A hydrogen fuel nozzle and combustion chamber

By designing the nozzle and flame cylinder structure suitable for hydrogen fuel, the problems of uneven injection of hydrogen fuel and low combustion efficiency are solved, and the full mixing of hydrogen and air and efficient combustion are achieved.

CN116123563BActive Publication Date: 2025-05-09AECC HUNAN AVIATION POWERPLANT RES INST
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Patent Information

Application Number
CN202310172163.7
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2023-02-27
Publication Date
2025-05-09
Estimated Expiration
2043-02-27

AI Technical Summary

Technical Problem

Existing fuel nozzles and flame drums are not suitable for hydrogen fuel injection, resulting in uneven injection of hydrogen fuel in the combustion chamber and inefficient combustion efficiency.

Method used

A hydrogen fuel nozzle is designed, including a hydrogen distribution ring, an intake pipe and a hydrogen spray tube. A multi-row oblique hole is provided on the hydrogen spray tube to control the flow rate and angle of the hydrogen fuel. The end of the hydrogen spray tube is arranged as a spherical surface to reduce the formation of the return zone and cooperate with the specific structure of the flame barrel, including interlaced flange holes to enhance the mixing of air and hydrogen.

Benefits of technology

Through this design, the hydrogen fuel is uniformly controlled during the injection process, the temperature near the nozzle is reduced, ablation is avoided, and the hydrogen in the flame cylinder is fully mixed with the air, improving combustion efficiency and ignition stability.

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Abstract

The present invention belongs to the field of turbojet engines, and specifically relates to a hydrogen fuel nozzle and a combustion chamber. One type of hydrogen fuel nozzle includes a hydrogen distribution ring, an air intake pipe, and a hydrogen injection pipe, wherein the air intake pipe is connected to the hydrogen distribution ring, one end of the hydrogen injection pipe is connected to the hydrogen distribution ring, and the other end of the hydrogen injection pipe is closed; a plurality of hydrogen injection pipes are arranged, and the plurality of hydrogen injection pipes are evenly arranged on the hydrogen distribution ring, and the orientations of the plurality of hydrogen injection pipes are the same; an inclined hole is arranged around the hydrogen injection pipe. The nozzle of the present invention is suitable for injecting hydrogen fuel into the flame tube, and the inclined hole arranged on the nozzle can control the hydrogen fuel to be sprayed at an appropriate flow rate and angle, so that the sprayed hydrogen is more uniform.
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Description

Technical Field

[0001] The invention belongs to the field of turbojet engines, and in particular relates to a hydrogen fuel nozzle and a combustion chamber. Background Art

[0002] The nozzle and the flame tube are important components of the combustion chamber. The fuel nozzle in the combustion chamber of a conventional engine is responsible for atomizing the fuel delivered to the combustion chamber and spraying it into the flame tube for combustion. The new cycle engine concept replaces the existing fuel and other complex components with high specific heat and small molecular weight hydrogen fuel. This new engine can be used as a power system for supersonic cruise missiles, high-speed reconnaissance aircraft, long-range attack aircraft, and is also an ideal power system for the first stage of an orbital vehicle. It has great performance advantages and broad application prospects.

[0003] Since hydrogen fuel engines use gaseous hydrogen as fuel, the structure of the hydrogen fuel nozzle is different from that of conventional fuel nozzles, and the aerodynamic layout of the flame tube is also different from that of conventional combustion chambers. Therefore, the existing fuel nozzles and flame tubes are not suitable for hydrogen fuel, so it is necessary to design hydrogen fuel nozzles and flame tubes.

[0004] In view of this, the present invention is proposed. Summary of the invention

[0005] In order to solve the technical problems existing in the prior art, the present invention proposes a hydrogen fuel nozzle and a combustion chamber. The nozzle of the present invention is suitable for spraying hydrogen fuel into a flame tube. At the same time, the inclined holes arranged on the nozzle can control the hydrogen fuel to be sprayed to an appropriate flow rate and angle, so that the sprayed hydrogen is more uniform.

