An experimental system for measuring the convective heat transfer coefficient with a rotating isothermal wall
The rotating equal wall temperature system addresses the precision issues in convective heat transfer measurements by allowing independent temperature control of copper blocks, enhancing experimental accuracy and efficiency.
Patent Information
- Application Number
- CN202510592379.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2025-05-09
- Publication Date
- 2025-07-15
- Estimated Expiration
- 2045-05-09
AI Technical Summary
In the prior art, the experimental method of rotating blade cooling channels cannot accurately simulate the actual isowave temperature conditions on the blade surface, resulting in low experimental accuracy and inability to quantify the heat conductivity caused by temperature difference.
An experimental system for measuring the rotational isowave temperature convection heat transfer coefficient is designed to achieve isowave temperature or arbitrary temperature distribution by independently controlling and detecting the temperature of each copper block, and adopting heating components and temperature detection components, combining computer control to achieve accurate temperature regulation and heat transfer coefficient calculation.
It realizes accurate control and measurement of copper block temperature, and can simulate real iso-wall temperature boundary conditions under rotation conditions, improves experimental accuracy and efficiency, and shortens experimental time.
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Figure CN120102630B_ABST
Abstract
Description
Technical Field
[0001] The present application relates to the field of rotary heat transfer experiments, and particularly to an experimental system for measuring the convective heat transfer coefficient of a rotating isothermal wall. Background Art
[0002] To improve the performance of aeroengines and gas turbines, increasing the turbine inlet temperature and, on this basis, enhancing the compressor pressure ratio are important technical paths. However, the turbine inlet temperature has reached 2000K, which far exceeds the allowable temperature of superalloys. Therefore, to ensure the normal operation of turbine blades, various advanced cooling measures are adopted. The outside of the turbine blade is cooled by a thermal barrier coating and film cooling, and the inside of the turbine blade uses enhanced heat transfer means to take away the heat of the blade with cold air. The internal cooling technology of the turbine blade includes impingement cooling at the leading edge, ribbed serpentine channels in the middle, and wedge ribbed column channels at the trailing edge, etc.
[0003] For turbine rotor blades, the blades rotate at a speed of tens of thousands of revolutions per minute. Rotation not only affects the strength of the blades, but the additional force induced by rotation also affects the flow of cold air in the blade cooling channels, thereby affecting the cooling of the blade wall surface. To study the influence of rotation on the flow and heat transfer in the cooling channels, relevant experiments are needed. The copper block method is a mature method for studying such problems. It uses a series of copper block units to form a cooling channel. However, in previous research processes, the heating films on the back of the copper blocks were generally connected in series, and the formed thermal boundary condition was close to an isothermal heat flux boundary. Due to the different convective heat transfer coefficients on the surface of the copper blocks, there must be heat conduction caused by temperature differences between the copper blocks, and the amount of heat transfer in this part cannot be quantified through heat loss experiments. Therefore, the accuracy of the experiment is low, and the actual temperature distribution on the blade surface is closer to an isothermal wall thermal boundary condition. So this experimental method cannot simulate the true physical boundary of the blade. Summary of the Invention
[0004] In view of this, the present application provides an experimental system for measuring the convective heat transfer coefficient of a rotating isothermal wall, which solves the problems in the prior art and realizes an isothermal wall system with equal temperatures of all copper blocks and can also realize any temperature distribution.
[0005] The experimental system for measuring the convective heat transfer coefficient of a rotating isothermal wall provided by the present application adopts the following technical solutions:
[0006] An experimental system for measuring the convective heat transfer coefficient of a rotating isothermal wall, comprising:
[0007] A test bench;
[0008] A rotating shaft, rotatably installed on the test bench;
[0009] A driving component, fixedly arranged relative to the test bench, is used to drive the rotation of the rotating shaft, and the rotation axis of the rotating shaft is parallel to the length direction of the rotating shaft;
[0010] A rotating arm, fixedly installed on the rotating shaft;
[0011] A test piece, including a skeleton and a plurality of copper blocks, the skeleton is fixed on the rotating arm, the plurality of copper blocks are fixed on the skeleton, the plurality of copper blocks are spliced to form a cooling channel, one side surface of the copper block serves as the inner wall surface of the cooling channel, the other side surface of the copper block serves as the outer wall surface of the cooling channel, and a heating component is provided on the outer wall surface of the cooling channel corresponding to each copper block. The heating component is used to heat the copper block, and the heating components on each copper block are independently arranged;
[0012] A plurality of temperature detection components, corresponding to the plurality of copper blocks one by one, are used to detect the temperature of the copper blocks;
[0013] A cooling medium conveying pipeline, fixed on the rotating shaft and the rotating arm, one end of the cooling medium conveying pipeline is communicated with a cooling medium source, and the other end of the cooling medium conveying pipeline is used to be communicated with the cooling channel of the test piece.
