Unified Second-order Moment Research Articles

Two-fluid turbulence modeling of swirling gas-particle flows — A review

Swirling gas-particle/droplet flows are commonly encountered in various engineering equipments, such as gas-turbine combustors, gas-solid cyclone separators, cyclone combustors, hydro-cyclones and swirl burners/combustors in furnaces. To better understand the flow behavior by using numerical simulation is important for optimization and scaling-up of design, in order to increase the combustion efficiency and separation efficiency, reduce the pressure drop and pollutant formation, and stabilize the flame. Many-year systematic two-fluid modeling studies of swirling gas-particle flows were done by the research group directed by the present author, including Reynolds-averaged Navier–Stokes simulation (RANS modeling) using k-ε-kp, unified second-order moment (USM), Reynolds-stress-PDF (DSM-PDF), SOM-Monte-Carlo, and non-linear k-ε-kp two-phase turbulence models, proposed by the author and two-fluid large-eddy simulation (LES) using a two-phase sub-grid stress model, proposed by the author. The results give the two-phase time-averaged velocities, two-phase RMS fluctuation velocities, and particle concentration distribution, which indicate the advantage of E–E modeling over the E–L modeling and show the complex recirculation structures in the two-phase axial velocities and the Rankine-vortex (solid-body rotation plus potential vortex) structures in the two-phase tangential velocities, the anisotropic two-phase turbulence properties, and the effect of different closure methods on the two-phase flow behavior of swirling gas-particle flows. These results will help to develop highly efficient and low pollutant separators and combustors. This paper gives a brief review of our studies and will help the readers to understand in more detail the specific features of two-fluid modeling of complex turbulent gas-particle flows

Two-phase Turbulence Models in Eulerian-Eulerian Simulation of Gas-particle Flows and Coal Combustion

Eulerian-Eulerian (two-fluid) simulation of gas-particle flows and coal combustion are widely used because of its convenience in simulating large-size facilities. The key point is that it needs more complex closure models, compared to those in Eulerian gas-Lagrangian DEM modeling of particles. This keynote lecture will give a brief review on our many-year studies to solve these problems. The first one is the particle turbulence model. To overcome the shortcomings of the Hinze-Tchen's “particle-tracking-fluid” model, about 20 years ago, a transport equation of particle turbulent kinetic energy and transport equations of both gas and particle Reynolds stresses were proposed by us and subsequently constitute the so-called “k-ɛ-kp”, “unified second-order moment (USM)” and “non-linear k-ɛ-kp” two-phase turbulence models. Furthermore, for simulating reacting gas-particle flows and coal combustion, a full two-fluid model and a combined two-fluid-trajectory model, accounting for both particle turbulent diffusion and particle history effect due to moisture evaporation, devolatilization and char oxidation were proposed. The next is the particle-rough wall interaction. A particle-wall collision model accounting for wall roughness was proposed. Then, to overcome the limitation of the well-known kinetic theory of dense gas-particle flows, an anisotropic two-phase turbulence model, called “USM-Θ” model, accounting for both particle turbulence (large-scale fluctuation) and inter-particle collision (small-scale fluctuation) was proposed. Next, the particle-wake effect on gas turbulence modulation was studied to construct a sub-model and was added to the two-fluid modeling. At last, in recently developed two-fluid large-eddy simulation of gas-particle flows and combustion the particle sub-grid-scale (SGS) stress model is insufficiently studied. Some of them are based on a simple extension of the gas Smagorinsky SGS model without theoretical justification. Therefore, a USM-SGS two-phase stress model was proposed by us, properly accounting for the anisotropy of two-phase SGS stresses and the interaction between them.

Investigation on Swirling Gas-particle Hydrodynamics Using an Improved Momentum Transfer Coefficient

Abstract Based on the Wen's 1966 empirical momentum transfer coefficient relation of gas-particle two-phase turbulent flows, a new model to make up for the discontinuous characteristics is developed using a three-stage continuous function with switch weight function. Incorporated into the kinetic theory of granular flows to consider particle collisions and the unified second-order moment two phase turbulent model, it is utilized to predict the hydrodynamics of swirl gas-particle turbulent flows and the validation from the experimental measurements by Sommerfeld and Qiu 1991 is also carried out as well. Numerical simulated results showed that the prediction results by this model are well in agreements with experimental results. The particle dispersion distributions have the distinctively anisotropic behaviors due to complicated effects of centrifugal force, turbulent diffusion and particle inertia, which are quietly different from gas flows. Meanwhile, distributions of axial-axial particle-gas correlated velocity fluctuation is always greater than axial-tangential particle-gas and the tangential-tangential particle-gas velocity fluctuation is also greater than tangential-axial particle-gas phase. At the stronger shear and the vortex flow regions, its results agreed with experiments are much better than Wen's model.

