Gas-particle Flow Research Articles

Continuum modeling of gas–particle flows: an overview

Continuum modeling of gas–particle flows: an overview

An Open-Source Code for High-Speed Non-Equilibrium Gas–Solid Flows in OpenFOAM

This paper details the development and verification tests of an open-source code named hy2LPTFoam intended for solving high-speed non-equilibrium gas-particle flows in OpenFOAM. The solver, based on hy2Foam for high-speed non-equilibrium gas flow, integrates multiple particle force models, heat transfer models, the diffusion-based smoothing method, and the MPPIC method. The verification tests incorporate interactions between shock waves and particle curtains with varying particle volume fractions, a JPL nozzle generating a two-phase gas–particle flow, and a Mars entry body with two particle inflow mass fractions. The tests yield good physical agreement with numerical and experimental data from the literature.

Effect of particle Froude number on sub-grid effective drag, filtered and residual stresses in fluidized gas-particle flows

Sub-grid effective drag, filtered and residual stresses in the meso-scale of gas-particle fluidized flows are intrinsically affected by underlying micro-scale conditions as well as non-local effects related to macro-scale conditions. In this work we applied microscopic two-fluid modeling to experiment with particle Froude number in order to evaluate the impact of this micro-scale condition over the concerning meso-scale derived sub-grid parameters. We performed highly resolved simulations in periodic domains for particle Froude numbers from 12.21 to 799.22, for a wide range of macro-scale conditions. Results were filtered and classified by ranges of meso-scale markers for the various particle Froude numbers. The particle Froude number was found to considerably affect the structural refinement of the heterogeneous flow fields thereby directly impacting effective drag, filtered and residual stresses. All of those parameters showed systematic behaviors in relation to particle Froude number, thereby providing sound data for new sub-grid modeling propositions.

An inertial number regulated constitutive model for the gas-fluidization of binary mixtures across dilute and dense regimes

In this study, a constitutive model that is applicable to both dilute and dense regimes for simulating gas-particle flows with polydisperse particles is proposed. In dilute regime, solid stress is closed by kinetic theory of granular flow (KTGF). In dense regime, solid stress is closed by the η(Is) rheology. The transition from dilute to dense regimes is realized smoothly by the dynamic blending function χmix, which is a function of the inertial number of mixture Imix. The dynamic blending function χmix is also used to link the solid–solid drag force at different regimes. This new model was validated with the experimental data of polydisperse bubbling fluidized bed of Girimonte et al. (2018). When compared with the conventional baseline model, this new model improves the transition from dilute to dense regimes and the predictions in both density and size segregations.

Numerical modeling of heat transfer behavior for two-phase flow in a nozzle considering phase change

The heat transfer and phase change of alumina particles in the gas-particle flow of the nozzle plays an important role in solid rocket motors (SRM) due to the coupling between the heat transfer and two-phase flow. However, it lacks precise modeling of the heat transfer behaviors of condensed particles in the nozzle, especially the phase change effect. In this article, we determine that the Drake model has the highest accuracy in calculating the convective heat flux between two phases, and propose a correlation to obtain radiative heat flux between the particle and walls. Then, a one-dimensional two-phase non-equilibrium model is established to consider the effects of heat transfer and solidification of particles on the two-phase flow in the nozzle. The results show that considering the phase change of particle improves the outlet thrust of the nozzle, but such increment decreases with the gas inlet temperature. When the supercooling phenomenon is considered, the nozzle thrust is reduced by 1.14% compared with that considering no supercooling. As the particle size increases, the outlet temperature of the particle phase rises and can even surpass the solidification temperature of particles and the velocity of the particle phase decreases significantly.

A general drag coefficient model for a spherical particle incorporating rarefaction and particle-to-gas temperature ratio effects

A concept and model of two critical Reynolds numbers Rep,cr1 and Rep,cr2 corresponding respectively to onsets of drag crisis and recovery are proposed. A drag model at limits of zero particle Mach and Knudsen numbers is constructed. On this basis, we develop a general drag coefficient model applicable for a spherical particle traveling in a gas by using a large number of available data derived from the previous experiments, direct numerical simulations and direct simulation Monte-Carlo methods. The scope of applicability of the proposed drag model covers all flow regimes relative to the particle characterized by particle Reynolds and Mach (or Knudsen) numbers and different particle-to-gas temperature ratios. Its comparison with two latest general drag models shows the significantly smaller relative error. Furthermore, quasi-one dimensional simulations against two supersonic nozzle gas-particle flow experiments are conducted with an in-house code to validate its accuracy in comparison with the two drag models.