[0014] Optionally, the rotating isothermal wall convective heat transfer coefficient measurement experimental system further includes a heating controller, a temperature acquisition module, a computer, and a DC power supply;
[0015] The heating controller is electrically connected to all the heating components, the temperature acquisition module is electrically connected to the temperature detection components, both the heating controller and the temperature acquisition module are electrically connected to the computer, and the heating controller is electrically connected to the DC power supply;
[0016] Wherein, the temperature acquisition module is used to convert the voltage analog signal of the temperature detection component into a digital signal, the computer receives the temperature data of each copper block sent by the temperature acquisition module, the computer calculates the heating power of the heating component for heating each copper block to a preset temperature according to the real-time temperature data of each copper block, and the heating controller controls the heating power output by each heating component according to the received heating power of each copper block.
[0017] Optionally, a slip ring is installed on the rotating shaft, the heating controller and the temperature acquisition module are installed on the rotating shaft, the heating controller is electrically connected to the computer through the slip ring, the heating controller is electrically connected to the DC power supply through the slip ring, and the temperature acquisition module is electrically connected to the computer through the slip ring.
[0018] Optionally, the heating controller adjusts the heating power of the heating component through a pulse width modulation generator.
[0019] Optionally, the heating component is a resistive film, the resistive film is covered on one side of the copper block corresponding to the outer wall surface of the cooling channel, an adiabatic cover plate is provided on the side of the resistive film facing away from the copper block, the adiabatic cover plate is fixed on the copper block and the adiabatic cover plate covers the resistive film.
[0020] Optionally, the temperature detection component is a thermocouple, and the detection probe of the thermocouple contacts one side of the copper block corresponding to the outer wall surface of the cooling channel.
[0021] Optionally, adjacent copper blocks are sealed by a sealed adiabatic structural member.
[0022] Optionally, a rotary joint is installed at one end of the rotating shaft. One end of the rotary joint is a fixed end, the fixed end is fixedly arranged relative to the rotating shaft, the other end of the rotary joint is a free end, the fixed end is communicated with the cooling medium conveying pipeline, and the free end is communicated with the cooling medium source.
[0023] In summary, the present application includes the following beneficial technical effects:
[0024] In the present application, the temperature of each copper block is measured separately, controlled separately and heated separately, and can be set to the same wall temperature distribution or non-uniform wall temperature distribution form according to needs. It can not only realize an isothermal wall temperature system with equal temperatures of all copper blocks, but also realize any temperature distribution, and can also achieve strict isothermal flux boundary conditions by adjusting the algorithm, which greatly facilitates the experimental study of various heat transfer boundary conditions. Moreover, since the constant wall temperature boundary condition can be realized, when the flow rate changes, there is no need to wait for the thermal equilibrium time, which can greatly shorten the experimental time and improve the experimental efficiency. Description of the Drawings
[0025] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required to be used in the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, other drawings can be obtained according to these drawings without creative efforts.
[0026] Figure 1 It is a schematic diagram of the overall structure of the experimental system for measuring the rotating isothermal wall convection heat transfer coefficient of the present application;
[0027] Figure 2 It is a schematic diagram of the assembled structure of the copper block, the heating component and the temperature detection component of the present application;
[0028] Figure 3 It is a circuit diagram of the experimental system for measuring the rotating isothermal wall convection heat transfer coefficient of the present application.
