Integrated bending forming marine double-wall pipe and system and machining method thereof

By using integrated bending forming technology and vacuum maintenance mechanism, the problem of weld marks at the bend of marine double-walled pipes has been solved, realizing a marine double-walled pipe system with no weld seams, no leakage, low energy consumption, high-efficiency production and intelligent management.

CN122040968APending Publication Date: 2026-05-15GUANGDONG LINGSHI SHIP TECH CO LTD
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Patent Information

Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
GUANGDONG LINGSHI SHIP TECH CO LTD
Filing Date
2026-02-05
Publication Date
2026-05-15

AI Technical Summary

Technical Problem

Existing marine double-walled pipes have weld marks at bends, resulting in a large number of welds, high risk of leakage, difficulty in ensuring vacuum sealing, low production efficiency, high cost, high fluid resistance, poor precision and consistency, and low level of system intelligence.

Method used

Employing integrated bending forming technology, the design features weld-free elbows with an inner and outer tube coaxiality of ≤1mm, a bending radius of 2D≤R≤3D, a roundness of E≤3%, a maximum wall thickness reduction rate of T≤12%, and no visible wrinkles on the inner tube wall. Combined with elastic support components and a vacuum maintenance mechanism, weld-free bending forming is achieved, and online monitoring and management are implemented through a vacuum compensation pump and sensors.

Benefits of technology

Completely eliminate or significantly reduce the number of welds, improve the reliability and structural integrity of vacuum seals, achieve efficient automated production, reduce operating energy consumption, ensure product consistency and precision, facilitate installation, and enable real-time monitoring and centralized management of multiple pipelines.

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Abstract

The invention discloses an integrated bending forming marine double-wall pipe and a system and a machining method thereof. The distance between the inner pipe wall and the outer pipe wall of the double-wall pipe is 20-50 mm, and the double-wall pipe is provided with at least two elbows without welding marks; the system further comprises a vacuum maintenance mechanism. The machining method is used for manufacturing the double-wall pipe. According to the scheme, integral bending forming of the large-gap double-wall pipeline is achieved, the number of welding seams at the elbow of the marine double-wall pipeline system is thoroughly eliminated or greatly reduced, and the vacuum sealing reliability and the overall structural integrity of the marine double-wall pipeline system are remarkably improved; the problem that in the prior art, welding marks existing at the bent position of the double-wall pipeline cannot be eliminated is practically solved. And the vacuum maintenance mechanism can more accurately identify a fault pipeline and give an early warning in time, accurate and active vacuum maintenance is achieved by automatically starting a compensation program for the loop, and the safety and the operation and maintenance efficiency are greatly improved.
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Description

Technical Field

[0001] This invention relates to the technical field of marine double-walled pipes, and more particularly to integrally bent marine double-walled pipes, their systems, and processing methods. Background Technology

[0002] Against the backdrop of the shipbuilding industry's transformation towards green and low-carbon practices, low-flash-point fuels such as LNG, methanol, and ammonia have become mainstream alternative fuels. The pipeline systems that transport these fuels are the "lifeline" of ships, and their safety is paramount. Currently, the industry generally adopts double-walled pipe systems as a safe transport solution, consisting of an inner pipe (for transporting fuel) and an outer pipe (for protection), with an annular gap between the inner and outer pipes.

[0003] The annular gap is typically evacuated to a high vacuum to provide insulation. The vacuum interlayer minimizes cold leakage, preventing excessive evaporation and icing of the outer pipe. Another design involves an external mechanical ventilation system within the annular gap to prevent gas accumulation in case of leakage from the inner pipe. Simultaneously, elastic supports are required between the inner and outer pipes to maintain concentricity and prevent relative movement and vibration damage.

[0004] However, the current manufacturing of double-walled pipes, especially the elbows, mainly relies on traditional segmented welding processes. The specific process is as follows: first, using standard prefabricated elbows (such as 90° and 45° elbows), the inner and outer pipes are cut into corresponding sections. Then, through multiple welding operations, the straight pipe sections are connected to the elbows, and the elbows are connected to each other, ultimately assembling into the required three-dimensional pipe shape. This process is currently the mainstream method used by shipbuilding equipment manufacturers to produce double-walled pipes.

[0005] Specifically, the main drawbacks of existing technologies are as follows: 1. Numerous welds and high leakage risk: Each bend means that at least two welds are required on both the inner and outer pipes. A complex three-dimensional pipeline may have dozens of welds. Welds are the weakest link in the piping system, and there is an inherent risk of leakage due to welding defects, material fatigue, and low-temperature brittle fracture, which seriously threatens the safety of ships.

[0006] 2. Difficulty in ensuring vacuum sealing: Numerous welds significantly increase the probability of leakage in the vacuum interlayer. Even a single microscopic leak in a weld can cause the entire double-walled pipe system to malfunction, leading to insulation failure, energy waste, and potential safety hazards.

[0007] 3. Low production efficiency and high costs: Welding is a labor-intensive process that relies on highly skilled welders and has a long production cycle. Multiple clamping, positioning, and welding operations also lead to high labor and time costs.

[0008] 4. High fluid resistance and high energy consumption: The use of shaped elbows for welding will create obvious weld protrusions and abrupt changes in flow channels inside the pipe, increasing fluid transport resistance and thus increasing the energy consumption of fuel pumping.

[0009] 5. Poor precision and consistency: Welding thermal deformation is difficult to control precisely, resulting in poor dimensional accuracy and geometric tolerance consistency of the finished pipelines, which brings difficulties to the shipyard for installation.

[0010] 6. Low system intelligence and lack of effective status maintenance methods: Existing monitoring functions are mostly single, discrete local alarms, which cannot centrally manage multiple double-walled pipelines throughout the ship. More importantly, even if vacuum decay is detected, it can only provide an alarm and cannot automatically intervene. It still requires manual inspection of specific leaking pipelines and manual restoration operations, resulting in slow response and difficulty in quickly and accurately locating the source of the problem in complex pipeline systems.

[0011] Clearly, the root cause of the above-mentioned shortcomings lies in the presence of weld marks at the bends of the double-walled pipes. Therefore, how to eliminate the weld marks at the bends of the double-walled pipes has become an urgent problem to be solved. Summary of the Invention

[0012] The purpose of this invention is to provide a marine double-walled pipe system and its manufacturing method to solve the problem that the prior art cannot eliminate weld marks at the bends of double-walled pipes.

[0013] To address the aforementioned technical problems, in a first aspect, this invention proposes an integrally bent-formed marine double-walled pipe, wherein the coaxiality d of the inner and outer pipes of the double-walled pipe is ≤1mm; the double-walled pipe is provided with at least two weld-scar-free elbows; the bending radius R of the weld-scar-free elbows satisfies 2D≤R≤3D, where D is the outer diameter of the double-walled pipe; the roundness E of the weld-scar-free elbows is ≤3%; the maximum wall thickness reduction rate T of the weld-scar-free elbows is ≤12%; the inner wall of the weld-scar-free elbows has a structure without visible wrinkles; the integrally bent-formed marine double-walled pipe... The double-walled pipe includes an outer pipe, an inner pipe, and elastic supports; the outer pipe is sleeved over the inner pipe, and there is a gap of 20-50mm between the inner circumferential wall of the outer pipe and the outer circumferential wall of the inner pipe, forming a heat insulation cavity between the inner circumferential wall of the outer pipe and the outer circumferential wall of the inner pipe; multiple elastic supports are disposed in the heat insulation cavity, and the multiple elastic supports are arranged separately along the extension trajectory of the bent marine double-walled pipe, and some of the elastic supports are disposed adjacent to the end of the weld-free elbow.

[0014] Secondly, the present invention also proposes a marine double-walled piping system, including the double-walled pipe as described above and a vacuum maintenance mechanism. The vacuum maintenance mechanism includes a vacuum compensation pump, a vacuum valve, and a vacuum sensor. The pumping end of the vacuum compensation pump is connected to the heat-insulating cavity through the vacuum valve. The vacuum sensor is used to monitor the vacuum level in the heat-insulating cavity. When the measured vacuum level in the heat-insulating cavity exceeds a preset value, the marine double-walled piping system controls the vacuum compensation pump to perform vacuum compensation until the vacuum level in the heat-insulating cavity reaches the preset range.

[0015] Thirdly, the present invention also provides a method for manufacturing a marine double-walled pipe system, which is used to manufacture the above-mentioned marine double-walled pipe, comprising the following steps: S1. Based on the task requirements, design the specifications and parameters of the double-walled pipe; S2, connect and fix multiple elastic support members to the outer wall of the inner tube so that the multiple elastic support members are arranged separately along the length direction of the inner tube; then fit the inner tube into the outer tube so that the multiple elastic support members elastically abut against the inner wall of the outer tube, thereby forming a double-walled pipe. S3, install an eccentric end cap at one end of the double-walled pipe, and then fill the heat insulation cavity formed between the outer wall of the inner pipe and the inner wall of the outer pipe with filler until the filling rate of the filler reaches the requirement. S4, Install an eccentric end cap at the other end of the double-walled pipe to pre-compensate for the relative displacement of the outer pipe and the inner pipe on the axis caused by differential rebound; S5, using a pipe bending machine to bend the double-walled pipe using an over-bending process to form a weld-free elbow on the double-walled pipe; S6, Remove the eccentric end cap and clear the filler in the heat insulation cavity; S7, the vacuum maintenance mechanism is connected to the heat insulation cavity via the vacuum pump end.

