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# Pressure distribution (i.e. pressure over cell ID) of the setups with strongly different edge porosity

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In multi-layer insulation (MLI) for space or terrestrial cryogenic applications, large densities of gas molecules (particles) between individual layers reduce the thermal performance of the insulation because particle collisions transfer heat. This poses an incentive to provide pathways for particles to escape the system quickly, such as perforatio...

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... Other models such as McIntosh [6] investigations, have tried a more analytical approach based on rarefied gas theory [7]. To precise the latter, softwares as MOLFLOW+ [8] intend to simulate the behavior of particles in high vacuum (<10 -6 torr) using Test-Particle Monte Carlo (TPMC), a method based on statistics and a high number of particle trajectories to assess characteristics (pressure, density, velocity…) [9] within a given geometry and with given parameters (temperature, outgassing, pumping, species characteristics). ...

... Few previous studies have investigated the characterisation of residual pressure in MLI, such as Eizinger [9] who showed that outgassing and pumping could induce a bell distribution that is impacted by the perforation characteristics (size, coverage, absence of it) as well as the interlayer spacing. "U" or "L" distributions are also mentioned in [11] where a similar approach in layer-by-layer is also proposed using machine learning. ...

... It is interesting to dive more into the tool that made possible the development in [9], called MOLFLOW+. This software, developed by CERN [9] relies on the TPMC (Test Particle Monte-Carlo) method, a derivative of DSMC (Direct simulation Monte-Carlo) : it follows the trajectory of particles in a free molecular state (HV state) one by one. ...

Cryogenic Systems require a highly efficient insulation so as to limit the heat ingress and boil-off, which is generally achieved through the use of vacuum combined with an insulated media. The performance of Multi layer Insulation (MLI) will be investigated with detailed thermal models developed to account for all the heat transfer contributions, solid conduction, gaseous conduction and radiation. Results are presented for an usual cold vacuum pressure (CVP) corresponding to high vacuum (<10 ⁻⁶ torr) and compared with available experimental measurements for state of the art technologies. The nominal thermal performances are then evaluated for a cold temperature of 20K (representative of liquid hydrogen storage temperature), for a degraded CVP with hydrogen and nitrogen as residual gasses and for increased hot boundary temperatures. Other parameters are also discussed such as, the number of layers, material, layers density, venting options, assembly process and material optical properties. Finally, a sensitivity of the thermal performance is also presented with a pressure gradient through the insulation thickness, that could be induced by cryopumping, materials outgassing, pumping times or small leakages.

... The current state-of-the-art work is on molecular dynamics simulation of interlayer gases for MLI. Martin [13] used the Test Particle Monte Carlo (TPMC) method to investigate the outgassing behavior of MLI setups at the end of pumping. Theoretically, simulations with TPMC methods can provide pressure values at arbitrary locations inside the MLI and even the pressure distribution through the thickness of the MLI [13]. ...

... Martin [13] used the Test Particle Monte Carlo (TPMC) method to investigate the outgassing behavior of MLI setups at the end of pumping. Theoretically, simulations with TPMC methods can provide pressure values at arbitrary locations inside the MLI and even the pressure distribution through the thickness of the MLI [13]. In their study, a set of symmetric, separated, perforated, square-shaped layers were investigated. ...

Revealing the interlayer pressure distribution in multilayer insulation (MLI) for cryogen (e.g., liquid hydrogen) containers is very important to improve the insulation-performance-predicting quality. This paper proposed an inversion method to reconstruct the interlayer pressure of multilayer insulations on the basis of experimentally measuring the reflectors’ temperatures. The layer-by-layer (LBL) model was modified by considering the interlayer pressure distribution in MLIs to calculate the reflectors’ temperatures. Groups of pre-given interlayer pressure distributions and the corresponding temperature distributions calculated by the LBL model were used to train an extreme learning machine (ELM) algorithm. Finally, the interlayer pressure distribution of the MLI was reconstructed by the trained ELM algorithm based on the measured reflectors’ temperatures. The method was validated by four additional testing cases. The results showed that the proposed algorithm was accurate in reconstructing the interlayer pressures. Published experimentally measured temperature distributions of a 60-layer MLI were used as input data. The abovementioned inversion method was adopted, and a reasonable interlayer pressure distribution was obtained. Moreover, the thermal insulation performance of the MLI was calculated by the LBL model considering the reconstructed interlayer pressure distribution. We found that the predicted heat flux of the MLI deviated from the experimental results by only 2.77%, while the error of the classical LBL model ignoring the non-ideal vacuum condition was as high as 89%. Meanwhile, the predicted corresponding temperature distribution deviated from the tested value by less than 1.13 K. The proposed method can be applied to assess the interlayer pressure distribution of industrial cryogen containers and precisely predict the thermal insulation performance of a practical multilayer insulation structure.

... The experiment of sun [5] indicated that the apparent thermal conductivity of MLI can reach 0.001W/(K· m) at 0.01 Pa. Meanwhile, The heat transfer mechanisms were investigated in past paper [6,7,8]. Martin [6] adopted Monte Carlo method to investigate the residual gas in MLI. ...

... Meanwhile, The heat transfer mechanisms were investigated in past paper [6,7,8]. Martin [6] adopted Monte Carlo method to investigate the residual gas in MLI. These researches provide the basis for the efficient use of MLI. ...

... where the qout,k is radiation thermal fluxes from k surface to other radiation surface; the qin,k is radiation thermal fluxes from other radiation surface to k surface; the qk is the heat flux entering k surface in non-radiative way; Tk is the temperature of k surface; the ɛk is the emissivity of k surface; the σ is Stephen Boltzmann constant; the Fk-j is the view factor from k surface to j surface. The surface is heat balanced and no geometric boundary in enclosure radiation theory [6]. Accordingly, the enclosure radiation theory is divided into six surfaces in Fig. 1, their radiation heat flux can be written as follows: ...

The calculation of radiant heat leakage is a part of the design of cryogenic insulation system. The numerical radiation simulation considering geometric structure of cryogenic insulation system is established through Monte Carlo method and view factor. The difference of the multi-layer insulation outer surface temperature is about 0.5% between the simulation and experimental results. Additionally, the structure and shape of the insulation system would make radiation to redistribute between surfaces. The surface would have less heat leakage with large aspect ratio and small radius.