Double helix continuous variable diameter jacketed heat exchanger for dilution refrigerator and method of manufacture
By designing a double-helix continuous variable diameter tube heat exchanger, the problems of high parasitic heat loss and unstable flow in the dilution refrigeration machine are solved, achieving efficient countercurrent heat exchange and stable flow, thus improving the performance and reliability of the dilution refrigeration machine.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SHANGHAI INSTITUTE OF TECHNICAL PHYSICS CHINESE ACADEMY OF SCIENCES
- Filing Date
- 2026-04-03
- Publication Date
- 2026-07-17
AI Technical Summary
Existing dilution refrigerators with shell-and-tube heat exchangers suffer from high parasitic heat loss, unstable flow, and poor structural reliability in extremely low temperature environments, making it difficult to meet the design requirements of high-performance dilution refrigerators.
The double-helix continuous variable diameter shell-and-tube heat exchanger is adopted. The central inner tube is a spring-shaped primary helical structure, and the outer tube is a constant diameter structure throughout. The inner tube consists of a constant diameter section and a nonlinear gradually expanding section. The inner diameter expansion gradient is matched with the viscosity of the helium-3 Fermi fluid to form a nested double helix structure, which is manufactured by chemical micro-etching and CNC servo winding process.
Achieving efficient countercurrent heat exchange within a compact space reduces parasitic heat in the extremely low temperature region, thereby improving the overall performance and stability of the dilution chiller.
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Figure CN122408490A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of refrigeration and cryogenic engineering, and in particular to a double-helix continuous variable diameter tube heat exchanger for a dilution refrigeration machine and a method for manufacturing it. Background Technology
[0002] Dilution refrigerators primarily serve cutting-edge scientific and engineering fields such as superconducting quantum computing, fundamental research in condensed matter physics, and deep space exploration payloads, providing these fields with a long-term, continuously maintainable mK-level ultra-low temperature environment. The core performance indicators of a dilution refrigerator, such as its cooling efficiency, achievable minimum base temperature, and operational stability, are directly constrained by the performance of its internal heat exchangers. The shell-and-tube heat exchanger is the core component of the dilution unit in the dilution refrigerator; its core function is to utilize the recovered cooling capacity of the upward-flowing dilute-phase fluid to deeply pre-cool the downward-flowing dense-phase fluid, thus making it a key component determining the upper limit of the dilution refrigerator's performance.
[0003] Ideally, a shell-and-tube heat exchanger needs to perform the following three functions:
[0004] 1) High-efficiency countercurrent heat exchange. It is necessary to achieve near-ideal countercurrent heat exchange between the downward dense phase helium-3 fluid and the upward dilute phase helium-3 / helium-4 solution, so that the temperature of the dense phase helium-3 fluid before entering the mixing chamber is as close as possible to the operating temperature of the mixing chamber, and to maximize the utilization of the enthalpy difference cooling capacity of the dilution process;
[0005] 2) Extremely low parasitic heat generation. In mK-level extremely low temperature environments, it is necessary to minimize parasitic heat generated by fluid flow, such as viscous heat dissipation and heat conduction loss from pipe walls, to avoid losing the effective cooling capacity of the dilution process and ensure that the dilution refrigerator can reach a lower base temperature;
[0006] 3) Stable flow and structural reliability. The outlet fluid of the heat exchanger must have a stable flow rate and pressure to prevent high-speed fluid from impacting the porous medium of the downstream separated silver powder sintered heat exchanger, thus preventing medium damage and additional throttling heat generation, thereby ensuring the long-term stability of the dilution refrigerator.
[0007] Currently, the pre-stage heat exchangers of split-type silver powder sintered heat exchangers in dilution refrigerators mostly adopt spiral sleeve structures with constant or stepped diameter variations. Among them, the flow channel cross-section of the conventional constant-diameter central inner tube is constant throughout, and the viscous frictional resistance and power dissipation of the fluid flow increase sharply with the increase of fluid viscosity. In the extremely low temperature region, a large amount of parasitic heat is generated, which seriously reduces the effective cooling capacity of the dilution refrigeration process. Although the stepped diameter variation structure can reduce viscous dissipation to a certain extent through segmented diameter expansion, there are often abrupt changes in the flow channel cross-section at the diameter change, which can easily induce local eddies and throttling heating. At the same time, the stepped discrete diameter expansion cannot be precisely matched with the nonlinear continuous increase characteristic of helium-3 viscosity with decreasing temperature, and there is still a problem of excessively high local viscous dissipation, which is difficult to meet the design requirements of current high-performance dilution refrigerators. Summary of the Invention
[0008] The purpose of this invention is to provide a double-helix continuous variable diameter tube heat exchanger for a dilution refrigeration machine and a manufacturing method thereof, which mainly solves the problems existing in the prior art.
