Free Convection Model Development for the Thermal Analysis of Cavities in Subsea Christmas Trees

Abstract

A free convective heat transfer model was developed in ANSYS CFX for trapped fluid volumes located inside subsea christmas trees. Analytical and numerical solutions to the heat transfer problem were generated for a vertical concentric cylinder enclosure containing water in the annulus, with aspect ratios D_o/D_i = 3/2 and H = 10 D_o. The inner, vertical wall of the cylinder was fixed at a high temperature whereas the outer cylinder wall was fixed at 4 degrees Celsius. Different cases were investigated, with the temperature of the inner cylinder wall varying from 50 to 100 degrees Celsius. The upper and lower walls were insulated.The analytical solution was based on four literature correlations, each estimating a Nusselt number that was used to compute the respective heat flux and heat transfer coefficient in each case, for comparison with the numerical results. Two of the correlations were based on rectangular enclosures, while the other two were based on vertical concentric cylinders. Numerical results were obtained with two models: 1) a simplified model with an effective thermal conductivity and 2) a fully resolved model taking into account the free convection effects. The simplified model based its effective thermal conductivity on the Nusselt numbers obtained from the literature correlations.A 2D and a 3D model were developed, tested and compared. For the simplified model based on conduction, the 2D and 3D model estimated approximately the same heat flux values as expected. The fully resolved 2D and 3D model differed with up to 20\% for a inner wall temperature of 100 degrees Celsius. The simplified conduction model overestimated the heat flux with up to 60\%, while the correlation that predicted heat flux values closest to the fully resolved CFD model, underestimated the heat flux with 11%. The correlations for rectangular boxes were concluded as inadequate in predicting the heat flux across the annulus for the free convection model developed in this study.