A Turbulent Model for Gas-Particle Jets

2000 ◽  
Vol 122 (3) ◽  
pp. 505-509 ◽  
Author(s):  
J. Garcı´a ◽  
A. Crespo
Keyword(s):  
Mixing Layer ◽  
Stokes Number ◽  
Particle Dispersion ◽  
Lagrangian Model ◽  
Grid Turbulence ◽  
Mean Velocity ◽  
Dissipation Term ◽  
Particle Flows ◽  
Integral Scales ◽  
Kolmogorov Constant

This work is concerned with turbulent diffusion in gas-particle flows. The cases studied correspond to dilute flows and small Stokes number, this implies that the mean velocity of the particles is very similar to that of the fluid element. The classical k-ε method is used to model the gas-phase, modified with additional terms for the k and ε equations, that takes into account the effect of particles on the carrier phase. The additional dissipation term included in the equation for k is due to the slip between phases at an intermediate scale, far from both the Kolmogorov and the integral scales. This term has a proportionality constant equal to 3/2 of Kolmogorov constant, C0. In this paper, a value of 3.0 has been used for this constant as suggested by Du et al., 1995, “Estimation of the Kolmogorov Constant C0 for the Langarian Structure Using a Second-Order Lagrangian Model of Grid Turbulence,” Phys. Fluids 7, (12), pp. 3083–3090. The additional source term for the ε equation is taken as proportional to ε/k, as is usually done. In all experiments analyzed the particles increased the dissipation of turbulent kinetic energy. A comparison is made between the results obtained with the model proposed in this work and the experiments of Shuen et al., 1985, “Structure of Particle-Laden Jets: Measurements and Predictions,” AIAA Journal, 23, No. 3, and Hishida et al., 1992, “Experiments on Particle Dispersion in a Turbulent Mixing Layer,” ASME Journal of Fluids Engineering, 119, pp. 181–194. [S0098-2202(00)02103-9]

Estimation of the Kolmogorov constant (C0) for the Lagrangian structure function, using a second‐order Lagrangian model of grid turbulence

1995 ◽  
Vol 7 (12) ◽  
pp. 3083-3090 ◽  
Author(s):  
Shuming Du ◽  
Brian L. Sawford ◽  
John D. Wilson ◽  
David J. Wilson
Keyword(s):  
Structure Function ◽  
Second Order ◽  
Lagrangian Model ◽  
Grid Turbulence ◽  
Kolmogorov Constant

The shearless turbulence mixing layer

1989 ◽  
Vol 207 ◽  
pp. 191-229 ◽  
Author(s):  
S. Veeravalli ◽  
Z. Warhaft
Keyword(s):  
Transverse Velocity ◽  
Mixing Layer ◽  
Perforated Plate ◽  
Energy Budgets ◽  
Grid Turbulence ◽  
Self Similarity ◽  
Mean Velocity ◽  
Spacing Ratio ◽  
Turbulence Mixing ◽  
Mesh Spacing

The interaction of two energy-containing turbulence scales is studied in the absence of mean shear. The flow, a turbulence mixing layer, is formed in decaying grid turbulence in which there are two distinct scales, one on either side of the stream. This is achieved using a composite grid with a larger mesh spacing on one side of the grid than the other. The solidity of the grid, and thus the mean velocity, is kept constant across the entire flow. Since there is no mean shear there is no turbulence production and thus spreading is caused solely by the fluctuating pressure and velocity fields. Two different types of grids were used: a parallel bar grid and a perforated plate. The mesh spacing ratio was varied from 3.3:1 to 8.9:1 for the bar grid, producing a turbulence lengthscale ratio of 2.4:1 and 4.3:1 for two different experiments. For the perforated plate the mesh ratio was 3:1 producing a turbulence lengthscale ratio of 2.2:1. Cross-stream profiles of the velocity variance and spectra indicate that for the large lengthscale ratio (4.3:1) experiment, a single scale dominates the flow while for the smaller lengthscale ratio experiments, the energetics are controlled by both lengthscales on either side of the flow. In all cases the mixing layer is strongly intermittent and the transverse velocity fluctuations have large skewness. The downstream data of the second, third and fourth moments for all experiments collapse well using a single composite lengthscale. The component turbulent energy budgets show the importance of the triple moment transport and pressure terms within the layer and the dominance of advection and dissipation on the outer edge. It is also shown that the bar grids tend toward self-similarity with downstream distance. The perforated plate could not be measured to the same downstream extent and did not reach self-similarity within its measurement range. In other respects the two types of grids yielded qualitatively similar results. Finally, we emphasize the distinction between intermittent turbulent penetration and turbulent diffusion and show that both play an important role in the spreading of the mixing layer.

