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Experimental investigation on the discharge and suction gas performance in the multilayer insulation microchannels

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Efficient insulation technology is one of the key technologies for the development of large LH2 storage tanks. This paper aimed at a 4000 m3 LH2 spherical tank, many insulation schemes were designed, including multilayer insulation systems integrated with a vapor-cooled shield (VCS) and liquid-nitrogen-cooled shield (LN2CS). The heat transfer model was developed to predict the insulation performance of a LH2 spherical tank. The effect of the VCS position on insulation performance was studied, and the different configurations of double VCSs were compared and discussed. The results showed that the daily evaporation rate of MLI, hollow glass microspheres (HGMs) and vacuum was only 2.05 × 10−3%, 3.62 × 10−3% and 7.94 × 10−2% at 1.34 Pa, respectively. MLI was still the optimal insulation scheme for a 4000 m3 LH2 spherical tank. Meanwhile, it was found that when the single VCS was placed at the 10th layer, the heat leakage was reduced by approximately 40.5% compared with MLI. The heat leakage of parallel VCS(P-VCS) was 76.6% lower than that of MLI. The minimum heat leakage of series VCS(S-VCS) was 83.79%, 72.75% and 37.36% lower than that of MLI, single VCS and P-VCS, respectively. Additionally, the heat leakage of the LH2 tank could be reduced to less than 10 W when LN2CS was installed. These results provide a design reference for the highly efficient storage of large LH2 tanks.
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Of cryogenic liquid hydrogen tanks for future airliners, their volumetric and gravimetric efficiencies, their robustness and their environmental adaptability are all strengthened via a novel thermal insulation concept proposed in this work. A conventional cryogenic tank is insulated either purely by a layer/layers of Polyurethane (PU) foam or by a vacuum-based multilayer insulation (MLI). In the new concept, an extra layer is inserted into the PU foam. The intermediate layer can be filled with liquid nitrogen while on the ground or with ambient air during flight. By this new design, analysis shows an approximate 33% volumetric saving compared to PU insulation. Furthermore, a 6-fold amount of passive heat input during cruise flight is easily achieved compared to the rest two concepts. This showcases an increased robustness against possible failure of the tank's active heating system, and the potential for significant parasitic power loss reduction.
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Hydrogen has been attracting attention as a fuel in the transportation sector to achieve carbon neutrality. Hydrogen storage in liquid form is preferred in locomotives, ships, drones, and aircraft, because these require high power but have limited space. However, liquid hydrogen must be in a cryogenic state, wherein thermal insulation is a core problem. Inner materials, including glass bubbles, multi-layer insulation (MLI), high vacuum, and vapor-cooled shields, are used for thermal insulation. An analytic study is preferred and proceeds liquid hydrogen tanks due to safety regulations in each country. This study reviewed the relevant literature for thermodynamic modeling. The literature was divided into static, dynamic, and systematic studies. In summary, the authors summarized the following future research needs: The optimal design of the structure, including suspension, baffle, and insulation system, can be studied to minimize the boil-off gas (BOG). A dynamic study of the pressure, mass flow, and vaporizer can be completed. The change of the components arrangement from the conventional diesel–electric locomotive is necessary.
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With the development of both cryogenic and motor pump technologies, the cryogenic variable thrust liquid rocket engines that using motor pumps have gained considerable attention. However, the heavy battery limits its performance if engine operates for high thrust. To address this challenge, the electric expander cycle system scheme for variable thrust liquid rocket engines is creatively proposed and designed. Subsequently, the system parameters are calculated based on mass and energy conservation with chamber heat transfer considered. As well, the distribution of this novel system state parameters is investigated. Further, a comparison is conducted between the electric expander cycle system, electric pump, and expander cycle systems. The comparison results demonstrate that this innovative system scheme has advantages of simple structure, low battery mass, convenient throttling, and high reusability. The system state parameters distribution indicates that the feed system can achieve the propellants' pressurization requirements throughout the designed 5:1 throttle range, which suggests the feasibility of this system scheme. Moreover, although the proposed system requires more battery power than does the turbine, the turbine power proportion in the entire system increases with thrust. However, the turbine efficiency drops steeply with a decrease in thrust, whereas the double pump efficiency presents a narrow variation range.
