Fuel cell seal structure with annular cavity and positioning bump and design method
Patent Information
- Application Number
- CN202311718641.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-12-14
- Publication Date
- 2026-10-30
- Estimated Expiration
- 2043-12-14
AI Technical Summary
[0005]本发明的目的就是为了克服上述现有技术存在的难以同时解决密封件装配偏差问题和保证密封件密封性能,以减缓密封件应力松弛速度的缺陷而提供一种具有环状空腔和定位凸起的燃料电池密封结构及设计方法
[0023]1、本发明提出的燃料电池密封结构中,阳极板和阴极板的对应位置上均设有多个流体腔口,流体腔口的周向和两极板的周向均设有密封凹槽,密封件与密封凹槽内壁接触,并且两极板对应位置的密封件互相连接、一体成型,相较于传统的分离式阴、阳密封件设计,一体包边的结构从根源上解决了分离式密封件的层内装配偏差问题,有效降低层内密封件不对中导致的应力分布不均匀,提高燃料电池密封性能及使用寿命;
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Figure CN117976934B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of hydrogen fuel cell technology, and in particular to a fuel cell sealing structure and design method having an annular cavity and positioning protrusions. Background Technology
[0002] Ultra-thin flexible metal electrode plates, multilayer polymer membrane electrode assemblies (MEAs), and precision-assembled seals are the core components of a hydrogen fuel cell unit. High-power proton exchange membrane fuel cells are typically assembled by stacking 400-500 individual cells to meet the high-power requirements of vehicles. Under precise compression ratios, the ultra-thin metal electrode plates and the MEA frame jointly compress the seals, forming sufficient contact stress and contact area to achieve a static seal at the complex rigid-flexible heterogeneous interface.
[0003] There are two main types of existing sealing structures: (1) a prefabricated or glued sealing structure with separate male and female electrodes formed by mold processing; and (2) a membrane electrode frame integrated sealing structure formed by injection molding. The sealing components in the above structures are generally made of electrically insulating rubber-like elastic polymer materials and rely on long-term external compression to generate sufficient interfacial elastic contact stress and contact area to form a stable seal. This can easily lead to stress relaxation of the compressed sealing components in the complex environment inside the fuel cell, resulting in a decrease in airtightness and thus affecting the normal use of the fuel cell stack. Chinese patent CN111224127A proposes an inner and outer core sealing structure made of multiple materials to alleviate the stress relaxation problem. However, the structure is only suitable for simple circular cross-section sealing structures, and its sealing performance is poor.
[0004] Furthermore, unavoidable assembly deviations during manufacturing can lead to significant stress relaxation in localized areas of the seals, and even large assembly deviations may cause leaks. Typically, ultra-thin metal electrode plates are stamped with sealing grooves for placing the seals. To prevent excessive compression of the seals after compression, which could damage the sidewalls of the sealing grooves, the width of the seals must be smaller than the width of the sealing grooves. Due to unavoidable assembly errors, it is difficult for the seals to fit perfectly in their theoretical positions. This results in the actual contact area of the seals on both sides of the membrane electrode being smaller than the theoretical area, thus reducing the gas tightness of the fuel cell. It also further exacerbates the uneven distribution of contact stress on the seal surface and accelerates stress relaxation in areas of high contact stress, thereby reducing the lifespan of the seals. Chinese patents CN111785988A and CN102804468A have made special designs for the contact surfaces of the seals, improving the sealing performance to some extent. However, they do not consider the negative impact of assembly deviations on sealing performance, nor do they consider the accelerated stress relaxation caused by uneven stress under long-term external compression. Therefore, how to effectively solve the assembly deviation problem of the seal while ensuring the sealing performance of the seal, and thus avoid the accelerated stress relaxation of the seal under long-term working conditions, has become a problem that needs to be solved in this field. Summary of the Invention
[0005] The purpose of this invention is to overcome the shortcomings of the prior art, which makes it difficult to simultaneously solve the problem of seal assembly deviation and ensure the sealing performance of the seal, so as to slow down the stress relaxation rate of the seal, and to provide a fuel cell sealing structure and design method with an annular cavity and positioning protrusions.
