Two-phase Turbulence Model Research Articles

CFD of turbulent transport of particles behind a backward-facing step using a new model— k- ε- Sp

The k- ε- S p model, describing two-dimensional gas–solid two-phase turbulent flow, has been developed. In this model, the diffusion flux and slip velocity of solid particles are introduced to represent the particle motion in two-phase flow. Based on this model, the gas–solid two-phase turbulent flow behind a vertical backward-facing step is simulated numerically and the turbulent transport velocities of solid particles with high density behind the step are predicted. The numerical simulation is validated by comparing the results of the numerical calculation with two other two-phase turbulent flow models ( k- ε- A p, k- ε- k p) by Laslandes and the experimental measurements. This model, not only has the same virtues of predicting the longitudinal transport of the solid particles as the present practical two-phase flow models, but also can predict the lateral transport of the solid particles correctly.

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.

Numerical simulation of pulverized coal combustion and NO formation

A pure two-fluid model, instead of the Eulerian gas-Lagrangian particle models (particle trajectory models), is used for simulating three-dimensional (3-D) turbulent reactive gas–particle flows and coal combustion. To improve the simulation of the flow field and NO X formation, a modified k– ε– k p two-phase turbulence model and a second-order-moment (SOM) reactive rate model are proposed. The proposed models are used to simulate NO formation (fuel NO produced by NH 3) of methane–air combustion, and the prediction results are compared with those using the pure presumed PDF-finite-reaction-rate model and experimental data. The modified k– ε model and SOM model are more reasonable than the standard k– ε model and the pure presumed PDF-finite-reaction-rate model. The proposed models are also used to predict the coal combustion and NO formation at the exit of a double air register swirl pulverized-coal burner. The predicted results indicate that a pulverized-coal concentrator installed in the primary-air tube of burner has a strong effect on the coal combustion and NO X formation.

Critical Heat Flux Prediction Method Based on Two-Phase Turbulence Model

In this paper, we present an analytical methodology to predict forced convective CHF (Critical Heat Flux) for DNB (Departure from Nucleate Boiling) type boiling transition that occurs inside of uniformly heated round tubes. Axial directional two-phase flow analysis was conducted based on one-dimensional two-fluid model and typical constitutive models. At the same time, the radial directional distribution of void fraction at any axial location was calculated based on the bubble diffusion model, which was coupled with two-phase turbulence model for boiling bubbly flow. The calculated void fraction showed the wall peak distribution, and was compared with experimental data, which was derived from subcool boiling experiments. IPNVG (Incipient Point of Net Vapor Generation), which means the starting point of two-phase flow analysis, was also investigated well, since it was revealed that IPNVG had a significant influence on CHF prediction. By using this methodology for calculating radial directional void fraction distribution, we carried out CHF prediction for water on the assumption that DNB would occur when the local void fraction near the heated wall exceeds a critical value. The predicted CHF agreed well with experimental data, and the accuracy was within about 20%.

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.

Critical Heat Flux Prediction Method Based on Two-Phase Turbulence Model

In this paper, we present an analytical methodology to predict forced convective CHF (Critical Heat Flux) for DNB (Departure from Nucleate Boiling) type boiling transition that occurs inside of uniformly heated round tubes. Axial directional two-phase flow analysis was conducted based on one-dimensional two-fluid model and typical constitutive models. At the same time, the radial directional distribution of void fraction at any axial location was calculated based on the bubble diffusion model, which was coupled with two-phase turbulence model for boiling bubbly flow. The calculated void fraction showed the wall peak distribution, and was compared with experimental data, which was derived from subcool boiling experiments. IPNVG (Incipient Point of Net Vapor Generation), which means the starting point of two-phase flow analysis, was also investigated well, since it was revealed that IPNVG had a significant influence on CHF prediction. By using this methodology for calculating radial directional void fraction distribution, we carried out CHF prediction for water on the assumption that DNB would occur when the local void fraction near the heated wall exceeds a critical value. The predicted CHF agreed well with experimental data, and the accuracy was within about 20%.

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.

