Time-averaging of volume-averaged conservation equation of multiphase flow

Volume averaging of equations of conservation for a multiphase system yields equations in terms of volume averaged products of density, velocity, energy, stresses and field forces, together with interface transfer integrals. Solutions of these equations call for expressing these volume averaged products,in terms of products of averages. The present study shows that such a determination can be made via time averaging over a duration T such that tau/sub BF is dominated by T is dominated by tau/sub DF/ where tau/sub DF/ is the characteristic time of low frequency change such as in a blow down process. Time averaging reduces the volume and area averaged products to products of averages plus terms representing eddy diffusions of mass, Reynolds stresses, and eddy conductivities of heat, etc., arising from high frequency fluctuations. The interface transfer integrals, after time averaging, give transfer integrals of low and high frequency components. This procedure of time averaging after volume averaging, but not in the reverse order, leads to a complete set of equations of conservation for pure stratified flow.