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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 perforation. This paper uses two quality metrics for an MLI-setup: the perforation escape ratio (PER), defined as the ratio of the number of particles escaping through the layers (broadside pumping) to the total number of outgassed particles, and the pressure distribution across the layers. The present stationary Monte Carlo simulations investigate the outgassing behaviour of MLI-setups at the end of pumping, where an equilibrium state is approached and molecular flow is assumed. Some of the findings of the “Lockheed report” (Keller et al., 1974) [1] are reproduced, and the two aforementioned quality metrics are analysed for different cases. We find that the residual pressure decreases and the parameter PER increases as (a) the perforated area increases, (b) the perforation size decreases, and (c) the number of layers decreases. Both the pressure and the parameter PER increase as (a) the layer size increases, (b) the distance between layers decreases, and (c) the porosity of the edges decreases.
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In this manuscript, the temperature model of multilayer insulation (MLI) on a spacecraft solar panel in thermal radiation is considered. The thermal insulation performance of MLI and the stress of the spacecraft are also considered. The thermal equilibrium equation of the surface temperature of MLI spacecraft in the presence of current transfer, and the iterative temperature acquisition algorithm of the front and back surface of solar panel MLI are derived. The Gaussian elimination method is used to invert the high order sparse matrix composed of error coefficients, thus realizing the real-time calculation of thermal re-radiation(TRR). The thermodynamic model was applied to the motion simulation of GPS Block IIR satellites, and the theoretical model was verified based on the actual temperature measurement data of several GPS Block IIR satellites. The simulation results have certain reference value for studying the thermodynamic modeling of MLI spacecraft and TRR perturbation calculation.
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Neutron imaging enables direct visualization of evaporation and condensation of cryogenic propellants in metal containers such as aluminum and stainless steel. CFD models of propellant behaviors inside the large tanks have shown that a thin liquid film is formed along the interior surface, but this had not been verified experimentally. In the present study, neutron imaging is used to study evaporation and condensation rates of liquid methane inside a cylindrical 10 mm, Al 6061 cell. The liquid meniscus is clearly shown, but the spatial resolution is insufficient to directly image thin liquid films that may be on the interior surface. Optical density (neutron attenuation) analysis enables quantitative measurements of these liquid films. An optical density image is formed by removing the background noise and normalizing the liquid image with that of the empty cell. Optical densities are then transformed into a liquid transmission thickness using the Beer-Lambert law. This technique enables measurement of film thicknesses smaller than the spatial resolution of the imaging system. The above graphic shows an optical density image during condensation of methane and the corresponding horizontal scan which suggests that a 11 μm film exists on the wall. The images indicate that methane undergoes film-wise condensation and is perfectly wetting to aluminum. These experiments were conducted at the NIST Center for Neutron Research in the Neutron Imaging Facility and the relevant work is supported by an Early stage Innovations Grant from NASA's Space Technology Research Grants Program (Grant # NNX14AB05G).
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An accurate estimation of the effective thermal conductivity of various insulation materials is essential in the evaluation of heat leak and boil-off rate from liquid hydrogen storage tanks. In this work, we review the existing experimental data and various proposed correlations for predicting the effective conductivity of insulation systems consisting of powders, foams, fibrous materials, and multilayer systems. We also propose a first principles-based correlation that may be used to estimate the dependence of the effective conductivity as a function of temperature, interstitial gas composition, pressure, and structural properties of the material. We validate the proposed correlation using available experimental data for some common insulation materials. Further improvements and testing of the proposed correlation using laboratory scale data obtained using potential LH2 tank insulation materials are also discussed.
