Post-CHF heat transfer during two-phase upflow boiling of R-407C in a vertical pipe

Abstract

This paper reports a study of heat transfer in the post-critical heat flux (post-CHF) regime under forced convective upflow conditions in a uniformly heated vertical tube of 12.7 mm internal diameter and 3 m length. Experiments were conducted with non-azeotropic ternary refrigerant mixture R-407C for reduced pressures ranging from 0.37 to 0.75, mass flux values from 1200 to 2000 kg/m² s and heat flux from 50 to 80 kW/m². Data shows a considerable effect of system pressure on the post-CHF heat transfer coefficient for specified mass and heat fluxes. The post-CHF heat transfer coefficients for R-407C are compared with three existing correlations which are found to over predict the current data. A modified correlation to represent the experimental data for R-407C is presented.

Introduction

Convective boiling at high heat flux levels above the critical heat flux (CHF) is known as post-CHF heat transfer and is of importance in steam generators, nuclear reactors, cryogenic systems, refrigeration plants, etc. At the dryout (DO) location, the liquid film disappears resulting in the deterioration of convective heat transfer mechanism due to poor heat transfer characteristics of the vapor. Various physical mechanisms governing post-dryout heat transfer have been reviewed in the literature [1]. Post-dryout heat transfer studies using thermal non-equilibrium methods available for the prediction of post-dryout surface temperature [2], [3] and analytical models for the dispersed flow regime have also been reported [4], [5].

Ünal and Van Gasselt [6] conducted experiments on post-dryout heat transfer in a non-uniformly heated steam generator tube of 10 m length and 7.86 mm ID and for a pressure range of 14.8–19.9 MN/m². Based on this experimental data and existing literature data on uniformly heated tubes, a correlation for the estimation of post-dryout heat transfer coefficient was developed using dimensional analysis. This correlation is applicable for both uniform and non-uniform heated tubes. Nishikawa et al. [7] experimentally studied the post-dryout heat transfer at subcritical pressures with Refrigerant 22 in an upward flowing circular tube. A new correlation was proposed by introducing a non-dimensional parameter to take into account the non-equilibrium existing between the vapor and liquid droplets. This correlation was therefore able to successfully predict the wall temperatures at subcritical pressures, whereas conventional models failed to reproduce the experimental measurements. Experimental studies on flow visualization have also been reported in steady state inverted annular flow film boiling of Refrigerant 113 in a transparent test section to investigate the effects of jet core hydrodynamics and correlate the axial extent of each of the flow zone [8], [9]. Kefer et al. [10] performed experimental investigations of post-dryout heat transfer on horizontal tubes and inclined tubes to quantify the effects of gravity on flow patterns and heat transfer. Effect of curvature on post-dryout dispersed flow in complex geometries like coils and bends have been studied by Wang and Mayinger [11].

Attempts have also been made to predict dryout and post-dryout heat transfer by incorporating the phenomenological models in a three-fluid model framework in which the mass, momentum and energy conservation equations are solved simultaneously for three phases namely, the liquid film, the liquid droplets and the vapor. Hoyer [12] proposed a set of constitutive relations to supplement the conservation equations and used the data of Becker et al. [13], [14] to validate the model up to 70 bar with uniform and non-uniform axial heat flux distribution. Hoyer also compared the wall temperature variation in the post-dryout region for selected cases and reported good agreement. Recently, Jayanti and Valette [15] presented a one-dimensional three-fluid model for the prediction of dryout and post-dryout heat transfer at high pressures (P/P_cr > 0.3). They reported good agreement with the data of Becker et al. [13] for the dryout quality and the tube wall temperature variation in the post-dryout region except for the cases of low mass flux at high pressures.

As a logical sequel to the development of the successful CHF look-up table by Groeneveld et al. [16], an improved look-up table for film boiling heat transfer coefficients was derived for steam-water flow inside vertical tubes [17]. Significant improvements were made to the Lueng et al. [18], [19] look-up table referred to as PDO-LW-96 in order to expand the database of the original table, thus providing a better accuracy for calculating film boiling heat transfer coefficients. Recently, Vijayarangan [20] conducted experimental studies to obtain post-CHF data for R-134a over a wide range of pressures approaching critical conditions. It was found that the correlations of Groeneveld [21] and Ünal and Van Gasselt [6] failed to predict the post-dryout heat transfer coefficient at high reduced pressures approaching critical conditions and therefore a new correlation was developed by modifying the Groeneveld [21] correlation by correcting for the over prediction of post-dryout heat transfer coefficients at high reduced pressures.

The experimental studies reported on CHF and post-CHF behavior are limited to steam-water and pure refrigerants. Even though several non-azeotropic refrigerant mixtures of hydrofluorocarbons (HFCs) have been accepted as replacements for the chlorofluorocarbon (CFC) refrigerants, the post-CHF behavior of such mixtures has not been addressed. It was earlier observed that DO and the corresponding CHF are mainly a result of hydrodynamic behavior and mixture effects are relatively negligible [22], [23]. In the present work, an attempt is made to obtain the post-CHF data for ternary refrigerant mixture R-407C considering it to be an equivalent pure fluid with an overall bulk fluid composition. It is to be noted that CHF in the present study is concerned with the high quality DO corresponding to annular flow regime. The data for R-407C is obtained under vertical upflow conditions over a range of system pressure, mass flux and heat flux conditions with a fixed inlet subcooling conditions. In large evaporators with multiple-parallel refrigerant flow paths, a significant evaporation area is present in the form of vertical headers or distributors. Moreover, some special evaporator designs (e.g. flooded evaporators) invariably contain vertical tubes. Hence, a knowledge of boiling of refrigerants in vertical tubes is essential.