Dilute Flow Research Articles

A pseudo point source model based on velocity coupled method for dilute particle-laden flow with dissipation scale particles

The interphase interaction between the particle and fluid is one of the most fundamental issues in the research of particle-laden flow. Neither the conventional point source model nor the particle-resolved method is an appropriate choice to study the interphase interaction when the order of magnitude of particle diameter is the same as the turbulence dissipation length scale or the grid spacing. In the present study, a pseudo point source model is proposed to consider the finite size effect of particles under the limitation of an acceptable calculation consumption. In this model, the feedback effect of particles on the fluid is represented by coupling the particle-induced disturbance flow with the carrier flow. The disturbance flow of the particle is solved by Stokes approximation or Oseen correction based on the particle Reynolds number, and the geometric relationships between the particle along with its disturbance and grid are also considered. Meanwhile, the no-slip boundary condition on the particle surface is reconstructed as much as possible. The free settling of a single particle and the particle-laden turbulent channel flow are applied to verify the pseudo point source model. For each simulation case, the results of the pseudo point source model are compared with that obtained by the conventional point source model. From the preliminary results, it is concluded that the pseudo point source model behaved much better than the conventional point source model in predicting the free settling process when the particle diameter is greater than the grid spacing. In simulations of the particle-laden channel turbulence, the pseudo point source model can obtain more reasonable results, especially in the cases where the particle diameter is larger than the Kolmogorov dissipation scale. Finally, some outlooks which needs further study are discussed.

A square‐force cohesion model and its extraction from bulk measurements

Accurate modeling of interparticle forces in DEM is critical to predicting the rheology of cohesive particles. Rigorous cohesion models usually include parameters associated with particle surface roughness. However, both roughness measurement and its distillation into appropriate model parameters remain challenging. We propose a square‐force cohesion model, where cohesive force remains constant until a cutoff separation, above which cohesion vanishes. We demonstrate the square‐force model is a valid surrogate of more rigorous models. Specifically, when two parameters of square‐force model are chosen to match the two key quantities governing dense and dilute flows, namely maximum cohesive force and critical cohesive energy, respectively, DEM results using square‐force and more rigorous models show good agreement. For practical application of the square‐force model to lightly cohesive systems, a method is established to extract its parameters via defluidization, enabling determination of particle–particle cohesion from simpler bulk measurements than complicated and expensive scans on individual grains. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2329–2339, 2018

DWT-based adaptive decomposition method of electrostatic signal for dilute phase gas-solid two-phase flow measuring

The inner flush-mounted electrostatic sensors are widely used for measuring gas-solid two-phase flow in many industries. The measured signal contains induced charge signal (ICS) and transferred charge signal (TCS). According to the band characteristics of the ICS, an adaptive decomposition method based on discrete wavelet transform (DWT) is proposed to extract ICS from measured signals of the sensors. In the measurement of the cross-correlation particle velocity, the mean cross-correlation coefficient between the extracted ICS from upstream and downstream electrodes is 0.74, increased from the previous coefficient 0.48 between the overall measured signals collected from the electrodes. This significant increase shows that the ICS better serves the measurement with higher accuracy. Meanwhile, the mean relative standard deviation (RSD) of the solid velocity is reduced from 3.35% to 2.69% after decomposition, which brings better stability. In addition, the root-mean-square (RMS) of the extracted TCS shows a trend of linear increase as the solid mass flow rate and superficial air velocity rise, indicating that TCS can also serve as an effective method to predict the solid mass flow rate as an alternative to ICS.

Simple relations for electron temperature and potential in dilute cold plasma flows

This short note presents concise semi-analytical expressions for electron temperature and potential in unsteady dilute cold plasma flows. The analysis is based on the detailed fluid model for electrons. Ionizations and normalized electron number density gradients are neglected, and the transport properties are assumed as local constants. Flow is unsteady and Maxwell's equations are adopted in the analysis. With these treatments, the partial differential equations for unsteady electron temperature and potential degenerate as ordinary differential equations. Along an electron streamline, two simple formulas for unsteady electron temperature and plasma potential are obtained. These formulas offer some insights, for example, the electron temperature and plasma potential distributions along an electron streamline include two exponential functions: one for spatial distance along a streamline and the other for time.

