High-efficiency low-emission solid-liquid separator for fast reactor spent pool corrosion products
The solid-liquid separator designed with nozzles and ejectors solves the problem of insufficient corrosion product treatment capacity in the fast reactor spent fuel pool purification system, achieving efficient separation of corrosion products and pool water recovery, thus reducing operational risks and economic costs.
Patent Information
- Application Number
- CN202610006107.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-01-05
- Publication Date
- 2026-02-13
AI Technical Summary
Existing fast reactor spent fuel pool purification systems have limited capacity to handle corrosion products, leading to frequent replacement of resins and filter cartridges, increasing operational risks and economic costs. Meanwhile, the wastewater discharged from the cyclone solid-liquid separator increases the burden of radioactive wastewater treatment.
The design employs a nozzle and ejector device, which creates a stable swirling flow field through the impeller and utilizes density differences to achieve solid-liquid separation. Combined with the structure of the inverted conical separation tank and ejector tube, it promotes the sedimentation of corrosion products and recovers pool water, thereby reducing wastewater discharge.
It achieves effective separation of corrosion products and efficient recovery of radioactive pool water, reduces maintenance risks and economic costs, reduces the burden of radioactive wastewater treatment, and has strong compatibility with existing circulation systems.
Smart Images
Figure CN121513533A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the technical field of fast reactor spent fuel pool purification devices, specifically relating to a high-efficiency, low-emission solid-liquid separator for corrosion products in fast reactor spent fuel pools. Background Technology
[0002] Currently, the ferritic-martensitic stainless steel in the spent fuel pool of fast reactor units is facing severe corrosion problems. The amount of corrosion products generated has exceeded the processing capacity of the existing spent fuel pool purification system, resulting in a significant increase in the pool's radioactivity level. Therefore, a new purification device needs to be designed for the spent fuel pool of fast reactor units.
[0003] The current spent fuel pool purification system usually adopts a combination of mechanical filters and desalination beds, and mainly relies on nuclear-grade resin to play a purification role. However, the amount of corrosion products generated by fast reactor operation is large, which makes the resin replacement frequency of the purification system high, increases the operating time, and leads to an increase in the collective dose of nuclear power plants [1]. Hu Hai, Su Kai, Jiang Chunhua, et al. Research on reducing the amount of nuclear-grade resin solid waste in VVER nuclear power units [J]. China Nuclear Power, 2020, 13(02): 165-170. At the same time, the filter under this condition also needs to be replaced frequently, which increases the operating risk and economic cost. In addition, the current cyclone solid-liquid separator will discharge wastewater when separating solid particles, but since the pool water in the spent fuel pool is radioactive, the discharged wastewater will further increase the burden of radioactive wastewater treatment. Therefore, this project proposes a high-efficiency low-emission solid-liquid separator for corrosion products in the spent fuel pool of fast reactors. The separator achieves effective separation of corrosion products and efficient recovery of pool water through nozzle and ejector design, thereby achieving the goal of purifying the pool water of spent fuel pool. Summary of the Invention
[0004] The purpose of this invention is to address the limitations of existing purification systems in handling large amounts of corrosion products from spent fuel pools in fast reactors through the design of nozzles and ejector devices. This leads to frequent replacement of resins and filter elements, increasing operational risks and costs. Furthermore, current cyclone solid-liquid separators discharge wastewater during solid particle separation, thereby increasing the amount of radioactive wastewater discharged and the burden of radioactive wastewater treatment. The invention aims to achieve effective separation of corrosion products and efficient recovery of radioactive pool water.
[0005] The technical solution of this invention for a high-efficiency, low-emission solid-liquid separator for corrosion products in the spent fuel pool of fast reactors is as follows:
[0006] A high-efficiency, low-emission solid-liquid separator for corrosion products in fast reactor waste ponds includes an inlet component, an impeller, a solid-liquid separation component, an ejector tube, and a solid storage and discharge component.
[0007] One end of the inlet component is inserted into the solid storage and discharge component and connected to one end of the solid-liquid separation component; the other end of the solid-liquid separation component is connected to one end of the ejector tube; the impeller is installed inside the inlet component.
[0008] The inlet component, impeller, solid-liquid separation component, and ejector tube are all concentrically connected and interconnected.
