Numerical simulation of non-adiabatic capillary tubes 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 behavior of capillary tube–suction line heat exchangers has been carried out. The governing equations (continuity, momentum, energy and entropy) for fluid flows, together with the energy equation in solids, are solved iteratively in a segregated manner. The discretized governing equations in the zones with fluid flow are coupled using a fully implicit step-by-step method. An implicit central difference numerical scheme and a line-by-line solver were used in solids. 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 (enthalpies, temperatures, pressures, mass fractions, heat fluxes, etc.) together with the thermophysical and transport properties are evaluated at each point of the grid in which the domain is discretized. The numerical model allows analysis of aspects such as geometry, type of fluid, critical or non-critical flow conditions, metastable regions and transient cases. Comparison of the numerical simulation with experimental data presented in the technical literature will be shown in Part II of the present paper.