A multi-stage distributed cold trap based on lunar environment
By integrating a selectively permeable membrane and a microcapsule phase change layer into the cold trap unit, the porosity distribution of the porous medium is optimized, solving the problem of low water vapor capture efficiency in traditional cold traps under extreme environments. This achieves efficient and stable water vapor capture and sublimation, improving the space utilization and temperature stability of the cold trap, and enhancing the water ice collection rate and purity.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- XI AN JIAOTONG UNIV
- Filing Date
- 2025-07-24
- Publication Date
- 2026-07-10
AI Technical Summary
Traditional cold trap technology has low water vapor capture efficiency in extreme low temperature and rarefied pressure environments, and suffers from competition between the sublimation rate and the solar radiation ablation rate, flow channel coupling effect and vapor escape problems, making it difficult to meet the requirements of lightweight, low power consumption and high reliability for deep space exploration.
The cold trap employs a multi-stage distributed design, including a sealing membrane attached to the inner surface of the arched shell, and cold trap units arranged in an array on the inner surface of the arched shell. Each cold trap unit consists of a framework, a selectively permeable membrane, a microcapsule phase change layer, and a porous medium. The porous medium comprises a selectively permeable membrane with molecular sieve effect, a microcapsule phase change layer, and a porous medium. The selectively permeable membrane precisely separates water vapor molecules, the microcapsule phase change layer buffers radiation fluctuations, and the porous medium optimizes the porosity distribution to reduce flow resistance and enhance condensation heat transfer.
It achieves efficient capture and sublimation of water vapor under extreme conditions, improves the space utilization and temperature stability of the cold trap, enhances the water ice collection rate and purity, reduces flow resistance, improves the energy and mass transfer synergy efficiency, and extends the service life of the cold trap.
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Figure CN120939601B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of cryogenic refrigeration technology and relates to a multi-level distributed cold trap based on the lunar environment. Background Technology
[0002] With the increasing urgency of deep space exploration missions to utilize water ice resources in situ, how to efficiently collect and store water ice in the extreme low temperature and thin pressure environments of the moon or other planets has become a key challenge that restricts the success or failure of long-term missions. Under the dual constraints of extreme low temperature environment and thin water vapor conditions, traditional water vapor capture technology faces a complex problem of thermodynamic imbalance, space limitation and phase change runaway.
[0003] Traditional water collection methods combining mechanical excavation with active heating suffer from high energy consumption, bulky equipment, and susceptibility to lunar dust contamination, making them unsuitable for the lightweight, low-power, and high-reliability requirements of deep space exploration. Existing passive cold trap technology, which captures and sublimates water vapor from the environment on a low-temperature surface, offers advantages such as no moving parts and low energy consumption. However, dynamic interference from fluctuations in radiative heat flow on the cold trap surface leads to a continuous competition between the water vapor sublimation rate and the solar radiation ablation rate, resulting in low water collection efficiency for single-point cold traps. Furthermore, the strict space constraints of lander payloads require high-density distributed deployment of cold trap systems within a limited volume. However, the high pressure drop caused by flow channel coupling effects in traditional array layouts severely hinders the directional migration efficiency of rarefied gases. Even more critically, the vapor escape phenomenon caused by the gradient distribution of the temperature and pressure field inside the arch shell directly threatens the reliability of the seal.
[0004] Because the collection efficiency of cold traps is affected by the thermal radiation characteristics of cold trap materials, structural layout and space heat and mass transfer coupling effect, especially under the constraint of a finite dome shell, the dynamic balance mechanism between the radiative heat load, vapor diffusion resistance and sublimation phase change efficiency of the cold trap system is not yet clear. This causes existing cold trap systems to face problems such as low sublimation rate, uncontrollable frost growth and unstable temperature and pressure inside the shell, which seriously restricts the sustainable collection and storage of lunar water ice resources.
