Development and validation of a variational formulation of Two-Phase flow distribution

Nonuniform flow distribution in vertical headers has been an ongoing challenge that limits the advantages of transfer and fluidic technologies, especially in microchannel heat exchangers (MCHXs). This issue has been typically addressed in empirical studies and case-specific computational fluid dynamics (CFD) simulations; however, efforts toward the theoretical understanding and modeling of this phenomenon are lacking in literature. Therefore, this paper presents the development and validation of a theoretical model to reproduce the flow and phase distributions in adiabatic multibranch channels. A variational formulation of the phenomenon is obtained using Prigogine's theorem of minimum entropy production to cope with the inherent high variability of the mathematical problem. The individual flow rates, vapor quality, and pressure distributions yielding the minimum entropy generation rate provide a complete representation of the steady-state fluidic network for an arbitrary structure of the device and any working fluid. This paper presents a first experimental validation of the model when applied to the vertical header of a MCHX circulating R410A refrigerant. The theoretical results provide a coherent representation of the experimental data.