Estimating Discharge and Nonpoint Source Nitrate Loading to Streams From Three End‐Member Pathways Using High‐Frequency Water Quality Data

AbstractThe myriad hydrologic and biogeochemical processes taking place in watersheds occurring across space and time are integrated and reflected in the quantity and quality of water in streams and rivers. Collection of high‐frequency water quality data with sensors in surface waters provides new opportunities to disentangle these processes and quantify sources and transport of water and solutes in the coupled groundwater‐surface water system. A new approach for separating the streamflow hydrograph into three components was developed and coupled with high‐frequency nitrate data to estimate time‐variable nitrate loads from chemically dilute quick flow, chemically concentrated quick flow, and slowflow groundwater end‐member pathways for periods of up to 2 years in a groundwater‐dominated and a quick‐flow‐dominated stream in central Wisconsin, using only streamflow and in‐stream water quality data. The dilute and concentrated quick flow end‐members were distinguished using high‐frequency specific conductance data. Results indicate that dilute quick flow contributed less than 5% of the nitrate load at both sites, whereas 89 ± 8% of the nitrate load at the groundwater‐dominated stream was from slowflow groundwater, and 84 ± 25% of the nitrate load at the quick‐flow‐dominated stream was from concentrated quick flow. Concentrated quick flow nitrate concentrations varied seasonally at both sites, with peak concentrations in the winter that were 2–3 times greater than minimum concentrations during the growing season. Application of this approach provides an opportunity to assess stream vulnerability to nonpoint source nitrate loading and expected stream responses to current or changing conditions and practices in watersheds.

Numerical Investigation of the Ability of Salt Tracers to Represent the Residence Time Distribution of Fluidized Catalytic Cracking Particles

For a long time, salt tracers have been used to measure the residence time distribution (RTD) of fluidized catalytic cracking (FCC) particles. However, due to limitations in experimental measurements and simulation methods, the ability of salt tracers to faithfully represent RTDs has never been directly investigated. Our current simulation results using coarse-grained computational fluid dynamic coupled with discrete element method (CFD-DEM) with filtered drag models show that the residence time of salt tracers with the same terminal velocity as FCC particles is slightly larger than that of FCC particles. This research also demonstrates the ability of filtered drag models to predict the correct RTD curve for FCC particles while the homogeneous drag model may only be used in the dilute riser flow of Geldart type B particles. Thus, the RTD of large-scale reactors can be efficiently investigated with our proposed numerical method as well as by using the old-fashioned salt tracer technology.

Direct Molecular Simulation of Nonequilibrium Dilute Gases

This paper summarizes research performed over the past decade on the direct molecular simulation of dilute gas flows. Similar to the molecular dynamics method, a potential energy surface is the sole model input to a direct molecular simulation calculation. However, instead of simulating the motion of all atoms in the system deterministically, the direct molecular simulation method uses stochastic techniques and assumptions, adopted from the well-established direct simulation Monte Carlo method, which are accurate for dilute gases. Using the same potential energy surface as input, the direct molecular simulation method is verified to exactly reproduce pure molecular dynamics results for shock-wave flows. The direct molecular simulation method is then used to investigate nonequilibrium flows such as strong shock waves and dissociating nitrogen systems involving rotation–vibration coupling and coupling between internal energy and dissociation. Direct molecular simulation algorithms are detailed, and a number of new results relevant to hypersonic flows are presented along with a summary of other recent results in the literature.

Methane bursts as a trigger for intermittent lake-forming climates on post-Noachian Mars

Lakes existed on Mars later than 3.6 billion years ago, according to sedimentary evidence for deltaic deposition. The observed fluvio-lacustrine deposits suggest that individual lake-forming climates persisted for at least several thousand years (assuming dilute flow). But the lake watersheds' little weathered soils indicate a largely dry climate history, with intermittent runoff events. Here we show that these observational constraints, while inconsistent with many previously-proposed triggers for lake-forming climates, are consistent with a methane burst scenario. In this scenario, chaotic transitions in mean obliquity drive latitudinal shifts in temperature and ice loading that destabilize methane clathrate. Using numerical simulations, we find that outgassed methane can build up to atmospheric levels sufficient for lake forming climates, for past clathrate hydrate stability zone occupancy fractions >0.04. Such occupancy fractions are consistent with methane production by water-rock reactions due to hydrothermal circulation on early Mars. We further estimate that photochemical destruction of atmospheric methane curtails the duration of individual lake-forming climates to less than a million years, consistent with observations. We conclude that methane bursts represent a potential pathway for intermittent excursions to a warm, wet climate state on early Mars.

