of optical properties of Si QD thin films. Based on WVASE32 modeling tool, a homogeneous mixture model is developed to extract the absorption coefficient of this material. From these results, we extract the effective optical band gap and analyze optical properties of Si QDs materials. (© 2015 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

A numerical method to simulate turbulent cavitating flows

The objective of this paper is to develop a numerical method for simulating multiphase cavitating flows on unstructured grids. The multiphase medium is represented using a homogeneous mixture model that assumes thermal equilibrium between the liquid and vapor phases. We develop a predictor–corrector approach to solve the governing Navier–Stokes equations for the liquid/vapor mixture, together with the transport equation for the vapor mass fraction. While a non-dissipative and symmetric scheme is used in the predictor step, a novel characteristic-based filtering scheme with a second order TVD filter is developed for the corrector step to handle shocks and material discontinuities in non-ideal gases and mixtures. Additionally, a sensor based on vapor volume fraction is proposed to localize dissipation to the vicinity of discontinuities. The scheme is first validated for simple one dimensional canonical problems to verify its accuracy in predicting jump conditions across material discontinuities and shocks. It is then applied to two turbulent cavitating flow problems – over a hydrofoil using RANS and over a wedge using LES. Our results show that the simulations are in good agreement with experimental data for the above tested cases, and that the scheme can be successfully applied to both RANS and LES methodologies.

받음각 변화에 대한 수중익형의 캐비테이션 해석

Cavitation causes a great deal of noise, damage to components, vibrations, and a loss of efficiency in devices, such as propellers, pump impellers, nozzles, injectors, torpedoes, etc. Thus, the cavitating flow simulation is of practical importance for many engineering systems. In the present work, a two-phase flow solver based on the homogeneous mixture model has been developed. The solver employs an implicit preconditioning, dual time steppin g algorithm in curvilinear coordinates. The flow characteristics around Clark-Y hydrofoil were calculated and then validated by comparing with the experimental data. The lift and drag coefficients with changes of angle of attack and cavitation number were obtained. The results show that cavity length and lift, drag coefficient increase with increasing angle of attack.

A continuous adjoint approach to design optimization in cavitating flow using a barotropic model

A continuous adjoint method is developed for design optimization in multiphase flow based on a homogeneous multiphase mixture model. The mixture model consists of variable-density mass and momentum equations and uses a barotropic equation of state for the density that depends on only the local static pressure and the vapor pressure of the liquid. In that case, the primary equations are homogeneous, and a conventional hybrid multistage explicit method based on central differencing and second- and fourth-order scalar artificial dissipation can be applied to solve both the primary and adjoint systems. Results are presented for both surface- and volume-based vapor minimization cost functions for a two-dimensional cavitating hydrofoil in which the geometry is parameterized using B-splines. The cost function gradients computed using the adjoint method are shown to compare well with gradients computed using the complex-step method.

Comparison of Mixture and Multifluid Models for In-Nozzle Cavitation Prediction

Fuel injectors often feature cavitation because of large pressure gradients, which in some regions lead to extremely low pressures. The main objective of this work is to compare the prediction capabilities of two multiphase flow approaches for modeling cavitation in small nozzles, like those used in high-pressure diesel or gasoline fuel injectors. Numerical results are assessed against quantitative high resolution experimental data collected at Argonne National Laboratory using synchrotron X-ray radiography of a model nozzle. One numerical approach uses a homogeneous mixture model with the volume of fluid (VOF) method, in which phase change is modeled via the homogeneous relaxation model (HRM). The second approach is based on the multifluid nonhomogeneous model and uses the Rayleigh bubble-dynamics model to account for cavitation. Both models include three components, i.e., liquid, vapor, and air, and the flow is compressible. Quantitatively, the amount of void predicted by the multifluid model is in good agreement with measurements, while the mixture model overpredicts the values. Qualitatively, void regions look similar and compare well with the experimental measurements. Grid converged results have been achieved for the prediction of mass flow rate while grid-convergence for void fraction is still an open point. Simulation results indicate that most of the vapor is produced at the nozzle entrance. In addition, downstream along the centerline, void due to expansion of noncondensable gases has been identified. The paper also includes a discussion about the effect of turbulent pressure fluctuations on cavitation inception.