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Multilayer insulation (MLI) is a kind of high-temperature insulation which employs multiple high-reflective screens to retard the radiation heat, but analyzing and optimizing its heat transfer characteristics by experimental and theoretical models remains low-efficiency and non-visualization. In this work, finite element analysis (FEA) models verified by comparing the simulation and experiment results are established to systematically reveal the numerous and complex effect factors, including the number of layers, thermal boundary, fibrous insulation density and emissivity of reflective screens. The results show that the top temperature of MLIs can be reduced by increasing the number and the emissivity of reflective screens, and the density of fibrous insulation, but there is a reasonable number of layers to achieve the best comprehensive performance of MLI. In addition, the proportion of radiative heat transfer in the total heat transfer increases with increasing heating temperature. The feasibility of optimizing thermal insulation performance based on the FEA models is confirmed by designing the MLIs with stainless steel and aluminum as reflective screens. And the results indicate that the FEA methods can significantly reduce the number of trials and realize the optimal design of MLI.
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High temperature thermal insulation performance plays a crucial role in the application of thermal contact resistance precision measurement to reduce systematic heat loss and ensure 1D axial heat flow. In this paper, a compound insulation system composed of carbon fibrous materials and multilayer insulation (CFMLI) with non-interlayer-contact space was proposed in terms of high temperature sustainability, low thermal conductivity and thermal performance stability. An experimental set-up was designed and fabricated to measure the temperature distribution and the effective thermal conductivity of CFMLI as a function of temperature (800 K−1325 K). The experimental results showed that the temperature gradually decreases from inner to external radius of CFMLI, and a temperature jump of 40 K−80 K appears at the interface between two segments under vacuum conditions. It also reveals that the thermal performance of CFMLI is strongly dependent on the gas pressure and the number of reflective layers, while it is hardly affected by the filling materials when the temperature is above 1050 K. Meanwhile, the effective thermal conductivity of CFMLI varies around 0.2 W/m/K for two levels of pressure (10⁻⁴ Pa and 0.1 MPa), and it decreases by 14.7% when the number of reflective layers increases from 6 to 21 at 1325 K. Additionally, a theoretical model with thermal resistance network was developed for heat transfer analysis of CFMLI. The model could predict the external temperature of CFMLI with high accuracy so that the difference between the theoretical results and experimental data was less than 2.61%.
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The long-term storage of liquid hydrogen (LH2)-liquid oxygen (LO2) pair with extremely low heat leakage is essential for future deep space exploration. Vapor-cooled shield (VCS) is considered an effective insulation structure that can significantly reduce the heat penetration into the LH2 tanks, however it is relatively ineffective for the LO2 tanks. Novel coupled VCS insulation schemes for LH2-LO2 bundled tanks were proposed to achieve optimal performance not only for the LH2 but also for the LO2 tanks. A thermodynamic model had been developed and validated by experiments. The optimal VCS location, the temperature profile within the insulation, the heat leakage reduction contributed by the VCS, and the thermal performance versus scheme structural mass had been parametrically investigated. A comparison indicated that the proposed single integrated shield configuration can reduce the heat flux of the LH2 and the LO2 tanks by 64.0% and 54.8%, respectively compared with the non-VCS structure. In addition, the results also confirmed that zero boil-off storage of LO2 can be achieved by only utilizing the exhausted hydrogen vapor, with no need for an extra cryocooler.
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In a high-vacuum-multilayer insulation structure (HVMLIS), H2 is released into the vacuum jacket by manufactured materials, resulting in the deterioration of the insulation vacuum. Palladium oxide (PdO), which is expensive, is typically used as an H2 getter in HVMLIS. However, PdO generates sparks by vigorously reacting with H2, which are a potential threat to HVMLIS. Therefore, in this work, silver-exchanged zeolite is optimised to obtain an inexpensive and safe Ag–Z getter and a silver molecular sieve (SMS) together with a low-temperature active material getter (AMG). Moreover, an experimental platform was designed to test the H2 sorption properties of the three getters and compare them with traditional PdO. The experiment revealed that the cumulative sorption capacities of PdO, Ag–Z, SMS and AMG were 184.8, 63.1, 124.9 and 5.28 mL/g, respectively. However, the costs of SMS, Ag–Z and AMG were only ∼7.37%, 5.08% and 6.13% of the cost of PdO, respectively, indicating that SMS is a promising alternative to PdO, which is expensive. Simultaneously, the microstructure of the H2 getters was analysed via X-ray powder diffraction. Further, PdH0.706 and Pd2H1.5 were obtained in addition to Pd, after H2 was absorbed by PdO. Ag⁺ was reduced to Ag in SMS, and Cu8O was produced by the reaction of CuO in AMG. These findings provide a basis for the subsequent optimisation of the H2 getters.
