Droplet breakup calculated

The substantial effect of secondary breakup of droplets on the final droplet size distributions in sprays has been reported by many researchers, particularly for overheated hydrocarbon fuel sprays. 557 A quantitative analysis of the secondary breakup process must deal with the aerodynamic effects caused by the flow around each individual, moving droplet, introducing additional difficulty in theoretical treatment. Aslanov and Shamshev 557 presented an elementary mathematical model of this highly transient phenomenon, formulated on the basis of the theory of hydrodynamic instability on the droplet-gas interface. The model and approach may be used to make estimations of the range of droplet sizes and to calculate droplet breakup in high-speed flows behind shock waves, characteristic of detonation spray processes. 

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. 

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. 

Droplet breakup In uniaxial extenslonal flow is more efficient (10). The theoretical calculations estimate that (21) ... 

O Rourke, P. J. and Amsden, A. A. The TAB Memod for Numerical Calculation of Spray Droplet Breakup, SAE Paper 872089. 

P.J. O Rourke, A.A. Amsden, The TAB method for numerical calculation of spray droplet breakup, SAE Technical Paper 872089, 1987. 

Droplet breakup and coalescence are the primary physical processes in the mixing of liquids with very different viscosities. Computational tools for the breakup of individual Newtonian droplets are well developed Figure 13 shows a boundary element calculation of the sequence of shapes of a polydimethylsilox-ane droplet in a polyisobutylene of nearly the same viscosity, together with experimental data. Computational tools for breakup with viscoelastic constitutive... 

From the above equations it is possible to calculate the size of the largest drop that exists in a fluid undergoing distortion at any shear rate. In these equations, the governing parameters for droplet breakup are the viscosity ratio p (viscosity of the dispersed phase to that of the matrix) the type of flow (elongational, shear, combined, etc.) the capillary number Cfl, which is the ratio between the deforming stress (matrix viscosity x shear rate) imposed by the flow on the droplet and the interfacial forces a/R, where ais the interfacial... 

After breakup, droplets continue to interact with the surrounding environment before reaching thein final destination. In theory (24), each droplet group produced during primary breakup can be traced by using a Lagrangian calculation procedure. Droplet size and velocity can be deterrnined as a function of spatial locations. 

From a liquid film such as a water film, the diameter of a drop formed under the action of gravity is calculated to be 9 mm with the above equation. Similarly to the liquid dripping mode, the liquid film breakup mode governed by the dripping mechanism is also typified by large droplets and low liquid flow rates. 

Recently, Knoll and Sojka[263] developed a semi-empirical correlation for the calculation of the Sauter mean diameter of the droplets after primary breakup of flat-sheets in twin-fluid atomization of high-viscosity liquids ... 

MMD/SMD that may be 1.1, 1.2 or 1.5J2491 Thus, once the SMD is calculated, the entire droplet size distribution after primary breakup can be determined. 

Within the scope of this work, the initial spray breakup process, providing information about the dense spray core, will be investigated. The formation of fuel drops will be simulated based on first-principles and will offer detailed insight into primary atomization. The three-dimensional, transient calculation will track the interface evolution through droplet formation and breakup. Because the results will be based on conservation laws, they will be extremely general. This will lead to better models that can be used with confidence in the engine design process. 

During mixing, the dispersed phase progressively breaks down until a rninimum drop diameter is reached. As the drop diameter decreases, further breakup becomes increasingly difficult. For emulsions, the size of the smallest drop that can be broken can be calculated from Taylor s theory, but experiments have shown that in most cases the equUibrium droplet size is larger than predicted. Furthermore, the deviation increases with concentration of the dispersed phase, ( ) - ( ), where experimentally the smallest value for which the deviation occurs, ( ) 0.005 [Utracki and Shi, 1992]. 

By contrast, it is clear that dUatant liquids should demonstrate an increased stability in the necking sections of capillary jets and a deceleration of the later stages of the capillary breakup. A relatively rapid growth of the initial axisymmetric perturbations leads to an increase of the effective viscosity in the necking sections of the jet and its transformation into a net of practically spherical droplets connected by tiny threads. The results of the numerical calculations for dilatant liquids by Yarin [29] are depicted in Fig. 1.23. 

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