D. Pnueli

A MODEL FOR TURBULENT DEPOSITION OF AEROSOLS

A model is developed for particle deposition to smooth surfaces in turbulent flow. The model is based on the calculation of particle trajectories in the wall region, using a detailed description of the flow in this region. The particle trajectories are derived from the equations of motion, including the lift force induced by the shear flow. This lift force, as is shown, is very important for particles with τ+ > 1, and clarifies the mechanism of deposition for these particles. The calculated particle flux compares favorably with the experimental data of various authors reported in the literature.

ON THE DRIFT OF AEROSOL PARTICLES IN SONIC FIELDS

Abstract The drifting motion of aerosol particles enclosed in vessels subject to ultrasonic oscillations is analysed theoretically. The geometry considered here is of vessels with dimensions not exceeding the ultrasonic wavelength. This geometry is quite different from previously treated cases, where the flow field dimensions measured many times the ultrasonic wavelength and where the aerosol particles were found to move towards nodes and towards loci of maximum amplitudes, according to their sizes. The results obtained here are rather different and indicate that all particles move away from the oscillating wall and towards the stationary one. These results conform to the motivation of the investigation, which is to protect a clean site from settling particles. The analysis incorporates two-scale expansions methods applied to the multiphase flow equations for a one-dimensional flow model. The results are constructed by the superposition of a slow mean motion of the gas and a fast oscillatory motion associated with the eigenfunctions of the standing waves solution. The combined effect on the particles is a drift in the direction of the stationary wall.

Dynamics of suspended particles in a two-dimensional high-frequency sonic field

Abstract The interaction of two-dimensional standing sonic waves with particles suspended in a fluid is analyzed. The domain considered is bounded below by a plane plate which performs harmonic oscillations, and above by a stationary plate which is slightly curved. The size of the gap at the axis of symmetry exceeds the sonic wavelength, so that there is at least one velocity node of the standing wave inside the region. The domain is filled with a fluid which contains spherical particles. The steady sonic wave causes a steady particle drift. The curvature of the stationary upper wall produces a two-dimensional standing wave, which causes the suspended particles to move in a direction transverse to the wave front of the applied field. It is shown that in addition to the well known particle drift toward the fluid velocity nodes or antinodes there exists a side drift along the nodes and the antinodes. The direction of the drift depends on the sonic wave frequency and on the fluid-to-particle density ratio. The analysis employs a small parameter perturbation method.

A Turbulent-Brownian Model for Aerosol Coagulation

Aerosol coagulation is a process by which small particles of the aerosol join together to form larger particles, still within aerosol size. This process takes place continuously, and causes the aerosol to change in time. The process may be useful or harmful, according to the use made of the aerosol. There are several mechanisms that influence the coagulation process, but two are the most important. One is Brownian diffusion, which causes particles to come into contact and stick together. The other is due to relative motion induced by spatial turbulent fluctuations in a turbulent flow field. Each of these mechanisms has been investigated rather widely, but always alone, i.e., Brownian motion only or turbulent flow only. Still, in many important cases coagulation is affected by both mechanisms operating simultaneously. The present investigation considers a model in which coagulation takes place between two spherical particles of different sizes, placed in a turbulent flow field. The motion of the larger par...

EFFECT OF PARTICLE LOADING ON GRANULAR BED FILTRATION--THE CLUSTER ENHANCED FILTER MODEL

Abstract A cluster enhanced filter (CEF) model is proposed for the filtration process in granular bed filters. The formulation is made in terms of particle deposition on a single spherical collector. The model accounts for the effect of particle loading on the dynamic behavior of the filter. It predicts the formation of a high porosity layer, which consists of clusters of particles, on the surface of the collector, with a very high increase in the calculated filtration efficiency. The theory is presented in terms of filtration efficiency data as a function of the mass of the loaded material. The results compare favorably with experimental data.

Effect of particle loading on granular bed filtration—Extension of the CEF model to polydisperse systems

Abstract The CEF (cluster enhanced filtration) model, which predicts filtration efficiencies of monodisperse aerosols as a function of the mass loading of granular bed filters, is extended to deal with polydisperse aerosols. The new model considers the porous regions taken up by the clusters to act as secondary filters. The resulting calculated efficiencies are much more sensitive to particle sizes than are those of the original CEF model. Experimental results are reported, which agree well with the suggested model.

Aerosol Deposition in the Vicinity of a Stagnation Point

A method is presented to compute the trajectories of aerosol particles in the vicinity of a stagnation point and thus to obtain their rates of deposition. According to this method a particle starts its motion on the initial streamline, moves from one streamline to another under the influence of inertia, and touches the collector surface while on the interceptional streamline. The method takes advantage of the fact that in stagnation flow close to the splitting streamline most of the changes take place in a small region of high streamline curvature. The method of singular perturbation analysis is applied to calculate the particle trajectory in this region. This paper considers small Stokes numbers for which the particles are shown to have a stopping distance equal to their Stokes number. The computation of the particle trajectories depends on the ratio of these stopping distances s to the radii of curvature of the fluid streamline r. For large and medium s/r ratios the trajectories exhibit boundary layer t...

A modified model for the deposition of dust in a granular bed filter

Abstract There exist several models for the filtering efficiency of granular bed filters. The theoretical calculations of the efficiencies according to all these models are based on a calculation for a single-sphere model and then extension to the many-sphere case. This extension is essentially just the modification of the flow field to correspond to the many-sphere filter. There is a systematic deviation between the theoretical values thus computed and experimental results. The modified model described here permits geometrical interferences between neighboring spheres during the filter process, and that in addition to the accepted modification of the flow filed. The computations lead to expressions only slightly more complicated than the classical ones. The theoretical values thus obtained, however, show considerable improvement when compared with experimental results.

Ignition of fuel mixtures by standing acoustic waves

Abstract The paper considers a stationary problem of ignition of a fuel mixture enclosed between two parallel walls which are kept at a constant temperature. A one-step, Arrhenius reaction of large activation energy with negligible reactant depletion represents the chemistry. The Frank-Kamenetskii parameter is assumed to be very small, so that a thermal explosion does not occur without the action of some external source. A standing plane sonic wave is imposed in the longitudinal direction. The distance between the walls is much smaller than the sound wavelength. Rayleigh’s type vortical acoustic streaming that appears in the region leads to forced heat convection. The effect of that forced convection on heat transfer in the presence of heat release due to the chemical reaction is analyzed theoretically. The analysis demonstrates that acoustic streaming at large streaming Reynolds numbers results in ignition of the mixture.

Particle motion in simple shear flow with gravity

The motion of aerosol particles in simple shear flow, subject to gravity, is analyzed. The combination of gravity and shear-induced lift is shown to give rise to particle drift. It is shown that in shear flow near a wall, when gravity points in the direction of flow, particles drift towards the wall, while for gravity pointing against the flow the drift is away from the wall. These results are also demonstrated experimentally, with fair qualitative agreement between analysis and experiments.