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In many applications, the heat flux at the surface is known instead of the surface temperature. In addition, in some applications, like vacuum drying or high altitude flights, the pressure is below atmospheric pressure, so the rarefaction effects become important, and therefore, the Navier-Stokes-Fourier equations fail to predict gas thermal behavior. In this paper, a constant heat flux boundary condition is developed and implemented in the frame of the Shakhov model kinetic equation, with the possibility to simulate the diffuse-specular reflexion of the molecules from the surface. The developed technique is implemented for the simulation of gas heat transfer in a two concentric cylinders configuration, similar to vacuum drying of used nuclear fuel canisters. The numerical results obtained using developed approach are compared with experimental data of heat transfer through rarefied gas between two concentric cylinders.
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At present, several composite insulation systems were proposed that can be used for passive insulation systems, including foam-variable density multilayer insulation (VDMLI), aerogel-VDMLI and hollow glass microspheres (HGMs)-VDMLI. The passive insulation systems with different inner material (IM) showed different performances. However, the relationship between the average thermal conductivity of IM and the insulation performance of the whole system has rarely been investigated. It is of great significance for efficient configuration and matching of the passive insulation system. In this paper, a series of average thermal conductivity of IM were assumed to predict the insulation performance of the whole system at 20 K–300 K and high vacuum. In order to further illustrate the relationship between IM and MLI/VDMLI, the foam was replaced by the HGMs as 5 mm a unit forming a series of HGMs-foam-MLI/VDMLI insulation systems. The performance of the systems was investigated. After the foam was completely replaced by the HGMs, the performance of MLI and VDMLI systems was improved 33% and 13%, respectively. Moreover, each mode of heat transfer including solid conduction, radiation, and gas conduction for foam-MLI/VDMLI and HGMs-MLI/VDMLI insulation systems were calculated and analyzed.
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Liquid natural gas and liquid hydrogen are promising and economical clean energy sources for reducing CO2 emissions and slowing global warming. Characterization and monitoring of the vacuum pressure inside tank containers with multilayer insulation (MLI) are essential for the safe storage and convenient transportation of these cryogenic fuels. Herein, a new method for characterizing the vacuum pressure of tank containers with MLI is proposed. A theoretical analysis revealed that the temperature of the outer surface of the MLI material (To) is a good indicator of the vacuum pressure inside the tanks. Experimental verification was conducted using an MLI performance-testing apparatus, To was measured under 10 different vacuum pressures. The results showed that when the vacuum pressure was <10⁻¹ Pa, To kept almost. However, when the vacuum pressure was >1 Pa, To decreased sharply with the increase of vacuum pressure. The mechanism of the proposed method was also discussed based on the thermal analysis of the experimental system at different vacuum pressures. This study provides a simple and reliable method for vacuum pressure monitoring of tank containers with MLI, which allows the large-scale and safe utilization of clean energy with a low boiling temperature.
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In this study, a high-performance multilayer super insulation with improved thermal characteristics was manufactured by novolac aerogel/polyester mat as a spacer layer. The novolac aerogel blankets were prepared through the sol–gel polymerization method under vapor of solvent-saturated atmosphere in the presence of the polyester mat. The effect of novolac resin concentration in the initial sol and the layer density on the thermal performance of the novolac aerogels and the multilayer insulations (MLIs) with and without aerogel blankets were studied in details from morphological and thermo-physical points of view. The results indicated that the MLI with 12 aerogel blanket spacer layers, each spacer layer of which had a density of 0.173 g/cm³, a porosity of 85%, a thermal conductivity of 0.0424 W/m.K and a low thermal diffusivity of 2.16 × 10⁻⁷ m²/s, was achieved as an adequate specimen. Such an MLI system presented a low thermal conductivity of 2.79 × 10⁻⁵ W/m.K at room temperature, making it a preferential candidate for thermal insulation systems.