[0016] In one embodiment, step S1 specifically includes: Obtain task parameters; based on the task parameters, select inner and outer tube materials; calculate the theoretical inner diameter based on flow rate and velocity requirements; calculate the minimum wall thickness based on thin-walled cylinder theory; calculate the final theoretical wall thickness based on the minimum wall thickness, combined with manufacturing tolerances, bending thinning, and corrosion allowance; select from the candidate library according to the theoretical inner diameter and the final theoretical wall thickness to obtain the final inner tube specification; verify the final inner tube specification using strength, flow capacity, and bending range as constraints; calculate the minimum annular gap between the inner circumferential wall of the outer tube and the outer circumferential wall of the inner tube based on the task parameters; and perform inner tube rupture testing... Furthermore, the pressure of the medium within the annular gap is calculated, and the maximum allowable gap is calculated in conjunction with the external pressure; the range of process-feasible gaps is determined based on a preset bending process database; the final annular gap is determined based on the minimum annular gap, the maximum allowable gap, and the range of process-feasible gaps; the inner diameter of the outer pipe is determined based on the inner pipe specifications and the final annular gap, and the wall thickness and outer diameter of the outer pipe are calculated in conjunction with the task parameters; the bending radius and bending angle of each bending segment are determined based on the three-dimensional pipeline layout information, and the springback compensation angle is determined; the maximum allowable spacing of the elastic support members of the straight pipe section is calculated based on the structural stiffness of the inner and outer pipes and the final annular gap.

[0017] The beneficial effects of this invention are as follows: 1. Completely eliminate or significantly reduce the number of welds at bends in marine double-wall piping systems.

[0018] 2. Significantly improves the vacuum sealing reliability and overall structural integrity of marine double-walled piping systems.

[0019] 3. Achieve high-efficiency, low-cost, and automated production of marine double-walled piping systems.

[0020] 4. Obtain a curved flow channel with smooth inner wall and low flow resistance, thereby reducing operating energy consumption.

[0021] 5. Ensure the product has extremely high consistency and precision, and is easy to install.

[0022] 6. The vacuum maintenance mechanism enables online real-time monitoring, centralized management, and independent control of multiple double-walled pipe circuits distributed on the ship. When a vacuum decay is detected in a specific circuit, the system can not only accurately identify the faulty pipe and issue a timely warning, but also automatically initiate a compensation program for that circuit, achieving precise and proactive vacuum maintenance, which greatly improves safety and operation and maintenance efficiency.

[0023] 7. Provide a readily available, low-cost, and high-performance temporary filler material to support the high-quality, large-scale implementation of the "one-step bending forming" process; 8. It can efficiently and reliably determine all key design parameters, process feasibility, safety redundancy and economy of double-walled tubes based on given working conditions, functional requirements and installation constraints. Attached Figure Description

[0024] Figure 1 This is a structural schematic diagram provided by an embodiment of the double-walled tube of the present invention; Figure 2 This is a schematic diagram of the structure provided in an embodiment of the marine double-walled pipe system of the present invention; Figure 3 yes Figure 2 A schematic diagram of the elastic support structure; Figure 4 This is a schematic diagram of the filling method provided by the processing method of the marine double-walled pipe system of the present invention; Figure 5 yes Figure 4 A schematic diagram of the eccentric end cap structure; Figure 6 This is a flowchart of the processing method of the present invention; Figure 7 This is a flowchart illustrating the steps of an embodiment of the present invention for calculating the inner tube specifications; Figure 8 This is a flowchart illustrating the steps of determining the annular gap in an embodiment of the present invention.

[0025] The attached figures are labeled as follows: 100. Double-walled pipe; 110. Insulated cavity; 120. Outer pipe; 130. Inner pipe; 140. Elastic support; 141. Base; 142. Spring; 143. Cap; 144. Guide post; 145. Arc-shaped mating surface; 150. Weld-free elbow; 200. Vacuum maintenance mechanism; 210. Vacuum compensation pump; 220. Vacuum valve; 230. Central control unit; 300. Filler; 400. Eccentric end cap. Detailed Implementation

[0026] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0027] Reference Figure 1 The present invention provides an integrally bent and formed marine double-walled pipe, specifically a double-walled pipe 100.

[0028] Regarding the aforementioned double-walled pipe 100, as Figure 1As shown, in this embodiment, the distance between the inner and outer walls of the double-walled pipe 100 is set to 20-50mm, thereby forming a heat insulation cavity 110. Specifically, the double-walled pipe 100 includes an outer pipe 120, an inner pipe 130, and elastic support members 140. The outer pipe 120 is sleeved on the outside of the inner pipe 130, and the inner peripheral wall of the outer pipe 120 and the outer peripheral wall of the inner pipe 130 form a heat insulation cavity 110. Multiple elastic support members 140 are disposed in the heat insulation cavity 110, and the multiple elastic support members 140 are arranged separately along the extension trajectory of the double-walled pipe 100.

[0029] For both the outer tube 120 and the inner tube 130, they are preferably made of austenitic stainless steel, specifically including but not limited to grades such as 304, 304L, 316, and 316L. This material selection scheme aims to fully utilize the excellent corrosion resistance and good low-temperature toughness of this type of steel to meet the requirements of marine environments and the transportation of low-temperature media.

[0030] Furthermore, the specifications of the outer pipe 120 and the inner pipe 130 strictly comply with the ASME B36.19 standard, ensuring that the outer pipe 120 and the inner pipe 130 have a regular annular gap, excellent structural compatibility, and interchangeability with other standard pipe interfaces on the ship after assembly. For example, it is preferable to set a gap of 20-50mm between the inner peripheral wall of the outer pipe 120 and the outer peripheral wall of the inner pipe 130. This large gap design provides sufficient space for obtaining the heat insulation cavity 110, which significantly improves the overall heat insulation performance of the double-walled pipe 100.

[0031] The core pairing examples are shown in Table 1 below (the pipe size standard is ASME B36.19): Table 1 The elastic support 140 is a core component that ensures the concentricity of the outer tube 120 and the inner tube 130 and participates in the rebound control. Figure 2 and Figure 3 As shown, in this embodiment, the elastic support 140 includes a base 141, a spring 142, and a cap 143. The base 141 is fixedly connected to the outer wall of the inner tube 130, and a guide post 144 extending from the base 141 to the inner wall of the outer tube 120 is provided on the base 141. The spring 142 is sleeved on the guide post 144 and compressed between the base 141 and the cap 143. The spring 142 is used to push the cap 143 to elastically abut against the inner wall of the outer tube 120. The cap 143 is made of heat-insulating material, and the surface of the cap 143 that abuts against the inner wall of the outer tube 120 is an arc-shaped abutment surface 145. The curvature of the arc-shaped abutment surface 145 matches the curvature of the inner wall of the outer tube 120.

[0032] In this embodiment, the base 141 is made of stainless steel and is fixed to the outer wall of the inner tube 130 by spot welding.

[0033] In this embodiment, the spring 142 serves as the core elastic element. It is made of high-performance stainless steel wire and undergoes a precise processing technique to maintain its elasticity in the long-term complex environment of a ship, with a fatigue life exceeding 105 cycles.

[0034] The specific settings for spring 142 can be found in Table 2 below: Table 2 In this embodiment, the cap 143 is a bowl-shaped polytetrafluoroethylene (PTFE) component, and its outer arc-shaped contact surface 145 forms a sliding fit with the inner wall of the outer tube 120. By selecting PTFE material with low thermal conductivity, the design can minimize the contact area with metal, effectively reduce the "thermal bridge" effect, and ensure the overall thermal insulation performance of the double-walled pipe 100.

[0035] It should be noted that one of the functions of the elastic support 140 is to enable the inner tube 130 to be suspended in the outer tube 120. Therefore, in order to ensure sufficient support for the inner tube 130 at all points, this embodiment not only sets multiple elastic support 140s separately arranged along the extension trajectory of the double-walled pipe 100, but also sets multiple elastic support 140s at the locations where the inner tube 130 is supported, so as to use multiple elastic support 140s to support the inner tube 130 at the same time.

[0036] For example, when using two elastic supports 140 to support a portion of the inner tube 130, the two elastic supports 140 can be respectively set on opposite sides of the inner tube 130; when using three elastic supports 140 to support a portion of the inner tube 130, the three elastic supports 140 can be arranged at the three endpoints of a triangle around the inner tube 130; when using four elastic supports 140 to support a portion of the inner tube 130, the four elastic supports 140 can be arranged at the four endpoints of a cross around the inner tube 130; that is, there are various ways to set the elastic supports 140, and technicians can choose according to specific needs.

[0037] It should also be noted that the aforementioned double-walled pipe 100 is provided with at least two weld-free elbows 150. All curved sections with varying spatial orientations are presented as "one-time continuous bending forming structures without butt welds", ensuring the integrity of the structure and the reliability of the seal. Moreover, multiple weld-free elbows 150 can be arranged in the same two-dimensional plane or in different planes to achieve a three-dimensional spatial arrangement, thereby meeting the complex pipe laying requirements of different application scenarios.

[0038] Furthermore, in order to ensure the structural integrity and stability of the double-walled pipe 100, this embodiment also provides some elastic support members 140 located adjacent to the ends of the weld-free elbow 150. For example, they can be located adjacent to only one end of the weld-free elbow 150, or adjacent to both ends of the weld-free elbow 150. Technicians can choose according to specific needs.

[0039] In addition, during the production of the aforementioned double-walled pipe 100, it is necessary to ensure that the various indicators of the double-walled pipe 100 meet the following requirements: 1. The coaxiality d of the inner and outer pipes of a double-walled pipe of 100 mm is ≤ 1 mm.

