WO2024193161A1

WO2024193161A1 - Non-axisymmetric endwall profile of dredging mud pump impeller

Info

Publication number: WO2024193161A1
Application number: PCT/CN2023/141837
Authority: WO
Inventors: 郭涛; 胡京招; 刘明明; 王文魁; 庄海飞; 夏铖; 曹蕾; 林挺; 吴腾伟; 马源
Original assignee: 中交疏浚技术装备国家工程研究中心有限公司
Priority date: 2023-03-17
Filing date: 2023-12-26
Publication date: 2024-09-26
Also published as: CN116379000B; CN116379000A

Abstract

The present invention provides a non-axisymmetric endwall profile of a dredging mud pump impeller. The endwall of the impeller is not axisymmetric and has relative concave-convex changes on the same meridian plane radius, and is thus applied to a closed impeller or a semi-open impeller. The start point of the non-axisymmetric endwall profile is located behind an impeller inlet and the end point is located at an impeller outlet or before the impeller outlet. The portion of the endwall surface of the impeller outside the non-axisymmetric endwall profile is still an axisymmetric annular surface; and the non-axisymmetric endwall profile has periodic repeatability between blade flow passages. Compared with an original impeller which does not use a non-axisymmetric endwall profile, the mud pump impeller using the non-axisymmetric endwall profile of the present invention has the beneficial effects of obviously improving the solid-liquid flow uniformity of the impeller, reducing the abrasion of the middle rear parts of the flow passages and other parts of the impeller, and improving the pump efficiency.

Description

Non-axisymmetric end wall modeling of dredging mud pump impeller

Technical Field

The invention belongs to the technical field of dredging centrifugal mud pumps, and in particular relates to a non-axisymmetric structural modeling on an impeller end wall surface of a centrifugal mud pump in the dredging industry.

Background Art

Mud pumps, also known as slurry pumps and slurry pumps, use water power to continuously transport soil, gravel, crushed ore and other materials through pumping, and are widely used in dredging, mining, and chemical industries. Mud pumps in the dredging industry are mostly single-stage single-suction centrifugal pumps, which usually have the characteristics of large flow, large diameter of solid particles allowed to pass, wear resistance, high efficiency, and easy disassembly. However, the sharp medium and coarse sand soil has a huge wear effect on the internal surface of the mud pump. Under this condition, the life of common mud pump inner surface wear-resistant materials such as high-chromium white cast iron alloy is only 1/10 to 1/30 of that under fine and silty sand soil conditions, which reduces construction efficiency and greatly increases construction costs.

The wear of the inner surface of the mud pump is inevitable and uneven. The specific location of the wear is affected by the internal solid-liquid flow and is closely related to factors such as the pump type and operating conditions. In the impeller of a centrifugal mud pump, the wear is mostly concentrated on the leading edge of the blade, the position on the impeller end wall close to the leading edge of the blade, and the middle and rear part of the blade (including the trailing edge of the blade). The end wall of the impeller refers to the wall connecting the two ends of the blade, that is, the inner side of the front and rear cover plates of the impeller. Since the flow direction changes significantly near the above-mentioned position, the solid particles are affected by inertia and deviate from the main flow direction and hit the nearby wall that constrains the flow.

Mud pumps are different from water pumps. The flow loss in conventional water pumps can be avoided and performance can be improved by technical means such as blade bending and twisting, and adding short blades. However, there are a large number of solid particles in the conveyed materials of mud pumps. In order to ensure the passing performance of coarse solid particles, the blade height (blade height, also known as blade span, blade width) of mud pumps does not decrease significantly with the increase of the radius of the impeller axial surface (also known as the meridian surface), and the number of blades is small. Under normal conditions, short blades or long blades with excessive bending and twisting cannot be used. Due to its own characteristics, the cross-sectional area of the blade flow channel of the mud pump is severely expanded in the middle and rear part of the flow channel, the blade constraint ability is reduced, and the average radial flow velocity decreases rapidly with the increase of the axial radius. The particles in the mud pump are constantly turning in the flow channel with the flow, which makes it easier to hit the blades, causing relatively concentrated wear in the middle and rear parts of the blades, and at the same time causing the mud pump to be significantly less efficient in conveying mud than in the clear water condition. Therefore, it is necessary to provide a technical solution for the mud pump impeller to solve the problem of concentrated wear in the impeller flow channel caused by the serious diffusion of the impeller flow channel.

