The MLI (multi-layer insulation), commonly used in liquid hydrogen tank, acts to reduce HLF (heat leakage flux) into the tank and slow down tank pressurization. It is usually optimally designed into three or four regions, with the same RS spacing in every region, which is regarded as the discontinuous variable density and called VDMLI (variable-density multi-layer insulation). However, the VCS (vapor-cooled shield) and P-O (para-to-ortho hydrogen conversion) in VDMLI are not considered in the optimal design of VDMLI. Therefore, a kind of nonlinear programming algorithm named SQP (sequential quadratic programming), in which HLF solver of liquid hydrogen tank is embedded, is firstly introduced to obtain the optimized distribution of RS (radiative shield) spacing to minimize HLF of liquid hydrogen storage tank. The HLF solver is a numerical model of VDMLI coupled with VCS and P-O, and SQP can be regarded as the optimization process of searching for an optimal solution in high dimensional space, under inequality constraints. The calculation results show that the best SN (serial number) of RS for SVCS (single vapor-cooled shield) setting to minimize HLF, in three cases of before optimization with P-O, after optimization with P-O, and after optimization without P-O is 16, 11, and 14 respectively. With P-O, the minimum HLF after optimization is reduced by 8.45% compared with the minimum HLF before optimization. When SVCS is set at the 4th RS, P-O leads to the most decreasing range of HLF, which is 28.3%, while the optimization process leads to the most decreasing range of 48.1% under condition that SVCS is set at the 2nd RS and P-O is coupled. Under condition of no P-O, after optimization, the minimum HLF occurs when the SN of RS where DVCS (double vapor-cooled shield) is set is (8,21), and the minimum HLF is reduced by 9.0%, compared to that before optimization with DVCS, and is reduced by 50.43% compared to that after optimization with SVCS.
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