[0006] The present invention includes the following technical solutions:

[0007] In one aspect, the present invention provides a hydrogen fuel nozzle, comprising a hydrogen distribution ring, an air intake pipe, and a hydrogen injection pipe, wherein the air intake pipe is connected to the hydrogen distribution ring, one end of the hydrogen injection pipe is connected to the hydrogen distribution ring, and the other end of the hydrogen injection pipe is sealed;

[0008] The hydrogen injection pipes are provided in plurality, and the plurality of hydrogen injection pipes are evenly arranged on the hydrogen distribution ring, and the plurality of hydrogen injection pipes have the same orientation;

[0009] The hydrogen injection pipe is surrounded by inclined holes.

[0010] Furthermore, the inclined holes are arranged in multiple rows, and the inclined holes in two adjacent rows are arranged in a staggered manner.

[0011] Furthermore, the inclination angle of the inclined hole is 20°-25°.

[0012] Furthermore, a plurality of intake pipes are provided, and the plurality of intake pipes are evenly arranged on the hydrogen distribution ring.

[0013] Furthermore, the end of the hydrogen injection pipe is configured as a spherical surface.

[0014] Furthermore, it also includes a plug, and the end of the hydrogen injection pipe is sealed by the plug; the plug includes a hemispherical surface and a cylindrical boss, and the hemispherical surface is fixedly connected to the cylindrical boss;

[0015] The outer diameter of the cylindrical boss is matched with the inner diameter of the hydrogen injection pipe, and the cylindrical boss is arranged in the hydrogen injection pipe;

[0016] The diameter of the bottom surface of the hemispherical surface is equal to the diameter of the hydrogen injection pipe.

[0017] A second aspect of the present invention provides a combustion chamber, comprising a flame tube and the above-mentioned nozzle, wherein the flame tube comprises a flame tube head, an outer ring and an inner ring, the flame tube head is an annular structure, a mounting hole corresponding to a hydrogen spray pipe is arranged on the flame tube head, the outer edge of the flame tube head is connected to one end of the outer ring, and the inner edge of the flame tube head is connected to one end of the inner ring; the hydrogen spray pipe of the nozzle is connected to the mounting hole, and the oblique hole of the hydrogen spray pipe is located between the inner ring and the outer ring;

[0018] The inner ring is provided with a first air inlet hole; the outer ring is provided with a second air inlet hole.

[0019] Further, the first air inlet hole comprises a first circular hole and a first flange hole, and the first circular hole and the first flange hole are sequentially arranged on the inner ring from an end close to the flame tube head to an end far from the flame tube head;

[0020] The second air inlet hole includes a second flange hole.

[0021] Furthermore, the aperture of the first flange hole gradually decreases from one end close to the flame tube head to one end away from the flame tube head; and / or the aperture of the second flange hole gradually decreases from one end close to the flame tube head to one end away from the flame tube head.

[0022] Furthermore, the first circular holes are arranged in multiple rows, and two adjacent rows of first circular holes are arranged alternately; the first flanging holes are arranged alternately with the first circular holes, and the first flanging holes are arranged in multiple rows; and the second flanging holes are arranged in multiple rows.

[0023] By adopting the above technical solution, the present invention has the following advantages:

[0024] 1. The nozzle of the present invention is suitable for spraying hydrogen fuel into the flame tube. At the same time, the inclined holes arranged on the nozzle can control the hydrogen fuel to spray at an appropriate flow rate and angle, so that the sprayed hydrogen is more uniform.

[0025] 2. The end of the hydrogen spray pipe of the present invention is set as a spherical surface. The spherical surface can use the viscosity of the gas boundary layer to pull the gas sprayed from the row of inclined holes closest to the plug backward, avoiding the formation of a reflux zone rotating toward the head between the hole rows, thereby reducing the temperature near the nozzle in the flame tube and avoiding nozzle ablation.

[0026] 3. In the combustion chamber of the present invention, hydrogen and air can be fully mixed in the flame tube; the flanged holes on the flame tube can increase the injection depth of air in the flame tube, which is conducive to the mixed combustion of air and hydrogen.