The non-axisymmetric end wall molding technology originated from a concept of turbomachinery flow control proposed in the 1980s and 1990s. The concept was developed into a new design technology for advanced turbines/compressors in the early 21st century: changing the upper and lower end walls of the long static blade cascade flow passage of the diffuser section (i.e., the upper and lower annular surfaces of the blade cascade) so that it is no longer an axisymmetric frustum, but has specially designed ups and downs, which can improve the secondary flow near the wall, thereby improving the efficiency of the turbine. As shown in Figure 1, it is a schematic diagram of the use of a non-axisymmetric end wall design at the bottom of the blade cascade. CN201910173245.7 discloses a single-stage axial flow high-pressure compressor with asymmetric end wall shaping; CN 201110459987.X discloses a non-axisymmetric end wall shaping method for a compressor/turbine annular blade cascade; the non-axisymmetric end wall shaping technology is currently limited to the field of turbines/compressors with gas as the medium, and its function is to reduce the total pressure loss of the gas; there is no record of research or use in pump machinery.

Summary of the invention

The purpose of the present invention is to overcome the shortcomings of the prior art and provide a non-axisymmetric end wall shape for a dredging mud pump impeller, which has different axial positions on the same axial radius, showing non-axisymmetric concave-convex changes in the end wall surface. This design is based on the basic principle of flow control, and uses the end wall shape to suppress the flow deterioration caused by severe diffusion in the mud pump flow channel, reasonably adjust the blade load, and reduce the concentrated wear in the middle and rear parts of the dredging mud pump impeller.

In order to achieve the above object, the present invention adopts the following technical solution:

A non-axisymmetric end wall shape of a dredging mud pump impeller, wherein the end wall of the impeller is not axisymmetric, but has relative concave-convex changes on the same axial radius, the starting point of the non-axisymmetric end wall shape is located after the impeller inlet, and the end point is located at the impeller outlet or before the impeller outlet, and the end wall surface of the impeller outside the non-axisymmetric end wall shape is still an axisymmetric annular surface; and the non-axisymmetric end wall shape has periodic repeatability between each blade flow channel.

The present invention is further configured such that the end wall curved surface of the non-axisymmetric end wall shape is differentiable in both radial and circumferential directions, and the degree of its concavity and convexity gradually increases from zero at the starting point and gradually decreases to zero at the end point that is not the outlet.

The present invention is further configured such that the non-axisymmetric end wall shape can be applied to a closed impeller or a semi-open impeller.

The present invention is further configured such that the maximum undulation ratio of the non-axisymmetric end wall shape, that is, in the entire non-axisymmetric end wall shape, the maximum value of the ratio of the difference between the most convex point and the most concave point on the same axial radius to the average flow channel height at the same radius is not less than 5% and not more than 20%; wherein the average flow channel height is, for a closed impeller, the average spacing between the end walls on both sides at the same radius; and for a semi-open impeller, the average value of the sum of the blade height and the blade tip clearance at the same radius.

The present invention is further configured such that the non-axisymmetric end wall shape is specifically configured as one of the following situations in a single blade flow channel:

The end wall is convex on the pressure surface side of the blade flow channel and concave on the suction surface side, which is used to improve the suction surface wear caused by the large channel vortex; the end wall is concave on the pressure surface side of the blade flow channel and convex on the suction surface side, which is used to improve the pressure surface wear; the end wall is convex in the middle of the blade flow channel, which is used to improve the wear concentration of the pressure surfaces and suction surfaces on both sides and improve efficiency; the end wall is concave in the middle of the blade flow channel, which is used to enhance the passing performance of the flow channel.

The present invention is further configured such that there is a smoothly connected arc chamfer between the non-axisymmetric end wall shape and the intersecting impeller blade top and root surfaces.

The present invention is further configured such that the non-axisymmetric end wall shape can be generated by using a plurality of theoretical flow surface edges as a skeleton skin, and the relative concavity and convexity of the non-axisymmetric end wall shape is consistent along the flow surface edges under the infinite blade assumption.

The present invention is further configured such that, on the same flow surface edge line, the non-axisymmetric end wall shape may have a similar or different degree of concavity as the edge line length changes.