Experimental development of packing structures in a gas-particle trickle flow heat exchanger for application in concentrating solar tower systems

Ceramic particles represent a viable alternative as heat transfer and storage medium in concentrating solar tower systems. The particles are heated in solar-receivers close to 1000 °C. To utilize the stored energy in the particles, an air-particle direct-contact trickle-flow heat exchanger has been identified as suitable for this task. To date, no design recommendations exist that identify an optimized packing structure capable of providing a high particle volume fraction and a uniform spatial particle density distribution for a given grain type. Consequently, an experimental selection process is presented in this work to assess various packing structures for a given grain type in a trickle-flow reactor. The experiments were conducted with countercurrent flowing air at ambient conditions and 1 mm bauxite particles. A variety of packing structures were investigated at varying media flow rates. For each flow condition, the particle volume fraction was determined, as well as the particle distribution in a separate analysis. The cold experiments yielded a clear image of a preferred packing geometry, which will be discussed in detail. The results will serve as the basis for further hot experiments and thermal performance analysis in future work, where the packing geometry can be refined iteratively if necessary.

Mathematical Modeling and Design of Parboiled Paddy-Impinging Stream Dryer Using the CFD-DEM Model.

Impinging stream dryers (ISDs) are effective for removing moisture from particulate materials because of the complex multiphase transport of air particles in ISDs. Nowadays, computational techniques are powerful to simulate multiphase flows, including dilute and dense-phase gas-solid flows and hence, the use of a reliable computational model to simulate the phenomena and design a dryer has recently received more attention. In this study, computational fluid dynamics, combined with the discrete element method (CFD-DEM) and falling drying rate model, were used to predict the multiphase transport phenomena of parboiled paddy in a coaxial ISD. The design of an impinging stream pattern for improving residence time in a drying chamber of ISD was also investigated. The results showed that the CFD-DEM, in combination with the falling drying model, could be well-utilized to predict the particle motion behavior and lead to more physically realistic results. The predicted change of moisture content in parboiled paddy was in good agreement with the experimental data for 17 cycles of drying. Although the prediction of mean residence time was lower than the experimental data, the predicted mean residence time was a similar trend to the experimental data. For ISD design, the simulation revealed that the use of two stages of impinging stream region (two streams collide at the top of the drying chamber at the first stage and then the gas particles flow on the incline floor to collide with the other stream at second stage) in a drying chamber could increase the residence time approximately 75% and reduce drying cycle from 17 to 10 cycles when it was considered at the same final moisture content.

CFD modelling of Close-Coupled Gas Atomisation (CCGA) process by employing the Euler-Lagrange approach to understand melt flow instabilities

This paper presents a CFD analysis of the melt and flow-field instabilities in a close-coupled gas atomisation process (CCGA) caused by the gas–melt interactions. The melt mass flow is coupled to the atomiser internal pressure, which varies over time due to the unsteady flow field. A two-phase flow of Argon gas and melt particles is modelled using a coupled Euler-Lagrange framework. Three different initial gas-to-melt ratios (GMRs) of 5.5, 2.6 and 1.32 are considered to study the gas–melt interaction. The results show that in the case GMR = 1.32, sustained instability both in the melt and in the flow-field are distinctly observed, resembling physical atomisation process. This melt fluctuation corresponded to an alternating flow-field fluctuation; alternating between open- to closed-wake condition, where the local maxima of the melt corresponded to an open-wake condition, and the local minima of the melt corresponded to a closed-wake condition.