[0027] 4. The second flange hole on the outer ring of the flame tube of the present invention gradually decreases in diameter from the end close to the flame tube head to the end away from the flame tube head, which can not only ensure that ignition will not fail due to excessive air, but also ensure that the fuel gas gradually obtains more mixed air during the flow to the outlet to achieve sufficient combustion.

[0028] 5. The first flange hole on the inner ring of the present invention has a relatively large aperture at one end close to the flame tube head, which can provide sufficient combustion-supporting air; the first flange hole has a relatively small aperture at one end away from the flame tube head and is close to the guide, so that the incompletely burned mixture is relatively reduced, avoiding excessive mixing that causes a decrease in the gas temperature.

[0029] 7. The nozzle structure of the present invention is small and compact, and has little effect on the flow field of the combustion chamber after being combined with the flame tube.

[0030] 8. The hydrogen spray pipe of the nozzle of the present invention is provided with multiple rows of inclined holes, which can evenly transport high-pressure hydrogen into the flame tube at a suitable speed.

[0031] 9. The relative relationship between the opening position of the flame tube of the present invention and the angular position of the nozzle can ensure that hydrogen and air are fully mixed in the flame tube, which is beneficial to combustion.

[0032] 10. The end of the hydrogen spray pipe of the present invention is configured as a spherical surface, which can affect the flow field of hydrogen after it is sprayed from the inclined hole and has a certain anti-ablation effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0034] Figure 1 A schematic diagram of the structure of a hydrogen fuel nozzle in an embodiment of the present invention Figure 1 ;

[0035] Figure 2 A schematic diagram of the structure of a hydrogen fuel nozzle in an embodiment of the present invention Figure 2 ;

[0036] Figure 3 Schematic diagram of the structure of the hydrogen injection pipe in the embodiment of the present invention;

[0037] Figure 4 This is a schematic diagram of the structure of the plug in an embodiment of the present invention;

[0038] Figure 5 A schematic diagram of the structure of a combustion chamber in an embodiment of the present invention Figure 1 ;

[0039] Figure 6 A schematic diagram of the structure of a combustion chamber in an embodiment of the present invention Figure 2 ;

[0040] Figure 7 It is a structural schematic diagram of the flame tube head in an embodiment of the present invention;

[0041] Figure 8 The structure of the flame tube in the embodiment of the present invention is shown in FIG. Figure 1 ;

[0042] Fig. 9 The structure of the flame tube in the embodiment of the present invention is shown in FIG. Figure 2 ;

[0043] In the accompanying drawings: 10-hydrogen distribution ring, 20-inlet pipe, 30-hydrogen injection pipe, 31-inclined hole, 40-plug, 41-hemispherical surface, 42-cylindrical boss, 50-flame tube, 51-flame tube head, 511-mounting hole, 52-outer ring, 521-second air inlet hole, 5211-second flange hole, 53-inner ring, 531-first air inlet hole, 5311-first circular hole, 5312-first flange hole. DETAILED DESCRIPTION

[0044] The following description provides many different embodiments or examples for implementing different features of the present invention. The components and arrangements described in the following specific examples are only used to simplify the present invention and are only used as examples, not to limit the present invention.

[0045] In the description of the present invention, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, "plurality" means multiple or more, unless otherwise clearly and specifically defined.

[0046] In the description of the present invention, it should be noted that, unless otherwise clearly specified and limited, the terms "installation", "connection", and "connection" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection, an electrical connection, or mutual communication; it can be a direct connection, or an indirect connection through an intermediate medium, it can be the internal connection of multiple components or the interaction relationship of multiple components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0047] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0048] like Figure 1 , Figure 2 As shown, the first aspect of this embodiment provides a hydrogen fuel nozzle, including a hydrogen distribution ring 10, an air intake pipe 20, and a hydrogen injection pipe 30, wherein the air intake pipe 20 is connected to the hydrogen distribution ring 10, one end of the hydrogen injection pipe 30 is connected to the hydrogen distribution ring 10, and the other end of the hydrogen injection pipe 30 is closed; a plurality of hydrogen injection pipes 30 are provided, and the plurality of hydrogen injection pipes 30 are evenly arranged on the hydrogen distribution ring 10, and the plurality of hydrogen injection pipes 30 have the same orientation (specifically, as shown in FIG. Figure 1 As shown, the hydrogen injection pipes 30 are vertically arranged on the plane where the hydrogen distribution ring 10 is located, and are all extended in one direction); the hydrogen injection pipes 30 are surrounded by inclined holes 31.

