CN110173462B - Mixed flow pump bionic volute based on drag reduction and noise reduction - Google Patents

Mixed flow pump bionic volute based on drag reduction and noise reduction Download PDF

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Publication number
CN110173462B
CN110173462B CN201910529952.5A CN201910529952A CN110173462B CN 110173462 B CN110173462 B CN 110173462B CN 201910529952 A CN201910529952 A CN 201910529952A CN 110173462 B CN110173462 B CN 110173462B
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needle
volute
shaped
section group
profile
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CN110173462A (en
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王凯
罗光钊
刘厚林
夏瑞超
谈明高
王勇
董亮
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Jiangsu University
Zhenjiang Fluid Engineering Equipment Technology Research Institute of Jiangsu University
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Jiangsu University
Zhenjiang Fluid Engineering Equipment Technology Research Institute of Jiangsu University
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    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04DNON-POSITIVE-DISPLACEMENT PUMPS
    • F04D29/00Details, component parts, or accessories
    • F04D29/40Casings; Connections of working fluid
    • F04D29/406Casings; Connections of working fluid especially adapted for liquid pumps
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04DNON-POSITIVE-DISPLACEMENT PUMPS
    • F04D29/00Details, component parts, or accessories
    • F04D29/66Combating cavitation, whirls, noise, vibration or the like; Balancing
    • F04D29/68Combating cavitation, whirls, noise, vibration or the like; Balancing by influencing boundary layers
    • F04D29/688Combating cavitation, whirls, noise, vibration or the like; Balancing by influencing boundary layers especially adapted for liquid pumps

Abstract

The invention provides a mixed flow pump bionic volute based on drag reduction and noise reduction, which is provided with a partition tongue and a volute spiral section, wherein the inner surface of the volute spiral section, which is close to one end of the partition tongue, is provided with a needle-shaped outline structure; the needle-shaped profile structure is divided into a profile front section group and a profile staggered section group along the inner surface of the spiral section of the volute from the position of the partition tongue; the profile front section group and the profile staggered section group are arranged at intervals, each profile front section group and each profile staggered section group respectively comprises a plurality of parallelly arranged needle-shaped depressions, and at least part of the needle-shaped depressions are provided with drag reduction microstructures. The invention can effectively utilize the needle-shaped outline structure to combine with the drag reduction microstructure and realize the effects of drag reduction and noise reduction in a matching mode of the impeller and the volute tongue, and the flow resistance and the fluid noise near the tongue are reduced to the greatest extent.

Description

Mixed flow pump bionic volute based on drag reduction and noise reduction
Technical Field
The invention belongs to the technical field of water pumps, and particularly relates to a mixed flow pump bionic volute based on drag reduction and noise reduction.
Background
The mixed flow pump is widely applied to various departments of national economy, is mainly used for agricultural irrigation water, municipal water supply and drainage, power plant circulating water supply, regional water mixing and the like, and is also applied to the aspects of nuclear power and ship water spray propulsion. Due to the complex internal flow structure of the pump, friction losses and intense noise are often associated with the operation of the pump.
The flow-through part in the mixed flow pump is complex, the liquid impacts the partition tongue part to cause serious friction loss, the dynamic and static interference action between the impeller and the partition tongue and the uneven flow at the impeller outlet cause far-field flow noise, and the inside of the mixed flow pump is three-dimensional unsteady turbulence. In order to reduce friction resistance at the partition tongue and reduce the influence of the partition tongue on the pulsation characteristic of the centrifugal pump, based on a bionics principle, biological prototype morphological characteristics are extracted, a bionic noise reduction structural model is established, and a matching mode of the partition tongue and the impeller is improved.
At present, the application of the bionic fan volute in the aspect of structural design of the fan volute is based on a fan volute with a bionic asymmetric inclined volute tongue structure as described in a Chinese patent document CN 107676304A; patent document CN106855062a describes a noise reduction volute tongue based on variable depth and a multi-wing centrifugal fan; patent document CN104929953a discloses a volute tongue with a bionic structure and a volute using the volute tongue, and the design is designed for modeling a fan volute tongue, and is suitable for gas transportation.