[0040] After the double-walled pipe 100 is bent to form a weld-free elbow 150, the coaxiality d of the outer pipe 120 and the inner pipe 130 in the entire annular cavity must be maintained at ≤1.0 mm, or less than 5% of the theoretical clearance on one side (whichever is smaller).

[0041] 2. The bending radius R of the weld-free elbow 150 satisfies 2D≤R≤3D, where D is the outer diameter of the double-walled pipe 100.

[0042] This range has been verified through precise calculations and process tests, achieving the best balance between preventing excessive thinning or cracking of the outer wall of the outer tube 120 and suppressing wrinkling of the inner side of the inner tube 130 due to pressure.

[0043] 3. The roundness E of the 150mm elbow without weld marks is ≤3%.

[0044] The roundness error E of any section after the double-walled pipe 100 is bent (i.e., the difference between its maximum and minimum outer diameter) shall not exceed 3% of the nominal outer diameter at that point. This standard aims to control cross-sectional distortion and provide a uniform gap between the outer pipe 120 and the inner pipe 130.

[0045] 4. The maximum wall thickness reduction rate T of the 150mm weld-free elbow is ≤12%.

[0046] The maximum wall thickness reduction rate T on the outer side of the 150° bend of the weld-free elbow must be strictly controlled within ≤12%. This limitation is based on the theory of plastic deformation of materials and engineering safety principles, aiming to prevent significant weakening of pipe wall strength due to excessive stretching, thereby ensuring the long-term structural safety of the pipeline under internal pressure and external load.

[0047] 5. The inner wall of the 150mm weld-free elbow has no visible wrinkles.

[0048] The inner wall surface of the weld-free elbow 150 is not allowed to have any visible wrinkles, wavy folds or dents.

[0049] In addition to the aforementioned double-walled pipes, this invention also provides a marine double-walled pipe system, see reference. Figure 2 It includes the aforementioned double-walled pipe and vacuum maintenance mechanism 200.

[0050] Regarding the vacuum maintenance mechanism 200, as Figure 2 As shown, in this embodiment, the vacuum maintenance mechanism 200 is connected to the heat insulation cavity 110, and the vacuum maintenance mechanism 200 is used to maintain the vacuum level of the heat insulation cavity 110 within a preset range.

[0051] Specifically, the vacuum maintenance mechanism 200 includes a vacuum compensation pump 210, a vacuum valve 220, and a vacuum sensor. The pumping end of the vacuum compensation pump 210 is connected to the heat insulation cavity 110 through the vacuum valve 220. The vacuum sensor is used to monitor the vacuum level in the heat insulation cavity 110. When the measured vacuum level in the heat insulation cavity 110 exceeds the preset value, the marine double-walled pipeline system controls the vacuum compensation pump 210 to perform vacuum compensation until the vacuum level in the heat insulation cavity 110 reaches the preset range.

[0052] It should be noted that the vacuum valve 220 can be a wired or wireless control model, and technicians can choose according to specific needs. For example, in this embodiment, the vacuum valve 220 used is a high vacuum remote control valve, so as to facilitate remote control.

[0053] Of course, the aforementioned vacuum maintenance mechanism 200 can not only monitor a single double-walled pipe 100, but also perform one-to-many monitoring and management; such as Figure 2 As shown, a central control unit 230 can be used as the "brain" of the vacuum system for all double-walled pipes 100 on the ship, simultaneously connecting to and polling multiple (N) independent double-walled pipes 100. A built-in database establishes independent vacuum level profiles and safety thresholds for each double-walled pipe 100. When any pipe's vacuum data becomes abnormal, the system can immediately and accurately locate and highlight the specific pipe that has malfunctioned on the central human-machine interface (HMI).

[0054] Furthermore, through distributed sensing and execution terminals (each pipeline is independently configured), each double-walled pipeline 100 is independently equipped with a vacuum sensor and a high-vacuum remote control valve, which facilitates the connection of the central control unit 230 with each terminal through the control network.

[0055] Finally, when the central control unit 230 detects that the vacuum level of the i-th double-walled pipe 100 exceeds the standard, it will issue a command to open only the high-vacuum remote control valve of the i-th pipe and start the shared or dedicated vacuum compensation device (such as the vacuum compensation pump 210) to perform vacuum compensation only on the i-th double-walled pipe 100. This avoids waste of resources and prevents cross-contamination between circuits.

[0056] Reference Figure 6The present invention also provides a processing method for manufacturing the above-mentioned integrally bent marine double-walled pipe, which specifically includes the following steps: S1. Based on the task requirements, design the specifications of the double-walled pipe; and obtain the corresponding straight pipes 120 and 130 that meet the length requirements. If the cleanliness of the outer pipe 120 and the inner pipe 130 does not meet the requirements, the outer pipe 120 and the inner pipe 130 need to be thoroughly cleaned, especially the inner wall of the outer pipe 120 and the outer wall of the inner pipe 130. S2, multiple elastic support members 140 are connected and fixed to the outer wall of the inner tube 130 so that the multiple elastic support members 140 are arranged separately along the length direction of the inner tube 130; then the inner tube 130 is inserted into the outer tube 120 so that the multiple elastic support members 140 elastically abut against the inner wall of the outer tube 120, thereby forming a double-walled pipe 100.

[0057] After the above operation is performed, the precision assembly of the internal core structure of the double-walled pipe 100 can be completed in a straight state. Moreover, since the base 141 of the elastic support 140 in this embodiment is supported by stainless steel, the elastic support 140 can be fixed to the outer wall of the inner pipe 130 by spot welding the base 141.

[0058] It should be noted that since the double-walled pipe 100 needs to be bent later, the fixing position of the elastic support 140 needs to be determined in advance to ensure that the setting position of the multiple elastic support 140 can meet the construction requirements.

[0059] S3, as Figure 4 and Figure 5 As shown, an eccentric end cap 400 is installed at one end of the double-walled pipe 100, and then filler 300 is filled into the heat insulation cavity 110 formed between the outer wall of the inner pipe 130 and the inner wall of the outer pipe 120 until the filling rate of filler 300 reaches the requirement. At this time, it is generally required that filler 300 fill or almost fill the heat insulation cavity 110.

[0060] It should be noted that the filler 300 used in this embodiment is natural sand. The natural sand can be washed, dried and screened before use so that the various performance indicators of the natural sand can reach a better state. Specifically, the particle size of the natural sand is preferably 0.06-0.25mm, the Mohs hardness of the natural sand is preferably not less than 7, and the uniaxial compressive strength of the natural sand is preferably not less than 50MPa.

[0061] To achieve continuous cold bending of double-walled tubes with a gap (20-50mm) in one go, and to ensure that there are no wrinkles and the roundness meets the standards after bending, this invention creatively proposes to fill the annular gap with a temporary support medium. The determination of the core parameters of this support medium (material, particle size, hardness, strength, and humidity) stems from an in-depth analysis of the mechanical requirements of the bending process and a comprehensive application of materials science. The derivation process is as follows: During the bending process, the filler must simultaneously meet the following core functions: Function 1 (Compression Support): On the outer side of the bend, it resists the stretching tendency of the inner tube to expand outward, preventing it from becoming unstable and wrinkling due to loss of support; on the inner side of the bend, it resists the collapse tendency of the outer tube to compress inward, preventing the cross-section from becoming excessively elliptic.

[0062] Function 2 (Stress Balance): When the double-walled pipe is subjected to bending stress, the supporting medium must behave like a uniform and continuous support to avoid uneven support, which could lead to localized stress imbalance, uneven deformation of the pipe wall, forming "dents" or "wrinkles", or even back tearing.

[0063] Function 3 (Flowable Dense): It must have good flowability during filling and subsequent cleaning to ensure that complex gaps can be filled quickly and thoroughly without dead corners and completely removed.

[0064] Function 4 (Chemical Inertness): It does not react chemically with the pipe wall of austenitic stainless steel (304 / 316L, etc.), thus avoiding contamination or corrosion of the pipe.

[0065] Function 5 (Economical and Environmentally Friendly): Widely available, low cost, reusable or easy to dispose of.

[0066] Derivation of key parameters: The selection of the particle size range primarily serves the goals of "fluid density" and "uniform force transmission." This stems from considerations of gap size and support uniformity. The single-sided width of the annular gap in the double-walled tube is 20-50mm. Filling this narrow annular gap with granules allows for bending, with the core objective of ensuring the supporting medium behaves as a uniform and continuous support under stress, avoiding uneven force transmission. The upper limit of the particle size is precisely to prevent the "particle arching effect," which disrupts this uniformity.

[0067] The theoretical constraints of particle arching effect and particle size / gap ratio: When particles accumulate in a confined space, they form a stable force chain structure near the opening or wall, dispersing the pressure from above to both sides, resulting in local stress discontinuity, just like forming an "arch bridge" in a sand pile.

[0068] Hazards to the bending process: If granular arches form within the annular gap, it will lead to uneven stress on the pipe wall. During bending, the support force at the top of the arch is strong, while the support force at the bottom of the arch is weak, which can easily cause uneven deformation of the pipe wall (especially the pressure-bearing inner side), forming "depressions" or "polygonalization" defects, severely damaging the roundness.

[0069] Key Ratio: Particle mechanics studies have shown that to fundamentally avoid the formation of stable particle arches within a gap channel, an important empirical criterion is that the ratio (G / d) of the minimum characteristic size of the channel (here, the width of the gap on one side) to the average particle diameter d should be sufficiently large. It is generally believed that when G / d > 20 ~ 30, the influence of boundary effects on the overall mechanical behavior of the particle system is significantly reduced, the system is closer to a "continuum," and it is less likely to form stable local force chain structures that affect macroscopic properties.