[0005] Therefore, for future lunar base construction and Mars exploration missions, developing efficient distributed cold trap structures for water collection is not only a core breakthrough for realizing in-situ utilization of water resources, but also a necessary foundation for building a closed-loop life support system. It is expected that by revealing the multi-dimensional interaction law of cold trap materials, structure and environment, we can innovatively design distributed cold trap configurations, thereby breaking through the technical bottlenecks of water vapor collection efficiency and system stability under limited space constraints, and providing theoretical support and technical reserves for the autonomous power supply of deep space exploration equipment. Summary of the Invention
[0006] The purpose of this invention is to provide a multi-level distributed cold trap based on the lunar environment, which not only reduces vapor flow resistance and enhances the density of surface sublimation active sites, but also achieves spatial matching of heat flux density and vapor flux, improves energy and mass transfer synergy efficiency, and can buffer external radiation fluctuations, thereby maintaining the long-term stability of the internal temperature of the cold trap.
[0007] This invention is achieved through the following technical solution:
[0008] A multi-level distributed cold trap based on the lunar environment includes an arch shell, the inner surface of which is covered with a sealing film, and several cold trap units arranged in an array are installed on the inner surface of the arch shell.
[0009] The cold trap unit includes a skeleton, the outer side of which is attached to a sealing membrane, the inner side of which is the cold trap inlet and covered with a selectively permeable membrane with a molecular sieve effect, a microcapsule phase change layer fixedly disposed on the bottom surface of the skeleton, and a porous medium made of a high thermal conductivity material embedded inside the skeleton.
[0010] The porous medium is arranged inside the skeleton with a gradually varying porosity or a gradient porosity.
[0011] Furthermore, the cold trap units are arranged along the inner surface of the arch shell in a bisected, quadrated, octetated, or dodecetted circular arc, and several cold trap units located on the same bisected circular arc are connected end to end in sequence.
[0012] Furthermore, the cross-section of the cold trap unit is a curved shape formed by straight segments and curved segments, and the curvature of the curved segments matches the curvature of the arch shell.
[0013] The curved shape is a curved triangle, a curved trapezoid, a circular arc, or a sawtooth, wherein: the curved triangles corresponding to several cold trap units have equal widths, equal heights, or equal arc lengths; the curved trapezoids corresponding to several cold trap units have equal lower bases.
[0014] Furthermore, the cold trap inlet of the cold trap unit is arc-shaped, straight, bow-shaped, or corrugated.
[0015] Furthermore, the sealing film is a composite film of polyamide and polyethylene, a fluororubber film, a polychlorotrifluoroethylene film, or a modified polyurethane film.
[0016] Furthermore, the microcapsule phase change layer includes microcapsules and a phase change material encapsulated inside the microcapsules. The phase change material is any one or more of hydrated salts, straight-chain alkanes, polyethylene glycol, fatty alcohols, and fatty acids.
[0017] Furthermore, the high thermal conductivity material is copper, aluminum, and silicon.
[0018] Furthermore, the selectively permeable membrane is a molecular sieve membrane, a modified fluoropolymer membrane, a graphene-based separation membrane, or a polyacrylonitrile-based separation membrane.
[0019] Furthermore, the porous medium includes a high-porosity medium and a low-porosity medium arranged according to a gradual or gradient porosity.
[0020] The gradient porosity is either a decrease in porosity gradient or an increase in porosity gradient.
[0021] Furthermore, the arch shell is hemispherical.
[0022] The present invention has the following beneficial technical effects:
[0023] First, this invention integrates a microcapsule phase change layer and a selectively permeable membrane with a molecular sieve effect into the cold trap unit. Through the synergy between phase change energy storage and the molecular sieve membrane, a dual protection mechanism of "dynamic screening-thermal buffering" is formed. This ensures good operational efficiency even under extreme conditions such as large diurnal temperature variations and strong lunar surface radiation, thus extending its service life. Specifically: 1) The selectively permeable membrane precisely separates water vapor molecules and blocks impurity gases such as CO2 through sub-nanometer pore sizes, improving the purity of water ice and preventing pore blockage caused by impurity sublimation, effectively addressing the problem of gas cross-contamination in traditional physical adsorption materials; 2) The microcapsule phase change layer efficiently absorbs external radiation fluctuations through solid-liquid phase change, controlling internal temperature fluctuations within the cold trap within a set range, improving temperature uniformity and maintaining long-term stability of the cold trap's operating temperature, providing a relatively constant temperature environment for water ice storage. Second, this invention integrates a gradient porous medium and a distributed array layout cold trap unit. This not only optimizes the spatial arrangement of the cold trap to achieve spatial matching of heat flux density and vapor flux, but also maximizes... This invention utilizes the space inside the domed shell and adjusts the pore distribution of the porous medium along the direction of water vapor flow. High-porosity regions reduce flow resistance, while low-porosity regions enhance sublimation heat transfer. This reduces vapor flow resistance while increasing the density of active sublimation sites on the surface, balancing permeation rate and phase change efficiency. Compared to traditional homogenized cold trap structures, this invention improves the synergistic efficiency of energy and mass transfer. Furthermore, the coupling of the high thermal conductivity porous medium with gradient pores increases the specific surface area, significantly improving the heat transfer coefficient. Combined with a flexible and low-temperature resistant sealing membrane, the synergistic effect of multiple factors significantly enhances the water ice collection rate. In summary, this invention, through multi-dimensional synergistic design from materials to structure, constructs a highly efficient, stable, and adaptable cold trap for water ice collection and storage. It improves the heat exchange and water collection efficiency of the cold trap, and its structure is reasonable, simple, and easy to implement. It provides reliable water resource security for deep space exploration and polar scientific research, and offers new technical support for water resource utilization in extreme environments. This marks a leap from single-function devices to integrated thermal and mass management platforms for cold trap systems, and its modular design gives rise to powerful scenario adaptability.