[0009] When the solid-liquid mixture flows in from the other end of the inlet component, the impeller creates a stable and uniform swirling field, resulting in a uniform centrifugal distribution. Due to the density difference between the solid and the liquid, the solid particles, which have a much higher density than the liquid, are driven by a greater centrifugal force and move towards the inner wall area of the inlet component. After passing through the solid-liquid separation component, the solid particles and some of the liquid accompanying the solid particles are discharged from the solid-liquid separation component into the solid storage and discharge component, while the liquid continues to flow into the ejector tube along the solid-liquid separation component, thus achieving solid-liquid separation.
[0010] Furthermore, the solid-liquid separation component includes a separation pipe section, multiple radial nozzles, and multiple inclined nozzles.
[0011] The diameter of the separation tube section is larger than that of the ejector tube, and the end face of the separation tube section connected to the ejector tube is provided with a through hole with the same diameter as the ejector tube for connecting the separation tube section and the ejector tube; the plurality of radial nozzles are evenly distributed on the circumferential outer wall of the separation tube section and communicate with the interior of the separation tube section; the plurality of inclined nozzles are evenly distributed along the circumferential cross-section of the separation tube section and communicate with the interior of the separation tube section.
[0012] The multiple inclined nozzles are used to enhance the guiding effect, so that solid particles and some liquid accompanying the solid particles can be smoothly injected into the solid storage and discharge component.
[0013] The solid particles and a portion of the liquid accompanying the movement of the solid particles are discharged from the plurality of radial nozzles and the plurality of inclined nozzles into the solid storage and discharge component.
[0014] Furthermore, the solid storage and discharge component includes a liquid outlet component, a mixing chamber, a reflux pipe, a separation tank, and a solid discharge outlet.
[0015] One end of the liquid outlet component is concentrically connected to one end of the mixing chamber, and the other end of the mixing chamber is concentrically connected to and communicates with one end of the reflux pipe; the other end of the reflux pipe is concentrically connected to and communicates with the large-diameter end of the separation tank; the solid discharge outlet is connected to and communicates with the small-diameter end of the separation tank.
[0016] Furthermore, the liquid outlet component, mixing chamber, reflux pipe, and separation tank are all concentrically installed with the inlet component, impeller, solid-liquid separation component, and ejector pipe.
[0017] One end of the separation tank has an inverted conical structure, and the inclination angle of the inverted conical surface is smaller than the angle of repose. This is used to utilize gravity to allow the solid particles to settle to the bottom of the inverted conical end of the separation tank, thereby preventing the solid particles from statically accumulating on the inner wall of the separation tank.
[0018] When the liquid accompanying the solid particles is ejected from the radial nozzle and the inclined nozzle, the liquid accompanying the solid particles immediately enters an expansion state, the flow rate decreases, and thus increases the settling time of the solid particles, allowing the solid particles to settle completely.
[0019] Furthermore, a valve is installed at the solid discharge port; when the solid particles reach a preset accumulation level, the valve is opened to discharge the solid particles from the bottom of the inverted conical end of the separation tank through the solid discharge port.
[0020] Furthermore, the other end of the ejector tube is provided with an ejector port, the diameter of which is smaller than the diameter of the ejector tube, and the cross-sectional area of the pipe from the ejector tube to the ejector port gradually decreases.
[0021] Furthermore, after the solid particles are discharged through the solid discharge outlet, the separated liquid flows into the return pipe along the gap between the inner wall of the separation tank and the outer wall of the ejector tube; the liquid in the ejector tube is ejected through the ejector port to form a high-speed jet, which reduces the pressure and forms a local low-pressure area, so that the separated liquid in the return pipe is drawn into the mixing chamber by the liquid ejected through the ejector port.
[0022] Furthermore, the liquid ejected through the ejector port and the separated liquid are mixed in the mixing chamber and undergo momentum exchange, so that the flow rate of the mixed liquid gradually becomes equal and finally flows out through the liquid outlet component.
[0023] Furthermore, the root line of the impeller blades follows an elliptical equation, and the blade exit angle is 45° to 60°.
