Gas-particle Flow Research Articles

A comprehensive modeling study of particulate coalescence and breakup mechanisms in solid propellant motor nozzles

Gas-particle flows are modeled to account for the coalescence and breakup of liquid aluminum oxide particles dispersed within the gas phase in solid propellant motors. The one-way coupled population balance equation, which addresses a change in number concentration of particles by the particle to particle and surrounding to particle interactions, is solved using the direct quadrature method of moments (DQMOM). Simulations are performed on the converging-diverging nozzles attached to solid propellant motors and the mass mean diameter at the nozzle exit is compared to previous measurements and a correlation derived from numerous existing measurements data. The results from a series of simulations are presented to assess the effects of chamber pressure, initial particle concentration and size, and nozzle scale on resulting particle size growth.

Nonlinear modeling of industrial boiler NOx emissions

ABSTRACT Pollutant emissions into the atmosphere are recognized as a significant problem in fossil fuel combustion. The pollution emission measurement in industrial boilers is difficult and expensive but fundamental for monitoring and controlling. Frequently continuous emissions monitoring (CEM) system is out of service or useless due to obsolescence, high maintenance cost, and so on or simply is not installed. When a system for measuring pollutant emissions is not available, an alternative method must be employed to get the pollutant emission value. According to the black-box model approach, this article describes the nonlinear modeling of NOx emissions from a utility boiler. Bayesian-Gaussian (BG), multilayer perceptron (MLP), and Volterra polynomial basis functions (VPBF) neural networks are developed for model benchmarking. Experimental data from a utility boiler was acquired in order to model definition and evaluation. The models process three boiler variables oxygen excess, fuel mass flow and flue gas recirculation gates for NOx emission estimation. Models with BG show better performance than models with MLP and VPBF for NOx prediction. Implications: The technology to control NOx emissions generated by combustion operates under strict regulations. In order to reduce NOx emissions, theoretical models of NOx generation have been studied extensively, including nitrogen chemistry and the dynamic flow of gas particles which is very complex. The new technology trends would require the continuous measurement of high precision NOx emissions to achieve further reductions in NOx emissions. Currently, NOx emissions are measured by a Continuous Emission Monitoring system, which turns out to be extremely expensive and difficult to maintain, so alternative low-cost solutions are desirable. Our contribution shows how algorithms based on different artificial intelligence techniques are viable and quality alternatives for the measurement of continuous NOx emissions. The NOx emissions models based on IA algorithms are viable alternatives that have versatility and self-tuning capacity due to the fact that they are based on boiler operation parameters which have valuable information few explored nowadays.

Numerical simulation of complex thermal decomposition processes in pyrolysis furnace for recycling solid waste Mg(NO3)2.2H2O

This study aims to reveal the complex thermal decomposition processes in a pilot-scale pyrolysis furnace for recycling solid waste Mg(NO3)2.2H2O produced in nitric acid leaching process of laterite nickel ore, by using CFD method. Specifically, an integrated mathematical model combining the gas-particle flow and the thermal decomposition reaction as well as the heat, mass transfer between gas and particle was developed based on the Euler-Lagrange method. And then, the developed model was used to study the flow characteristics of the gas and particle and the thermal decomposition processes for Mg(NO3)2.2H2O in the pyrolysis furnace. Furthermore, the effect of operating parameters (gas inlet temperature, mass flow rate and particle size of Mg(NO3)2.2H2O) on the performance of pyrolysis furnace (decomposition rate of Mg(NO3)2.2H2O) was studied. The results show that the developed model is reasonable. Increasing gas inlet temperature, decreasing mass flow rate and particle size of Mg(NO3)2.2H2O can effectively promote the decomposition rate of Mg(NO3)2.2H2O. Under the conditions of gas inlet temperature 1123 K, mass flow rate of Mg(NO3)2.2H2O 200 kg/h, and average particle size of Mg(NO3)2.2H2O 75 µm, the dehydration reaction mainly occurs in the furnace height of 11–8 m, while the denitration reaction mainly occurs in the furnace height of 10.5–1 m. The total decomposition rate of Mg(NO3)2.2H2O is 99.75%.

