Inchul Kim

On the equation for spherical-particle motion : effect of Reynolds and acceleration numbers

The existing model equations governing the accelerated motion of a spherical particle are examined and their predictions compared with the results of the numerical solution of the full Navier–Stokes equations for unsteady, axisymmetric flow around a freely moving sphere injected into an initially stationary or oscillating fluid. The comparison for the particle Reynolds number in the range of 2 to 150 and the particle to fluid density ratio in the range of 5 to 200 indicates that the existing equations deviate considerably from the Navier–Stokes equations. As a result, we propose a new equation for the particle motion and demonstrate its superiority to the existing equations over a range of Reynolds numbers (from 2 to 150) and particle to fluid density ratios (from 5 to 200). The history terms in the new equation account for the effects of large relative acceleration or deceleration of the particle and the initial relative velocity between the fluid and the particle. We also examine the temporal structure of the near wake of the unsteady, axisymmetric flow around a freely moving sphere injected into an initially stagnant fluid. As the sphere decelerates, the recirculation eddy size grows monotonically even though the instantaneous Reynolds number of the sphere decreases.

Three-dimensional flow over two spheres placed side by side

Three-dimensional flow over two identical (solid or liquid) spheres which are held fixed relative to each other with the line connecting their centres normal to a uniform I stream is investigated numerically at Reynolds numbers 50, 100, and 150. We consider the lift, moment, and drag coefficients on the spheres and investigate their dependence on the distance between the two spheres. The computations show that, for a given Reynolds number, the two spheres are repelled when the spacing is of the order of the diameter but are weakly attracted at intermediate separation distances. For small spacing, the vortical structure of the near wake is significantly different from that of the axisymmetric wake that establishes at large separations. The partially confined flow passing between the two spheres entrains the flows coming around their other sides. Our results agree with available experimental and numerical data.

Three-dimensional wave distortion and disintegration of thin planar liquid sheets

Three-dimensional dilational and sinuous wave propagation on infinite or semi-infinite thin planar sheets flowing into a gas of negligible density is investigated. The assumption of thin sheets allows the reduction of the problem dimensionality by integration across the sheet thickness. For finite-amplitude disturbances, the strongest nonlinear effects occur when the cross-sectional wavenumber (l) is close to the streamwise wavenumber (k). First, dilational wave propagation is considered. When l is close to k for infinite sheets, higher harmonics are generated in the streamwise direction, and the standing wave with finite amplitude in the cross-sectional plane becomes flat. As time passes, the waves return to the initial wave shape. This process is repeated in a cycle

Diffusion flame in a two-dimensional, accelerating mixing layer

A theoretical and computational study of a laminar, two-dimensional, compressible, mixing, reacting layer with a pressure gradient that accelerates the flow in the direction of the primary stream is performed. One objective is to analyze the problems of a new technology related to combustion occurring in an accelerating transonic flow. Potential exists for reduction in nitric oxide formation and improvement in engine efficiency and/or power/weight. A similarity solution is found that reduces the partial differential equations to a system of ordinary differential equations. The solution is found in terms of a new acceleration parameter for compressible flows. The parameter is also useful for nonreacting mixing layers and for reacting or nonreacting wall boundary layers. For a low Mach number, the parameter reduces to the classical incompressible parameter. A numerical solution to these equations was performed. In the presence of exothermic reaction and accelerating pressure gradients, there are nonmonotoni...

Axisymmetric flame spread across propanol pools in normal and zero gravities

Axisymmetric ignition and flame propagation across propanol pools is investigated numerically with finite-rate one-step chemical kinetics, variable properties, and an adaptive finite-difference gridding scheme without forced gas-phase flow. Propanol fuel is allowed to evaporate into the air after filling the fuel tray and before the igniter is activated. The propanol vapor profile in the gas phase is examined numerically as a function of time. At 1 -g0, a steady fuel vapor-concentration boundary layer is established in the gas phase 5 s after filling a fuel tray. Conversely, at 0-g0, the profile of fuel vapor concentration is always unsteady and keeps growing in the gas phase as time elapses. Axisymmetric flame spread over a shallow circular pool is examined as a function of oxygen concentration. The flame spread rate at \-g0 is comparable to but lower than that at 0-g 0 for χO2,∞ ≥ 21% and T0 = 22.1°C with ΔtPI = 5s, where ΔtPI denotes the time lapse between filling the fuel tray and activating the ignit...

