EVALUATION OF LAGRANGIAN PARTICLE DISPERSION MODELS IN TURBULENT FLOWS

This work evaluates the performance of Lagrangian turbulent particle dispersion models based on the Langevin equation. A family of Langevin models, extensively reported in the open literature, decompose the fluctuating fluid velocity seen by the particle in two components, one correlated with the previous time step and a second one randomly sampled from a Wiener process, i.e., the closure is at the level of the fluid velocity seen by the particle. We will call those models generically the “standard model.” On the other hand, the model proposed by Minier and Peirano (2001) is considered; this approach is based on the probability density function (PDF) and performs the closure at the level of the acceleration of the fluid seen by the particle. The formulation of a Langevin equation model for the increments of fluid velocity seen by the particle allows capturing some underlying physics of particle dispersion in general turbulent flows while keeping simple the mathematical manipulation of the stochastic model, avoiding some pitfalls, and simplifying the derivation of macroscopic relations. The performance of the previous dispersion models is evaluated in the configurations of grid-generated turbulence (Snyder and Lumley, 1971; Wells and Stock, 1983), simple shear flow (Hyland et al., 1999), and confined axisymmetric jet flow laden with solids (Hishida and Maeda, 1987).     

DIRECT NUMERICAL SIMULATION OF VORTEX STRUCTURES AND PARTICLE DISPERSION IN TURBULENT FREE SHEAR FLOWS

In order to provide references for the study of jets from combustor and associated industrial applications, direct numerical simulation was employed to study a three-dimensional temporally evolving plane mixing layer laden with particles in the upper region initially. The coherent structures in the mixing layer between two parallel streams were simulated using a pseudo-spectral method. Particles with different Stokes numbers were traced using the Lagrangian approach based on one-way coupling between the continuous and the dispersed phases. Both the large-scale vortex structures and the particle dispersion patterns with different Stokes numbers were investigated. The results clearly showed that particle dispersion is closely related to the large-scale organized structures and the three-dimensionality. Particles with Stokes number of the order of unity were found to have the largest concentration on the outer edges of the large-scale vortex structures, and the variation of particle concentration along the spanwise direction increased with the development of the three-dimensionality, which was mainly due to the presence of the streamwise large-scale structures. When the counter-rotating “rib” large-scale vortices paired, part of the particles were thrown out from the high concentration area in the upper region to the lower region of the mixing layer and finally developed into a “mushroom” pattern of the particle distribution along the spanwise direction.     

DIRECT NUMERICAL SIMULATION OF VORTEX STRUCTURES AND PARTICLE DISPERSION IN TURBULENT FREE SHEAR FLOWS

In order to provide references for the study of jets from combustor and associated industrial applications, direct numerical simulation was employed to study a three-dimensional temporally evolving plane mixing layer laden with particles in the upper region initially. The coherent structures in the mixing layer between two parallel streams were simulated using a pseudo-spectral method. Particles with different Stokes numbers were traced using the Lagrangian approach based on one-way coupling between the continuous and the dispersed phases. Both the large-scale vortex structures and the particle dispersion patterns with different Stokes numbers were investigated. The results clearly showed that particle dispersion is closely related to the large-scale organized structures and the three-dimensionality. Particles with Stokes number of the order of unity were found to have the largest concentration on the outer edges of the large-scale vortex structures, and the variation of particle concentration along the spanwise direction increased with the development of the three-dimensionality, which was mainly due to the presence of the streamwise large-scale structures. When the counter-rotating “rib” large-scale vortices paired, part of the particles were thrown out from the high concentration area in the upper region to the lower region of the mixing layer and finally developed into a “mushroom” pattern of the particle distribution along the spanwise direction.     

PREDICTION OF DENSE TURBULENT PARTICLE LADEN RISER FLOW WITH A EULERIAN AND LAGRANGIAN COMBINED MODEL

This paper formulates a new numerical model for the dense gas-solid flows, combining Eulcrian/Eulerian approach and Eulerian/Lagrangian approach together. The model takes account of inter-particle interactions in Eulerian coordinate using the kinetic theory of granular flow based on the Chapman-Enskog theory of dense gases. A stochastic particle dispersion model is incorporated in the model to calculate the turbulence diffusion of particles in Lagrangian coordinate. A comparison with published experimental results is made, and good agreement is shown.     

THE CONVECTIVE VELOCITY OF HEAVY PARTICLES IN TURBULENT AIR FLOWS

This paper examines the influence of the “crossing trajectories” effect on the convective velocity for heavy particles suspended in a turbulent air flow. The fluid energy spectrum “experienced” by a falling particle is deduced from experimental data and is used to evaluate the turbulent component of the convective velocity. The results indicate a significant increase in the rms value of the turbulent component due to the “crossing trajectories” effect.     