Numerical analysis on particle dispersions of swirling gas-particle flow using a four-way coupled large eddy simulation

Subgrid-scale (SGS) gas flow and particle-particle collision are closely related to the particle dispersions in swirling gas-particle flow. However, investigations which consider the four-way coupled large eddy simulation (LES) are scant. The objective of the present contribution is to propose firstly a novel particle SGS kinetic turbulent energy-granular temperature (SGS-kp-θp) model to describe the interactions of gas-particle, particle-gas and particle-particle collision based on the kinetic energy of granular flow. Reynolds stresses transport equations are modeled by the second-order moment strategy. Numerical analysis on particle hydrodynamics that effected by particle diameters using LES is carried out and validations by both experiment and OpenFoam software reported are in good agreements. Results of this study showed flow structures of micro and larger size particles ranging from 12.5 μm to 105 μm significantly differ in the vortex evolutions and coherent structures. SGS particles collision incurs on the additional particle energy dissipations. Micro-particle contributes to the formation of stable vortex indicating the excellent followability and incapable of exerting counteractivity on gas flow. SGS axial interactions between gas and medium size particle of dp = 30 μm is approximately 3.5 times larger than those of largest size particle of dp = 105 μm. Moreover, maximum energy dissipation caused by largest particle collision is 1.6 times larger than that of micro particle at developing flow region.

Hydrodynamic modeling of non-swirling and swirling gas-particle two-phase turbulent flow using large eddy simulation

Flow structures of non-swirling and swirling particle-laden turbulence are modeled using the large eddy simulation. Four-way coupling to reveal the interaction mechanism of gas to particle, particle to gas and particle-particle collisions is adopted by a new proposed subgrid scale (SGS) particle kinetic energy-granular temperature model. Evolution of particle vortices, particle coherent structures and particle dynamics are predicted numerically, and comparisons are also conducted. Predictions are in good agreement with experimental measurements. For non-swirling flows, the typical coherent structures, and larger vortices at downward region of gas flow are dominantly. However, particle transport characteristics are significantly different, distinctly coherent structures and more vortices have not been generated in additions to fewer ones at far distance from entrance. Meanwhile, fewer coherent structures and vortices that dispersed at corner recirculation are observed for swirling flow. Compared to gas flow, the number of particle vortices is less and Reynolds stress and kinetic energy transport behaviors of particle flow are relatively independent due to inertia. Gas fluctuations of shear stresses are approximately twice greater than those of particle in non-swirling flows. A novelty finding is that turbulent fluctuations and instantaneous gas vortices of non-swirling flow are stronger than swirling case.

Modeling high-speed gas–particle flows relevant to spacecraft landings

The interactions between rocket exhaust plumes and the surface of extraterrestrial bodies during spacecraft landings involve complex multiphase flow dynamics that pose significant risk to space exploration missions. The two-phase flow is characterized by high Reynolds and Mach number conditions with particle concentrations ranging from dilute to close-packing. Low atmospheric pressure and gravity typically encountered in landing environments combined with reduced optical access by the granular material pose significant challenges for experimental investigations. Consequently, numerical modeling is expected to play an increasingly important role for future missions. This article presents a review and perspectives on modeling high-speed disperse two-phase flows relevant to plume–surface interactions (PSI). We present an overview of existing drag laws, with origins from 18th-century cannon fire experiments and new insights from particle-resolved numerical simulations. While the focus here is on multiphase flows relevant to PSI, much of the same physics are shared by other compressible gas–particle flows, such as coal-dust explosions, volcanic eruptions, and detonation of solid material.

Unified gas-kinetic wave–particle method for gas–particle two-phase flow from dilute to dense solid particle limit

A unified framework for particulate two-phase flow is presented with a wide range of solid particle concentration from dilute to dense limit. The two-phase flow is simulated by two coupled flow solvers, that is, the gas-kinetic scheme (GKS) for the gas phase and unified gas-kinetic wave–particle method (UGKWP) for the solid particle phase. The GKS is a second-order Navier–Stokes flow solver. The UGKWP is a multiscale method for all flow regimes. The wave and particle decomposition in UGKWP depends on the cell's Knudsen number (Kn). At a small Kn number, the highly concentrated solid particle phase will be modeled by the Eulerian hydrodynamic wave due to the intensive particle–particle collisions. At a large Kn number, the dilute solid particle will be followed by the Lagrangian particle to capture the non-equilibrium transport. In the transition regime, a smooth transition between the above limits is obtained according to the local Kn number. The distribution of solid particles in UGKWP is composed of analytical function and discrete particle, and both condensed and dilute phases can be automatically captured in the most efficient way. In the current scheme, the two-phase model improves the previous one in many aspects, such as drag force model, the frictional pressure formulation, and flux limiting model. The scheme is tested in many typical gas–particle two-phase problems, including the interaction of shock wave with solid particle layer, horizontal pneumatic conveying, bubble formation, and particle cluster phenomena in the fluidized bed. The results validate the GKS-UGKWP for the simulation of gas–particle flow.

