On the consistency conditions of averaging operators in 2-phase flow models and on the formulation of magnetohydrodynamic 2-phase flow

Abstract

An analysis has been carried out on the space averaged form of 2-phase flow conservation equations in which are also included the electromagnetic fields in the low frequency (MHD) approximation. The analysis considers ensemble and time averages of the space integral operators and attempts to derive their consistency conditions. It is shown that it is possible to rigorously derive the consistency conditions between averaging operators, provided that the stochastic process for the “noise” of the space integral operators can be identified. A plausible choice for this “noise” has been made and the parameters of its description have been identified. The 2-phase flow MHD model is formulated so that it satisfies the consistency conditions of the integral operators and in which the space integral operator is defined over an area. A simplified 1-dimensional MHD model is developed in terms of the conservation equations for the 2-phase mixture. The boundary conditions and constitutive equations which enter into the model are discussed for applications dealing with 2-phase flow in magnetohydrodynamic generators and in magnetically confined plasma fusion reactors.