Dilute Gas-particle Flows Research Articles

Efficient Two-Way Coupled Analysis of Steady-State Particle-Laden Hypersonic Flows

A direct solution approach for surface erosion in particle-laden hypersonic flows is extended for use in low-cost two-way coupled solutions of dilute gas-particle flows. The trajectory control volume method, which uses a sparse set of probe particles to predict surface erosion distributions on general vehicles, is reformulated for the solution of source terms by mean trajectory subdivision and computing a flux differencing. The approach is verified successfully against a boundary-layer solution and shown to agree well with experimental measurements. A representative Mars entry case, with conditions and geometry based on the ExoMars Schiaparelli capsule, is solved with the approach to study the impact of two-way coupling on surface heating and erosion. Results indicate that, for realistic loading conditions, heating is largely unmodified compared to one-way coupled results at peak heating trajectory conditions, and no measureable difference is observed in the surface erosion rate. At exaggerated loading conditions high enough to observe coupling effects, the worst-case collisional heating can increase heating by up to 60%.

Heat transfer effects on multiphase Richtmyer–Meshkov instability of dense gas–particle flow

Multiphase Richtmyer–Meshkov instability (RMI) widely exists in nature and engineering applications, such as in supernova explosions, inertial confinement fusion, particle imaging velocimetry measurements, and supersonic combustion. Few studies on the effects of heat transfer on the mix zone width have been conducted, and those that do exist are limited to dilute gas–particle flow. To address this research gap, the effects of dense particle heat transfer in a multiphase RMI flow were investigated in this study, and a dimensionless variable that integrates the particle volume fraction and particle parameters was derived for the first time. The results indicate that the effects of dense particle heat transfer cannot be neglected because the volume fraction increases by over three orders of magnitude compared to those in previous studies. Subsequently, numerical studies using the improved compressible multiphase particle-in-cell method were conducted to investigate the effects of heat transfer on the mix zone width. A detailed wave system structure and quantitative budget analyses were performed to investigate the inherent flow characteristics. The heat transfer effect was found to influence the fluid velocity by changing the fluid pressure gradient, thereby reducing the velocity and growth rate of the mix zone. With a Mach number of 2 and a 10% particle volume fraction, the heat transfer reduced the mix zone width by approximately 22%. In addition, simulations with different particle volume fractions and temperature self-similarity demonstrated the correctness and validity of the dimensionless heat transfer time, which is beneficial for predicting the effects of dense particle heat transfer.

The Analysis of Particle Number Densities in Dilute Gas-Particle Flows: The Eulerian and Lagrangian Methods

The Analysis of Particle Number Densities in Dilute Gas-Particle Flows: The Eulerian and Lagrangian Methods

Numerical method for compressible gas-particle flow coupling using adaptive parcel refinement (APR) method on non-uniform mesh

The Eulerian–Lagrangian (EL) approach is usually used for simulating the compressible gas-particle flows. In our previous study, we have developed the compressible multiphase particle-in-cell method (CMP-PIC) and achieved good results for both dilute and dense compressible gas-particle flow. However, the original CMP-PIC was only implemented on the uniform mesh, which limits its resolution, efficiency, and application in the field of engineering. Therefore, in the present study, we have implemented the developed algorithms for coupling terms and the adaptive parcel refinement APR method on the non-uniform mesh. The algorithm of coupling terms is a new method for interpolating between a parcel with definite volume and cells with different volumes; this has not been investigated in previous particle-in-cell (PIC) research. The improved operator of the multiphase coupling terms is put forward to adapt the wide range size ratios since directly using the original operator causes the loss of coupling effects. The APR sets up a numerical “breakup model” of a parcel from the computational perspective, which represents a new approach to a parcel-type numerical method. In the APR method, the parcel resolution can automatically match the resolution of the local Eulerian cell. Therefore, the improved CMP-PIC can handle the simulation when a large parcel enters the fine cell and prevents the abnormal termination due to non-physical packing of particles. Based on conservation and scaling laws, the strategy, split criterion, and split configuration are identified to correlate the parameters of the parent and child parcels. Additionally, the algorithms of the multiphase HLL/HLLC solvers are derived for flux and nozzling terms to adapt the Cartesian grid with varying cell sizes, which is a type of non-uniformity. Several one-dimensional and two-dimensional tests show the correctness and advantages of using the non-uniform mesh, improved operator, and APR method. Results show that the combination of improved interpolation operator and APR method can significantly improve the reliability, resolution of simulation results, and robustness of the algorithm. The simulation time is also reduced due to regional refinement.