[0029] Description of reference numerals in the drawings: 1. Test bench; 11. Support frame; 2. Rotating shaft; 21. Rotary joint; 3. Motor; 31. Belt; 4. Rotating arm; 5. Test piece; 51. Copper block; 52. Heating assembly; 53. Heat insulation cover plate; 54. Temperature detection assembly; 6. Heating controller; 61. Pulse width modulation generator; 7. Temperature acquisition module; 8. Computer; 9. DC power supply; 10. Electrical slip ring. Detailed implementation manners
[0030] The embodiments of the present application will be described in detail below with reference to the drawings.
[0031] The following uses specific specific examples to illustrate the implementation manners of the present application. Those skilled in the art can easily understand other advantages and effects of the present application from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. The present application can also be implemented or applied through other different specific implementation manners. Various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present application. It should be noted that, without conflict, the following embodiments and the features in the embodiments can be combined with each other. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present application.
[0032] It should be noted that the following describes various aspects of the embodiments within the scope of the appended claims. It should be obvious that the aspects described herein can be embodied in a wide variety of forms, and any specific structure and / or function described herein is illustrative only. Based on the present application, those skilled in the art should understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects described herein can be used to implement the device and / or practice the method. In addition, this device and / or this method can be implemented using other structures and / or functions in addition to one or more of the aspects described herein.
[0033] It should also be noted that the drawings provided in the following embodiments only illustrate the basic concept of the present application in a schematic manner. The drawings only show the components related to the present application, rather than being drawn according to the number, shape and size of the components in actual implementation. The type, quantity and proportion of each component in its actual implementation can be an arbitrary change, and the component layout type may also be more complex.
[0034] In addition, in the following description, specific details are provided to facilitate a thorough understanding of the examples. However, those skilled in the art will understand that the described aspects can be practiced without these specific details.
[0035] An embodiment of the present application provides an experimental system for measuring the convective heat transfer coefficient with a rotating equal wall temperature.
[0036] As Figure 1 、 Figure 2 and Figure 3 shown, an experimental system for measuring the convective heat transfer coefficient with a rotating equal wall temperature includes:
[0037] A test bench 1, including two support frames 11 arranged at intervals.
[0038] A rotating shaft 2, rotatably installed on the test bench 1. Bearing seats are provided on both support frames 11, and at least two positions of the rotating shaft 2 are installed on the two support frames 11 through bearings and bearing seats.
[0039] A driving assembly, fixedly arranged relative to the test bench 1. The driving assembly is used to drive the rotating shaft 2 to rotate, and the rotation axis of the rotating shaft 2 is parallel to the length direction of the rotating shaft 2. In the embodiment of the present application, the driving assembly includes a motor 3, a belt 31 and belt pulleys. Belt pulleys are fixedly installed on the output shaft of the motor 3 and the outer periphery of the rotating shaft 2 respectively, and the two belt pulleys are driven by the belt 31. The motor 3 is fixed on the ground or on the test bench 1.
[0040] A rotating arm 4, fixedly installed on the rotating shaft 2; the rotating arm 4 is located between the two support frames 11, and the space between the two support frames 11 provides space for the rotation of the rotating arm 4.
[0041] A test piece 5, including a skeleton and a plurality of copper blocks 51. The skeleton is fixed on the rotating arm 4, and a plurality of copper blocks 51 are fixed on the skeleton. The adjacent copper blocks 51 are sealed by a sealing and heat-insulating structural member. A plurality of the copper blocks 51 are spliced to form a cooling channel. One side surface of the copper block 51 serves as the inner wall surface of the cooling channel, and the other side surface of the copper block 51 serves as the outer wall surface of the cooling channel. A heating assembly 52 is provided on the outer wall surface of the cooling channel corresponding to each copper block 51. The heating assembly 52 is used to heat the copper block 51, and the heating assemblies 52 on each copper block 51 are independently arranged; wherein, the skeleton is made of nylon, and the sealing and heat-insulating structural member is made of nylon and sealant.
[0042] A plurality of temperature detection components 54, corresponding to the plurality of copper blocks 51 one by one. The temperature detection component 54 is used to detect the temperature of the copper block 51.
