A single-stage tandem high energy density blade design method and the blade pump designed thereby

Abstract

The present invention discloses a single-stage tandem high energy density vane design method and a vane pump designed thereby. Among them, in the single-stage tandem vane design, the front row vane profile and the rear row vane profile are determined by the base profile. The front row vane profile is jointly determined by the base profile and the rear edge modification profile of the front row vane. The rear row vane profile is determined by a cubic Bezier curve jointly determined by the rear endpoint of the base profile, the front edge point of the rear row vane, the front edge tangent point of the rear row vane, and the tangent intersection point of the rear row vane. The shape of the base profile is determined by the given chord length of the base profile and the installation angle of the base profile. The vanes obtained by this design method can effectively improve the energy density of the vane pump, broaden the stable operation range of the pump, and improve the energy utilization efficiency and safe operation stability of the vane pump.

Description

Technical Field

[0001] The present invention belongs to the technical field of vane pumps, and particularly relates to a single-stage tandem high energy density vane design method and a vane pump designed thereby. Background Art

[0002] In recent years, vane pumps have been widely used in many fields such as energy power, aerospace, and marine power, and the requirement for the energy density of the pump is increasing day by day. Therefore, there is an urgent need to develop a single-stage tandem high energy density vane pump to output higher energy under limited space constraints.

[0003] At present, the main method to improve the energy density of vane pumps is to modify the profile of the vanes and the flow channels of the pump to improve the energy density of the pump under the design conditions. However, the improvement effect of such methods is very limited, and there will be a serious head drop under off-design conditions, resulting in unstable operation of the pump. Summary of the Invention

[0004] The present invention aims to solve at least one of the technical problems existing in the prior art. To this end, an object of the present invention is to provide a single-stage tandem high energy density vane design method, which can effectively improve the energy density of the vane pump and broaden the stable operation range of the pump.

[0005] The single-stage tandem high energy density vane design method according to the first aspect embodiment of the present invention is used to design a single-stage tandem vane, and the single-stage tandem vane is composed of a front row vane and a rear row vane; the design method includes the following steps:

[0006] Determine the chord length of the base profile and the installation angle of the base profile, which are determined by given parameters;

[0007] Determine the base profile, which is determined by a hyperbolic spiral uniquely determined by the chord length of the base profile and the installation angle of the base profile;

[0008] Determine the separation point on the base profile, which is determined by the tangent slope at the front end point and the tangent slope at the rear end point of the base profile;

[0009] Determine the separation point tangent line, which is a tangent line passing through the separation point and tangent to the base profile, and is determined by the separation point and the base profile;

[0010] Determine the leading edge tangent line of the rear row vane, which is determined by a parallel line passing through the leading edge end point of the hyperbolic spiral and parallel to the separation point tangent line;

[0011] Determine the leading edge point of the rear row vane, which is determined by the intersection of a vertical line passing through the separation point and perpendicular to the leading edge tangent line of the rear row vane and the leading edge tangent line of the rear row vane;

[0012] Determine the tangent point at the leading edge of the rear row of blades, which is determined by the intersection of the tangent line at the leading edge of the rear row of blades and the basic profile line;

[0013] Determine the intersection point of the tangent lines of the rear row of blades, which is determined by the intersection of the tangent line at the tangent point at the leading edge of the rear row of blades and the tangent line at the rear end point of the basic profile line;

[0014] Determine the profile line of the rear row of blades, which is determined by a third-order Bezier curve jointly determined by the rear end point of the basic profile line, the leading edge point of the rear row of blades, the tangent point at the leading edge of the rear row of blades, and the intersection point of the tangent lines of the rear row of blades;

[0015] Determine the flow area of the rear row, which is jointly determined by the leading edge point of the rear row of blades and the separation point;

[0016] Determine the trailing edge point of the front row of blades, which is jointly determined by the leading edge point of the rear row of blades, the profile line of the rear row of blades, and the flow area of the rear row;

[0017] Determine the trailing edge modification line of the front row of blades, which is jointly determined by the trailing edge point of the front row of blades and the tangent line at the separation point;

[0018] Determine the profile line of the front row of blades, which is jointly determined by the basic profile line and the trailing edge modification line of the front row of blades;

[0019] Determine the thickness distribution laws of the front row of blades and the rear row of blades, which are determined by given parameters.