[0024] The multi-stage cold trap units of this invention are arranged closely in the arched shell space in the configuration of bi-, quadr-, octagonal, and dodecagonal circles, and combined with asymmetric cold trap unit shapes such as triangles and sawtooth shapes, which significantly improves space utilization and increases the functional density in a limited space.
[0025] This invention utilizes a low-temperature resistant membrane material to create a selectively permeable membrane, enabling the cold trap to maintain extremely high selective permeability over a wide temperature range. This allows for more efficient separation of water vapor molecules and reduces contamination of water vapor by other gases. Attached Figure Description
[0026] Figure 1 This is a schematic diagram of the arched shell structure of the multi-stage distributed cold trap of the present invention;
[0027] Figure 2 A cross-sectional view of the multi-stage distributed cold trap of the present invention. Figure 1 ;
[0028] Figure 3 A cross-sectional view of the multi-stage distributed cold trap of the present invention. Figure 2 ;
[0029] Figure 4 A cross-sectional view of the multi-stage distributed cold trap of the present invention. Figure 3 ;
[0030] Figure 5 A cross-sectional view of the multi-stage distributed cold trap of the present invention. Figure 4 ;
[0031] Figure 6 A cross-sectional view of the multi-stage distributed cold trap of the present invention. Figure 5 ;
[0032] Figure 7 A cross-sectional view of the multi-stage distributed cold trap of the present invention. Figure 6 ;
[0033] Figure 8 A cross-sectional view of a single cold trap unit of the present invention. Figure 1 ;
[0034] Figure 9 A cross-sectional view of a single cold trap unit of the present invention. Figure 2 ;
[0035] Figure 10 A cross-sectional view of a single cold trap unit of the present invention. Figure 3 ;
[0036] Figure 11 A cross-sectional view of a single cold trap unit of the present invention. Figure 4 ;
[0037] Figure 12 A cross-sectional view of a single cold trap unit of the present invention. Figure 5 ;
[0038] Figure 13 A cross-sectional view of a single cold trap unit of the present invention. Figure 6 ;
[0039] Figure 14 A cross-sectional view of a single cold trap unit of the present invention. Figure 7 ;
[0040] Figure 15 A cross-sectional view of a single cold trap unit of the present invention. Figure 8 ;
[0041] Figure 16 Top view of the multi-stage distributed cold trap of the present invention Figure 1 ;
[0042] Figure 17 Top view of the multi-stage distributed cold trap of the present invention Figure 2 ;
[0043] Figure 18 Top view of the multi-stage distributed cold trap of the present invention Figure 3 ;
[0044] Figure 19 Top view of the multi-stage distributed cold trap of the present invention Figure 4 .
[0045] In the figure: 1. Sealing membrane; 2. Dome shell; 3. Cold trap unit; 4. Microcapsule phase change layer; 5. Selective permeable membrane; 6. Porous medium; 61. Low porosity porous medium; 62. High porosity porous medium. Detailed Implementation
[0046] The present invention will be further described in detail below with reference to specific embodiments. These descriptions are for explanation purposes only and are not intended to limit the scope of the invention.
