Particle Velocity Fluctuations Research Articles

Influence of internal turbulent structure on intensity of velocity and temperature fluctuations of particles

The hypothesis of “independent averaging” suggested by Corrsin [J. Atmos. Sci. 20 (1963) 115] is generalized for investigating the influence of turbulent microstructure on the intensity of velocity and temperature fluctuations of inertial particles. It has been shown that parameters of turbulent motion and heat transfer in a dispersed phase also depend on dynamic and thermal relaxation times of particles. It is established that amplitudes of velocity and temperature fluctuations of the dispersed phase are expressed in terms of the Eulerian space-time correlation functions measured in the system of coordinates moving with mean velocity of fluid flow. Association between Lagrangian and Eulerian turbulent time macroscales of various types of flows was estimated. These parameters were evaluated on the basis of published experimental data.

Measurement of phase interaction in dispersed gas/particle two-phase flow

For simultaneous measurement of size and velocity distributions of continuous and dispersed phases in a two-phase flow a method is proposed and applied to increase the sensitivity of a phase-Doppler-anemometry (PDA) system. Design considerations are presented to increase the detectable size range of the PDA system to approximately 1:200 (in diameter) for simultaneous detection of tracers and particles. For this the optical properties for light scattering of the particles are properly adjusted to the measurement problem by using homogeneously coloured particles and a special signal processing procedure, which is developed to guarantee reliable signal processing of the tracer signals even with poor signal-to-noise ratios (SNR). The application of the experimental configuration is described by simultaneous measurements of gas and particle velocity and velocity fluctuation profiles in a two-phase jet arrangement with a particle diameter range from 1 (tracers) up to 160 μm (particles). In this two-phase flow at high Stokes numbers ( St≫1) different turbulence structure modification effects are identified. The height of influence of these effects depends on the local position in the jet. Near the nozzle exit high gas velocity gradients exist and therefore high turbulence production in the shear layer of the jet is observed. Here the turbulence structure in the jet mainly depends on lateral turbulence transport. Due to a changed turbulence structure with reduced intensity of large eddies, this lateral transport in the two-phase jet is decreased in comparison to the single-phase jet in this area. In the area at greater nozzle distances where the jet is nearly developed, the velocity gradient in the shear layer is lower and due to this lateral turbulence transport effects become less important. Here axial turbulence transport along the jet dominates and turbulence intensity reduction is higher.

Memory effect in the Eulerian particle deposition in a fully developed turbulent channel flow

The constitutive relation for the particle Reynolds normal stress in the presence of the memory effect are derived in a form usable in the Eulerian transport equation through averaging the particle–turbulence interactions over an intermediate diffusion time scale. The memory effect in the aerosol deposition in a two-dimensional fully developed turbulent channel flow is estimated by applying the constitutive equation into the turbophoresis term. The calculated results reasonably predicted that with the memory effect a high level of fluctuating particle velocity is maintained down to much closer to the wall than with the simple equilibrium model, and an additional drift velocity towards the wall is induced very near the wall ( y +≈8). In the diffusional-impaction regime (0.3< τ p +<30), the additional drift velocity augments the deposition of particles densely accumulated in the viscous sublayer. All the calculated results are in good agreement with the available, though limited, experimental and numerical data.

Estimation of velocity fluctuation in internal combustion engineexhaust systems through beamforming techniques

The knowledge of the particle velocity fluctuations associated withacoustic pressure oscillation in the exhaust system of internal combustionengines may represent a powerful aid in the design of such systems, from thepoint of view of both engine performance improvement and exhaust noiseabatement. However, usual velocity measurement techniques, even if applicable,are not well suited to the aggressive environment existing in exhaust systems.In this paper, a method to obtain a suitable estimate of velocity fluctuationsis proposed, which is based on the application of spatial filtering (beamforming) techniques to instantaneous pressure measurements. Making use ofsimulated pressure-time histories, several algorithms have been checked bycomparison between the simulated and the estimated velocity fluctuations.Then, problems related to the experimental procedure and associated with theproposed methodology are addressed, making application to measurements made ina real exhaust system. The results indicate that, if proper care is taken whenperforming the measurements, the application of beamforming techniques gives areasonable estimate of the velocity fluctuations.