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.

LDV measurements of particle fluctuation velocities in dilute gravity-driven gas-particle flows

Particle instantaneous velocities were measured by a laser-Doppler velocimeter (LDV) in a vertical channel, where particles were supplied from the top of the channel and gas superficial velocity was close to zero. According to kinetic theory of granular flows, particle instantaneous velocities are decomposed into two components, a local Eulerian velocity that represents bulk motion of neighboring particles and a residual component, by three different local averaged methods. Results indicate that the local averaged method based on inter-particle collision time fails to accurately estimate the rapid variation of local Eulerian velocity. In contrast, the local Eulerian velocity estimated by both the simple moving averaged method and the robust local regression method could well represent the collective motions of neighboring particles. Moreover, the magnitude of the residual component (i.e., granular temperature) estimated by the robust local regression method was less sensitive to the number of neighboring data points used in the decomposition process. Overall trends of granular temperature and particle-phase turbulent kinetic energy in the wall normal direction are different from each other, indicating that the granular temperature and particle-phase turbulent kinetic energy must be treated separately to accurately predict energy balance. The probability density function of the residual component is compared with a Gaussian distribution. At the center of the channel, it follows a Gaussian distribution, while in the vicinity of the wall it retains a long tail.

Modeling and verification of the Richtmyer–Meshkov instability linear growth rate of the dense gas-particle flow

The multiphase Richtmyer–Meshkov instability (RMI) often occurs in supernova events and inertial confinement fusion processes, where it plays a critical role. In the evolution of the RMI process, the particle phase may have either a dilute or a dense pattern. Previous studies have mainly focused on the dilute pattern. Currently, there is no published research on the theoretical growth model of the dense gas-particle flow. In this work, a new Atwood number model was developed with the assumption of a small Stokes number and shown to be effective for the RMI of the dense gas-particle flow. The Atwood number model was characterized by the moment coupling parameters and the ratio of the volume fractions of the two phases. Further derivation showed that it was consistent with the original Richtmyer’s model and the dilute gas-particle flow model. In addition, the theoretical growth rate was modeled to predict the evolution law of the mix zone width for the dense gas-particle flow. The presence of the particle phase inhibited the growth rate of the RMI, which emphasized the effect of the solid phase. The corresponding numerical simulations were also performed based on the compressible multiphase particle-in-cell method for different cases of the particle volume fraction. The numerical results demonstrated the accuracy of the theoretical growth rate model. Additionally, a brief analysis of the flow structures and cloud motion during the RMI process was performed.

Dilute gas-particle flow through thin and thick orifice: a computational study through two fluid model

The present work deals with the three-dimensional computational study of dilute gas-particle suspension through thin and thick orifice. The objective of the study is to predict the two phase pressure drop across an orifice for relatively higher solid loading but within the limit of dilute phase flow situation. The study involves the investigation of effect of five pertinent parameters namely area ratio, thickness of orifice, particle phase volume fraction, particle size, and particle phase density on the two phase pressure drop across orifice. The Eulerian–Eulerian model (Two fluid model) has been used for this purpose. The numerical procedure adopted in the present work has been validated with the experimental data for gas-particle flow through a horizontal sudden expansion pipe and good agreement has been revealed. The study reveals that the two phase pressure drop across orifice increases with increases in solid volume fraction and particle density, whereas it decreases with increase in particle diameter and area ratio of the pipe. Moreover, slight increase in pressure drop across orifice is observed with increase in thickness of orifice. Thus, higher pressure drop is observed for thick orifice as compared to thin orifice.

Complex wave patterns in dilute gas–particle flows based on a novel discontinuous Galerkin scheme

The present work investigates complex wave patterns in dilute gas–particle flows based on a novel discontinuous Galerkin (DG) method. For this purpose, a high order DG method was for the first time applied to two-fluid model equations for dusty gas flows. The new DG scheme not only meets the demand for high order accuracy and the positivity/monotonicity preserving property for accurately simulating dusty gas flows, but it can also handle the numerically problematic source terms efficiently, without resorting to the complicated operator splitting method commonly employed in the conventional finite volume method (FVM). For verification, several benchmark problems in one- and two-dimensional space were calculated. Special attention was then paid to the complex mechanisms of wave patterns in the dusty gas flows, which have rarely been studied in previous works, and to the physical justifications of such abnormal behaviors. In particular, it was shown that when a dust contact discontinuity is present in the flow, a pseudo-compound wave (a reflected shock attached to the rarefaction wave) as well as a composite wave (a contact discontinuity attached to the relaxation zone) can form.

