Spray modeling

A spray is a turbulent, two-phase, particle-laden jet with droplet collision, coalescence, evaporation (solidification), and dispersion, as well as heat, mass and momentum exchanges between droplets and gas. In spray modeling, the flow of gas phase is simulated typically by solving a series of conservation equations coupled with the equations for spray process. The governing equations for the gas phase include the equations of mass, momentum and energy... 

Most current multidimensional spray simulations have adopted the thin or very thin spray assumptions,[55°1 i.e., the volume occupied by the dispersed phase is assumed to be small. This can be justified if a simulation starts some distance downstream of the nozzle exit, where the gas volume fraction is large enough, or if the computational cells are relatively large. Accordingly, two major classes of models have been used in spray modeling locally homogeneous flow (LHF) models and two-phase-flow or separated-flow (SF) models. 

To date, spray modeling has been largely dependent on solving the governing equations of multiphase flows and specifying initial and... 

Some early spray models were based on the combination of a discrete droplet model with a multidimensional gas flow model for the prediction of turbulent combustion of liquid fuels in steady flow combustors and in direct injection engines. In an improved spray model,[438] the full Reynolds-averaged Navier-Stokes equations were... 

Suspended Model Free (spray) Suspended Burning—free and suspended Free (spray) Model Suspended... 

The FSCBG aerial spray models and computer program are a result of more than a decades effort in the development, refinement and application of models for use by the U. S. Army and USDA Forest Service in predicting drift, deposition and canopy penetration from aerial releases. During the 1960 s, the U. S. 

Considering the continued development, verification and improvement of these aerial spray modeling techniques and their acceptance by the U. S. Army and U. S. Forest Service, we believe the concepts deserve wider use in civil spray operations, pesticide development programs and environmental assessment studies. We therefore welcome the opportunity presented by this symposium for discussing the mathematical framework of the models and to illustrate their applications. 

Teske ME, Scott RL. 2000. AgDRIFTTM An update of the aerial spray model AGDISP. http //www.agdrift.com (accessed October 23, 2000). 

Jodoin, B., Raletz, F., and Vardelle, M. (2006) Cold spray modelling and validation using an optical method. Surf. Coat. Technol.,... 

Current spray models in multidimensional computational fluid dynamics (CFD) codes achieve moderately good results under a limited range of conditions by speculating on the atomization process and including adjustable parameters. The user must estimate values for these parameters in order to match experimental results. Furthermore, the need to constantly vary these parameters may indicate that the model construction is not based on the correct assumptions. These unknown quantities create a significant uncertainty in the breakup behavior of the spray. 

Current spray models may not have the correct physics, may have unknown limits of applicability, and may contain empirical constants. In a recent test conducted by the author and United Technologies Research Center (UTRC), models of primary atomization, secondary atomization, droplet breakup, droplet collision, and turbulent dispersion were applied to an air blast spray. The predictions were compared to experimental data taken at UTRC. The predicted drop size was as much as 35% different from the measured values [8]. In contrast to the typical conference or journal publication, the models were not adjusted to make the agreement as close as possible. They were taken from the literature as is. The conclusion is that physical models of high-speed spray behavior are still lacking, despite years of research in this area. Primary atomization, the beginning of the spray, is one area that is particularly poorly understood. 

It is anticipated that the results of calculations will show the governing mechanisms of primary atomization. They will indicate the relative importance of turbulence, the Kelvin-Helmholtz instability, the Rayleigh-Taylor instability, the initial perturbation level (attributable to cavitation or oscillations in fuel injection equipment), and other phenomena. The quantitative detail of the simulations will provide information and inspiration for the construction of a new generation of spray models. The proposed code can be used for other kinds of simulations, including wall impingement, liquid film flow, and impinging injections. 

Thermal plasma spray modeling is focused on the description of RF and DC plasma torches, on plasma-particle interactions, as well as on the behavior of particles at impact and the coating development. Both two- and three-dimensional models are applied to calculate velocity, enthalpy, and temperature distributions at the nozzle exit, matching with the plasma gas flow rate and enthalpy. The properties are presented as follows (Dussoubs, 1998 Freton, Gonzalez, Gleizes, 2000 Wan et al., 2002) ... 

Ronsse, F., Pieters, J.G., and Dewettinck, K., Numerical spray model of the fluidized bed coating process, Drying TechnoL, 25, 1491-1514, 2007. 

Desantes et al. [21] presented a description of how the effects discussed so far can be incorporated into spray calculations, as also detailed by O Rourke et al. [23]. The commonly used correlations for drag coefficient used in spray models are... 

T. B. Gradinger. Spray Modeling with Application to Fuel-Air Premixing. PhD thesis, ETH Zurieh, Diss. ETH Nr. 13497, 2000. 

This implies that the spray tends to approach a saturation state unless additional heat and oxygen are supplied from the outside of the spray stream. It also implies that the behavior of the outer diffusion flame dominates the subsequent evolution of spray combustion from the spray boundary side. In real spray combustion, this boundary-layer type of change occurs dynamically because the boundary of the spray stream is located in the coherent vertical structure of the shear layer. In addition, turbulent effects are inevitable. However, such fluid dynamic effects have not yet been well characterized. Therefore, we focus on the behavior of the outer diffusion flame based on a quasi-steady continuum spray model. Chiu s theory is developed on this basis to classify the combustion modes excited by the penetration of the outer diffusion flame into the spray region. 

Keywords Atomization Chemical reactions Craiservation equations Constitutive equations Drop breakup Drop deformation Drop collisions Evaporation LES Newtonian fluids RANS Spray modeling Spray PDF Stochastic discrete particle method Source terms Turbulence... 

The remainder of the chapter focuses on the actual spray modeling. The exposition is primarily done for the RANS method, but with the indicated modifications, the methodology also applies to LES. The liquid phase is described by means of a probability density function (PDF). The various submodels needed to determine this PDF are derived from drop-drop and drop-gas interactions. These submodels include drop collisions, drop deformation, and drop breakup, as well as drop drag, drop evaporation, and chemical reactions. Also, the interaction between gas phase, liquid phase, turbulence, and chemistry is examined in some detail. Further, a discussion of the boundary conditions is given, in particular, a description of the wall functions used for the simulations of the boundary layers and the heat transfer between the gas and its confining walls. 

Gosman, A. D., and Clerides, D., Diesel Spray Modelling A Review, Coirference of Uquid Atomization and Spray Systems, 1998. 

Spray Modeling and Predictive Simulations in Realistic Gas-Turbine Engines... 

Droplet deformation and collision are also important features in the intermediate regime. In addition, in the intermediate region, the droplet loading could be severe. The variations in the local liquid-phase volume fraction also become important and should be considered in order to capture the droplet dynamics correctly. A robust algorithm capable of addressing all numerical issues related to spray modeling is necessary. 

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