[0024] Furthermore, the ellipse equation followed by the root line of the blade is:
[0025]
[0026] in, This represents the projection of the leaf root line onto the horizontal plane. The height of the leaf root line in the axial direction. and These are the major axis control parameters and minor axis control parameters for the blade development line, respectively. The torsional parameters of the blade are... This represents the blade twist angle.
[0027] Compared with existing technologies, this invention employs a nozzle and inverted conical separation tank design. The nozzle is radially symmetrical and inclined, ensuring uniform injection of pool water into the inverted conical separation tank while generating a composite flow field of tangential and axial directions. This enhances centrifugal force, promoting faster settling of solid particles towards the wall. Simultaneously, the nozzle acts as a converging agent, directing pool water containing corrosion products into the separation tank. The large flow space within the separation tank slows the water flow velocity during expansion, extending the natural settling time of solid particles and thus improving the slow settling speed and separation efficiency. Furthermore, the ejector device's tapered nozzle allows pool water to flow out at high speed, creating a localized low pressure that drives the pool water in the return pipe to be drawn into the mixing chamber. This avoids the wastewater discharge problem found in traditional cyclone separation, achieving efficient pool water recovery and reducing the burden of radioactive wastewater treatment. This centrifugal separation method eliminates reliance on nuclear-grade resins and filters, eliminating the need for frequent component replacements in radioactive environments. It enables long-term, continuous, and efficient separation of corrosion products, thereby reducing maintenance risks, waste treatment burden, and economic costs. In addition, the overall structure is simple and highly compatible with the existing circulation system of the spent fuel water tank. It does not require large-scale modification of the water tank structure and can be directly installed in the pipeline. Attached Figure Description
[0028] Figure 1 This is a schematic diagram of the structure of the present invention.
[0029] Figure 2 This is a three-dimensional structural diagram of the present invention.
[0030] In the figure: Inlet component 1, Impeller 2, Separation pipe section 3, Radial nozzle 4, Inclined nozzle 5, Separation tank 6, Solid discharge outlet 7, Ejector pipe 8, Ejector port 9, Return pipe 10, Mixing chamber 11, Outlet component 12. Detailed Implementation
[0031] The following is in conjunction with the appendix Figures 1 to 2 The present invention will be further described below.
[0032] A high-efficiency, low-emission solid-liquid separator for corrosion products in the spent fuel pool of a fast reactor includes an inlet component 1, an impeller 2, a solid-liquid separation component, an ejector tube 8, and a solid storage and discharge component.
[0033] One end of the inlet component 1 is inserted into the solid storage and discharge component and connected to one end of the solid-liquid separation component; the other end of the solid-liquid separation component is connected to one end of the ejector tube 8; the impeller 2 is installed inside the inlet component 1.
[0034] The inlet component 1, impeller 2, solid-liquid separation component and ejector tube 8 are all concentrically connected, and the inlet component 1, solid-liquid separation component and ejector tube 8 are all interconnected.
[0035] When the solid-liquid mixture flows in from the other end of the inlet component 1, the impeller 2 causes the solid-liquid mixture to form a stable and uniform swirling field, thereby generating a uniform centrifugal distribution. Due to the density difference between the solid and the liquid, the solid particles, which have a density much higher than that of the liquid, will be driven by a greater centrifugal force and will move towards the inner wall area of the inlet component 1. After flowing through the solid-liquid separation component, the solid particles and part of the liquid that moves with the solid particles are discharged from the solid-liquid separation component into the solid storage and discharge component, while the liquid still flows into the ejector tube 8 along the solid-liquid separation component, thereby achieving solid-liquid separation.
[0036] Furthermore, the solid-liquid separation component includes a separation pipe section 3, multiple radial nozzles 4, and multiple inclined nozzles 5.
[0037] The diameter of the separation tube section 3 is larger than that of the ejector tube 8, and the end face of the separation tube section 3 connected to the ejector tube 8 is provided with a through hole with the same diameter as the ejector tube 8 for connecting the separation tube section 3 and the ejector tube 8; the plurality of radial nozzles 4 are evenly distributed on the circumferential outer wall of the separation tube section 3 and communicate with the interior of the separation tube section 3; the plurality of inclined nozzles 5 are evenly distributed along the circumferential cross-section of the separation tube section 3 and communicate with the interior of the separation tube section 3.