[0020] Since the flow separation phenomenon on the surface of traditional blades will have serious adverse effects on the vane pump, and in vane pumps with high energy density, the blade load is greater and the blade bending angle is greater, resulting in a more serious flow separation phenomenon along the pressure surface of the blade. The single-stage tandem blades obtained by the single-stage tandem high-energy density blade design method of the first aspect embodiment of the present invention can well alleviate this negative phenomenon under the design requirements of high power and high energy density, effectively improve the energy density of the vane pump and broaden the stable operation range of the pump, and improve the energy utilization efficiency and safe operation stability of the vane pump.

[0021] In some embodiments, for the chord length of the basic profile line and the installation angle of the basic profile line given in the blade height direction, the basic profile line obtained is:

[0022]

[0023] Among them, α is the installation angle of the basic profile line, L is the chord length of the basic profile line, c is the hyperbolic spiral parameter, θ0 is the initial rotation angle, and c and θ0 are obtained by iterative solution from L and α.

[0024] In some embodiments, the relational expression for determining the separation point is:

[0025]

[0026] Among them, the derivative at each point on the basic profile line is is the derivative at the front-end point of the basic profile line, is the derivative at the rear-end point of the basic profile line, θ S is the rotation angle corresponding to the separation point, is the derivative at the separation point.

[0027] In some embodiments, the relational expression for determining the tangent line of the separation point is:

[0028]

[0029] In some embodiments, the relational expression for determining the tangent line of the leading edge of the rear row of blades is:

[0030]

[0031] In some embodiments, the relational expression for determining the leading edge point of the rear row of blades is:

[0032]

[0033] Among them, (x hq , y hq ) are the abscissa and ordinate of the leading edge point of the rear row of blades.

[0034] In some embodiments, the relational expression for determining the tangent point of the leading edge of the rear row of blades is:

[0035]

[0036] Among them, θ Q is the rotation angle of the tangent point of the leading edge of the rear row of blades.

[0037] In some embodiments, the relational expression for determining the intersection point of the tangent lines of the rear row of blades is:

[0038]

[0039] Among them, (x hj , y hj ) are the abscissa and ordinate of the intersection point of the tangent lines of the rear row of blades.

[0040] In some embodiments, the relational expression for determining the profile line of the rear row of blades is:

[0041]

[0042] Among them, t is the curve parameter, and t ∈ (0, 1).

[0043] In some embodiments, the relational expression for determining the rear row flow-through area is:

[0044]

[0045] Among them, S t is the rear row flow-through area.

[0046] In some embodiments, the relational expression for determining the trailing edge point of the front row blades is:

[0047]

[0048] Among them, (x qh , y qh ) are the abscissa and ordinate of the trailing edge point of the front row blades, and t s is the Bezier curve parameter value of the trailing edge profile of the rear row blades, which is obtained by the following formula:

[0049]

[0050] In some embodiments, the relational expression for determining the trailing edge modified profile of the front row blades is:

[0051]

[0052] The second aspect of the present invention also proposes a vane pump.

[0053] For the vane pump according to the embodiment of the second aspect of the present invention, the vane pump includes a single-stage tandem vane, and the single-stage tandem vane is designed according to the single-stage tandem high energy density vane design method of any one of the embodiments of the first aspect of the present invention.

[0054] Since the vane pump of the embodiment of the second aspect of the present invention adopts the single-stage tandem vane designed by the single-stage tandem high energy density vane design method of any one of the embodiments of the first aspect of the present invention, it can effectively improve the energy density of the vane pump, broaden the stable operation range of the pump, and improve the energy utilization efficiency and safe operation stability of the vane pump.