Drag coefficient for micron-sized particle in high-speed flows

The drag force on the small particle in high-speed flows is influenced by the combined effects of fluid viscosity, compressibility, and rarefaction. The existing drag coefficient models are still insufficient in accuracy and efficiency for gas-particle flow simulation. This study comprehensively considers these effects and conducts high-fidelity numerical simulations. A new drag coefficient is generated using a symbolic regression method reasonably based on the particle Mach number, Reynolds number, and Knudsen number, which are related to particle diameter, gas-particle relative velocity, and other parameters. The new drag coefficient possesses clear physical significance, high predictive accuracy, low computational cost, and consistency with theory in limiting conditions. The application of the new drag coefficient to three typical gas-solid two-phase flow cases demonstrated its excellent performance.

The effect of collision parameters on the 3D Eulerian simulation of a thin rectangular bubbling fluidized bed

It is well known that the hydrodynamics of dense gas–particle flows depends heavily on inter-particle and particle–wall collisions; however, the subtleties of these interactions are not always fully recognized or appreciated. In this study, the two-fluid model is used to systematically examine the effects of collision parameters, i.e., particle–particle restitution coefficient, particle–wall restitution coefficient, and wall specularity coefficient, on simulations of the hydrodynamics of a pseudo two-dimensional bubbling fluidized bed.The utilization of high-resolution Eulerian simulations facilitates the representation of meso-scale structures without the use of a sub-grid scale model, while qualitatively reflecting the experimental data. To ensure statistically robust results and increase confidence in the simulations, a careful assessment of the time-averaging interval was first undertaken to smooth out the fluctuations that persist even after the bed reaches steady state.A quantitative analysis was then performed to analyze important facets of the flow, including bubble characteristics, particle velocity fields, and granular temperature. The underlying physical formulation was employed to elucidate how collision parameters impact the hydrodynamics of the flow.The notable findings of this study are threefold. First, the specific details of the collisions between particles are shown to significantly influence the bubble characteristics and overall flow pattern. However, the effect of the particle–particle restitution coefficient turns out to be minimal on the bed circulation time except in the limit of particle elastic collisions. It is also found that the elastic collision of particles highly affects the bubble count and unexpectedly changes the role of the wall from a source to a sink of granular temperature. Second, the effect of the particle–wall restitution coefficient is appreciable on the granular temperature while having a minimal effect on the flow hydrodynamics. Third, the effect of the wall specularity coefficient is felt across the bed such that an increase in this parameter increases the bed circulation time. The results of this systematic study enhance the understanding of how collision parameters impact flow characteristics while also providing insight into the selection of their values in simulations.

Gas-particle flow induced erosion of economizer in low-low temperature electrostatic precipitators: Numerical prediction and engineering application

In this work, the gas-particle flow and the induced erosion in the economizer region in low-low temperature electrostatic precipitator were investigated by CFD-DPM-EPM coupling approach. The results show that positioning the economizer on the vertical flue or employing a vertical tubes arrangement for the heat exchange tubes, utilizing a small expansion angle (less than 35°) in the expansion section, ensuring a more uniform distribution of inlet gas velocity and dust concentration, and incorporating short and densely positioned guide plates in the expansion section can effectively reduce erosion in the low-temperature economizer. The above results were applied to the economizer equipped with the low-low temperature electrostatic precipitator of a 1000 MW unit in a certain power plant, and the wear situation was significantly improved. The research findings can serve as a reference for diagnosing and analyzing erosion phenomena in low-temperature economizer, and can guide the improvement design to prevent erosion.

Unified gas-kinetic wave–particle method for polydisperse gas–solid particle multiphase flow

The gas-particle flow with multiple dispersed solid phases is associated with a complicated multiphase flow dynamics. In this paper, a unified algorithm is proposed for the gas-particle multiphase flow. The gas-kinetic scheme (GKS) is used to simulate the gas phase and the multiscale unified gas-kinetic wave–particle (UGKWP) method is developed for the multiple dispersed solid particle phase. For each disperse solid particle phase, the decomposition of deterministic wave and statistic particle in UGKWP is based on the local cell's Knudsen number. The method for solid particle phase can become the Eulerian fluid approach at the small cell's Knudsen number and the Lagrangian particle approach at the large cell's Knudsen number. This becomes an optimized algorithm for simulating dispersed particle phases with a large variation of Knudsen numbers due to different physical properties of the individual particle phase, such as the particle diameter, material density, etc. The GKS-UGKWP method for gas-particle flow unifies the Eulerian–Eulerian and Eulerian–Lagrangian methods. The particle and wave decompositions for the solid particle phase and their coupled evolution in UGKWP come from the consideration to balance the physical accuracy and numerical efficiency. Two cases of a gas–solid fluidization system, i.e. one circulating fluidized bed and one turbulent fluidized bed, are simulated. The typical flow structures of the fluidized particles are captured, and the time-averaged variables of the flow field agree well with the experimental measurements. In addition, the shock particle–bed interaction is studied by the proposed method, which validates the algorithm for the polydisperse gas-particle system in the highly compressible case, where the dynamic evolution process of the particle cloud is investigated.