A Large Eddy Simulation Study of Cyclones: The Effects of Interparticle Collisions on Erosion Prediction

Cyclone separators are widely used in fluid catalytic cracking (FCC) units due to their lack of moving parts and relatively low-pressure drop. However, cyclone separators are prone to erosion-related issues, which is a major drawback. In this paper, a large eddy simulation (LES) of the particle-gas flow in a cyclone separator is investigated using a four-way Euler-Lagrange approach to model inter-particle collisions and the exchange of momentum between particles and fluid. The effects of inter-particle and particle-wall collisions are characterized in terms of erosive wear. Additional effects involving the exchange of momentum between the fluid and the particles are also discussed. The results show that considering the interparticle collisions between solid particles may be the key to predicting erosion.

Impact of radial air staging on gas-particle flow characteristics in an industrial pulverized coal boiler

Radial air staging is a new air staging method for industrial pulverized coal boilers. In this paper, its impact on the gas-particle flow characteristics of industrial pulverized coal boilers was studied experimentally. The gas-particle flow experiments were carried out on a 1:6 scale boiler platform by a particle dynamics anemometer. The three-dimensional velocities of the gas-particle, average particle size and particle volume flux under different air stoichiometries in the furnace were measured. When the air stoichiometry was 0.2, the burner outlet could not form a stable reflux zone to establish a good combustion process. When the air stoichiometry is greater than 0.8, the maximum particle volume flow is also located near the water wall, increasing the slagging tendency on the wall. The appropriate air stoichiometry range for the new burner was 0.4–0.8.

Direct Numerical Simulation of Fully Developed Turbulent Gas–Particle Flow in a Duct

Direct numerical simulation of a fully developed turbulent flow of a viscous compressible fluid containing spherical solid particles in a channel is carried out. The formation of regions with an increased concentration of solid particles in a fully developed turbulent flow in a channel with solid walls is considered. The fluid flow is simulated with unsteady three-dimensional Navier – Stokes equations. The discrete trajectory approach is applied to simulate the motion of particles. The distributions of the mean and fluctuating characteristics of the fluid flow and distribution of the concentration of the dispersed phase in the channel are discussed. The formation of regions with an increased concentration of particles is associated with the instantaneous distribution of vorticity in the near-wall region of the channel. The results of numerical simulation are in qualitative and quantitative agreement with the available data of physical and computational experiments.

Model of non-spherical particles' rebound and scattering at high speed interaction with a streamlined surface

A new model is proposed for a non-spherical solid particles' impact interaction with a surface as applied to gas-particle flows over surfaces. The range of a particle impact speed typical for a vehicle flight in a dusty atmosphere is considered. The model is based on the laws of mechanics and experimental data on the restitution coefficient of the particle normal velocity. The tangential force impulse during a particle-surface interaction is assumed to be proportional to both the normal impulse and the mean tangential velocity of the particle contact point. The space orientation of incident particles relative to the surface is considered as random. The rebound of particles of different shape with varying shape parameters and of a particle mixture is studied numerically. Statistical characteristics of particles' rebound and scattering are obtained. Comparison with the known experimental data of numerical results for the mean values of the normal and tangential velocities of the particles' gravity centers in the plane of impact after rebound showed their good agreement. Keywords: dispersed particles, 3D model of impact, numerical investigation, statistical characteristics of rebound and scattering, comparison with experimental data.