In the technical field of water pumps, the bionic structure based on the lining of a large snail shell pump is applied to the aspect of structural design as described in China patent document CN204126964U, and the main purpose is to improve the wear resistance and corrosion resistance by adopting the lining of a stainless steel pump shell; CN109026726a discloses a centrifugal mud pump with bionic non-smooth surface, which is based on the surface of the pump body contacted with silt to form the bionic non-smooth surface, thereby reducing friction loss and improving wear resistance; CN108213534a discloses a device and a method for processing a bionic groove on the inner wall of a conical water inlet pipe based on a water pump, and introduces a device and a method based on the design for processing the bionic groove on the inner wall of the conical water inlet pipe; CN102042264a discloses a vibration-damping noise-reducing centrifugal pump with a bionic structure, and the vibration-damping noise-reducing optimization is carried out on the pump by using the bionic structure at the tongue-separating position, and the influence of the vibration-damping noise-reducing centrifugal pump on the overall hydraulic performance of the pump is not considered; and the existing papers focused on the aspects of volute bionics are: the method comprises the steps of carrying out structural bionics on a volute close to a diaphragm section by utilizing an elastic region of the outer contour of a wing to improve pressure pulsation, but destroying hydraulic performance, and being more chaotic in a flow field of the spiral section and larger in loss.
In summary, the present bionic design for the volute structure of the centrifugal pump is less, and most bionic structures are suitable for fans and centrifugal pumps, and the bionic structure for the mixed flow pump is less.
Disclosure of Invention
In order to solve at least one technical problem, the invention discloses a mixed flow pump bionic volute based on resistance reduction and noise reduction, wherein the bionic volute is provided with a partition tongue and a volute spiral section, and the inner surface of the volute spiral section, which is close to one end of the partition tongue, is provided with a needle-shaped contour structure;
The needle-shaped profile structure is divided into a profile front section group and a profile staggered section group along the inner surface of the spiral section of the volute from the position of the partition tongue; the profile front section group and the profile staggered section group are arranged at intervals, each profile front section group and each profile staggered section group respectively comprises a plurality of parallelly arranged needle-shaped depressions, and at least part of the needle-shaped depressions are provided with drag reduction microstructures.
Optionally, a tongue-separating mounting angle
Radius r= (0.005-0.021) D of rounded tongue head 2
Wherein n is the rated rotation speed, Q is the design flow of the pump, H is the pump lift, and D 2 is the diameter of the outlet of the impeller.
Optionally, the baffle tongue is arranged in parallel with an impeller blade outlet of the mixed flow pump, the projection of the impeller blade outlet edge on the axial plane is marked as delta with an axis included angle, and the projection of the baffle tongue on the axial plane is marked as delta 11=δ=arctan[(D2a-D2e)/(2b2 with the axis included angle;
The inclined angle theta 1 of the partition tongue is equal to the inclined angle theta of the outlet edge of the impeller blade;
the distance between the partition tongue and the impeller outlet is recorded as delta, delta= (0.03-0.06) D 2;
The length of the tongue is denoted as c, c=2b 3/[ cos (delta-theta) +cos (delta + theta) ];
Wherein, D 2a is the streamline outer diameter of the front cover of the impeller, D 2e is the streamline outer diameter of the rear cover of the impeller, b 2 is the impeller outlet width, D 2 is the impeller outlet diameter, and b 3 is the volute inlet width.
Optionally, the contour of the needle-shaped recess is triangular, and the axis of the needle-shaped recess is perpendicular to the blade outlet.
Optionally, an acute angle vertex of the needle-shaped concave of the profile front section group and a bottom shrinkage surface obtuse angle vertex distance f= (0.045-0.075) b 3 of the needle-shaped concave of the profile staggered section group;
The axes of the needle-shaped depressions of the contour front section group and the axes of the needle-shaped depressions of the contour staggered section group are staggered, the staggered interval e 1=(0.008~0.045)b3, and the adjacent needle-shaped contour axis interval e= (0.017-0.045) b 3.
Optionally, a cylindrical drag reduction microstructure is arranged on the needle-shaped concave of the profile front section group.