[0055] The additional aspects and advantages of the present invention will be partially given in the following description, partially become obvious from the following description, or be understood through the practice of the present invention. Description of the Drawings

[0056] The above and / or additional aspects and advantages of the present invention will become apparent and be readily understood from the following description of embodiments in conjunction with the accompanying drawings, in which:

[0057] Figure 1 is a three-dimensional schematic diagram of a vane pump according to an embodiment of the present invention;

[0058] Figure 2 is a schematic diagram of the formation process of the front-row vane profile and the rear-row vane profile at a certain calculation section of the vane pump according to an embodiment of the present invention.

[0059] Reference numerals:

[0060] Front-row vane A; rear-row vane B; trailing edge C of the front-row vane; leading edge D of the rear-row vane; rear-row flow-through area E; chord length 1 of the basic profile; installation angle 2 of the basic profile; basic profile 3; separation point 4; tangent line 5 at the separation point; tangent line 6 at the leading edge of the rear-row vane; leading edge point 7 of the rear-row vane; tangent point 8 at the leading edge of the rear-row vane; intersection point 9 of the rear-row vane tangent lines; rear endpoint 10 of the basic profile; rear-row vane profile 11; trailing edge point 12 of the front-row vane; trailing-edge modified profile 13 of the front-row vane; front-row vane profile 14. Detailed Description of the Embodiment

[0061] The embodiments of the present invention will be described in detail below. Examples of the embodiments are shown in the accompanying drawings, where the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below by referring to the accompanying drawings are exemplary and are only used to explain the present invention and should not be construed as a limitation of the present invention.

[0062] The following will be combined with Figures 1 to 2 to describe a single-stage tandem high-energy density vane design method and the vane pump designed thereby according to an embodiment of the present invention.

[0063] In a first aspect of the present invention, a single-stage tandem high-energy density vane design method is proposed, and the vanes are designed based on the plane cascade theory of the radial equilibrium equation. Cylindrical sections at different radius heights are intercepted along the radial direction and unfolded into a plane, that is, plane cascades at different heights are formed. The plane cascade is a single-stage tandem cascade, which is composed of the airfoil sections of the front and rear vanes. The airfoils of the front and rear vanes are jointly generated by combining the mean camber line and the thickness distribution along the mean camber line. In the design, first, the cascade shape is determined, and then the complete vane is obtained by lofting and stretching along the radial direction.

[0064] As Figure 1 and Figure 2As shown, a single-stage tandem high energy density blade design method according to an embodiment of the first aspect of the present invention is used to design a single-stage tandem blade. The single-stage tandem blade is composed of a front row blade A and a rear row blade B. The front end and the rear end of the front row blade A in the flow-through direction are respectively referred to as the leading edge of the front row blade and the trailing edge C of the front row blade. The front end and the rear end of the rear row blade B in the flow-through direction are respectively referred to as the leading edge D of the rear row blade and the trailing edge of the rear row blade. The leading edge of the front row blade is connected to the inlet, and the trailing edge of the rear row blade is connected to the outlet. The single-stage tandem blade has a hub side and a rim side in the blade height direction. The front row blade A and the rear row blade B of the tandem blade are respectively obtained by thickening according to the given blade thickness distribution law through the middle arc line of the front row blade A (abbreviated as the front row blade profile 14, as shown in Figure 1 ), and the middle arc line of the rear row blade B (abbreviated as the rear row blade profile 11, as shown in Figure 1 ).

[0065] As shown in Figure 2 , the single-stage tandem high energy density blade design method according to an embodiment of the first aspect of the present invention includes the following steps:

[0066] Determine the chord length 1 of the basic profile line and the installation angle 2 of the basic profile line. The chord length 1 of the basic profile line and the installation angle 2 of the basic profile line are determined by the given parameters. Here, the chord length 1 of the basic profile line and the installation angle 2 of the basic profile line refer to the chord length 1 of the basic profile line and the installation angle 2 of the basic profile line along the blade height direction.