Experimental study of fluctuations of particle velocity in a turbulent flow of air in a pipe

The distribution of longitudinal and normal components of the fluctuation velocity of particles in their motion in a downward turbulent airflow in a pipe is obtained. The effect of the concentration of particles on the intensity of fluctuations of their velocity is studied. A high rise of the longitudinal fluctuation of the velocity of particles in the pipe wall region with an increase in their concentration is revealed.

Effect of particle concentration on fluctuating velocity of the disperse phase for turbulent pipe flow

Abstract This paper presents the results of an experimental investigation of the fluctuation velocity distributions of solid particles when they move in the downward gas turbulent pipe flow. The glass particles (StkL≈1) having an average diameter of 50 μm were used as a disperse phase. The average particle mass concentration varied within the range of M =0 to 1.2. The results obtained showed the particle fluctuation velocity to be strongly dependent on their mass loading. There has been observed an influence of the particle concentration on the significant increasing of their axial fluctuation velocity in the pipe wall region.

Design and scale-up methodology for multi-phase reactors based on non-linear dynamics

Multi-phase reactors exhibit chaotic behaviors due to the highly turbulent motions of bubbles and phase interactions, leading to the formation of a complex spatio-temporal flow structure. The instantaneous motions of bubbles and wakes were studied by local measurements of bubble and particle-velocity fluctuations, bubble–wake structure, bubble shape and orientation. The chaotic dynamics of bubble and particle motions in multi-phase reactors were characterized in terms of the correlation dimension obtained by the deterministic chaos analysis for the series of time intervals between successive bubbles or particles by means of the embedding method. Three different methods, the deterministic chaos analysis, the short-term predictability analysis and the rescaled range (R/S) analysis, were applied to the non-linear dynamics of multi-phase reactors. The scale-up effect in the dynamic behavior of multi-phase reactors was investigated by using columns of different diameters. In addition, the non-linear hydrodynamic motions of bubbles and particles in multi-phase reactors have been modeled by means of an ANN (Artificial Neural Network) trained with time series data of voidage fluctuations for gas and solid phases. By successively adapting its output to input, the ANN can generate time-series data for any superficial gas velocity. The bifurcation diagrams of both bubble and particle motions generated by the trained ANN demonstrated that the ANN is capable of predicting and modeling the chaotic dynamics of multi-phase reactors.

Structure, density, and velocity fluctuations in quasi-two-dimensional non-Brownian suspensions of spheres

Non-Brownian sedimenting suspensions exhibit density and velocity fluctuations. We have performed experiments on a quasi-two-dimensional counter-flow stabilized suspension of 2000 spherical particles, namely a liquid–solid fluidized bed in a Hele–Shaw cell. This two-dimensional suspension displays a uniform concentration but the particle radial distribution function and the fluctuations of the particle number in a subvolume of the suspension suggest that the microstructure is far from being random. We have also measured the velocity fluctuations of a test particle and the fluctuations of the mean particle velocity in a subvolume. It happens that the relation between velocity and concentration fluctuations in a subvolume can be deduced from a balance between buoyancy and parietal friction forces.

Predictive model of the turbulent flow of dilute gas–particulate suspension in a vertical pipe