[0047] refer to Figures 1 to 19 As shown, the present invention provides a multi-level distributed cold trap based on the lunar environment, including a hemispherical arch shell 2, the inner surface of the arch shell 2 is covered with a sealing membrane 1, and several cold trap units 3 are installed on the inner surface of the arch shell 2 in an array. The cold trap unit 3 includes a skeleton, the outer side of the skeleton is attached to the sealing membrane 1, the inner side of the skeleton is the cold trap inlet and is covered with a selectively permeable membrane 5 with molecular sieve effect, a microcapsule phase change layer 4 is fixedly disposed on the bottom surface of the skeleton, and a porous medium 6 is embedded inside the skeleton, which serves as a carrier for water ice collection and storage.
[0048] like Figure 2 As shown, the cross-section of the skeleton is a curved shape formed by a horizontal straight line segment, a vertical straight line segment, and an arc segment. The curvature of the arc segment matches the arc shape of the arch shell. The length of the horizontal straight line segment in the cross-section of each skeleton is equal. For ease of description, [the text is incomplete and requires further context to translate accurately]. Figure 2 The curved shape in the diagram is simply called a curved triangle. Therefore, several cold trap units 3 arranged in an array can be regarded as several curved triangles of equal width arranged closely along the circumference of the arch shell 2. The length of the horizontal straight line segment of the cold trap unit 3 of the equal width curved triangle is constant, so that the bottom width of the microcapsule phase change layer of all cold trap units 3 in the array is consistent, which improves the synchronicity of the melting and solidification process of the phase change material and reduces the local thermal runaway caused by large temperature fluctuations in the horizontal direction.
[0049] like Figure 3As shown, the cross-section of the skeleton is a curved shape formed by two horizontal straight line segments, one vertical straight line segment, and one arc segment. The curvature of the arc segment matches the arc shape of the arch shell. The length of the horizontal straight line segment at the bottom of each skeleton cross-section is equal. For ease of description, [the text is incomplete and requires further context to translate accurately]. Figure 3 The curved shape in the diagram is simply called a curved trapezoid. Therefore, several cold trap units 3 arranged in an array are several equal-width curved trapezoids closely arranged around the circumference of the arch shell 2. The boundaries of the equal-width curved trapezoids of the cold trap units 3 extend towards the center of the sphere to expand the internal space, which can increase the heat exchange area and the density of the cold trap array, prolong the residence time of water vapor in the cold trap, and enhance the condensation heat transfer rate.
[0050] like Figure 4 As shown, the cross-section of the skeleton is a curved shape formed by a horizontal straight line segment, a vertical straight line segment, and an arc segment. The curvature of the arc segment matches the arc shape of the arch shell. The length of the vertical straight line segment in the cross-section of each skeleton is equal. For ease of description, [the text is incomplete and requires further context to translate accurately]. Figure 4 The curved shape in the diagram is simply called a curved triangle. Therefore, several cold trap units 3 arranged in an array can be regarded as several curved triangles of equal height arranged closely along the circumference of the arch shell 2. The vertical sections of the cold trap units 3 of the curved triangles of equal height have the same height, which improves the synchronicity of the melting and solidification process of the phase change material and reduces local thermal runaway caused by large temperature fluctuations in the height direction.
[0051] like Figure 5 As shown, the cross-section of the skeleton is a curved shape formed by a horizontal straight line segment, a vertical straight line segment, and an arc segment. The curvature of the arc segment matches the arc shape of the arch shell. The length of the arc segment in the cross-section of each skeleton is equal. For ease of description, [the text is incomplete and requires further context to translate accurately]. Figure 5 The curved shape in the diagram is simply called a curved triangle. Therefore, several cold trap units 3 arranged in an array can be regarded as several curved triangles of equal arc length arranged closely along the circumference of the arch shell 2. The curvature of the cold trap unit 3 of the curved triangle of equal arc length is constant, which can improve the uniformity of edge stress distribution of selective permeable membrane 5 and help reduce the probability of membrane material breaking during thermal cycling.