Second-order moment modeling of dispersed two-phase turbulence—Part 1: USM, k-ɛ-k p, and non-linear k-ɛ-k p two-phase turbulence models

Turbulent dispersed multiphase flows, including gas-particle, gas-droplet and bubble-liquid flows, are widely encountered in various engineering facilities. Modeling of two-phase turbulence, in particular the dispersed phase turbulence, is the key problem in the Eulerian-Eulerian simulation of practical dispersed multiphase flows. Although different models were developed and used, the experimental validation shows that they cannot always give satisfactory prediction results. In this paper the present author give a detailed review of the unified second-order moment (USM), k-ɛ-k p and nonlinear k-ɛ-k p two-phase turbulence models, proposed by him. The derivation and closure of these models are described in detail and the experimental validation and application of these models are extensively discussed.

Second-order moment modeling of dispersed two-phase turbulence-Part 2-USM-Θ two-phase turbulence model and USM-SGS two-phase stress model

Dense gas-particle flows are frequently encountered in fluidized beds, riser and downer reactors, pneumatic transport and the near-wall zone of dilute gas-particle flows. Particle-particle collision plays an important role in the behavior of two-phase flows. In this paper a USM-Q two-phase turbulence model for dense gas-particle flows is proposed to account for both two-phase turbulence and inter-particle collision. For two-fluid large-eddy simulation of gas-particle flows, the author proposed a unified second-order moment (USM) two-phase SGS stress model and a two-phase k-kp SGS energy-equation stress model. The proposed models can fully account for the interaction between the gas and particle SGS stresses.

Comparison of gas particle flow prediction from large eddy simulation and Reynolds-averaging Navier-Stokes modeling

In order to account for the effect of particle existence on gas-particle turbulence flow in large-eddy simulation (LES), a new gas-particle turbulent kinetic energy subgrid-scale (SGS) turbulence model is established, and the effect of particle wake is also considered in gas turbulent kinetic energy SGS turbulence model. Simulation of gas-particle turbulence flow in backward-facing step is carried out by LES using present model and by unified second-order moment (USM) model. The prediction statistical results including mean velocity and fluctuation velocity by LES using present model are in reasonable agreement with the experimental results. It is shown that present model is with higher calculating accuracy than USM model, which indicates that the turbulent kinetic energy SGS turbulence model is suitable.

Large-eddy simulation of swirling gas-particle flows using a USM two-phase SGS stress model

In large-eddy simulations (LES) of gas-particle flows most investigators use single-phase subgrid scale (SGS) stress models. The Interaction between the two-phase SGS stresses is not fully taken into account. In this paper, a unified second-order moment (USM) two-phase SGS stress model for the LES of gas-particle flows is proposed, in which the interaction between the two-phase SGS stresses and anisotropy of the two-phase SGS stresses is fully taken into account. The proposed model is used in the LES of swirling gas-particle flows, together with RANS modeling using the USM two-phase turbulence model. The instantaneous results exhibit the multiple recirculating gas flow structure similar to that of the single-phase swirling flows, but the particle flow structure shows less vortices. The two-phase time-averaged velocities and RMS fluctuation velocities predicted by both LES-USM and RANS-USM models are almost the same and are in good agreement with the experimental results. However, for two-phase RMS fluctuation velocities, the LES-USM results are somewhat better than the RANS-USM results.

Two-Fluid Models for Simulating Dispersed Multiphase Flows-A Review

The development of two-fluid models for simulating dispersed multiphase flows (gas-particle, gas-droplet, bubble-liquid, liquid-particle flows) by the present author within the last 20 years is systematically reviewed. The two-fluid models based on Reynolds expansion, time averaging and mass-weighed averaging, and also PDF transport equations are described. Different versions of two-phase turbulence models, including the unified second-order moment (USM) and k-ε-kp models, the DSM-PDF model, the SOM-MC model, the nonlinear k-e-kp model, and the USM-Θ model for dense gas-particle flows and their application and experimental validation are discussed.

