Turbulence and cavitation models for time-dependent turbulent cavitating flows

Cavitation typically occurs when the fluid pressure is lower than the vapor pressure at a local thermodynamic state,and the flow is frequently unsteady and turbulent.To assess the state-of-the-art of computational capabilities for unsteady cavitating flows,different cavitation and turbulence model combinations are conducted.The selected cavitation models include several widely-used models including one based on phenomenological argument and the other utilizing interface dynamics.The kε turbulence model with additional implementation of the filter function and density correction function are considered to reduce the eddy viscosity according to the computed turbulence length scale and local fluid density respectively.We have also blended these alternative cavitation and turbulence treatments,to illustrate that the eddy viscosity near the closure region can significantly influence the capture of detached cavity.From the experimental validations regarding the force analysis,frequency,and the cavity visualization,no single model combination performs best in all aspects.Furthermore,the implications of parameters contained in different cavitation models are investigated.The phase change process is more pronounced around the detached cavity,which is better illus-trated by the interfacial dynamics model.Our study provides insight to aid further modeling development.     

Modeling the indentation, penetration and cavitation of elastic membranes

An energy argument is used to predict the penetration of an elastic membrane by a rigid cylindrical indenter. We study a sequence of axisymmetric equilibrium deformations beginning with the indentation of a solid disc, followed by penetration of the membrane at a critical value of the indenter displacement, and ending in a state of cavitation in which the membrane is detached from the indenter and a central traction-free hole is maintained by boundary data alone.     

Wake impacts on aerodynamic and aeroelastic behaviors of a horizontal axis wind turbine blade for sheared and turbulent flow conditions

The magnitude and temporal variations of wind speed considerably influence aerodynamic and structural responses of MW-sized horizontal axis wind turbines. Thus, this paper investigates the variations in airloads and blade behavior of a wind turbine blade resulting from operations in sheared and turbulent flow conditions. First, in order to validate the present methods, comparisons of aerodynamic results were made among the blade element momentum method, free-wake method, and numerical results from the previous studies. Then, the validated methods were applied to a national renewable energy laboratory 5 MW reference wind turbine model for fluid–structure interaction analyses. From the numerical simulations, it can be clearly seen that unfavorable airloads and blade deformations occur due to the sheared and turbulent flow conditions. In addition, it is clear that wake impacts are not as substantial at those of high wind speeds; however, the effects obviously affect the aerodynamic and structural behaviors of the blade at lower wind speeds. Therefore, it is concluded that the numerical results markedly indicate the demand for accurate assessment of wake dynamics for accurate estimations of the aerodynamic and structural responses for sheared and turbulent flow environments.     

Modeling droplet dispersion and interphase turbulent kinetic energy transfer using a new dual-timescale Langevin model

Dispersion of spray droplets and the modulation of turbulence in the ambient gas by the dispersing droplets are two coupled phenomena that are closely linked to the evolution of global spray characteristics, such as the spreading rate of the spray and the spray cone angle. Direct numerical simulations (DNS) of turbulent gas flows laden with sub-Kolmogorov size particles, in the absence of gravity, report that dispersion statistics and turbulent kinetic energy (TKE) evolve on different timescales. Furthermore, each timescale behaves differently with Stokes number, a non-dimensional flow parameter (defined in this context as the ratio of the particle response time to the Kolmogorov timescale of turbulence) that characterizes how quickly a particle responds to turbulent fluctuations in the carrier or gas phase. A new dual-timescale Langevin model (DLM) composed of two coupled Langevin equations for the fluctuating velocities, one for each phase, is proposed. This model possesses a unique feature that the implied TKE and velocity autocorrelation in each phase evolve on different timescales. Consequently, this model has the capability of simultaneously predicting the disparate Stokes number trends in the evolution of dispersion statistics, such as velocity autocorrelations, and TKE in each phase. Predictions of dispersion statistics and TKE from the new model show good agreement with published DNS of non-evaporating and evaporating droplet-laden turbulent flow.     