Unsteady flow interactions between an advected cylindrical vortex tube and a spherical particle

The unsteady, three-dimensional, incompressible, viscous flow interactions between a vortical (initially cylindrical) structure advected by a uniform free stream and a spherical particle held fixed in space is investigated numerically for a range of particle Reynolds numbers 20≤Re≤100. The counter-clockwise rotating vortex tube is initially located ten sphere radii upstream from the sphere centre. The finite-difference computations yield the flow properties and the temporal distributions of lift, drag, and moment coefficients of the sphere. Initially, the lift force is positive owing to the upwash on the sphere, then becomes negative owing to the downwash as the vortex tube passes the sphere. Varying the size of the vortex core (σ) shows that the r.m.s. lift coefficient is linearly proportional to the circulation of the vortex tube at small values of σ. At large values of σ, the r.m.s. lift coefficient is linearly proportional to the maximum fluctuation velocity (υ max ) induced by the vortex tube but independent of σ. For intermediate values of σ, the r.m.s. lift coefficient depends on both σ and υ max (or equivalently both σ and the circulation). We observe some interesting flow phenomena in the near wake as a function of time owing to the passage of the vortex tube

Unsteady flow interactions between a pair of advected vortex tubes and a rigid sphere

Abstract An idealized representation of the interaction of spherical particles with turbulent eddies of comparable length scale is considered by means of a three-dimensional, unsteady finite-difference Navier-Stokes solution of the interaction between a fixed rigid sphere and a pair of advecting vortex tubes. Initially the sphere is suddenly placed in the flow and held fixed in space. First, a doubly symmetric interaction with vortices of opposite rotation is considered. The resulting time-dependent drag differs from the drag in axisymmetric flows; however, the lift and torque on the sphere remain zero. Next, an interaction with two vortices of like rotation is studied. Here, non-zero lift and torque, as well as drag deviation from the axisymmetric case occur and would result in a deflection in the trajectory of a nonfixed sphere. The flow in this case behaves like that of a single vortex. Finally, a linear array of like-rotating vortices, interacting with a freely moving sphere, is considered. The two-dimensional deflection depends strongly upon the sphere/fluid density ratio and initial sphere Reynolds number. Lift and moment coefficients are shown to be linearly proportional to the maximum induced velocity due to the vortices. Moment coefficients are an order of magnitude less than lift coefficients.

Parametric investigations of pulsating flame spread across 1-butanol pools

The experimental realization of pulsating flame spread across a flammable liquid in microgravity was accomplished for the first time through systematic tests in a forced, opposed flow of oxygen-enriched air across shallow and intermediate-depth pools. In tests with the deeper pools, the sequential transition through all three subflash flame spread regimes—from pseudo-uniform to pulsating to uniform spread behavior—was achieved. Normal gravity tests were performed for many of the same conditions and showed similar behavior. In addition, agreement between a detailed numerical model and experiments in both normal gravity and in microgravity was newly obtained through changes in the mass diffusivity and the addition of a heat loss parameter in the two-dimensional model of flame spread over a subflash pool of 1-butanol. The model now uniquely captures the differences in flame spread character in going from normal to microgravity and provides quantitative agreement in flame spread rate and surface temperature at either gravity level. An earlier hypothesis that lateral thermal expansion in the gas-phase accounted for the initial discrepancy between the two-dimensional model and the three-dimensional experiment is no longer supported: this is because experiments designed to directly eliminate lateral expansion resulted in flame extinction rather than the desired pulsation.

Computational study of opposed-force-flow flame spread across propanol pools

Abstract Two-dimensional flame-spread across sub-flash-point propanol pools in opposed-forced airflow is investigated numerically for normal and zero gravities with finite-rate, one-step chemical kinetics, variable properties, and an adaptive finite-difference gridding scheme. Effects of air speed, liquid depth, and gravity on the characteristics of the flame-spread are examined with correct initial profiles for the gas-phase velocity and the mass-fraction of fuel vapor before ignition. Some of the results are as follows: (1) 10-mm pools are deep enough to examine flame-spread rates on deep pools in the uniform regime and pulsation frequencies on deep pools in the pulsating regime; (2) the pseudo-uniform regime is found only in deep pools and not in shallow pools; (3) the effect of opposed-forced airflow on the flame-spread rate is different, depending on the regime for T 0 , where T 0 denotes the initial pool temperature. Effects of pool depth on the liquid phase are also investigated: there is only a surface-tension-driven flow in the liquid phase of shallow pools. Finally, the flame-spread regime is displayed as a function of initial pool temperature, air speed, pool depth, and gravity.

Forces on a spherical particle in shear flow at intermediate Reynolds numbers

When particles are submerged in a shear flow, there are lateral (lift) forces on the particles, and these lateral forces affect the dispersion of the particles very much. Recent literature survey indicates that there are large discrepancies among the results from the previous numerical investigations on this subject. A small computational domain ranging between 20–30 sphere radii was used in all the previous numerical investigations. However, the result from the present study reveals that the value of lift coefficient strongly depends on the size of computational domain. To provide correct numerical data and physical interpretation for the forces on a spherical particle in linear shear flow, accurate numerical computations were performed for 5≤Re≤200 using a computational domain of 101 sphere radii.