A second-order moment turbulence model for power law fluid with particles

The USM - θ model of power law fluid for dense two-phase turbulent flow was developed, which combines the unified second-order moment model for two-phase turbulence with the particle kinetic theory for the inter-particle collision. This model was used to simulate the turbulent flow of power law fluid single-phase in pipe. It is shown that the USM - θ model has better prediction result than the κ f - ɛ- f - k p - ɛ p - θ model. The USM - θ model was then used to simulate the dense two-phase turbulent up flow of power law fluid with particles. With the increase of the flow exponent, the velocities of power law fluid and particles increase near the pipe centre. Comparison between the two-phase flow of power law fluid-particle and of liquid-particle indicates that the axial fluctuation velocity of fluid phase and particle phase in liquid-particle two-phase flow is smaller than that in the power law fluid two-phase flow, but the two-phase velocities of power law fluid-particle and liquid-particle are close to each other.

Studies of the effect of a coal concentrator on NO formation in swirling coal combustion

To develop low-pollution burners, the effect of a coal concentrator on NO formation in swirling coal combustion is studied using both numerical simulation and experiments. The isothermal gas–particle two-phase velocities and particle concentration in a cold model of swirl burners with and without coal concentrators were measured using the phase Doppler particle anemometer (PDPA). A full two-fluid model of reacting gas–particle flows and coal combustion with an algebraic unified second-order moment (AUSM) turbulence-chemistry model for the turbulent reaction rate of NO formation are used to simulate swirling coal combustion and NO formation with different coal concentrators. The results give the turbulent kinetic energy, particle concentration, temperature and NO concentration in cases of with and without coal concentrators. The predicted results for cold two-phase flows are in good agreement with the PDPA measurement results, showing that the coal concentrator increases the turbulence and particle concentration in the recirculation zone. The combustion modeling results indicate that although the coal concentrator increases the turbulence and combustion temperature, but still can remarkably reduce the NO formation due to creating high coal concentration in the recirculation zone.

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 coal combustion by AUSM turbulence-chemistry char combustion model and a full two-fluid model

An algebraic unified second-order moment (AUSM) turbulence-chemistry model of char combustion is introduced in this paper, to calculate the effect of particle temperature fluctuation on char combustion. The AUSM model is used to simulate gas-particle flows, in coal combustion in a pulverized coal combustor, together with a full two-fluid model for reacting gas-particle flows and coal combustion, including the sub-models as the k-ε- k p two-phase turbulence model, the EBU-Arrhenius volatile and CO combustion model, and the six-flux radiation model. A new method for calculating particle mass flow rate is also used in this model to correct particle outflow rate and mass flow rate for inside sections, which can obey the principle of mass conservation for the particle phase and can also speed up the iterating convergence of the computation procedure effectively. The simulation results indicate that, the AUSM char combustion model is more preferable to the old char combustion model, since the later totally eliminate the influence of particle temperature fluctuation on char combustion rate.

04/01108 Numerical simulation of effect of swirl on NO formation in coal combustion: Zhang, Y. et al. Gongcheng Rewuli Xuebao, 2003, 24, (1), 165–168. (In Chinese)

The gas-particle flows, coal combustion and NO formation in a coal burner with different swirl numbers are simulated using a unified second-order moment algebraic model of NO turbulent reaction with Solomon's model of HCN release and a two-fluid model of coal combustion. The prediction results are in good agreement with the experimental results reported in references. The results indicate that as the swirl number increases, the NO emission at first decreases and then increases, while the burnout rate at first increases and then decreases. This phenomena is similar to that obtained in gas combustion.

04/00396 Simulation of swirling coal combustion using a full two-fluid model and an AUSM turbulence-chemistry model: Zhou, L. X. et al. Fuel, 2003, 82, (8), 1001–1007

Abstract A full two-fluid model of reacting gas-particle flows with an algebraic unified second-order moment turbulence-chemistry model for the turbulent reaction rate of NO formation are used to simulate swirling coal combustion. The sub-models are the k – e – k p two-phase turbulence model, the EBU–Arrhenius volatile and CO combustion model, the six-flux radiation model, coal devolatilization model and char combustion model. The prediction results are in good agreement with the experimental results taken from references.

