Two-phase Velocity Correlation Research Articles

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 facilities. 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-Θ 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.

Numerical Simulation of Gas-Particle Turbulent Flow Using k<sub>g</sub>-ε<sub>g</sub> -k<sub>p</sub>-εp-k<sub>pg</sub>-θ Turbulence Model

kg-εg-kp-εp-kpg-θ turbulence model is proposed which considers particle-particle collision and gas-particle turbulence. This model includes turbulent kinetic energy equation, turbulent kinetic energy dissipation rate equation, particle pseudo-temperature transportation equation and the two-phase velocity correlation transport equation. To close the turbulence model, algebraic expressions of two-phase Reynolds stresses and two-phase velocity correlation variable are established which considered both gas-particle interaction and anisotropy. This model is used to simulate gas-particle in swirling sudden-expansion chamber. Comparing with kg-εg-kp-εp-θ model which is simply closed using a semi-empirical dimensional analysis, the present model has better predicted capability. It is shown that the present model gives simulation results in much better agreement with the experimental results than the kg-εg-kp-εp-θ model.

Fluctuation velocity correlation closure model for dense gas-particle turbulent flow

Turbulence model of kg-ɛg-kp-ɛp-kpg-θ is proposed. In the model, the two-phase velocity correlation turbulent kinetic energy kpg is modeled by transport equation. To close this turbulence model, algebraic expressions of two-phase Reynolds stresses and two-phase velocity correlation variable are established by considering both gas-particle interaction and anisotropy. This turbulence model is used to simulate dense gas-particle flow in a riser and in a downer. The predicted results show the core-annulus flow structure observed in the riser and the skin effect of particle concentration in the downer. The present model gives simulation results in much better agreement with the experimental results than those obtained by kg-ɛg-kp-ɛp-θ model which is simply closed using a semi-empirical dimensional analysis.

Measurement and simulation of the two-phase velocity correlation in sudden-expansion gas-particle flows

In this paper the present authors measured the gas-particle two-phase velocity correlation in sudden expansion gas-particle flows with a phase Doppler particle anemometer (PDPA) and simulated the system behavior by using both a Reynolds-averaged Navier-Stokes (RANS) model and a large-eddy simulation (LES). The results of the measurements yield the axial and radial time-averaged velocities as well as the fluctuation velocities of gas and three particle-size groups (30 µm, 50 µm, and 95 µm) and the gas-particle velocity correlation for 30 µm and 50 µm particles. From the measurements, theoretical analysis, and simulation, it is found that the two-phase velocity correlation of sudden-expansion flows, like that of jet flows, is less than the gas and particle Reynolds stresses. What distinguishes the two-phase velocity correlations of sudden-expansion flow from those of jet and channel flows is the absence of a clear relationship between the two-phase velocity correlation and particle size in sudden-expansion flows. The measurements, theoretical analysis, and numerical simulation all lead to the above-stated conclusions. Quantitatively, the results of the LES are better than those of the RANS model.

Modeling of Fluid Turbulence Modification Using Two-time-scale Dissipation Models and Accounting for the Particle Wake Effect

Presently developed two-phase turbulence models under-predict the gas turbulent fluctuation, because their turbulence modification models cannot fully reflect the effect of particles. In this paper, a two-time-scale dissipation model of turbulence modification, developed for the two-phase velocity correlation and for the dissipation rate of gas turbulent kinetic energy, is proposed and used to simulate sudden-expansion and swirling gas-particle flows. The proposed two-time scale model gives better results than the single-time scale model. Besides, a gas turbulence augmentation model accounting for the finite-size particle wake effect in the gas Reynolds stress equation is proposed. The proposed turbulence modification models are used to simulate two-phase pipe flows. It can properly predict both turbulence reduction and turbulence enhancement for a certain size of particles observed in experiments.

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 two-phase 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-ɛ-kp-Θ model and the k-ɛ-kp-ɛp-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.

Simulation of Swirling Gas-Particle Flows Using Different Time Scales for the Closure of Two-Phase Velocity Correlation in the Second-Order Moment Two-Phase Turbulence Model1

Three different time scales—the gas turbulence integral time scale, the particle relaxation time, and the eddy interaction time—are used for closing the dissipation term in the transport equation of two-phase velocity correlation of the second-order moment two-phase turbulence model. The mass-weighted averaged second-order moment (MSM) model is used to simulate swirling turbulent gas-particle flows with a swirl number of 0.47. The prediction results are compared with the PDPA measurement results taking from references. Good agreement is obtained between the predicted and measured particle axial and tangential time-averaged velocities. There is some discrepancy between the predicted and measured particle axial and tangential fluctuation velocities. The results indicate that the time scale has an important effect. It is found that the predictions using the eddy interaction time scale give the right tendency—for example, the particle tangential fluctuation velocity is smaller than the gas tangential fluctuation velocity, as that given by the PDPA measurements.

Simulation of swirling gas–particle flows using a nonlinear k– ε– kp two-phase turbulence model

The linear k– ε– k p two-phase turbulence model is rather simple, but it cannot predict the anisotropic turbulence of strongly swirling gas–particle flows. The second-order moment, two-phase turbulence model can better predict strongly swirling flows, but it is rather complex. Hence, the algebraic Reynolds stress expressions are derived based on two-phase Reynolds stress equations, and then the nonlinear relationships of two-phase Reynolds stresses and two-phase velocity correlation with the strain rates are obtained. These relationships, together with the transport equations of gas and particle turbulent kinetic energy and the two-phase correlation turbulent kinetic energy constitute the nonlinear k– ε– k p turbulence model. The proposed model is applied to simulate swirling gas–particle flows. Predictions give the two-phase time-averaged velocities and Reynolds stresses. The prediction results are compared with phase Doppler particle anemometer (PDPA) measurements and those predicted using the second-order moment model. The results indicate that the nonlinear k– ε– k p model has modeling capability nearly equal to that of the second-order moment model, but the former can save much computation time.