[0067] Determine the basic profile line 3. The basic profile line 3 is determined by a hyperbolic spiral line uniquely determined by the chord length 1 of the basic profile line and the installation angle 2 of the basic profile line.

[0068] Determine the separation point 4 on the basic profile line 3. The separation point 4 is determined by the tangent slope at the front end point and the tangent slope at the rear end point of the basic profile line 3.

[0069] Determine the separation point tangent line 5. The separation point tangent line 5 is a tangent line passing through the separation point 4 and tangent to the basic profile line 3, and is determined by the separation point 4 and the basic profile line 3.

[0070] Determine the leading edge tangent line 6 of the rear row blade. The leading edge tangent line 6 of the rear row blade is determined by a parallel line passing through the leading edge end point of the hyperbolic spiral line and parallel to the separation point tangent line 5.

[0071] Determine the leading edge point 7 of the rear row blade. The leading edge point 7 of the rear row blade is determined by the intersection of a vertical line passing through the separation point 4 and perpendicular to the leading edge tangent line 6 of the rear row blade and the leading edge tangent line 6 of the rear row blade.

[0072] Determine the leading edge tangent point 8 of the rear row blade. The leading edge tangent point 8 of the rear row blade is determined by the intersection of the leading edge tangent line 6 of the rear row blade and the basic profile line 3.

[0073] Determine the tangent intersection point 9 of the rear row blade. The tangent intersection point 9 of the rear row blade is determined by the intersection of the tangent line at the leading edge tangent point 8 of the rear row blade and the tangent line at the rear end point 10 of the basic profile line.

[0074] Determine the trailing blade profile 11, which is determined by a third-order Bezier curve jointly determined by the trailing endpoint 10 of the base profile, the leading edge point 7 of the trailing blade, the leading edge tangent point 8 of the trailing blade, and the tangent intersection point 9 of the trailing blade.

[0075] Determine the trailing flow area E, which is jointly determined by the leading edge point 7 of the trailing blade and the separation point 4.

[0076] Determine the trailing edge point 12 of the leading blade, which is jointly determined by the leading edge point 7 of the trailing blade, the trailing blade profile 11, and the trailing flow area E.

[0077] Determine the trailing edge modification profile 13 of the leading blade, which is jointly determined by the trailing edge point 12 of the leading blade and the separation point tangent 5.

[0078] Determine the leading blade profile 14, which is jointly determined by the base profile 3 and the trailing edge modification profile 13 of the leading blade.

[0079] Determine the thickness distribution laws of the leading blade A and the trailing blade B, which are determined by the given parameters.

[0080] That is to say, the leading blade profile 14 and the trailing blade profile 11 are determined by the base profile 3. The leading blade profile 14 is jointly determined by the base profile 3 and the trailing edge modification profile 13 of the leading blade. The trailing blade profile 11 is determined by a third-order Bezier curve jointly determined by the trailing endpoint 10 of the base profile, the leading edge point 7 of the trailing blade, the leading edge tangent point 8 of the trailing blade, and the tangent intersection point 9 of the trailing blade. The shape of the base profile 3 is determined by the given base profile chord length 1 and the base profile installation angle 2.

[0081] Since the flow separation phenomenon on the surface of traditional blades will have a serious adverse impact on the vane pump, and in high-energy-density vane pumps, the blade load is greater and the blade bending angle is greater, resulting in a more serious flow separation phenomenon along the pressure surface of the blade. The single-stage tandem blades obtained by the single-stage tandem high-energy-density blade design method of the first aspect embodiment of the present invention can well alleviate this negative phenomenon under the design requirements of high power and high energy density, can effectively improve the energy density of the vane pump and broaden the stable operation range of the pump, and improve the energy utilization efficiency and safe operation stability of the vane pump.

