A USM-Θ two-phase turbulence model for simulating dense gas-particle flows

A second-order moment two-phase turbulence model for simulating dense gas-particle flows （USM-Θ model）, combining the unified second-order moment twophase turbulence model for dilute gas-particle flows with the kinetic theory of particle collision, is proposed. The interaction between gas and particle turbulence is simulated using the transport equation of two-phase velocity correlation with a two-time-scale dissipation closure. The proposed model is applied to simulate dense gas-particle flows in a horizontal channel and a downer. Simulation results and their comparison with experimental results show that the model accounting for both anisotropic particle turbulence and particle-particle collision is obviously better than models accounting for only particle turbulence or only particle-particle collision. The USM-Θ model is also better than the k-ε-kp-Θ model and the k-ε-kp-εp-Θ model in that the first model can simulate the redistribution of anisotropic particle Reynolds stress components due to inter-particle collision, whereas the second and third models cannot.

Experiments on two-phase flow in hydraulic jump on pebbled rough bed:Part 1–Turbulence properties and particle chord time and length

This study reported and discussed turbulence characteristics,such as turbulence intensity,correlation time scales,and advective length scales.The characteristic air–water time scale,including the particle chord time and length and their probability density functions(PDFs),was investigated.The results demonstrated that turbulence intensity was relatively greater on a rough bed in the roller length,whereas further downstream,the decay rate was higher.In addition,the relationship between turbulence intensity and dimensionless bubble count rate reflected an increase in turbulence intensity associated with the number of entrained particles.Triple decomposition analysis(TDA)was performed to determine the contributions of slow and fast turbulent components.The TDA results indicated that,regardless of bed type and inflow conditions,the sum of the band-pass(T'_(u))and high-pass(T″_(u))filtered turbulence intensities was equal to the turbulence intensity of the raw signal data(T_(u)).T″_(u) highlighted a higher turbulence intensity and larger vorticities on the rough bed for an identical inflow Froude number.Additional TDA results were presented in terms of the interfacial velocity,auto-and cross-correlation time scales,and longitudinal advection length scale,with the effects of low-and high-frequency signal components on each highlighted parameter.The analysis of the air chord time indicated an increase in the proportion of small bubbles moving downstream.The second part of this research focused on the basic properties of particle grouping and clustering.

Heat and Mass Transfers in a Two-Phase Stratified Turbulent Fluid Flow in a Geothermal Pipe with Chemical Reaction

This research focused on the study of heat and mass transfers in a two-phase stratified turbulent fluid flow in a geothermal pipe with chemical reaction. The derived non-linear partial differential equations governing the flow were solved using the Finite Difference Method. The effects of various physical parameters on the concentration, skin friction, heat, and mass transfers have been determined. Analysis of the results obtained indicated that the coefficient of skin friction decreased with an increase in Reynolds number and solutal Grasholf number, the rate of heat transfer increased with an increase in Eckert number, Prandtl number, and angle of inclination, and the rate of mass transfer increased with increase in Reynolds number, Chemical reaction parameter and angle of inclination. The findings would be useful to engineers in designing and maintaining geothermal pipelines more effectively.

Numerical simulation of the effect of void fraction and inlet velocity on two-phase turbulence in bubble-liquid flows

There are contradicted opinions on whether bubbles enhance or reduce the liquid turbulence. In this paper, the effect of void fraction and inlet velocity on the bubble-liquid two-phase turbulence of the multiple bubble-liquid jets in a two-dimensional channel is studied by using the two-phase second-order moment turbulence model. The results confirm the phenomena observed in experiments and reported in references that at a low void fraction and low inlet velocities the bubbles enhance the liquid turbulence, whereas at a high void fraction and high inlet velocities the bubbles reduce the liquid turbulence.

