Axial force balancing device of multi-stage vertical molten salt pump and multi-stage vertical molten salt pump
By setting up an axial force balance device between the space guide vane and the impeller of the multi-stage vertical molten salt pump, the elastic damping and sealing structure are used to achieve the balance of the axial force, and the operation process of the multi-stage vertical molten salt pump is solved. The wear and vibration problems caused by axial forces improve the operating safety and reliability of the pump.
Patent Information
- Application Number
- CN202411925805.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-25
- Publication Date
- 2025-02-18
- Estimated Expiration
- 2044-12-25
AI Technical Summary
During operation, due to the asymmetry of the front and rear covers of the impeller and the self-weight of the rotor, the multi-stage vertical molten salt pump will generate force in the axial direction, causing the rotor assembly to come into contact with the stationary components, causing wear and enlargement of the device. Vibration and noise reduce pump operation efficiency and can cause serious problems such as overheating damage to support bearings and shaft breakage.
Design a multi-stage vertical molten salt pump axial force balance device, by setting up an axial force balance device between the space guide vane and the impeller, and using elastic damping between the third balance chamber and the first balance chamber, the elastic damping is achieved. The balance of the axial force that the impeller is subjected to. The device includes a cylinder, elastic damping and adjusting slide, and real-time monitoring and automatic balance of axial forces are achieved through sealing structure and infrared ranging device.
Effectively reduce the axial force changes encountered by the pump rotor, achieve rapid response and automatic balance to the axial force, reduce wear and vibration noise of the rotor assembly, and improve the operation safety of the multi-stage vertical molten salt pump and reliability.
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Figure CN119467411A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the field of molten salt pumps, and in particular to an axial force balancing device for a multi-stage vertical molten salt pump and a multi-stage vertical molten salt pump. Background Art
[0002] The vertical multi-stage molten salt pump is the core power device of the solar thermal power station. In actual operation, due to the asymmetry of the front and rear covers of the impeller, the difference in the flow channels of the front and rear cavities of the impeller, and the influence of the rotor's own weight, an axial force will be generated during operation. The molten salt pump of the solar thermal system adopts a structure in which the multi-stage impellers are arranged in the same direction. The vertical installation method makes the axial force on the rotor structure gradually increase from top to bottom along the pump shaft, and accumulates at the first-stage impeller on the lower shaft.
[0003] Axial force will cause the rotor to move axially, causing the rotor assembly to contact the stationary parts, resulting in wear, increasing the vibration and noise of the device, and reducing the operating efficiency of the pump. Excessive axial force will cause the impeller to move toward the inlet, increase the friction between the impeller and the pump casing, increase the motor load, and then damage the sealing structure, resulting in increased leakage of the device and increased pump power consumption. For multi-stage pumps, the impact of axial force is more prominent. Excessive axial force will cause the support bearing to overheat and damage, and may even cause serious problems such as shaft breakage, posing a threat to the safe and stable operation of the pump. Summary of the invention
[0004] In view of the deficiencies in the prior art, the present invention provides an axial force balancing device for a multi-stage vertical molten salt pump and a multi-stage vertical molten salt pump, which have a novel structure and can balance the axial force exerted on the pump rotor, thereby effectively improving the safety and reliability of the operation of the multi-stage molten salt pump.
[0005] The present invention achieves the above technical objectives through the following technical means.
[0006] An axial force balancing device for a multi-stage vertical molten salt pump is provided, wherein the axial force balancing device is provided between a spatial guide vane and an impeller, wherein the axial force balancing device comprises a third balancing chamber and a first balancing chamber, wherein a labyrinth gap is provided between the first balancing chamber and a pressure chamber of the impeller; wherein the third balancing chamber is located inside the spatial guide vane, and an elastic damping is provided between the first balancing chamber and the third balancing chamber for balancing the axial force exerted on the impeller.