Numerical studies of pulverized coal combustion in a tubular coal combustor with slanted oxygen jet ☆

A pure two-fluid model for turbulent reacting gas-particle flow of coal particles is developed using a unified Eulerian treatment of both the gas and particle phases. The particles' history caused by mass transfer due to moisture evaporation, devolatilization and char reaction is described. Both velocity and temperature of the coal particles and the gas phase are predicted by solving the momentum and energy equations of the gas and particle phases, respectively. A k– ε– k k two-phase turbulence model, EBU–Arrhenius turbulent combustion model and four-flux radiation heat transfer model are incorporated into a comprehensive model. The above comprehensive mathematical model is used to simulate two-dimensional gas-particle flows and pulverized coal combustion in a newly designed tubular oxygen–coal combustor of blast furnace. Predicted results of isothermal gas-particle flows are in good agreement with those obtained by measurements. The results also show that the proposed tubular oxygen–coal combustor prolongs the coal particle residence time and enhances the mixing of coal and oxygen. Results indicate that smaller coal particles of 10 μm diameter are heated and devolatilized rapidly and have volatile combustion in the combustor, while larger coal particles of 40 and 70 μm in diameter are heated but not devolatilized, and combustion of such particles does not occur in the tubular combustor.

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.

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.

A double-k–ε and multi-δ pdf model for turbulent gas–liquid reacting flows

The gas–liquid reacting two-phase flow of a gaseous SF6 jet submerged in liquid metal Li is numerically simulated by a two-fluid model. To describe the changes of the flow pattern in the two-phase flow, a double-k–ε two-phase turbulence model is developed and adopted. A multi-δ-pdf model is proposed and applied to simulate the turbulent combustion of gaseous SF6 with liquid metal Li. The gas and liquid velocities, void fraction, shape of the penetrating region (the region containing the gas phase) and the mixture fraction related to gas temperature and species concentration are predicted. Comparison with the results using a single-fluid model shows that current predictions are reasonable in reflecting the influence of velocity slip between the two phases and capable of predicting Li/SF6 submerged combustion.

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 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.

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.

Simulation of swirling gas–particle flows using a DSM–PDF two-phase turbulence model

A DSM–PDF two-phase turbulence model, namely a Reynolds stress equation (DSM) model of gas turbulence combined with a probability density distribution function (PDF) equation model of particle turbulence, is proposed to simulate the swirling sudden-expansion gas–particle flows with swirl number of 0.47. The predicted axial and tangential gas and particle time-averaged velocities and RMS fluctuation velocities using the DSM–PDF and k– ε– kp models are compared with measurements reported in references. The results show that for weakly swirling flows both models can reasonably predict the mean-flow behavior, but the DSM–PDF model can better predict the anisotropy of two-phase turbulence and turbulence interaction between two phases, and hence may have the potential superiority in predicting strongly swirling flows.

Two-Fluid Models for Simulating Reacting Gas-Particle Flows, Coal Combustion and NOxFormation

Abstract Unlike the widely used Eulenan gas-Lagrangian particle models (particle trajectory models), two versions of two-fluid models—a pure two-fluid (FTF) model and a two-fluid-trajectory (continuum-trajectory, CT) model are proposed for simulating turbulent reacting gas-particle flows and coal combustion. Both of diem are based on Eulerian gas-phase equations, Eulenan particle-phase continuity and momentum equations, κ-ϵ-κ two-phase turbulence model, EBU-Arrhenius turbulent combustion model, six-flux radiation model, coal moisture evaporation, devolatilization and char combustion models with simultaneous three reactions. To account for the particle history effect, including the mass change due to moisture evaporation, devolatilization and char combustion and the particle temperature change due to the heat transfer between two phases, the FTF model uses Eulerian or partial differential conservation equations of particle mass, particle daf-coal mass, particle moisture and energy, while the CT model uses ...

Strongly swirling gas-particle flows and coal combustion in a cyclone combustor

Strongly swirling gas-particle flows with swirl numbers 1.5 and 1.0 in a cyclone combustor are measured using a 3-D phase Doppler particle anemometer system (PDPA), and the case of swirl number 1.5 is simulated using a unified second-order moment (USM) model of anisotropic two-phase turbulence. The prediction results using the USM model are then compared with those obtained using the isotropic k-epsilon-kp two-phase turbulence model and the PDPA measurements. The measurements and predictions show that for strongly swirling flows with axial and tangential inlets there is no recirculation zone in axial velocity profiles: the gas and particle tangential velocity profiles have the Rankine-vortex structure, but the solid-body rotation zone is much larger than that for weakly swirling flows: the axial gas and particle fluctuations are at first stronger than, then near to, and finally slightly smaller than the tangential ones: both axial and tangential particle time-averaged and fluctuation velocities lag behind the gas one: and the USM model can better predict the Rankine-vortex structure of tangential velocity profiles and the anisotropy of two-phase turbulence in strongly swirling flows than the k-ε-kp model. The research results of two-phase flows are used for optimum design of the coal-fired cyclone combustor burning 3- to 5-mm coal particles, which finally gives higher combustion efficiency and lower NO x formation, and for developing the combustion modeling.

