An approach for modeling of multiphase flows as random processes

TL;DR

This paper models multiphase flows as stochastic processes, deriving conservation equations and analyzing flow parameters statistically, especially for heterogeneous two-phase flows, to better understand flow regimes and phase interactions.

Contribution

It introduces a novel approach by applying probabilistic and dynamical systems methods to model multiphase flows, linking flow parameters with statistical phase probabilities.

Findings

Derived conservation equations incorporating phase probabilities.

Established relationships between flow parameters and statistical phase states.

Proposed coefficients for dynamical systems based on flow parameters.

Abstract

The basic system of differential equations for a multiphase flow with the introduction of the probability of each phase in the flow is considered. The main analysis is focused on the case of a heterogeneous two-phase flow. The conservation equations for mass, momentum and energy are obtained under the assumption that parameters of the interacting phases are players of the statistical process. In parallel, dynamical system by the Kolmogorov's theorem for two states of a statistical system (phases of a two-phase mixture) is considered. Probability of phases in a flow is taken further for comparison with the probability and parameters of a two-phase flow from the equations of flow dynamics. Analysis of the parameters of a two-phase flow is performed as relating to available flow regimes from a statistical point of view on the basis of achievable parameter values and, first of all, on the condition that the probability is strictly in the range from 0 to 1. Correspondence of parameters by the equation array for flow dynamics and by solution of the dynamical system of two phases (two interacting statistical states) revealed the values of the coefficients for dynamical system, expressed in terms of the flow parameters. The results obtained are intended for further discussion, research, comparison with experimental data and with results of other researchers of the multiphase flows.