Droplet Size Distribution in Sprays Based on Maximization of Entropy Generation (original) (raw)
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The Maximum Entropy Formalism and the Prediction of Liquid Spray Drop-Size Distribution
Entropy, 2009
The efficiency of any application involving a liquid spray is known to be highly dependent on the spray characteristics, and mainly, on the drop-diameter distribution. There is therefore a crucial need of models allowing the prediction of this distribution. However, atomization processes are partially known and so far a universal model is not available. For almost thirty years, models based on the Maximum Entropy Formalism have been proposed to fulfill this task. This paper presents a review of these models emphasizing their similarities and differences, and discusses expectations of the use of this formalism to model spray drop-size distribution.
Prediction of the droplet size and velocity joint distribution for sprays
Fuel, 2001
This work addresses the development of a mathematical model to predict the joint distribution for both size and velocity of the droplets in sprays, based on the maximum entropy formalism. Using this joint distribution, models to obtain separated distributions for size and velocity of sprays are also presented. Correlations for the average velocity for both pressure jet and airblast atomisers, based on assumed pro®les in the atomiser gun, are obtained as a function of easily measurable parameters. Several distributions for different types of atomisers are then predicted. Agreement between available data for the velocity distribution and the corresponding predictions is satisfactory.
Particle & Particle Systems Characterization, 1999
This work is an extension of a previous investigation on the determination of mathematical volume-spray drop size distributions by the application of the maximum entropy formalism. A two-parameter drop size distribution was derived and was found to give reasonable ®ts with experimental distributions obtained under different experimental conditions. However, as it is discussed, this two-parameter distribution shows critical limitations and cannot be applied in any situations of interest as far as drop size distributions in liquid sprays are concerned. To overcome this problem, a third parameter, equivalent to a drop diameter, is introduced into the procedure. This correction leads to a three-parameter drop size distribution with independent mean, width and symmetry. This function is a generalized gamma distribution and it can cover more practical situations than the previous twoparameter distribution. Furthermore, it is found that, contrary to the two-parameter distribution, the new volume-based drop size distribution shows a corresponding number-based drop size distribution with a physical behavior as the drop diameter decreases. This last result shows the importance of using three parameters to describe spray drop size distributions and that one of these parameters must represent the population of small drops.
Drop dynamics and size distribution in a dense spray produced by a twin-fluid atomizer
International Conference on Liquid Atomization and Spray Systems (ICLASS)
Motivated by industrial applications, the spray assessment of twin-fluid atomizers is paramount for improving their design and performance. Although several studies have addressed the spray characteristics, the coupled analysis of the droplet sizes and velocities at high flow rates is still not sufficiently understood. Therefore, the present study investigates the spray instabilities from a specific variance of a Y-jet atomizer correlated to droplet size and axial velocity distribution along the spray centerline. The atomizer was operated at Reynolds numbers in the order of 10 4 , resulting in different air-to-liquid mass ratios. For that, an experimental rig operated with air and water is available for spray analysis. Data obtained with a phase Doppler anemometer showed that the mass flow rate of both fluids is directly proportional to the velocities and inversely proportional to droplet diameters. The size-velocity correlations showed that closer to the spray, the smaller droplets had higher velocities than the bigger ones. As they flowed downstream the nozzle, the impingement between the droplets and their interaction with the surrounding air decelerated them and increased their size.
Numerical Simulation of the Drop Size Distribution in a Spray
Springer Proceedings in Mathematics & Statistics, 2012
Classical methods of modeling predict a steady-state drop size distribution by using empirical or analytical approaches. In the present analysis, we use the maximum of entropy method as an analytical approach for producing the initial data; then we solve the coagulation equation to approximate the evolution of the drop size distribution. This is done by a quasi-Monte Carlo simulation of the conservation form of the equation. We compare the use of pseudo-random and quasi-random numbers in the simulation. It is shown that the proposed method is able to predict experimental phenomena observed during spray generation.
