E. A. Ibrahim

Modeling of spray droplets deformation and breakup

A droplet deformation and breakup (DDB) model is proposed to study shear-type mechanism of spray droplets in pure extentional flows. A numerical solution of the DDB model equation is obtained using a fourth-order Runge-Kutta initial-value solver. The predictions of the DDB model as well as semianalytical and the Taylor analogy models are compared with the experimental data (Krzeczkowski, 1980) for shear breakup, which depict the dimensionless deformation of the drop vs dimensionless time.

Impinging jets atomization

An analysis of the characteristics of the spray produced by an impinging‐jet injector is presented. Predictions of the spray droplet size and distribution are obtained through studying the formation and disintegration of the liquid sheet formed by the impact of two cylindrical jets of the same diameter and momentum. Two breakup regimes of the sheet are considered depending on Weber number, with transition occurring at Weber numbers between 500 and 2000. In the lower Weber number regime, the breakup is due to Taylor cardioidal waves, while at Weber number higher than 2000, the sheet disintegration is by the growth of Kelvin–Helmholtz instability waves. Theoretical expressions to predict the sheet thickness and shape are derived for the low Weber number breakup regime. An existing mathematical analysis of Kelvin–Helmholtz instability of radially moving liquid sheets is adopted in the predictions of resultant drop sizes by sheet breakup at Weber numbers greater than 2000. Comparisons of present theoretical results with experimental measurements and empirical correlations reported in the literature reveal favorable agreement.

Instability of a viscous liquid jet surrounded by a viscous gas in a vertical pipe

The instability of a cylindrical liquid jet encapsulated by a viscous gas in a pipe is analysed in a parameter space spanned by the Reynolds number, the Froude number, the Weber number, the density ratio, the viscosity ratio, and the diameter ratio. A convergent solution of the problem is constructed by a Galerkin projection with two orthogonal sets of functions. Two distinctively different modes of instability are obtained. The first is the Rayleigh mode which tends to break up the jet into drops of diameter comparable with the jet diameter. The amplification rate of the disturbance belonging to this mode depends weakly on all parameters except the Weber number which represents the ratio of the surface tension force to the inertia force at the interface. The mechanism of the instability remains that of capillary pinching even in the presence of a viscous gas and gravity. However, the surface tension is stabilizing in the other mode termed the Taylor mode. The Taylor mode instability is due to the pressure and shear fluctuations at the interface. This mode tends to produce droplets of diameters much smaller than that of the jet. It is shown that the former mode appears when the Weber number is much larger than the gas to liquid density ratio. When this ratio is of order one, the instability can be due to either modes depending on the values of the rest of the parameters. When the density ratio is much larger than the Weber number, Taylors atomization mode replaces the Rayleigh mode.

Analysis of operational filtration data part I. Ideal candle filter behavior

Operating data for the hot-gas filtration system of the Integrated Gasification and Cleanup Facility (IGCF) at the Federal Energy Technology Center are carefully analyzed. A model for candle filters is developed and used to describe the ideal filtration process. The parameters of the model are evaluated with a least-square error fit procedure. It is shown that the model predicts the time variation of the pressure drop with reasonable accuracy. The model is used to evaluate the buildup of filter-cake thickness and the filter-cake permeability.

Instability of a liquid jet of parabolic velocity profile

Abstract A linear instability analysis is performed to arrive at the dispersion relation that governs the instability of an inviscid liquid jet emanated into an inviscid gas. The velocity profile within the jet is varied from parabolic to uniform in order to model the effects of its relaxation on jet instability and intact length. The results indicate that the closer the profile to uniform the more pronounced the instability. In the jet atomization regime, increasing Weber number and/or gas to liquid density ratio promote instability.

An Experimental Investigation of the Effect of Subcooling on Bubble Growth and Waiting Time in Nucleate Boiling

The effect of subcooling on bubble waiting time and growth time for water boilng on a copper surface was examined in conjunction with measurements obtained over a range of subcooling from 0 to 15/sup 0/C and three different levels of heat flux 166, 228, and 291 kW/m/sup 2/. The growth-time data was successfully correlated with a model that combined the bubble growth theory of Mikic Rohsenow, and Griffith with the bubble departure diameter relationship of Staniszewski, thereby establishing confidence in the measuring procedure. The waiting time data agreed with the predictions of the Han and Griffith waiting time theory at lower levels of subcooling but then showed a behavior contrary to that predicted for higher levels of subcooling.