[0006] The objective of this invention can be achieved through the following technical solutions:
[0007] According to a first aspect of the present invention, a fuel cell sealing structure having an annular cavity and positioning protrusions is provided, comprising an anode plate, a cathode plate, a membrane electrode assembly, and a sealing element. The anode plate and the cathode plate each include a plurality of fluid ports. A sealing groove is provided in the circumferential direction of the edge of the anode plate, the circumferential direction of the edge of the cathode plate, and the circumferential direction of each fluid port. The sealing grooves are not interconnected. The positions of the sealing grooves on the anode plate and the sealing grooves on the cathode plate correspond one-to-one. The sealing element contacts the inner wall of the sealing groove. The sealing elements at corresponding positions on the anode plate and the cathode plate are interconnected. The membrane electrode assembly is snapped into the connection of the sealing elements of the two plates.
[0008] As a preferred technical solution, the sealing groove includes a groove bottom and a groove wall, and the sealing element is tightly fitted with the groove bottom at the corresponding position, with the width of the fitting area being smaller than the width of the groove bottom.
[0009] As a preferred technical solution, the sealing member includes a protrusion on the side near the membrane electrode assembly, and the outer end face of the protrusion is in close contact with the groove wall.
[0010] As a preferred technical solution, the protrusion, the bottom of the groove, and the groove wall form a cavity.
[0011] As a preferred technical solution, the sealing element is a gasket made of an electrically insulating rubber-like elastic polymer material.
[0012] As a preferred technical solution, both the anode plate and the cathode plate include an oxygen inlet, a cooling water inlet, a hydrogen inlet, an oxygen exhaust inlet, a cooling water outlet, and a hydrogen exhaust inlet.
[0013] As a preferred technical solution, the membrane electrode assembly includes a membrane electrode frame with an electrode layer and a membrane-electrode composite sandwiched between the membrane electrode frames, wherein a slot is provided at the connection point, and the end of the membrane electrode frame is fitted into the slot.
[0014] As a preferred technical solution, the height of the slot is equal to the thickness of the membrane electrode frame.
[0015] According to a second aspect of the present invention, a design method for the structure is provided, comprising the following steps:
[0016] S1, Obtain compression simulation parameters. The compression simulation parameters include material models, geometric models, and boundary conditions. The material models include constitutive models of polymer materials, proton exchange membrane frameworks, and metal bipolar plates. The geometric models include bipolar plate geometric models and sealing component geometric models. The boundary conditions include compression load, contact interface friction coefficient, internal and external air pressure, and initial cavity air pressure.
[0017] S2, Discretize the geometric model and perform compression simulation to obtain the contact stress and contact area of the contact surface between the seal and the inner wall of the sealing groove under compression, and obtain the current contact width and contact length.
[0018] S3, obtain the surface roughness, gas temperature, gas molar mass and sealing coefficient of the contact surface, and combine the current contact stress, pressure difference on both sides of the seal, contact width and contact length, and use the leakage rate prediction model to calculate the leakage rate and cavity pressure of the contact surface;
[0019] S4, determine whether the current cavity air pressure meets the stop condition. If not, return to S2; if yes, execute S5.
[0020] S5, when determining whether the current leakage rate meets the preset design requirements, if not, adjust the contact width and return to S2; if yes, output the current leakage rate and the current cavity pressure, and design the fuel cell sealing structure based on the corresponding parameters.
[0021] As a preferred technical solution, the leakage rate prediction model is the Ross model.
[0022] Compared with the prior art, the present invention has the following beneficial effects:
[0023] 1. In the fuel cell sealing structure proposed in this invention, multiple fluid ports are provided at corresponding positions of the anode plate and the cathode plate. Sealing grooves are provided in the circumferential direction of the fluid ports and the circumferential direction of the two plates. The sealing element contacts the inner wall of the sealing groove, and the sealing elements at corresponding positions of the two plates are connected to each other and integrally formed. Compared with the traditional separate anode and cathode sealing element design, the integrated edge structure solves the problem of in-layer assembly deviation of separate sealing elements from the root, effectively reduces the uneven stress distribution caused by misalignment of in-layer sealing elements, and improves the sealing performance and service life of fuel cells.