[0038] The plurality of inclined nozzles 5 are used to enhance the guiding effect, so that solid particles and some liquid accompanying the movement of solid particles can be smoothly injected into the solid storage and discharge component.
[0039] The solid particles and a portion of the liquid accompanying the movement of the solid particles are discharged from the plurality of radial nozzles 4 and the plurality of inclined nozzles 5 into the solid storage and discharge component.
[0040] Furthermore, the solid storage and discharge component includes a liquid outlet component 12, a mixing chamber 11, a return pipe 10, a separation tank 6, and a solid discharge outlet 7.
[0041] One end of the liquid outlet component 12 is concentrically connected to one end of the mixing chamber 11, and the other end of the mixing chamber 11 is concentrically connected to and communicates with one end of the return pipe 10; the other end of the return pipe 10 is concentrically connected to and communicates with the large-diameter end of the separation tank 6; the solid discharge outlet 7 is connected to and communicates with the small-diameter end of the separation tank 6.
[0042] Furthermore, the liquid outlet component 12, mixing chamber 11, return pipe 10, and separation tank 6 are all concentrically installed with the inlet component 1, impeller 2, solid-liquid separation component, and ejector pipe 8.
[0043] One end of the separation tank 6 has an inverted conical structure, and the inclination angle of the inverted conical surface is smaller than the angle of repose. This is used to utilize gravity to allow the solid particles to settle to the bottom of the inverted conical end of the separation tank 6, thereby preventing the solid particles from statically accumulating on the inner wall of the separation tank 6.
[0044] When the liquid accompanying the solid particles is ejected from the radial nozzle 4 and the inclined nozzle 5, the liquid accompanying the solid particles immediately enters an expansion state, the flow rate decreases, and thus increases the settling time of the solid particles, allowing the solid particles to settle completely.
[0045] Furthermore, a valve is installed at the solid discharge port 7; when the solid particles reach a preset accumulation level, the valve is opened to discharge the solid particles from the bottom of the inverted conical end of the separation tank 6 through the solid discharge port 7.
[0046] Furthermore, the other end of the ejector tube 8 is provided with an ejector port 9, the diameter of which is smaller than the diameter of the ejector tube 8, and the cross-sectional area of the pipe from the ejector tube 8 to the ejector port 9 gradually decreases.
[0047] Furthermore, after the solid particles are discharged through the solid discharge port 7, the separated liquid flows through the gap between the inner wall of the separation tank 6 and the outer wall of the ejector tube 8 into the return pipe 10; the liquid in the ejector tube 8 is ejected through the ejector port 9 to form a high-speed jet, which reduces the pressure and forms a local low-pressure area, so that the separated liquid in the return pipe 10 is drawn into the mixing chamber 11 by the liquid ejected through the ejector port 9.
[0048] Furthermore, the liquid ejected through the ejector port 9 and the separated liquid are mixed in the mixing chamber 11 and momentum exchange occurs, so that the flow rate of the mixed liquid gradually becomes equal and finally flows out through the liquid outlet component 12.
[0049] Furthermore, the root line of the blades of the impeller 2 follows an elliptical equation, and the blade exit angle is 45° to 60°.
[0050] Furthermore, the ellipse equation followed by the root line of the blade is:
[0051]
[0052] in, This represents the projection of the leaf root line onto the horizontal plane. The height of the leaf root line in the axial direction. and These are the major axis control parameters and minor axis control parameters for the blade development line, respectively. The torsional parameters of the blade are... This represents the blade twist angle.