Enhancement of automotive exhaust heat recovery by thermoelectric devices

Abstract In an effort to improve automobile fuel economy, an experimental study was undertaken to explore the practical aspects of implementing thermoelectric devices for exhaust gas energy recovery. An experimental apparatus consisting of a hot-side (exhaust gas) rectangular duct and a cold-side (coolant liquid) rectangular duct enclosing six thermoelectric elements has been built and instrumented. Measurements of the thermoelectric voltage output, fluid and surface temperatures, and flowrates were acquired and analysed to investigate the power generation and heat transfer properties of the apparatus. The effects of inserting aluminium wool packing material inside the hot-side duct on augmentation of the heat transfer from the gas stream to duct walls were studied. Data were collected for both the unpacked and the packed cases to allow for deduction of the packing influence on the flow and surface temperatures. The effects of variations in the gas inlet temperature (300°C, 320°C, 340°C, 360°C, 380°C, and 400°C), coolant inlet temperature (40°C, 50°C, 70°C, and 90°C), and gas flowrate (40sl/min, 60sl/min, and 80sl/min) on the thermoelectric power output were examined. The results indicate that thermoelectric power production is increased at higher gas inlet temperatures or flowrates at a fixed coolant temperature. However, thermoelectric power generation decreases with a higher coolant temperature as a consequence of the reduced temperature differential between the hot side and the cold side. For the unpacked hot-side duct, a large temperature difference of up to 140°C existed between the gas and solid surface temperatures owing to poor heat transfer through the gaseous medium. Adding the packing material inside the exhaust duct enhanced heat transfer and hence raised the hot-side duct surface temperature by as much as 30°C and thermoelectric power by up to twofold, compared with the unpacked duct, particularly where the gas-to-surface temperature differential is highest. Therefore, it is recommended that packing of the exhaust duct becomes common practice in thermoelectric waste-energy-harvesting applications.

Liquid sheet instability

SummaryA linear instability analysis is presented for an inviscid liquid sheed emanated into an inviscid gas medium. The influence of Weber number and gas to liquid density ratio on the evolution of two and three dimensional disturbances of symmetrical and antisymmetrical type is studied. It is found that two dimensional disturbances always dominate the instability process at low Weber number. When the Weber number is large, symmetrical three dimensional disturbances become more unstable than two dimensional ones for long waves. The effect of increasing the gas to liquid density ratio is to promote the dominance of long three dimensional symmetrical waves over their two dimensional counterpart. For antisymmetrical waves, two dimensional disturbances always prevail over three dimensional disturbances regardless of Weber number or gas to liquid density ratio especially for long waves. For short waves, both two and three dimensional disturbances grow at approximately the same rate. It is demonstrated that a critical Weber number exists, above which three dimensional disturbances become unstable. Furthermore, a finite wave number is necessary for the onset of three dimensional instability. The wave number range that leads to a higher growth of, symmetrical three dimensional disturbances than two dimensional ones is investigated. An explanation of the differences in the behavior of three dimensional symmetrical and antisymmetrical instabilities is provided.

Instability of a liquid sheet of parabolic velocity profile

A power series mathematical solution is advanced for the problem of instability of an inviscid liquid sheet of parabolic velocity profile emanated from a nozzle into an inviscid gas. A comparison of the instability of a sheet of parabolic velocity profile with one of a uniform velocity profile is performed in order to deduce the effects of velocity profile relaxation on instability. The results show that for both antisymmetrical and symmetrical disturbances departure from uniformity of the velocity profile causes the instability to be reduced. The physical interpretation and practical implications of the present findings are discussed.

EFFECTS OF COMPRESSIBILITY ON THE INSTABILITY OF LIQUID SHEETS

The effect of compressibility of fluids on the instability of a liquid sheet issued from a nozzle into an ambient gas is investigated by use of linear stability analysis. It is found that increasing the gas Mach number from subsonic to transonic causes the maximum growth rate, dominant wave number, and cut-off wave number of disturbances to increase. Liquid compressibility has a minimal effect on instability. At a constant wave number, the growth rate of disturbances increases as the gas Mach number tends to 1 and then begins to decline with further increase in the gas Mach number. Hence, liquid sheet breakup is due to surface disintegration not gross fracturing in agreement with experimental observations. At small values of wave number, antisymmetrical disturbances grow faster than symmetrical ones while the growth rate of both types of disturbances approach each other at large wave numbers. At small Weber number, antisymmetrical disturbances exhibit a higher maximum growth rate and a lower dominant wave...