[0009] To achieve the above objectives, the technical solution adopted by the present invention is to provide a double-helix continuous variable diameter shell-and-tube heat exchanger for a dilution refrigerator, characterized in that it comprises a central inner tube and an outer tube; the double-helix continuous variable diameter shell-and-tube heat exchanger is a counter-current heat exchange structure, used as a pre-stage heat exchanger for a separate silver powder sintered heat exchanger of the dilution refrigerator; the dense phase fluid of the dilution refrigerator flows in the cooling direction within the central inner tube, and the dilute phase fluid flows in the opposite direction of heating within the annular gap between the outer tube and the central inner tube; the central inner tube is a spring-shaped primary helical structure, coaxially inserted into the inner cavity of the outer tube; the inserted central inner tube and the outer tube together constitute a secondary helix, forming a nested double helix structure; along the cooling flow direction of the dense phase fluid, the central inner tube is sequentially divided into an integrally formed constant diameter section and a nonlinear gradually expanding section; the outer tube is a seamless tube with a constant inner diameter throughout.
[0010] Furthermore, the inner diameter of the nonlinear expanding section expands nonlinearly and continuously along the flow direction of the dense phase fluid, and the expansion gradient of the inner diameter matches the nonlinear growth characteristic of the dynamic viscosity of the dense phase helium-3 Fermi fluid at extremely low temperatures as the temperature decreases.
[0011] Furthermore, the inner wall of the nonlinear expanding section is a continuous funnel shape without physical steps, and its inner diameter expansion gradient monotonically increases as the temperature of the dense phase fluid decreases.
[0012] Furthermore, the inner diameter expansion function of the nonlinear expanding section satisfies the following: at any axial position, its hydraulic diameter is directly proportional to the reciprocal of the temperature of the dense phase fluid at that position.
[0013] Furthermore, the constant diameter section corresponds to the high-temperature heat transfer zone of the dense phase fluid; the nonlinear gradually expanding section corresponds to the extremely low-temperature heat transfer zone of the dense phase fluid.
[0014] Furthermore, the total length of the central inner tube is more than twice the total length of the outer tube, and the pitch of the secondary helix is greater than the pitch of the primary helix.
[0015] The present invention also discloses a method for manufacturing the above-mentioned double-spiral continuous variable diameter tube heat exchanger for a dilution refrigeration machine, characterized by comprising the following steps:
[0016] Step S100: Based on the nonlinear growth characteristic of the dynamic viscosity of dense phase helium-3 Fermi fluid at extremely low temperatures as the temperature decreases, determine the inner diameter expansion function of the nonlinear expanding section of the central inner tube.
[0017] Step S200: Using a chemical micro-etching process, a gradually expanding section with a non-linearly continuously expanding inner diameter is processed at the end of the central inner tube to form the non-linear gradually expanding section.
[0018] Step S300: The central inner tube, after the nonlinear expanding section processing is completed, is wound into a primary spiral structure.
[0019] Step S400: Prepare the outer tube;
[0020] In step S500, the coiled inner central tube is coaxially nested and inserted into the inner cavity of the outer tube, and the inserted outer tube and the inner central tube are coiled together to form a secondary spiral structure, thus forming a nested double spiral structure.
[0021] Furthermore, in step S200, after processing the nonlinear expanding section using a chemical micro-etching process, the inner wall of the central inner tube is also polished, so that the inner wall of the nonlinear expanding section is a continuous trumpet shape without physical steps.
[0022] Furthermore, in step S300, the central inner tube is wound into a primary helical structure using a CNC servo winding process, and the maximum outer diameter of the primary helical structure is controlled to be smaller than the inner diameter of the outer tube, and the axial length of the primary helical structure is matched with the total length of the outer tube.
