Understanding thermal stratification in cryogenic storage tanks

Abstract

In this study, a numerical investigation is conducted to understand thermal stratification inside cryogenic storage tanks. A numerical model is developed by coupling a 2-D liquid model with a 1-D ullage model. The model is validated against liquid nitrogen tank experiments and accurately reproduces the axial temperature distribution within +/- 3%. Using the validated model, the temporal evolution of a stratified layer is examined in tanks with various liquid heights, radii, and wall heat fluxes. The results show that the stratified-layer ratio-defined as the stratified-layer thickness normalized by the liquid height-increases more rapidly in tanks with smaller liquid heights or radii, as well as under stronger wall heating. A quantitative analysis of stratified-layer growth is performed by comparing the 2-D numerical results with 1-D theoretical predictions based on Sparrow's naturalconvection solution. The mass flow rate governing the growth of the stratified layer can be evaluated with the 1D solution, with average deviations within +/- 12%. However, because the bulk temperature varies with time, the fixed-bulk-temperature assumption in the 1-D model is not valid. Consequently, the 1-D correlation for predicting the stratified-layer ratio is valid only if an appropriate criterion is established to distinguish the warm stratified layer from the colder bulk liquid. Accordingly, a stratification criterion that enables the 1-D correlation to be extended to the 2-D domain is proposed and shown to predict the numerical results within +/- 8%. These findings advance the understanding of stratification behavior and help bridge the gap between theoretical models and numerical simulations.