Basic Equations of Multicomponent Reacting Flows

Consistent with the objective of this chapter, it is important to return to the type of flow encountered in the freeboard of the rotary kiln and address reacting flows. The freeboard flow of interest involves the reacting flow type, which is almost always multicomponent, composed of fuel, oxidizer, combustion products, particulates, and so forth. The thermodynamic and transport properties of multicomponent reacting fluids are functions, not only of temperature and pressure, but also of species concentration. The basic equations that describe the simplest case of reacting turbulent flow include conservation equations for mass, concentration, momentum, and enthalpy equations as well as the associated reaction and equations of state for the system (Zhou, 1993), 

For fluid flow, the Euler number might be defined as the ratio of the pressure head and the velocity head and is expressed as  

As we saw earlier, the Reynolds number represents the ratio of the inertial force and the viscous force, that is. 

The Mach number is a similarity parameter defined as the ratio between kinetic energy and thermal energy. 

For heat transfer within the fluid the similarity parameter of importance is the Peclet number, which is the ratio of heat convection and heat conduction. We will revisit heat transfer modes later but for the purposes of flow characterization, the Peclet number is defined in Equation (3.26) below, where it is also given as the product of the Reynolds number and the Prandtl number, Pr (kinematic viscosity thermal diffusivity) 

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