[0049] The inclined hole 31 of the hydrogen injection pipe can control the hydrogen to be sprayed at an appropriate flow rate and angle, and make the sprayed hydrogen more uniform, which is conducive to the full mixing and combustion of the hydrogen and the air in the flame tube 50.

[0050] It should be noted that the hydrogen distribution ring 10 is an annular structure, preferably a circular ring, which is more conducive to evenly arranging the hydrogen injection pipes 30.

[0051] Furthermore, if Figure 3 As shown, the inclined holes 31 are arranged in multiple rows, and the inclined holes 31 in two adjacent rows are arranged in a staggered manner.

[0052] Furthermore, if Figure 3As shown, the inclination angle of the inclined hole 31 is α (the inclination angle relative to the axis of the hydrogen injection pipe), and the inclination angle of the inclined hole 31 is 20°-25°. Based on this, the hydrogen gas can be fully mixed with the air in the flame tube 50. Of course, the above inclination angle is only the best implementation method, and other inclination angles that can achieve the purpose of the present invention should also be within the protection scope of the present invention.

[0053] Preferably, the inclined hole 31 has an inclination angle of 22°. Based on this, the inclined hole 31 can control the hydrogen to be ejected at an appropriate flow rate and angle, and make the ejected hydrogen more uniform, which is conducive to the full mixing and combustion of hydrogen and air in the flame tube.

[0054] Furthermore, a plurality of the air inlet pipes 20 are provided, and the plurality of air inlet pipes 20 are evenly arranged on the hydrogen distribution ring 10, so that the hydrogen received by the hydrogen distribution ring 10 is even, and the hydrogen entering the hydrogen injection pipe 30 through the hydrogen distribution ring 10 is even.

[0055] Furthermore, the end of the hydrogen injection pipe 30 is configured to be a spherical surface.

[0056] Furthermore, if Figure 4 As shown, it also includes a plug 40, and the end of the hydrogen injection pipe 30 is sealed by the plug 40; the plug 40 includes a hemispherical surface 41 and a cylindrical boss 42, and the hemispherical surface 41 is fixedly connected to the cylindrical boss 42; the outer diameter of the cylindrical boss 42 is adapted to the inner diameter of the hydrogen injection pipe 30, and the cylindrical boss 42 is arranged in the hydrogen injection pipe 30; the diameter of the bottom surface of the hemispherical surface 41 is equal to the diameter of the hydrogen injection pipe 30. Based on this, processing and manufacturing are more convenient, and production costs are reduced.

[0057] like Figure 5 , Figure 6 , Figure 7 As shown, the second aspect of this embodiment provides a combustion chamber, including a flame tube 50 and the nozzle, the flame tube 50 includes a flame tube head 51, an outer ring 52 and an inner ring 53, the flame tube head 51 is an annular structure, and a mounting hole 511 corresponding to the hydrogen injection pipe 30 is provided on the flame tube head 51, the outer edge of the flame tube head 51 is connected to one end of the outer ring 52, and the inner edge of the flame tube head 51 is connected to one end of the inner ring 53;

[0058] The hydrogen injection pipe 30 of the nozzle is connected to the mounting hole 511, and the inclined hole 31 of the hydrogen injection pipe 30 is located between the inner ring 53 and the outer ring 52;

[0059] The inner ring 53 is provided with a first air inlet hole 531 ; the outer ring 52 is provided with a second air inlet hole 521 .

