Second-order Moment Two-phase Turbulence Model Research Articles

Hydrodynamic modeling of coaxial confined particle-laden turbulent flow

A new particle subgrid scale model is proposed to consider the effect of gas flow on particle motions. Multiphase gas-particle turbulent flow is modeled by a second-order moment two-phase turbulence model involving a four-way coupling strategy to describe the interactions among gas-particle, particle-gas and particle-particle collisions. A large eddy simulation algorithm is developed to solve the hydrodynamic parameters of confined swirling and non-swirling particle-laden flow in coaxial chamber. Results show that predictions are well agreed with experimental data. Vortex structures and vortices distributions of gas and particle flow are quietly different. Coherent structures of swirling particle flows are not observed, and length of recirculation region is almost one quarter of non-swirling flow. Compared to developed flow region of non-swirling flow, standard deviation values of granular temperature at near entrance decreased by 5.5 times. Dominant frequencies of particle number density of non-swirling and swirling flows are 18 Hz and 10 Hz. Particle dispersions exhibit anisotropic characteristics, and their distributions are not in accordance with the normal distribution. The 2D turbulence model needs to be further improved due to the failure of describing vortex stretch in this job.

Effects of Particles Collision on Separating Gas–Particle Two-Phase Turbulent Flows

A second-order moment two-phase turbulence model incorporating a particle temperature model based on the kinetic theory of granular flow is applied to investigate the effects of particles collision on separating gas–particle two-phase turbulent flows. In this model, the anisotropy of gas and solid phase two-phase Reynolds stresses and their correlation of velocity fluctuation are fully considered using a presented Reynolds stress model and the transport equation of two-phase stress correlation. Experimental measurements (Xu and Zhou in ASME-FED Summer Meeting, San Francisco, Paper FEDSM99-7909, 1999) are used to validate this model, source codes and prediction results. It showed that the particles collision leads to decrease in the intensity of gas and particle vortices and takes a larger effect on particle turbulent fluctuations. The time-averaged velocity, the fluctuation velocity of gas and particle phase considering particles collision are in good agreement with experimental measurements. Particle kinetic energy is always smaller than gas phase due to energy dissipation from particle collision. Moreover, axial–axial and radial–radial fluctuation velocity correlations have stronger anisotropic behaviors.

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.

Numerical simulation of sudden-expansion two-phase flows with two-scale second-order moment particle turbulence model

A two-scale second-order moment particle turbulence model is developed, based on the concept of particle large-scale fluctuation due to turbulence and particle small-scale fluctuation due to collision. The model is employed to simulate gas-particle flows in a sudden-expansion chamber. Simulation results are compared with the experimental results and with those obtained by the single-scale second-order moment two-phase turbulence model. It is shown that the two-scale model is with higher calculating accuracy than the single-scale model.

Numerical simulation of gas turbulence enhancement by particle-wake effect

A new turbulence enhancement model was incorporated into the second-order moment two-phase turbulence model and was used to simulate gas-particle flows in swirling chambers and channels with different wall roughness. The results show that compared with the turbulence modification model not accounting for the wake effect, this model, together with the conventional particle source term, gives simulation results in better agreement with the experimental data.

Large Eddy Simulation of Particle Wake Effect and RANS Simulation of Turbulence Modulation in Gas-Particle Flows

The turbulence enhancement by particle wake effect is studied by large eddy simulation (LES) of turbulent gas flows passing a single particle. The predicted time-averaged and root-mean-square fluctuation velocities behind the particle are in agreement with the Reynolds-averaged Navier-Stokes modeling results and experimental results. A semi-empirical turbulence enhancement model is proposed by the present authors based on the LES results. This model is incorporated into the second-order moment two-phase turbulence model for simulating vertical gas-particle pipe flows and horizontal gas-particle channel flows. The simulation results show that compared with the model not accounting for the particle wake effect, the present model gives simulation results for the gas turbulence modulation in much better agreement with the experimental results

A two-scale second-order moment particle turbulence model for gas-particle flow

A two-scale second-order moment two-phase turbulence model was developed and used to simulate gas-particle flow in a sudden-expansion chamber and a channel. The simulation results were in agreement with the experimental results, and the results were compared with those of the single-scale second-order moment two-phase turbulence model. Several improved features show that the two-scale model is to a certain extent better than the single-scale model, which may be attributed to the fact that particle turbulence is well characterized by the two-scale turbulence model.

