S. P. Fisenko

EVAPORATIVE COOLING OF WATER IN A MECHANICAL DRAFT COOLING TOWER

Abstract A new mathematical model of a mechanical draft cooling tower performance has been developed. The model represents a boundary-value problem for a system of ordinary differential equations, describing a change in the droplets velocity, its radii and temperature, and also a change in the temperature and density of the water vapor in a mist air in a cooling tower. The model describes available experimental data with an accuracy of about 3%. For the first time, our mathematical model takes into account the radii distribution function of water droplets. Simulation based on our model allows one to calculate contributions of various physical parameters on the processes of heat and mass transfer between water droplets and damp air, to take into account the cooling tower design parameters and the influence of atmospheric conditions on the thermal efficiency of the tower. The explanation of the influence of atmospheric pressure on the cooling tower performance has been obtained for the first time. It was shown that the average cube of the droplet radius practically determines thermal efficiency. The relative accuracy of well-defined monodisperse approximation is about several percent of heat efficiency of the cooling tower. A mathematical model of a control system of the mechanical draft cooling tower is suggested and numerically investigated. This control system permits one to optimize the performance of the mechanical draft cooling tower under changing atmospheric conditions.

Evaporative cooling of water in a natural draft cooling tower

A mathematical model of the performance of a cooling tower is presented. The model consists of two interdependent boundary-value problems, a total of 9 ODE, and the algorithm of self-consistent solution. The first boundary-value problem describes evaporative cooling of water drops in the spray zone of a cooling tower; the second boundary-value problem describes film cooling in the pack. Simulation of the boundary-value problems has been made. The comparison between experimental data and calculated results showed that the model correctly describes the basic regularities of the cooling tower performance. In the effective droplet-radius approximation the difference in the thermal efficiency between calculated and experimental results does not exceed 3%. The limits of applicability of the developed mathematical model and its possibilities are discussed.

Simulation of Cooling of Water Droplet and Film Flows in Large Natural Wet Cooling Towers

An iterational algorithm for calculation of evaporative cooling of water droplets and films in a cooling tower is proposed. It is found from a comparison of results of theoretical calculation and experimental data that the effective radius of the droplets is approximately equal to 3·10−4 m. The contribution of film cooling is shown to constitute at least 70% of the overall temperature decrease of cooled water in the cooling tower.

Nucleation in a catalytic nanodroplet and growth of nanowires

The kinetics of basic physical processes governing the growth of nanowires by the vapor-liquid-solid mechanism is considered. The role of geometrical, thermodynamic, and kinetic factors early in the growth of the nanowire is studied. Approximate expressions for the nucleation rate and nanowire growth rate are derived, and the influence of transfer processes in the vapor phase is estimated. In terms of the Stefan problem, the effect the release of the latent heat of phase transition has on the nanowire growth is calculated. Numerical estimates are made for carbon nanowires.

Mathematical Modeling of Evaporative Cooling of Water in a Mechanical-Draft Tower

A mathematical model of the operation of a mechanical-draft tower is proposed. The model represents a boundary-value problem for five differential equations and for the first time takes into account the following parameters: temperature of inflowing water, its discharge, mean radius of water droplets, mean air velocity inside the water-cooling tower, rate of fall of a droplet, height from which droplets fall, and meteorological conditions, including atmospheric pressure. The basic parameters of the water-cooling tower influencing its thermal efficiency have been revealed. The dissipation of the kinetic energy of the air flow due to the air friction against the surface of falling droplets has been taken into account.

Brownian deposition of nanoparticles from a laminar gas flow through a channel

Investigation of nanoparticle deposition by Brownian diffusion is conducted by mathematical simulation. The mobility of nanoparticles is calculated in the free-molecular approximation. The influence of the nanoparticle radius, flow parameters, and channel length on the process is studied. Variation of the distribution function and broadening of the nanoparticle beam as the particles move along the channel are calculated.

Kinetics of picoliter binary droplet evaporation on a substrate at reduced pressure

The effects of different factors on the time of evaporation of a single picoliter droplet of a water-alcohol solution on a metal substrate with a high thermal conductivity have been studied in the free molecular regime. It has been experimentally shown that the evaporation of such droplets occurs in the pinning mode. The evaporation times have been measured for droplets of water-alcohol solutions of different concentrations on the substrate at a reduced pressure. The calculations performed in terms of a one-dimensional mathematical model have shown that the rates of evaporation of pico- and femtoliter droplets of water-alcohol solutions nonlinearly depend on alcohol concentration, initial droplet height, and substrate temperature.

Coalescence and diffusion growth of nanoparticles in closed microvolume of supersaturated solution

A model is developed and numerically studied for the diffusion growth of nanoparticles in a closed microvolume of supersaturated solutions resulting from the evaporation cooling of microsized droplets of multicomponent aqueous solutions. Limits are established for the regimes that correspond to the stable growth of all nanoparticles and the onset of isothermal distillation. It is revealed that, in highly supersaturated solutions, the final nanoparticle radius is independent of the radius of primary particles. The final nanoparticle radius can be controlled by varying the concentration of primary particles. Specific calculations are performed for nickel oxide nanoparticles.

Equalization of the Concentration of a Scalar Impurity in a Flow‐Type Chamber

Experimental and theoretical investigations of the time of equalization of the concentration of an impurity in a rectangular flow‐type chamber have been carried out. It has been shown that the process of equalization of the concentration with time is exponential in character. The characteristic equalization time has been computed using the theory of turbulent diffusion. Theoretical results describe experimental regularities with an accuracy of about 10%. The value of the coefficient of turbulent diffusion for different configurations of flows in the chamber has been obtained from a comparison of experimental and calculated results.

Investigation of the Internal Aerodynamics of the Chimney-Type Evaporative Cooling Tower

We propose a technique for determining the hydrodynamic drag of the chimney-type evaporative cooling tower on the basis of temperature measurements and the mathematical model developed by us. The presence of return vortex flows in the upper part of the subsprinkling compartment of the cooling tower is shown. The air velocity in the sprinkler and the radius of the stagnant zone in the central part have been estimated.