[0060] Furthermore, the first air inlet hole 531 includes a first circular hole 5311 and a first flange hole 5312 , and the first circular hole 5311 and the first flange hole 5312 are sequentially arranged on the inner ring 53 from an end close to the flame tube head 51 to an end far from the flame tube head 51 .

[0061] The second air inlet hole 521 includes a second flange hole 5211 .

[0062] One end close to the flame tube head 51 includes a main combustion zone, and the temperature and fuel gas ratio of the main combustion zone need to be controlled; if the amount of air entering the main combustion zone is too large, or the air injection depth is too large, it will cause flameout, so the first circular hole 5311 and the second flange hole 5211 are used to control the air volume and injection depth to improve ignition efficiency and avoid flameout.

[0063] Furthermore, if Figure 8 As shown, the aperture of the first flange hole 5312 gradually decreases from one end close to the flame tube head 51 to one end away from the flame tube head 51; and / or the aperture of the second flange hole 5211 gradually decreases from one end close to the flame tube head 51 to one end away from the flame tube head 51.

[0064] Furthermore, unlike the case where the aperture of the first flange hole 5312 gradually decreases from the end close to the flame tube head 51 to the end far from the flame tube head 51, Fig. 9 As shown, the first flange holes 5312 are arranged in three rows, the apertures of the first flange holes in the two rows on the left in the figure are the same, and the aperture of the first flange holes 5312 in the rightmost row is smaller than the apertures of the first flange holes 5312 in the two rows on the left (i.e., the apertures of the two rows of first flange holes 5312 in the mixing zone decrease from left to right). Based on this, it is used to ensure the gas volume in the mixing zone.

[0065] Furthermore, the first circular holes 5311 are arranged in multiple rows, and two adjacent rows of first circular holes 5311 are arranged alternately; the first flanged holes 5312 are arranged alternately with the first circular holes 5311, and the first flanged holes 5312 are arranged in multiple rows; and the second flanged holes 5211 are arranged in multiple rows. Based on this, the depth and flow rate of the air entering the flame tube 50 can be controlled, which is more conducive to ignition and combustion.

[0066] Furthermore, the first circular holes 5311 are arranged in three rows, and the distances from any first circular hole 5311 in the first row to the two most adjacent hydrogen spray pipes 30 are equal. Based on this, an appropriate amount of evenly distributed air can be provided to the main combustion zone of the flame tube 50, which is conducive to ignition. Among them, the first row is the row of first circular holes 5311 closest to the flame tube head 51.

[0067] Preferably, Figure 8As shown, the first round holes 5311 are arranged in three rows, any two adjacent rows of the first round holes 5311 are arranged alternately, the first flange holes 5312 are arranged in three rows; the second flange holes 5211 are arranged in three rows; from right to left in the figure, they are respectively called the first row of first round holes 5311, the second row of first round holes 5311, and the third row of first round holes 5311; the first row of first flange holes 5312, the second row of first flange holes 5312, and the third row of first flange holes 5312; the first row of second flange holes 5211, the second row of second flange holes 5211, and the third row of second flange holes 5211; the first row of first flange holes 5312 and the first row of first round holes 5311 cooperate. Based on this, the amount of air injected into the main combustion zone and the injection depth can be better controlled.

[0068] Preferably, the first row of first flange holes 5312 and the third row of first circular holes 5311 are staggered, thereby making the air entering the flame tube 50 more uniform.

[0069] Of course, the above specific implementations are only examples. For example, providing a third circular hole and a third flange hole on the outer ring 52 and providing a fourth flange hole on the inner ring 53 should also be within the protection scope of the present invention.

[0070] It should be noted that the flanging hole is a well-known technology for those skilled in the art, but in the present invention, the flanging of the flanging hole is all facing outside the ring (that is, outside the outer ring 52 and outside the inner ring 53).