Energy-saving “NF/EDR” integrated membrane process for seawater desalination. Part II. The optimization of ED process

For the high pressure and high energy consumption of Seawater reverse osmosis (SWRO) desalination technology, an energy-saving “NF/EDR” integrated membrane process for seawater desalination was proposed in our study. The seawater desalination by Nanofiltration (NF) membrane with high desalination capacity has been reported in our previous paper. This manuscript is the second part of this system about the optimization of electrodialysis (ED) process, where ED process with polarity reverse (EDR) was applied to treat the NF output with the conductivity of 8790μS/cm. A series of operation parameters of the ED process were optimized. More specifically, the effects of the concentrate and dilute flow, internal water flow model, as well as temperature of raw water on separation performances were well investigated. Besides, the optimal period of polarity reverse was determined. The results showed that with the dilute stream flow of 150L/h, concentrate stream flow of 120L/h and the ED stack consisted of one stage with two passages, with the proportion of 27/23 in cell pairs, together with suitable raw water temperature, the desalination rate of ED process could be about 90% and the energy consumption was 0.98KWh/(m3 produced water). Furthermore, the membrane fouling could be effectively avoided by EDR with a period of reversing electrodes at 3h. All the results demonstrated that the optimization of ED process is beneficial to the increasing of desalination rate as well as the decreasing of energy consumption in the “NF/EDR” integrated system, besides, it provided research basis and data support for the pilot-scale system of the “NF/EDR” integrated membrane process.

The properties of dilute debris flow and hyper-concentrated flow in different flow regimes in open channels

Particle Image Velocimetry (PIV) technique was used to test the analogues of hyper-concentrated flow and dilute debris flow in an open flume. Flow fields, velocity profiles and turbulent parameters were obtained under different conditions. Results show that the flow regime depends on coarse grain concentration. Slurry with high fine grain concentration but lacking of coarse grains behaves as a laminar flow. Dilute debris flows containing coarse grains are generally turbulent flows. Streamlines are parallel and velocity values are large in laminar flows. However, in turbulent flows the velocity diminishes in line with the intense mixing of liquid and eddies occurring. The velocity profiles of laminar flow accord with the parabolic distribution law. When the flow is in a transitional regime, velocity profiles deviate slightly from the parabolic law. Turbulent flow has an approximately uniform distribution of velocity and turbulent kinetic energy. The ratio of turbulent kinetic energy to the kinetic energy of time-averaged flow is the internal cause determining the flow regime: laminar flow (k/K 1). Turbulent kinetic energy firstly increases with increasing coarse grain concentration and then decreases owing to the suppression of turbulence by the high concentration of coarse grains. This variation is also influenced by coarse grain size and channel slope. The results contribute to the modeling of debris flow and hyper-concentrated flow.

Particle migration in planar die-swell flows

We present a numerical study on particle migration in a planar extrudate flow of suspensions of non-Brownian hard spheres. The suspension is described as a Newtonian liquid with a concentration-dependent viscosity, and shear-induced particle migration is modelled according to the diffusive flux model. The fully coupled set of nonlinear differential equations governing the flow is solved with a stabilized finite element method together with the elliptic mesh generation method to compute the position of the free surface. We show that shear-induced particle migration inside the channel leads to a highly non-uniform particle concentration distribution under the free surface. It is found that particle migration dramatically changes the shape of the free surface when the suspension is compared to a Newtonian liquid with the same bulk properties. Remarkably, we observed extrudate expansion in the Newtonian and dilute suspension flows; in turn, at high concentrations, a die contraction appears. The model does not account for normal stress differences, and this result is a direct consequence of variations in the flow stress field caused by shear-induced particle migration.

Turbulence modulation model for gas-particle flow based on probability density function approach**Project supported by the National Natural Science Foundation of China (Grant No. 51176044).

The paper focuses on the turbulence modulation problem in gas–particle flow with the use of probability density function (PDF) approach. By means of the PDF method, a general statistical moment turbulence modulation model without considering the trajectory difference between two phases is derived from the Navier–Stokes equations. A new turbulence production term induced by the dispersed-phase is analyzed and considered. Furthermore, the trajectory difference between two media is taken into account. Subsequently, a new k–ε turbulence modulation model in dilute particle-laden flow is successfully set up. Then, the changes to several terms, including the turbulence production, dissipation, and diffusion terms, are well described consequently. The promoted model provides a more probable explanation for the modification of particles on the turbulence. Finally, we applied the model to simulate a gas–particle turbulence flow case in a wall jet, and found that the simulation results agree well with the experimental data.

Universality in quasi-two-dimensional granular shock fronts above an intruder.

We experimentally study quasi-two-dimensional dilute granular flow around intruders whose shape, size, and relative impact speed are systematically varied. Direct measurement of the flow field reveals that three in-principle independent measurements of the nonuniformity of the flow field are in fact all linearly related: (1) granular temperature, (2) flow-field divergence, and (3) shear-strain rate. The shock front is defined as the local maxima in each of these measurements. The shape of the shock front is well described by an inverted catenary and is driven by the formation of a dynamic arch during steady flow. We find universality in the functional form of the shock front within the range of experimental values probed. Changing the intruder size, concavity, and impact speed only results in a scaling and shifting of the shock front. We independently measure the horizontal lift force on the intruder and find that it can be understood as a result of the interplay between the shock profile and the intruder shape.