Optionally, the cylindrical drag reduction microstructures are symmetrically distributed along the axis of the needle-shaped concave, the radius of the cylinder r 1=-0.0028n1/2(Q/H)3/4 + (0.13-0.15), the bottom of the column groove is semicircular, the radius of the circular arc of the column groove is r 0, and the ratio m 1/n1 =0.85-1.25 of the depth m 1 of the column groove to the width n 1 of the column groove.
Optionally, the needle-shaped concave of the profile staggered section group is provided with a dome-shaped drag reduction microstructure.
Optionally, the dome-shaped drag reduction microstructures are symmetrically distributed along the axis of the needle-shaped concave, the radius r 2=(0.21~0.35)b3×10-2 of the dome is square at the bottom of the groove, and the ratio of the groove depth m 2 to the groove width n 2 is m 2/n2 =0.85-1.15.
Optionally, an upper maximum width w 1=(0~0.012)b3 of the spike-shaped recess;
the upper included angle alpha of the needle-shaped concave part is=2-6 degrees;
the maximum width w 2=(0.012~0.03)b3 of the middle part of the needle-shaped concave part;
The maximum width w 3=(0.03~0.048)b3 of the lower part of the needle-shaped concave part;
The width w= (0.035-0.048) b 3 of the bottom edge of the needle-shaped concave, the bottom of the needle-shaped concave is an obtuse angle contraction surface, the length h 1=(0.01~0.015)b3 of the obtuse angle contraction surface, and the obtuse angle beta = 106-128 degrees of the obtuse angle contraction surface;
The total length h= (0.45-0.75) b 3 of the needle-shaped concave.
By adopting the technical scheme, the mixed flow pump bionic volute has the following beneficial effects:
1) By adopting the matching mode that the partition tongue is parallel to the outlet edge of the impeller blade, low-speed vortex near the partition tongue can be reduced, vortex pulsation and pressure pulsation in the gap between the impeller and the partition tongue are reduced, and meanwhile, the hydraulic performance of the pump is improved.
2) The hydrophobic property of the column groove microstructure can reduce the viscous action of liquid and solid surfaces, reduce the flow resistance and increase the working efficiency.
3) The triangular concave surface of the needle-shaped profile guides the liquid impacting the isolation tongue to flow forwards, and the streamline of the impeller outlet impacting the isolation tongue is combed, so that the flowing state of the fluid in the impeller runner and the diffusion section can be better improved, the pressure pulsation in the isolation tongue area is reduced, the pulsation amplitude is more gentle, and the purposes of vibration reduction and noise reduction are achieved.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the description of the embodiments will be briefly described below, and it is apparent that the drawings in the following description are only some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic view of a part of a bionic partition tongue of a mixed flow pump according to an embodiment of the present invention;
FIGS. 2 (a) and 2 (b) are schematic diagrams of cylindrical and dome-shaped drag reducing microstructures according to embodiments of the present invention;
FIG. 3 is a diagram of a volute block according to an embodiment of the present invention;
FIG. 4 is a schematic view of an impeller according to an embodiment of the present invention;
FIG. 5 is a schematic view showing the matching of the projection of the impeller and the axial plane of the tongue in an embodiment of the present invention;
FIG. 6 is a front view of a single spike-shaped depression according to an embodiment of the present invention;
FIG. 7 is an external characteristic curve of an embodiment of the present invention;
fig. 8 is a time domain plot of the volute outlet pressure pulsation characteristic of an embodiment of the present invention.
In the figure: 1-partition tongue, 2-profile front section group, 3-cylindrical drag reduction microstructure, 4-spiral section, 5-profile staggered section group, 6-dome type drag reduction microstructure and 7-spiral casing diffusion section.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. It will be apparent that the described embodiments are only some, but not all, embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Reference herein to "one embodiment" or "an embodiment" means that a particular feature, structure, or characteristic may be included in at least one implementation of the invention. In the description of the present invention, it should be understood that the directions or positional relationships indicated by the terms "upper", "lower", "top", "bottom", etc. are based on the directions or positional relationships shown in the drawings, are merely for convenience of description and simplification of the description, and do not indicate or imply that the apparatus or element in question must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as limiting the invention.