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Multi-layer insulation (MLI) blankets are one of the main components of satellite thermal control system. The past studies have considered infinite heat transfer coefficient in modeling the MLI shields due to the use of reflective thin films such as aluminized Kapton (Polyimide Film Developed by DuPont Company) or aluminized PET (Polyethylene Terephthalate) in MLI shields. Therefore, equal temperature was considered on two sides of a shield and the effect of thermal resistance has been ignored in the total thermal resistance. In the present study, the effects of thermal conductivity of thin film and shield thickness are analyzed. For this purpose, numerical analyses are performed on three types of blankets that are made of Kapton, PET and null shields. The results indicate that the difference in effective emittance of Kapton and PET blanket is 17% to 2% from the thinnest film to the thickest film, respectively. In order to confirm the numerical results, the effective emittance of two types of MLI blankets made of Kapton and PET films is measured under identical conditions. It is concluded that the Kapton blanket has lower effective emittance than PET.
Article
Cryogenic transfer lines are very important to transport cryogenic fluid in the fields of fusion energy and hydrogen energy. The main aim of this work is to assess and minimize heat leakage of cryogenic transfer line. A three-channel coaxial liquid helium pipe with three support structures and typical multilayer insulation (MLI) materials was designed. Cryogenic transfer lines installed three support structures and MLI with different layer density & number of layer were studied based on a horizontal cryogenic transfer line test platform with liquid nitrogen. Thermal performance including heat leakage and temperature distribution of straight and elbow pipe have been numerically and experimentally analyzed for boundary temperature 77 K–293 K. By comparing simulated results with experimental heat leakages of supports, MLI and cryogenic transfer lines, the largest deviations are less than 10%, 10.7% and 6.6%, respectively. Based on above analysis, the minimal heat leakages of two-plate support and MLI with 50 layers and 25 layers/cm are 0.200 W and 0.488 W, respectively. Furthermore, the minimal heat leakages of straight pipe and elbow pipe were acquired as the values of 0.688 W and 0.858 W with two-plate support and MLI under 50 layers and 25 layers/cm. The results have been successfully applied in 250 [email protected] K helium cryogenic refrigerator. The new and useful assessment method could also be applied to minimize heat leakage of cryogenic transfer lines with different size, support and MLI, etc, and then to improve the energy efficiency of system.
Article
Performance of multilayer thermal insulators (MLIs) are depends on spacers density and number of reflector layers. In optimum density, aerogel spacer has the lowest thermal conduction. In the other hand, optimum layers density of MLI depend on temperature situation, which the minimum heat flux is flow through the thickness. In this work, aerogel spacer with density of 76 kg/m³ and MLI layer density of 25 layer/cm (number of layers per one centimeter of thickness) were designed as adequate insulators. Therefore, a novel class of MLI system with thermal conductivity of 5.43 × 10⁻⁴ W/m.K was evaluated as a high performance thermal insulator.
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Hydrogen has more energy per unit mass (141.8 MJ/kg) than any other fuel but also has the lowest gaseous density (0.084 kg/m ³ ), and liquid hydrogen (LH 2 ) storage is a solution with high energy density. However, LH 2 storage has the characteristics of low temperature (20 K) and easy evaporation, putting forward higher requirements for insulation system. At present, the improvement and optimization of insulation system consisting of spray on foam insulation (SOFI), multilayer insulation (MLI) and variable density MLI (VDMLI) is a hot topic. Considering the considerable sensible heat of hydrogen, this paper introduces self-evaporation vapor cooled shield (VCS) into the above-mentioned insulation systems to fully recover its sensible heat to improve insulation performance. A thermodynamic model has been established to study the insulation properties of composite insulation system for LH 2 tank, and the results have good agreement with test data. Coupling effects among them are analyzed and the optimization strategies of MLI, VDMLI and VCS are quantitatively explained to obtain better insulation performance. The heat flux and temperature profile of four insulation structures (MLI, VDMLI, MLI + VCS and VDMLI + VCS) have also been quantitatively analyzed, which can provide guidance for insulation system optimization. The insulation performance of composite insulation system under different vacuum conditions have also been compared.