Experimental and numerical investigation of turbulent cross-flow in a staggered tube bundle

This paper presents the results of measurements and numerical predictions of turbulent cross-flow in a staggered tube bundle. The bundle consists of transverse and longitudinal pitch-to-diameter ratios of 3.8 and 2.1, respectively. The experiments were conducted using a particle image velocimetry technique, in a flow of water in a channel at a Reynolds number of 9300 based on the inlet velocity and the tube diameter. A commercial CFD code, ANSYS CFX V10.0, is used to predict the turbulent flow in the bundle. The steady and isothermal Reynolds–Averaged Navier–Stokes (RANS) equations were used to predict the turbulent flow using each of the following four turbulence models: a k-epsilon, a standard k-omega, a k-omega-based shear stress transport, and an epsilon-based second moment closure. The epsilon-based models used a scalable wall function and the omega-based models used a wall treatment that switches automatically between low-Reynolds and standard wall function formulations.

The experimental results revealed extremely high levels of turbulence production by the normal stresses, as well as regions of negative turbulence production. The convective transport by mean flow and turbulent diffusion were observed to be significantly higher than in classical turbulent boundary layers. As a result, turbulence production is generally not in equilibrium with its dissipation rate. In spite of these characteristics, it was observed that the Reynolds normal stresses approximated from the k-based two-equation models were in a closer agreement with experiments than values obtained from the second moment closure. The results show that none of the turbulence models was able to consistently reproduce the mean and turbulent quantities reasonably well. The omega-based models predicted the mean velocities better in the developing region while the epsilon-based models gave better results in the region where the flow is becoming spatially periodic.     

Numerical study of shear band instability and effect of cavitation on the response of a specimen under undrained biaxial loading

This paper presents an extension of the local second gradient model to multiphasic materials (solids particles, air, water) and including the cavitation phenomenon. This new development was made in order to model the response of saturated dilatant materials under deviatoric stress and undrained conditions and possibly, in future, the behavior of unsaturated soils. Some experiments have showed the significance of cavitation for the hydromechanical response of materials. However, to date and as far as we are aware, no attempt was made to implement the cavitation as a phase change mechanism with a control of pore pressure. The first part of the results section explores the effects of permeability, dilation angle and loading rate on the stability of shear bands during a localization event. The reasons underlying the band instability are discussed in detail, which helps defining the conditions required to maintain stability and investigating the effects of cavitation without parasite effect of materials parameters or loading rate. The model showed that, if a uniform response is obtained, cavitation triggers localization. However, in case of a localized solution, cavitation follows the formation of the shear band, with the two events being quite distinct.     

Heat transfer in turbocharger turbines under steady,pulsating and transient conditions

Heat transfer is significant in turbochargers and a number of mathematical models have been proposed to account for the heat transfer, however these have predominantly been validated under steady flow conditions. A variable geometry turbocharger from a 2.2 L Diesel engine was studied, both on gas stand and on-engine, under steady and transient conditions. The results showed that heat transfer accounts for at least 20% of total enthalpy change in the turbine and significantly more at lower mechanical powers. A convective heat transfer correlation was derived from experimental measurements to account for heat transfer between the gases and the turbine housing and proved consistent with those published from other researchers. This relationship was subsequently shown to be consistent between engine and gas stand operation: using this correlation in a 1D gas dynamics simulation reduced the turbine outlet temperature error from 33 °C to 3 °C. Using the model under transient conditions highlighted the effect of housing thermal inertia. The peak transient heat flow was strongly linked to the dynamics of the turbine inlet temperature: for all increases, the peak heat flow was higher than under thermally stable conditions due to colder housing. For all decreases in gas temperature, the peak heat flow was lower and for temperature drops of more than 100 °C the heat flow was reversed during the transient.     

Level set method for numerical simulation of a cavitation bubble,its growth,collapse and rebound near a rigid wall

A level set method of non-uniform grids is used to simulate the whole evolution of a cavitation bubble, including its growth, collapse and rebound near a rigid wall. Single-phase Navier–Stokes equation in the liquid region is solved by MAC projection algorithm combined with second-order ENO scheme for the advection terms. The moving interface is captured by the level set function, and the interface velocity is resolved by “one-side” velocity extension from the liquid region to the bubble region, complementing the second-order weighted least squares method across the interface and projection inside bubble. The use of non-uniform grid overcomes the difficulty caused by the large computational domain and very small bubble size. The computation is very stable without suffering from large flow-field gradients, and the results are in good agreements with other studies. The bubble interface kinematics, dynamics and its effect on the wall are highlighted, which shows that the code can effectively capture the “shock wave”-like pressure and velocity at jet impact, toroidal bubble, and complicated pressure structure with peak, plateau and valley in the later stage of bubble oscillating. The project supported by the National Natural Science Foundation of China (10272032 and 10672043). The English text was polished by Keren Wang.     