Euler–euler anisotropic gaussian mesoscale simulation of homogeneous cluster‐induced gas–particle turbulence

An Euler–Euler anisotropic Gaussian approach (EE‐AG) for simulating gas–particle flows, in which particle velocities are assumed to follow a multivariate anisotropic Gaussian distribution, is used to perform mesoscale simulations of homogeneous cluster‐induced turbulence (CIT). A three‐dimensional Gauss–Hermite quadrature formulation is used to calculate the kinetic flux for 10 velocity moments in a finite‐volume framework. The particle‐phase volume‐fraction and momentum equations are coupled with the Eulerian solver for the gas phase. This approach is implemented in an open‐source CFD package, OpenFOAM, and detailed simulation results are compared with previous Euler–Lagrange simulations in a domain size study of CIT. The results demonstrate that the proposed EE‐AG methodology is able to produce comparable results to EL simulations, and this moment‐based methodology can be used to perform accurate mesoscale simulations of dilute gas–particle flows. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2630–2643, 2017

THE FULLY LAGRANGIAN APPROACH TO THE ANALYSIS OF PARTICLE/DROPLET DYNAMICS: IMPLEMENTATION INTO ANSYS FLUENT AND APPLICATION TO GASOLINE SPRAYS

The fully Lagrangian approach (FLA) to the calculation of the number density of inertial particles in dilute gas-particle flows is implemented into the CFD code ANSYS Fluent. The new version of ANSYS Fluent is applied to modeling dilute gas-particle flow around a cylinder and liquid droplets in a gasoline fuel spray. In a steady-state case, the predictions of the FLA for the flow around a cylinder and those based on the equilibrium Eulerian method (EE) are almost identical for small Stokes number, Stk, and small Reynolds number, Re, (Re = 1, Stk = 0.05). For the larger values of these numbers (Re = 10, 100; Stk = 0.1, 0.2) the FLA predicts higher values of the gradients of particle number densities in front of the cylinder compared with the ones predicted by the EE. For transient flows (Re = 200), both methods predict high values of the number densities between the regions of high vorticity and very low values in the vortex cores. For Stk ≥ 0.1 the maximal values predicted by FLA are shown to be several orders of magnitude higher than those predicted by the EE. An application of FLA to a direct injection gasoline fuel spray has focused on the calculation of the number densities of droplets. Results show good qualitative agreement between the numerical simulation and experimental observations. It is shown that small droplets with diameters dp = 2 μm tend to accumulate in the regions of trajectory intersections more readily, when compared with larger droplets (dp = 10 μm, dp = 20 μm). This leads to the prediction of the regions of high number densities of small droplets.

Numerical prediction of erosion in elbow based on CFD-DEM simulation

A new erosion model, which is referred to as SIEM (shear impact energy model), is used to investigate elbow erosion under different working conditions using numerical simulations. The fluid motions are predicted by CFD (computational fluid dynamics), and the particle movements are calculated using DEM (discrete element method) in the simulations. Both a one-way coupling method and a two-way coupling method in CFD-DEM are adopted to calculate the gas-solid interaction. The prediction results of elbow erosion subject to a condition of dilute gas-particle flow are validated against corresponding experimental data. Because DEM and SIEM can be easily applied to dense gas-particle flows, the effect of the particle concentration on the erosion is also investigated. The simulation results show that the coupling methods have little influence on the erosion prediction when the particle concentration is low, whereas erosion in the elbow is significantly sensitive to the particle concentration. Finally, the effects of the friction coefficient, restitution coefficient and spring stiffness coefficient on elbow erosion are also investigated using simulations, and the effects were not as remarkable as the concentration.