Particle modulations to turbulence in two-phase round jets

The particle modulations to turbulence in round jets were experimentally studied by means of two-phase velocity measurements with Phase Doppler Anemometer （PDA）. Laden with very large particles, no significant attenuations of turbulence intensities were measured in the farfields, due to small two-phase slip velocities and particle Reynolds number. The gas-phase turbulence is enhanced by particles in the near-fields, but it is significantly attenuated by the small particles in the far-fields. The smaller particles have a more profound effect on the attenuation of turbulence intensities. The enhancements or attenuations of turbulence intensities in the far-fields depends on the energy production, transport and dissipation mechanisms between the two phases, which are determined by the particle prop- erties and two-phase velocity slips. The non-dimensional parameter CTI is introduced to represent the change of turbulence intensity.

A K-εTWO-EQUATION TURBULENCE MODEL FOR THE SOLID-LIQUID TWO-PHASE FLOWS

A two-equation turbulence model has been dereloped for predicting two-phase flow the two equations describe the conserration of turbulence kinetic energy and dissipation rate of that energy for the incompressible carrier fluid in a two-phase flow The continuity, the momentum, K and εequations are modeled. In this model,the solid-liquid slip veloeites, the particle-particte interactions and the interactions between two phases are considered,The sandy water pipe turbulent flows are sueeessfuly predicted by this turbulince model.

NUMERICAL SIMULATION OF 3-D DENSE SOLID-LIQUID TWO-PHASE TURBULENT FLOW IN A NON-CLOGGING MUD PUMP

A mathematical model is set to evaluate the 3-D dense solid-liquid two-phaseturbulent flow in a non-clogging mud pump, the flow feature in the impeller channel is simulatedwith the tool of IPSA. Meanwhile, resort to TECPLOT as the post-processor, the simulation results isvisualized. The results show the main flow characteristics: There exists backflow and aberrantvelocities at inlet area and a relative velocity slip between two phases; A jet-wake flow pattern isdiscerned around the shroud-suction side area; The relative velocity vector of solid phase iscloser to the pressure surface than that of liquid phase and the trend is more obvious with theincrease of diameter; The kinetic energy of turbulence k and the dissipation rate e reach theirpeaks at the corner of pressure and suction surface. The simulation results show a good agreementwith the experimental flow features in the impeller channel, which prove the turbulent model used isvalid and provide a theoretical design basis to non-clogging pumps.

IMPROVED SUBGRID SCALE MODEL FOR DENSE TURBULENT SOLID-LIQUID TWO-PHASE FLOWS

The dense solid-phase governing equations for two-phase flows are obtained by using the kinetic theory of gas molecules.Assuming that the solid-phase velocity distributions obey the Maxwell equations,the collision term for particles under dense two-phase flow conditions is also derived. In comparison with the governing equations of a dilute two-phase flow,the solid-particle's governing equations are developed for a dense turbulent solid-liquid flow by adopting some relevant terms from the dilute two-phase governing equations.Based on Cauchy-Helmholtz theorem and Smagorinsky model, a second-order dynamic sub-grid-scale(SGS)model,in which the sub-grid-scale stress is a function of both the strain-rate tensor and the rotation-rate tensor,is proposed to model the two-phase governing equations by applying dimension analyses.Applying the SIMPLEC algorithm and staggering grid system to the two-phase discretized governing equations and employing the slip boundary conditions on the walls,the velocity and pressure fields,and the volumetric concentration are calculated.The simulation results are in a fairly good agreement with experimental data in two operating cases in a conduit with a rectangular cross-section and these comparisons imply that these models are practical.

An improved large eddy simulation of two-phase flows in a pump impeller

An improved large eddy simulation using a dynamic second-order sub-grid-scale （SGS） stress model has been developed to model the governing equations of dense turbulent particle-liquid two-phase flows in a rotating coordinate system, and continuity is conserved by a mass-weighted method to solve the filtered governing equations. In the cur- rent second-order SGS model, the SGS stress is a function of both the resolved strain-rate and rotation-rate tensors, and the model parameters are obtained from the dimensional consistency and the invariants of the strain-rate and the rotation-rate tensors. In the numerical calculation, the finite volume method is used to discretize the governing equations with a staggered grid system. The SIMPLEC algorithm is applied for the solution of the discretized governing equations. Body- fitted coordinates are used to simulate the two-phase flows in complex geometries. Finally the second-order dynamic SGS model is successfully applied to simulate the dense turbu-lent particle-liquid two-phase flows in a centrifugal impeller. The predicted pressure and velocity distributions are in good agreement with experimental results.