Modelling compressible dense and dilute two-phase flows

Many two-phase flow situations, from engineering science to astrophysics, deal with transition from dense (high concentration of the condensed phase) to dilute concentration (low concentration of the same phase), covering the entire range of volume fractions. Some models are now well accepted at the two limits, but none are able to cover accurately the entire range, in particular regarding waves propagation. In the present work, an alternative to the Baer and Nunziato (BN) model [Baer, M. R. and Nunziato, J. W., “A two-phase mixture theory for the deflagration-to-detonation transition (DDT) in reactive granular materials,” Int. J. Multiphase Flow 12(6), 861 (1986)], initially designed for dense flows, is built. The corresponding model is hyperbolic and thermodynamically consistent. Contrarily to the BN model that involves 6 wave speeds, the new formulation involves 4 waves only, in agreement with the Marble model [Marble, F. E., “Dynamics of a gas containing small solid particles,” Combustion and Propulsion (5th AGARD Colloquium) (Pergamon Press, 1963), Vol. 175] based on pressureless Euler equations for the dispersed phase, a well-accepted model for low particle volume concentrations. In the new model, the presence of pressure in the momentum equation of the particles and consideration of volume fractions in the two phases render the model valid for large particle concentrations. A symmetric version of the new model is derived as well for liquids containing gas bubbles. This model version involves 4 characteristic wave speeds as well, but with different velocities. Last, the two sub-models with 4 waves are combined in a unique formulation, valid for the full range of volume fractions. It involves the same 6 wave speeds as the BN model, but at a given point of space, 4 waves only emerge, depending on the local volume fractions. The non-linear pressure waves propagate only in the phase with dominant volume fraction. The new model is tested numerically on various test problems ranging from separated phases in a shock tube to shock–particle cloud interaction. Its predictions are compared to BN and Marble models as well as against experimental data showing clear improvements.

Structure-dependent analysis of energy dissipation in gas-solid flows: Beyond nonequilibrium thermodynamics

Gas-solid fluidized bed is a typical dissipative system, featuring meso-scale structures with bimodal distribution of parameters. The energy-minimization multi-scale (EMMS) model focuses on such dissipative characteristics and has shown many successful applications. In previous work, through structure-dependent analysis of mass, momentum and energy conservation, we have discussed the consistency between the hydrodynamic equations of two-fluid model (TFM) and those of the EMMS model. In this work, we extend this structure-dependent analysis to the extremum behavior of dissipation processes, revealing that the solution based on the minimum energy dissipation rate applies only to homogeneous, dilute flow states, but fails in the particle-fluid compromising fluidization regime, in particular, fails to predict choking transition. By comparison, the EMMS variational stability condition that is based on the principle of compromise in competition between dominant mechanisms well describes the flow regimes of fluidization. This work unfolds a fresh viewpoint to understand the EMMS stability condition that is beyond the analysis of extremum of energy dissipation. And it is expected to boost the development of EMMS-based meso-scale modeling in broader realm of multiphase flow systems.

Simulations of natural transition in viscoelastic channel flow

Orderly, or natural, transition to turbulence in dilute polymeric channel flow is studied using direct numerical simulations of a FENE-P fluid. Three Weissenberg numbers are simulated and contrasted to a reference Newtonian configuration. The computations start from infinitesimally small Tollmien–Schlichting (TS) waves and track the development of the instability from the early linear stages through nonlinear amplification, secondary instability and full breakdown to turbulence. At the lowest elasticity, the primary TS wave is more unstable than the Newtonian counterpart, and its secondary instability involves the generation of $\unicode[STIX]{x1D6EC}$-structures which are narrower in the span. These subsequently lead to the formation of hairpin packets and ultimately breakdown to turbulence. Despite the destabilizing influence of weak elasticity, and the resulting early transition to turbulence, the final state is a drag-reduced turbulent flow. At the intermediate elasticity, the growth rate of the primary TS wave matches the Newtonian value. However, unlike the Newtonian instability mode which reaches a saturated equilibrium condition, the instability in the polymeric flow reaches a periodic state where its energy undergoes cyclical amplification and decay. The spanwise size of the secondary instability in this case is commensurate with the Newtonian $\unicode[STIX]{x1D6EC}$-structures, and the extent of drag reduction in the final turbulent state is enhanced relative to the lower elasticity condition. At the highest elasticity, the exponential growth rate of the TS wave is weaker than the Newtonian flow and, as a result, the early linear stage is prolonged. In addition, the magnitude of the saturated TS wave is appreciably lower than the other conditions. The secondary instability is also much wider in the span, with weaker ejection and without hairpin packets. Instead, streamwise-elongated streaks are formed and break down to turbulence via secondary instability. The final state is a high-drag-reduction flow, which approaches the Virk asymptote.