A Chapman–Enskog closure approximation for the third order fluctuating velocity correlations in the particle phase of a turbulent dilute gas–particulate suspension is used to formulate the closed system of equations and boundary conditions for fully developed flow of dilute but densely loaded suspension of “high-inertia” particles in a vertical pipe. The particle size and concentration are assumed to be sufficiently small so that direct interparticle interactions (e.g., collisions) can be neglected, and the main mechanism inducing particle velocity fluctuations is the interaction between particles and turbulent flow. The case of moderate gas pressure gradient is studied thus modeling a number of practical applications (e.g., riser flow). The resulting set of continuum equations, consisting of mass and momentum conservation and Reynolds stress equations for the particulate phase, is free of empirical parameters. Although in a general case the effective stress in the particulate phase is anisotropic, the criterion is obtained showing that in a wide range of parameters typical for applications, this anisotropy may be neglected so that the equations for the individual diagonal components of the Reynolds stress tensor may be reduced to just one conservation equation for the particle fluctuation energy. The numerical solution shows the bifurcation of flow properties at a certain gas pressure gradient, thus providing an explicit criterion (i.e., a critical pressure gradient for the given total mass flux of solid particles) for upward particulate flow. The profiles of particle volume fraction and velocity are calculated, the former demonstrating the phenomenon of particle segregation toward the wall. A generalization of the model for the nearly developed flow is discussed, and an estimate is derived for the vertical distance required for the flow to become fully developed.A Chapman–Enskog closure approximation for the third order fluctuating velocity correlations in the particle phase of a turbulent dilute gas–particulate suspension is used to formulate the closed system of equations and boundary conditions for fully developed flow of dilute but densely loaded suspension of “high-inertia” particles in a vertical pipe. The particle size and concentration are assumed to be sufficiently small so that direct interparticle interactions (e.g., collisions) can be neglected, and the main mechanism inducing particle velocity fluctuations is the interaction between particles and turbulent flow. The case of moderate gas pressure gradient is studied thus modeling a number of practical applications (e.g., riser flow). The resulting set of continuum equations, consisting of mass and momentum conservation and Reynolds stress equations for the particulate phase, is free of empirical parameters. Although in a general case the effective stress in the particulate phase is anisotropic, the cr...

A novel non-intrusive probe of particle motion and gas generation in the feed injection zone of the feed riser of a fluidized bed catalytic cracking unit

The random impact of particles with diameters less than 500 μm at the wall of a gas fluidized bed or transfer line is a frequency independent “white noise” excitation source, for frequencies below 50 kHz, of the wall vibrational energy. In previous papers it has been demonstrated that the average acceleration power spectrum over the wall of a laboratory fluidized bed generated by such an “Acoustic Shot Noise” (ASN) source can supply the first quantitative data on the average mean squared particle fluctuation velocity, or granular temperature, T*, at the wall as a function of superficial gas velocity and particle diameter. In this paper we present and analyze the first experimental data on ASN excitation of the wall of 14 transfer lines with inner diameters ranging from 2–9 ft, carrying 10–80 tons of catalyst and coke particles per minute. Our focus is the first data on the particle normal velocity and density, derived from this data, along the wall of a Fluid Bed Catalytic Cracking Unit (FCCU) where gas generated by thermal and catalytic cracking of injected heavy oil at one location is the dominant source of particle motion along the entire transfer line. Simultaneous RMS acceleration measurements of the wall vibrational energy produced by acoustic shot noise are presented along the length of such “feed risers”, with inner diameters ranging from 12 to 68 in., before and after feed injection on four FCCUs converting 15 to 110 kbbl of heavy oil per day into lighter fractions that are appropriate for gasoline production. The data includes measurements of significant changes in the RMS acceleration along the feed riser on the same unit that result from changes in significant process variables. The field data demonstrates the power of the acoustic shot noise probe to detect changes in the chemistry and physics of gas generation and particle motion in the feed injection zone of a fluidized bed catalytic cracking unit, The direct acoustic shot noise data is a unique measure of the particle normal velocity and density at the wall. Estimates of the axial velocity and mean density of the particles are readily derived from this data using heuristic models. Both sets of data can serve as unique and critical boundary condition for validating computer flow codes, numerical simulations, and fundamental two phase theories of particle motion and density at the wall of such transfer lines which are major components of such significant processes as the catalytic cracking of oil into gasoline or fluidized bed coal combustion.

Particle Fluctuation Velocity in Gas Fluidized Beds - Fundamental Models Compared to Recent Experimental Data

ABSTRACTThe first measurements of the mean squared fluctuation velocity, or granular temperature, of monodispersed glass spheres in gas fluidized beds were recently obtained by two independent techniques: Power Spectral analysis of wall vibrational energy excited by random particle impact or Acoustic Shot Noise (ASN), and Diffusing Wave Spectroscopy (DWS) of reflected laser light multiply scattered by random particle motion. We explore the relevance of this data to the initial stability of the uniform fluidized state and to recent fundamental models for the magnitude, gas flow, and particle diameter dependence of the steady state granular temperature.