[0070] Derivation process: When the minimum single-sided gap When the particle size is 20mm, to ensure uniform support even in the narrowest gap, after repeated experiments, G / d = 80 was finally adopted as the lower limit of the design (this value is the best data after numerous experiments). At this point, the particle size d = 20 / 80 = 0.25mm. This experiment shows that when using particles with a particle size no larger than 0.25mm, in the smallest 20mm gap, the gap size is more than 80 times the particle size. This ensures that the particle system can be regarded as a continuous and uniform medium on a macroscopic level, which can smoothly and linearly transmit the pressure applied by the bending mold and the reaction force of the pipe wall, thereby effectively preventing local stress concentration and wall depression. However, the particle size cannot be infinitely small. Excessively fine powder (data from repeated experiments shows <0.06mm) has a large specific surface area, and the adsorption force between particles (van der Waals force, electrostatics) is enhanced, which will lead to poor flowability, easy bridging and voids during filling; difficult cleaning, and easy adsorption in the gaps of the pipe wall and elastic support. Based on this inference, the preferred particle size range is between 0.06mm and 0.25mm.

[0071] This embodiment sets the particle size to ≤0.25mm. To prevent uneven support and pipe wall deformation caused by the "particle arching effect," the required G / d ratio at the minimum gap is derived, thus deriving the theoretical value of the upper limit of the particle size. This theoretical value is tested throughout the entire process (filling → bending → cleaning) to confirm that it simultaneously meets the requirements of flowability and cleanability. Actual bending process tests verify that using particles within this particle size range, combined with appropriate hardness and strength, can consistently achieve the high-quality requirements of the bent cross-section.

[0072] The derivation of Mohs hardness directly serves the "compression support" function, preventing particles from being crushed under high pressure. During bending, the filler particles will bear extremely high local contact pressure. The Mohs hardness of stainless steel pipe walls (such as 304, 316) is approximately 5.5. According to materials science principles, to prevent the support medium from being pressed into or plowed by the steel under pressure (i.e., the medium hardness should be significantly higher than the supported body), the Mohs hardness of the support medium should be at least 1-2 levels higher than that of the pipe material. To ensure that the particles do not break under peak bending stress (breakage will lead to support failure, void formation, and uneven pressure), after repeated experiments, a Mohs hardness value of 6-15 is considered optimal. Silica in nature (… With a Mohs hardness of 7, it perfectly meets this requirement and is a widely found high-hardness mineral in nature. This hardness ensures that the particle's structure remains intact when subjected to bending stress, and the load is stably transmitted through the force chains between the particles.

[0073] The derivation of uniaxial compressive strength is crucial for quantifying the strength guarantee of the "compression support" function. During bending, the pressure exerted on the filler by the pipe wall is not uniform hydrostatic pressure, but rather extremely high local stress transmitted through point contact. To simplify the analysis, the most unfavorable condition (the compression zone of the outer pipe inside the bend) is simplified to a thick-walled cylinder under external pressure, whose circumferential compressive stress can be estimated using the Lamé formula. For typical marine double-walled pipe specifications and bending radii (R=3D), the peak compressive stress transmitted by the filler in this region, based on engineering estimations and empirical data feedback, can reach 30-40 MPa. To ensure absolute support reliability and prevent any particles from crushing under extreme conditions, this invention requires a sufficient margin in the compressive strength of a single filler particle. Through repeated testing, a range of 50-120 MPa was set, with a safety factor of approximately 1.25–1.67. This quantitative requirement filters out loose sedimentary sand with insufficient strength, pointing to quartz river or sea sand that has undergone long-distance water transport, has good roundness, few internal microcracks, and a dense structure. The uniaxial compressive strength of such sand grains can typically reach 60-100 MPa or even higher, fully meeting the support requirements.

[0074] Comprehensive Optimization and Innovative Approach: In summary, through repeated screening and testing, this invention transforms a common natural material—quartz sand of a specific specification—into a high-performance "flowable temporary mold material." Its parameter combination achieves a perfect balance in engineering applications. With a hardness of 6~15+ and a compressive strength of 50~120 MPa, it solves the mechanical problem of "being able to withstand pressure"; with a particle size of 0.06~0.25 mm, it solves the process problem of "filling completely and obtaining clean material"; and with the material being natural SiO2, it solves the material problems of "chemical compatibility" and "low cost".

[0075] The determination of the required sand weight per meter of the annular gap in the double-walled tube is crucial for ensuring full filling, uniform support, and cost control. This is because the double-walled tube of this invention requires filling the annular gap with dry natural sand as temporary support before bending and forming. The derivation is based on geometric volume and material bulk density, and the specific process is as follows: Sand condition: dry (optimal data from repeated tests: moisture content <0.9%), clean, with a particle size distribution of 0.06~0.25mm, meeting the aforementioned technical parameters.

[0076] In addition, the bulk density of sand is a key parameter, denoted as . (Unit: kg / m³). For qualified quartz sand, the typical bulk density after vibration compaction is 1550±50 kg / m³ (this value is the optimal value after repeated experiments).

[0077] Weight calculation formula: , in, G is the outer diameter of the inner tube (unit: m), and G is the width of one side of the annular gap (unit: m). The design value is usually between 0.02 and 0.05 m.

[0078] In summary, natural sand is not only chemically stable and inert, and does not react with austenitic stainless steel, but also, because it is formed under natural conditions, its unique spherical and multi-faceted particle shape is formed by years of water erosion. Therefore, after filling, it can form a stable support with high density, high compressive strength and excellent flowability, perfectly serving as a removable "internal mold". This provides a low-cost and efficient solution to the problem of instability of the inner tube 130 when bending.

[0079] When selecting filler 300, low-melting-point alloys, high-strength water-soluble ceramic core materials, or thermally decomposable polymer foams can also be used as filler 300, but natural sand has comprehensive advantages in terms of cost, environmental protection, and process adaptability.

[0080] S4. An eccentric end cap 400 is installed at the other end of the double-walled pipe 100 to pre-compensate for the relative displacement of the outer pipe 120 and the inner pipe 130 on the axis caused by differential rebound.

[0081] It should be noted that in S3 and S4, the eccentric end cap 400 with a specific eccentricity is installed at the end of the double-walled pipe 100, which can pre-compensate for differential springback in terms of geometry. The specific vector formula based on this is as follows: The pre-compensation amount e of the eccentric end cap 400 is e = -(ΔR_o - ΔR_i) + e_offset.

[0082] Wherein, ΔR_o is the outer tube springback displacement vector, which is a vector describing the direction and magnitude of the displacement of a point on the outer tube 120 (usually the mounting point of the eccentric end cap 400) from its position after bending and unloading to its final stable position; ΔR_i is the inner tube springback displacement vector, describing the springback displacement of the corresponding point on the inner tube 130; (ΔR_o-ΔR_i) is the relative springback displacement vector, which is the most crucial item. It directly represents the relative eccentricity between the outer tube 120 and the inner tube 130 after springback, and its direction points towards the outer tube 120 after springback. The offset direction relative to the inner tube 130; (ΔR_o-ΔR_i) is the pre-compensation vector. In order to counteract the above relative eccentricity, a pre-offset of equal magnitude and opposite direction needs to be applied during installation. This is the theoretical eccentricity that the eccentric end cap 400 needs to achieve; e_offset is the process fine-tuning offset, which is an empirical value used to compensate for system errors, such as the small creep of the elastic support 140, assembly gaps, and welding deformation. It is usually a small value, generally 0.1mm≤e_offset≤0.3mm.

[0083] The most crucial and complex part of the above vector formula is determining the springback displacement vector ΔR of the pipeline, which can be accomplished through the following steps: 1. Establish the geometric model of the curve. Idealizing the curved section as a circular arc, for a point on the pipe, its springback displacement vector ΔR mainly comes from the superposition of two parts.

[0084] The tangential displacement caused by the angle rebound is due to the bending angle rebounding from θ_b (the bending angle of the pipe before the bending process) to θ_f (the bending angle of the pipe after the bending process).

[0085] The normal displacement caused by radius springback is due to the bending radius springing back from ρ_b (the bending radius of the pipe before the bending process) to ρ_f (the bending radius of the pipe after the bending process).

[0086] 2. Calculation method of springback displacement vector ΔR Through geometric analysis, a general formula for calculating ΔR can be derived. For a bend in a pipe with a bending angle of θ and a bending radius of ρ, the springback displacement vector ΔR of the pipe can be calculated using the following formula: .

[0087] ρ_b is the bending radius of the pipe before springback after bending treatment; ρ_f is the bending radius of the pipe after springback after bending treatment; θ_b is the bending angle of the pipe before springback after bending treatment; θ_f is the bending angle of the pipe after springback after bending treatment; n is the normal unit vector pointing to the center line of the pipe bend; t is the tangential unit vector along the pipe axis. This represents the radial contraction displacement caused by the change in bending radius; This represents the tangential retraction displacement caused by the change in bending angle.

[0088] 3. Difference Calculation With the above calculation basis in place, ΔR_o and ΔR_i can both be obtained according to the calculation formula of ΔR.

[0089] Specifically, the parameters (ρ_b_i,ρ_f_i,θ_b_i,θ_f_i and ρ_b_o,ρ_f_o,θ_b_o,θ_f_o) of the outer tube 120 and the inner tube 130 are substituted into the above model to calculate the springback displacement vector ΔR_i of the inner tube 130 and the springback displacement vector ΔR_o of the outer tube 120.

