Breakup models

Current breakup models need to be extended to encompass the effects of liquid distortion, ligament and membrane formation, and stretching on the atomization process. The effects of nozzle internal flows and shear stresses due to gas viscosity on liquid breakup processes need to be ascertained. Experimental measurements and theoretical analyses are required to explore the mechanisms of breakup of liquid jets and sheets in dense (thick) spray regime. 

As described previously, in the atomization sub-model, 232 droplet parcels are injected with a size equal to the nozzle exit diameter. The subsequent breakups of the parcels and the resultant droplets are calculated with a breakup model that assumes that droplet breakup times and sizes are proportional to wave growth rates and wavelengths obtained from the liquid jet stability analysis. Other breakup mechanisms considered in the sub-model include the Kelvin-Helmholtz instability, Rayleigh-Taylor instability, 206 and boundary layer stripping mechanisms. The TAB model 310 is also included for modeling liquid breakup. 

On the basis of the experimental observations,l160 169 327 Liu[325] conceived a liquid film-sheet breakup model for atomization of liquid metals with close-coupled atomizers. In this atomization model, it was postulated that atomization of a liquid metal with a close-coupled atomizer may occur in the following sequence (1) formation of a liquid film, (2) conversion of the liquid film into a liquid sheet, (3) primary breakup of the liquid sheet into droplets, (4) droplet... 

The solution of the gas flow and temperature fields in the nearnozzle region (as described in the previous subsection), along with process parameters, thermophysical properties, and atomizer geometry parameters, were used as inputs for this liquid metal breakup model to calculate the liquid film and sheet characteristics, primary and secondary breakup, as well as droplet dynamics and cooling. The trajectories and temperatures of droplets were calculated until the onset of secondary breakup, the onset of solidification, or the attainment of the computational domain boundary. This procedure was repeated for all droplet size classes. Finally, the droplets were numerically sieved and the droplet size distribution was determined. 

Spalding developed a successful eddy-breakup model for describing rates of flame spread in high-intensity flows of this type [143]-[146]. There are a number of difYerent versions of the model one employs... 

The mean species source term, It, requires further examination. Because this term is usually highly nonlinear as illustrated in Equation 4.8 and its value directly controls the reaction progress, a proper closure model is necessary. Indeed, various methods are available from the literature.21-22 For the purpose of discussion, we consider the eddy breakup model of Magnussen and Hjertager.23 Note that this model is chosen for its simplicity rather than accuracy, much as the A - e model was selected for turbulence closure. In this model, a turbulent reaction rate is computed which is then compared with the kinetic rate. The smaller of the two is used as the reaction rate because it limits the reaction progress. The kinetic rate is simply the laminar reaction rate evaluated at the mean temperature, pressure, and concentrations ... 

Politano MS, Carrica PM, Bahno JL (2003) About bubble breakup models to predict bubble size distributions in homogeneous flows. Chem Eng Comm... 

Wang T, Wang J, Jin Y (2005) Population Balance Model for Gas-Liquid Flows Influence of Bubble Coalescence and Breakup Models. Ind Eng Chem Res 44 7540-7549... 

An analytical NOX chemical kinetic model has been developed by the DLR to investigate the influence of various parameters on the formation of pollutants. It has been coupled with an eddy breakup model for the combustion process [133]. 

Dombrowski and John [12] combined a linear model for temporal instability and a sheet breakup model for an inviscid liquid sheet in a quiescent inviscid gas, to predict the ligament and droplet sizes after breakup. The schematic of their wavy sheet is reproduced in Fig. 3.7. The equation of motion of the neutral axis mid-way... 

Abstract In an effort to characterize fuel sprays using Computational Fluid Dynamics (CFD) codes, a number of spray breakup models have been developed. The primary atomization of liquid jets and sheets is modeled considering growing wave instabilities on the liquid/gaseous interface or a combination of turbulence perturbations and instability theories. The most popular approaches for the secondary atomization are the Taylor Analogy Breakup (TAB) model, the Enhanced-TAB (E-TAB) model, and the WAVE model. Variations and improvements of these models have also been proposed by other researchers. In this chapter, an overview of the most representative models used nowadays is provided. 