Mass transfer between solid and liquid in a gas-stirred vessel

Mass transfer between solid and bulk liquid in an axisymmetric gas-stirred water model of a metallurgical reactor has been investigated both experimentally and theoretically. To this end, mass transfer rates from benzoic acid compacts submerged in an aqueous gas bubble driven system were measured via a weight loss technique. In conjunction with the weight loss measurements, liquid velocity and turbulence kinetic energy distributions in the bath were also mapped via laser doppler velocimetry (LDV). From the detailed LDV measurements, relevant dimensionless groups such as \(\operatorname{Re} _{loc,r} \left( { = \frac{{d\rho \sqrt {u^2 + v^2 } }}{\mu }} \right)\) and \(\operatorname{Re} _t \left( { = \frac{{d\rho \hat u}}{\mu }} \right)\) were estimated. Experimental measurements indicated that flow parameters varied from one location to another within the system. The corresponding variation in dissolution rates was, however, less pronounced. Such a trend was observed for all three gas flow rates studied. It was found that experimentally measured dissolution rates can be correlated with the measured flow and turbulence parameters (viz., √u2+v2 and u) in terms of a previously reported dimensionless correlation, viz., Sh=0.73 (Reloc,r)0.25 (Ret)0.32 (Sc)0.33. Parallel to flow measurements, a two-phase turbulent flow model was also applied to numerically compute the distributions of mean and fluctuating velocity components in the vessel. Embodying the predicted velocity components in the aforementioned correlation, mass transfer rates were recalculated. A comparison between the two sets of Sherwood numbers (estimated on the basis of the experimentally measured and theoretically predicted flow fields) suggests that solid-liquid mass transfer rates in a gas-stirred vessel can be predicted reasonably well via an axisymmetric, steady-state, two-dimensional turbulent flow model.

A Two-Fluid Turbulence Model for Gas-Solid Two-Phase Flows.

On the basis of a two-equation turbulence model of single-phase flows, two-fluid turbulence models, namely, the k–e–kp–ep model and the k–e–kp model are developed to describe turbulent gas-solid two-phase flows. Governing equations for the turbulent kinetic energy and the kinetic energy dissipation rate of the particulate phase are derived from their momentum equations, and unknown terms at two-equation closure level are modeled. The developed models show that the turbulence intensity of the particulate phase is often larger than that of the gaseous phase in the gas-solid flow in a 90° bend, which is quite in accordance with the experimental results. The conventional k–e–Ap model using a k–e turbulence model for the carrier fluid and Tchen-Hinze’s formula for the eddy viscosity of the particulate phase, however, shows that the particulate turbulence intensity is always smaller than that of the gaseous phase. Therefore, the two-phase turbulence models developed here are superior to the conventional turbulence model. The turbulence models are also applied to predict the effect of particles on gaseous phase turbulence in the gas-solid flow in a vertical pipe. The predicted results are favorably compared with the available experimental data.

Simulation of particle-fluid turbulence interaction in sudden-expansion flows

Turbulence interaction between gas and particle phases has been studied by numerical simulation in axisymmetric sudden-expansion chambers in this paper. A two-fluid model coupled with a k− ϵ− k p two-phase turbulence model proposed by the present authors was used in the computations. The predicted axial mean velocity, the turbulence intensity of the single phase (flow without particles) and the particle phase in two-phase flows are in agreement with the experimental data reported by Shahnam and Morris in 1989. Furthermore, predictions show that the particle mass loading strongly modifies gas-phase turbulence but has only a slight effect on particle turbulence. Comparison of the numerical results calculated by different of the k− ϵ− k p models with the experimental data indicates that the k− ϵ− k p model is inadequate and that the k− ϵ− k p model can properly predict the gas-particle turbulence in recirculating flows.