[0082] In some embodiments, the base profile 3 is determined by a hyperbolic spiral line uniquely determined by the base profile chord length 1 and the base profile installation angle 2. For the given base profile chord length 1 and the base profile installation angle 2 in the blade height direction, the base profile 3 is obtained:

[0083]

[0084] Among them, α is the installation angle 2 of the basic profile line, L is the chord length 1 of the basic profile line, c is the hyperbolic spiral parameter, θ0 is the initial rotation angle, and c and θ0 are obtained by iterative solution from L and α. That is to say, according to the relational expression (1), the basic profile line 3 can be determined.

[0085] In some embodiments, the separation point 4 is determined by the tangent slopes at the front endpoint and the rear endpoint of the basic profile line 3, and the relational expression for determining the separation point 4 is:

[0086]

[0087] Among them, the derivative at each point on the basic profile line 3 is is the derivative at the front endpoint of the basic profile line 3, is the derivative at the rear endpoint of the basic profile line 3, θ S is the rotation angle corresponding to the separation point 4, is the derivative at the separation point 4. That is to say, through the relational expression (2), the separation point 4 on the basic profile line 3 can be determined.

[0088] In some embodiments, the separation point tangent 5 is the tangent passing through the separation point 4 and tangent to the basic profile line 3, and is determined by the separation point 4 and the basic profile line 3. The relational expression for determining the separation point tangent 5 is:

[0089]

[0090] That is to say, through the relational expression (3), the separation point 4 on the basic profile line 3 can be determined.

[0091] In some embodiments, the leading edge tangent 6 of the rear row blades is determined by the parallel line passing through the leading edge endpoint of the hyperbolic spiral and parallel to the separation point tangent 5. The relational expression for determining the leading edge tangent 6 of the rear row blades is:

[0092]

[0093] That is to say, through the relational expression (4), the leading edge tangent 6 of the rear row blades can be determined.

[0094] In some embodiments, the leading edge point 7 of the rear row blades is determined by the intersection of the perpendicular line passing through the separation point 4 and perpendicular to the leading edge tangent 6 of the rear row blades and the leading edge tangent 6 of the rear row blades. The relational expression for determining the leading edge point 7 of the rear row blades is:

[0095]

[0096] Among them, (x hq , y hq ) are the abscissa and ordinate of the leading edge point 7 of the rear row blades.

[0097] That is to say, through the relational expression (5), the leading edge point 7 of the rear row of blades can be determined.

[0098] In some embodiments, the leading edge tangent point 8 of the rear row of blades is determined by the intersection of the leading edge tangent line 6 of the rear row of blades and the basic profile line 3, and the relational expression for determining the leading edge tangent point 8 of the rear row of blades is:

[0099]

[0100] where θ Q is the rotation angle of the leading edge tangent point 8 of the rear row of blades.

[0101] That is to say, through the relational expression (6), the leading edge tangent point 8 of the rear row of blades can be determined.

[0102] In some embodiments, the tangent intersection point 9 of the rear row of blades is determined by the intersection of the tangent line at the leading edge tangent point 8 of the rear row of blades and the tangent line at the rear end point 10 of the basic profile line, and the relational expression for determining the tangent intersection point 9 of the rear row of blades is:

[0103]

[0104] where (x hj , y hj ) are the abscissa and ordinate of the tangent intersection point 9 of the rear row of blades.

[0105] That is to say, through the relational expression (7), the tangent intersection point 9 of the rear row of blades can be determined.

[0106] In some embodiments, the profile line 11 of the rear row of blades is determined by a third-order Bezier curve jointly determined by the rear end point 10 of the basic profile line, the leading edge point 7 of the rear row of blades, the leading edge tangent point 8 of the rear row of blades, and the tangent intersection point 9 of the rear row of blades, and the relational expression for determining the profile line 11 of the rear row of blades is:

[0107]

[0108] where t is the curve parameter, and t ∈ (0, 1).

