Spray PDF

GSK (2006). Imitrex (sumatriptan) nasal spray. Prescribing information. GlaxoSmithKline, Research Triangle Park, NC. Available at http //us.gsk.com/products/assets/us imitrex nasal spray.pdf accessed 1/29/2007. 

One of the most widely used approaches for the simulation of sprays is the stochastic discrete droplet model introduced by Williams [30]. In this approach, the droplets are described by a probability density fxmction (PDF),/(t,X), which represents the probable number of droplets per unit volume at time t and in state X. The state of a droplet is described by its parameters that are the coordinates in the particle state space. Typically, the state parameters include the location x, the velocity v, the radius r, the temperature Td, the deformation parameter y, and the rate of deformation y. As discussed in more detail in Chapter 16, this spray PDF is the solution of a spray transport equation, which in component form is given by... 

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 discretization of the liquid phase is achieved by the discrete particle method (c.f. Ref. [4]). In this method, the domain, X, of the spray PDF,/(t, X), is subdivided into hyper-rectangles, and all droplets that fall within one particular hyper-rectangle are identified as one representative particle. In other words, the spray PDF/(t, X) is approximated with a discrete PDF, where each discretization point corresponds to a representative particle consisting of droplets of identical states. The evolution of the spray PDF is then determined in analogy to the Monte Carlo method by using a sampling process on these particles. 

Assume that the components of the spray system are independent with respect to failure, and that the reliability of each is I — P. One may associate success with the failure of a component. Then X, the number of failures, has a binomial PDF and the reliability of the random system is... 

Frolov We must keep in mind that prospective PDFs are supposed to operate on a liquid fuel. In view of it, obstacles inside a tube seem to be avoided as fuel sprays will impinge to their surface that may deteriorate the performance. 

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. 

The spray source terms in the gas phase equations, shown in Table 19.4, can be computed when all the spray submodels are in place, and the drop PDF f t,, , r,Td,y,y) in (19.45) is determined. These source terms are obtained by summing up the rates of change of mass, momentum, and energy of all droplets at a fixed location x and time t. This leads to the expressions... 

Number distributions are not the only type of PDF. Area and volume distributions are also used, with volume distributions being by far the more popular of the two. The volume distribution, /3(D), gives the fraction of a spray s volume for drops in group D - AD/2 to D + AD/2 and has dimensions of 1/diameter (see Fig. 23.1). 

S. D. Sovani, P. E. Sojka, Y. R. Sivathanu Prediction of Drop Size Distributions from First Principles Joint-PDF Effects, Atomization Sprays 10, 587-602 (2000). 

The native phosphocaseinate suspension (NPCS) was prepared from skim milks of cow, ewe, and goat by microfiltration and diafiltration. Whey protein concentrate (WPG) was separated from previous cow milk microfiltrate. Combined cow casein powders (CCP) were obtained by two techniques (i) WPC and Polydextrose Litesse (PDL) from Pfizer Co. (Orsay, France) were first mixed into cow NPCS retentate before freeze-drying to obtain 4%, 8%, and 12% PDF/total solid (TS) and 4%, 8%, and 12% WPC/TS powders and (ii) mineral salts were added to cow NPCS concentrate at 50°C for 30 min before spray co-drying. In the NMT measurements, the samples include 1 g of a powder per 20 mL of water. 

M. The data upon which Figures 3.6 and 3.7 are based is courtesy of Spraying Systems Corporation. Their URL is http //www. spray.com/applica tions/pdf/c20c.pdf. 

BASF SE PVP and more. .. Luvitec, Luvicross. 2009. online 2015-08-31. http //www.spp-prozess-spray.uni-bremen.de/spp 1423-Dateien/PVP techn.pdf... 

Veterinary Medicinal Products (dips, injectables, pour-ons, sprays and drenches) authorised in the UK for use against ectoparasites in sheep. Veterinary Medicines Directorate, Weybridge, 14 December 2011. http // www.vmd.defra.gov.uk/pdf/ectoparasiticide.pdf... 

---