Powder conveying and modifying equipment

By designing a powder conveying modification equipment including powder conveying pipes, cyclone sprayers and countercurrent sprayers, the problem of the existing powder conveying and modification processes is solved, and the full mixing and efficient coating of powder and modifier are achieved.

CN120133050APending Publication Date: 2025-06-13CHINA ENERGY INVESTMENT CORP LTD +1
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Patent Information

Application Number
CN202311715993.6
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2023-12-13
Publication Date
2025-06-13

AI Technical Summary

Technical Problem

The existing powder conveying and modification processes are carried out separately, the operation is complicated, the equipment cost and maintenance costs are high, the powder and the modifier are not easy to mix fully, and the coating effect is not good.

Method used

A powder conveying modification equipment is designed, including a powder conveying pipe, a cyclone sprayer and a countercurrent sprayer. The powder is continuously conveyed through the modified tube and the modifier is sprayed during the conveying process to achieve full mixing of the powder and the modifier.

Benefits of technology

The process is simplified, the equipment cost and maintenance cost are reduced, the powder conveying efficiency is improved, and the powder is fully mixed and uniformly coated with the modifier are ensured.

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Abstract

The invention discloses powder conveying and modifying equipment. Comprising a powder conveying pipeline, a rotational flow sprayer and a countercurrent sprayer, the powder conveying pipeline is used for continuously conveying powder, the pipe diameter of part of the powder conveying pipeline is expanded to define a modified pipe, and an agent outlet is formed in the pipe wall of the modified pipe; the rotational flow sprayer is arranged in the modifying pipe, the rotational flow sprayer comprises a rotating shaft and a spraying pipe mounted on the rotating shaft, the spraying pipe is provided with an agent outlet hole for spraying a modifying agent, and the spraying pipe can spray the modifying agent in a rotating manner; the countercurrent sprayer comprises an agent conveying pipe arranged on the periphery of the modified pipe, a conveying opening is formed in the agent conveying pipe and communicated with the agent outlet of the modified pipe, and the countercurrent sprayer sprays a modifier into the modified pipe through the agent outlet. According to the powder conveying and modifying equipment, the powder is mixed with the modifier in the conveying process, the powder conveying efficiency is improved, the equipment cost and the maintenance cost are reduced, the powder and the modifier are fully mixed, and the powder coating effect is improved.
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Description

Technical Field

[0001] This application relates to the technical field of powder modification, and particularly to a powder conveying and modifying device. Background Art

[0002] Powder surface modification refers to using various materials or additives to treat the powder surface by physical or chemical methods, and purposefully improving the physical and chemical properties or physical and technical properties of the powder surface according to application needs to meet the development needs of modern new materials, new processes, and new technologies.

[0003] In the prior art, the processes of powder conveying and modification are carried out separately. Generally, special modification equipment needs to be additionally added during the conveying process for powder modification. The modification equipment is generally an intermittently opened and closed stirring kettle. After a specific amount of powder is conveyed into the stirring kettle, the stirring kettle is closed. The stirring kettle mixes the powder and the modifier and then conveys them out of the stirring kettle, and then the stirring kettle is opened to receive new powder. The stirring kettle needs to be additionally equipped with a series of equipment such as a buffer tank for cooperation operations, which is complex in operation, increases the equipment cost and maintenance cost, and the intermittent powder conveying also reduces the powder conveying efficiency. In addition, by using the stirring blades in the stirring kettle to mix the powder and the modifier, the powder and the modifier are not easily fully mixed, and the powder film coating effect is not good. Summary of the Invention

[0004] The purpose of the solution of this application is to provide a powder conveying and modifying device, which realizes the mixing of the powder and the modifier during the conveying process, improves the powder conveying efficiency, reduces the equipment cost and maintenance cost, fully mixes the powder and the modifier, and improves the powder film coating effect.