[0024] 2. This invention employs a structure in which the sealing element is tightly fitted to the bottom of the corresponding sealing groove, and the width of the fitting area is smaller than the width of the bottom of the sealing groove. Furthermore, the high-pressure side of the sealing element includes a protrusion, the outer end face of which is tightly fitted to the wall of the sealing groove. This allows the sealing element to form a first sealing surface and a second sealing surface with the bottom and wall of the sealing groove of the anode and cathode plates under the action of external compression load. When the external compression load is applied, the height of the sealing element decreases and the width increases. At the same time, a certain amount of pre-compression is formed between the protrusion and the groove wall. The multiple seals formed by the first sealing surface and the second sealing surface can effectively improve the airtightness of the fuel cell.
[0025] 3. The outer end face of the protrusion used in this invention fits tightly with the groove wall, so that the assembly accuracy of the membrane electrode assembly with sealing edge is not affected by the width difference between the sealing element and the sealing groove during the insertion of the cathode and anode plates. This can reduce the interlayer assembly error of the sealing element and effectively improve the airtightness of the fuel cell stack.
[0026] 4. In this invention, the protrusion, the bottom of the sealing groove, and the wall of the sealing groove form a cavity. This cavity is located between the flow field region and the external environment, and the air pressure value is also between the air pressure value of the flow field region and the air pressure value of the external environment. Under the action of the pressure difference, the protrusion is subjected to air pressure towards the bottom of the groove, which makes its outer end face fit more tightly with the wall of the sealing groove. This gives the sealing surface between the two a self-sealing effect that fluctuates with air pressure. That is, only when the fuel cell is working and the internal air pressure of the fuel cell increases, does the sealing surface play a sealing role. In other operating conditions where sealing is not required, the sealing surface is only subjected to a small pre-compression force, which shortens the time that the protrusion is under high compression conditions, alleviates the stress relaxation problem caused by long-term high compression, and increases the service life of the seal. Attached Figure Description
[0027] Figure 1 This is a schematic diagram of the structure of a single-layer battery seal in an embodiment of the present invention;
[0028] Figure 2 This is a top view of the metal electrode plate in an embodiment of the present invention;
[0029] Figure 3 This is a cross-sectional schematic diagram of the single-layer battery sealing structure in an embodiment of the present invention.
[0030] Figure 4 This is a cross-sectional schematic diagram of the fuel cell stack sealing structure in an embodiment of the present invention;
[0031] Figure 5 This is a cloud map of the equivalent stress results from numerical simulation under external compression only in an embodiment of the present invention;
[0032] Figure 6 This is an equivalent stress cloud diagram from a numerical simulation of the combined effects of external compression and air pressure in an embodiment of the present invention.
[0033] Figure 7 This is a flowchart illustrating the design method of the sealing structure in an embodiment of the present invention.
[0034] The components include: 1. Anode plate; 2. Cathode plate; 3. Membrane electrode assembly; 41. Plate edge seal; 42. Oxygen inlet seal; 43. Cooling water inlet seal; 11. Anode plate edge sealing groove; 12. Anode oxygen inlet sealing groove; 13. Anode cooling water inlet sealing groove; 14. Anode hydrogen inlet sealing groove; 15. Anode oxygen exhaust sealing groove; 16. Anode drain sealing groove; 17. Anode hydrogen exhaust sealing groove; 21. Cathode plate edge sealing groove; 22. 1. Cathode oxygen inlet sealing groove; 23. Cathode cooling water inlet sealing groove; 24. Cathode hydrogen inlet sealing groove; 25. Cathode oxygen exhaust chamber sealing groove; 26. Cathode drainage chamber sealing groove; 27. Cathode hydrogen exhaust chamber sealing groove; 411. Edge retaining groove; 412. Upper end face; 413. Lower end face; 414. Upper protrusion; 415. Lower protrusion; 416. First cavity; 417. Second cavity; 4141. Outer end face of upper protrusion; 4151. Outer end face of lower protrusion. Detailed Implementation
[0035] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are implemented based on the technical solution of the present invention, providing detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.