Turbulence,aeration and bubble features of air-water flows in macro-and intermediate roughness conditions

Free surface flows aeration potential causing the in macro- and intermediate flow characteristics to vary roughness conditions have a high with slopes and discharges. The underlying mechanism of two-phase flow characteristics in macro- and intermediate roughness conditions were analyzed in an experimental setup assembled at the Laboratory of Hydraulic Protection of the Territory （PITLAB） of the University of Pisa, Italy. Crushed angular rocks and hemispherical boulders were used to intensify the roughness of the bed. Flow rates per unit width ranging between 0.03 m^2/s and 0.09 m^2/s and slopes between 0.26 and 0.46 were tested over different arrangements of a rough bed. Analyses were mainly carried out in the inner flow region, which consists of both bubbly and intermediate flow regions. The findings revealed that the two-phase flow properties over the rough bed were much affected by rough bed arrangements. Turbulence features of two-phase flows over the rough bed were compared with those of the stepped chute data under similar flow conditions. Overall, the results highlight the flow features in the inner layers of the two-phase flow, showing that the maximum turbulence intensity decreases with the relative submergence, while the bubble frequency distribution is affected by the rough bed elements.

Two-phase turbulence models for simulating dense gas-particle flows

The two-fluid model is widely adopted in simulations of dense gas-particle flows in engineering facili- ties. Present two-phase turbulence models for two-fluid modeling are isotropic. However, turbulence in actual gas-particle flows is not isotropic. Moreover, in these models the two-phase velocity correlation is closed using dimensional analysis, leading to discrepancies between the numerical results, theoretical analysis and experiments. To rectify this problem, some two-phase turbulence models were proposed by the authors and are applied to simulate dense gas-particle flows in downers, risers, and horizontal channels; Experimental results validate the simulation results. Among these models the USM-O and the two-scale USM models are shown to give a better account of both anisotropic particle turbulence and particle-particle collision using the transport equation model for the two-phase velocity correlation.

Turbulence modulation model for gas–particle flow based on probability density function approach

he paper focuses on the turbulence modulation problem in gas–particle flow with the use of probability density function（PDF） approach. By means of the PDF method, a general statistical moment turbulence modulation model without considering the trajectory difference between two phases is derived from the Navier–Stokes equations. A new turbulence production term induced by the dispersed-phase is analyzed and considered. Furthermore, the trajectory difference between two media is taken into account. Subsequently, a new k–ε turbulence modulation model in dilute particle-laden flow is successfully set up. Then, the changes to several terms, including the turbulence production, dissipation, and diffusion terms, are well described consequently. The promoted model provides a more probable explanation for the modification of particles on the turbulence. Finally, we applied the model to simulate a gas–particle turbulence flow case in a wall jet, and found that the simulation results agree well with the experimental data.

THE FLOW STRUCTURE OF DILUTE GAS-PARTICLE SUSPENSIONS BEHIND A SHOCK WAVE MOVING ALONG A FLAT SURFACE

The asymptotic and numerical investigations of shock-induced boundary layers in gas-particle mixtures are presented. The Saffman lift force acting on a particle in a shear flow is taken into account. It is shown that particle migration across the boundary layer leads to intersections of particle trajectories. The corresponding modification of dusty gas model is proposed in this paper.The equations of two-phase sidewall boundary layer behind a shock wave moving at a constant speed are obtained by using the method of matched asymptotic expansions. The method of the calculation of particle phase parameters in Lagrangian coordinates is described in detail. Some numerical results for the case of small particle concentration are given.