[0052] like Figure 6 As shown, the cross-section of the skeleton is an arc formed by two straight line segments and two circular arc segments. The curvature of the circular arc segments matches the arc shape of the arch shell. Several cold trap units 3 arranged in an array are several circular arcs closely arranged around the circumference of the arch shell 2. The continuous curvature of the circular arc-shaped cold trap units 3 can disperse thermal stress, reduce the risk of fatigue damage, and thus extend the service life of the cold trap under large temperature changes on the lunar surface.
[0053] like Figure 7As shown, the cross-section of the skeleton is a curved shape formed by two straight segments and one arc segment. The curvature of the arc segment matches the arc shape of the arch shell. Several cold trap units 3 arranged in an array are arranged in a serrated pattern on the inner surface of the arch shell 2. The serrated cold trap units 3 can guide water vapor from the upper part of the cold trap to the lower part of the cold trap by gravity, thereby enhancing the water vapor capture capability and inhibiting the accumulation of frost at the inlet.
[0054] like Figure 8 As shown, the cross-section of the skeleton is a curved shape formed by a straight line segment and an arc segment. The curvature of the arc segment matches the arc shape of the arch shell, so that the cold trap inlet of the cold trap unit 3 is a straight line.
[0055] like Figure 9 As shown, the cross-section of the skeleton is a curved shape formed by several straight line segments and one arc segment. The straight line segments are connected end to end to form a bow shape, and the curvature of the arc segment matches the arc shape of the arch shell, so that the cold trap inlet of the cold trap unit 3 is bow-shaped.
[0056] like Figure 10 As shown, the cross-section of the skeleton is a fan ring formed by two circular arc segments and two straight line segments. The curvature of the circular arc segments matches the arc shape of the arch shell, so that the cold trap inlet of the cold trap unit 3 is circular arc-shaped.
[0057] like Figure 11 As shown, the cross-section of the skeleton is a curved shape formed by a corrugated line segment and an arc segment. The curvature of the arc segment matches the arc shape of the arch shell. The cold trap inlet of the cold trap unit 3 is corrugated.
[0058] like Figures 12-15 As shown, the porosity of the porous medium 6 inside the cold trap unit 3 along the water vapor flow direction is designed with a non-uniform arrangement based on the principle of "high heat transfer efficiency and low flow resistance". Specifically, the high-porosity region is used to reduce flow resistance, while the low-porosity region is used to enhance sublimation heat transfer, balancing permeation rate and phase change efficiency. Therefore, the porous medium 6 inside the cold trap unit 3 is divided into a high-porosity medium 62 and a low-porosity medium 61, with their relative positions as follows: Figure 12 As shown, the low-porosity medium 61 is located to the left of the high-porosity medium 62, making the high-porosity medium 62 adjacent to the selectively permeable membrane 5, and the porous medium 6 inside the cold trap unit 3 is arranged with a gradually changing porosity; as Figure 13 As shown, the low-porosity medium 61 is located to the left of the high-porosity medium 62, making the high-porosity medium 62 adjacent to the selectively permeable membrane 5, and the porous medium 6 inside the cold trap unit 3 is arranged with a gradient porosity; as shown Figure 14 As shown, the low-porosity medium 61 is positioned above the high-porosity medium 62, making the high-porosity medium 62 adjacent to the microcapsule phase change layer 4; as Figure 15As shown, the low-porosity medium 61 is located below the high-porosity medium 62, so that the low-porosity medium 61 is adjacent to the microcapsule phase change layer 4.
[0059] like Figures 16-19 As shown, the plurality of cold trap units 3 arranged in an array are uniformly arranged along the circumference of the arch shell 2 on its inner surface, specifically: as Figure 16 As shown, several cold trap units 3 are arranged along the bisected arc of the arch shell 2; as Figure 17 As shown, several cold trap units 3 are arranged along the four equally divided circular arcs of the arch shell 2; as Figure 18 As shown, several cold trap units 3 are arranged along eight equally divided circular arcs of the arch shell 2; as Figure 19 As shown, several cold trap units 3 are arranged along the twelve equally divided arcs of the arch shell 2; several cold trap units 3 located on the same equally divided arc are connected end to end in sequence.
[0060] Preferably, the sealing membrane 1 must simultaneously meet the requirements of flexibility, sealing performance, low temperature resistance, and structural stability. The sealing membrane 1 is a polyamide and polyethylene composite membrane, a fluororubber film, a polychlorotrifluoroethylene film, or a modified polyurethane film.