AN IMPROVEMENT TO THE SSF MODEL FOR PREDICTION OF LIGHT PARTICLE DISPERSION

This study investigates the predicted motion of small, light particles using the stochastic separated flow models proposed by Shuen et al. (1983 Shuen , J. S. , Chen , L. D. , and Faeth , G. M. ( 1983 ). Evaluation of a stochastic model of particle dispersion in a turbulent round jet , AIChE J. , 29 , 167 – 170 . [CSA] [CROSSREF] [Crossref], [Web of Science ®] , [Google Scholar]) and Lightstone and Raithby (1998 Lightstone , M. F. and Raithby , G. D. ( 1998 ). A stochastic model of particle dispersion in a turbulent gaseous environment , Combust. Flame , 113 , 424 – 441 . [CSA] [CROSSREF] [Crossref], [Web of Science ®] , [Google Scholar]). Model predictions are compared to the benchmark experiment of Snyder and Lumley (1971 Snyder , W. H. and Lumley , J. L. ( 1971 ). Some measurements of particle velocity autocorrelation functions in a turbulent flow , J. Fluid Mech. , 48 , 41 – 71 . [CSA] [CROSSREF] [Crossref], [Web of Science ®] , [Google Scholar]) for particles released from a point source in grid-generated turbulence. It is found that the predictions of particle velocity variance and dispersion exhibit nonphysical waves. This behavior is explored in order to understand its mathematical basis arising from the model formulation. A modification to the model is presented. The modified model is successful in removing the characteristic waves.     

NUMERICAL CALCULATIONS OF TUBE BUNDLES EROSION BY TURBULENT PARTICLE-LADEN GAS FLOWS

Erosion of tubes in tube bundles by particles suspended in gas flows is a major problem in the power industry. In this paper, a numerical study has been conducted for the flow of a dilute particle-laden gas moving past two row in-line tubes undergoing erosion. An orthogonal-curvilinear co-ordinate system was used to calculate turbulent flow around the tubes. The prediction of particle trajectories took into account the effect of the turbulence with a stochastic particle dispersion model. The results from this study included the distributions of particle collision frequency and erosion damage of tube surfaces.     

PARTICLE CONCENTRATION AND SIZE MEASUREMENTS IN TWO-PHASE TURBULENT COAXIAL JETS

Particle concentration and particle size distributions have been measured for two-phase (solid/air) turbulent coaxial jets using the Laser Diffraction Method (LDM) and a tomography data transform technique. Effects of velocity ratio, particle loading ratio, and particle size on the dispersions of gas and particles were determined. Experimental results show that the gas disperses much more rapidly than the particles and particle dispersion decreases with increasing in particle size. Increasing velocity ratio significantly increases gas dispersion, while effects of other variables are less significant. The mean particle size at the jet edge is about 15-20% smaller than that at the jet centerline. The turbulent Schmidt number Sc_p for two-phase turbulent coaxial jets ranges from 1.4 to 1.5.     

NUMERICAL CALCULATIONS OF TUBE BUNDLES EROSION BY TURBULENT PARTICLE-LADEN GAS FLOWS

Erosion of tubes in tube bundles by particles suspended in gas flows is a major problem in the power industry. In this paper, a numerical study has been conducted for the flow of a dilute particle-laden gas moving past two row in-line tubes undergoing erosion. An orthogonal-curvilinear co-ordinate system was used to calculate turbulent flow around the tubes. The prediction of particle trajectories took into account the effect of the turbulence with a stochastic particle dispersion model. The results from this study included the distributions of particle collision frequency and erosion damage of tube surfaces.     

THE EFFECT OF BUOYANCY ON PHASE DISTRIBUTION IN DISPERSED TURBULENT TWO-PHASE FLOWS

Advanced generation three-dimensional (3-D) two-fluid models and computational multiphase fluid dynamic (CMFD) solvers give good predictions of dispersed flows on earth (i.e., at 1 g), where the lift, wall, and turbulent dispersion forces determine the lateral void fraction distribution. However, for microgravity (μ-g) conditions these buoyancy-related forces become quite small and two-fluid model predictions are generally inadequate. This implies that some of the physics lost during ensemble averaging was not included back into the two-fluid model with the closure laws that were used.

Recent modeling advances that include the effect of the phasic velocity fluctuations on the phase distribution are presented. The resultant two-fluid model was evaluated and compared with various data sets for steady, fully developed turbulent conditions using a novel one-dimensional (1-D) CMFD solver that is numerically very efficient. It was found that with the addition of these new physical mechanisms to the closure laws, one is able to achieve good predictions of both the gas/liquid and solid/liquid dispersed phase distribution over a wide range of particle/bubble buoyancies and gravity levels.     