Turbulence structure of the solid phase in transition region of a circulating fluidized bed

Turbulence structures in transition region were characterized in a circulating fluidized bed (CFB) with square cross section. The investigations were carried out using a Particle Dynamic Analyzer (PDA). Both the axial and lateral velocity profiles of the solid phase were obtained. The axial profiles show the core-annulus structure in this region. Temporal evolutions of the particle velocity fluctuation indicate their great agitation and non-homogeneity with time and space coordinate. The studies on turbulent density and turbulent energy illustrate that the turbulence in the CFB is an anisotropic turbulence, and the particle turbulent density decreased sharply as the measurement points move away from the wall. To further understand the microstructure of the particle velocity fluctuation, wavelet analysis was also adopted. The vivid imagines show that it is an anisotropic turbulence at all scales and its fractal and dissipative structure.

Profiles of particle velocity and solids fraction in a high-density riser

Radial profiles of particle velocity and solids fraction in a high density circulating fluidized bed (HDCFB) at average cross-sectional solids fraction up to 0.21 were measured by an improved optical fiber laser doppler velocimeter and an optical fiber density sensor. The axial development of these radial profiles and the influence of operating conditions on the profiles were examined. The results showed that similar radial profiles of solids fraction exist in the HDCFB. The following Boltzman function can correlate well the solids fraction profile: (1 − ɛ)/(1 − ɛ) = 2.2 − (2)/(1 + exp(10· r/ R −7.665)). The radial profiles of particle velocity in HDCFB can also be described by the Boltzman function, that is, ( V p)/ ( U g) = (2.7)/(1 + exp(10· r/ R −10· X o) − 0.2). The Boltzman profiles of particle velocity in the high density operating regime was different with the parabolic shape operating in dilute phase regime. The local particle fluctuation velocity in the center of the riser increases with average solids concentration, while the fluctuation velocity decreases sharply as the radial position near the wall.

Collisional sheet flows of sediment driven by a turbulent fluid

We consider a sheet flow in which heavy grains near a packed bed interact with a unidirectional turbulent shear flow of a fluid. We focus on sheet flows in which the particles are supported by their collisional interactions rather than by the velocity fluctuations of the turbulent fluid and introduce what we believe to be the simplest theory for the collisional regime that captures its essential features.We employ a relatively simple model of the turbulent shearing of the fluid and use kinetic theory for the collisional grain flow to predict profiles of the mean fluid velocity, the mean particle velocity, the particle concentration, and the strength of the particle velocity fluctuations within the sheet. These profiles are obtained as solutions to the equations of balance of fluid and particle momentum and particle fluctuation energy over a range of Shields parameters between 0.5 and 2.5. We compare the predicted thickness of the concentrated region and the predicted features of the profile of the mean fluid velocity with those measured by Sumer et al. (1996). In addition, we calculate the volume flux of particles in the sheet as a function of Shields parameter.Finally, we apply the theory to sand grains in air for the conditions of a sandstorm and calculate profiles of particle concentration, velocity, and local volume flux.

Granular flow and viscous fluctuations in low Bagnold number granitic magmas

Recent thermal and fluid dynamical models have shown that density-driven ascent of isoviscous granitic melt through the crust in narrow dykes is geologically instantaneous, provided the role of suspended crystals is ignored. However, it is well known that solids in suspension can aVect significantly the rheology and hence flow properties of magmas, leading to the subjective criticism that granite ascent and emplacement rates based on simple dyke transport models may be unrealistic. By estimating the magnitude of shear stresses developed during continuous flow in a 6 m wide granitic dyke, we show yield strengths in excess of 10 4 pascals are required to stop flow entirely if the pressure gradient driving the flow is high. Using granular flow theory, we show how fluctuations in particle velocity in the shear field can be used to predict the rheological behaviour of magmas with crystal contents (solidosity) in the range 0.1&lt;Φ&lt;0.25. Specimen calculations for the solidosity and fluctuation on particle velocity for ascending granitic magmas show that the energy associated with these irregular movements is much greater than that expected on purely Brownian grounds. We find no clear correlation between viscosity ì and the yield strength, and while it is possible that magma has curious, unexpected bonding properties, magmatic suspensions where the grain size is on the scale of centimetres (e.g. some coarsely porphyritic magmas), low estimated Bagnold numbers ( c. 10 " 8 ) render Bingham flow models inappropriate. Self-organization of the flow into a crystal-poor margin and crystal-rich core (flow differentiation) by diffusion of particles towards the region of minimal shear results in the familiar plug-type flow profiles traditionally associated with an inherent yield strength. Shear-enhanced diffusion is an inevitable consequence of granular flow that leads to flow differentiation, providing a simple mechanistic explanation for high concentrations of pheoncrysts in the cores of porphyritic dykes (Bagnold effect). Deviation from simple Newtonian flow is unlikely to be significant until the magma has stopped ascending and emplacement begins.

