Modeling of a local vaporization front in pellets during energy-saving drying

Recovery of waste and side products of apatite-nepheline ores processing is a high energy-intense ptocess. The results of modeling of phosphorite pellet drying are presented in this paper. To make the phosphorite pellet manufacturing process more energy efficient, it is essential to understand inner processes of local vaporization from a pellet’s surface to its core under the thermal influence of heat transferring gas. The results of modeling of other changes appearing in pellets during their drying on conveyor equipment are also presented in this research.

Water transport during bread baking: Impact of the baking temperature and the baking time

The impact of the baking temperature on the moisture profile (in terms of water content), during bread baking was analyzed using a convection oven (three oven temperatures and different baking times). During baking, local water content and temperature were measured at different regions of the crust and crumb. There was found an increase in water content at the core. Water content reached a maximum level (at about 2.5%), with no effect of the baking temperature, and decreased slowly at advanced baking times. Regarding the crust, a theoretical model relating water flux to the driven force (temperature difference between the oven environment and the vaporization front) and the crust thermal resistance was validated with experimental values. Water losses were also reported. The water lost by bread contributes significantly to the energy consumption by this process and its reduction is of concern for conducting the process in a more sustainable manner. A better optimization of heat transfer between the surface (for coloration purposes) and the core (for inflation purposes) could help in this way, together with shorter baking duration and hence higher yield.

Sheath vaporization of a monodisperse fuel-spray jet

The group vaporization of a monodisperse fuel-spray jet discharging into a hot coflowing gaseous stream is investigated for steady flow by numerical and asymptotic methods with a two-continua formulation used for the description of the gas and liquid phases. The jet is assumed to be slender and laminar, as occurs when the Reynolds number is moderately large, so that the boundary-layer form of the conservation equations can be employed in the analysis. Two dimensionless parameters are found to control the flow structure, namely the spray dilution parameter λ, defined as the mass of liquid fuel per unit mass of gas in the spray stream, and the group vaporization parameter ϵ, defined as the ratio of the characteristic time of spray evolution due to droplet vaporization to the characteristic diffusion time across the jet. It is observed that, for the small values of ϵ often encountered in applications, vaporization occurs only in a thin layer separating the spray from the outer droplet-free stream. This regime of sheath vaporization, which is controlled by heat conduction, is amenable to a simplified asymptotic description, independent of ϵ, in which the location of the vaporization layer is determined numerically as a free boundary in a parabolic problem involving matching of the separate solutions in the external streams, with appropriate jump conditions obtained from analysis of the quasi-steady vaporization front. Separate consideration of dilute and dense sprays, corresponding, respectively, to the asymptotic limits λ ≪ 1 and λ ≫ 1, enables simplified descriptions to be obtained for the different flow variables, including explicit analytic expressions for the spray penetration distance.

Steady Propagation of the Vaporization Front in Metastable Liquid

The boiling up of a metastable liquid when the vaporization fronts appear is considered theoretically and experimentally. Boiling up occurs usually on the surface of a heater. At the first stage, the growth of a spherical vapor bubble is observed. If the temperature of liquid exceeds the threshold value, the vaporization fronts develop near to the line of contact of a vapor bubble and heater. Fronts of vaporization extend along a heater with constant speed. It is a direct transition from one phase convection to film boiling. Such scenario of crisis of a convective heat transfer is also possible in the nuclear reactor equipment. The model of steady propagation of the vaporization front is developed. The temperature and velocity of propagation of the interface are determined from the balance equations for the mass, momentum, and energy in the neighborhood of the vaporization front and the condition of stability of motion of the interface. It is shown that a solution of these equations exists only if the liquid is heated above a threshold value. The velocity of propagation of the vaporization front also has a threshold value. The calculated velocity of the interface motion and the threshold value of temperature are in reasonable agreement with available experimental data for various liquids within wide ranges of saturation pressures and temperatures of the overheated liquid. The developed model adequately describes the experimental data for various substances in a wide range of temperature of an overheated fluid. In this model, the steady propagation of the vaporization front is possible only if the temperature of a metastable liquid exceeds some threshold value. The velocity of the vaporization front also has a threshold value.

Steady Propagation of the Vaporization Front in Metastable Liquid

The boiling up of a metastable liquid when the vaporization fronts appear is considered by theoretically and experimentally. Boiling up occurs as usually on a surface of a heater. At the first stage the growth of a spherical vapor bubble is observed. If the temperature of liquid exceeds threshold value, the vaporization fronts develop near to line of contact of a vapor bubble and heater. Fronts of vaporization extend along a heater with constant speed. It is direct transition from one-phase convection to a film boiling. Such scenario of crisis of a convective heat transfer also is possible in the nuclear reactor equipment. The model of steady propagation of the vaporization front is developed. The temperature and velocity of propagation of the interface are determined from the balance equations for the mass, momentum, and energy in the neighborhood of the vaporization front and the condition of stability of motion of the interface. It is shown that a solution of these equations exists only if the liquid is heated above a threshold value. The velocity of propagation of vaporization front has threshold value also. The calculated velocity of interface motion and the threshold value of temperature are in reasonable agreement with available experimental data for various liquids within wide ranges of saturation pressures and temperatures of the overheated liquid.

Liquid-fuel thermocapillary flow induced by a spreading flame

An analysis is presented of the flow in a layer of liquid whose surface tension varies under the action of a moving surface heat flux distribution chosen to model the spread of a flame over the liquid. Subject to this heat flux, the surface temperature increases from the ambient temperature of the liquid, far upstream, to its vaporization temperature at a moving vaporization front, and stays constant at this value downstream of the vaporization front. The speed of the front is determined by a condition of regularity of the temperature. Three different regimes are found which correspond to the uniform, pulsating and pseudo-uniform regimes of flame spread observed experimentally when the ambient temperature of the liquid, or the strength of the surface heat flux, is decreased. The first and third of these are stationary regimes of high and low front speed, and the second is an oscillatory regime featuring long phases of low speed and short pulses of high speed. An asymptotic description is given of the flow relative to the moving vaporization front in the stationary regime of low speed, which includes a long recirculation eddy ahead of the front and a small region around the front that controls its speed. An explanation of the mechanism of oscillation is proposed based on the interplay between the quasi-steady response of this small controlling region and the delay introduced by the recirculating flow.