[0090] Then, by substituting ΔR_o and ΔR_i into the core formula e=-(ΔR_o-ΔR_i)+e_offset, the magnitude and direction of the pre-compensation amount e required for the eccentric end cap 400 can be calculated.

[0091] S5, using a pipe bending machine to bend the double-wall pipe 100 using an over-bending process to form a weld-free elbow 150 on the double-wall pipe 100; that is, when the pipe bending machine performs bending, it does not stop bending at the theoretical design angle, but actively performs an "over-bending" process according to the predicted total springback amount Δθ, bending to a larger "target forming angle", and after the pipe material undergoes elastic springback, its final shape is exactly equal to the design requirements.

[0092] This process is achieved through a high-precision CNC system. The total springback amount Δθ is determined based on material properties (such as yield strength σy, elastic modulus E), geometric dimensions (such as pipe diameter D, wall thickness t), and process parameters (such as bending radius R). The springback amount Δθ of the pipe under these conditions is predicted through theoretical models and experimental data.

[0093] The calculation of the over-bending compensation angle is roughly as follows: I. Theoretical Basis and Formula Model The most classic and widely used theoretical model is the springback calculation formula that considers the relationship between bending moment and curvature.

[0094] 1. Curvature calculation model after springback For plastic bending, the curvature (ρ) after springback t ) and the curvature before rebound (ρ) t The following relationship exists between them: Where: ρ_b: radius of curvature of the neutral layer of the pipe during bending (i.e., the theoretical radius of the mold + the radius of the pipe); ρ_f: radius of curvature of the neutral layer of the pipe after springback (i.e., the actual radius we obtain); M: bending moment applied to the cross-section of the pipe before unloading; E: elastic modulus of the pipe; I: moment of inertia of the cross-section of the pipe (for a circular pipe, ... (where D is the outer diameter and d is the inner diameter).

[0095] This formula is the theoretical foundation for springback calculation. Its core idea is that the springback amount (1 / ρ_f - 1 / ρ_b) is proportional to the applied bending moment M and related to the material stiffness. Inversely proportional.

[0096] 2. Springback Angle Calculation Model According to geometric relationships, the bending angle (θ) is related to the radius of curvature (ρ) and the bending arc length (L): θ = L / ρ.

[0097] Therefore, the rebound angle Δθ can be expressed as: Substituting the first formula, we get: This formula clearly shows that the springback angle Δθ is directly proportional to the bending arc length L and the unloading bending moment M, and is related to the material stiffness. Inversely proportional.

[0098] II. Derivation of the Formula (Simplified) This derivation originates from the bending theory of beams and elastoplastic mechanics in mechanics of materials. It treats the pipe as a beam and makes the following assumptions: Plane section assumption: The cross section remains planar before and after bending.

[0099] The material is an ideal elastoplastic material, and its stress-strain relationship is known.

[0100] Bending moment calculation (M): During bending, when the deformation is large enough, the cross-section of the pipe is divided into a plastic zone and an elastic zone from the outside to the inside.

[0101] The bending moment M is the integral result of all stress elements on the cross section. It is a complex function of the material's yield strength σ_s, the cross section shape, and the bending curvature ρ_b. M increases as the curvature ρ_b decreases (the more severe the bending).

[0102] Uninstallation process: Unloading is considered as applying a virtual elastic moment that is equal in magnitude and opposite in direction to the initial bending moment M.

[0103] According to elasticity theory, the curvature change caused by this virtual bending moment is... .

[0104] Therefore, the curvature 1 / ρ_f after rebound is equal to the curvature 1 / ρ_b before rebound minus the curvature of elastic recovery. Thus, the core formula was derived. .

[0105] The difficulty lies in the fact that the bending moment M itself is a quantity with a highly nonlinear relationship to the curvature 1 / ρ_b, which depends on the precise plastic behavior of the material. This is why it can be described in theory, but is difficult to calculate directly and accurately.

[0106] III. Application Methods in Practical Engineering When a double-walled pipe is bent at 100°, the compensation angle (i.e., the over-bending angle θ_over) is determined through a combination of theoretical and experimental approaches.

[0107] Specifically, θ_over = θ_design + Δθ, where the process for determining Δθ is as follows: 1. Construct a process database (experimental calibration) This is the most crucial step. Process tests are conducted for each batch of materials and each combination of pipe diameter and wall thickness.

[0108] Specific operation: Cut a short tube sample, bend it on a tube bending machine with different die radii, record the die angle (θ_die), and then measure the actual angle after springback (θ_actual).

[0109] The rebound angle Δθ = θ_die - θ_actual is recorded directly.

[0110] A springback database was created by setting Δθ values ​​for different bending radii and angles.

[0111] 2. Implementation of differential springback compensation: For double-walled pipes, it is necessary to establish springback databases for the inner pipe 130 and the outer pipe 120 respectively.

[0112] When a pipe fitting with θ_design=90° needs to be bent, the database is consulted and it is found that under this condition, the inner tube 130 needs to be bent to 93°, and only after springback will it reach 90°.

[0113] A database query revealed that under these conditions, the outer tube 120 needs to be bent to 92.5° before springing back to 90°.

[0114] Therefore, the target value for "overbending" of a CNC pipe bending machine is not a single angle, but an optimized value that integrates the differential springback of the inner and outer tubes (e.g., 92.8°) to ensure that the inner and outer tubes reach 90° synchronously and are concentric after springback.

[0115] Therefore, the above operations can be summarized as follows: In S5, the over-bending process is performed based on θ_over=θ_design+Δθ.

[0116] θ_over is the actual bending angle during the bending process; θ_design is the expected bending angle of the double-walled pipe 100 after springback; Δθ is the compensation value provided by the springback database, which is used to output the specific value of Δθ based on θ_design, the input parameters of the outer pipe 120, and the input parameters of the inner pipe 130.

[0117] After obtaining the input parameters of the outer tube 120 from the springback database, the springback database will output the outer tube bending compensation angle θ_w.

[0118] After obtaining the input parameters of inner tube 130 from the springback database, the springback database will output the inner tube bending compensation angle θ_n.

[0119] At this time Δθ=(θ_w+θ_n) / 2.

[0120] For example, as mentioned above, "the outer tube 120 needs to be bent to 92.5°, and after springback it will be 90°", that is, at this time θ_w=92.5°-90°=2.5°.

[0121] Similarly, as mentioned above, "the inner tube 130 needs to be bent to 93°, and after springback it will be 90°", meaning that at this point θ_n = 93° - 90° = 3°.

[0122] S6, remove the eccentric end cap 400 and remove the filling material 300 in the heat insulation cavity 110. The removal method can be vibration, vacuum suction or high-pressure airflow purging.

[0123] S7, the vacuum maintenance mechanism 200 is connected to the heat insulation cavity 110 through the air extraction end; before installing the vacuum maintenance mechanism 200, chemical cleaning can be carried out in accordance with the standard "CB / T 4452-2016 Chemical Cleaning of Marine Stainless Steel Pipes".

[0124] In some feasible embodiments, step S1 specifically includes: S1.1, Obtain task parameters, including: type of conveying medium, flow rate requirements, flow velocity requirements, design pressure, temperature range, environmental conditions, requirements for handling annular gaps, design life, design flow rate, three-dimensional pipeline routing model, installation space limitations, etc.

[0125] S1.2, Select the inner tube material and outer tube material based on the task parameters.

[0126] Based on the corrosiveness of the medium, low-temperature toughness requirements, and bending processability, the materials for the inner and outer tubes are selected from the material database. Austenitic stainless steel series (such as 304, 304L, 316, 316L, etc.) or nickel-based alloys are preferred.

[0127] S1.3, Calculate the inner tube specifications and outer tube specifications based on the task parameters; S1.4, determine the final annular gap by combining task parameters, safety constraints and process-feasible gap range; S1.5, Determine the inner diameter of the outer tube based on the inner tube specifications and the final annular gap, and calculate the wall thickness and outer diameter of the outer tube in conjunction with the task parameters; S1.6. Based on the three-dimensional layout information of the pipeline, determine the bending radius and bending angle of each bending section, and determine the springback compensation angle. S1.7. Based on the structural stiffness of the inner and outer pipes and the final annular gap, calculate the maximum allowable spacing of the elastic support members of the straight pipe section.

[0128] In some feasible embodiments, the calculation process of the inner tube specification in S1.3 specifically includes the steps of calculating the theoretical inner diameter value, calculating the minimum wall thickness, calculating the final theoretical wall thickness, and selecting the final inner tube specification. The overall logical process is as follows: Figure 7 .

[0129] Formula for calculating the theoretical inner diameter: in, Indicates flow rate. Indicates flow rate, Indicates the theoretical inner diameter value; As the main pressure-bearing pipeline, the inner pipe's wall thickness must primarily meet the strength requirements of the internal medium's working pressure. Based on the thin-walled cylinder theory, its theoretical minimum wall thickness is calculated using the following formula: in, Indicates design pressure; Indicates the outer diameter of the inner tube; Indicates allowable stress; This represents the effective coefficient, which is 1.0 for seamless steel pipes; Initial estimation: Assuming outer diameter (Empirical coefficient); renew: ; Repeat this process until the change in the theoretical outer diameter is less than 0.01 mm, to obtain the theoretical inner diameter of the inner tube. and theoretical minimum wall thickness Taking into account manufacturing tolerances, bending thinning, and corrosion allowance, the final theoretical wall thickness is... for: Where a represents the manufacturing negative tolerance of the pipe wall thickness, usually taken as 12.5% ​​(according to ASME B36.19); b represents the bending wall thickness reduction rate (according to the process database); and c represents the corrosion allowance.