[0023] Furthermore, in step S500, when the central inner tube is coaxially nested and inserted into the inner cavity of the outer tube, while applying a pulling force at the traction end, a follow-up torque is applied in accordance with the geometric direction of the primary spiral, so that the central inner tube is smoothly screwed into the inner cavity of the outer tube.
[0024] In view of the above technical features, the present invention provides a double-spiral continuous variable diameter sleeve heat exchanger for a dilution refrigerator and a manufacturing method thereof, which have the following significant advantages compared with the prior art: the present invention can significantly increase the heat exchange area in a compact space, thereby achieving efficient countercurrent heat exchange; at the same time, it reduces parasitic heat in the extremely low temperature region and provides a certain degree of protection for the rear-end separated silver powder sintered heat exchanger, so as to effectively improve the overall performance of the dilution refrigerator. Attached Figure Description
[0025] Figure 1 This is a schematic diagram of a preferred embodiment of the double-helix continuous variable diameter tube heat exchanger for a dilution refrigeration machine according to the present invention;
[0026] Figure 2 This is a schematic diagram of the central inner tube in a preferred embodiment of the double-helix continuous variable diameter sleeve heat exchanger for a dilution refrigeration machine according to the present invention.
[0027] Figure 3This is an assembly diagram of a preferred embodiment of the double-spiral continuous variable diameter sleeve heat exchanger for a dilution refrigeration machine of the present invention (without secondary spiral winding).
[0028] Figure 4 This is a schematic diagram of the overall structure of a preferred embodiment of the double-helix continuous variable diameter tube heat exchanger for a dilution refrigeration machine according to the present invention.
[0029] Figure 5 In a preferred embodiment of the double-spiral continuous variable diameter shell-and-tube heat exchanger for a dilution refrigeration machine of the present invention, the dynamic viscosity of the dense phase helium-3 fluid as a function of temperature is matched with the nonlinear gradually expanding section inner diameter curve.
[0030] Figure 6 This is a flowchart of a preferred embodiment of the manufacturing method of a double-helix continuous variable diameter shell-and-tube heat exchanger for a dilution refrigeration machine according to the present invention.
[0031] In the diagram: 1 - inner central tube, 2 - outer tube;
[0032] 11 - Constant diameter section, 12 - Nonlinear gradually expanding section. Detailed Implementation
[0033] The present invention will be further described below with reference to specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. Furthermore, it should be understood that after reading the teachings of this invention, those skilled in the art can make various alterations or modifications to the invention, and these equivalent forms also fall within the scope defined by the appended claims.
[0034] Please see Figures 1 to 5 This invention discloses a double-spiral continuous variable-diameter shell-and-tube heat exchanger for a dilution refrigerator, used as a pre-stage heat exchanger for a separate silver powder sintered heat exchanger in the dilution refrigerator. As shown in the figure, a preferred embodiment includes a central inner tube 1 and an outer tube 2, forming a counter-current heat exchange structure. Generally, the dense phase fluid flows in the cooling direction within the central inner tube 1, while the dilute phase fluid flows in the heating direction in the opposite direction within the annular gap between the outer tube 2 and the central inner tube 1, thereby achieving efficient counter-current heat exchange between the dense and dilute phase fluids. This allows for deep pre-cooling of the descending dense phase fluid using the recovered cooling capacity of the ascending dilute phase fluid.
[0035] The central inner tube 1 is a spring-shaped primary helical structure, coaxially inserted into the inner cavity of the outer tube 2. Then, the inserted central inner tube 1 and outer tube 2 together form a secondary helix, creating a nested double helix structure. This nested double helix structure significantly increases the heat exchange area within a limited installation space, while simultaneously inducing secondary flow to enhance heat transfer. The total length of the central inner tube 1 is more than twice the total length of the outer tube 2, and the pitch of the secondary helix is greater than the pitch of the primary helix.