Article
H2 released from materials in the vacuum chamber of high-vacuum-multilayer-insulation tank (HVMIT) and is adsorbed by the expensive getter PdO. However, in addition to its disadvantageous high cost, PdO produces sparks and burns easily during H2 adsorption process, thereby compromising the safety of storage tanks. Therefore, we designed an experimental platform for studying composite H2 getters based on transition metal oxides. The getter consists of copper oxide (CuO), active carbon (C), and copper (Cu). The obtained optimal C and Cu mass contents are 68.086% and 21.276%, respectively. The addition of C facilitates the H2 absorption by CuO. The adsorption rate increases by one order of magnitude with the addition of Cu. The adsorption isotherm of CuO & C & Cu is classified as type I as accurately described by the Langmuir model. At the equilibrium pressure not higher than 5.0 × 10⁻² Pa, the H2 adsorption capacity is 397.00 mL(stp)/g, and Langmuir saturated adsorption amount was 415.913 mL(stp)/g at room temperature. The new getter offers the advantages of low cost, high efficiency, and ease of production. This getter can directly replace PdO as H2 getter and be used in vacuum storage tanks.
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The transient heat transfer characteristics of a new kind of combined multilayer thermal insulation material (MTIM) were numerically investigated in this paper. This new kind of multilayer thermal insulation is composed by silica aerogel and alumina aerogel doping with erythritol and stearic acid phase change materials. Finite Volume method combined with Enthalpy method as well as the Discrete Ordinate method is used to consider the combined conduction and radiation heat transfer with phase change problems. Based on the constructed numerical model, the transient heat transfer characteristics of the MTIM with two kinds of different arrangements were calculated and analyzed in detail. The results indicated that: (1) putting the PCMs at the bottom of the MTIM fails to enhance the thermal insulation performance of the MTIM; (2) in contrast, putting the PCMs at the middle of the MTIM can enhance the thermal insulation performance of the MTIM successfully; (3) there is an optimum doping content of the PCMs that can lead to the lowest of the temperature of the MTIM which makes the thermal insulation performance of the MTIM to be the best.
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This paper developed one quasi-steady state model to investigate the thermal performances of foam and MLI for a cryogenic liquid hydrogen tank during the ascent and on-orbit process. The corresponding parameters of MLI were calculated with temperature range from 55 K to 700 K, and pressure range between 10−6 Pa and 105 Pa during the whole process. Changes of physical properties with the flight height or the flight cycle were fully considered. The present developed model was validated by the experimental results and turned out to have high prediction ability. Iterated from outside to inside of the MLI layer with the dichotomy method, three main heat transfer forms were specially investigated and compared. Thermal resistance distributions of foam and MLI were compared in detail, and their contributions to reduce the heat leakage were analyzed thoroughly. Some valuable conclusions were of significance to optimize the design of foam/MLI for cryogenic storage tanks.
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This paper was to experimentally investigate the thermal response of high-vacuum-multilayer-insulation (HVMLI) cryogenic tank after sudden, catastrophic loss of insulation vacuum (SCLIV). The venting and no-venting experiments were conducted with the breakdown of the insulating vacuum with nitrogen. There was a great temperature gradient in the thickness direction of the MLI in both the venting and no-venting experiments. Temperature jump appeared on the external wall of the inner vessel after gas was introduced into the insulation vacuum jacket. Thermal stratification in liquid nitrogen (LN 2) was serious with 25 K axial temperature difference in the no-venting experiment. The no-venting experiment included four stages. The fourth stage was the most dangerous and must be strictly avoided because the pressure of the tank full of superheated LN 2 could surpass the safety pressure in a few minutes and the tank could blast at any moment.