The present invention is further configured that when the concave-convex degree on the same stream surface edge line is different, the present invention provides two formulas for the change of the concave-convex degree of the end wall with the edge line length, formula (1) is a linear change equation, and formula (2) is a hyperbolic tangent function equation:

Where l is the length of the local edge, I is the degree of concavity of the end wall when the edge length is l, that is, the difference between the actual position of the end wall and the average position at the same radius; I _max is the maximum concavity of the end wall on the edge of the stream surface, positive for convex and negative for concave; l _max is the total length of the edge; b and c are intermediate parameters, which jointly determine the position of the end wall shaping; b determines the degree of inclination at the main change of the end wall shaping.

The present invention is further configured such that the non-axisymmetric characteristics of the non-axisymmetric end wall shape result in different concavities or different degrees of concavity along different flow surface edges of the end wall.

The present invention is further configured as follows: the present invention provides two relationship equations for the change of the end wall concavity with different stream surface edges (distinguished by the circumferential position angle θ of the starting point of the stream surface edge). Formula (3) is a trigonometric function equation; Formula (4) is a parameter fitting equation based on pressure difference:

h(θ)＝h _max cos(nθ+β) Formula (3)

Wherein, θ is the circumferential position angle used to distinguish the starting points of different flow surfaces and their edges. The θ value of the starting point of any flow surface can be defined as 0, and the θ values of the starting points of other flow surfaces are the rotation angles relative to the starting point of the flow surface; h is the difference between the actual position of the upper end wall on the flow surface edge with the starting point being the circumferential position angle θ and the average position at the same radius, with a positive value being convex and a negative value being concave; h _max is the maximum degree of convexity of the upper end wall on the same circumference. Preferably, h _max is related to the length of the flow surface edge from the inlet to the local area, which can be obtained by equations (1) and (2).

n is the repetition period of the end wall modeling feature within a circle, which is an integer multiple of the number of blades; β is the phase angle;

ΔP _θ is the difference between the local pressure on the stream surface edge with the starting point at the circumferential position angle θ and the circumferential average pressure; ΔP _max is the maximum difference between the stream surface edge pressure and the circumferential average pressure on the same circumference; OSL is the ordinary least squares fitting operation, and the polynomial form obtained after fitting is in [].

Compared with the prior art, the present invention has the following beneficial effects:

(1) Through the non-axisymmetric end wall shape of the present invention, while ensuring the passability of coarse solid particles in the dredging mud pump, the situation in which the blade constraint ability decreases and the flow deteriorates due to severe diffusion in the middle and rear parts of the impeller flow channel is suppressed; the generation of large vortices can be avoided, the relative flow velocity near the wall is reduced, and the wear of the middle and rear parts of the impeller is reduced.

(2) The non-axisymmetric characteristics of the non-axisymmetric end wall shape of the present invention distribute the wear of the blades to a certain extent, further suppressing concentrated wear.

(3) The non-axisymmetric end wall shape of the present invention can also improve the flow in the middle and rear parts of the blade flow channel to improve efficiency and enhance the performance of the mud pump. It also has other functions such as improving wear near the impeller inlet, in the diffuser chamber, and in the volute.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a schematic diagram of the design of the non-axisymmetric end wall at the bottom of the cascade;

FIG2 is a three-dimensional cross-sectional view of an impeller having a non-axisymmetric end wall (the section passes through the axis of rotation);

Figure 3 shows several specific non-axisymmetric end wall shapes: PS (pressure side), SS (suction side);

FIG4A shows multiple S2 flow surfaces of a non-axisymmetric end wall impeller under the assumption of infinite blades;

FIG4B is a single blade flow passage of a non-axisymmetric end wall in an impeller;

FIG5 is an axial projection of the impeller, including axial projections of the theoretical flow surfaces of FIG4 ;

Among them, 1. Stationary blades; 2. Undulating end wall; 3. Impeller inlet; 4. Impeller blades; 5. Impeller Front shroud; 6. Impeller rear shroud (hub); 7. Impeller section through the rotation axis; 8. Impeller outlet; 9. Rotation axis of centrifugal impeller; 10. Multiple S2 flow surfaces of impeller with non-axisymmetric end wall modeling under the assumption of infinite blades (blade flow path surface intercepted by the middle bone surface of the real blade of the circular array); 11. Flow surface edge line on the front shroud (Shroud) side; 12. Flow surface edge line on the rear shroud (hub) side; 13. Single blade flow path with non-axisymmetric end wall modeling (generated by lofting multiple S2 flow surfaces); 14. Axial plane projection of impeller flow path with axisymmetric end wall (the part before the blade flow path); 15. Axial plane projection of multiple S2 flow surfaces; 16. Projection of the edge lines of multiple S2 flow surfaces on the axial plane.