[0043] A cooling medium delivery pipeline, fixed on the rotating shaft 2 and the rotating arm 4. One end of the cooling medium delivery pipeline is communicated with a cooling medium source, and the other end of the cooling medium delivery pipeline is used to be communicated with the cooling channel of the test piece 5.
[0044] The usage method of the experimental system for measuring the rotating equal-wall-temperature convective heat transfer coefficient of this application is as follows:
[0045] Step 1: Start the motor 3. The rotating shaft 2 drives the rotating arm 4 to rotate, and the test piece 5 on the rotating arm 4 simulates the working condition of the internal cooling channel when the turbine rotor blade rotates.
[0046] Step 2: Detect the temperature T0 of each copper block 51 through the temperature detection component 54, calculate the difference between the current temperature T0 of each copper block 51 and the preset temperature T, and use the PID algorithm to calculate the heating power of the heating component 52 on each copper block 51 respectively, so that the temperature of each copper block 51 is finally stabilized at T W At this time, the heating power of the heating component 52 on each copper block 51 is Q W .
[0047] Step 3: Pass the cooling medium into the cooling channel through the cooling medium delivery pipeline. In the embodiment of this application, the cooling medium is high-pressure cold air, and the pressure of the high-pressure cold air is 0.1 - 0.5 MPa and the flow rate is 0 - 150 kg / h; at this time, the cold air exchanges heat with the wall surface of the cooling channel composed of the copper blocks 51. Therefore, the power of the heating component 52 will change to keep the temperature of the copper blocks 51 stable at T W , and at this time the heating power of the heating component 52 is Q t .
[0048] Step 4: Stuff the cold air channel with heat insulation materials, and repeat Step 1 and Step 2. After the copper blocks 51 are heated to the preset temperature T W , the heating power of the heating component 52 to keep the temperature of each copper block 51 stable at T W is the heat loss power Q l .
[0049] Step 5: Calculate the local average convective heat transfer coefficient h at each copper block 51;
[0050]
[0051] where h is the convective heat transfer coefficient, Q t is the heating power, Q l is the heat loss power, A is the contact area between the copper block 51 and the cold air, T W is the temperature of the copper block 51, and T in is the temperature of the cold air.
[0052] In other embodiments, by adjusting the rotation speed of the rotating shaft 2, the flow rate of the cold air, and the preset temperature of the copper blocks 51, the rotating heat transfer characteristics of the cooling channel of the turbine rotor blade can be obtained.
[0053] In other embodiments, when the rotational speed of the motor 3 is set to zero, the heat transfer characteristics of the cooling channels under the stationary condition can be obtained. By comparing the heat transfer differences between rotation and rest, the influence of rotation on the heat transfer of the cooling channels can be obtained. Setting the rotational speed of the motor 3 to zero enables the measurement of the heat transfer characteristics of the cooling channels in the turbine guide vanes. In this application, the temperature of each copper block 51 is measured, controlled, and heated separately, and can be set to the same wall temperature distribution or a non-uniform wall temperature distribution form as needed. It can not only achieve an isothermal wall temperature system with equal temperatures for all copper blocks 51, but also achieve any temperature distribution. Additionally, strict isothermal flux boundary conditions can be achieved by adjusting the algorithm, greatly facilitating experimental research on various heat transfer boundary conditions. Moreover, since the temperature of the copper blocks 51 can be kept constant, when the flow rate changes, there is no need to wait for the thermal equilibrium time, which can greatly shorten the experimental time and improve the experimental efficiency.
[0054] For the heating, temperature measurement, and control of the copper blocks 51, the following embodiments are provided in this application:
[0055] The experimental system for measuring the convective heat transfer coefficient of rotation with an isothermal wall also includes a heating controller 6, a temperature acquisition module 7, a computer 8, and a DC power supply 9; the heating controller 6 is electrically connected to all heating components 52, the temperature acquisition module 7 is electrically connected to the temperature detection components 54, both the heating controller 6 and the temperature acquisition module 7 are electrically connected to the computer 8, and the heating controller 6 is electrically connected to the DC power supply 9.