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In any manned mission architecture, upwards of seventy percent of all payload delivered to orbit is propellant, and propellant mass fraction dominates almost all transportation segments of any mission requiring a heavy lift launch system like the Saturn V. To mitigate this, the use of an orbital propellant depot has been extensively studied. In this paper, a thermal model of an orbital propellant depot is used to examine the effects of passive and active thermal management strategies. Results show that an all passive thermal management strategy results in significant boil-off for both hydrogen and oxygen. At current launch vehicle prices, these boil-offs equate to millions of dollars lost per month. Zero boil-off of propellant is achievable with the use of active cryocoolers; however, the cooling power required to produce zero-boil-off is an order of magnitude higher than current state-of-the-art cryocoolers. This study shows a zero-boil-off cryocooler minimum power requirement of 80–100 W at 80 K for liquid oxygen, and 100–120 W at 20 K for liquid hydrogen for a representative Near-Earth Object mission. Research and development effort is required to improve the state-of-the-arts in-space cryogenic thermal management.
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We investigate oscillatory shear-driven gas flows in the transition and free-molecular-flow regimes. Analytical results valid through slip flow and the early transition regime are obtained using a recently proposed, rigorous second-order slip model with no adjustable coefficients. Analytical solution of the collisionless Boltzmann equation provides a description of the high Knudsen number limit (Kn⪢1) including the bounded shear layers present in the limit of high oscillation frequency. These layers are analogous to the Stokes layers observed in the Kn⪡1 limit, but contrary to the latter, they exhibit a nonconstant wave speed as demonstrated by Park, Bahukudumbi, and Beskok in Phys. Fluids. 16, 317 (2004) . All theoretical results are validated by direct Monte Carlo simulations. We find that the second-order slip results are in good agreement with direct simulation Monte Carlo (DSMC) solutions up to Kn ≈ 0.4; in some cases these results continue to provide useful approximations to quantities of engineering interest, such as the shear stress, well beyond Kn ≈ 0.5. The collisionless theory provides, in general, a good description of DSMC results for Kn≳10, while in the high frequency limit the agreement is very good for Knundsen numbers as low as Kn ≈ 5.
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The combined radiation/conduction heat transfer in high-temperature multi-layer insulations was modeled using a finite volume numerical model. The numerical model was validated by comparison with steady-state effective thermal conductivity measurements, and by transient thermal tests simulating re-entry aerodynamic heating conditions. A design of experiments technique was used to investigate optimum design of multi-layer insulations for re-entry aerodynamic heating. It was found that use of 2 mm foil spacing and locating the foils near the hot boundary with the top foil 2 mm away from the hot boundary resulted in the most effective insulation design. A 76.2 mm thick multi-layer insulation using 1, 4, or 16 foils resulted in 2.9, 7.2, or 22.2 percent mass per unit area savings compared to a fibrous insulation sample at the same thickness, respectively.
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The combined radiation and conduction heat transfer in multilayer perforated insulation material (MLPIM) using in space has been investigated. The model for the calculation of temperature field in MLPIM and the model of inner radiation have been presented according to energy balance equation. The difference equations have been solved by iterative method combining with ADI method. Comparison between the numerical results by the models in this paper and the experimental results in the literature shows that the models are feasible to be applied in engineering. The effect of the main parameters such as layer density, screen emissivity and perforation coefficient on the thermal performance has been analyzed. The study on the performance of MLPIM will present active instruction to improve the insulating performance and accomplish optimum design of MLPIM.
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The problem of heat conduction in a multi-layer, two-dimensional, orthotropic cylinder subject to asymmetric and periodic temperature distribution on the outer wall is solved analytically. Dimensional analysis of the problem shows that heat conduction through the cylinder is a function of the Biot number (Bi) and the following four non-dimensional parameters in each layer: frequency ratio (α*n), thickness ratio (x*n) and radial (K*r,n) and tangential (K*t,n) conduction ratios. The derivation is valid for an arbitrary number of layers and has been used to study the effect of layer order on inter-layer and overall heat transfer. A cylinder composed of two layers is discussed as an example.
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Two design criteria for unevacuated horizontal multi-layer insulation systems, with equal spacings of the intermediate plates yielding the minimum heat transfer rate, are described.
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