Numerical study of ventilated cavitating flows with free surface effects

Cavitating flow is usually formed on the surface of a high-speed underwater object. When the object moves near the free surface at high speed, the cavitation signature becomes a main factor to be overcome by the sensors of a military satellite. This paper studies the free surface effect on the ventilated cavitation process. The governing equations are Navier-Stokes equations based on a homogeneous mixture model. The multiphase flow solver used here relies on an implicit preconditioning scheme in curvilinear coordinates. The cavitation model used is a new cavitation model developed by Merkle et al. (2006). Computations of free surface effects were carried out with a NACA0012 hydrofoil to enable comparisons with experimental data presented in the literature. Calculations were then performed considering the ventilated cavitation process, including the effect of a noncondensable gas with free surface effect.

Numerical analysis of cavitating flow past an axisymmetric cylinder with comparison to experiments

Simulation of cavitating flow is of practical importance for many engineering systems such as propellers, pump impellers, nozzles, injectors, and torpedoes. In this study, a two-phase flow solver based on a homogeneous mixture model was developed. Computations were carried out for an axisymmetric cylinder, and the present code was validated by comparing the calculation results with experimental results. The results showed that the system is suitable for simulating evaporation and condensation processes in water flow. What’s more, the changes of cavity length with various operational conditions were calculated including the water depth, angle of attack, and free stream velocity. The conditions for cavitation inception were also studied to show the relationship between the operational conditions in multiphase flows.

Numerical Simulation of Cavitation Flow in a Centrifugal Pump

Based on two phase homogeneous mixture model, numerical simulation of the cavitating flow was performed on a centrifugal pump. Cavity shapes and performance of the pump in variable cavitation numbers were obtained. Numerical results show that the numerical method can be used to predict the cavitation performance of centrifugal pump; the incipient cavitation number is predicted, and the cavity shape is similar with the experiment; cavitation usually appears in the suction surface of the blade and locates in the inlet side, and becomes longer to the outlet direction with lower cavitation number; when the cavitation number is relatively higher, cavitating region locates in the inlet area of the blade and is relatively stable, while develops and separates when cavitation number becomes lower; when the cavitation number equals to the incipient cavitation number, performance of the centrifugal pump has no change almost, only when cavitation number reduces to some extent, the head decreases abruptly and also the efficiency, which means the pump operates in a bad condition and this condition should be avoided in the practical operation.

Numerical Simulation of Cavitation Flow in a Centrifugal Pump

Based on two phase homogeneous mixture model, numerical simulation of the cavitating flow was performed on a centrifugal pump. Cavity shapes and performance of the pump in variable cavitation numbers were obtained. Numerical results show that the numerical method can be used to predict the cavitation performance of centrifugal pump; the incipient cavitation number is predicted, and the cavity shape is similar with the experiment; cavitation usually appears in the suction surface of the blade and locates in the inlet side, and becomes longer to the outlet direction with lower cavitation number; when the cavitation number is relatively higher, cavitating region locates in the inlet area of the blade and is relatively stable, while develops and separates when cavitation number becomes lower; when the cavitation number equals to the incipient cavitation number, performance of the centrifugal pump has no change almost, only when cavitation number reduces to some extent, the head decreases abruptly and also the efficiency, which means the pump operates in a bad condition and this condition should be avoided in the practical operation.