[0053] Example
[0054] The pool water containing corrosion products flows into the separator pipe from the inlet component 1. Under the action of the impeller 2, whose blade root line conforms to a specific elliptical equation, a stable and uniform swirling field is formed, thereby generating a uniform centrifugal force distribution. Due to the significant difference in density between the solid and liquid phases, solid particles with a density much higher than that of the pool water are driven by a greater centrifugal force. As a result, the corrosion products move towards the pipe wall area, while the less dense pool water moves towards the central area of the pipe, thus achieving solid-liquid phase separation. When the pool water flows through the separation pipe section 3, the radial nozzles 4 on the pipe provide a direct radial outflow channel for the pool water, while the inclined nozzles 5 are set at a certain angle to enhance the guiding effect, ensuring that the corrosion products and a portion of the pool water accompanying the corrosion products can be smoothly sprayed into the inverted conical separation tank 6. Another portion of the pool water continues to flow in the pipe, directly entering the ejector pipe 8, and finally flowing to the ejector port 9. In the inverted conical separation tank 6, the corrosion products are separated from the pool water by the combined action of gravity and centrifugal force and settle to the bottom of the inverted conical separation tank 6. Because the flow space of the inverted conical separation tank 6 is significantly increased, the pool water immediately enters an expanded state upon entry, resulting in a substantial decrease in flow velocity. This increases the time for corrosion products to settle naturally within the collection tank, effectively promoting full settling and ensuring that even smaller corrosion products can completely settle. Furthermore, the inclination angle of the wall of the inverted conical separation tank 6 is smaller than the cone's angle of repose, effectively preventing static accumulation of corrosion products on the wall. Therefore, the corrosion products can smoothly slide down the wall, eventually accumulating at the solid discharge port 7 at the bottom of the inverted conical separation tank 6. When the corrosion products accumulate to a certain level, the valve at the solid discharge port 7 can be opened to discharge them. The separated pool water flows along the gap between the outer wall of the inverted conical separation tank 6 and the nozzle to the return pipe 10, finally reaching the ejector port 9. Because the cross-sectional area of the pipe at the ejector port 9 gradually decreases, the flow velocity of the pool water in the original pipe flowing through the ejector port 9 significantly increases, forming a high-speed jet. The pressure decreases accordingly, creating a localized low-pressure area. The pool water in the return pipe 10 is drawn into the mixing chamber 11 under the influence of the pressure difference. Within the mixing chamber 11, the original pool water and the entrained pool water exchange momentum, gradually achieving velocity equilibrium during the flow. Finally, the pool water flows back from the outlet component 12 to the spent fuel water pool circulation system pipeline, completing the pool water recycling.
[0055] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.
Claims
1. A high efficiency low emission solid-liquid separator for fast reactor spent pool corrosion products, characterized in that: The application relates to a solid-liquid separation device, which comprises an inlet component (1), an impeller (2), a solid-liquid separation component, an ejector pipe (8) and a solid storage and discharge component. One end of the inlet component (1) is inserted into the solid storage and discharge component and connected with one end of the solid-liquid separation component; the other end of the solid-liquid separation component is connected with one end of the ejector pipe (8); and the impeller (2) is installed in the inlet component (1). The inlet component (1), the impeller (2), the solid-liquid separation component and the ejector pipe (8) are concentrically connected, and the inlet component (1), the solid-liquid separation component and the ejector pipe (8) are communicated with each other. When the solid-liquid mixture flows from the other end of the inlet component (1), the impeller (2) makes the solid-liquid mixture form a stable and uniform cyclone field, thereby generating a uniform centrifugal distribution; due to the density difference between the solid and the liquid, the solid particles with a density much higher than that of the liquid are driven by a greater centrifugal force, thereby moving to the inner wall surface area of the inlet component (1), and after flowing through the solid-liquid separation component, the solid particles and part of the liquid moving along with the solid particles are discharged from the solid-liquid separation component into the solid storage and discharge component, while the liquid still flows into the ejector pipe (8) along the solid-liquid separation component, thereby realizing solid-liquid separation.
2. The high efficiency low emission solid-liquid separator for fast reactor spent pool corrosion products of claim 1, wherein: The solid-liquid separation component comprises a separation pipe section (3), a plurality of radial nozzles (4) and a plurality of inclined nozzles (5). The diameter of the separation pipe section (3) is greater than that of the ejector pipe (8), and the end face of the connection end of the separation pipe section (3) and the ejector pipe (8) is provided with a through hole with the same diameter as that of the ejector pipe (8) for communicating the separation pipe section (3) and the ejector pipe (8); the plurality of radial nozzles (4) are uniformly distributed on the circumferential outer wall of the separation pipe section (3) and communicated with the inside of the separation pipe section (3); and the plurality of inclined nozzles (5) are uniformly distributed along the cross section of the separation pipe section (3) and communicated with the inside of the separation pipe section (3). The plurality of inclined nozzles (5) are used for enhancing the guiding effect, so that the solid particles and part of the liquid moving along with the solid particles can be smoothly injected into the solid storage and discharge component. The solid particles and part of the liquid moving along with the solid particles are discharged from the plurality of radial nozzles (4) and the plurality of inclined nozzles (5) into the solid storage and discharge component.
