J. N. Chung

Particle mixing in free shear flows

Abstract The mixing of particles or droplets in free shear layers is encountered in a variety of combustion systems and industrial applications. Free shear layers are characterized by large scale vortical structures which evolve and interact with time. These vortex structures can play a major role in particle or droplet dispersion. It has recently been postulated that the organized rotating motion of the large-scale structures can enhance the dispersion of intermediate size particles. This paper first reviews the currently-accepted mechanisms and models for particle dispersion in homogenoue, isotropic turbulence and addresses the difference between such flows and free shear layers. The essential features of free shear flows are then described and experiments on particle dispersion in free jets and mixing layers are reviewed. Numerical models which have been developed for particle dispersion in free shear layers, such as plane mixing layers, jets and wakes, are outlined and the results are interpreted in light of the postulated physical model. Both experimental results and numerical simulations strongly imply that particle dispersion in free shear layers is controlled by the motion of large scale vortex structures.

Self-organizing particle dispersion mechanism in a plane wake

Experimental and numerical results concerning solid particle motion in a plane wake are presented that demonstrate the importance of large‐scale vortex structures in self‐organizing dispersion processes. Previous studies have demonstrated that a time scale ratio involving the aerodynamic response time of the particles and a characteristic time of the vortex structures is an important parameter for indicating the qualitative and quantitative nature of the dispersion process. A stretching and folding mechanism associated with vortex development and merging interactions has been suggested as a description for characterizing particle dispersion in plane mixing layers at intermediate time scale ratios. For plane wakes where large‐scale vortex mergers rarely occur, a highly organized particle dispersion process focuses intermediate time scale ratio particles along the boundaries of the large‐scale vortices. The fractal correlation dimension associated with chaotic systems is found to be a useful parameter for q...

Particle Dispersion by Vortex Structures in Plane Mixing Layers

The dispersion of particles in a plane mixing layer between two air streams is investigated using experimental and numerical techniques. The results show that large-scale spanwise vortices strongly influence the particle dispersion process. Particles with aerodynamic response times on the order of the large scale vortex time scales are found to concentrate near the outer edges of the vortex structures. Time average velocity measurements also demonstrate that these particles tend to move away from the center of the mixing layer

Direct numerical simulation of a three-dimensional temporal mixing layer with particle dispersion

The three-dimensional mixing layer is characterized by both two-dimensional and streamwise large-scale structures. Understanding the effects of those large-scale structures on the dispersion of particles is very important. Using a pseudospectral method, the large-scale structures of a three-dimensional temporally developing mixing layer and the associated dispersion patterns of particles were simulated. The Fourier expansion was used for spatial derivatives due to the periodic boundary conditions in the streamwise and the spanwise directions and the free-slip boundary condition in the transverse direction. A second-order Adam–Bashforth scheme was used in the time integration. Both a two-dimensional perturbation, which was based on the unstable wavenumbers of the streamwise direction, and a three-dimensional perturbation, derived from an isotropic energy spectrum, were imposed initially. Particles with different Stokes numbers were traced by the Lagrangian approach based on one-way coupling between the continuous and the dispersed phases. The time scale and length scale for the pairing were found to be twice those for the rollup. The streamwise large-scale structures develop from the initial perturbation and the most unstable wavelength in the spanwise direction was found to be about two thirds of that in the streamwise direction. The pairing of the spanwise vortices was also found to have a suppressing effect on the development of the three-dimensionality. Particles with Stokes number of the order of unity were found to have the largest concentration on the circumference of the two-dimensional large-scale structures. The presence of the streamwise large-scale structures causes the variation of the particle concentrations along the spanwise and the transverse directions. The extent of variation also increases with the development of the three-dimensionality, which results in the ‘mushroom’ shape of the particle distribution.

EFFECTS OF VORTEX PAIRING ON PARTICLE DISPERSION IN TURBULENT SHEAR FLOWS

Abstract Particle dispersion in large-scale dominated turbulent shear flow is investigated numerically with special emphasis on the effects of the vortex-pairing phenomenon. The particle dispersion is visualized numerically by following the particle trajectories in a flow consisting of large vortices which are undergoing pairing interaction. The flow field is generated by a discrete vortex method. Important global and local fiow quantities from the numerical simulation compare reasonably well with experimental measurements. For both cases of point sources with continuous particle release and an initially distributed line source, the particle dispersion results demonstrate that the extent of particle dispersion depends strongly on the Stokes number, the ratio of the particle aerodynamic response time to the characteristic time of the vortex-pairing flow field. Particles with relatively small Stokes numbers disperse laterally at approximately the saine rate as that of the fluid particles and particles with large Stokes numbers disperse much less than the fluid particles. Particles with intermediate Stokes numbers (0.5-5) may be dispersed laterally farther than the fiuid particles and may actually be flung out of the vortex structures. Due to the strong particie entrainment power, the flow during the vortex-pairing process seems to produce higher particle lateral dispersion than the pre-pairing and post-pairing flows.