[0007] Furthermore, the axial force balancing device includes a cylinder, an elastic damper and an adjusting slide; the cylinder includes an end cover and an outer cylinder wall, the end cover is installed at one end of the outer cylinder wall, the end cover is located inside the space guide vane, and the end cover is connected to the space guide vane; the other end of the outer cylinder wall is matched with the impeller gap; the adjusting slide is located inside the cylinder, and the adjusting slide is connected to the rear cover plate of the impeller, the adjusting slide divides the cylinder into a first balancing chamber and a third balancing chamber, and an elastic damper is provided between the adjusting slide and the cylinder; one side of the adjusting slide, the outer cylinder wall and the rear cover plate constitute the first balancing chamber; the area between the other side of the adjusting slide and the end cover constitutes the third balancing chamber.
[0008] Furthermore, a sealing structure is provided between the adjusting slide plate and the inner wall surface of the outer cylinder wall.
[0009] Furthermore, the sealing structure is an annular metal brush wire, and one end of the adjusting slide plate is provided with a plurality of spaced grooves, and the annular metal brush wire is located in the grooves.
[0010] Furthermore, a first gap is provided between the rear cover plate and the space guide vane, and a second gap is provided between the rear cover plate and the outer cylinder wall, and the first gap and the second gap constitute a labyrinth gap between the first balance chamber and the pressure chamber.
[0011] Furthermore, a protrusion is provided on the inner wall of the outer cylinder wall, and a spring is provided between the protrusion and the adjusting slide plate.
[0012] Furthermore, a second balancing chamber is provided between the first balancing chamber and the pressure chamber, and the second balancing chamber is an area surrounded by the space guide vane, the cylinder and the rear cover plate.
[0013] A multi-stage vertical molten salt pump comprises a multi-stage impeller, wherein the axial force balancing device is arranged between at least one stage of the impeller and its corresponding space guide vane.
[0014] The beneficial effects of the present invention are:
[0015] The axial force balancing device of the multi-stage vertical molten salt pump described in the present invention is provided with an axial force balancing device between the spatial guide vane and the impeller, and an elastic damping is provided between the first balancing chamber and the third balancing chamber, which can achieve a rapid response to changes in the axial force exerted on the pump rotor. When the pump rotor is subjected to different axial forces, the pressure chamber, the labyrinth gap, the third balancing chamber and the elastic damping realize automatic balancing of the axial force exerted on the pump rotor. At the same time, an infrared ranging device in the balancing device is used to realize real-time monitoring of the axial force of the pump body during operation, thereby improving the safety of the operation of the multi-stage vertical molten salt pump. BRIEF DESCRIPTION OF THE DRAWINGS
[0016] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. The drawings described below are some embodiments of the present invention. For ordinary technicians in this field, it is obvious that other drawings can be obtained based on these drawings without paying any creative work.
[0017] Figure 1 This is a schematic diagram of the multi-stage vertical molten salt pump described in the present invention.
[0018] Figure 2 This is a schematic diagram of the installation of the axial force balancing device described in the present invention.
[0019] Figure 3 for Figure 2 Partial enlarged image.
[0020] Figure 4 The figure is a schematic diagram of the installation of the sealing structure described in the present invention.
[0021] Figure 5 This is a three-dimensional diagram of the axial force balancing device described in the present invention.
[0022] Figure 6 This is a force comparison diagram between the installed axial force balancing device and the prior art.
[0023] Figure 7 This is a flow comparison chart under different flow conditions when installing the balancing device.
[0024] Figure 8 The figure is a comparison chart of the external characteristic parameters of a single-stage pump with the present balancing device installed and without balancing measures installed and in the prior art.
[0025] In the figure:
[0026] 1-inlet section; 2-first-stage impeller; 3-secondary impeller; 4-space guide vane; 5-pump shaft; 6-middle section; 7-outlet section; 8-balancing device; 9-rear cover; 10-fixed module; 11-adjusting slide plate; 12-spring; 13-end cover; 14-outer cylinder wall; 15-infrared ranging device; 16-sealing structure; 17-balancing hole; 18-sliding bearing; a-first gap; b-second gap; 101-pressure chamber; 102-second balancing chamber; 104-first balancing chamber; 103-third balancing chamber. DETAILED DESCRIPTION
[0027] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, and should not be construed as limiting the present invention.
