Finite element modelling of insulation thickness for cryogenic products for spherical storage pressure vessels

Abstract

This study investigates various insulation thicknesses requirements for double-walled spherical pressure vessels for the storage of cryogenic liquids. The inner tank is suspended from the outer tank by straps or cables and the annular space between the tanks is filled with insulation. The outer tank is not subjected to the freezing temperatures and is thus assumed to be a standard carbon steel sphere. In the Finite Element Analysis model of the system, one dimensional analysis was employed. This is due to the assumption that temperature gradient does only exist along the spherical radial direction. In the developed model, once the thickness of the inner shell has been determined based on relevant standards and codes—ASME Sec VIII Div 1 or 2, BS 5500 etc. and the thickness of the outer shell is known; the required insulation material thicknesses were calculated for different insulating materials. Set of equations resulting from Finite Element Analysis were solved with computer programme code which was written in FORTRAN 90 programming language. The results obtained are validated by analytical method. The results showed no significant difference (P > 0.05) with values obtained through analytical method. The thicknesses for different insulating materials in-between inner and outer tank shells were compared. The results showed that as the insulating material thickness was increased, the heat flux into the stored product was decreasing and at a certain thickness; it started increasing. The insulating thickness at which this happens is termed as critical thickness of insulating material—the thickness of insulation at which the heat influx to the stored products is minimal; this would therefore reduce boil-off of the stored cryogenic product. High thermal conductivity insulating materials need to be thicker than lower thermal conductivity insulating materials if the system is conditioned to have the same heat flux into the stored product for all insulating materials. In the simulation, different insulating material gives different minimal heat influx into the stored products.