Spray characterization: Numerical prediction of Sauter mean diameter and droplet size distribution
Fuel, 1996
A simplified equation of the Nukiyama-Tanasawa type for droplet size distribution in sprays is obtained from the synergetic concept of entropy information, assuming spherical droplets and zero and infinity as their limit sizes. The introduction of Sauter mean diameter (SMD) definition in that equation yields a new distribution function dependent solely on SMD, which is calculated from available correlations for pressurejet and pre-filming airblast atomizers. For plain-jet airblast atomizers a new and dimensionally consistent correlation is determined. Several droplet size distributions are then predicted. Experimental data are compared with predictions of SMD; the agreement is satisfactory.
Acta Metallurgica et Materialia, 1995
A~traet--A computer model has been developed to describe the in-flight dynamic and thermal histories of gas atomised droplets as a function of distance during spray forming. The model has been used to investigate the effects of the dynamic and thermal behaviour of individual gas atomised droplets and the cooling and solidification behaviour of the overall spray. The most influential parameters for a given alloy system, in order of importance, are: (i) droplet diameter and, therefore, the droplet size distribution within the spray; (ii) initial axial gas velocity at the point of atomisation and the subsequent gas velocity decay profile; (iii) melt mass flow rate; (iv) melt superheat at the point of atomisation; and (v) alloy composition. Experimental measurements of gas velocities and droplet size distributions during spray forming allow the spray solid fraction at deposition to be calculated and used in a subsequent computer model of billet heat flow to predict the billet top surface temperatures and solid fractions.
LES of atomizing spray with stochastic modeling of secondary breakup
International Journal of Multiphase Flow, 2003
A stochastic subgrid model for large-eddy simulation of atomizing spray is developed. Following KolmogorovÕs concept of viewing solid particle-breakup as a discrete random process, atomization of liquid blobs at high relative liquid-to-gas velocity is considered in the framework of uncorrelated breakup events, independent of the initial droplet size. KolmogorovÕs discrete model of breakup is rewritten in the form of differential Fokker-Planck equation for the PDF of droplet radii. Along with the Lagrangian tracking of spray dynamics, the size and number density of the newly produced droplets is governed by the evolution of this PDF in the space of droplet-radius. The parameters of the model are obtained dynamically by relating them to the local Weber number with two-way coupling between the gas and liquid phases. Computations of spray are performed for the representative conditions encountered in idealized diesel and gas-turbine engine configurations. A broad spectrum of droplet sizes is obtained at each location with coexistence of large and small droplets. A novel numerical algorithm capable of simultaneously simulating individual droplets as well as a group of droplets with similar properties commonly known as parcels is proposed and compared with standard parcels-approach usually employed in the computations of multiphase flows. The present approach is shown to be computationally efficient and captures the complex fragmentary process of liquid atomization.
Droplet dynamics in internally mixed twin-fluid spray
Advances in Fluid Mechanics X, 2014
Effervescent atomizers are based on the mixing of gas with liquid prior to discharge. We describe the discharge of a two-phase mixture and movement of droplets in a gas jet using simple theoretical models, following with elucidation of droplets dynamics using experimental data for an effervescent spray. Discharge of the liquid-gas mixture from the nozzle is solved using a combination of two discharge models. Depending on operation conditions, 59-64% of the total discharged mass corresponds to the Separated Flow Model and the rest to the Homogeneous Flow Model. Discharge velocity of the liquid is 12-27% of the gas exit velocity. The liquid-gas velocity ratio is negatively correlated with gas-to-liquid mass ratio (GLR) and positively correlated with inlet pressure. Radial profiles of axial droplet velocity, as measured using Phase Doppler anemometry, are axisymmetric bell-shaped with a maximum in the centreline analogous to the profile defined for a simple gas jet which, however, is more flat near the centreline and declines much faster for higher radial positions. Mean velocity in individual spray positions varies with particle size within a range of several m/s typically. This variation is closely related to particle Stokes number, Stk. Variation of mean velocity with operation pressure and GLR can be explained with discharge conditions; higher pressures and GLRs lead to higher discharge velocities that are reflected in the spray downstream. Stokes numbers are generally << 1 for particle sizes D d up to 10 µm so these particles smoothly follow the gas flow. Stk for sizes 10 µm < D d < 50 µm depends on flow regime and position in the spray and can be found typically within 0.1 < Stk < 10. Particles with D d ≥ 100 µm have usually Stk > 10 and very weakly interact with the gas.