ABSTRACT
The formal volume averaging procedures developed in Appendix B are applied to the continuity, momentum and energy equations of the carrier phase.
C.1 Continuity equation The continuity equation for the continuous phase is
+
() = 0 (C.1)
Taking the local volume average of each term
+
() = 0 (C.2)
and applying the volume-averaging equations gives
+
Z ( + ˙) + ()−
Z = 0 (C.3)
At the droplet surface, the velocity of the gas crossing the surface is
= + (˙ + ) (C.4) where is the velocity of the particle center and is the velocity of the gases with respect to the particle surface1. Substituting this equation into Equation C.3 results in
i
i
+
() =
Z (C.5)
The average density can be written as hi The average mass flux is
= 1 Z (C.6)
The average velocity ˜ is defined such that
˜ = 1hi 1
Z (C.7)
which is the mass-averaged velocity. For a constant density fluid, the massaveraged velocity is equal to the local volume average, ˜ = hi The velocity can be expressed as the sum of the mass-averaged velocity and the deviation therefrom.