[0036] Example
[0037] This embodiment provides a fuel cell sealing structure with an annular cavity and positioning protrusions, such as Figure 1 As shown, the fuel cell is a single-layer cell. The sealed structure includes an anode plate 1, a cathode plate 2, a membrane electrode assembly 3, and sealing elements. The figure shows a partially enlarged view of the plate edge seal 41, the oxygen inlet seal 42, and the cooling water inlet seal 43. The membrane electrode assembly 3 includes a membrane-electrode composite with an electrode layer and a membrane electrode frame. The membrane electrode assembly 3 is sandwiched between the anode plate 1 and the cathode plate 2 and is snapped into place at the connection point of the two electrode seals. The sealing element is a gasket made of an electrically insulating, rubber-like elastic polymer material, which can be made of silicone rubber.
[0038] like Figure 2As shown, the anode plate 1 and cathode plate 2 each include six fluid inlets (oxygen inlet, cooling water inlet, hydrogen inlet, oxygen exhaust inlet, cooling water outlet, and hydrogen exhaust inlet). Each fluid inlet has a circumferential sealing groove, and the edges of both the anode plate 1 and cathode plate 2 also have circumferential sealing grooves. These sealing grooves are not interconnected. The positions of the sealing grooves on the anode plate 1 and the cathode plate 2 correspond one-to-one. The seals are in contact with the inner walls of the sealing grooves, and the corresponding seals on the anode plate 1 and cathode plate 2 are interconnected. Therefore, the single-layer battery has a total of 14 sealing grooves and 7 seals made of silicone rubber or similar materials. The 14 sealing grooves are as follows: anode plate edge sealing groove 11, cathode plate edge sealing groove 21, anode oxygen inlet sealing groove 12, cathode oxygen inlet sealing groove 22, anode cooling water inlet sealing groove 13, cathode cooling water inlet sealing groove 23, anode hydrogen inlet sealing groove 14, cathode hydrogen inlet sealing groove 24, anode oxygen exhaust chamber sealing groove 15, cathode oxygen exhaust chamber sealing groove 25, anode drainage chamber sealing groove 16, cathode drainage chamber sealing groove 26, anode hydrogen exhaust chamber sealing groove 17, and cathode hydrogen exhaust chamber sealing groove 27. Since the seals at corresponding positions on the two plates are interconnected, the 14 sealing grooves correspond to 7 seals, namely: plate edge seal 41, oxygen inlet seal 42, cooling water inlet seal 43, hydrogen inlet seal, oxygen exhaust seal, cooling water outlet seal, and hydrogen exhaust seal. The seven sealing grooves are not interconnected.
[0039] All of the aforementioned seals are swept annular structures. Figure 3 The plate edge seal 41 and the oxygen inlet seal 42 are shown. It can be seen that the cross-section of the swept annular structure is a rectangular shape with a cavity and positioning protrusions, and has a total of 4 structural features.
[0040] The first structural feature is an integrated edging with a rectangular cross-section, which integrates the cathode plate seal and the anode plate seal at corresponding positions. Taking the plate edge seal 41 as an example, the plate edge seal 41 includes an edge-sealing groove 411. Utilizing the elasticity of silicone rubber, the membrane electrode assembly 3 is connected to the plate edge seal 41 through the edge-sealing groove 411. The height of the edge-sealing groove 411 is equal to or slightly lower than the thickness of the membrane electrode frame to form an interference fit and prevent internal gas leakage; the depth of the edge-sealing groove 411 is half the total width of the cross-section of the plate edge seal 41.
[0041] The second structural feature is the upper end face 412 and the lower end face 413 of the plate edge seal 41. Both the upper end face 412 and the lower end face 413 are flat and respectively closely contact the bottom of the corresponding anode plate edge sealing groove 11 and the cathode plate edge sealing groove 21. Under the action of external compressive force, a first sealing surface is formed. The contact width of the upper end face 412 and the lower end face 413 is two-thirds of the contact width of the groove bottom to ensure that the lateral deformation of the seal during compression will not excessively compress the groove wall, thus preventing groove damage. Simultaneously, combined with... Figure 4 As shown, under the action of external load F, the upper end face 412 and the lower end face 413 make precise contact with the bottom of the corresponding anode plate edge sealing groove 11 and the bottom of the cathode plate edge sealing groove 21, respectively, forming a sufficient contact area and sufficient contact stress.