3. A high efficiency low emission solid-liquid separator for fast reactor spent pool corrosion products according to claim 2, characterized in that: The solid storage and discharge component comprises a liquid outlet component (12), a mixing cavity (11), a reflux pipe (10), a separation groove (6) and a solid discharge outlet (7). One end of the liquid outlet component (12) is concentrically connected with one end of the mixing cavity (11), the other end of the mixing cavity (11) is concentrically connected with one end of the reflux pipe (10) and communicated, the other end of the reflux pipe (10) is concentrically connected with the large-diameter end of the separation groove (6) and communicated, and the solid discharge outlet (7) is connected with the small-diameter end of the separation groove (6) and communicated.
4. A high efficiency low emission solid-liquid separator for fast reactor spent pool corrosion products according to claim 3, characterized in that: The liquid outlet component (12), the mixing cavity (11), the reflux pipe (10) and the separation groove (6) are concentrically installed with the inlet component (1), the impeller (2), the solid-liquid separation component and the ejector pipe (8). One end of the separation tank (6) is a reverse taper structure, the inclination angle of the reverse taper is less than the angle of repose, for using gravity to make the solid particles settle to the bottom of the reverse taper end of the separation tank (6), and then avoid the static accumulation of solid particles on the inner wall of the separation tank (6); When the part of the liquid accompanying the movement of the solid particles is sprayed from the radial nozzle (4) and the inclined nozzle (5), the part of the liquid accompanying the movement of the solid particles immediately enters the expansion state, the flow rate is reduced, and then the settling time of the solid particles is increased, so that the solid particles are completely settled.
5. A high efficiency low emission solid-liquid separator for fast reactor spent pool corrosion products according to claim 4, characterized in that: The solid discharge port (7) is provided with a valve; when the solid particles reach the preset accumulation degree, the valve is opened, and the solid particles are discharged from the bottom of the reverse taper end of the separation tank (6) through the solid discharge port (7).
6. A high efficiency low emission solid-liquid separator for fast reactor spent pool corrosion products according to claim 4, characterized in that: The other end of the ejector pipe (8) is provided with an injection port (9), the diameter of the injection port (9) is smaller than the diameter of the ejector pipe (8), and the pipe cross-sectional area of the ejector pipe (8) to the injection port (9) gradually decreases.
7. A high efficiency low emission solid-liquid separator for fast reactor spent pool corrosion products according to claim 6, characterized in that: When the solid particles are discharged through the solid discharge port (7), the separated liquid flows into the return pipe (10) through the gap between the inner wall of the separation tank (6) and the outer wall of the ejector pipe (8); the liquid in the ejector pipe (8) is sprayed out of the injection port (9) to form a high-speed jet, so that the pressure is reduced, and then a local low-pressure area is formed, so that the separated liquid in the return pipe (10) is sucked into the mixing chamber (11) by the liquid sprayed out of the injection port (9).
8. A high efficiency low emission solid-liquid separator for fast reactor spent pool corrosion products according to claim 7, characterized in that: The liquid sprayed out of the injection port (9) and the separated liquid mix in the mixing chamber (11) and exchange momentum, so that the flow rate of the mixed liquid gradually balances, and finally flows out through the liquid outlet component (12).
9. The high efficiency low emission solid-liquid separator for fast reactor spent pool corrosion products of claim 1, wherein: The blade root line of the impeller (2) blade follows an elliptical equation, and the blade outlet angle is 45° to 60°.
10. A high efficiency low emission solid-liquid separator for fast reactor spent pool corrosion products according to claim 9, characterized in that, The elliptical equation followed by the blade root line is: wherein is the projected position of the blade root line in the horizontal plane, is the height of the blade root line in the axial direction, and are the long axis control parameter and the short axis control parameter of the blade spread line, respectively, is the twist parameter of the blade, is the twist angle of the blade.