DETAILED DESCRIPTION

The technical scheme of the present invention is clearly and completely described below with specific embodiments. It should be understood that the described embodiments are only part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of the present invention.

In the dredging mud pump impeller of the present invention, the end wall of the impeller is not axisymmetric, but has relative concave-convex changes on the same axial radius (i.e., the non-axisymmetric end wall shape of the present invention), wherein the end wall of the impeller is the inner surface of the impeller cover plate, therefore, the end wall of the impeller has obvious three-dimensional characteristics and cannot be represented or determined by a two-dimensional axial surface. As shown in FIG2, it is a three-dimensional cross-sectional view of a mud pump impeller with a non-axisymmetric end wall shape, the starting point of the non-axisymmetric end wall shape is located after the impeller inlet 3, and the end point is located at the impeller outlet 8 or before the impeller outlet 8, the end wall surface of the impeller is still an axisymmetric annular surface in other parts outside the non-axisymmetric end wall shape, that is, the impeller inlet 3 and the impeller outlet 8 when the end point is located before the impeller outlet 8 are axisymmetric annular surfaces; and the non-axisymmetric end wall shape has a specific regularity in a single blade flow channel, that is, between two adjacent impeller blades 4, and the non-axisymmetric end wall shape has periodic repeatability between each blade flow channel (circumferential mirroring).

The non-axisymmetric end wall shape of the present invention has an effect that is difficult to achieve with a simple bending and twisting shape of the blade, and can significantly assist the blade to constrain the flow of sand and water near the end wall: the raised end wall will reduce the local blade height, resulting in a relative increase in flow speed and pressure; the recessed end wall will increase the local blade height, resulting in a relative decrease in flow speed and pressure; reasonable control of the pressure gradient can minimize adverse flows such as flow separation, backflow, and vortexes; and the circumferentially asymmetric undulations will inhibit the occurrence of circumferential secondary flows near the end wall.

Furthermore, the end wall curved surface of the non-axisymmetric end wall shape is differentiable in both radial and circumferential directions, that is, the rate of change is continuous, and the degree of concavity and convexity thereof gradually increases from zero at the starting point and increases from zero at the end point other than the outlet. Gradually fades to zero.

Furthermore, the non-axisymmetric end wall shape can be applied to a closed impeller or a semi-open impeller. Specifically, as shown in FIG2 , a closed impeller has front and rear cover plates 5 and 6, and the non-axisymmetric end wall shape can be used on both sides or on any one side of the cover plate end wall; a semi-open impeller has a cover plate on one side, and the non-axisymmetric end wall shape can only be used on the end wall of the cover plate on the side; a fully open impeller does not include a cover plate, so the end wall shape cannot be used.

Furthermore, the maximum undulation ratio of the non-axisymmetric end wall shape, that is, in the entire non-axisymmetric end wall shape, the maximum value of the ratio of the difference between the most convex point and the most concave point on the same axial radius to the average flow channel height at the same radius is not less than 5% and not more than 20%; wherein the average flow channel height for a closed impeller is the average spacing between the end walls on both sides at the same radius; for a semi-open impeller, it is the average value of the sum of the blade height and the blade tip clearance at the same radius.

Furthermore, as shown in FIG3 , four overall forms of the non-axisymmetric end wall shape in a single blade flow channel are disclosed, wherein PS is the pressure surface and SS is the suction surface.

As shown in FIG3-1 , the end wall of the impeller is convex on the pressure side of the blade flow channel and concave on the suction side, which is mainly suitable for improving the wear of the suction surface caused by the large channel vortex;

As shown in FIG3-2 , the end wall of the impeller is concave on the pressure side of the blade flow channel and convex on the suction side, which is mainly suitable for improving the wear of the pressure surface;

As shown in FIG3-3 , the end wall of the impeller is raised in the middle of the blade flow channel, which is mainly suitable for improving the wear concentration of the pressure surface and the suction surface on both sides and improving the efficiency;

As shown in FIG. 3-4 , the end wall of the impeller is recessed in the middle of the blade flow channel, which is mainly used to enhance the passing performance of the flow channel.