[0056] Among them, the temperature acquisition module 7 is used to convert the voltage analog signal of the temperature detection components 54 into a digital signal. The computer 8 receives the temperature data of each copper block 51 sent by the temperature acquisition module 7. The computer 8 calculates the heating power of the heating components 52 for heating each copper block 51 to the preset temperature using the PID algorithm based on the real-time temperature data of each copper block 51. The heating controller 6 controls the heating power output by each heating component 52 according to the received heating power of each copper block 51. The local average convective heat transfer coefficient h at each copper block 51 is also calculated by the computer 8. The heating controller 6 adjusts the heating power of the heating components 52 through a pulse width modulation generator 61. The full English name of pulse width modulation is Pulse-Width Modulation, abbreviated as PWM; the heating controller 6 adjusts the pulse frequency of the pulse width modulation generator 61 according to the received heating power of each copper block 51 to change the average heating power output by the heating components 52.
[0057] This application can automatically adjust the heating power according to the set temperature through the feedback control algorithm of the computer 8, ensuring the adjustment speed and accuracy; the signal transmission between the rotating system and the stationary computer is carried out through digital signals.
[0058] The heating component 52 is a resistive film, which covers one side of the copper block 51 corresponding to the outer wall surface of the cooling channel. An adiabatic cover plate 53 is provided on the side of the resistive film facing away from the copper block 51. The adiabatic cover plate 53 is fixed on the copper block 51 and covers the resistive film. The specific installation method of the resistive film is as follows: a groove is provided on the side surface of the copper block 51 corresponding to the outer wall surface of the cooling channel, the resistive film is placed in the groove, and a lead groove is provided on the side of the groove for the power supply cable of the resistive film to pass through, and the adiabatic cover plate 53 closes the opening of the groove.
[0059] The temperature detection component 54 is a thermocouple, and the detection probe of the thermocouple contacts one side of the copper block 51 corresponding to the outer wall surface of the cooling channel.
[0060] A slip ring 10 is installed on the rotating shaft 2. The heating controller 6 and the temperature acquisition module 7 are installed on the rotating shaft 2. The heating controller 6 is electrically connected to the computer 8 through the slip ring 10, the heating controller 6 is electrically connected to the DC power supply 9 through the slip ring 10, and the temperature acquisition module 7 is electrically connected to the computer 8 through the slip ring 10. There are multiple copper blocks 51, and the copper blocks 51, heating components 52 and temperature detection components 54 correspond one by one. Therefore, there are also multiple heating components 52 and temperature detection components 54. The heating controller 6 controls all the heating components 52, and the temperature acquisition module 7 collects multiplexed temperature signals. In this application, the heating controller 6 and the temperature acquisition module 7 are installed on the rotating shaft 2. The signal transmission between the heating controller 6 and the computer 8, the power transmission between the heating controller 6 and the DC power supply 9, and the signal transmission between the temperature acquisition module 7 and the computer 8 are carried out through the slip ring 10 for the transmission between the rotating unit and the stationary unit, reducing the number of channels that need to be converted between the rotating unit and the stationary unit and reducing the number of channels of the slip ring 10.
[0061] A rotary joint 21 is installed at one end of the rotating shaft 2. One end of the rotary joint 21 is a fixed end, which is fixedly arranged relative to the rotating shaft 2. The other end of the rotary joint 21 is a free end. The fixed end is communicated with the cooling medium conveying pipeline, and the free end is communicated with the cooling medium source. In the embodiment of this application, the rotating shaft 2 and the rotating arm 4 are hollow, and the cooling medium conveying pipeline is laid inside the rotating shaft 2 and the rotating arm 4. The cooling medium conveying pipeline is a polyurethane pipe.
[0062] The above is only the specific implementation manner of this application, but the protection scope of this application is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed in this application should be covered within the protection scope of this application. Therefore, the protection scope of this application should be subject to the protection scope of the claims.