[0028] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "upper", "lower", "axial", "radial", "vertical", "horizontal", "inner", "outer" and the like indicate positions or positional relationships based on the positions or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first" and "second" are only used for descriptive purposes, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, the features defined as "first" and "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, the meaning of "multiple" is two or more, unless otherwise clearly and specifically defined.
[0029] In the present invention, unless otherwise clearly specified and limited, the terms "installed", "connected", "connected", "fixed" and the like should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be an indirect connection through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.
[0030] like Figure 1 As shown, the multi-stage vertical molten salt pump described in the present invention is composed of five-stage impellers, and the impellers of each stage are installed in series on the pump shaft 5 in the same direction. The axial force balancing device of the multi-stage vertical molten salt pump described in the present invention can be arranged on one side of a certain stage of impeller or several stages of impellers according to the actual model of the multi-stage pump. Generally, an axial force balancing device 8 is provided between a certain stage of the spatial guide vane 4 and the impeller corresponding thereto. The axial force balancing device has a third balancing chamber 103 and a first balancing chamber 104, and a labyrinth gap is provided between the first balancing chamber 104 and the pressure chamber 101 of the impeller; the third balancing chamber 103 is located inside the spatial guide vane 4, and an elastic damping is provided between the first balancing chamber 104 and the third balancing chamber 103, which is used to balance the axial force exerted on the impeller.
[0031] like Figure 2 , Figure 3 and Figure 5As shown, a sliding bearing 20 is provided between the space guide vane 4 and the pump shaft 5, and the axial force balancing device 8 includes a cylinder, an elastic damper and an adjusting slide 11; the cylinder includes an end cover 13 and an outer cylinder wall 14, and the end cover 13 is installed at one end of the outer cylinder wall 14, and the end cover 13 is located inside the space guide vane 4, and the end cover 13 is connected to the space guide vane 4; a mechanical seal is provided between the sliding bearing 20 and the end cover 13. The other end of the outer cylinder wall 14 is in clearance with the impeller; the adjusting slide 11 is located inside the cylinder, and the adjusting slide 11 is connected to the rear cover 9 of the impeller through the fixing module 10, and the adjusting slide 11 divides the cylinder into a first balancing chamber 104 and a third balancing chamber 103, and an elastic damper is provided between the adjusting slide 11 and the cylinder; one side of the adjusting slide 11, the outer cylinder wall 14 and the rear cover 9 constitute the first balancing chamber 104; the area between the other side of the adjusting slide 11 and the end cover 13 constitutes the third balancing chamber 103. The end cover 13 is fixedly mounted on the first-stage space guide vane 4 by bolts, and the end cover 13 is fixedly connected to the outer cylinder wall 14 by bolts. A first gap a is provided between the rear cover plate 9 and the space guide vane 4, and a second gap b is provided between the rear cover plate 9 and the outer cylinder wall 14. The first gap a and the second gap b constitute a labyrinth gap between the first balance chamber 104 and the pressure chamber 101 of the impeller. The second gap b is 0.5mm to 0.6mm, and the axial length of the second gap b can change with the change of the axial force. A second balance chamber 102 is provided between the first balance chamber 104 and the pressure chamber 101, and the second balance chamber 102 is an area surrounded by the space guide vane 4, the cylinder and the rear cover plate 9.
[0032] The rear cover plate 9 and the fixing module 10 are connected by a key to achieve synchronization of position changes during the operation of the molten salt pump. The fixing module 10 and the adjusting slide plate 11 are locked in the axial direction and move freely in the radial direction through corresponding concave-convex structures, that is, the rotation of the fixing module 10 will not drive the rotation of the adjusting slide plate 11, but the axial movement of the fixing module 10 will cause the axial movement of the adjusting slide plate 11. A spring 12 is installed between the adjusting slide plate 11 and the outer cylinder wall 14. An infrared ranging device 15 is installed on the corresponding surface of the adjusting slide plate 11 and the end cover 13 to monitor the axial force during the operation of the rotor, and then monitor the actual operation status of the entire molten salt pump.