Модель отскока и рассеяния несферических частиц при высокоскоростном взаимодействии с обтекаемой поверхностью

A new model is proposed for a non-spherical solid particles' impact interaction with a surface as applied to gas-particle flows over surfaces. The range of a particle impact speed typical for a vehicle flight in a dusty atmosphere is considered. The model is based on the laws of mechanics and experimental data on the restitution coefficient of the particle normal velocity. The tangential force impulse during a particle-surface interaction is assumed to be proportional to both the normal impulse and the mean tangential velocity of the particle contact point. The space orientation of incident particles relative to the surface is considered as random. The rebound of particles of different shape with varying shape parameters and of a particle mixture is studied numerically. Statistical characteristics of particles' rebound and scattering are obtained. Comparison with the known experimental data of numerical results for the mean values of the normal and tangential velocities of the particles' gravity centers in the plane of impact after rebound showed their good agreement.

Experimental Investigation on Turbulent Flow Deviation in a Gas-Particle Corner-Injected Flow

An experimental model of a corner-injected flow is built to investigate the turbulent flow behavior by employing the PIV technique. The influences of the ideal tangential circle, the additive particles and the initial gas mass flux on the corner-injected flow are analyzed systematically. To be specific, the flow deviation, the velocity profile, the vortex evolution and the turbulent flow development are discussed quantitatively. The influences of the increasing ideal tangential circle on the turbulent jet deviation are shortened gradually, and the impinging circles are obviously narrowed with the injection of particles. The gas-particle corner-injected flow can obtain a good rotation when the ideal tangential circle is 0.25 times the width of the impinging chamber. The momentum decay of the corner-injected flow diminishes with the increasing ideal tangential circle and the decreasing initial gas velocity. The rotation strength of the vortex is more affected by the injection of laden particles, while the angular distortion enhances when increasing the ideal tangential circle. The increasing initial gas mass flux plays a dominant role in the development of the corner-injected flow, secondly the increasing ideal tangential circle, and last the injection of particles. All these findings can provide theoretical support in the design of a corner-fired furnace.

Implementation of CHyQMOM in OpenFOAM for the simulation of non-equilibrium gas-particle flows under one-way and two-way coupling

The modeling of dilute gas-particle flows is challenging due to particle-trajectory crossing (PTC). Lagrangian particle tracking can be used, but requires a large number of parcels resulting in high computational costs. A less costly method is the Eulerian number density function (NDF) approach, based on the Boltzmann equation, often solved in terms of lower-order moments of the NDF. In this context the conditional hyperbolic quadrature method of moments (CHyQMOM) was developed and is here implemented for the first time in the OpenFOAM-7, together with high-order advection schemes and a new operator splitting procedure. The resulting solver is used to simulate different test cases: phase segregation problems, collision-less and weakly-collisional PTC flows, asymmetric and symmetric Taylor-Green vortex flow and a dilute gas-particle riser. Results, validated against analytical solutions and predictions obtained with Lagrangian particle tracking, show that the implemented CHyQMOM can be used to handle highly non-equilibrium flows.

A hybrid mesoscale closure combining CFD and deep learning for coarse-grid prediction of gas-particle flow dynamics

This study develops filtered two-fluid model (fTFM) closures by coupling computational fluid dynamics (CFD) and deep learning algorithm (DL) for enabling coarse-grid simulations at reactor scales. Mesoscale drag, solids pressure and viscosity are modeled using an isotropic or anisotropic method. Subsequently, a priori analysis and a posteriori analysis of the present models along with other previously proposed closures are conducted. Comparison with the experimental data covering a broad range of operating conditions indicates that the mesoscale solids stress can be neglected in bubbling and turbulent fluidization regimes. However, the contribution of solids stress is clearly not insignificant at very low superficial gas velocities. Moreover, the drag model considering the anisotropy shows better prediction performance in the turbulent fluidization regime. In short, the present study develops and validates a DL-fTFM coupling algorithm applicable for gas-particle simulations.

Inverting sediment bedforms for evaluating the hazard of dilute pyroclastic density currents in the field

Pyroclastic density currents are ground hugging gas-particle flows associated to explosive volcanic eruptions and moving down a volcano's slope, causing devastation and deaths. Because of the hostile nature they cannot be analyzed directly and most of their fluid dynamic behavior is reconstructed by the deposits left in the geological record, which frequently show peculiar structures such as ripples and dune bedforms. Here, a set of equations is simplified to link flow behavior to particle motion and deposition. This allows to construct a phase diagram by which impact parameters of dilute pyroclastic density currents, representing important factors of hazard, can be calculated by inverting bedforms wavelength and grain size, without the need of more complex models that require extensive work in the laboratory.

