Numerical simulation of capillary tube expansion devices behaviour with pure and mixed refrigerants considering metastable region. Part I: mathematical formulation and numerical model

A detailed one-dimensional steady and transient numerical simulation of the thermal and fluid-dynamic behaviour of capillary tube expansion devices working with pure and mixed refrigerants has been developed. The discretised governing equations are coupled using an implicit step by step method. A special treatment has been implemented in order to consider transitions (subcooled liquid region, metastable liquid region, metastable two-phase region and equilibrium two-phase region). All the flow variables (enthalpy, temperatures, pressures, vapour quality, velocities, heat fluxes, etc.) together with the thermophysical properties are evaluated at each point of the grid in which the domain is discretised. The numerical model allows analysis of aspects such as geometry, type of fluid (pure substances and mixtures), critical or non-critical flow conditions, metastable regions, adiabatic or non-adiabatic capillary tubes and transient aspects. Comparison of the numerical simulation with experimental data presented in the technical literature will be shown in part II of the present article.