Impact of Laval nozzle structure on the flow characteristics of supersonic gas-solid two-phase flow

This study introduces a mathematical coupling model within the Euler-Lagrange framework to conduct numerical simulations for supersonic gas-particles flow. After validating the model, the gas flow characteristics and particle dynamics within supersonic gas-particle flow under various nozzle configurations are investigated. The findings are as follows: (1) A Laval nozzle with a smoothly connected throat suppresses the generation of fan-shaped Prandtl-Meyer expansion waves and other complex wave systems, effectively mitigating significant changes in gas pressure at the throat and enhancing the stability of supersonic jets. (2) The presence of a particle-free zone in the nozzle divergent segment reduces the collision frequency between particles and the walls, thereby restricting the radial expansion of particles. (3) Utilizing an internally smooth-lined nozzle and expanding the radial divergence angle to 2.5–2.8 times, while ensuring particles maintain consistent axial penetration performance, increases the reflective contact area. This leads to an improvement in the utilization efficiency of particles. These findings provide valuable insights for optimizing nozzle configurations and enhancing the performance of supersonic gas-particle systems.

Anisotropic turbulence of dense and dilute phases of particles in fluidized risers characterized using four-way coupled second-order moment method

The gas-particle flow in a fluidized bed is characterized as a “core-annulus” pattern with transient clusters moving along the circulating fluidized bed riser. These clusters exist as regions with a higher concentration of particles and are surrounded by dispersed particles at lower concentrations. In this study, fluid dynamics of both the clusters and dispersed particles suspended in the risers were investigated using the four-way coupled second-order moment method of the fluid–particle Eulerian–Eulerian two-fluid model. In the simulation, the anisotropic turbulence of either phase in the clusters and dispersed particles was studied in the risers. According to the turbulence intensities of both phases, the gas-particle flow in the fluidized riser was classified into six zones, the wall effect, cluster edge, cluster rising, cluster falling, and transient zone between the cluster rising and falling zones. As the volume fraction of the particles increased, the anisotropic ratios of the turbulence intensities in both phases increased in the dispersed zone and decreased in the cluster zone, respectively.

Experimental and numerical studies on the wall-roughness effect to particle dynamics in various gas-particle flows

Experimental and numerical studies on the wall-roughness effect to particle dynamics in various gas-particle flows

Instabilities of a circular moderately dense particle cloud impacted by an incident shock

Shock-driven gas-particle flows exist in a wide variety of physical systems, covering the range from dilute to dense regime. There are a lot of fundamental questions remaining to be answered, like the evolutions of flow instability, two-phase interactions, and inter-particle collision effects. In this work, the Eulerian-Lagrangian approach with gas-particle four-way coupling is applied to model two-dimensional shock-driven gas-particle flow under the moderately dense regime. For the gas flow, the formation mechanism of primary and secondary vortexes is discussed. The primary vortex is caused by the roll-up of slip line, while the secondary vortexes are induced by the velocity and density difference between the penetrating flow of particle-laden zone and the outside mainstream. Parametric studies of different Mach numbers, particle diameters and initial volume fractions have been performed to investigate the effects on shock behaviours and slip line instabilities. For the particle phase, a high-volume-fraction compression region forms at the upstream cloud zone, which blocks the penetrating gas, and results in the formation of slip line. The cloud tail is mainly composed of the upstream edge particles. The inter-particle collisions have impact on the particle distributions, and greatly affect the slip line stability at the upstream cloud edge. This work provides valuable insights into the instability mechanism of compressible gas-solid flow and the particle dispersion behaviours. However, it is important to note that our analysis is based on a two-dimensional configuration. In a real three-dimensional context, the generation of vortices is likely to differ, and may affect the particle dynamics to a certain degree.