[0005] A powder conveying and modifying device provided by the technical solution of this application includes: a powder conveying pipeline, a cyclone sprayer, and a countercurrent sprayer; the powder conveying pipeline is used for continuously conveying powder, the diameter of a part of the pipeline in the powder conveying pipeline is enlarged to define a modification pipe, and a reagent outlet is opened on the pipe wall of the modification pipe; the cyclone sprayer is arranged in the modification pipe, the cyclone sprayer includes a rotating shaft and a spray pipe installed on the rotating shaft, the spray pipe is provided with reagent outlets for spraying the modifier, and the spray pipe can rotate to spray the modifier; the countercurrent sprayer includes a reagent conveying pipe arranged on the outer periphery of the modification pipe, the reagent conveying pipe is provided with a conveying port, the conveying port is communicated with the reagent outlet of the modification pipe, the countercurrent sprayer sprays the modifier into the modification pipe through the reagent outlet, and the spraying direction of the modifier at the reagent outlet is opposite to the flowing direction of the powder.

[0006] Optionally, the diameter of a part of the pipeline in the powder conveying pipeline is reduced to define a reduced-diameter pipe, and the reduced-diameter pipe is connected behind the modification pipe along the conveying direction of the modifier.

[0007] Optionally, the conveying port and the agent outlet are connected through an intermediate pipe, and the number of the agent outlets is at least two, and at least two of the agent outlets are arranged along the circumferential direction of the modification pipe.

[0008] Optionally, along the conveying direction of the modifier, the countercurrent sprayer is located behind the swirl sprayer, and the included angle between the central axis of the agent outlet and the central axis of the modification pipe is an acute angle, so that the included angle between the direction of the modifier sprayed from the agent outlet and the conveying direction of the powder is an obtuse angle, and the modifier and the powder are in countercurrent contact.

[0009] Optionally, the intermediate pipe includes an inclined pipe section, the inclined pipe section is connected to the agent outlet, and the central axis of the inclined pipe section is collinear with the central axis of the agent outlet.

[0010] Optionally, the included angle between the central axis of the agent outlet and the central axis of the modification pipe is θ, and 30° ≤ θ ≤ 60°.

[0011] Optionally, the powder conveying pipeline further includes a first conveying pipe and a second conveying pipe. Along the conveying direction of the powder, the first conveying pipe is connected in front of the modification pipe, the second conveying pipe is connected behind the reduced-diameter pipe, the diameters of the first conveying pipe and the second conveying pipe are both R1, the radius of the modification pipe is R2, and the diameter of the reduced-diameter pipe is R3, and 3R1 ≤ R2 ≤ 10R1, 0.3R1 ≤ R3 ≤ 0.7R1.

[0012] Optionally, the number of the spray pipes is at least two, and at least two of the spray pipes are arranged circumferentially along the axial plane of the rotating shaft.

[0013] Optionally, the rotating shaft extends into the interior of the modification pipe, the rotating shaft is located below the central axis of the modification pipe, and the vertical distance between the rotating shaft and the central axis of the modification pipe is H, and 0.2R2 ≤ H ≤ 0.49R2.

[0014] Optionally, at least two agent holes are formed in the spray pipe along the length direction, the length of the spray pipe is L, and 0.5L ≤ H ≤ 0.9L.

[0015] Adopting the above technical solution, the following beneficial effects are achieved:

[0016] The powder conveying and modifying equipment provided by this application. The modifying pipe is a part of the powder conveying pipeline. The powder passes through the modifying pipe in a continuous fluidized state of conveying. The two processes of powder conveying and spraying the modifying agent are completed in the modifying pipe in the state of continuously conveying the powder, without separately setting up equipment and processes for spraying the modifying agent, simplifying the processes, reducing equipment costs and maintenance costs, and improving the powder conveying efficiency; the diameter of the modifying pipe is enlarged to reduce the speed of the powder conveyed into the modifying pipe, increasing the time required for the powder to pass through the modifying pipe. The modifying agent is mixed with the powder once by rotary spraying of the swirl sprayer and twice by countercurrent spraying of the countercurrent sprayer to make the modifying agent fully contact with the powder, which is beneficial to evenly coating the powder with a film. Description of the Drawings

[0017] Figure 1 It is a cross-sectional view along the axial direction of the modifying pipe in the powder conveying and modifying equipment in an embodiment of this application;

[0018] Figure 2 It is the front view of the powder conveying and modifying equipment in an embodiment of this application.