Transport of Heavy Particles in a Three-Dimensional Mixing Layer

Particle transport in a three-dimensional, temporally evolving mixing layer has been calculated using large eddy simulation of the incompressible Navier-Stokes equations. The initial fluid velocity field was obtained from a separate simulation of fully developed turbulent channel flow. The momentum thickness Reynolds number ranged from 710 in the initial field to 4460 at the end of the calculation. Following a short development period, the layer evolves nearly self-similarly. Fluid velocity statistics are in good agreement with both the direct numerical simulation results of Rogers and Moser (1994) and experimental measurements of Bell and Mehta (1990). Particles were treated in a Lagrangian manner by solving the equation of motion for an ensemble of 20,000 particles. The particles have the same material properties as in the experiments of Hishida et al. (1992), i.e., glass beads with diameters of 42, 72, and 135 μm. Particle motion is governed by drag and gravity, particle-particle collisions are neglected, and the coupling is from fluid to particles only. In general, the mean and fluctuating particle velocities are in reasonable agreement with the experimental measurements of Hishida et al. (1992). Consistent with previous studies, the Stokes number (St) corresponding to maximum dispersion increases as the flow evolves when defined using a fixed fluid timescale. Definition of the Stokes number using the time-dependent vorticity thickness, however, shows a maximum in dispersion throughout the simulation for St ≈ 1.

An experimental investigation of the intrinsic convection in a sedimenting suspension

The sedimentation of spheres in a Newtonian fluid is experimentally studied under creeping flow conditions. The mean particle settling velocity and the particle velocity fluctuations are measured across the width of the sedimentation cell. We show that there can be a global intrinsic convection of the suspension superimposed on the settling motion of the particles. Unlike the predictions of the dilute theories of intrinsic convection, this effect is found to be small and even to disappear with increasing concentrations. We also find that there is an ordering of the suspension near the wall, which may be responsible for the observed small magnitude of the convection.

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

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

Using the FHP-BGK-Model to Get Effective Dispersion Constants for Spatially Periodic Model Geometries

Tracer dispersion is governed by the velocity fluctuations that the particles are subjected to during their movement. The fluctuation of particle velocity is due to deviations from the mean velocity in the flow field and also to the change of the streamline caused by diffusion. The lattice-BGK method is a good tool to investigate the interaction of both of them, because it models the flow field in detail with even small flow structures. A serious drawback of direct simulations are the requirements in computer time and memory. For spatially periodic media, this can be overcome by using the generalized Taylor-dispersion method to calculate the asymptotic effective dispersion from a solution in an elementary cell. This solution is obtained by simulations with an FHP-BGK-lattice gas. Joining the two methods yields a tool to study the effective dispersion constant of a given periodic geometry.

Asymptotic theory of two-phase gas-solid flow through a vertical tube at moderate pressure gradient

Based on the equations, constitutive relations and boundary conditions of the kinetic theory of colliding particles in a gas-solid suspension, the approximate theory of the steady, developed vertical flow of a gas-particulate mixture is developed for the case of moderate gas pressure gradient in a vertical tube. The basic equations and boundary conditions show a singular behaviour of the solution of the problem at the wall. The method of matched asymptotic expansions is applied to develop a boundary layer-type theory for the flow parameters of the particulate phase. The basic equations in the bulk flow are reduced to a system of two ordinary integrodifferential equations for the particle-phase concentration and mean kinetic energy of particle velocity fluctuations (particle-phase pseudotemperature). The distributions of the particle concentration and velocity are found in both the bulk and the boundary layer. The solutions shows the bifurcation of flow parameters, and an explicit criterion is derived to identify a range of the given macroscopic parameters corresponding to upward or downward particulate flow. The integrated parameters (total fluxes of the gas and particle phase) are calculated.