[0109] That is to say, through the relational expression (8), the profile line 11 of the rear row of blades can be determined.

[0110] In some embodiments, the flow area E of the rear row is jointly determined by the leading edge point 7 of the rear row of blades and the separation point 4, and the relational expression for determining the flow area E of the rear row is:

[0111]

[0112] where S t is the flow area E of the rear row.

[0113] That is to say, through the relational expression (9), the flow area E of the rear row can be determined.

[0114] In some embodiments, the trailing edge point 12 of the front row blades is jointly determined by the leading edge point 7 of the rear row blades, the profile line 11 of the rear row blades, and the flow area E of the rear row. The relational expression for determining the trailing edge point 12 of the front row blades is as follows:

[0115]

[0116] where (x qh , y qh ) are the horizontal and vertical coordinates of the trailing edge point 12 of the front row blades, and t s is the Bezier curve parameter value of the profile line of the rear row blades, which is obtained by the following formula:

[0117]

[0118] That is to say, through relational expression (10) and relational expression (11), the trailing edge point 12 of the front row blades can be determined.

[0119] In some embodiments, the trailing edge modification line 13 of the front row blades is jointly determined by the trailing edge point 12 of the front row blades and the separation point tangent line 5. The relational expression for determining the trailing edge modification line 13 of the front row blades is as follows:

[0120]

[0121] That is to say, through relational expression (12), the trailing edge modification line 13 of the front row blades can be determined.

[0122] The second aspect of the present invention also proposes a vane pump.

[0123] The vane pump according to the embodiment of the second aspect of the present invention includes single-stage tandem vanes, and the single-stage tandem vanes are designed according to the single-stage tandem high energy density vane design method of any one of the embodiments of the first aspect of the present invention.

[0124] Since the vane pump according to the embodiment of the second aspect of the present invention adopts the single-stage tandem vanes designed by the single-stage tandem high energy density vane design method of any one of the embodiments of the first aspect of the present invention, it can effectively improve the energy density of the vane pump, broaden the stable operation range of the pump, and improve the energy utilization efficiency and safe operation stability of the vane pump.

[0125] In the description of this specification, the descriptions referring to terms such as "one embodiment", "some embodiments", "schematic embodiments", "examples", "specific examples", or "some examples", etc., mean that the specific features, structures, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, or characteristics described can be combined in a suitable manner in any one or more embodiments or examples.

[0126] Although the embodiments of the present invention have been shown and described, those of ordinary skill in the art can understand that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention, and the scope of the present invention is defined by the claims and their equivalents.