Numerical investigation of cavitating flows for marine propulsors using an unstructured mesh technique

In the present study, the cavitating flows around marine propulsors have been numerically investigated by using a multi-phase RANS flow solver based on pseudo-compressibility and a homogeneous mixture model using unstructured meshes. To handle the relative motion between the rotating rotor and the stator, an overset mesh technique was adopted. The mass transfer rate between the liquid and vapor phases was determined by Merkle’s cavitation model based on the difference between the local and vapor pressure. The calculations were made for the P4381 marine propeller with different cavitation numbers at several advancing ratios. It was shown that the vapor structure, such as cavitation size and shape, was well captured at cavitating flow conditions. It was observed that the cavitation breakdown behavior was also well captured by the present method. Good agreement was obtained between the present results and the experiment for the integrated blade loadings, such as thrust and torque. The calculations were also made for a water-jet pump configuration at several flow conditions, and the cavitation breakdown behaviors for total headrise, power and thrust were validated by comparing the results with the experiment. The blade area covered by the cavitation and the shape of tip leakage cavitation were also compared with the experiment. Reasonable agreement between the predicted results and the experiment was obtained.

Modelling of an Homogeneous Equilibrium Mixture Model (HEM)

We present here a model for two phase flows which is simpler than the 6-equations models (with two densities, two velocities, two temperatures) but more accurate than the standard mixture models with 4 equations (with two densities, one velocity and one temperature). We are interested in the case when the two-phases have been interacting long enough for the drag force to be small but still not negligible. The so-called Homogeneous Equilibrium Mixture Model (HEM) that we present is dealing with both mixture and relative quantities, allowing in particular to follow both a mixture velocity and a relative velocity. This relative velocity is not tracked by a conservation law but by a closure law (drift relation), whose expression is related to the drag force terms of the two-phase flow. After the derivation of the model, a stability analysis and numerical experiments are presented.

자유표면 영향을 고려한 환기공동 전산유동해석

Cavitating flow is usually formed on the surface of a high speed underwater object. When a object moves near a free surface at very high speed, the cavity signature becomes one of the major factors to be overcome by sensors of military satellite. The present work was to study the free surface effect on the ventilated cavitation. The governing equations were Navier-Stokes equations based on a homogeneous mixture model. The multiphase flow solver used an implicit preconditioning method in the curvilinear coordinate system. The cavitation model used here was the one first presented by Merkle et al.(2006) and redeveloped by Park & Ha(2009). Computations considered the free surface effects were carried out with a NACA0012 hydrofoil and the corresponding results were compared with the experimental data to have a good agreement. Calculations were then performed considering the ventilated cavitation, including the effect of non-condensable gas under the free surface effects.

Cavitation performance prediction of mixed-flow pump based on CFD

The computational fluid dynamics (CFD) method is used to investigate the three-dimensional cavitation flow fields in a mixed-flow pump with high specific speed. In the numerical modeling, the homogeneous mixture model and Navier-Stokes equation with RNG k−ε turbulence model are employed. At the best efficiency condition, the cavitation location on the impeller blades and the distribution situation of vapor volume fraction were analyzed, as well as the performance curve between the pump's NPSHA and efficiency were predicted. The results show that, the cavitation directly affects the pressure distribution on impeller blade surfaces, and also results in change of the pump external characteristic. Under the primary cavitation condition, Water vapors first accumulate on the suction surface of blade's leading edge, which is close to the tip. With the decrease of inlet total pressure, the cavitation region extended towards the trailing edge and water vapor fraction volume become larger gradually. When cavitation is serious, water vapors mainly accumulate on the suction surface of blade's trailing edge. The prediction curve has the same trend as the practical curve, which can reveal the mixed-flow pump cavitation within the static characteristics.

Numerical simulation of cavitating flow past axisymmetric body

Cavitating flow simulation is of practical importance for many engineering systems, such as marine propellers, pump impellers, nozzles, torpedoes, etc. The present work has developed the base code to solve the cavitating flows past the axisymmetric bodies with several forebody shapes. The governing equation is the Navier-Stokes equation based on homogeneous mixture model. The momentum is in the mixture phase while the continuity equation is solved in liquid and vapor phase, separately. The solver employs an implicit preconditioning algorithm in curvilinear coordinates. The computations have been carried out for the cylinders with hemispherical, 1-caliber, and 0-caliber forebody and, then, compared with experiments and other numerical results. Fairly good agreements with experiments and numerical results have been achieved. It has been concluded that the present numerical code has successfully accounted for the cavitating flows past axisymmetric bodies. The present code has also shown the capability to simulate ventilated cavitation.