Numerical assessment of condensation time relaxation coefficients for accurate prediction under atmospheric and subatmospheric conditions in two-phase thermosiphon systems

Abstract

The numerical simulation of Two-Phase Thermosiphon (TPT) systems is highly complex due to the simultaneous occurrence of physical phenomena such as phase change, vapor bubble dynamics, boiling, and condensation. Among the various computational approaches, a commonly used method combines the Volume of Fluid (VOF) technique with the Lee model for phase change. This combination allows for the simulation of two-phase interactions without explicitly modeling detailed processes such as wall bubble nucleation, wall boiling, quenching, and bubble interaction length scales. The condensation time relaxation coefficient ${\beta }_c$ in the Lee model significantly influences the phase change process. In TPT simulations, it plays a crucial role in determining result accuracy, particularly in terms of mass balance, pressure distribution, flow regimes, and temperature predictions. This paper conducts 2D, unsteady numerical simulations using the STAR-CCM+ software for two different cases of a two-phase closed-pipe thermosiphon (TPCT) system that employs water as an environmentally friendly working fluid. The first case consists of a vertical copper pipe with a height of 500 mm and an inner diameter of 20.2 mm, operating at standard atmospheric pressure (1.01325 bar). In contrast, the second case features a taller copper pipe measuring 1000 mm in height with a smaller inner diameter of 17.5 mm, functioning under a lower pressure of 0.2 bar (absolute pressure). The primary aim of this study is to evaluate different formulations of the condensation time relaxation coefficients within the Lee phase change model, in order to identify the most suitable approach for both atmospheric and subatmospheric conditions. Four correlation strategies are assessed, including three common classical models such as the Consistency model, the Density model, and the Transient Mass Transfer model, and our newly tuned version called as the Density-Pressure model. The results are validated by comparison with established experimental benchmarks. This study examines how the different models influence key phase change parameters in the TPCT, including total mass, condensation and evaporation mass rates, temperature, volume fraction, and pressure. Among the evaluated approaches, the Density-Pressure model method demonstrated the highest accuracy, with relative errors remaining below 2.06% for Case 1 and 4.33% for Case 2, based on the conventional model validation method using temperature distributions on the exterior wall. The Density-based model also performed reasonably well, with deviations below 3.78% and 5.40% for the respective cases. In contrast, the Consistency model exhibited significantly higher relative errors, reaching 16.62% in Case 1 and 117.47% in Case 2. The study introduced methods to visualize spatiotemporal evolution nucleation sites and condensation onset using the vapor volume fraction (${\alpha }_V$) variation over the inner wall. The Density-Pressure, Density, and Transient Mass Transfer models provided more realistic predictions and successfully captured geyser boiling phenomena, in Case 2.