[0130] The corrosion allowance c is determined using a dual-track system: in, Indicates the minimum value required by the specification; Indicates the predicted value; Indicates the corrosion rate of the inner and outer walls (refer to the AMPP / EFC database); ER indicates the erosion rate; N indicates the design life. This represents the safety factor, which is between 1.5 and 2.0.

[0131] Candidate specifications are selected from the standard library based on the theoretical inner diameter and the final theoretical wall thickness: Theoretical outer diameter: Standard outer diameter Select a value not less than in ASME B36.19 And the closest standard value; Standard wall thickness T: Under the same outer diameter, select the wall thickness specification with nominal wall thickness T≥t and the most economical.

[0132] In some feasible embodiments, verification of the final inner tube specifications is also included: Verification 1, Strength after bending: If the requirements are not met, then select the next thicker standard wall thickness.

[0133] Verification 2, Actual flow capacity: Actual inner diameter: = - 2T; Actual flow velocity: v1 = 4Q / (π ²); The actual flow rate must not exceed the range specified in industry standards. If the flow rate is too high, select a larger outer diameter. If the flow rate is too low, choose a smaller outer diameter. .

[0134] Verification 3, Process Feasibility: Verification Is it within the bendable range? If it exceeds the bendable range, the design parameters need to be adjusted and recalculated.

[0135] In some feasible embodiments, the calculation process for the final annular gap is referred to Figure 8Specifically, it includes: S1.4.1, Based on the task parameters, calculate the theoretical minimum clearance using adiabatic performance: Set an insulation target: Ensure the total heat loss through the annular gap of the double-walled tubes. Below the allowable value To maintain system energy efficiency; to ensure the temperature of the outer surface of the outer tube. Temperature above ambient dew point This prevents condensation from forming.

[0136] Physical model construction: The annular gap of the double-walled tube is simplified as a closed cavity between two infinitely long concentric cylindrical surfaces. The heat transfer path includes: radiative heat transfer. Heat transfer occurs via electromagnetic waves and is related to the gap size; residual gas also contributes to heat transfer. Heat transfer occurs through gas molecules within the interlayer and is related to pressure and gap size; the total heat transfer is the sum of both and is a parallel superposition. = + .

[0137] Core constraints: According to the law of conservation of energy, heat is transferred from the inner tube through the annular gap and the outer tube wall to the environment, which must simultaneously satisfy the following: heat balance: = ,in Heat dissipation from the outer surface of the outer tube to the environment; Anti-condensation condition: outer wall temperature of the outer tube. > , This refers to the ambient dew point temperature.

[0138] Establishment of anti-condensation boundary conditions and determination of allowable heat flow: outer tube outer surface temperature ( ) and ambient temperature ( The heat transfer mechanisms are natural convection and thermal radiation, which can be combined into a single overall heat transfer coefficient. (A conservative estimate is usually taken, covering typical values ​​for hot and humid marine environments), and its environmental heat transfer equation is: in: This refers to the outer surface area of ​​the outer tube.

[0139] Establish the relationship between anti-condensation and allowable heat flow: To prevent condensation, a minimum allowable temperature is set for the outer surface of the outer pipe. : = +Δ Where: Δ For safety margin, 1-3K is usually taken.

[0140] Substitute this temperature into the heat transfer equation on the ambient side, and the maximum allowable heat flux density of the system is derived as : = = ·( ) Up to this point, the safety requirement of anti-condensation is quantified as a specific heat transfer boundary condition . It is the input constraint for the entire derivation process

[0141] Physical modeling and calculation of the heat transfer mechanism in the gap: The total heat leakage must penetrate the thermal resistance formed by the gap G and the outer pipe wall. The temperature drop through the outer pipe wall is very small (usually <0.1 K), and it can be approximately considered that the temperature of the inner wall of the outer pipe ≈ . Therefore, the temperature difference between both sides of the annular gap is: Radiative heat transfer modeling. For two concentric cylindrical surfaces, the functional relationship between the radiative heat flux density and the annular gap is derived, specifically as: where represents the Stefan-Boltzmann constant, which is used to describe the relationship between the energy of radiation and temperature; represents the emissivities of the inner wall of the outer pipe and the outer wall of the inner pipe; represents the outer diameter of the inner pipe; G represents the unilateral annular gap. In addition, the denominator part represents the total radiative thermal resistance, which is a function of the gap G. As G increases, the inner diameter of the outer pipe increases, the second term in the denominator decreases, resulting in a decrease in the total thermal resistance and a slight increase in radiative heat transfer .

[0142] Residual gas heat transfer modeling: This is the most complex part of the derivation. Its heat transfer mechanism is closely related to the relative magnitudes of the mean free path λ of gas molecules and the gap G (i.e., the Knudsen number Kn = λ / G). Gas heat transfer is divided into three flow regimes: free molecular flow (Kn > 10), transitional flow (0.01 < Kn < 10), and continuum flow (Kn < 0.01). To calculate gas heat transfer, the mean free path needs to be determined first

[0143] The mean free path λ (referring to the average distance that gas molecules travel between two consecutive collisions, with the unit of m): where: is the Boltzmann constant J / K; The average temperature of the gas in the gap The unit is K; The effective diameter of a gas molecule (for air, take...) m); This represents the absolute pressure of the annular gap, expressed in Pa.

[0144] Mean free path increases with increasing vacuum level ( As the temperature decreases, the probability of collisions between gas molecules decreases, and the heat transfer mechanism changes from continuous conduction to free molecular flow.

[0145] Determine the heat transfer model based on the flow regime: Free molecular flow (Kn>10): Gas molecules hardly collide, and heat and pressure transfer are minimal. It is directly proportional to the gap G and is independent of the gap G: in, This is the thermal adaptability coefficient (which depends on the interaction between the gas and the wall material; for air and stainless steel surfaces, it is typically taken as 0.8 to 1.0). The free molecular conductivity coefficient is given by the value of air at an average temperature. The following can be calculated as: in, Indicates the molecular mass of a gas (kg); Indicates the specific heat ratio of a gas; This represents the Prandtl number.

[0146] Continuous flow (Kn < 0.01): Gas can be considered a continuous medium, and heat transfer follows Fourier's law of thermal conductivity, but the temperature jump effect must be considered: in, For the gas at the average temperature The thermal conductivity of W / (m·K) is given by the following formula: , This represents the temperature jump distance between the two side walls.

[0147] Temperature jump distance Calculation: For the same gas and wall material, the temperature jump distance can be expressed as: in This represents the thermal adaptability coefficient of the corresponding wall surface. When the conditions of both walls are the same... - = For air and the stainless-steel surface, usually ≈ 2λ.

[0148] Unified model of transitional flow regime (for engineering application): To simplify the calculation process, in this embodiment, a transitional flow model with higher accuracy is adopted as the general formula, which is applicable to the range of 0.01 < Kn < 10. The functional relationship between the heat flux density of residual gas heat transfer and the annular gap is derived as follows: Where: β is the rarefaction coefficient related to the gas species (for air, β ≈ 2).

[0149] Model characteristics: When Kn → 0 (continuous flow), G is much larger than , the formula degenerates into, ≈ / ; when Kn → ∞ (free molecular flow), G is much smaller than , the formula degenerates into, ≈ / ( ), and is inversely proportional to , so the heat transfer is inversely proportional to the pressure value ; this model has sufficient accuracy within the engineering range of < 100 Pa and is convenient for numerical iterative solution.

[0150] Solving equation for the theoretical minimum gap : Establish the total heat transfer equation, substitute the radiation and residual gas heat transfer models into the total heat flux equation, and make it equal to the allowable heat flux: This is an implicit transcendental equation about G because also contains G. Since the analytical solution cannot be directly obtained, the design method adopts the following numerical iterative algorithm: Initialization: Let ; The k-th iteration: Calculate the radiation heat flux density under the current , and calculate the required gas heat transfer flux density: Judgment: If , it means that only radiation heat transfer has exceeded the allowable value. Output and prompt "The adiabatic requirement is dominated by radiation. It is necessary to reduce the emissivity or increase the vacuum degree".

[0151] like If the value is greater than 0, then the gap value satisfying this heat flux density can be obtained from the inverse solution of the gas heat transfer model. : Check convergence: If <0.01mm (set value), then The iteration ends. Otherwise, update. Return to the initialization step.

[0152] If the solution is found A negative value indicates that, under the current vacuum level and surface emissivity, the gas heat transfer term makes a negative contribution (without physical significance). This usually means that radiative heat transfer constitutes the majority of the total heat transfer, and the gap size has minimal impact on insulation performance. In this case, the minimum gap will be determined by process requirements. If the solution is found If the vacuum level is significantly larger than the feasible range (e.g., >50 mm), it indicates that the current vacuum level is too low and gas heat transfer is excessive. The vacuum level needs to be increased or a surface with lower emissivity should be used to guide design optimization.

[0153] S1.4.2, Calculate the maximum allowable clearance.

[0154] Under the condition of an inner tube rupture, when the inner tube ruptures completely, the high-pressure medium will flow to the vent through the annular gap. In the most conservative instantaneous condition, assuming the effective flow area of ​​the vent is less than or equal to the flow area of ​​the annular gap, sonic flow (critical flow) will form at the narrowest point of the leakage path. At this point, the flow rate reaches its maximum, and further decreases in downstream pressure will not affect the upstream pressure (within the annular gap). This transient peak pressure... It is the load input for external pipe verification.