[0042] The third structural feature is a positioning protrusion, i.e., an upper and lower protrusion, provided on the side of the sealing element near the membrane electrode assembly 3. Taking the plate edge seal 41 as an example, its side near the membrane electrode assembly 3 includes an upper protrusion 414 and a lower protrusion 415. The outer end face 4141 of the upper protrusion and the outer end face 4151 of the lower protrusion are parallel to the groove wall of the anode plate edge sealing groove 11 and the groove wall of the cathode plate edge sealing groove 21, respectively, and are in contact with each other, forming a positioning surface and a second sealing surface, ensuring that the sealing element is accurately placed into the center position of the corresponding sealing groove when the membrane electrode assembly 3 with the sealing element is assembled.
[0043] The fourth structural feature is the cavity formed by the positioning protrusion, the bottom of the sealing groove, and the wall of the sealing groove. Taking the edge seal 41 as an example, its upper protrusion 414, together with the wall and bottom of the anode plate edge sealing groove 11, forms the first cavity 416, and its lower protrusion 415, together with the wall and bottom of the cathode plate edge sealing groove 21, forms the second cavity 417. For example... Figure 5 and Figure 6 As shown in the stress cloud diagram, when the fuel cell is working, the internal air pressure of the fuel cell increases. Under the action of the pressure difference, the upper protrusion 414 and the lower protrusion 415 are subjected to air pressure force towards the sealing groove, which makes the outer end face of the protrusion and the groove wall of the sealing groove more tightly fit together, thereby improving the sealing performance of the second sealing surface.
[0044] The aforementioned structural features improve the gas tightness of the fuel cell through multiple seals using both the first and second sealing surfaces. At the same time, the second sealing surface compensates for the impact of stress relaxation of the seals under long-term compression conditions on the lifespan of the first sealing surface under long-term performance characterization, thereby improving the service life of the fuel cell seal.
[0045] Furthermore, such as Figure 7 As shown, this embodiment also provides a design method for the aforementioned sealing structure, including the following steps:
[0046] Step S1: Determine the input parameters for the compression simulation, including the material model, geometric model, and boundary conditions. The material model includes the constitutive model of the polymer material, the linear elastic constitutive models of the proton exchange membrane framework and the metal bipolar plate (i.e., MEA and BPP linear elastic constitutive models); the geometric model includes the bipolar plate geometric model and the sealing component geometric model; the boundary conditions include the compressive load F, the contact interface friction coefficient f, the internal and external air pressures P0 and P1, and the initial cavity air pressure. Among them, a quadratic polynomial constitutive model can be adopted, as shown in equation (1):
[0047]
[0048] In the formula, W is the strain energy density; c 01 ,c 10 ,c 11 ,c 02 ,c 20 D1 and D1 are the coefficients of the quadratic polynomial constitutive model; and These are the first and second deviatoric strain invariants, and J is the volume ratio.
[0049] Step S2: Discretize the geometric model and perform compression numerical simulation to obtain the contact stress and contact area of the first and second sealing surfaces of the seal under compression, and obtain the current contact width and contact length.
[0050] Step S3: Input parameters such as the surface roughness A of the contact surface, gas temperature T, gas molar mass M, and sealing coefficient R, and combine them with the contact stress σ of the first sealing surface and the second sealing surface, the pressure difference Δp on both sides of the seal, the contact length L, and the contact width w obtained from numerical simulation. j j can be 1 or 2, corresponding to the contact width of the first sealing surface and the contact width of the second sealing surface, respectively. The leakage rate Q of the first and second sealing surfaces and the cavity air pressure are calculated using the leakage rate prediction model. Among them, the leakage rate prediction model is the Ross model, which is represented by equation (2):
[0051]
[0052] Step S4: Determine whether iterative calculation is needed based on equation (3):
[0053]
[0054] In the formula, δ1 is the convergence condition. If the above formula is not satisfied, it is considered that the cavity pressure P2 has not converged to the true value, and the cavity pressure obtained at the current iteration number i is... The next iteration is performed using the input conditions of the numerical simulation. Steps S2 to S3 are repeated until the above formula is satisfied, at which point the iteration ends. In order to make the cavity air pressure as close to the true value as possible, δ1 = 0.01 is taken, the external gauge pressure is 0 kPa, and the internal gauge pressure is 200 kPa, resulting in cavity air pressure P2 = 182 kPa.
