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Graf Isolan
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Untersuchte Arbeit:
Seite: 117, Zeilen: 4-19
Quelle: Laurent et al 2003
Seite(n): 506, Zeilen: 4, 19-31
6.1 Introduction

Spray models have a common basis at what can be called "the kinetic level" under the form of a probability density function (PDF or distribution function) satisfying a Boltzmann type equation, the so-called Williams equation (Williams, 1985). The variables characterizing one droplet are the size, the velocity, and the temperature. Such a transport equation describes the evolution of the distribution function of the spray due to evaporation, to the drag force of the gaseous phase, to the heating of the droplets by the gas, to breakup phenomena, and finally to the droplet-droplet interaction such as collision. The spray transport equation is then coupled to the gas phase equations. The two-way coupling of the phases occurs first in the spray transport equations through the rate of evaporation, drag force, and the heating rate, which are functions of the gas phase variables, and second through exchange terms in the gas phase equations.

There are several strategies in order to solve the liquid phase.


Williams, F.A. (1985). Combustion Theory. Addison-Wesley, Redwood, CA.

1. Introduction

[...]

Spray models (where a spray is understood as a dispersed phase of liquid droplets, i.e. where the liquid volume fraction is much smaller than one) have a common basis at what can be called ‘‘the kinetic level’’ under the form of a probability density function (p.d.f. or distribution function) satisfying a Boltzmann type equation, the so-called Williams equation [6–8]. The variables characterizing one droplet are the size, the velocity and the temperature, so that the total phase space dimension involved is usually of twice the space dimension plus two. Such a transport equation describes the evolution of the distribution function of the spray due to evaporation, to the drag force of the gaseous phase, to the heating of the droplets by the gas and finally to the droplet-droplet interactions (such as coalescence and fragmentation phenomena) [2,8–13]. The spray transport equation is then coupled to the gas phase equations. The two-way coupling of the phases occurs first in the spray transport equations through the rate of evaporation, drag force and heating rate, which are functions of the gas phase variables and second through exchange terms in the gas phase equations.

There are several strategies in order to solve the liquid phase.


[6] F.A. Williams, Spray combustion and atomization, Phys. Fluids 1 (1958) 541–545.

[7] F.A. Williams, Combustion theory, in: F.A. Williams (Ed.), Combustion Science and Engineering Series, Addison-Wesley, Reading, MA, 1985.

[8] F. Laurent, M. Massot, Multi-fluid modeling of laminar poly-diperse spray flames: origin, assumptions and comparison of sectional and sampling methods, Combust. Theory Modelling 5 (4) (2001) 537–572.

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Though in large parts identical, nothing has been marked as a citation.

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