[0033] like Figure 4 As shown, a sealing structure 16 is provided between the adjusting slide plate 11 and the inner wall surface of the outer cylinder wall 14. The sealing structure 16 is an annular metal brush wire, and a plurality of spaced grooves are provided at one end of the adjusting slide plate 11. The annular metal brush wire is located in the grooves to minimize the leakage of the liquid in the first balancing chamber 104 to the third balancing chamber 103 through the gap therein.
[0034] The axial force balancing principle of the present invention is to balance the axial force by utilizing the relatively low pressure of the pressure chamber 101, the labyrinth gap, the third balancing chamber 103 and the bidirectional action of the spring 12 when the pump rotor is subjected to different axial forces, specifically:
[0035] The axial force on the impeller can be mainly divided into two parts: one part is the axial force of the pressure chamber 101 on the upper part of the impeller rear cover 9, and the other part is the axial force of the first balance chamber 104 on the lower part of the impeller rear cover. The former part of the axial force can be balanced with the axial force on the impeller front cover, so it is necessary to focus on the force condition of the lower part of the impeller rear cover.
[0036] When the pump rotor is subjected to an axial force to the right, the fixed module 10 and the impeller move to the right synchronously, driving the adjustment slide plate 11 to move to the right, and the spring 12 is compressed to generate a force to the left. In addition, due to the existence of the first gap a and the second gap b, the high-pressure fluid in the pressure chamber 101 will partially leak into the second balance chamber 102, and the fluid in the second balance chamber 102 will partially leak into the first balance chamber 104. The flow process of the fluid conforms to the law of conservation of mass. When the flow channel surface decreases, the flow velocity of the fluid increases. At the same time, according to the Bernoulli equation, the pressure of the incompressible fluid in a stable flow state will decrease as the flow velocity increases in order to maintain energy conservation during the flow process. Therefore, under the above action, the pressure of the first balance chamber 104 will always be lower than that of the second balance chamber 102, and the pressure of the second balance chamber 102 will always be lower than that of the pressure chamber 101. Under the action of the two radial gaps, the pressure in the first balance chamber 104 is always at a lower level than that in the pressure chamber 101. In the first balancing chamber 104, the axial force on the lower left side of the impeller rear cover plate 9 and the force on the right side of the adjusting slide plate 11 offset each other, and the main axial force source in the impeller is converted to the force on the left side of the adjusting slide plate 11 and the force on the lower section of the front side of the impeller rear cover plate. Since the lower section of the front side of the impeller rear cover plate is close to the suction area of the impeller, the suction port of the impeller inlet is a low-pressure area, and the axial force of this part of the fluid on the structure is very small. The left side of the adjusting slide plate 11 is located in the third balancing chamber 103. Part of the fluid in the cavity is derived from the liquid of the first balancing chamber 104 leaking from the sealing structure 16, and the other part is derived from the liquid of the first balancing chamber 104 infiltrating from the gap between the lower end fixed module 10 and the adjusting slide plate 11. The cavity is basically a static cavity and due to the conservation of mass energy when the fluid flows through the seal and the gap, the pressure is always less than the pressure in the first balancing chamber 104. At this time, through the action of the two gaps and the sealing structure, the third balancing chamber 103 will maintain a relatively low pressure state, greatly reducing the axial force to the right on the lower section of the impeller rear cover plate.
[0037] When the pump rotor is subjected to a leftward axial force, the fixed module 10 and the impeller move to the left, driving the adjustment slide 11 to move to the left. At this time, the spring 12 is pulled, generating a force to the right. The pressure state of the three balancing chambers is similar to that when the rotor is subjected to a rightward axial force, but due to the leftward movement of the impeller, the space guide vane 4 and the outer cylinder wall 14 of the balancing device are fixed structures. At this time, the axial lengths of the first gap a and the second gap b are increased, resulting in an increase in the loss along the way when the fluid passes through the gap, thereby increasing the pressure difference between the second balancing chamber 102 and the pressure chamber 101, the first balancing chamber 104 and the second balancing chamber 102, making the pressure of the first balancing chamber 104 and the second balancing chamber 102 smaller than the pressure of the chamber when the impeller is not subjected to a leftward force, and the force of the liquid on the impeller rear cover is reduced. At the same time, the existence of the third balancing chamber 103 also has a certain inhibitory effect on the leftward movement of the adjustment slide 11 (i.e., the impeller).