Example 1:
As shown in fig. 1-2 (b) and fig. 6, a mixed flow pump bionic volute based on resistance and noise reduction is provided with a partition tongue 1 and a volute spiral section 4, wherein a needle-shaped outline structure is arranged on the inner surface of one end, close to the partition tongue 1, of the volute spiral section 4;
The needle-shaped profile structure is divided into a profile front section group 2 and a profile staggered section group 5 along the inner surface of the spiral section 4 of the volute from the position of the partition tongue 1; the profile front section group 2 and the profile staggered section group 5 are arranged at intervals, the profile front section group 2 and the profile staggered section group 5 respectively comprise a plurality of parallelly arranged needle-shaped depressions, and at least part of the needle-shaped depressions are provided with drag reduction microstructures.
In some embodiments, the tongue 1 is placed at an angle
Radius r= (0.005-0.021) D of radius of head of partition tongue 1 2
Wherein n is the rated rotation speed, Q is the design flow of the pump, H is the pump lift, and D 2 is the diameter of the outlet of the impeller.
In some embodiments, in the matching manner of the bionic volute of the mixed flow pump (shown in fig. 3) and the impeller (shown in fig. 4), the partition tongue 1 is arranged in parallel with the impeller blade outlet of the mixed flow pump, the projection of the edge of the impeller blade outlet on the axial plane is marked as delta with the axis, the projection of the partition tongue 1 on the axial plane is marked as delta 11=δ=arctan[(D2a-D2e)/(2b2 with the axis in the arrangement manner, as shown in fig. 5;
the inclined angle theta 1 of the partition tongue 1 is equal to the inclined angle theta of the outlet edge of the impeller blade;
The distance between the partition tongue 1 and the impeller outlet is recorded as delta, delta= (0.03-0.06) D 2;
The length of the partition tongue 1 is marked as c, c=2b 3/[ cos (delta-theta) +cos (delta+theta) ];
Wherein, D 2a is the streamline outer diameter of the front cover of the impeller, D 2e is the streamline outer diameter of the rear cover of the impeller, b 2 is the impeller outlet width, D 2 is the impeller outlet diameter, and b 3 is the volute inlet width.
In some embodiments, the contour of the needle-shaped recess is triangular, the axis of the needle-shaped recess being perpendicular to the blade outlet.
In some embodiments, the acute angle vertex of the needle-shaped recess of the profile front section group 2 is separated from the bottom constriction plane obtuse angle vertex distance f= (0.045-0.075) b 3 of the needle-shaped recess of the profile staggered section group 5;
the axes of the needle-shaped depressions of the contour front section group 2 and the axes of the needle-shaped depressions of the contour staggered section group 5 are staggered, the staggered interval e 1=(0.008~0.045)b3 and the adjacent needle-shaped contour axis interval e= (0.017-0.045) b 3.
In some embodiments, the cylindrical drag reducing microstructures 3 are provided on the needle-shaped depressions of the profile front section group 2, as shown in fig. 2 (a).
In some embodiments, the cylindrical drag reduction microstructures 3 are symmetrically distributed along the axis of the needle-shaped concave, the radius of the cylinder r 1=-0.0028n1/2(Q/H)3/4 + (0.13-0.15), the bottom of the column groove is semicircular, the radius of the circular arc is r 0, and the ratio of the depth m 1 of the column groove to the width n 1 of the column groove is m 1/n1 =0.85-1.25.
In some embodiments, the needle-shaped depressions of the set of staggered profile segments 5 are provided with dome-shaped drag reducing microstructures 6, as shown in fig. 2 (b).
In some embodiments, the dome-shaped drag reducing microstructures 6 are symmetrically distributed along the axis of the needle-shaped concave, the dome radius r 2=(0.21~0.35)b3×10-2, the bottom of the groove is square, and the ratio of the groove depth m 2 to the groove width n 2 is m 2/n2 =0.85-1.15.