[0019] Reference Numerals in the Drawings

[0020] 1 - Powder conveying pipeline, 10 - Modifying pipe, 100 - Agent outlet, 11 - Reducing pipe, 12 - First conveying pipe, 13 - Second conveying pipe;

[0021] 2 - Swirl sprayer, 20 - Rotating shaft, 21 - Spraying pipe, 22 - Agent outlet hole;

[0022] 3 - Countercurrent sprayer, 30 - Agent conveying pipe, 31 - Intermediate pipe. Detailed Embodiments

[0023] The following further describes the detailed embodiments of the present invention with reference to the drawings.

[0024] It is easy to understand that according to the technical solution of the present invention, under the condition of not changing the essence of the present invention, there are various structural ways and implementation ways that can be mutually replaced by those of ordinary skill in the art. Therefore, the following detailed embodiments and the drawings are only exemplary descriptions of the technical solution of the present invention, and should not be regarded as the whole of the present invention or as a limitation or restriction on the technical solution of the invention.

[0025] The orientation terms such as up, down, left, right, front, back, front side, back side, top, bottom, etc. mentioned or possibly mentioned in this specification are defined relative to the structures shown in the respective drawings. They are relative concepts, and therefore may change accordingly depending on their different positions and different usage states. Therefore, these or other orientation terms should not be interpreted as restrictive terms.

[0026] The present application provides a powder conveying and modifying device, including: a powder conveying pipeline 1, a cyclone sprayer 2 and a countercurrent sprayer 3.

[0027] The powder conveying pipeline 1 is used for continuously conveying powder. The diameter of a part of the pipeline in the powder conveying pipeline 1 is enlarged to define a modifying pipe 10, and a chemical agent outlet 100 is opened on the pipe wall of the modifying pipe 10. The modifying pipe 10 in the embodiment of the present application can be integrally formed or separately formed with other pipe segments in the powder conveying pipeline 1.

[0028] The cyclone sprayer 2 is arranged in the modifying pipe 10. The cyclone sprayer 2 includes a rotating shaft 20 and a spraying pipe 21 installed on the rotating shaft 20. A chemical agent outlet hole 22 for spraying a modifying agent is arranged on the spraying pipe 21, and the spraying pipe 21 can rotate to spray the modifying agent. A positioning seat can be arranged on the inner wall of the modifying pipe 10, and the rotating shaft 20 is rotatably arranged on the positioning seat through shaft hole cooperation or on a fixed positioning seat. When the rotating shaft rotates on the positioning seat, the spraying pipe 21 is installed on the rotating shaft and rotates together with the rotating shaft 20. When the rotating shaft 20 is fixedly arranged on the positioning seat, the spraying pipe 21 is rotatably connected to the rotating shaft 20 through a sleeve. When the airflow for conveying powder acts on the spraying pipe 21 and the rotating shaft 20, it drives the spraying pipe 21 to rotate or the rotating shaft 20 drives the spraying pipe 21 to rotate. The rotating spraying pipe 21 turbulently disturbs the powder while spraying the modifying agent, so that the powder and the modifying agent are fully contacted to realize effective film coating of the modifying agent on the powder.

[0029] The rotating shaft 20 in the embodiment of the present application is hollowly arranged to serve as a conveying channel for the modifying agent to supply the modifying agent to the spraying pipe 21.

[0030] The countercurrent sprayer 3 includes a chemical agent conveying pipe 30 arranged on the outer periphery of the modifying pipe 10. A conveying port is opened on the chemical agent conveying pipe 30, and the conveying port is communicated with the chemical agent outlet 100 of the modifying pipe 10, and an intermediate pipe 31 communicated between the chemical agent conveying pipe 30 and the chemical agent outlet 100 of the modifying pipe 10. The countercurrent sprayer 3 sprays the modifying agent into the modifying pipe 10 through the chemical agent outlet 100, and the spraying direction of the modifying agent at the chemical agent outlet 100 is reverse to the flowing direction of the powder, so as to realize enhanced mixing of the powder and the modifying agent. The included angle between the spraying direction of the modifying agent at the chemical agent outlet 100 and the flowing direction of the powder is an obtuse angle or a flat angle, which has an effect of reversely loosening and enhancing mixing of the powder.