[0061] Preferably, the selectively permeable membrane 5 is made of a membrane material that combines molecular sieve effect, low temperature resistance, structural stability and low volatility. This membrane material includes, but is not limited to, molecular sieve membranes, modified fluoropolymer membranes, graphene-based separation membranes and polyacrylonitrile-based separation membranes.
[0062] Preferably, the microcapsule phase change layer 4 includes microcapsules and a phase change material encapsulated inside the microcapsules. The phase change material is any one or more of hydrated salts, straight-chain alkanes, polyethylene glycol, fatty alcohols, or fatty acids.
[0063] Preferably, the porous medium 6 is a metallic or non-metallic solid material with high thermal conductivity, including but not limited to copper, aluminum and silicon.
[0064] The arrayed multi-level distributed cold trap unit 3 with gradient porosity proposed in this embodiment can effectively improve the heat exchange and water collection efficiency of the cold trap. It has a simple structure, is easy to manufacture, and has the advantages of high reliability, light weight and small size, and has wide applicability.
Claims
1. A multi-level distributed cold trap based on the lunar environment, characterized in that, It includes an arch shell (2), the inner surface of which is covered with a sealing film (1), and several cold trap units (3) arranged in an array are installed on the inner surface of the arch shell (2). The cold trap unit (3) includes a skeleton, the outer side of which is attached to a sealing membrane (1), the inner side of which is the cold trap inlet and covered with a selectively permeable membrane (5) with a molecular sieve effect, a microcapsule phase change layer (4) is fixedly disposed on the bottom surface of the skeleton, and a porous medium (6) made of a high thermal conductivity material is embedded inside the skeleton. The porous medium (6) is arranged inside the skeleton with a gradually varying porosity or a gradient porosity.
2. The multi-level distributed cold trap based on the lunar environment according to claim 1, characterized in that, The cold trap units (3) are arranged along the bisection, quadrisection, octuplet or dodecuplet arcs of the arch shell (2) on the inner surface of the arch shell (2), and several cold trap units (3) located on the same bisection arc are connected end to end in sequence.
3. The multi-level distributed cold trap based on the lunar environment according to claim 1 or 2, characterized in that, The cross-section of the cold trap unit (3) is a curved shape formed by straight segments and curved segments, and the curvature of the curved segments matches the curvature of the arch shell (2). The curved shape is a curved triangle, a curved trapezoid, a circular arc or a sawtooth, wherein: the width, height or arc length of the curved triangles corresponding to several cold trap units (3) are equal; the lower base of the curved trapezoids corresponding to several cold trap units (3) is equal.
4. The multi-level distributed cold trap based on the lunar environment according to claim 1 or 2, characterized in that, The cold trap inlet of the cold trap unit (3) is arc-shaped, straight, bow-shaped, or corrugated.
5. The multi-level distributed cold trap based on the lunar environment according to claim 1 or 2, characterized in that, The sealing film (1) is a composite film of polyamide and polyethylene, a fluororubber film, a polychlorotrifluoroethylene film, or a modified polyurethane film.
6. The multi-level distributed cold trap based on the lunar environment according to claim 1 or 2, characterized in that, The microcapsule phase change layer (4) includes microcapsules and a phase change material encapsulated inside the microcapsules. The phase change material is any one or more of hydrated salts, straight-chain alkanes, polyethylene glycol, fatty alcohols, or fatty acids.
7. The multi-level distributed cold trap based on the lunar environment according to claim 1 or 2, characterized in that, The high thermal conductivity materials are copper, aluminum, and silicon.
8. The multi-level distributed cold trap based on the lunar environment according to claim 1 or 2, characterized in that, The selectively permeable membrane (5) is a molecular sieve membrane, a modified fluoropolymer membrane, a graphene-based separation membrane, or a polyacrylonitrile-based separation membrane.
9. The multi-level distributed cold trap based on the lunar environment according to claim 1 or 2, characterized in that, The porous medium (6) includes a high-porosity medium (62) and a low-porosity medium (61) arranged according to a gradual porosity or gradient porosity. The gradient porosity is either a decrease in porosity gradient or an increase in porosity gradient.
10. The multi-level distributed cold trap based on the lunar environment according to claim 1 or 2, characterized in that, The arch shell (2) is hemispherical.