In some embodiments, the upper maximum width w 1=(0~0.012)b3 of the needle-like depression;
the upper included angle alpha of the needle-shaped concave part is=2-6 degrees;
the maximum width w 2=(0.012~0.03)b3 of the middle part of the needle-shaped concave part;
The maximum width w 3=(0.03~0.048)b3 of the lower part of the needle-shaped concave part;
The width w= (0.035-0.048) b 3 of the bottom edge of the needle-shaped concave, the bottom of the needle-shaped concave is an obtuse angle contraction surface, the length h 1=(0.01~0.015)b3 of the obtuse angle contraction surface, and the obtuse angle beta = 106-128 degrees of the obtuse angle contraction surface;
The total length h= (0.45-0.75) b 3 of the needle-shaped concave.
Specifically, taking a mixed flow pump as an example, the design parameters are as follows: design flow q=1200m 3/H, lift h=10m, power p=45 kW, rated rotation speed n=1450 rpm, specific rotation speed n s =543, impeller outlet width b 2 =37 mm, volute inlet width b 3 =43 mm, impeller outlet diameter D 2 =248 mm. And carrying out subsequent calculation by using the formula.
The projection of the partition tongue 1 on the axial plane and the axial included angle are recorded as delta 11 =delta=31.4 degrees;
The inclination angle theta 1 of the partition tongue 1 is equal to the impeller blade outlet side inclination angle theta, theta 1 =theta=8°;
the distance between the partition tongue 1 and the impeller outlet is recorded as delta=8mm;
The length of the tongue 1 is denoted c=51 mm, wherein D 2a=270.6mm,D2e =225.4 mm.
The maximum width w 1 of the upper part of the needle-shaped concave is=0.51 mm, the included angle alpha of the upper part is=4°, the maximum width w 2 of the middle part of the needle-shaped concave is=1.275 mm, the maximum width w 3 of the lower part of the needle-shaped concave is=2.04 mm, the width w of the bottom edge is=2.04 mm, the bottom part is an obtuse angle shrink surface, the length h 1 of the obtuse angle shrink surface is=0.51 mm, the obtuse angle beta=127°, the total length h of the needle-shaped concave is=30 mm, and a schematic diagram of a single needle-shaped concave is shown in fig. 6.
The distance f=3 mm between the acute angle vertex of the needle-shaped concave of the contour front section group 2 and the obtuse angle vertex of the bottom contraction surface of the needle-shaped concave of the contour staggered section group 5,
The axes of the needle-shaped depressions of the contour front section group 2 and the axes of the needle-shaped depressions of the contour staggered section group 5 are staggered, the staggered interval e 1 = 1.02mm, and the adjacent needle-shaped contour axis interval e = 1.02mm.
The cylindrical drag reduction microstructure 3 is arranged on the needle-shaped concave of the profile front section group 2. The cylindrical drag reduction microstructures 3 are symmetrically distributed along the axis of the needle-shaped concave, the cylindrical radius r 1 =0.13 mm of the hydrophobic drag reduction microstructures is semicircular, the circular arc radius of the cylindrical groove is r 0 =0.13 mm, and the ratio m 1/n1 =1 of the depth m 1 of the cylindrical groove to the width n 1 of the cylindrical groove.
The needle-shaped concave of the profile staggered section group 5 is provided with a dome-shaped drag reduction microstructure 6. The dome-shaped drag reduction microstructures 6 are symmetrically distributed along the axis of the needle-shaped concave, the radius of the dome is r 2 =0.12 mm, the bottom of each groove is square, and the ratio of the depth m 2 of each groove to the width n 2 of each groove is m 2/n2 =1.
In order to verify the bionic drag reduction and noise reduction effects of the mixed flow pump, the CFD is adopted to calculate the bionic volute and the prototype volute, the external characteristic result is shown in fig. 7, the pressure pulsation at the outlet of the volute is more gentle, the flow state is improved, and the drag reduction and noise reduction effects are achieved.
The foregoing description of the preferred embodiments of the invention is not intended to limit the invention to the precise form disclosed, and any such modifications, equivalents, and alternatives falling within the spirit and scope of the invention are intended to be included within the scope of the invention.

