Numerical analysis of thermal stratification in cryogenic storage tanks

Abstract

To numerically investigate transient natural convection inside a cryogenic storage tank, a numerical model combining a 2-D axisymmetric model for the liquid region with a 1-D model for the ullage region is developed and validated against experimental data. A cylindrical tank subjected to a uniform heat flux along the side wall is considered, which induces thermal stratification—the phenomenon in which warmer liquid near the wall rises, flows towards the colder core of the liquid bulk, and accumulates near the liquid–vapor interface. The model accurately predicted stratified-layer thickness, i.e. the thickness of the accumulated hot-liquid layer, to within ±5% of experimental measurements. Using this model, the temporal evolution of stratified layer is examined for tanks with various liquid aspect ratios—defined as the product of tank aspect ratio and liquid-fill ratio—ranging from 0.125 to 1.5. The results show that the ratio of stratified-layer thickness to liquid height increases over time and increases more rapidly as the liquid aspect ratio decreases at a fixed radius. A quantitative analysis of stratified-layer growth over time is conducted and compared with results obtained from a correlation based on Sparrow’s 1-D natural-convection solution. It is found that the 1-D correlation is useful if an adequate criterion is defined to distinguish the stratified layer from the colder bulk liquid. Therefore, a criterion that enables the 1-D correlation to be applicable to a 2-D domain is proposed, and shown to predict numerical results for various liquid aspect ratios with an error of ±8%. These findings offer valuable guidance in choosing between 1-D and 2-D modelling approaches for cryogenic-tank analyses.