Flow about a fluid sphere at low to moderate Reynolds numbers

The steady-state equations of motion are solved for a fluid sphere translating in a quiescent medium. A semi-analytical series truncation method is employed in conjunction with a cubic finite-element scheme. The range of Reynolds numbers investigated is from 0.5 to 50. The range of viscosity ratios is from 0 (gas bubble) to 10 7 (solid sphere). The flow structure and the drag coefficients agree closely with the limited available experimental measurements and also compare favourably with published finite-difference solutions. The strength of the internal circulation was found to increase with increasing Reynolds number. The flow patterns and the drag coefficient show little variation with the interior Reynolds number. Based on the numerical results, predictive equations for drag coefficients are recommended for both moderate- and low-Reynolds-number flows.

Experiments on particle dispersion in a plane wake

Abstract Detailed experimental results are presented concerning the effects of vortex structures on the solid particle dispersion process in a plane wake. Previous numerical results have indicated that vortex structures in plane wakes can disperse intermediate Stokes number particles into highly organized patterns. The cross stream spatial dispersion values associated with these particles were computed to be several times greater than that associated with fluid elements. The major objective of this study was to obtain direct experimental results concerning the time dependent particle dispersion process in a plane wake. The experimental approach used in this work primarily involves laser sheet pulsed imaging of glass bead particles in a wake downstream of a blunt trailing edge. Two sizes of glass beads with nominal diameters of 10 and 30 μm were used as particles in an air flow. The associated Stokes numbers of the particles were 0.15 and 1.4. Digital image analysis techniques were employed to identify and determine particle locations and velocities. The results demonstrate that particle dispersion in plane wakes can produce highly organized patterns of particle concentrations. The particles at intermediate Stokes number are focused into sheet-like regions near the boundaries of the large scale vortex structures. In addition the spatial dispersion of the intermediate Stokes number particles was much larger than the smaller Stokes number particles. These experimental results strongly support previous numerical simulation findings.

The linear stability of mixed convection in a vertical channel flow

In this study, the linear stability of mixed-convection flow in a vertical channel is investigated for both buoyancy-assisted and -opposed conditions. The disturbance momentum and energy equations were solved by the Galerkin method. In addition to the case with a zero heat flux perturbation boundary condition, we also examined the zero temperature perturbation boundary condition. In general, the mixed-convection flow is strongly destabilized by the heat transfer and therefore the fully developed heated flow is very unstable and very difficult to maintain in nature. For buoyancy-assisted flow, the two-dimensional disturbances dominate, while for buoyancy-opposed flow, the Rayleigh–Taylor instability prevails for zero heat flux perturbation boundary condition, and for the zero temperature perturbation on the boundaries the two-dimensional disturbances dominate except at lower Reynolds numbers where the Rayleigh–Taylor instability dominates again. The instability characteristics of buoyancy-assisted flow are found to be strongly dependent on the Prandtl number whereas the Prandtl number is a weak parameter for buoyancy-opposed flow. Also the least-stable disturbances are nearly one-dimensional for liquids and heavy oils at high Reynolds numbers in buoyancy-assisted flows. From an energy budget analysis, we found that the thermal–buoyant instability is the dominant type for buoyancy-assisted flow. In buoyancy-opposed flow, under the zero temperature perturbation boundary condition the Rayleigh–Taylor instability dominates for low-Reynolds-number flow and then the thermal–shear instability takes over for the higher Reynolds numbers whereas the Rayleigh–Taylor instability dominates solely for the zero heat flux perturbation boundary condition. It is found that the instability characteristics for some cases of channel flow in this study are significantly different from previous results for heated annulus and pipe flows. Based on the distinctly different wave speed characteristics and disturbance amplification rates, we offer some suggestions regarding the totally different laminar–turbulent transition patterns for buoyancy-assisted and -opposed flows.

The influence of particles on the spatial stability of two‐phase mixing layers

A modified Rayleigh equation has been derived for the study of spatial instability of gas–particle two‐phase mixing layers. The particles are assumed to have a material density much greater than the carrier fluid. The mathematical model is based on the assumptions that the mean flow profile can be approximated as that of the particle‐free single‐phase mixing layer and that the two phases are in dynamic equilibrium at the start of the perturbation. The resulting eigenvalue problem was solved numerically. The major finding from the analysis is that the presence of the particles enhances the stability of the two‐phase flow and decreases the amplification rate of perturbations in the flow. The results show that the stability of the flow is enhanced with increased particle loading and decreased free‐stream velocity ratio. For a given free‐stream velocity ratio, the most amplified growth rates decrease almost linearly with the particle loading. The most amplified growth rate, however, occurs near the same angul...

MIXED TRANSFORM FINITE ELEMENT METHOD FOR SOLVING THE NON-LINEAR EQUATION FOR FLOW IN VARIABLY SATURATED POROUS MEDIA

A new computational method is developed for numerical solution of the Richards equation for flow in variably saturated porous media. The new method, referred to as the mixed transform finite element method, employs the mixed formulation of the Richards equation but expressed in terms of a partitioned transform. An iterative finite element algorithm is derived using a Newton–Galerkin weak statement. Specific advantages of the new method are demonstrated with applications to a set of one— dimensional test problems. Comparisons with the modified Picard method show that the new method produces more robust solutions for a broad range of soil– moisture regimes, including flow in desiccated soils, in heterogeneous media and in layered soils with formation of perched water zones. In addition, the mixed transform finite element method is shown to converge faster than the modified Picard method in a number of cases and to accurately represent pressure head and moisture content profiles with very steep fronts.