Simulation of NOx formation in turbulent swirling combustion using a USM turbulence-chemistry model

A unified second-order moment (USM) turbulence-chemistry model for simulating NOx formation in turbulent combustion is proposed. All of correlations, including the correlation of the reaction-rate coefficient fluctuation with the concentration fluctuation, are closed by the transport equations in the same form. This model discards the approximation of series expansion of the exponential function or the approximation of using the product of several 1-D PDF's instead of a joint PDF. It is much simpler than other refined models, such as the PDF transport equation model and the conditional moment closure model. The proposed model is used to simulate methane-air swirling turbulent combustion and NOx formation. The prediction results are in good agreement with the experimental results.

Simulation of swirling combustion and NO formation using a USM turbulence-chemistry model ☆

A unified second-order moment (USM) turbulence-chemistry model is used to simulate methane-air swirling combustion and NO formation for different swirl numbers. The simulation results are compared with those using the EBU–Arrhenius (E–A) combustion model, the simplified PDF model of NO formation in turbulent flows and the corresponding experimental results. The comparison indicates that the USM model is obviously better than the E–A model and the simplified PDF model. The E–A model cannot reasonably simulate the finite-rate kinetics, while the simplified PDF model, using a product of two single-variable PDF's instead of a joint PDF, remarkably under-predicts the NO reaction rate. The USM model gives the best agreement with the experimental results. Predictions show that as the swirl number increases the total NO formation at first decreases and then increases, which is in agreement with the experimental results.

Simulation of swirling coal combustion using a full two-fluid model and an AUSM turbulence-chemistry model ☆

A full two-fluid model of reacting gas-particle flows with an algebraic unified second-order moment turbulence-chemistry model for the turbulent reaction rate of NO formation are used to simulate swirling coal combustion. The sub-models are the k– ε– k p two-phase turbulence model, the EBU–Arrhenius volatile and CO combustion model, the six-flux radiation model, coal devolatilization model and char combustion model. The prediction results are in good agreement with the experimental results taken from references.

A USM turbulence-chemistry model for simulating NO x formation in turbulent combustion

A unified second-order moment (USM) turbulence-chemistry model for simulating NO x formation in turbulent combustion is proposed. All the correlations, including the correlation of the reaction-rate coefficient fluctuation with the concentration fluctuation, are closed by the transport equations in the same form. This model abandons the series expansion approximation of the exponential term or the approximation of using a product of two single-variable PDFs instead of a joint PDF. The proposed model is used to simulate methane–air jet diffusion combustion and NO x formation. The combustion prediction results are compared with those using the EBU-Arrhenius model and other two versions of the second-order moment model. The NO x prediction results are compared with those using the pure presumed PDF model. Validation of predictions using the experimental data given by the Sandia National Laboratory, USA indicates that the proposed model gives better results than other models, and it is much economical than other refined models.

A second-order-moment–Monte-Carlo model for simulating swirling gas–particle flows

A second-order moment (SOM) gas-phase turbulence model, combined with a Monte-Carlo (MC) simulation of stochastic particle motion using Langevin equation to simulate the gas velocity seen by particles, is called an SOM–MC two-phase turbulence model. The SOM–MC model was applied to simulate swirling gas–particle flows with a swirl number of 0.47. The prediction results are compared with the PDPA measurement data and those predicted using the Langevin-closed unified second-order moment (LUSM) model. The comparison shows that both models give the predicted time-averaged flow field of particle phase in general agreement with those measured, and there is only slight difference between the prediction results using these two models. In the near-inlet region, the SOM-MC model gives a more reasonable distribution of particle axial velocity with reverse flows due to free of particle numerical diffusion, but it needs much longer computation time. Both models underpredict the gas and particle fluctuation velocities, compared with those measured. This is possibly caused by the particle–wall and particle–particle interaction in the near-wall region, and the effect of particles on dissipation of gas turbulence, which is not taken into account in both models.

Simulation of swirling gas–particle flows using USM and k– ε– kp two-phase turbulence models

The turbulent swirling gas–particle flows with swirl numbers 0.47 and 1.5 are simulated using a unified second-order moment (USM) (two-phase Reynolds stress equations) and a k– ε– kp two-phase turbulence models. The results are compared with experiments. Both two models can well predict the axial time-averaged two-phase velocities in case of s=0.47, but the USM model is better than the k– ε– kp model in predicting the tangential time-averaged two-phase velocities of strongly swirling flows ( S=1.5). The anisotropic two-phase turbulence can well be described only using the USM model. The results give the difference in flow behavior between weakly swirling and strongly swirling gas–particle flows.