THE EFFECT OF PARTICLES ON FLUID TURBULENCE IN A TURBULENT BOUNDARY LAYER OVER A CYLINDER

The turbulent fluid and particle interaction in the turbulent boundary layer for cross how over a cylinder has been experimentally studied. A phase-Doppler anemometer was used to measure the mean and fluctuating velocities of both phases. Two size ranges of particles (30 mu m similar to 60 mu m and 80 mu m similar to 150 mu m) at certain concentrations were used for considering the effects of particle sizes on the mean velocity profiles and on the turbulent intensity levels. The measurements clearly demonstrated that the larger particles damped fluid turbulence. For the smaller particles, this damping effect was less noticeable. The measurements further showed a delay in the separation point for two phase turbulent cross how over a cylinder.

Modified Diffusion Flux Model for Analysis of Turbulent Gas-Particle Two-Phase Flows

A modified diffusion flux model (DFM) was developed to analyze turbulent multi-dimensional gas-particle two-phase flows. In the model, the solid particles move in a modified acceleration field, g′′ , which includes the effects of various forces on the particles as if all the forces have the same effect on the particles as the gravity. The accelerations due to various forces are then taken into account in the calcula- tion of the diffusion velocities of the solid particles in the gas-particle two-phase flow. The DFM was used to numerically simulate the gas-solid two-phase flow behind a vertical backward-facing step. The numerical simulation compared well with experimental data and numerical results using both the k-ε-Ap and k-ε-kp two- fluid models available in the literature. The comparison shows that the modified diffusion flux model correctly simulates the turbulent gas-particle two-phase flow.

PREDICTION OF CONFINED TURBULENT GAS-PARTICLE JETS BY AN ENERGY EQUATION MODEL OF PARTICLE TURBULENCE

Based on a kinetic energy equation of particle turbulence, a k-ε-kk model for turbulent gas-particle flows is proposed. The prediction of confined plane gas-particle jets shows a good agreement with experimental data. This model is proved to be far superior to the presently used k-ε-A.P. model based on the algebraic model of particle turbulence.

ON BASIC EQUATIONS OF TURBULENT SWIRLING GAS-SOLID FLOWS AND THEIR APPLICATION IN CYCLONES

The basic equations of turbulent gas-solid flows are derived by using the pseudo-fluid model of particle phase with a refined two-phase turbulence model.These equations are then applied to swirling gas-particle flows for analyzing the collection efficiency in cyclone separators.

A NEW TURBULENCE MODULATION IN SECOND-ORDER MOMENT TWO-PHASE MODEL AND ITS APPLICATION TO HORIZONTAL CHANNEL

A new second-order moment two- phase turbulence model accounting for particle wake effect was established and used to simulate gas-particle flow in a horizontal channel for different values of wall roughness. The results show that compared with the model without considering the particle wake effect, the present model gives simulation results agreeing much better with the experimental results for the gas turbulence modulation, but the predicted results for particle motion with the two kinds of models are quite close.

SECOND-ORDER MOMENT TWO-PHASE TURBULENCE MODEL ACCOUNTING FOR TURBULENCE MODULATION IN SWIRLING SUDDEN-EXPANSION CHAMBER

A semi-empirical turbulence enhancement model accounting for the particle-wake effect was incorporated into the second-order moment two-phase turbulence model and employed to simulate gas-particle flows in a swirling sudden-expansion chamber. The simulated results for two-phases mean velocities and fluctuation velocities coincide well with the experiment ones, which demonstrates that this model, in comparison with the turbulence model not accounting for the wake effect, leads to higher calculating accuracy.

Electrochemical machining gap prediction with multi-physics coupling model based on two-phase turbulence flow

Considering the influence of hydrogen gas generated during electrochemical machining on the conductivity of electrolyte, a two-phase turbulent flow model is presented to describe the gas bubbles distribution.The k-e turbulent model is used to describe the electrolyte flow field.The Euler–Euler model based on viscous drag and pressure force is used to calculate the twodimensional distribution of gas volume fraction.A multi-physics coupling model of electric field,two-phase flow field and temperature field is established and solved by weak coupling iteration method.The numerical simulation results of gas volume fraction, temperature and conductivity in equilibrium state are discussed.The distributions of machining gap at different time are analyzed.The predicted results of the machining gap are consistent with the experimental results, and the maximum deviation between them is less than 50 lm.