On the thermal entrance length of moderately dense gas-particle flows

The dissipative nature of heat transfer relaxes thermal flows to an equilibrium state that is devoid of temperature gradients. The distance to reach an equilibrium temperature – the thermal entrance length – is a consequence of diffusion and mixing by convection. The presence of particles can modify the thermal entrance length due to interphase heat transfer and turbulence modulation by momentum coupling. In this work, Eulerian–Lagrangian simulations are utilized to probe the effect of solids heterogeneity (e.g., clustering) on the thermal entrance length. For the moderately dense systems considered here, clustering leads to a factor of 2–3 increase in the thermal entrance length, as compared to an uncorrelated (perfectly mixed) distribution of particles. The observed increase is found to be primarily due to the covariance between volume fraction and temperature fluctuations, referred to as the fluid drift temperature. Using scaling arguments and Gene Expression Programming, closure is obtained for this term in a one-dimensional averaged two-fluid equation and is shown to be accurate under a wide range of flow conditions.

Particle-free zone of the two-phase flow in a convergent-divergent nozzle

The gas-particle two-phase flow in a convergent-divergent nozzle is encountered in many applications like solid-propellant rocket motors (SRMs). The “Particle-free Zone” adjacent to the nozzle wall is crucial for the nozzle performance which is closely related to the specific impulse of the motor. Though it has been usually observed by many investigators, the existence of the particle-free zone in different nozzles and its effect on nozzle performance are still ambiguous. In this research, we investigated the two-phase flow with monodispersed micron particles in a nozzle using a two-way coupled Eulerian-Lagrangian model and found that the particle-free zone does not exist for smallest particles (dp = 1.0 μm). Moreover, we built a theoretical model for predicting the extent of the particle-free zone by calculating the trajectory of the particle closest to the nozzle wall. The effects of the particle size, total pressure, total temperature and nozzle geometry on the particle-free zone were studied. Finally, we analyzed the nozzle performance and found that the gas velocity at the outlet and the thrust do not change with particle size monotonously, and the medium-sized particles cause the largest thrust loss.

A scale-independent modeling method for filtered drag in fluidized gas-particle flows

A scale-independent modeling method for filtered drag force is proposed for coarse-grid simulation of fluidized gas-solid flows based on the fine-grid data generated using kinetic theory-based two-fluid method in periodic sedimentation systems. In the modeling process, the filtered solid volume fraction at a larger scale whose side length is three times of the filter size is introduced as a new marker. New developed closures show an excellent performance in a priori test, and exhibit a fairly good agreement with the fine-grid data and the experimental data in a posteriori test for three typical fluidized regimes including bubbling, turbulent and fast fluidized beds. Furthermore, the available correction methods to consider the effect of the material properties via adding a multiplicative factor are tested. The results show that these correction methods are not suitable for the considered cases.

A dynamic multiphase turbulence model for coarse-grid simulations of fluidized gas-particle suspensions

The Spatially-Averaged Two-Fluid Model (SA-TFM) is a functional multiphase turbulence model aimed at predicting the influence of unresolved meso-scale structures on the macro-scale flow properties in coarse-grid simulations of gas-particle flows. In this study, we highlight the general applicability of the SA-TFM model due to the dynamic estimation of the model coefficients through test-filters, the anisotropic treatment of the Reynolds-stresses and the drag force correction, and additional wall-friction boundary conditions for the particle-phase velocity, Reynolds-stress and turbulent kinetic energy. The dynamic approach derives information on the unresolved meso-scale flow properties from the resolved macro-scale variables without the need for any intensive prior considerations of the specific flow structure. Thereby, the drift velocity, a measure for the drag-reduction due to the presence of meso-scale structures is estimated from the turbulent kinetic energies of the phases and the variance of the solids volume fraction. We validate the dynamic anisotropic SA-TFM against highly resolved fine-grid Two-Fluid Model simulation data and experimental measurements of Geldart type A and B particles in bubbling to turbulent flow regimes. In the course of this extensive study, we find that the predictions for the macro-scale flow properties, such as slip-velocity, bed expansion, volume fraction distribution, and mass-flux, are in good agreement with the experimental and fine-grid simulation data in a vast number of cases, ranging from unbound fluidization to pilot-scale fluidized beds, thus, implying a wide applicability of the dynamic model independent of the underlying grid-size.