[0155] According to the isentropic flow theory of gas dynamics, when critical flow occurs, the downstream pressure... upstream stagnation pressure The following relationship must be satisfied: Under the limit conservatism assumption, take At atmospheric pressure (approximately 0.101 MPa), its value is much smaller than that of atmospheric pressure. The above relationship simplifies to the critical pressure ratio formula. Therefore, the highest predicted pressure within the annular gap... Pressure can be designed directly from the inner tube. and the thermal insulation index of the medium Sure: Where P is the design pressure of the inner tube (MPa), and is the known operating condition input; The adiabatic index (specific heat ratio) of the medium / Its value is determined by the molecular structure and temperature of the medium itself.

[0156] With this pressure As the design internal pressure of the outer tube, verify whether its wall thickness meets the requirements of ASME B31.3, and calculate the maximum allowable gap that the outer tube can withstand without instability or rupture. .

[0157] S1.4.3, Determine the feasible clearance range for the process.

[0158] After repeated experiments, the feasible range for the process clearance was determined to be 20~50 mm. If the clearance is less than 20 mm, the thermal insulation elastic support will be difficult to install properly, or its designed thermal insulation and mechanical support performance cannot be guaranteed after installation. If the clearance is greater than 50 mm, during the mechanical cold bending process, the curved section is prone to problems such as excessive roundness, obvious wrinkles, and difficulty in controlling the wall thickness reduction rate, which will fail to meet the process quality requirements.

[0159] The establishment of this range is based on the systematic verification of the "support-bending" collaborative process. The lower limit of 20 mm is derived from the statistics of the standard dimensions of commonly used cylindrical thermal insulation elastic supports and the operating space required for installation tools, ensuring that the supports can be inserted without interference and maintain the designed pre-compression state. The upper limit of 50 mm is determined by both material mechanics and bending process limits; when the gap exceeds this value, the temporary filling medium in the annular gap is difficult to establish a uniform and continuous stress transfer path during bending, resulting in obvious wrinkles on the inner side of the outer tube due to insufficient support, and excessive thinning on the outer side of the inner tube due to excessive stretching, and the cross-sectional roundness cannot meet the process requirement of δ≤3%.

[0160] S1.4.4, The final clearance is determined to match the standard specifications.

[0161] The double-walled pipe product in this embodiment follows the design principles of prioritizing standard pipe materials and optimizing economic efficiency. The final value of the annular gap is not an independently calculated variable, but is determined through the following systematic matching process: Based on the standard specifications of the inner pipe and engineering design constraints, the most economical outer pipe specification is selected from the standard pipe material library, and then the actual gap is calculated and its compliance is verified.

[0162] Based on the outer diameter of the inner tube Select the standard outer diameter of the next larger size from the ASME B36.19 standard library. , in outer diameter From the corresponding standard wall thickness series, select the minimum wall thickness that simultaneously meets the following requirements. : Meets external pressure stability requirements (according to ASME BPVC Section VIII); Meets the safety leakage condition strength requirements (according to ASME B31.3); Meets the thinning requirements of bending processes (according to the company's process database).

[0163] Actual clearance calculation: Calculate the actual annular clearance based on the selected standard specifications. : In the formula: This refers to the standard outer diameter of the outer tube. For the standard wall thickness of the outer tube, This refers to the standard outer diameter of the inner tube.

[0164] Gap compliance verification, verification Does it meet the following requirements: ≥ and ≤ At the same time ensure Within the feasible process range of 20-50mm; if If the requirements are not met, select an adjacent standard specification and recalculate until the most economical and compliant specification combination is found.

[0165] In some feasible embodiments, step S1.6 specifically includes: The design angles of each bend are extracted from the input 3D model of the pipeline to obtain the bending angles; Due to the elasticity of the material, the pipe will spring back after bending and unloading, resulting in the actual angle being smaller than the target angle. This technology uses a pre-established "integrated bending and springback database" to query the corresponding springback compensation amount Δθ based on the material, pipe diameter, wall thickness, bending radius R, and θ.

[0166] The overall rebound compensation is calculated by vector superposition. ,in and These are the springback compensation angles for the outer tube and the inner tube, respectively, derived from a large amount of experimental data.

[0167] In some feasible embodiments, the method further includes calculating the maximum allowable spacing of the elastic supports for the straight pipe section based on the stiffness of the inner and outer pipe structures and the annular gap, and setting reinforcing supports near the curved section, wherein: Straight pipe section support spacing ( Based on the Euler-Bernoulli beam model, considering the stiffness of the inner and outer tubes, the annular gap G, and the weight of the fluid, calculate the maximum allowable support spacing to ensure a coaxiality deviation ≤ 1 mm. Actual spacing between arrangements. ≤ .

[0168] Strengthen support in curved areas: at a distance of (0.5-1) from the tangent endpoint of each curve. Within the OD range, elastic supports must be added to suppress relative displacement in the bending area caused by differential springback and vibration.

[0169] Finally, this method generates a complete design scheme, including: inner and outer tube specification tables, a bill of materials, and a bending parameter table (including each bending radius R and bending angle). The data includes rebound compensation Δθ), detailed support layout drawings, annular gap values, stress calculation sheets, and key verification conclusions such as strength, stability, thermal insulation, and safety leakage conditions.

[0170] Based on the above overall method, the present invention also provides specific data examples of the above processing method.

[0171] Input conditions: Medium: LNG (main component methane, k≈1.32); Design pressure P=1.0 MPa; Design temperature: -163℃ (medium) / 45℃ (ambient); Ambient relative humidity 60%, calculate ambient dew point temperature accordingly; Annular gap vacuum degree. To ensure that under this vacuum level, the temperature of the outer wall of the outer pipe is above the dew point, with no condensation; design life N=15 years; design flow rate Q=50 m³ / s. 3 / h, which is 0.01389m 3 / s.

[0172] Material selection: Based on the low-temperature characteristics, corrosiveness and bending processability of the medium, the inner and outer tubes are both made of 304L stainless steel, which has good low-temperature toughness and is suitable for LNG conditions.

[0173] Inner tube specifications: If the design flow velocity is selected as v = 2.0 m / s (the commonly used flow velocity range for LNG), then: Calculation of theoretical minimum wall thickness and determination of final wall thickness: Allowable stress K = 115 MPa (304L, -163°C, according to ASME B31.3); after iterative calculation, the theoretical minimum wall thickness satisfying a pressure strength of 1.0 MPa is obtained. .

[0174] The final theoretical wall thickness was determined as follows: manufacturing negative tolerance a = 12.5%; bending thinning rate b = 8% (process database); corrosion allowance c: the larger value between the specification requirement and the calculated prediction, c = 1.2 mm. The final theoretical wall thickness determined by combining these factors is t = 2.05 mm.

[0175] Standard specification selection and verification: theoretical outer diameter Consult ASME B36.19 standard and select the next closest and slightly larger nominal outside diameter. =114.3mm; in In the wall thickness series of 114.3mm, if the nominal wall thickness T=3.05mm is selected, the actual wall thickness is: Verification data: Bending strength: Satisfaction; Actual circulation capacity: mm actual flow velocity =1.51m / s Meets requirements; Process feasibility: Inner pipe outer diameter mm is within the range of the bendable database.

[0176] Therefore, the final specifications of the inner tube are determined as follows: =114.3mm, T=3.05mm.

[0177] Annular gap determination: Based on thermal performance calculation Set the minimum allowable temperature of the outer wall of the outer tube. Take the overall environmental heat transfer coefficient (Considering the ventilation environment at sea). Using an iterative algorithm, the minimum gap that meets the insulation requirements is obtained. =22mm.

[0178] Determined based on process requirements: According to the bending process database, for inner tubes =114.3mm To ensure stability during the bending process and accommodate the elastic support, a process clearance of 114.3mm is recommended. =23.6mm.

[0179] Verification based on safety leakage conditions =48mm.

[0180] Final gap determined: and Therefore, we take G = 23.6 mm.

[0181] Outer tube specifications: Calculate the inner diameter of the outer tube: = + 2 G = 114.3 + 23.6 x 2 = 161.5 mm.

[0182] Determining the outer tube wall thickness and selecting specifications: The outer tube needs to withstand the design internal pressure of Simultaneously, it must meet external pressure stability requirements. The wall thickness required for strength calculations is very small; the wall thickness is mainly determined by external pressure stability, manufacturing rigidity, and standard specifications. The nominal outer diameter is selected by consulting the standard library. =168.3mm, wall thickness =3.4mm.

[0183] The outer pipe specifications (according to ASME BPVC Section VIII) were checked and found to meet the requirements. Therefore, the final outer pipe specification is: =168.3mm, =3.4mm.

[0184] Determining the parameters for pipe bends: Bending radius (R): R = 3 x 168.3 = 504.9 mm; Bending angle θ and springback compensation Δθ: Bending angles extracted from the 3D model: θ is 90° and 45°; Checking the springback database (304L, =168.3mm, =3.4mm, R=504.9mm, θ=90°) yields an overall springback compensation Δθ=4.5°. Looking up the springback database (304L, =168.3mm, =3.4mm, R=504.9mm, θ=45°) yields an overall rebound compensation Δθ=2.2°. Section quality control: Dry natural sand with a particle size of 0.06–0.25mm, Mohs hardness ≥7, and compressive strength ≥50 MPa is used as the temporary filling medium. Calculation of sand usage per meter of double-walled pipe: Considering surplus, the actual amount of material prepared was 17. .