[0036] Specifically, the central inner tube 1, along the cooling flow direction of the dense phase fluid, is sequentially divided into an integrally formed constant-diameter section 11 and a non-linearly expanding section 12. The constant-diameter section 11 corresponds to the high-temperature heat transfer zone of the dense phase fluid and is a seamless metal tube with a constant inner diameter throughout. The non-linearly expanding section 12 corresponds to the extremely low-temperature heat transfer zone of the dense phase fluid. In this embodiment, the constant-diameter section 11 corresponds to the heat transfer temperature zone of the dense phase fluid from 1 K to 150 mK, while the non-linearly expanding section 12 corresponds to the extremely low-temperature heat transfer temperature zone of the dense phase fluid below 150 mK.
[0037] The inner wall of the nonlinear expanding section 12 is a continuous funnel shape without physical steps. Its inner diameter expands nonlinearly and continuously along the flow direction of the dense phase fluid. Its expansion gradient matches the nonlinear growth characteristic of the dynamic viscosity of the dense phase helium-3 Fermi fluid at extremely low temperatures as the temperature decreases, and it increases monotonically as the temperature of the dense phase fluid decreases. Specifically, at any axial position of the nonlinear expanding section 12, its hydraulic diameter is directly proportional to the reciprocal of the temperature of the dense phase fluid at that location.
[0038] In this embodiment, the inner central tube 1 is made of CuNi material with high yield strength, with an inner diameter of 0.6 mm to 0.75 mm, a wall thickness of 0.1 mm to 0.4 mm, and a total length of 6.0 m to 8.0 m. A nonlinear expanding section 12 is located at the end of the inner central tube 1, with a length controlled to be 20 cm to 50 cm. The outer tube 2 is made of 316 stainless steel material with low thermal conductivity, and its processing parameters are: inner diameter of 4.0 mm to 4.5 mm, wall thickness of 0.2 mm to 0.4 mm, and total length of 2.5 m to 3.0 m.
[0039] With the above structure, the double-helix continuous variable diameter sleeve heat exchanger for the dilution refrigerator in this embodiment can achieve efficient countercurrent heat exchange in a compact space. At the same time, the nonlinear gradually expanding section 12 effectively reduces the parasitic heat generated by viscous dissipation in the ultra-low temperature region and protects the downstream split silver powder sintered heat exchanger.
[0040] Please see Figure 1 and Figure 6 This embodiment also provides a method for manufacturing a double-helix continuous variable diameter shell-and-tube heat exchanger for a dilution refrigeration machine, used to manufacture the double-helix continuous variable diameter shell-and-tube heat exchanger as described in Embodiment 1. A preferred embodiment includes the following steps:
[0041] Step S100: Determine the inner diameter expansion function of the nonlinear gradually expanding segment.
[0042] Based on the nonlinear growth characteristic of the dynamic viscosity of dense-phase helium-3 Fermi fluid at extremely low temperatures as the temperature decreases, the inner diameter expansion function of the nonlinear expanding section 12 of the central inner tube 1 is determined.
[0043] Specifically, when the fluid temperature drops below 150 mK, the dense-phase helium-3 fluid deeply enters the Fermi degenerate state, and its dynamic viscosity follows... The temperature rises sharply, while the Carpitza thermal resistance at the solid-liquid interface follows... The temperature increases sharply. To prevent the heat generated by the fluid's mechanical work from offsetting the cooling capacity, the following physical inequality constraint must be satisfied at any axial position of the nonlinear expanding segment 12:
[0044]
[0045] In the formula, The nominal dense phase volumetric flow rate, The effective temperature difference of the near-wall thermal boundary layer. axial position of the flow channel Temperature of the dense phase fluid at that location To prevent thermal breakdown, in this embodiment, Take a value of 1.5. Substitute this into the dynamic viscosity. The Carpitza thermal resistance at the solid-liquid interface follows Temperature change characteristics, theoretical optimal inner diameter Strictly proportional to .
[0046] Step S200: Process the nonlinear gradually expanding segment.
[0047] High-yield-strength CuNi material is selected as the capillary blank for preparing the central inner tube 1. In this embodiment, the inner diameter of the capillary blank is 0.6 mm to 0.75 mm, the wall thickness is 0.1 mm to 0.4 mm, and the total length is 6.0 m to 8.0 m. Specifically, the blank size is a capillary with an inner diameter of 0.6 mm, a wall thickness of 0.2 mm, and a total length of 8.0 m. The central inner tube 1 is divided into a constant-diameter section 11 and a non-linearly expanding section 12, wherein the non-linearly expanding section 12 is located at the end of the central inner tube 1, and its length is controlled to be 20 cm to 50 cm, preferably 40 cm.