[0038] The multi-stage vertical molten salt pump described in the present invention comprises a multi-stage impeller, and the axial force balancing device described above is provided between at least one stage of the impeller and its corresponding space guide vane 4.
[0039] Example
[0040] The design flow rate of this multi-stage vertical molten salt pump is 950m 3 / h, the rated speed is 1450r / min, and one of the levels is selected to compare the model with the axial force balancing device 8 of the present invention and the model without balancing means. 3 / h), design flow (950m 3 / h) and larger flow (1141m 3 / h) with 25℃ clean water as the conveying medium. The turbulence model uses the standard k-ε model, the boundary conditions use the total pressure inlet and mass flow outlet, the impeller calculation area is the rotating domain, the guide vane, inlet pipe and outlet pipe are the static domain, the interface of the dynamic and static calculation domains uses the frozen rotor model, and the wall surface is a smooth wall condition.
[0041] The axial forces of the two under different working conditions were calculated by numerical simulation, and the results are as follows:
[0042] like Figure 6As shown, after installing the axial force balancing device 8 described in the present invention, the axial forces on the front and rear cover plates of the impeller are significantly reduced, and the axial force of the blades changes slightly. An important source of the axial force of the pump is the asymmetry of the front and rear cover plate structures of the impeller, that is, the force difference between the cover plates on both sides is the main part of the axial force of the pump. In the process of gradually increasing flow, the force difference of the impeller cover plates installed with the balancing device is 11503N, 1157.7N, and 1914.5N, respectively. The force difference of the cover plates on both sides without balancing measures is 25447N, 15216N, and 10729N. After installing the balancing device, the force difference of the cover plates on both sides is reduced by 54.8%, 92.3%, and 82.2% compared with the unbalanced model. At the same time, the corresponding total axial force is reduced by 40.7%, 56.9%, and 61.5% respectively compared with the model without the balancing device installed. It shows that the balancing device provided by the present invention can effectively reduce the axial force under different working conditions.
[0043] At present, there are two main ways to balance the axial force of multi-stage pumps in engineering, one is a balancing disc, and the other is a combination of a sealing ring and a balancing hole. The former can only be installed after the last stage impeller, the position cannot be changed, and a pipeline must be used to connect the pump inlet. Therefore, the axial force balancing device 8 of the present invention is compared with the second one, and the calculation model still uses the aforementioned single-stage pump model. The calculation results are shown as follows: Figure 7 As shown in the figure, it can be seen that the ability of the axial force balancing device 8 provided by the present invention to balance the axial force under different flow conditions is significantly better than that of the traditional balancing measures. 3 / h、950m 3 / h、1141m 3 / h condition, the axial force balancing device of the present invention reduces the stress on the device by 24.47%, 44.60% and 49.42% respectively compared with the balancing solution using the traditional sealing ring and balancing hole structure, and the balancing ability is enhanced with the increase of flow rate.
[0044] Considering that the axial force balancing device 8 should not have a significant impact on the hydraulic performance of the pump, efficiency, head and shaft power are the main characteristic parameters for judging the performance of the pump. Figure 8 As described above, the external characteristic parameters of a single-stage pump installed with the balancing device, a single-stage pump without balancing measures, and a single-stage pump using traditional balancing measures are compared. As for the impact on the hydraulic performance of the pump, under multi-flow conditions, the head and efficiency of the pump using the balancing device of the present invention are similar to those using traditional balancing measures, and the shaft power is smaller. The greater the head and efficiency, the smaller the shaft power, and the better the performance of the pump. Comprehensively comparing the axial force and hydraulic performance parameters of the pump, the balancing device of the present invention has less impact on the pump performance while providing a better balanced axial force. It can be seen that the balancing device has basically no effect on the hydraulic performance of the pump, and can be directly installed on the existing pump without adjusting the hydraulic design, thereby reducing the design cost.