Direct numerical simulation of turbulent boundary layer with fully resolved particles at low volume fraction

In the present work, a direct numerical simulation (DNS) of dilute particulate flow in a turbulent boundary layer has been conducted, containing thousands of finite-sized solid rigid particles. The particle surfaces are resolved with the multi-direct forcing immersed-boundary method. This is, to the best of the authors' knowledge, the first DNS study of a turbulent boundary layer laden with finite-sized particles. The particles have a diameter of approximately 11.3 wall units, a density of 3.3 times that of the fluid, and a solid volume fraction of 1/1000. The simulation shows that the onset and the completion of the transition processes are shifted earlier with the inclusion of the solid phase and that the resulting streamwise mean velocity of the boundary layer in the particle-laden case is almost consistent with the results of the single-phase case. At the same time, relatively stronger particle movements are observed in the near-wall regions, due to the driving of the counterrotating streamwise vortexes. As a result, increased levels of dissipation occur on the particle surfaces, and the root mean square of the fluctuating velocities of the fluid in the near-wall regions is decreased. Under the present parameters, including the particle Stokes number St+ = 24 and the particle Reynolds number Rep = 33 based on the maximum instantaneous fluid-solid velocity lag, no vortex shedding behind the particle is observed. Lastly, a trajectory analysis of the particles shows the influence of turbophoresis on particle wall-normal concentration, and the particles that originated between y+ = 60 and 2/3 of the boundary-layer thickness are the most influenced.

An erosion model for the discrete element method

A shear impact energy model (SIEM) of erosion suitable for both dilute and dense particle flows is proposed based on the shear impact energy of particles in discrete element method (DEM) simulations. A number of DEM simulations are performed to determine the relationship between the shear impact energy predicted by the DEM model and the theoretical erosion energy. Simulation results show that nearly one-quarter of the shear impact energy will be converted to erosion during an impingement. According to the ratio of the shear impact energy to the erosion energy, it is feasible to predict erosion from the shear impact energy, which can be accumulated at each time step for each impingement during the DEM simulation. The total erosion of the target surface can be obtained by summing the volume of material removed from each impingement. The proposed erosion model is validated against experiment and results show that the SIEM combined with DEM accurately predicts abrasive erosions.

Numerical analysis of frictional behavior of dense gas–solid systems

Dense gas–solid flows show significantly higher stresses compared with dilute flows, mainly attributable to particle–particle friction in dense particle flows. Several models developed have considered particle–particle friction; however, they generally underestimate its effect in dense regions of the gas–solid system, leading to unrealistic predictions in their flow patterns. Recently, several attempts have been made to formulate such flows and the impact of particle–particle friction on predicting flow patterns based on modified frictional viscosity models by including effects of bulk density changes on frictional pressure of the solid phase. The solid–wall boundary is also expected to have considerable effect on friction because particulate phases generally slip over the solid surface that directly affects particle–particle frictional forces. Polydispersity of the solid phase also leads to higher friction between particles as more particles have sustained contact in polydispersed systems. Their effects were investigated by performing CFD simulations of particle settlement to calculate the slope angle of resting material of non-cohesive particles as they settle on a solid surface. This slope angle is directly affected by frictional forces and may be a reasonably good measure of frictional forces between particles. The calculated slope angle, as a measure of frictional forces inside the system are compared with experimental values of this slope angle as well as simulation results from the literature.

Advection-diffusion sediment models in a two-phase flow perspective

ABSTRACTSediment profiles in open channels are usually predicted by advection-diffusion models. Most basic forms consider the terminal settling velocity of a single particle in still clear water. Alternative forms account for hindered settling at higher concentrations. It is not known, however, how these modifications relate to mass and momentum conservation of each phase. For dilute flow, it is known that the original form can be derived from a two-phase analysis, assuming a dilute suspension, neglect of inertial effects in the momentum balance and using a linear drag force formulation. Here we study how and if it is possible to understand the hindered-settling modifications for the non-dilute case, and formulate a relation between advection-diffusion models and parameters involved in the turbulent drag force. This note verifies that the transient two-phase flow solutions converge to steady state, and compares the results to experimental data.