Claims
1. A measurement experimental system for the convective heat transfer coefficient of rotation with equal wall temperature, characterized in that, Comprising: A test bench (1); A rotating shaft (2), rotatably installed on the test bench (1); A driving assembly, fixedly arranged relative to the test bench (1), the driving assembly being used to drive the rotating shaft (2) to rotate, the rotation axis of the rotating shaft (2) being parallel to the length direction of the rotating shaft (2); A rotating arm (4), fixedly installed on the rotating shaft (2); A test piece (5), including a skeleton and a plurality of copper blocks (51), the skeleton being fixed on the rotating arm (4), the plurality of copper blocks (51) being fixed on the skeleton, the plurality of copper blocks (51) being spliced to form a cooling channel, one side surface of the copper block (51) serving as the inner wall surface of the cooling channel, the other side surface of the copper block (51) serving as the outer wall surface of the cooling channel, and a heating assembly (52) being provided on the outer wall surface corresponding to each copper block (51) of the cooling channel, the heating assembly (52) being used to heat the copper block (51), and the heating assemblies (52) on each copper block (51) being independently arranged; A plurality of temperature detection assemblies (54), corresponding one by one to the plurality of copper blocks (51), the temperature detection assemblies (54) being used to detect the temperature of the copper blocks (51); A cooling medium delivery pipeline, the cooling medium delivery pipeline being fixed on the rotating shaft (2) and the rotating arm (4), one end of the cooling medium delivery pipeline being communicated with a cooling medium source, and the other end of the cooling medium delivery pipeline being used to communicate with the cooling channel of the test piece (5).
2. The experimental system for measuring the rotational isothermal wall temperature convective heat transfer coefficient according to claim 1, wherein The rotating equal wall temperature convective heat transfer coefficient measurement experimental system further includes a heating controller (6), a temperature acquisition module (7), a computer (8) and a DC power supply (9); The heating controller (6) is electrically connected to all the heating assemblies (52), the temperature acquisition module (7) is electrically connected to the temperature detection assemblies (54), both the heating controller (6) and the temperature acquisition module (7) are electrically connected to the computer (8), and the heating controller (6) is electrically connected to the DC power supply (9); Wherein, the temperature acquisition module (7) is used to convert the voltage analog signal of the temperature detection assembly (54) into a digital signal, the computer (8) receives the temperature data of each copper block (51) sent by the temperature acquisition module (7), the computer (8) calculates the heating power of the heating assembly (52) for heating each copper block (51) to a preset temperature according to the real-time temperature data of each copper block (51), and the heating controller (6) controls the heating power output by each heating assembly (52) according to the received heating power of each copper block (51).
3. The rotating isothermal convective heat transfer coefficient measurement experimental system according to claim 2, wherein A slip ring (10) is installed on the rotating shaft (2), the heating controller (6) and the temperature acquisition module (7) are installed on the rotating shaft (2), the heating controller (6) is electrically connected to the computer (8) through the slip ring (10), the heating controller (6) is electrically connected to the DC power supply (9) through the slip ring (10), and the temperature acquisition module (7) is electrically connected to the computer (8) through the slip ring (10).
4. The experimental system for measuring the convective heat transfer coefficient with a rotating isothermal wall according to claim 2, characterized in that, The heating controller (6) adjusts the heating power of the heating component (52) through a pulse width modulation generator (61).
5. The experimental system for measuring the convective heat transfer coefficient with a rotating isothermal wall according to claim 1, wherein The heating component (52) is a resistive film, which covers one side of the copper block (51) corresponding to the outer wall surface of the cooling channel. An adiabatic cover plate (53) is provided on the side of the resistive film facing away from the copper block (51). The adiabatic cover plate (53) is fixed on the copper block (51) and covers the resistive film.
6. The rotating isothermal convective heat transfer coefficient measurement experimental system according to claim 1, characterized in that The temperature detection component (54) is a thermocouple, and the detection probe of the thermocouple contacts one side of the copper block (51) corresponding to the outer wall surface of the cooling channel.
7. The rotating isothermal wall convective heat transfer coefficient measurement experimental system according to claim 1, characterized in that Adjacent copper blocks (51) are sealed by a sealed adiabatic structural member.
8. The experimental system for measuring the rotational isothermal wall temperature convective heat transfer coefficient according to claim 1, wherein One end of the rotating shaft (2) is equipped with a rotary joint (21). One end of the rotary joint (21) is a fixed end, which is fixedly arranged relative to the rotating shaft (2). The other end of the rotary joint (21) is a free end. The fixed end is communicated with the cooling medium conveying pipeline, and the free end is communicated with the cooling medium source.
Citation Information
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