[0048] First, a dynamic controlled chemical micro-etching process is used to machine a non-linearly expanding segment 12 at the end of the central inner tube 1, characterized by a continuously expanding inner diameter. During the machining process, the etching depth is monitored in real time to control the accuracy of the inner diameter expansion, ensuring that the deviation between the inner diameter expansion curve and the theoretical design value is less than ±5%, and that it is precisely fitted with the inner diameter expansion function determined in step S100. Then, a fluid-state flexible polishing process is used to polish the inner wall of the central inner tube 1, resulting in a continuous trumpet-shaped inner wall without physical steps in the non-linearly expanding segment 12.
[0049] Step S300: Wind the primary spiral structure.
[0050] The central inner tube 1, after the nonlinear expanding section 12 has been processed, is coiled into a primary spiral structure.
[0051] In this embodiment, a CNC servo winding process with flexible spacer wire is used to wind the central inner tube 1 into a primary helical structure. The flexible spacer wire is a high-strength metal wire with a diameter of 0.05 mm to 0.1 mm. The helical pitch is precisely controlled by controlling the feed speed and winding angle of the flexible spacer wire. At the same time, the maximum outer diameter of the primary helical structure is controlled to be smaller than the inner diameter of the outer tube 2, and the axial length of the primary helical structure matches the total length of the outer tube 2.
[0052] Step S400: Prepare outer tube 2.
[0053] The outer tube 2 is made of 316 stainless steel with low thermal conductivity. Since the dilute phase is a superfluid helium-3 / helium-4 solution, the viscous dissipation in the flow channel can be ignored. Therefore, there is no need to optimize the flow resistance by changing the diameter. The outer tube 2 is processed into a seamless metal tube with a constant inner diameter throughout. The processing parameters are controlled as follows: inner diameter 4.0 mm, wall thickness 0.2 mm, and total length 2.6 m.
[0054] Step S500: Nest and coil the secondary spiral structure.
[0055] The coiled inner tube 1 is coaxially nested within the inner cavity of the outer tube 2. During assembly, a high-strength, flexible guide wire penetrating the outer tube 2 is used to connect the front end of the inner tube 1. Simultaneously, anhydrous ethanol is introduced as a lubricating medium into the annular gap between the outer tube 2 and the inner tube 1. While applying a uniform pulling force at the traction end, a follow-up torque is applied in accordance with the geometric direction of the primary helix, allowing the inner tube 1 to smoothly screw into the outer tube 2. The magnitude of the follow-up torque is determined based on the pitch of the primary helix and the elastic modulus of the material, ensuring that the torsional stress of the inner tube during screwing is less than 50% of the material's yield strength, thereby preventing irreversible tensile distortion of the primary helix pitch due to frictional stress.
[0056] After the nesting is in place, a high-purity helium-4 cleaning gas flow is introduced to completely evaporate the lubricating medium and ensure the cleanliness of the cryogenic flow channel. The purity of the high-purity helium-4 cleaning gas flow is greater than 99.999%, and the cleaning time is 10 to 30 minutes.
[0057] Finally, a pipe bender is used to coil the outer pipe 2 and the central inner pipe 1 together into a secondary spiral structure, forming a nested double spiral structure.
[0058] Through the above steps, the double-helix continuous variable diameter shell-and-tube heat exchanger for dilution refrigerators prepared in this embodiment has a nested double-helix structure. The inner diameter expansion gradient of the nonlinear expanding section 12 of the central inner tube 1 matches the nonlinear growth characteristics of the dynamic viscosity of dense phase helium-3 Fermi fluid at extremely low temperatures, which can achieve efficient countercurrent heat exchange and effectively reduce parasitic heat in extremely low temperature environments.
[0059] The above description is merely a preferred embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural or procedural transformations made based on the content of the present invention's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of the present invention.