Modeling of dynamics, heat transfer, and combustion in two-phase turbulent flows: 1. Isothermal flows

This paper presents a review of authors' collective works in the field of two-phase flow modeling done in the past few decades. The paper is aimed at the construction of mathematical models for simulation of particle-laden turbulent flows. A kinetic equation was obtained for the probability density function (PDF) of the particle velocity distribution in turbulent flows. The proposed kinetic equation describes both the interaction of particles with turbulent eddies of the carrier phase and particle-particle collisions. This PDF equation is used for the derivation of different schemes describing turbulent momentum transfer in the dispersed particle phase. The turbulent characteristics of the gaseous phase are calculated on the basis of the k - turbulence model with a modulation effect of particles on the turbulence.

The constructed models have been applied to the calculation of various two-phase gas-particle turbulent flows in jets and channels as well as particle deposition in tubes and separators. For validating the theoretical and numerical results, a wide range of comparisons with experimental data from Russian and foreign sources has been done.     

Creation, transportation, and coalescence of liquid drops by means of a light beam

A novel principle of manipulation of discrete drops using concentration-capillary forces controlled by the thermal action of a light beam is proposed. The drops are created by the light beam in a thin layer of absorbing solution and in a film of that solution beneath an air bubble in the cell. The possibility of transporting both a single drop and a drop in an air bubble by means of a light beam is demonstrated. For the first time two drops are made to coalesce on a solid substrate by bringing them into contact by means of a light beam.     

Modeling of dynamics, heat transfer, and combustion in two-phase turbulent flows: 2. Flows with heat transfer and combustion

The objective of this part of the paper is to summarize the information concerning the authors' works in the field of simulation of two-phase gas-particle turbulent flows with heat transfer and combustion. A kinetic equation had been derived for the probability density function (PDF) of the particle velocity, temperature, and mass distributions in turbulent flows. This PDF equation is used for the construction of the governing conservation equations of mass, momentum, and heat transfer in the dispersed particle phase.The numerical scheme incorporates two-phase fluid dynamics, convective and radiative heat transfer, and combustion. The proposed models have been applied to the calculation of various particle-laden turbulent flows in jets, combustion and gasification chambers, and furnaces.     

Computational Fluid Dynamics (CFD) modelling of transfer chutes: Assessment of viscosity,drag and turbulence models

Computational Fluid Dynamics (CFD) has been successfully applied to evaluate potential dust emissions from bulk material transfer chutes. The implementation of appropriate models and modelling parameters is shown to be critical to the overall accuracy of the simulation results. This paper presents the influence of different models on the CFD simulation of transfer chutes and follows from an earlier study that details the influence of model parameters. The aim of this paper is to offer guidance to select models, and provide a better understanding of their influence in order to evaluate the most appropriate viscosity model, drag model and turbulence model for this application. A two-phase three-dimensional Euler–Euler model in commercial CFD software ANSYS FLUENT has been selected to model the granular and air flow in the transfer chute. The simulated air velocity profiles are discussed by comparing with each other and against experimental data obtained from Particle Image Velocimetry (PIV) results. The simulated particle velocity distributions were compared with results obtained using a well-established continuum method which was developed by Roberts. Furthermore, the air mass flow rates were analysed to evaluate the influence of different models. The results show that the granular viscosity model had a strong influence on the predictions of both air and particle flow. It was observed that both the drag model and turbulence model had limited influence on the outlet air velocities. The results also indicate that the Di-Felice drag model and SST k–ω turbulence model provide solutions closer to the experimental values than the other models investigated.     

Comparative study of Euler/Euler and Euler/Lagrange approaches simulating evaporation in a turbulent gas–liquid flow

This study deals with the Reynolds‐averaged Navier–Stokes simulation of evaporation in a turbulent gas–liquid flow in a three‐dimensional duct, focussing on the results obtained by a four‐equation turbulence model within the framework of the Euler/Euler approach for multiphase flow calculations: in addition to the two‐equation k?ε model describing the turbulence of the continuous (C) phase, the computational model employs transport equations for the turbulence kinetic energy of the disperse (D) phase and for the velocity covariance q=〈{u}^D{u}^C〉^D. In the present study, the evaporation model according to Abramzon and Sirignano (Int. J. Heat Mass Transfer 1989; 32 :1605–1618) has been extended by introducing an additional transport equation for a newly defined quantity ā, defined as the phase‐interface surface fraction. This allows the change in the drop diameter to be quantified in terms of a probability density function. The source term in the equation describing the dynamics of the volumetric fraction of the dispersed phase α^D is related to the evaporation time scale τ_Γ. The performance of the new model is evaluated by performing a comparative analysis of the results obtained by simulating a polydispersed spray in a three‐dimensional duct configuration with the results of the Euler/Lagrange calculations performed in parallel. Prior to these calculations, some selected (solid) particle‐laden flow configurations were computationally examined with respect to the validation of the background, four‐equation, eddy‐viscosity‐based turbulence model. Copyright © 2008 John Wiley & Sons, Ltd.     