[0031] In the embodiment of the present application, the modified pipe 10 is a part of the powder conveying pipeline 1. The powder passes through the modified pipe 10 in a continuous fluidized state. The two processes of powder conveying and spraying the modifier are completed in the modified pipe 10 in the state of continuously conveying the powder, without separately setting up the equipment and process for spraying the modifier, which simplifies the process, reduces the equipment cost and maintenance cost, and improves the powder conveying efficiency. The diameter of the modified pipe 10 is enlarged to reduce the speed of the powder conveyed into the modified pipe 10, increase the time required for the powder to pass through the modified pipe 10, and perform primary mixing by rotary spraying with the swirl sprayer 2 and secondary mixing by countercurrent spraying with the countercurrent sprayer 3 to enable the modifier to be in full contact with the powder, which is beneficial to evenly coating the powder with a film.

[0032] As an optional embodiment, the diameter of a part of the pipeline in the powder conveying pipeline 1 is reduced to define a reduced-diameter pipe 11. Along the conveying direction of the modifier, the reduced-diameter pipe 11 is connected behind the modified pipe 10. The reduced-diameter pipe 11 provided in the embodiment of the present application can enable the powder and the modifier mixed in the modified pipe 10 to flow at an accelerated speed in the reduced-diameter pipe 11, forcing the powder and the air flow with a certain settlement in the modified pipe 10 to restore a good conveying flow pattern again and prompting the powder and the modifier to accelerate contact for uniform mixing, which is beneficial to further improving the mixing effect of the powder and the modifier. The length of the reduced-diameter pipe 11 in the embodiment of the present application is selected between 100 mm and 1000 mm.

[0033] As an optional embodiment, the conveying port and the agent outlet 100 are connected and communicated through an intermediate pipe 31. The number of the intermediate pipes 31 is at least two, and at least two of the intermediate pipes 31 are arranged along the circumferential direction of the modified pipe 10. In the embodiment of the present application, the agent conveying pipe 30 is an annular pipe and extends along the circumferential direction of the modified pipe 10. In the embodiment of the present application, by arranging at least two intermediate pipes 31 to spray the modifier into the modified pipe 10 along the circumferential direction of the modified pipe 10, it is beneficial to further increase the film coating effect of the modifier on the powder.

[0034] As an alternative embodiment, the number of the agent outlets 100 is at least three. At least two of the agent outlets 100 are arranged along the lower half of the circumferential direction of the modification pipe 10, and at least one of the agent outlets 100 is arranged in the upper half of the modification pipe 10. In the embodiment of the present application, the agent conveying pipe 30 is an annular pipe that extends along the circumferential direction of the modification pipe 10. The lower half of the circumferential direction of the modification pipe 10 refers to the lower 1 / 2 part of the modification pipe 10, and the upper half refers to the upper 1 / 2 part of the modification pipe 10. Due to the density difference and its own gravity, the powder is prone to settle to the bottom of the modification pipe 10. It is more efficient to arrange at least two agent outlets 100 at the bottom of the modification pipe 10 for secondary spraying. In the embodiment of the present application, 3 to 8 agent outlets 100 can be arranged on the outer periphery of the lower half of the modification pipe 10, and 1 to 3 agent outlets 100 can be arranged on the outer periphery of the upper half, so as to better fluidize the powder at the bottom of the modification pipe 10, provide sufficient kinetic energy and convey it to the reduced-diameter pipe 11.

[0035] As an alternative embodiment, along the conveying direction of the modifier, the countercurrent sprayer 3 is located behind the cyclone sprayer 2. The included angle between the central axis of the agent outlet 100 and the central axis of the modification pipe 10 is an acute angle, so that the included angle between the direction of the modifier ejected from the agent outlet 100 and the conveying direction of the powder is an obtuse angle, and the modifier and the powder form a countercurrent contact. As Figure 1 shown, the included angle between the central axis of the agent outlet 100 and the central axis of the modification pipe 10 is an acute angle, so as to achieve that the direction of the modifier ejected from the agent outlet 100 is set in the reverse direction of the conveying direction of the powder, and further enable the countercurrent contact between the modifier and the powder. The airflow ejected together with the modifier has the function of "loosening air", further fluidizing the powder, preventing the powder from depositing at the bottom of the modification pipe 10, and smoothly sending the powder to the reduced-diameter pipe.

