Full spray equation method

Two numerical methods have been used for the solution of the spray equation. In the first method, i.e., the full spray equation method 543 544 the full distribution function / is found approximately by subdividing the domain of coordinates accessible to the droplets, including their physical positions, velocities, sizes, and temperatures, into computational cells and keeping a value of / in each cell. The computational cells are fixed in time as in an Eulerian fluid dynamics calculation, and derivatives off are approximated by taking finite differences of the cell values. This approach suffersfrom two principal drawbacks (a) large numerical diffusion and dispersion... 

Of major interest concerning these problems are influences of turbulence in spray combustion [5]. The turbulent flows that are present in the vast majority of applications cause a number of types of complexities that we are ill-equipped to handle for two-phase systems (as we saw in Section 10.2.1). For nonpremixed combustion in two-phase systems that can reasonably be treated as a single fluid through the introduction of approximations of full dynamic (no-slip), chemical and interphase equilibria, termed a locally homogeneous flow model by Faeth [5], the methods of Section 10.2 can be introduced reasonably successfully [5], but for most sprays these approximations are poor. Because of the absence of suitable theoretical methods that are well founded, we shall not discuss the effects of turbulence in spray combustion here. Instead, attention will be restricted to formulations of conservation equations and to laminar examples. If desired, the conservation equations to be developed can be considered to describe the underlying dynamics on which turbulence theories may be erected—a highly ambitious task. 

The traditional equilibrium method of flavor release study mentioned above is extremely time consuming, and several weeks are commonly needed to obtain full release profiles of flavors from powders. Recently, thanks to the pioneering work of Dronen and Reineccius (2003), proton transfer reaction mass spectrometry (PTR-MS) has been used as a rapid analysis to measure the release time-courses of flavors from spray-dried powders. The PTR-MS method has been applied extensively to analyze the release kinetics of volatile organic compounds from roasted and ground coffee beans. The release profiles could then be mathematically analyzed by means of Equation 1.1 to obtain the release kinetic parameters, A and n (Mateus et al., 2007). 

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