[0055] Step S5: Compare the leakage rate obtained in the last step of the above iterative process with the design requirements. If the leakage rate does not meet the design requirements, the contact width of the first and second sealing surfaces of the seal needs to be readjusted, and steps S2 to S4 are repeated until the calculated leakage rate meets the design requirements. The final leakage rate is 0.036 ml·min. -1 ·mm -1 Compared to traditional single-seal structures, the leakage rate is reduced by 11.6%.
[0056] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.
Claims
1. A fuel cell sealing structure having an annular cavity and positioning protrusions, comprising an anode plate, a cathode plate, a membrane electrode assembly, and a sealing element, characterized in that, The anode plate and the cathode plate each include multiple fluid ports. A sealing groove is provided in the circumferential direction of the edge of the anode plate, the circumferential direction of the edge of the cathode plate, and the circumferential direction of each fluid port. The sealing grooves are not interconnected. The positions of the sealing grooves on the anode plate and the sealing grooves on the cathode plate correspond one-to-one. The sealing element contacts the inner wall of the sealing groove. The sealing elements at corresponding positions on the anode plate and the cathode plate are connected to each other. The membrane electrode assembly is snapped into the connection of the sealing elements of the two plates. The sealing groove includes a groove bottom and a groove wall. The sealing element is tightly fitted to the groove bottom at the corresponding position, and the width of the fitting area is smaller than the width of the groove bottom. The sealing element includes a protrusion on the side near the membrane electrode assembly, and the outer end face of the protrusion is in close contact with the groove wall; The protrusion, the bottom of the groove, and the groove wall form a cavity.
2. The fuel cell sealing structure with an annular cavity and positioning protrusions according to claim 1, characterized in that, The sealing element is a gasket made of an electrically insulating, rubber-like elastic polymer material.
3. The fuel cell sealing structure with an annular cavity and positioning protrusions according to claim 1, characterized in that, Both the anode plate and the cathode plate include an oxygen inlet, a cooling water inlet, a hydrogen inlet, an oxygen exhaust inlet, a cooling water outlet, and a hydrogen exhaust inlet.
4. The fuel cell sealing structure with an annular cavity and positioning protrusions according to claim 1, characterized in that, The membrane electrode assembly includes a membrane electrode frame with an electrode layer and a membrane-electrode composite sandwiched between the membrane electrode frames. The connection is provided with a slot, and the end of the membrane electrode frame is fitted into the slot.
5. The fuel cell sealing structure with an annular cavity and positioning protrusions according to claim 4, characterized in that, The height of the slot is equal to the thickness of the membrane electrode frame.
6. A design method for a fuel cell sealing structure as described in any one of claims 1-5, characterized in that, Includes the following steps: S1, Obtain compression simulation parameters. The compression simulation parameters include material models, geometric models, and boundary conditions. The material models include constitutive models of polymer materials, proton exchange membrane frameworks, and metal bipolar plates. The geometric models include bipolar plate geometric models and sealing component geometric models. The boundary conditions include compression load, contact interface friction coefficient, internal and external air pressure, and initial cavity air pressure. S2, Discretize the geometric model and perform compression simulation to obtain the contact stress and contact area of the contact surface between the seal and the inner wall of the sealing groove under compression, and obtain the current contact width and contact length. S3, obtain the surface roughness, gas temperature, gas molar mass and sealing coefficient of the contact surface, and combine the current contact stress, pressure difference on both sides of the seal, contact width and contact length, and use the leakage rate prediction model to calculate the leakage rate and cavity pressure of the contact surface; S4, determine whether the current cavity air pressure meets the stop condition. If not, return to S2; if yes, execute S5. S5, when determining whether the current leakage rate meets the preset design requirements, if not, adjust the contact width and return to S2; if yes, output the current leakage rate and the current cavity pressure, and design the fuel cell sealing structure based on the corresponding parameters.
7. The design method according to claim 6, characterized in that, The leakage rate prediction model is the Ross model.
Citation Information
Patent Citations
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