[0036] As an alternative embodiment, the intermediate pipe 31 includes an inclined pipe section, the inclined pipe section is communicated with the agent outlet 100, and the central axis of the inclined pipe section is collinear with the central axis of the agent outlet 100. The central axis of the inclined pipe section is collinear with the central axis of the agent outlet 100, so as to play an inclined guiding role on the modifier in the intermediate pipe 31 through the inclination of the inclined pipe section, so that the modifier is ejected along the central axis direction of the agent outlet 100, and the countercurrent spraying effect on the powder is improved.

[0037] In the embodiment of the present application, the vertical distance between the rotating shaft 20 in the cyclone sprayer 2 and the front end face of the modification pipe 10 along the powder conveying direction is set to be between 80 and 200 mm. The spraying speed of the agent outlet 100 is preferably between 1 and 10 m / s.

[0038] As an alternative embodiment, the included angle between the central axis of the agent outlet 100 and the central axis of the modification tube 10 is θ, where 30° ≤ θ ≤ 60°. By setting the included angle between the central axis of the agent outlet 100 and the central axis of the modification tube 10 within the range of 30° and 60°, the modifier ejected from the agent outlet 100 can have a better loosening effect on the powder, prompting the powder deposited at the bottom of the modification tube 10 to flow again, and enabling the modifier and the powder to be mixed again.

[0039] As an alternative embodiment, the powder conveying pipeline 1 further includes a first conveying pipe 12 and a second conveying pipe 13. Along the powder conveying direction, the first conveying pipe 12 is connected in front of the modification tube 10, and the second conveying pipe 13 is connected behind the reduced-diameter pipe 11. The diameters of both the first conveying pipe 12 and the second conveying pipe 13 are R1, the radius of the modification tube 10 is R2, and the diameter of the reduced-diameter pipe 11 is R3, where 3R1 ≤ R2 ≤ 10R1 and 0.3R1 ≤ R3 ≤ 0.7R1. In the embodiment of the present application, both the first conveying pipe 12 and the second conveying pipe 13 are pipelines for normal powder conveying. The powder enters the modification tube 10 through the first conveying pipe 12, slows down the flow rate to fully contact the modifier, then accelerates and mixes through the reduced-diameter pipe 11, and finally enters the second conveying pipe 13 for normal powder conveying to complete the subsequent finished product conveying.

[0040] As an alternative embodiment, the number of the spraying pipes 21 is at least two, and at least two of the spraying pipes 21 are arranged circumferentially along the axial plane of the rotating shaft 20. In the embodiment of the present application, setting the number of the spraying pipes 21 to be more than one is beneficial to increasing the contact area between the modifier and the powder and the turbulence effect generated when the modifier is ejected. As Figure 1 shown, the number of the spraying pipes 21 can be set to five. The five spraying pipes 21 are arranged circumferentially around the rotating shaft 20, and the included angle between any two adjacent spraying pipes 21 is the same, which is convenient for the spraying pipes 21 to spray the modifier evenly on the powder.

[0041] As an alternative embodiment, the rotating shaft 20 extends into the interior of the modification tube 10. The rotating shaft 20 is located below the central axis of the modification tube 10, and the vertical distance between the rotating shaft 20 and the central axis of the modification tube 10 is H, where 0.2R2 ≤ H ≤ 0.49R2. The distance between the top surface of the rotating shaft 20 and the central axis of the modification tube 10 is H. In the embodiment of the present application, the rotating shaft 20 is located below the central axis of the modification tube 10 in the working state, so that the spraying pipe 21 rotated to above the rotating shaft 20 is located at the position of the central axis with the maximum air flow velocity in the modification tube 10, enabling the spraying pipe 21 to fully utilize the driving effect of the air flow in the powder conveying pipeline 1 to rotate.

[0042] As an alternative embodiment, at least two agent outlet holes 22 are formed in the spraying pipe 21 along the length direction. The length of the spraying pipe 21 is L, and 0.5L ≤ H ≤ 0.9L. By setting the length of the spraying pipe 21 to be greater than the vertical distance between the rotating shaft 20 and the central axis of the modification pipe 10, it is convenient for the spraying pipe 21 to fully contact the airflow where the powder is located. The spraying pipe 21 rotates and sprays the modifier under the driving action of the airflow to fully coat the powder with the film. The spraying speed of the agent outlet hole 22 is preferably 4 m / s to 20 m / s.

