On the Averaging of Equations of Change for Mass, Species Mass, Momentum and Energy – One-Dimensional Pipe Flows

Abstract

The single-phase and multiphase Eulerian equations of change are derived by applying a suitable averaging procedure to the local instantaneous equations of change. In the present work, the local instantaneous equations of change for mass, species mass, momentum and energy are gross-scale averaged over the cross-sectional area. In particular, the internal energy equation is achieved by subtracting the kinetic energy equation from the total energy balance. Thus, two paths are to our disposal for deriving the cross-sectional averaged internal energy balance: (i) the averaged kinetic energy equation is subtracted from the averaged total energy equation, or (ii) the local instantaneous kinetic energy equation is subtracted from the local instantaneous energy equation and the resulting equation is averaged. The resulting Euler equations of change for internal energy are not identical for these two approaches. Approach (ii) is recommended because of its simplicity.