Homogeneous dilute turbulent particle-laden water flows.

An experimental and theoretical study of a homogeneous particle-laden turbulent flow was conducted, involving glass particles falling in a stagnant (in the mean) water bath. The experiments included various loadings of nearly monodisperse particles having mean diameters of 0.5, 1.0 and 2.0 mm. Measurements included liquid and particle velocities, and the temporal spectra and spatial correlations of liquid-phase velocity fluctuations. The motion of isolated particles falling in stagnant water was also calibrated using shadowgraph movies. An approximate analysis for liquid-phase properties was developed, based on linear superposition of randomly-arriving particle velocity fields. In addition, stochastic simulations, solving the Lagrangian equations of motion of the particles, were used to predict particle properties. For present test conditions, liquid velocity fluctuations correlated solely as a function of the rate of dissipation of kinetic energy in the liquid. The correlation coefficients and temporal spectra were also independent of particle loading. The flows were highly anisotropic with streamwise velocity fluctuations being roughly twice the cross-stream velocity fluctuations. The temporal spectra indicated a large range of frequencies even when particle Reynolds numbers were low due to the fact that both mean and fluctuating velocities in the particle wakes contribute to the spectra because particle arrivals are random. The analysis predicted many of the features of the flows reasonably well but must be improved to obtain satisfactory predictions of the temporal and spatial scales of the flow. In addition to effects of turbulent dispersion, the particles exhibited self-induced lateral motion due to eddy-shedding and irregularities of shape--particularly the larger particles. Streamwise particle velocity fluctuations were large because particle size variations induced variations of terminal velocities. Cross-stream velocity fluctuations were dominated by effects of turbulent dispersion for the smallest particles with effects of self-induced lateral motion becoming more important with increasing particle size. After accounting for effects of particle size variations and self-induced motion, the stochastic simulation predicted particle properties reasonably well.Ph.D.Aerospace engineeringApplied SciencesMechanical engineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/128386/2/9001695.pd

Linear Temporal Stability Analysis of a Low-Density Round Gas Jet Injected into a High-Density Gas

It has been observed in previous experimental studies that round helium jets injected into air display a repetitive structure for a long distance, somewhat similar to the buoyancy-induced flickering observed in diffusion flames. In order to investigate the influence of gravity on the near-injector development of the flow, a linear temporal stability analysis of a round helium jet injected into air was performed. The flow was assumed to be isothermal and locally parallel; viscous and diffusive effects were ignored. The variables were represented as the sum of the mean value and a normal-mode small disturbance. An ordinary differential equation governing the amplitude of the pressure disturbance was derived. The velocity and density profiles in the shear layer, and the Froude number (signifying the effects of gravity) were the three important parameters in this equation. Together with the boundary conditions, an eigenvalue problem was formulated. Assuming that the velocity and density profiles in the shear layer to be represented by hyperbolic tangent functions, the eigenvalue problem was solved for various values of Froude number. The temporal growth rates and the phase velocity of the disturbances were obtained. The temporal growth rates of the disturbances increased as the Froude number was reduced (i.e. gravitational effects increased), indicating the destabilizing role played by gravity

Linear Stability Analysis of Gravitational Effects on a Low-Density Gas Jet Injected into a High-Density Medium

The objective of this study was to determine the effects of buoyancy on the absolute instability of low-density gas jets injected into high-density gas mediums. Most of the existing analyses of low-density gas jets injected into a high-density ambient have been carried out neglecting effects of gravity. In order to investigate the influence of gravity on the near-injector development of the flow, a spatio-temporal stability analysis of a low-density round jet injected into a high-density ambient gas was performed. The flow was assumed to be isothermal and locally parallel; viscous and diffusive effects were ignored. The variables were represented as the sum of the mean value and a normal-mode small disturbance. An ordinary differential equation governing the amplitude of the pressure disturbance was derived. The velocity and density profiles in the shear layer, and the Froude number (signifying the effects of gravity) were the three important parameters in this equation. Together with the boundary conditions, an eigenvalue problem was formulated. Assuming that the velocity and density profiles in the shear layer to be represented by hyperbolic tangent functions, the eigenvalue problem was solved for various values of Froude number. The Briggs-Bers criterion was combined with the spatio-temporal stability analysis to determine the nature of the absolute instability of the jet whether absolutely or convectively unstable. The roles of the density ratio, Froude number, Schmidt number, and the lateral shift between the density and velocity profiles on the absolute instability of the jet were determined. Comparisons of the results with previous experimental studies show good agreement when the effects of these variables are combined together. Thus, the combination of these variables determines how absolutely unstable the jet will be