[0043] In the embodiment of the present application, agent outlet holes 22 are formed on both sides of the spraying pipe 21 ( Figure 1 in the front-back direction), so as to fully coat the powder on both sides of the spraying pipe 21. Agent outlet holes 22 are formed in both the up-down direction of the spraying pipe 21 to coat the powder above and below the spraying pipe 21, increasing the sufficiency of film coating.

[0044] According to needs, the above technical solutions can be combined to achieve the best technical effect.

[0045] The above are only the principles and preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, based on the principles of the present invention, several other variations can also be made, which should also be regarded as the protection scope of the present invention.

Claims

1. A powder conveying and modifying device, characterized in that, it includes: a powder conveying pipeline, a cyclone sprayer and a countercurrent sprayer; The powder conveying pipeline is used for continuously conveying powder, and the diameter of part of the pipeline in the powder conveying pipeline is enlarged to define a modifying pipe, and a reagent outlet is opened on the pipe wall of the modifying pipe; The cyclone sprayer is arranged in the modifying pipe. The cyclone sprayer includes a rotating shaft and a spraying pipe installed on the rotating shaft. The spraying pipe is provided with reagent outlets for spraying a modifying agent, and the spraying pipe can rotate to spray the modifying agent; The countercurrent sprayer includes a reagent conveying pipe arranged on the outer periphery of the modifying pipe. The reagent conveying pipe is provided with a conveying port, and the conveying port is communicated with the reagent outlet of the modifying pipe. The countercurrent sprayer sprays the modifying agent into the modifying pipe through the reagent outlet, and the spraying direction of the modifying agent at the reagent outlet is reverse to the flowing direction of the powder.

2. The powder conveying and modifying device according to claim 1, characterized in that, The diameter of part of the pipeline in the powder conveying pipeline is reduced to define a reduced-diameter pipe, and along the conveying direction of the modifying agent, the reduced-diameter pipe is connected behind the modifying pipe.

3. The powder conveying and modifying device according to any one of claims 1-2, characterized in that, The conveying port and the reagent outlet are communicated through an intermediate pipe. The number of the reagent outlets is at least two, and at least two of the reagent outlets are arranged along the circumferential direction of the modifying pipe.

4. The powder conveying and modifying device according to claim 3, characterized in that, Along the conveying direction of the modifying agent, the countercurrent sprayer is located behind the cyclone sprayer. The included angle between the central axis of the reagent outlet and the central axis of the modifying pipe is an acute angle, so that the included angle between the direction of the modifying agent sprayed at the reagent outlet and the conveying direction of the powder is an obtuse angle, and the modifying agent and the powder form a countercurrent contact.

5. The powder conveying and modifying device according to claim 4, characterized in that, The intermediate pipe includes an inclined pipe section, and the inclined pipe section is communicated with the reagent outlet. The central axis of the inclined pipe section is collinear with the central axis of the reagent outlet.

6. The powder conveying and modifying device according to claim 4, characterized in that, The included angle between the central axis of the reagent outlet and the central axis of the modifying pipe is θ, and 30° ≤ θ ≤ 60°.

7. The powder conveying and modifying device according to claim 2, characterized in that, The powder conveying pipeline further includes a first conveying pipe and a second conveying pipe. Along the conveying direction of the powder, the first conveying pipe is connected in front of the modifying pipe, and the second conveying pipe is connected behind the reduced-diameter pipe. The diameters of the first conveying pipe and the second conveying pipe are both R1, the radius of the modifying pipe is R2, and the diameter of the reduced-diameter pipe is R3, and 3R1 ≤ R2 ≤ 10R1, 0.3R1 ≤ R3 ≤ 0.7R1.

8. The powder conveying and modifying device according to any one of claims 1-2, characterized in that, The number of the spraying pipes is at least two, and at least two of the spraying pipes are arranged along the circumferential direction of the axial plane of the rotating shaft.

9. The powder conveying and modifying device according to any one of claims 1-2, characterized in that, the rotating shaft extends into the interior of the modifying pipe, the rotating shaft is located below the central axis of the modifying pipe and the vertical distance between the rotating shaft and the central axis of the modifying pipe is H, and 0.2R2 ≤ H ≤ 0.49R2.

10. The powder conveying and modifying device according to claim 9, characterized in that, at least two agent outlet holes are formed in the spraying pipe along the length direction, the length of the spraying pipe is L, and 0.5L ≤ H ≤ 0.9L.