Richtmyer-Meshkov instability in dilute gas-particle mixtures with re-shock

The Richtmyer-Meshkov instability (RMI) is investigated in a dilute gas-particle mixture using three-dimensional numerical simulations. This work extends an earlier two-dimensional study [S. Ukai, K. Balakrishnan, and S. Menon, “On Richtmyer-Meshkov instability in dilute gas-particle mixtures,” Phys. Fluids 22, 104103 (2010)] to a larger parameter space consisting of variations in the mass loading and the particle size as well as considering both single-mode and multi-mode interface initializations. In addition, the effect of the presence of particles on re-shock RMI is also investigated. Single-phase numerical predictions of the mixing layer growth-rate are shown to compare well to both experimental and theoretical results. In a dilute gas-particle mixture, the initial growth-rate of RMI shows similar trends compared to previous work; however, the current numerical predictions show that there is an observable increase, not previously predicted, in the growth of the mixing layer at higher mass loadings. For the range of cases considered, an increase as much as 56% is observed. This increase is attributed to additional vorticity production in the mixing layer resulting from inter-phase momentum coupling. Moreover, the presence of particles introduces a continuous drag on the gas-phase resulting in a delay in the time at which re-shock occurs. This delay, which is observed to be as much as 6%, is largest for higher initial mass loadings and smaller particle radii and has a corresponding effect on both the growth-rate of the mixing-layer after re-shock and the final width of the mixing layer. A new semi-analytical correlation is developed and verified against the numerical data to predict the re-shocked RMI growth-rate in dilute gas-particle flows. The correlation shows that the re-shock RMI growth-rate is linearly proportional to the velocity jump at re-shock, the molecular mixing fraction, and the multi-phase Atwood number. Depending on the initial mass loading and particle radii, the re-shock RMI growth-rates were observed to be reduced by as much as 48% in some cases with variations of around 26% in the width of the mixing layer after re-shock.

Investigation of highly laden particle jet dispersion by the use of a high-speed camera and parameter-independent image analysis

Abstract The present work deals with dispersion experiments of highly laden particle jets in turbulent cross-flow. While measurement techniques like phase-doppler anemometry (PDA) work well for dilute gas-particle flows and can deliver particle velocity and concentration, all these methods fail in measuring physical quantities for cases with high particle volume fractions. Nevertheless validation and calibration of numerical simulation models covering this flow regime require experimental data. Due to the strong interaction between the dispersion behavior and cross-flow turbulence the experimental data should provide high spatial and temporal resolution. This is achieved by the use of a high-speed camera, which inherently leads to huge amounts of image data. To be able to process the recorded images automatically a simple image processing method is presented which is based on analyzing single pixel lines at a given distance downstream of the injection lance. The strength of this method lies in the fact that it is not dependent on any preset factors and can therefore cover a large range of mass loadings. The presented experiments are well reproducible and are able to picture different flow regimes.

An experimental study on turbulence modification in the near-wall boundary layer of a dilute gas-particle channel flow

Turbulence modifications of a dilute gas-particle flow are experimentally investigated in the lower boundary layer of a horizontal channel by means of a simultaneous two-phase PIV measurement technique. The measurements are conducted in the near-wall region with y + < 250 at Re τ (based on the wall friction velocity u τ and half channel height h) = 430. High spatial resolution and small interrogation window are used to minimize the PIV measurement uncertainty due to the velocity gradient near the wall. Polythene beads with the diameter of 60 μm (d + = 1.71, normalized by the fluid kinematic viscosity ν and u τ) are used as dispersed phase, and three low mass loading ratios (Φ m ) ranging from 10−4 to 10−3 are tested. It is found that the addition of the particles noticeably modifies the mean velocity and turbulent intensities of the gas-phase, as well as the turbulence coherent structures, even at Φ m = 0.025 %. Particle inertia changes the viscous sublayer of the gas turbulence with a smaller thickness and a larger streamwise velocity gradient, which increases the peak value of the streamwise fluctuation velocity ( $$ u_{\text{rms}}^{ + } $$ ) of the gas-phase with its location shifting to the wall. Particle sedimentation increases the roughness of the bottom wall, which significantly increases the wall-normal fluctuation velocity ( $$ v_{\text{rms}}^{ + } $$ ) and Reynolds shear stress ( $$ - \langle u^{ \prime } v^{\prime } \rangle^{ + } $$ ) of the gas-phase in the inner region of the boundary layer (y + < 10). Under effect of particle–wall collision, the Q2 events (ejections) of the gas-phase are slightly increased by particles, while the Q4 events (sweeps) are obviously decreased. The spatial scale of the coherent structures near the wall shrinks remarkably with the presence of the particles, which may be attributed to the intensified crossing-trajectory effects due to particle saltation near the bottom wall. Meanwhile, the $$ v_{\text{rms}}^{ + } $$ and $$ - \langle u^{ \prime } v^{\prime } \rangle^{ + } $$ of the gas-phase are significantly reduced in the outer region of the boundary layer (y + > 20).

