Thermo-Structural Behavior of Cryogenic Tanks During Cooldown: A Comparison Between Analytical and Numerical Methods

Cryogenic liquid-hydrogen tanks are subjected to significant thermal and mechanical loads during ground cooldown. However, in early design phases, the use of full finite-element analysis (FEA) is often impractical due to its computational cost. This thesis therefore develops and validates a closed-form analytical alternative, while also delineating the limits of applicability of classical structural mechanics to such problems.

The study utilized a horizontal 316L stainless steel cylinder with torispherical heads, modeled after the demonstrator developed in the Horizon Europe project ALRIGH2T (Grant Agreement ID: 101138105). The tank was idealized as a thin cylindrical shell to capture the effects of internal pressure, and as an Euler-Bernoulli beam to represent gravity and vertically stratified thermal loads. Circumferential thermal stresses were evaluated using two-dimensional thermoelasticity. The response was analyzed through superposition, under the assumptions of linear elasticity and temperature-independent material properties. The resulting analytical model was benchmarked against detailed LS-DYNA simulations that included internal pressure, idealized liquid-nitrogen thermal gradients, and self-weight.

The shell model accurately predicted both longitudinal and circumferential stresses due to pressure loading. The beam model similarly captured the longitudinal thermal stress caused by the vertical temperature gradient and correctly estimated the effect of gravity, although gravitational stresses were found to be negligible relative to those from pressure and thermal effects. Conversely, the 2D thermoelasticity model proved unsuitable for predicting circumferential thermal stress in this configuration.

The coupled analytical formulation, combining only the pressure shell and thermal beam models, successfully reproduced the stress distribution and peak values within margins acceptable for preliminary design. At the cylinder mid-span, the analytical von Mises stress differed by only 1% from FEA, while conservatively overestimating stresses at the weld seams. This boundary overprediction is attributed to the exclusion of torispherical cap elasticity, which locally stiffened the analytical model.

Overall, this study demonstrates that classical shell and beam theory can provide fast and sufficiently accurate stress predictions in early-stage design, while also identifying regions where higher-fidelity simulation remains necessary.