Modeling the deformation of rock with rough surfaces of block contact under quasistatic and dynamic loading conditions

The effect of layers consisting of small particles or asperities on contact surfaces on the deformation of a block medium as a whole and the failure of the blocks constituting the medium was studied experimentally. The samples were subjected to quasistatic uniaxial compression perpendicular to the contact surfaces. Numerical modeling was performed of wave propagation during pulse loading of a pair of blocks having rough surfaces of contact and made of a material with elastic characteristics close to the characteristics of marble and limestone. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 173–178, May–June, 2007.     

Modeling of heat and mass transfer in a hydrocarbon fluid under inductive heating

Results of numerical simulations of the thermal action on a high-viscosity hydrocarbon fluid with temperature-dependent viscosity and thermal conductivity are presented. A system of equations of thermal convection in the Boussinesq approximation is used as the constitutive equations to describe the convection of the hydrocarbon fluid. The dynamics of the temperature field and convective structures in the fluid is studied. The spatial motion of the fluid is found to be locally nonuniform; the motion is accompanied by vortex flows; as a result, two regions with significantly different temperatures are formed in the medium. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 1, pp. 95–100, January–February, 2009.     

The influence of fluid properties on electrohydrodynamic heat transfer enhancement in liquids under viscous and electrically dominated flow conditions

Fluid property effects on electrohydrodynamic (EHD) heat transfer enhancement were investigated. Heat transfer, pressure drop, electrical power requirements, and the transition between the viscous dominated and electrically dominated flow regimes as a function of fluid properties were examined using three cooling oils having widely varying physical properties. Low viscosity and low electrical conductivity gave the greatest heat transfer enhancement for a given electrical power input. The required electrical power to achieve a specified heat transfer enhancement was greater for working fluids that had a small charge relaxation time, defined as the ratio of the electrical permittivity to the electrical conductivity. These results correlate well with available experimental and analytical data. A theoretical prediction of the effect of fluid properties and forced flow rate on the onset of EHD enhancement was experimentally verified. The onset of significant EHD heat transfer enhancement occurs most readily in low viscosity liquids at low Reynolds number flows for a given electrical power input.     

DNS,LES and RANS of turbulent heat transfer in boundary layer with suddenly changing wall thermal conditions

The objectives of this study are to investigate a thermal field in a turbulent boundary layer with suddenly changing wall thermal conditions by means of direct numerical simulation (DNS), and to evaluate predictions of a turbulence model in such a thermal field, in which DNS of spatially developing boundary layers with heat transfer can be conducted using the generation of turbulent inflow data as a method. In this study, two types of wall thermal condition are investigated using DNS and predicted by large eddy simulation (LES) and Reynolds-averaged Navier–Stokes equation simulation (RANS). In the first case, the velocity boundary layer only develops in the entrance of simulation, and the flat plate is heated from the halfway point, i.e., the adiabatic wall condition is adopted in the entrance, and the entrance region of thermal field in turbulence is simulated. Then, the thermal boundary layer develops along a constant temperature wall followed by adiabatic wall. In the second case, velocity and thermal boundary layers simultaneously develop, and the wall thermal condition is changed from a constant temperature to an adiabatic wall in the downstream region. DNS results clearly show the statistics and structure of turbulent heat transfer in a constant temperature wall followed by an adiabatic wall. In the first case, the entrance region of thermal field in turbulence can be also observed. Thus, both the development and the entrance regions in thermal fields can be explored, and the effects upstream of the thermal field on the adiabatic region are investigated. On the other hand, evaluations of predictions by LES and RANS are conducted using DNS results. The predictions of both LES and RANS almost agree with the DNS results in both cases, but the predicted temperature variances near the wall by RANS give different results as compared with DNS. This is because the dissipation rate of temperature variance is difficult to predict by the present RANS, which is found by the evaluation using DNS results.