An improved CE/SE scheme and its application to dilute gas–particle flows

An improved space–time Conservation Element and Solution Element (CE/SE) scheme is constructed by proposing a new structure of solution elements and conservation elements based on the rectangular mesh. Furthermore, the improved CE/SE scheme was applied to dilute gas–particle two-phase flows. A two-fluid model and two corresponding chemical reaction models, i.e., two-step reaction model and detailed chemical reaction model, were used to describe the physical and chemical characteristics in the two-phase flows. Shock wave reflection in gas, shock wave diffraction in air–sand mixture, explosive synthesis of TiO2 nanoparticle and air–fuel two-phase detonation were simulated by the improved CE/SE scheme and appropriate physical and chemical models. All the numerical results were compared and discussed carefully. The results show that the improved CE/SE scheme is clear in physical concept, easy to be implemented and high accurate for the above-mentioned problems. Thus, the improved CE/SE scheme can be applied to gas–particle flows widely.

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.

Realizable high-order finite-volume schemes for quadrature-based moment methods

Dilute gas–particle flows can be described by a kinetic equation containing terms for spatial transport, gravity, fluid drag and particle–particle collisions. However, direct numerical solution of kinetic equations is often infeasible because of the large number of independent variables. An alternative is to reformulate the problem in terms of the moments of the velocity distribution. Recently, a quadrature-based moment method was derived for approximating solutions to kinetic equations. The success of the new method is based on a moment-inversion algorithm that is used to calculate non-negative weights and abscissas from the moments. The moment-inversion algorithm does not work if the moments are non-realizable, which might lead to negative weights. It has been recently shown [14] that realizability is guaranteed only with the 1st-order finite-volume scheme that has an inherent problem of excessive numerical diffusion. The use of high-order finite-volume schemes may lead to non-realizable moments. In the present work, realizability of the finite-volume schemes in both space and time is discussed for the 1st time. A generalized idea for developing realizable high-order finite-volume schemes for quadrature-based moment methods is presented. These finite-volume schemes give remarkable improvement in the solutions for a certain class of problems. It is also shown that the standard Runge–Kutta time-integration schemes do not guarantee realizability. However, realizability can be guaranteed if strong stability-preserving (SSP) Runge–Kutta schemes are used. Numerical results are presented on both Cartesian and triangular meshes.

Advanced continuum modelling of gas-particle flows beyond the hydrodynamic limit

The accurate prediction of dilute gas-particle flows using Euler–Euler models is challenging because particle–particle collisions are usually not dominant in such flows. In other words, in dilute flows the particle Knudsen number is not small enough to justify a Chapman–Enskog expansion about the collision-dominated near-equilibrium limit. Moreover, due to the fluid drag and inelastic collisions, the granular temperature in gas-particle flows is often small compared to the mean particle kinetic energy, implying that the particle-phase Mach number can be very large. In analogy to rarefied gas flows, it is thus not surprising that two-fluid models fail for gas-particle flows with moderate Knudsen and Mach numbers. In this work, a third-order quadrature-based moment method, valid for arbitrary Knudsen number, coupled with a fluid solver has been applied to simulate dilute gas-particle flow in a vertical channel with particle-phase volume fractions between 0.0001 and 0.01. In order to isolate the instabilities that arise due to fluid-particle coupling, a fluid mass flow rate that ensures that turbulence would not develop in a single phase flow (Re = 1380) is employed. Results are compared with the predictions of a two-fluid model with standard kinetic theory based closures for the particle phase. The effect of the particle-phase volume fraction on flow instabilities leading to particle segregation is investigated, and differences with respect to the two-fluid model predictions are examined. The influence of the discretization on the solution of both models is investigated using three different grid resolutions. Radial profiles of phase velocities and particle concentration are shown for the case with an average particle volume fraction of 0.01, showing the flow is in the core-annular regime.

Improved CFD transport and boundary conditions models for low-inertia particles

This paper presents a simple aerosol transport model together with specific boundary conditions, which can be easily implemented in a CFD code in order to calculate particulate concentrations at any point in a dilute gas-particle flow. The low-inertia of the particles considered (aerodynamic diameter less than 50 μm) enables a simplified Eulerian model to be proposed (“diffusion–inertia”), which consists of a single transport equation of aerosol concentration considering sedimentation, deviation from fluid streamlines and migration effects. Specific study of deposition has made it possible to develop a new boundary condition approach at smooth walls based on semi-empirical deposition laws, which determines the particle flux towards the wall in the boundary layer for any deposition regime and any surface orientation from the computed CFD variables. These transport and deposition models can be used for a very wide range of geometries (from elementary devices to rooms of various volumes), in industrial applications dealing with particulate contamination. In this paper, the models are validated for simple geometries, by comparing published data to the CFD results.