Furthermore, there is a smoothly connected arc chamfer between the non-axisymmetric end wall shape and the top and root surfaces of the intersecting impeller blades 4.

Furthermore, under the assumption of infinite blades of the impeller, the flow surface in the impeller coincides with the infinite blade surface, that is, the circumferential infinite array of the middle bone surface of the real blade (the surface with equal distance to the pressure surface and the suction surface of the blade), as shown in FIG4A, is a plurality of S2 flow surfaces 10 (blade flow path surfaces intercepted by the middle bone surface of the real blade of the circumferential array) of the impeller with non-axisymmetric end wall modeling under the assumption of infinite blades. Each flow surface in the figure is a theoretical flow surface, and 11 and 12 are the theoretical flow surface edges on the front cover plate side and the rear cover plate side, respectively. The non-axisymmetric end wall modeling can be generated by multiple theoretical flow surface edges as the bone line skin, as shown in FIG4B, and the single blade flow path with non-axisymmetric end wall modeling can be generated by lofting multiple theoretical flow surfaces.

In general designs, the relative convexity and concavity of the non-axisymmetric end wall shape is consistent along the stream surface edge under the infinite blade assumption. That is, if the non-axisymmetric end wall shape is convex (concave) at any position on a stream surface edge, then the end wall is also convex (concave) at other positions on the same stream surface edge. Of course, the specific degree of convexity and concavity may not be the same.

Specifically, the non-axisymmetric end wall shape can have the same or different concavity and convexity on the same flow surface edge line as the edge line length changes. When the concavity and convexity on the same flow surface edge line are different, the present invention provides two formulas for the change of the concavity and convexity of the end wall with the edge line length. Formula (1) is a linear change equation, and formula (2) is a hyperbolic tangent function equation:

Furthermore, the non-axisymmetric characteristics of the non-axisymmetric end wall shape result in different concavities or different degrees of concavity of the end wall along different flow surface edges.

The present invention provides two relationship equations for the change of the degree of end wall concavity with different stream surface edges (distinguished by the circumferential position angle θ of the starting point of the stream surface edge). Formula (3) is a trigonometric function equation; Formula (4) is a parameter fitting equation based on pressure difference:

h(θ)＝h _max cos(nθ+β) Formula (3)

As shown in Figure 5, it is the axial projection of each theoretical flow surface in Figure 4. It can be clearly seen from the projection that the width of each flow surface projection is different, which means that the concavity or degree of concavity of the end wall along different flow surface edges is different.

The non-axisymmetric end wall shape of the present invention includes but is not limited to the four overall forms of non-axisymmetric end wall shapes listed in the embodiments, the change law formula of the two same end wall flow surface edge lines, the relationship formula between the two end wall edge lines, and which end wall shape is actually used in the dredging mud pump impeller depends entirely on the flow characteristics in the impeller.

Compared with the original impeller without the axisymmetric end wall shape, the mud pump impeller adopting the non-axisymmetric end wall shape of the present invention has the beneficial effects of significantly improving the uniformity of solid-liquid two-phase flow in the impeller, reducing wear in the middle and rear parts of the impeller flow channel and other parts, and improving pump efficiency.

This application is described in detail for the purpose of enabling those skilled in the art to understand the contents of this application and implement them. This is not intended to limit the scope of protection of this application. Any equivalent changes or modifications made according to the spirit of this application should be included in the scope of protection of this application.