The Kelvin-Helmholtz (KH) breakup model, developed by Reitz and Diwakar [9] and further improved by Reitz [10], is based on a linearized analysis of a KH instability of a stationary, round liquid jet immersed into a quiescent. 

The Rayleigh-Taylor (RT) component has been added to the breakup model by Patterson et al. [11] to improve predictions of the secondary breakup of the droplets. The RT model predicts instabilities on the surface of the drop that grow until a certain characteristic breakup time is reached, when the drop finally breaks up. The RT waves are only allowed to form on droplets with diameters larger than the wavelength of the fastest growing disturbance. When the disturbances exceed the elapsed breakup time, the droplet is split into smaller droplets, with diameters proportional to the wavelength of the disturbances. 

This component of the breakup model results in reduced overall breakup rate and dispersion of the droplets. Adjusting the effective wavelength of the RT waves can affect the time between breakup events, and, consequently, the breakup rate and the resulting droplet size. 

In the CAB model the breakup condition is determined by means of the drop deformation dynamics of the standard Taylor analogy breakup model [5] (cf. TAB model above). In this approach, the drop distortion is described by a forced, damped, harmonic oscillator in which the forcing term is given by the aerodynamic droplet-gas interaction, the damping is due to the liquid viscosity and the restoring force is supplied by the surface tension. More specifically, the drop distortion is described by the deformation parameter, y = Ixjr, where x denotes the largest radial distortion from the spherical equilibrium surface, and r is the drop radius. The deformation equation in terms of the normalized distortion parameter, y, as provided in Eq. 9.29 is... 

The jet breakup modeling is illustrated in Fig. 9.3 for a non-evaporating spray. This figure illustrates the drop breakup cascade, which results in a fragmented liquid core at the nozzle exit. 

F.X. Tanner, Liquid jet atomization and droplet breakup modeling of non-evaporating diesel fuel sprays, SAE Technical Paper Series 970050, 1997. 

F.X. Tanner, G. Weisser, Simulation of liquid jet atomization for fuel sprays by means of a cascade drop breakup model, SAE Technical Paper Series 980808, 1998. 

C. Chryssakis, D.N. Assanis, A unified fuel spray breakup model for internal combustion engine applications. Atomization and Sprays, 18(5) 375-426, 2008. 

F.X. Tanner. Development and validation of a cascade atomization and drop breakup model for high-velocity dense sprays. Atomization and Sprays, 14(3) 211-242, 2004. 

O. Kaario, M. Larmi, and F.X. Tanner. Non-evaporating liquid spray simulations with the ETAB and wave droplet breakup models. In Proc. 18th ILASS-Europe Annual Conference, pp. 49-54, Zaragoza, September 2002. 

Drop breakup enters the spray equation via the source term/bu in (19.45). There are various ways of accounting for drop breakup, most of which are also used for a rudimentary description of the atomization process. Some of these approaches are discussed in more detail in Chap. 9, and include the TAB model of O Rourke and Amsden [37], the Wave Breakup model of Reitz and coworkers [46, 40], the Unified Spray Breakup model of Chryssakis and Assanis [10], and the Cascade Atomization and Drop Breakup model of Tanner [54]. 

Drop size distributions are typically described using raie of four methods empirical, maximum entropy formalism (MEF), discrete probability function (DPF) method, or stochastic. The empirical method was most popular before about the year 2000, when drop size distributions were usually determined by fitting spray data to predetermined mathematical functions. Problems arose when extrapolating to regimes outside the range of experimental data. Two analytical approaches were proposed to surmount this, MEF and DPF, as well as one numerical approach, the stochastic breakup model. 

The stochastic breakup model assumes that the spray fragments following a cascade for which the probability of forming a daughter drop via breakup is independent of its parent drop size. 

The ligament breakup model predicts drop diameter given a set of initial conditions. A distribution of drop sizes results because the initial cmiditions fluctuate, due to vibration of the atomizer, variations in liquid delivery rate, unsteady exit velocity, inhomogeneous liquid physical properties, cavitation-induced pulsations, turbulent flow fields, etc. PDFs are required for all fluctuating quantities. 

DPF requires a ligament instability model. The computational complexity can become unwieldy if a nonlinear or multidimensional breakup model is employed. 

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