Effect of empirical coefficients on simulation in two-scale second-order moment particle-phase turbulence model

A two-scale second-order moment two-phase turbulence model accounting for inter-particle collision is developed, based on the concept of particle large-scale fluctuation due to turbulence and particle small-scale fluctuation due to collision. The proposed model is used to simulate gas-particle downer reactor flows. The computational results of both particle volume fraction and mean velocity are in agreement with the experimental results. After analyzing effects of empirical coefficient on prediction results, we can come to a conclusion that, inside the limit range of empirical coefficient, the predictions do not reveal a large sensitivity to the empirical coefficient in the downer reactor, but a relatively great change of the constants has important effect on the prediction.

A two-scale second-order moment particle turbulence model and simulation of dense gas–particle flows in a riser

A two-scale second-order moment particle turbulence model is developed, based on the concept of particle large-scale fluctuation due to turbulence and particle small-scale fluctuation due to collision. It is then used to simulate dense gas–particle flows in a riser. The predicted results are in reasonable agreement with the experimental results and show the core-annulus flow structure observed in experiments. It is seen that the two-scale model is somewhat better than k f– ε f– k p– ε p– θ two-phase turbulence model and the single-scale second-order moment two-phase turbulence model (USM– θ model).

A two-scale second-order moment two-phase turbulence model for simulating dense gas-particle flows

A two-scale second-order moment two-phase turbulence model accounting for inter-particle collision is developed, based on the concepts of particle large-scale fluctuation due to turbulence and particle small-scale fluctuation due to collision and through a unified treatment of these two kinds of fluctuations. The proposed model is used to simulate gas-particle flows in a channel and in a downer. Simulation results are in agreement with the experimental results reported in references and are near the results obtained using the single-scale second-order moment two-phase turbulence model superposed with a particle collision model (USM-θ model) in most regions.

A second-order moment particle–wall collision model accounting for the wall roughness

A particle–wall collision model accounting for the wall roughness in the framework of second-order moment two-phase turbulence models is proposed, combining the advantages of the collision approach in the particle trajectory model and the PDF approach in the two-fluid model. The proposed model is incorporated into the second-order moment two-phase turbulence model to simulate axi-symmetric swirling and mixing-layer gas–particle flows. The simulation of swirling gas–particle flows and its comparison with the measurements show that the proposed model gives much better results than the widely used zero-gradient condition does, and is suggested to be used as wall boundary condition for particle phase instead of the widely used one. The simulation of mixing-layer gas–particle flows shows that the model accounting for the wall roughness gives smaller longitudinal mean velocities and greater longitudinal fluctuation velocities for particles, which are in better agreement with the experiment results, than those obtained using the model not accounting for the wall roughness. The results are qualitatively consistent with the simulation results using the particle trajectory model.

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.

On the second-order moment turbulence model for simulating a bubble column

Two versions of the second-order moment two-phase turbulence model are proposed in this study for simulating bubble–liquid two-phase turbulent velocity fluctuations and their interactions in bubble–liquid flows under the dispersed bubble regime. One of them is a full transport equation model; the other is an algebraic stresses model. The proposed model is used to simulate liquid and gas mean velocities, gas volume fraction, liquid and gas Reynolds stresses and turbulent kinetic energy in a 2-D bubble column. Furthermore, the bubble and liquid velocities, Reynolds stresses and gas volume fraction are measured using the PIV. The simulation results are in good agreement with the PIV results and experimental data in the literature. The studies reveal the liquid recirculation and bubble up-rising flow patterns, and anisotropic liquid and bubble normal Reynolds stresses. Bubble fluctuation is observed to be stronger than liquid fluctuation. Moreover, both the liquid velocity gradient and bubble–liquid interaction are important for the generation of liquid turbulence.

Simulation of swirling gas–particle flows using an improved second-order moment two-phase turbulence model

Swirling gas–particle flows in a co-axial sudden-expansion chamber with different swirl numbers are simulated using an improved second-order-moment two-phase turbulence model. The particle Reynolds stress equations and the two-phase fluctuation velocity correlation terms are closed based on a Lagrangian analysis, accounting for the crossing-trajectory effect, inertial effect and continuity effect. Predictions give the gas and particle axial and tangential averaged and fluctuation velocities for swirl numbers of s=0, s=0.47 and s=0.94. The swirl number is defined as the ratio of tangential momentum to axial momentum. Prediction results are in good agreement with the PDPA measurement results for both mean and fluctuation velocities of single-phase swirling flows and two-phase mean velocities of swirling gas–particle flows. However, the normal components of Reynolds stresses or the fluctuation velocities of two phases for swirling gas–particle flows are still underpredicted. The results show that increasing swirl number changes the shape and sizes of recirculation zones, the size of the solid-body rotation zone, reduces the turbulent fluctuation of two phases in the upstream region and enhances it in the downstream region.