Claims

1. A single-stage tandem high energy density blade design method, characterized in that, For designing a single-stage tandem blade, the single-stage tandem blade is composed of a front-row blade and a rear-row blade; the design method includes the following steps: Determine the chord length of the basic profile line and the installation angle of the basic profile line, where the chord length of the basic profile line and the installation angle of the basic profile line are determined by given parameters; Determine the basic profile line, which is determined by a hyperbolic spiral line uniquely determined by the chord length of the basic profile line and the installation angle of the basic profile line; Determine the separation point on the basic profile line, where the separation point is determined by the tangent slope at the front-end point of the basic profile line and the tangent slope at the rear-end point of the basic profile line; Determine the separation point tangent line, which is the tangent line passing through the separation point and tangent to the basic profile line, and is determined by the separation point and the basic profile line; Determine the leading-edge tangent line of the rear-row blade, which is determined by a parallel line passing through the leading-edge endpoint of the hyperbolic spiral line and parallel to the separation point tangent line; Determine the leading-edge point of the rear-row blade, where the leading-edge point of the rear-row blade is determined by the intersection of a vertical line passing through the separation point and perpendicular to the leading-edge tangent line of the rear-row blade and the leading-edge tangent line of the rear-row blade; Determine the leading-edge tangent point of the rear-row blade, which is determined by the intersection of the leading-edge tangent line of the rear-row blade and the basic profile line; Determine the intersection point of the tangent lines of the rear-row blade, which is determined by the intersection of the tangent line at the leading-edge tangent point of the rear-row blade and the tangent line at the rear-end point of the basic profile line; Determine the profile line of the rear-row blade, which is determined by a cubic Bezier curve jointly determined by the rear-end point of the basic profile line, the leading-edge point of the rear-row blade, the leading-edge tangent point of the rear-row blade, and the intersection point of the tangent lines of the rear-row blade; Determine the flow area of the rear row, which is determined jointly by the leading-edge point of the rear-row blade and the separation point; Determine the trailing-edge point of the front-row blade, which is determined jointly by the leading-edge point of the rear-row blade, the profile line of the rear-row blade, and the flow area of the rear row; Determine the trailing-edge modification line of the front-row blade, which is determined jointly by the trailing-edge point of the front-row blade and the separation point tangent line; Determine the profile line of the front-row blade, which is determined jointly by the basic profile line and the trailing-edge modification line of the front-row blade; Determine the thickness distribution law of the front-row blade and the rear-row blade, where the thickness distribution law of the front-row blade and the rear-row blade is determined by given parameters; For the chord length of the basic profile line and the installation angle of the basic profile line given in the blade height direction, the basic profile line obtained is: Where, α is the installation angle of the basic profile line, L is the chord length of the basic profile line, c is the hyperbolic spiral line parameter, θ0 is the initial rotation angle, and c, θ0 are obtained by iterative solution from L and α; Determine the relational expression of the separation point: Among them, the derivatives at each point on the base curve are is the derivative at the front endpoint of the base curve, is the derivative at the rear endpoint of the base curve, θ S is the rotation angle corresponding to the separation point, is the derivative at the separation point.

2. The single-stage tandem high energy density blade design method according to claim 1, characterized in that, Determine the relational expression of the separation point tangent line as:

3. The single-stage tandem high energy density blade design method according to claim 2, characterized in that, Determine the relational expression of the leading-edge tangent line of the rear-row blade as:

4. The single-stage tandem high energy density blade design method according to claim 1, characterized in that, Determine the relational expression of the leading-edge point of the rear-row blade as: where (x hq , y hq ) are the abscissa and ordinate of the leading edge point of the rear row of blades.

5. The single-stage tandem high energy density blade design method according to claim 4, characterized in that, Determine the relational expression of the leading-edge tangent point of the rear-row blade as: Among them, θ Q is the rotation angle of the tangent point at the leading edge of the rear row of blades.

6. The single-stage tandem high energy density blade design method according to claim 5, wherein Determine the relational expression of the intersection point of the tangent lines of the rear-row blade as: Among them, (x hj , y hj ) are the abscissa and ordinate of the tangent intersection point of the rear row of blades.

7. The single-stage tandem high energy density blade design method according to claim 6, wherein Determine the relational expression of the profile line of the rear-row blade as: Where, t is the curve parameter, t ∈ (0, 1).

8. The single-stage tandem high energy density blade design method according to claim 7, wherein Determine the relational expression of the flow area of the rear row as: Among them, S t is the rear row flow area.

9. The single-stage tandem high energy density blade design method according to claim 8, wherein Determine the relational expression of the trailing-edge point of the front-row blade as: Among them, (x qh , y qh ) are the horizontal and vertical coordinates of the trailing edge point of the front row blades, and t s is the Bezier curve parameter value of the trailing row blade profile, which is obtained by the following formula:

10. The single-stage tandem high energy density blade design method according to claim 9, wherein The relational expression for determining the trailing edge modification line of the front row of blades is as follows:

11. A vane pump, wherein The vane pump includes a single-stage tandem vane, and the single-stage tandem vane is designed according to the single-stage tandem high energy density vane design method described in any one of claims 1-10.

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