ON THE DEVELOPMENT OF MULTIDIMENSIONAL TWO-FLUID MODELS FOR VAPOR/LIQUID TWO-PHASE FLOWS

The status of multidimensional two-fluid modeling of vapor/liquid two-phase flows is reviewed. In particular, a three dimensional two-fluid model is derived using ensemble averaging. It is proposed that realistic interfacial closure laws should:

• Be mathematically objective

• Lead to well-posed models

• Satisfy the second law of thermodynamics

• Agree with all relevant experimental data.

Unfortunately, most two-fluid models in use today do not satisfy these fundamental constraints.     

MASS TRANSFER IN TURBULENT PULSATING FLOWS

The effect of flow oscillation to the mass transfer between turbulent fluid and solid wall was investigatedby measuring the mass transfer rate between fluid and pipe wall with imposed oscillating flow usingelectrochemical method.The velocity and concentration field in the viscous sublayer which controls the mass trans-fer in such a process was simulated by a simple wave model of single harmonics.Experimental results confirmthat the flow oscillation has no influene on time averaged mass transfer rate,but the phase difference betweenphase averaged velocity field and concentration field shifts with the frequency of imposed oscillating flow.Numeri-cal analysis reveals that the concentration boundarylayer which is responsible for the mass transfer is muchthinner than the viscous sublayer which greatly weakens the influence of imposed oscillating flow on mass transfer.     

A METHOD OF ESTIMATION OF TURBULENT DIFFUSION IN A CIRCULAR PIPE BASED ON SPATIAL-DEPENDENCE MATRIX

Considering that a scalar quantity (mass or heat) is transported on a turbulent lump where fluid particles show almost same behavior, a new method of numerical calculation for the turbulent diffusion is proposed. This method is based on the spatial-dependence matrix, which is one of the tools of pattern analysis. The usefulness of the method is examined by experiments on the turbulent diffusion of the tracer which is injected into the source point on the pipe axis and it is confirmed that the reasonable feature of turbulent diffusion is estimated by the method.     

A HEAT TRANSFER CORRELATION FOR VISCOELASTIC TURBULENT PIPE FLOWS

A modified version of Kale's heat transfer correlation for viscoelastic turbulent pipe flows in terms of drag reduction ratio and Weissenberg number is presented. The proposed correlation is validated with experimental data of Kwack and this study for Separan AP-273 and Polyox WSR-301 with concentrations ranging from 10 to 1000 ppm in thermally fully developed flow in pipes with diameters of 1·11 and 1·88 cm I.D. under constant wall heat flux. The agreement between the experimental data and the predictions is within a maximum deviation of 30%.     

A HEAT TRANSFER CORRELATION FOR VISCOELASTIC TURBULENT PIPE FLOWS

A modified version of Kale's heat transfer correlation for viscoelastic turbulent pipe flows in terms of drag reduction ratio and Weissenberg number is presented. The proposed correlation is validated with experimental data of Kwack and this study for Separan AP-273 and Polyox WSR-301 with concentrations ranging from 10 to 1000 ppm in thermally fully developed flow in pipes with diameters of 1·11 and 1·88 cm I.D. under constant wall heat flux. The agreement between the experimental data and the predictions is within a maximum deviation of 30%.     

INVESTIGATION OF THE USE OF LASER-DOPPLER VELOCIMETRY IN TWO-PHASE BUBBLY FLOWS

Understanding the dynamic phenomena of viability loss of shear sensitive cells and bubble breakage and coalescence within airlift reactors requires knowledge of local, liquid-phase hydrodynamics. The laser-Doppler velocimeter (LDV) is a non-invasive instrument which may be used to obtain this information. Experimental procedures and software were developed to detect and measure Doppler bursts in two-phase flow in a split-cylinder airlift reactor. Off-line analysis of the data indicated a detection rate approximately one order of magnitude greater than that observed using an available commercial frequency tracker. Approximately 400 to 500 observations are needed for the ensemble mean to characterize the local mean velocity to within ±5% for a superficial gas velocity of 10.4 cm/s, the highest superficial gas velocity used in these studies. The limitations, prospects, and signal-processing options for LDV in this application are also discussed     

A PROPOSAL FOR TREATMENT OF TURBULENT MIXING IN A TWO-PHASE SUBCHANNEL FLOW

We propose a practical method for the treatment of turbulent mixing rate in a two-phase subchannel flow in a hydrodynamic non-equilibrium state. Based on the assumption that the fundamental modes of the inter-subchannel fluid transfer in such a state are turbulent mixing, void drift, and diversion cross flow, the turbulent mixing rate is considered to be equal to that in the hydrodynamic equilibrium state that the flow will attain. The applicability of the method is examined by experiments concerning the axial variation in tracer concentration in a non-equilibrium flow without diversion cross flow. A good agreement is seen between the calculations and the measurements.