Lagrangian Simulation of Gas-Solid Flows in Homogeneous Isotropic Turbulence

2000 ◽  
Author(s):  
Daniel Huilier
Keyword(s):  
Isotropic Turbulence ◽  
Fluid Velocity ◽  
Particle Dispersion ◽  
Lagrangian Model ◽  
Primary Concern ◽  
Inertial Particles ◽  
Lagrangian Simulation ◽  
Particle Flows ◽  
Spatio Temporal ◽  
Turbulent Particle Dispersion

Abstract A Lagrangian approach is developed to describe particle’s dispersion in a stationary, homogeneous and isotropic turbulent flow. Obviously, the particles’ dispersion is influenced by the fluid velocity fluctuations, which are classically simulated by a Monte Carlo process or Markov chains. However, some studies have shown the restrictions of these methods generating the fluid turbulent velocity and have suggested improvements to ensure that the Lagrangian model accounts for the three main effects governing the dispersion in gas-particle flows, namely the inertia, crossing trajectories and continuity effects. The first aim of this paper is to present an improved Lagrangian model which integrates the spatio-temporal characteristics of the fluid turbulence experienced by the particle. The agreement between the numerical results obtained and the analytical expressions derived by Wang and Stock (1993) will be very satisfying. Another interest is to investigate the role of the traditionally-neglected and troublesome added mass and history terms in numerical studies when long time dispersion of inertial particles is the primary concern. Indeed, we will observe that for a large range of values of the ratio of particle to fluid density, these non-stationary forces have statistically no influence on the characteristics of the turbulent particle dispersion and can be safely omitted.

Effect of Particle Residence Time on Particle Dispersion in a Plane Mixing Layer

1993 ◽  
Vol 115 (4) ◽  
pp. 751-759 ◽  
Author(s):  
Tsuneaki Ishima ◽  
Koichi Hishida ◽  
Masanobu Maeda
Keyword(s):  
Gas Phase ◽  
Residence Time ◽  
Time Scale ◽  
Characteristic Time ◽  
Mixing Layer ◽  
Particle Dispersion ◽  
Laser Doppler Velocimeter ◽  
Characteristic Time Scale ◽  
Two Phase ◽  
Particle Residence Time

A particle dispersion has been experimentally investigated in a two-dimensional mixing layer with a large relative velocity between particle and gas-phase in order to clarify the effect of particle residence time on particle dispersion. Spherical glass particles 42, 72, and 135 μm in diameter were loaded directly into the origin of the shear layer. Particle number density and the velocities of both particle and gas phase were measured by a laser Doppler velocimeter with modified signal processing for two-phase flow. The results confirmed that the characteristic time scale of the coherent eddy apparently became equivalent to a shorter characteristic time scale due to a less residence time. The particle dispersion coefficients were well correlated to the extended Stokes number defined as the ratio of the particle relaxation time to the substantial eddy characteristic time scale which was evaluated by taking account of the particle residence time.

scholarly journals Assumptions about footprint layer heights influence the quantification of emission sources: a case study for Cyprus

2017 ◽  
Vol 17 (18) ◽  
pp. 10955-10967 ◽  
Author(s):  
Imke Hüser ◽  
Hartwig Harder ◽  
Angelika Heil ◽  
Johannes W. Kaiser
Keyword(s):  
Mixing Layer ◽  
Particle Dispersion ◽  
Reasonable Assumption ◽  
Night Time ◽  
Meteorological Model ◽  
Source Contributions ◽  
Time Sensitivity ◽  
Tracer Particles ◽  
Constant Height ◽  
The Impact