[0045] It should be understood that although this specification is described according to various embodiments, not every embodiment contains only one independent technical solution. This narrative method of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation methods that can be understood by those skilled in the art.
[0046] The series of detailed descriptions listed above are only specific descriptions of feasible embodiments of the present invention. They are not intended to limit the scope of protection of the present invention. All equivalent embodiments or changes that do not deviate from the technical spirit of the present invention should be included in the scope of protection of the present invention.
Claims
1. A multi-stage vertical molten salt pump axial force balancing device, characterized in that: An axial force balancing device is provided between the spatial guide vane (4) and the impeller, wherein the axial force balancing device comprises a third balancing chamber (103) and a first balancing chamber (104), wherein a labyrinth gap is provided between the first balancing chamber (104) and the pressure chamber (101) of the impeller; the third balancing chamber (103) is located inside the spatial guide vane (4), and an elastic damping is provided between the first balancing chamber (104) and the third balancing chamber (103) for balancing the axial force exerted on the impeller.
2. The multi-stage vertical molten salt pump axial force balancing device according to claim 1 is characterized in that: The axial force balancing device comprises a cylinder, an elastic damper and an adjusting slide plate (11); the cylinder comprises an end cover (13) and an outer cylinder wall (14); the end cover (13) is installed on one end of the outer cylinder wall (14); the end cover (13) is located inside the space guide vane (4), and the end cover (13) is connected to the space guide vane (4); the other end of the outer cylinder wall (14) is clearance-matched with the impeller; the adjusting slide plate (11) is located inside the cylinder, and the adjusting slide plate (11) is connected to the rear cover plate (9) of the impeller; the adjusting slide plate (11) divides the cylinder into a first balancing chamber (104) and a third balancing chamber (103); an elastic damper is provided between the adjusting slide plate (11) and the cylinder; one side of the adjusting slide plate (11), the outer cylinder wall (14) and the rear cover plate (9) constitute the first balancing chamber (104); the area between the other side of the adjusting slide plate (11) and the end cover (13) constitutes the third balancing chamber (103).
3. The multi-stage vertical molten salt pump axial force balancing device according to claim 2 is characterized in that: A sealing structure (16) is provided between the adjusting slide plate (11) and the inner wall surface of the outer cylinder wall (14).
4. The multi-stage vertical molten salt pump axial force balancing device according to claim 3 is characterized in that: The sealing structure (16) is an annular metal brush wire, and one end of the adjusting slide plate (11) is provided with a plurality of spaced grooves, and the annular metal brush wire is located in the grooves.
5. The multi-stage vertical molten salt pump axial force balancing device according to claim 2 is characterized in that: A first gap (a) is provided between the rear cover plate (9) and the space guide vane (4), and a second gap (b) is provided between the rear cover plate (9) and the outer cylinder wall (14), wherein the first gap (a) and the second gap (b) constitute a labyrinth gap between the first balancing chamber (104) and the pressure chamber (101).
6. The axial force balancing device of a multi-stage vertical molten salt pump according to claim 2 is characterized in that: The inner wall of the outer cylinder wall (14) is provided with a protrusion, and a spring (12) is provided between the protrusion and the adjusting slide plate (11).
7. The multi-stage vertical molten salt pump axial force balancing device according to claim 2 is characterized in that: A second balancing chamber (102) is provided between the first balancing chamber (104) and the pressure chamber (101), wherein the second balancing chamber (102) is an area partially surrounded by the space guide vane (4), the cylinder and the rear cover plate (9).
8. A multi-stage vertical molten salt pump, comprising a multi-stage impeller, characterized in that: An axial force balancing device according to any one of claims 1 to 7 is provided between at least one stage of the impeller and its corresponding spatial guide vane (4).
Citation Information
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