[0185] Design of flexible support system: Straight pipe section support spacing : Maximum allowable spacing calculated based on beam model =2.8m; Actual layout takes =2.5m Reinforced support in bend areas: Elastic supports are added within approximately 125mm of the tangent endpoint of each bend.

[0186] The complete parameter scheme is shown in Table 3 below. Table 3 By adopting the above-described solution disclosed in this invention, at least the following beneficial effects can be achieved: 1. The overall structure is a seamless continuous structure, which fundamentally reduces the risk of leakage, extends the vacuum life, and achieves a qualitative leap in safety; 2. The above method can realize automated pipe bending, eliminating the need for manual welding operations, shortening the cycle (5-7 days / batch), increasing efficiency by more than 70%, reducing reliance on manual labor, and significantly increasing production capacity; 3. High material utilization rate, low labor cost, and extremely low cost of natural sand, resulting in an overall reduction of production costs by approximately 30%-40%; 4. High precision, good consistency, smooth inner wall, reduced fluid resistance, convenient installation, and strong product competitiveness; 5. Active prediction and differential compensation: Before and during bending, the model predicts and actively compensates for the different springbacks of the inner and outer tubes; a fundamental revolution from "passive correction" to "active control", transforming springback from a negative problem that needs to be overcome into a forming factor that can be accurately predicted and utilized, representing a higher level of technology. 6. Small gaps are only for mechanical assembly and simple heat insulation, while this invention has large gaps, with a single-sided gap design of 20-50mm. It is designed to achieve the core function of "high vacuum insulation layer", which meets the strict heat insulation requirements for the transportation of cryogenic fuels such as marine LNG. 7. Multi-loop online vacuum monitoring and precise automatic compensation upgrades the system from an "isolated component" to an "intelligent system," achieving inherent safety; 8. Multiple continuous curved sections meet the complex two-dimensional and three-dimensional piping requirements, enhancing the ability to move from "manufacturing parts" to "building systems"; This invention has the ability to form complex three-dimensional pipelines in one go, which greatly improves the freedom and integration of ship pipeline design and reduces the number of welding and splicing steps for multiple bends; 9. The differential springback is solved by a triple mechanism of pre-set eccentric end cap 400, precise over-bending and elastic support 140, which solves the key technical problem hidden in the industry and ensures the concentricity and effectiveness of the support after molding. 10. The process is streamlined and near-net-shape forming is achieved. Relying on precise pre-compensation, the shaping and heat treatment processes can be significantly reduced or completely avoided, pursuing "double improvement in quality and efficiency". The active control strategy of this invention enables the product to reach or approach the final requirements after bending, which simplifies the process, reduces energy consumption, shortens the cycle, and avoids the material performance degradation that may be caused by heat treatment.

[0187] The above is a detailed description of the preferred embodiments of the present invention. However, the present invention is not limited to the embodiments described. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of the present invention. All such equivalent modifications or substitutions are included within the scope defined by the claims of this application.

Claims

1. A single-piece bent-form marine double-walled pipe, characterized in that: The coaxiality d of the inner and outer tubes of the integrally bent marine double-walled tube is ≤1mm. The integrally bent marine double-walled pipe is provided with at least two weld-free elbows. The bending radius R of the weld-free elbow satisfies 2D≤R≤3D, where D is the outer diameter of the integrally bent marine double-walled pipe. The roundness E of the weld-free elbow is ≤3%; The maximum wall thickness reduction rate T of the weld-free elbow is ≤12%; The inner wall of the weld-free elbow has a structure without visible wrinkles. The integrally bent and formed marine double-walled tube includes an outer tube, an inner tube, and an elastic support component; The outer tube is fitted over the inner tube, and there is a gap of 20-50mm between the inner circumferential wall of the outer tube and the outer circumferential wall of the inner tube. The inner circumferential wall of the outer tube and the outer circumferential wall of the inner tube form the heat insulation cavity. Multiple elastic support members are disposed within the heat insulation cavity. The multiple elastic support members are arranged separately along the extension trajectory of the double-walled pipe, and some of the elastic support members are disposed adjacent to the end of the weld-free elbow.

2. A marine double-walled piping system, characterized in that, Including the integrally bent marine double-walled tube and vacuum maintenance mechanism as described in claim 1, wherein: The vacuum maintenance mechanism includes a vacuum compensation pump, a vacuum valve, and a vacuum level sensor; The vacuum compensation pump's pumping end is connected to the heat-insulating cavity through the vacuum valve; The vacuum sensor is used to monitor the vacuum level inside the insulation cavity. When the measured vacuum level inside the insulation cavity exceeds a preset value, the marine double-walled pipeline system controls the vacuum compensation pump to perform vacuum compensation until the vacuum level inside the insulation cavity reaches the preset range.

3. A method for processing a double-walled tube, used to manufacture the integrally bent marine double-walled tube as described in claim 1, characterized in that... Includes the following steps: S1. Based on the task requirements, design the specifications and parameters of the double-walled pipe; S2, connect and fix multiple elastic support members to the outer wall of the inner tube so that the multiple elastic support members are arranged separately along the length direction of the inner tube; then fit the inner tube into the outer tube so that the multiple elastic support members elastically abut against the inner wall of the outer tube, thereby forming a double-walled pipe. S3, install an eccentric end cap at one end of the double-walled pipe, and then fill the heat insulation cavity formed between the outer wall of the inner pipe and the inner wall of the outer pipe with filler until the filling rate of the filler reaches the requirement. S4, Install an eccentric end cap at the other end of the double-walled pipe to pre-compensate for the relative displacement of the outer pipe and the inner pipe on the axis caused by differential rebound; S5, using a pipe bending machine to bend the double-walled pipe using an over-bending process to form a weld-free elbow on the double-walled pipe; S6, Remove the eccentric end cap and clear the filler in the heat insulation cavity; S7, the vacuum maintenance mechanism is connected to the heat insulation cavity via the vacuum pump end.

4. The processing method according to claim 3, characterized in that: In S3, the filler is natural sand with a particle size of 0.06-0.25 mm, a Mohs hardness of not less than 7, and a uniaxial compressive strength of not less than 50 MPa.

5. The processing method according to claim 3, step S1 specifically includes: Get task parameters; Based on the aforementioned task parameters, select the inner tube material and the outer tube material; Calculate the inner tube specifications and outer tube specifications based on the task parameters; The final annular gap is determined by combining the task parameters, safety constraints, and process-feasible gap range; Based on the inner tube specifications and the final annular gap, determine the inner diameter of the outer tube, and calculate the wall thickness and outer diameter of the outer tube in conjunction with the task parameters; Based on the three-dimensional layout information of the pipeline, the bending radius and bending angle of each bending segment are determined, and the springback compensation angle is determined. Based on the structural stiffness of the inner and outer tubes and the final annular gap, the maximum allowable spacing of the elastic support members of the straight pipe section is calculated.

6. The processing method according to claim 5, characterized in that, The calculation process for the inner tube specifications specifically includes: Calculate the theoretical inner diameter value based on flow rate and velocity requirements; Calculate the minimum wall thickness based on the thin-walled cylinder theory; Based on the minimum wall thickness, combined with manufacturing tolerances, bending thinning and corrosion allowance, the final theoretical wall thickness is calculated; The final inner tube specification is obtained by selecting from the candidate library based on the theoretical inner diameter value and the final theoretical wall thickness. The final inner tube specifications are verified using strength, flow capacity, and bending range as constraints.

7. The processing method according to claim 5, characterized in that, The step of determining the final annular gap by combining the task parameters, safety constraints, and process-feasible gap range specifically includes: Calculate the minimum annular gap between the inner circumferential wall of the outer tube and the outer circumferential wall of the inner tube based on the task parameters. Based on the internal tube rupture condition, the pressure of the medium inside the annular gap is calculated, and the maximum allowable gap is calculated in combination with the external pressure. Based on the pre-set bending process database, determine the feasible clearance range for the process; The final annular gap is determined based on the minimum annular gap, the maximum allowable gap, and the process-feasible gap range.

8. The processing method according to claim 5, characterized in that, The formula for calculating the rebound compensation angle is as follows: in, Indicates the springback compensation angle. This indicates the springback compensation angle of the outer tube under the corresponding bending parameters. This indicates the springback compensation angle of the inner tube under the corresponding bending parameters.

9. The processing method according to claim 7, characterized in that, The step of calculating the minimum annular gap between the inner circumferential wall of the outer tube and the outer circumferential wall of the inner tube based on the task parameters specifically includes: Set insulation targets; The annular gap of the double-walled pipe is simplified into a closed cavity between two infinitely long concentric cylindrical surfaces, and a physical model is constructed. Based on the physical model, the functional relationships between the maximum allowable heat flux density, the radiative heat transfer heat flux density and the annular gap, and the residual gas heat transfer heat flux density and the annular gap are derived. By combining the maximum allowable heat flux density, the functional relationship between the radiative heat transfer heat flux density and the annular gap, and the functional relationship between the residual gas heat transfer heat flux density and the annular gap, an implicit transcendental equation is constructed. The implicit transcendental equation is solved iteratively to output the minimum annular gap.

10. The processing method according to claim 9, characterized in that, The implicit transcendental equation is expressed as follows: in, Represents the heat flux density of radiative heat transfer. This represents the thermal conductivity of a gas at an average temperature. This represents the temperature difference across the annular gap. Indicates annular gap, This represents the rarefaction coefficient related to the type of gas. Indicates the mean free path, This indicates the maximum permissible heat flux density.