Abstract. Lagrangian particle dispersion models (LPDMs) in backward mode are widely used to quantify the impact of transboundary pollution on downwind sites. Most LPDM applications count particles with a technique that introduces a so-called footprint layer (FL) with constant height, in which passing air tracer particles are assumed to be affected by surface emissions. The mixing layer dynamics are represented by the underlying meteorological model. This particle counting technique implicitly assumes that the atmosphere is well mixed in the FL. We have performed backward trajectory simulations with the FLEXPART model starting at Cyprus to calculate the sensitivity to emissions of upwind pollution sources. The emission sensitivity is used to quantify source contributions at the receptor and support the interpretation of ground measurements carried out during the CYPHEX campaign in July 2014. Here we analyse the effects of different constant and dynamic FL height assumptions. The results show that calculations with FL heights of 100 and 300 m yield similar but still discernible results. Comparison of calculations with FL heights constant at 300 m and dynamically following the planetary boundary layer (PBL) height exhibits systematic differences, with daytime and night-time sensitivity differences compensating for each other. The differences at daytime when a well-mixed PBL can be assumed indicate that residual inaccuracies in the representation of the mixing layer dynamics in the trajectories may introduce errors in the impact assessment on downwind sites. Emissions from vegetation fires are mixed up by pyrogenic convection which is not represented in FLEXPART. Neglecting this convection may lead to severe over- or underestimations of the downwind smoke concentrations. Introducing an extreme fire source from a different year in our study period and using fire-observation-based plume heights as reference, we find an overestimation of more than 60  % by the constant FL height assumptions used for surface emissions. Assuming a FL that follows the PBL may reproduce the peak of the smoke plume passing through but erroneously elevates the background for shallow stable PBL heights. It might thus be a reasonable assumption for open biomass burning emissions wherever observation-based injection heights are not available.

Simulation of particle dispersion in an axisymmetric jet

1988 ◽  
Vol 186 ◽  
pp. 199-222 ◽  
Author(s):  
J. N. Chung ◽  
T. R. Troutt
Keyword(s):  
Mixing Layer ◽  
Jet Flow ◽  
Particle Dispersion ◽  
Vortex Rings ◽  
Local Flow ◽  
Discrete Vortex ◽  
Turbulent Mixing Layer ◽  
Axisymmetric Jet ◽  
Free Jet ◽  
Global And Local

Particle dispersion in an axisymmetric jet is analysed numerically by following particle trajectories in a jet flow simulated by discrete vortex rings. Important global and local flow quantities reported in experimental measurements are successfully simulated by this method.The particle dispersion results demonstrate that the extent of particle dispersion depends strongly on γτ, the ratio of particle aerodynamic response time to the characteristic time of the jet flow. Particles with relatively small γτ values are dispersed at approximately the fluid dispersion rate. Particles with large γτ values are dispersed less than the fluid. Particles at intermediate values of γτ may be dispersed faster than the fluid and actually be flung outside the fluid mixing region of the jet. This result is in agreement with some previous experimental observations. As a consequence of this analysis, it is suggested that there exists a specific range of intermediate γτ at which optimal dispersion of particles in the turbulent mixing layer of a free jet may be achieved.

LES and Hybrid RANS/LES of a Fundamental Trailing Edge Slot

2014 ◽  
Author(s):  
Elizaveta Ivanova ◽  
Gregory M. Laskowski
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Numerical Study ◽  
Mixing Layer ◽  
Detached Eddy Simulation ◽  
Trailing Edge ◽  
Adiabatic Wall ◽  
Mean Velocity ◽  
Eddy Simulation ◽  
Delayed Detached Eddy Simulation

This paper presents the results of a numerical study on the predictive capabilities of Large Eddy Simulation (LES) and hybrid RANS/LES methods for heat transfer, mean velocity, and turbulence in a fundamental trailing edge slot. The geometry represents a landless slot (two-dimensional wall jet) with adjustable slot lip thickness. The reference experimental data taken from the publications of Kacker and Whitelaw [1] [2] [3] [4] contains the adiabatic wall effectiveness together with the velocity and the Reynolds-stress profiles for various blowing ratios and slot lip thicknesses. The simulations were conducted at three different lip thickness and several blowing ratio values. The comparison with the experimental data shows a general advantage of LES and hybrid RANS/LES methods against unsteady RANS. The predictive capability of the tested LES models (dynamic ksgs-equation [5] and WALE [6]) was comparable. The Improved Delayed Detached Eddy Simulation (IDDES) hybrid method [7] also shows satisfactory agreement with the experimental data. In addition to the described baseline investigations, the influence of the inlet turbulence boundary conditions and their implication for the initial mixing layer and heat transfer development were studied for both LES and IDDES.