[0071] Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent substitutions for some of the technical features therein; and these modifications or substitutions do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A hydrogen fuel nozzle, characterized in that: It comprises a hydrogen distribution ring (10), an air intake pipe (20), and a hydrogen injection pipe (30), wherein the air intake pipe (20) is connected to the hydrogen distribution ring (10), one end of the hydrogen injection pipe (30) is connected to the hydrogen distribution ring (10), and the other end of the hydrogen injection pipe (30) is sealed; A plurality of hydrogen injection pipes (30) are provided, and the plurality of hydrogen injection pipes (30) are evenly arranged on the hydrogen distribution ring (10), and the plurality of hydrogen injection pipes (30) are oriented in the same direction; The hydrogen injection pipe (30) is surrounded by an inclined hole (31); The inclined holes (31) are arranged in multiple rows, and two adjacent rows of inclined holes (31) are arranged in a staggered manner; The end of the hydrogen spray pipe (30) is arranged as a spherical surface; the spherical surface can use the viscosity of the gas boundary layer to pull the gas sprayed from the row of inclined holes of the hydrogen spray pipe closest to the spherical surface backwards, thereby avoiding the formation of a reflow zone rotating toward the head of the flame tube between the rows of holes formed by the inclined holes, thereby reducing the temperature near the nozzle in the flame tube and avoiding nozzle ablation; The inclination angle of the inclined hole (31) is 20°-25°; The inclination angle is the inclination angle of the inclined hole (31) relative to the axis of the hydrogen injection pipe.

2. A hydrogen fuel nozzle as claimed in claim 1, characterized in that: A plurality of the air intake pipes (20) are provided, and the plurality of air intake pipes (20) are evenly arranged on the hydrogen distribution ring (10).

3. A hydrogen fuel nozzle as claimed in claim 1, characterized in that: It also includes a plug (40), and the end of the hydrogen injection pipe (30) is sealed by the plug (40); the plug (40) includes a hemispherical surface (41) and a cylindrical boss (42), and the hemispherical surface (41) is fixedly connected to the cylindrical boss (42); The outer diameter of the cylindrical boss (42) matches the inner diameter of the hydrogen injection pipe (30), and the cylindrical boss (42) is arranged inside the hydrogen injection pipe (30); The diameter of the bottom surface of the hemispherical surface (41) is equal to the diameter of the hydrogen injection pipe (30).

4. A combustion chamber, characterized in that: The invention comprises a flame tube (50) and a nozzle according to any one of claims 1 to 3, wherein the flame tube (50) comprises a flame tube head (51), an outer ring (52) and an inner ring (53), the flame tube head (51) being an annular structure, the flame tube head (51) being provided with a mounting hole (511) corresponding to a hydrogen injection pipe (30), the outer edge of the flame tube head (51) being connected to one end of the outer ring (52), and the inner edge of the flame tube head (51) being connected to one end of the inner ring (53); The hydrogen injection pipe (30) of the nozzle is connected to the mounting hole (511), and the inclined hole (31) of the hydrogen injection pipe (30) is located between the inner ring (53) and the outer ring (52); The inner ring (53) is provided with a first air inlet hole (531); and the outer ring (52) is provided with a second air inlet hole (521).

5. A combustion chamber according to claim 4, characterized in that: The first air inlet hole (531) comprises a first circular hole (5311) and a first flange hole (5312), and the first circular hole (5311) and the first flange hole (5312) are sequentially arranged on the inner ring (53) from an end close to the flame tube head (51) to an end far from the flame tube head (51); The second air inlet hole (521) comprises a second flange hole (5211).

6. A combustion chamber according to claim 5, characterized in that: The aperture of the first flange hole (5312) gradually decreases from one end close to the flame tube head (51) to one end away from the flame tube head (51); and / or the aperture of the second flange hole (5211) gradually decreases from one end close to the flame tube head (51) to one end away from the flame tube head (51).

7. A combustion chamber according to claim 5 or 6, characterized in that: The first circular holes (5311) are arranged in multiple rows, and two adjacent rows of first circular holes (5311) are arranged alternately; the first flanged holes (5312) are arranged alternately with the first circular holes (5311), and the first flanged holes (5312) are arranged in multiple rows; and the second flanged holes (5211) are arranged in multiple rows.

Citation Information

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