Claims (4)

1. A mixed flow pump bionic volute based on drag reduction and noise reduction is characterized in that: the bionic volute is provided with a partition tongue and a volute spiral section, and the inner surface of the volute spiral section, which is close to one end of the partition tongue, is provided with a needle-shaped outline structure;
The needle-shaped profile structure is divided into a profile front section group and a profile staggered section group along the inner surface of the spiral section of the volute from the position of the partition tongue; the profile front section group and the profile staggered section group are arranged at intervals, each profile front section group and each profile staggered section group respectively comprises a plurality of parallelly arranged needle-shaped depressions, and at least part of the needle-shaped depressions are provided with drag reduction microstructures;
the outline of the needle-shaped concave is triangular, and the axis of the needle-shaped concave is perpendicular to the impeller blade outlet of the mixed flow pump; the distance f= (0.045-0.075) b 3 between the acute angle vertex of the needle-shaped concave of the contour front section group and the obtuse angle vertex of the bottom contraction surface of the needle-shaped concave of the contour staggered section group; the axes of the needle-shaped depressions of the contour front section group and the axes of the needle-shaped depressions of the contour staggered section group are staggered, the staggered interval e 1=(0.008~0.045)b3, and the adjacent needle-shaped contour axis interval e= (0.017-0.045) b3;
A cylindrical drag reduction microstructure is arranged on the needle-shaped concave of the profile front section group; the cylindrical drag reduction microstructures are symmetrically distributed along the axis of the needle-shaped concave, the radius of the cylinder r 1=-0.0028n1/2(Q/H)3/4 + (0.13-0.15), the bottom of the column groove is semicircular, the radius of the circular arc is r 0, and the ratio m 1/n1 =0.85-1.25 of the depth m 1 of the column groove to the width n 1 of the column groove;
The needle-shaped concave of the profile staggered section group is provided with a dome-shaped drag reduction microstructure;
the maximum width w 1=(0~0.012)b3 of the upper part of the needle-shaped concave part;
the upper included angle alpha of the needle-shaped concave part is=2-6 degrees;
the maximum width w 2=(0.012~0.03)b3 of the middle part of the needle-shaped concave part;
The maximum width w 3=(0.03~0.048)b3 of the lower part of the needle-shaped concave part;
the width w= (0.035-0.048) b 3 of the bottom edge of the needle-shaped concave, the bottom of the needle-shaped concave is an obtuse angle contraction surface, the length h 1=(0.01~0.015)b3 of the obtuse angle contraction surface, and the obtuse angle beta = 106-128 degrees of the obtuse angle contraction surface; the total length h= (0.45-0.75) b 3 of the needle-shaped concave;
b 3 is the width of the inlet of the volute, n is the rated rotation speed, Q is the design flow of the pump, and H is the pump lift.
2. The mixed flow pump biomimetic volute of claim 1, wherein:
The placement angle of the partition tongue
The head rounding radius r= (0.005-0.021) D of the partition tongue 2
Wherein n is the rated rotation speed, Q is the design flow of the pump, H is the pump lift, and D 2 is the diameter of the outlet of the impeller.
3. The mixed flow pump bionic volute according to claim 1 or 2, wherein: the baffle tongue is arranged in parallel with an impeller blade outlet of the mixed flow pump, the included angle between the projection of the impeller blade outlet edge on the axial surface and the axis is shown as delta, and the included angle between the projection of the baffle tongue on the axial surface and the axis is shown as delta 11=δ=arctan[(D2a-D2e)/(2b2);
The inclined angle theta 1 of the partition tongue is equal to the inclined angle theta of the outlet edge of the impeller blade;
the distance between the partition tongue and the impeller outlet is recorded as delta, delta= (0.03-0.06) D 2;
The length of the tongue is denoted as c, c=2b 3/[ cos (delta-theta) +cos (delta + theta) ];
Wherein, D 2a is the streamline outer diameter of the front cover of the impeller, D 2e is the streamline outer diameter of the rear cover of the impeller, b 2 is the impeller outlet width, D 2 is the impeller outlet diameter, and b 3 is the volute inlet width.
4. The mixed flow pump biomimetic volute of claim 1, wherein: the dome-shaped drag reduction microstructures are symmetrically distributed along the axis of the needle-shaped concave, the radius r 2=(0.21~0.35)b3×10-2 of the dome is square at the bottom of the groove, and the ratio m 2/n2 =0.85-1.15 of the groove depth m 2 to the groove width n 2.
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