Compressibility effects in a turbulent annular mixing layer. Part 1. Turbulence and growth rate

2000 ◽  
Vol 421 ◽  
pp. 229-267 ◽  
Author(s):  
JONATHAN B. FREUND ◽  
SANJIVA K. LELE ◽  
PARVIZ MOIN
Keyword(s):  
Growth Rate ◽  
Mach Number ◽  
Mixing Layer ◽  
Mixing Layers ◽  
Velocity Difference ◽  
Mean Velocity ◽  
The Mean ◽  
Mach Numbers ◽  
High Mach ◽  
Compressibility Effects

This work uses direct numerical simulations of time evolving annular mixing layers, which correspond to the early development of round jets, to study compressibility effects on turbulence in free shear flows. Nine cases were considered with convective Mach numbers ranging from Mc = 0.1 to 1.8 and turbulence Mach numbers reaching as high as Mt = 0.8.Growth rates of the simulated mixing layers are suppressed with increasing Mach number as observed experimentally. Also in accord with experiments, the mean velocity difference across the layer is found to be inadequate for scaling most turbulence statistics. An alternative scaling based on the mean velocity difference across a typical large eddy, whose dimension is determined by two-point spatial correlations, is proposed and validated. Analysis of the budget of the streamwise component of Reynolds stress shows how the new scaling is linked to the observed growth rate suppression. Dilatational contributions to the budget of turbulent kinetic energy are found to increase rapidly with Mach number, but remain small even at Mc = 1.8 despite the fact that shocklets are found at high Mach numbers. Flow visualizations show that at low Mach numbers the mixing region is dominated by large azimuthally correlated rollers whereas at high Mach numbers the flow is dominated by small streamwise oriented structures. An acoustic timescale limitation for supersonically deforming eddies is found to be consistent with the observations and scalings and is offered as a possible explanation for the decrease in transverse lengthscale.

A k-ε Model for Particle-Laden Turbulent Flows

2009 ◽  
Author(s):  
J. D. Schwarzkopf ◽  
C. T. Crowe ◽  
P. Dutta
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Turbulent Flows ◽  
Carrier Phase ◽  
Critical Role ◽  
New Production ◽  
Mean Velocity ◽  
Production Term ◽  
Dissipation Term ◽  
Velocity Gradients

A dissipation transport equation for the carrier phase of particle-laden turbulent flows was recently developed. This equation shows a new production of dissipation term due to the presence of particles that is related to the velocity difference between the particle and the surrounding fluid. In the development, it was assumed that each coefficient was the sum of the coefficient for single phase flow and a coefficient quantifying the contribution of the particulate phase. The coefficient for the new production term (due to the presence of particles) was found from homogeneous turbulence generation by particles and the coefficient for the dissipation of dissipation term was analyzed using DNS. A numerical model was developed and applied to particles falling in a channel of downward turbulent air flow. Boundary conditions were also developed to ensure that the production of turbulent kinetic energy due to mean velocity gradients and particle surfaces balanced with the turbulent dissipation near the wall. The turbulent kinetic energy is compared with experimental data. The results show attenuation of turbulent kinetic energy with increased particle loading; however the model does under predict the turbulent kinetic energy near the center of the channel. To understand the effect of this additional production of dissipation term (due to particles), the coefficients associated with the production of dissipation due to mean velocity gradients and particle surfaces are varied to assess the effects of the dispersed phase on the carrier phase turbulent kinetic energy across the channel. The results show that this additional term plays a significant role in predicting the turbulent kinetic energy and a reason for under predicting the turbulent kinetic energy near the center of the channel is discussed. It is concluded that the dissipation coefficients play a critical role in predicting the turbulent kinetic energy in particle-laden turbulent flows.

Particle Dispersion in Fine Scales of Homogeneous Isotropic Turbulence

2007 ◽  
Author(s):  
M. Sato ◽  
M. Tanahashi ◽  
T. Miyauchi
Keyword(s):  
Isotropic Turbulence ◽  
Major Axis ◽  
Stokes Number ◽  
High Energy ◽  
Energy Dissipation Rate ◽  
Particle Dispersion ◽  
Fine Scale ◽  
Number Density ◽  
Homogeneous Isotropic Turbulence ◽  
Preferential Concentration

Direct numerical simulations of homogeneous isotropic turbulence laden with particles have been conducted to clarify the relationship between particle dispersion and coherent fine scale eddies in turbulence. Dispersion of 106 particles are analyzed for several particle Stokes numbers. The spatial distributions of particles depend on their Stokes number, and the Stokes number that causes preferential concentration of particles is closely related to the time scale of coherent fine scale eddies in turbulence. On the plane perpendicular to the rotating axes of fine scale eddies, number density of particle with particular Stokes number is low at the center of the fine scale eddy, and high in the regions with high energy dissipation rate around the eddy. The maximum number density can be observed at about 1.5 to 2.0 times the eddy radius on the major axis of the fine scale eddy.

Sign in / Sign up

Export Citation Format

Share Document