МЕТОДЫ ПРОЕКТИРОВАНИЯ ПНЕВМАТИЧЕСКИХ СИСТЕМ

In this paper, the parameters of a two-phase heterogeneous gas-particle flow (for example, “airseed”) are shown using the example of mathematical modeling of technological processes of a pneumatic system of a grain seeder. It is proposed to apply the mechanics of two-phase gas-particle flow to the theoretical description of the processes of motion and distribution of solid particles in pneumatic systems. The results of the study establish the possibility of using these methods to analyze and optimize the pneumatic system of grain seeders. Practical and theoretical methods were used to determine the air flow and speed of movement of seeds of various crops in pneumatic systems of grain drills. The values of the seed resistance coefficients necessary for mathematical modeling of the technical processes of the pneumatic system are also presented. The research will make it possible to effectively simulate the operation of the pneumatic system of the sowing complex using the mechanics of two-phase flows and computational fluid dynamics methods.

IMEX_SfloW2D v2: a depth-averaged numerical flow model for volcanic gas–particle flows over complex topographies and water

Abstract. We present developments to the physical model and the open-source numerical code IMEX_SfloW2D (de' Michieli Vitturi et al., 2019). These developments consist of a generalization of the depth-averaged (shallow-water) fluid equations to describe a polydisperse fluid–solid mixture, including terms for sedimentation and entrainment, transport equations for solid particles of different sizes, transport equations for different components of the carrier phase, and an equation for temperature/energy. Of relevance for the simulation of volcanic mass flows, vaporization and entrainment of water are implemented in the new model. The model can be easily adapted to simulate a wide range of volcanic mass flows (pyroclastic avalanches, lahars, pyroclastic surges), and here we present its application to transient dilute pyroclastic density currents (PDCs). The numerical algorithm and the code have been improved to allow for simulation of sub- to supercritical regimes and to simplify the setting of initial and boundary conditions. The code is open-source. The results of synthetic numerical benchmarks demonstrate the robustness of the numerical code in simulating transcritical flows interacting with the topography. Moreover, they highlight the importance of simulating transient in comparison to steady-state flows and flows in 2D versus 1D. Finally, we demonstrate the model capabilities to simulate a complex natural case involving the propagation of PDCs over the sea surface and across topographic obstacles, through application to Krakatau volcano, showing the relevance, at a large scale, of non-linear fluid dynamic features, such as hydraulic jumps and von Kármán vortices, to flow conditions such as velocity and runout.

Gas-particle flows in a microscale shock tube and collection efficiency in the jet impingement on a permeable surface

We investigate the flow physics of non-equilibrium gases in interaction with solid particles in a microscale shock tube and the collection efficiency in the jet impingement on a permeable surface. One interesting application of flows in shock tubes at low pressures or micro-shock tubes is needle-free injection technology where drug particles are delivered by shock waves. To investigate such problems, a new two-fluid model system coupled with second-order Boltzmann–Curtiss-based constitutive relationships for modeling a non-equilibrium gas was developed. We were specifically interested in how rarefaction affects the complex wave patterns observed in dusty gas flows and the role of bulk viscosity in diatomic and polyatomic gases exposed to moving shocks. Simulation results demonstrated how significantly the bulk viscosity can affect the topology of the solution in the Sod shock tube problem. Counter-intuitive flow features were noted, resulting from bulk viscosity effects and the incapability of the first-order theory, even when Stokes' hypothesis was abandoned (i.e., the Navier–Fourier model). After detailed analyses in one-, two-, and three-dimensional space for simplified flow problems, a case was designed to represent a needle-free injection device. In addition, a new concept of “collection efficiency” was introduced that quantifies the efficiency of drug delivery in the two-phase jet impingement on the skin. We also derived a new “vorticity transport equation” that takes the bulk viscosity and multiphase effects into account. Based on the new equation, the time evolution of vorticity growth rates was analyzed for all the contributing terms in the equation.