Claims
1. A double-helix continuous variable diameter shell-and-tube heat exchanger for a dilution refrigeration machine, characterized in that, It comprises a central inner tube and an outer tube; the double-helix continuous variable diameter sleeve heat exchanger is a counter-current heat exchange structure, used as a pre-stage heat exchanger for a separate silver powder sintered heat exchanger of a dilution refrigerator; the dense phase fluid of the dilution refrigerator flows in the cooling direction within the central inner tube, while the dilute phase fluid flows in the heating direction in the opposite direction within the annular gap between the outer tube and the central inner tube; the central inner tube is a spring-shaped primary helical structure, coaxially inserted into the inner cavity of the outer tube; the inserted central inner tube and the outer tube together form a secondary helix, forming a nested double helix structure; along the cooling flow direction of the dense phase fluid, the central inner tube is sequentially divided into an integrally formed constant diameter section and a non-linear gradually expanding section; the outer tube is a seamless tube with a constant inner diameter throughout.
2. The double-helix continuous variable diameter tube heat exchanger for a dilution refrigeration machine according to claim 1, characterized in that, The inner diameter of the nonlinear expanding section expands nonlinearly and continuously along the flow direction of the dense phase fluid, and the expansion gradient of the inner diameter matches the nonlinear growth characteristic of the dynamic viscosity of the dense phase helium-3 Fermi fluid at extremely low temperatures as the temperature decreases.
3. The double-helix continuous variable diameter tube heat exchanger for a dilution refrigeration machine according to claim 2, characterized in that, The inner wall of the nonlinear expanding section is a continuous funnel shape without physical steps, and its inner diameter expansion gradient increases monotonically as the temperature of the dense phase fluid decreases.
4. The double-helix continuous variable diameter tube heat exchanger for a dilution refrigeration machine according to claim 3, characterized in that, The inner diameter expansion function of the nonlinear gradually expanding section satisfies the following: at any axial position, its hydraulic diameter is directly proportional to the reciprocal of the temperature of the dense phase fluid at that position.
5. The double-helix continuous variable diameter tube heat exchanger for a dilution refrigeration machine according to claim 1, characterized in that, The constant diameter section corresponds to the high-temperature heat transfer zone of dense-phase fluid; the nonlinear gradually expanding section corresponds to the extremely low-temperature heat transfer zone of dense-phase fluid.
6. The double-helix continuous variable diameter tube heat exchanger for a dilution refrigeration machine according to claim 1, characterized in that, The total length of the central inner tube is more than twice the total length of the outer tube, and the pitch of the secondary helix is greater than the pitch of the primary helix.
7. A method for manufacturing a double-helix continuous variable diameter shell-and-tube heat exchanger for a dilution refrigerator as described in any one of claims 1 to 6, characterized in that, Includes the following steps: Step S100: Based on the nonlinear growth characteristic of the dynamic viscosity of dense phase helium-3 Fermi fluid at extremely low temperatures as the temperature decreases, determine the inner diameter expansion function of the nonlinear expanding section of the central inner tube. Step S200: Using a chemical micro-etching process, a gradually expanding section with a non-linearly continuously expanding inner diameter is processed at the end of the central inner tube to form the non-linear gradually expanding section. Step S300: The central inner tube, after the nonlinear expanding section processing is completed, is wound into a primary spiral structure. Step S400: Prepare the outer tube; In step S500, the coiled inner central tube is coaxially nested and inserted into the inner cavity of the outer tube, and the inserted outer tube and the inner central tube are coiled together to form a secondary spiral structure, thus forming a nested double spiral structure.
8. The manufacturing method according to claim 7, characterized in that, In step S200, after processing the nonlinear expanding section using chemical micro-etching, the inner wall of the central inner tube is also polished to make the inner wall of the nonlinear expanding section have a continuous trumpet shape without physical steps.
9. The manufacturing method according to claim 7, characterized in that, In step S300, the central inner tube is wound into a primary helical structure using a CNC servo winding process, and the maximum outer diameter of the primary helical structure is controlled to be smaller than the inner diameter of the outer tube. The axial length of the primary helical structure is matched with the total length of the outer tube.
10. The manufacturing method according to claim 7, characterized in that, In step S500, when the central inner tube is coaxially nested and inserted into the inner cavity of the outer tube, while applying a pulling force at the traction end, a follow-up torque is applied in accordance with the geometric direction of the primary spiral, so that the central inner tube is smoothly screwed into the inner cavity of the outer tube.