Claims

A non-axisymmetric end wall shape of a dredging mud pump impeller, characterized in that the end wall of the impeller has concave-convex changes on the same axial radius, the starting point of the non-axisymmetric end wall shape is located after the impeller inlet, the end point is located at the impeller outlet or before the impeller outlet, and the non-axisymmetric end wall shape has periodic repeatability between each blade flow channel.
The non-axisymmetric end wall shape of the dredging mud pump impeller according to claim 1 is characterized in that the end wall curved surface of the non-axisymmetric end wall shape is diffusible in both radial and circumferential directions, and its degree of concavity gradually increases from zero at the starting point and gradually decreases to zero at the non-outlet end point.
The non-axisymmetric end wall shape of the dredging mud pump impeller according to claim 1 is characterized in that the non-axisymmetric end wall shape is applied to a closed impeller or a semi-open impeller.
The non-axisymmetric end wall shape of the dredging mud pump impeller according to claim 1 is characterized in that the maximum fluctuation ratio of the non-axisymmetric end wall shape, that is, in the entire non-axisymmetric end wall shape, the maximum value of the ratio of the difference between the most convex point and the most concave point on the same axial radius to the average flow channel height at the same radius is not less than 5% and not more than 20%.
The non-axisymmetric end wall shape of the dredging mud pump impeller according to claim 1 is characterized in that the non-axisymmetric end wall shape is one of the following settings in a single blade flow channel:

The end wall is convex on the pressure surface side of the blade flow channel and concave on the suction surface side, so as to improve the wear of the suction surface caused by the large channel vortex;

The end wall is concave on the pressure surface side of the blade flow channel and convex on the suction surface side, so as to improve the wear of the pressure surface;

The end wall is raised in the middle of the blade flow channel to improve the wear concentration of the pressure surface and the suction surface on both sides and improve the efficiency;

The end wall is recessed in the middle of the blade flow channel to enhance the flow channel's passing performance.
The non-axisymmetric end wall shape of the dredging mud pump impeller according to claim 1 is characterized in that there is a smoothly connected arc chamfer between the non-axisymmetric end wall shape and the intersecting impeller blade top and root surfaces.
The non-axisymmetric end wall shape of the dredging mud pump impeller according to claim 1 is characterized in that the non-axisymmetric end wall shape is generated by a plurality of theoretical flow surface edges as a skeleton skin, and the relative concavity and convexity of the non-axisymmetric end wall shape is consistent along the flow surface edges under the infinite blade assumption.
The non-axisymmetric end wall shape of the dredging mud pump impeller according to claim 7 is characterized in that The non-axisymmetric end wall shape has the same or different concavity and convexity degrees on the same stream surface edge line as the edge line length changes; when the concavity and convexity degrees on the same stream surface edge line are different, one of the two formulas for the concavity and convexity degree of the end wall to change with the edge line length is satisfied. Formula (1) is a linear change equation, and formula (2) is a hyperbolic tangent function equation:

Where l is the length of the local edge, I is the degree of concavity of the end wall when the edge length is l, that is, the difference between the actual position of the end wall and the average position at the same radius; I max is the maximum concavity of the end wall on the edge of the stream surface, positive for convex and negative for concave; l max is the total length of the edge; b and c are intermediate parameters, which jointly determine the position of the end wall shaping; b determines the degree of inclination at the main change of the end wall shaping.
The non-axisymmetric end wall shape of the dredging mud pump impeller according to claim 1 is characterized in that the non-axisymmetric characteristics of the non-axisymmetric end wall shape result in different concavities or different degrees of concavity of the end wall along different flow surface edges.
The non-axisymmetric end wall shape of the dredging mud pump impeller according to claim 9 is characterized in that the non-axisymmetric end wall shape satisfies one of two relationship equations in which the degree of end wall concavity changes with different flow surface edges, formula (3) is a trigonometric function equation; formula (4) is a parameter fitting equation based on pressure difference:
h(θ)＝h max cos(nθ+β) Formula (3)

Wherein, θ is the circumferential position angle used to distinguish the starting points of different flow surfaces and their edges. The θ value of the starting point of any flow surface is defined as 0, and the θ values of the starting points of other flow surfaces are the rotation angles relative to the starting point of the flow surface; h is the difference between the actual position of the end wall on the edge of the flow surface with the starting point at the circumferential position angle θ and the average position at the same radius, with positive values being convex and negative values being concave; h max is the maximum degree of concavity of the end wall on the same circumference;

n is the repetition period of the end wall modeling feature within a circle, which is an integer multiple of the number of blades; β is the phase angle;

ΔP θ is the difference between the local pressure on the stream surface edge with the starting point at the circumferential position angle θ and the circumferential average pressure; ΔP max is the maximum difference between the stream surface edge pressure and the circumferential average pressure on the same circumference; OSL is the ordinary least squares fitting operation, and the polynomial form obtained after fitting is in [].