CN112879288A - Universal calculation method for flow pulsation coefficient of three-twisted-blade rotor pump - Google Patents

Universal calculation method for flow pulsation coefficient of three-twisted-blade rotor pump Download PDF

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CN112879288A
CN112879288A CN202110108507.9A CN202110108507A CN112879288A CN 112879288 A CN112879288 A CN 112879288A CN 202110108507 A CN202110108507 A CN 202110108507A CN 112879288 A CN112879288 A CN 112879288A
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twisted
flow
rotor
blade rotor
formula
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CN112879288B (en
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刘萍
李玉龙
张安民
宋安然
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Suqian College
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04C—ROTARY-PISTON, OR OSCILLATING-PISTON, POSITIVE-DISPLACEMENT MACHINES FOR LIQUIDS; ROTARY-PISTON, OR OSCILLATING-PISTON, POSITIVE-DISPLACEMENT PUMPS
    • F04C18/00—Rotary-piston pumps specially adapted for elastic fluids
    • F04C18/08—Rotary-piston pumps specially adapted for elastic fluids of intermeshing-engagement type, i.e. with engagement of co-operating members similar to that of toothed gearing
    • F04C18/12—Rotary-piston pumps specially adapted for elastic fluids of intermeshing-engagement type, i.e. with engagement of co-operating members similar to that of toothed gearing of other than internal-axis type
    • F04C18/126—Rotary-piston pumps specially adapted for elastic fluids of intermeshing-engagement type, i.e. with engagement of co-operating members similar to that of toothed gearing of other than internal-axis type with radially from the rotor body extending elements, not necessarily co-operating with corresponding recesses in the other rotor, e.g. lobes, Roots type
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
    • F04C—ROTARY-PISTON, OR OSCILLATING-PISTON, POSITIVE-DISPLACEMENT MACHINES FOR LIQUIDS; ROTARY-PISTON, OR OSCILLATING-PISTON, POSITIVE-DISPLACEMENT PUMPS
    • F04C25/00—Adaptations of pumps for special use of pumps for elastic fluids
    • F04C25/02—Adaptations of pumps for special use of pumps for elastic fluids for producing high vacuum
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/17—Mechanical parametric or variational design
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
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    • G06F30/20—Design optimisation, verification or simulation

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Abstract

The invention discloses a general calculation model of three-twisted-blade rotor pump flow pulsation coefficient,

Description

Universal calculation method for flow pulsation coefficient of three-twisted-blade rotor pump
Technical Field
The invention belongs to the technical field of rotor pumps, and particularly relates to a general calculation method for flow pulsation coefficients of a three-twisted-blade rotor pump.
Background
The rotor pump is a variable volume pump realized by conjugate rotation of a pair of non-contact rotors, is originally used for a roots vacuum pump, and is widely applied. With the gradual application of the pump in devices such as aerospace space simulation and the like, the requirements on the performance of the pump such as unit displacement volume (namely, light weight effect) and flow pulsation are higher and higher. Among them, the profile structure of the rotor is a direct factor for the performance of the pump, and the smaller the number of blades, the higher the shape factor, and the less leakage of the profile edge, the better the degree of weight reduction, and thus, methods for highly forming the rotor profile such as CN109779903B and CN109630407B have been proposed. Although the structure with a small conjugate form factor of the end face of the rotor can improve the flow pulsation with a small amplitude, the twisted blade structure in the axial direction of the rotor is the most effective means for reducing the flow pulsation factor, and therefore, the three twisted blades of the rotor are the best choice in view of the structural characteristics of the small number of blades and the wrap angle of the twisted blades required for the lightweight effect of the pump.
The half impeller profile of the three twisted blade rotor is a basic profile of the twisted blade rotor profile structure, and comprises an end face half impeller profile and an axial half impeller profile; the end surface half impeller profile is composed of a top arc section, an outer avoidance profile section, an outer conjugate profile section, an inner avoidance profile section and a valley arc section which are all seven points and six sections which are connected end to end.
The head and the tail of the end surface half impeller profile are respectively positioned on an end surface top symmetric axis (a top axis for short) of the impeller profile and an end surface valley symmetric axis (a valley axis for short) crossing the impeller profile, the included angle between the top axis and the valley axis is pi/3, the intersection point of the top axis and the valley axis is the rotor center, the intersection points of the top axis, the valley axis and a pitch circle are respectively a top node and a valley node, the intersection point of the end surface half impeller profile and the pitch circle is the middle point on a pitch arc between the top node and the valley node and is called a middle node, and the connecting line of the middle node and the rotor center is the middle axis of the end surface half impeller profile;
any point on the pitch arc between the top node and the valley node is called an instant node, the normal distance from the instant node to the inner and outer conjugate profile sections is an instant diameter, the radius of the instant diameter/pitch circle is a dimensionless instant diameter, the central angle of the pitch arc between the instant node and the valley node is an instant angle, and the conjugate shape coefficient of the inner and outer conjugate profile sections is a dimensionless instant diameter +1 at the top node;
the outer conjugate profile section and the inner conjugate profile section are respectively conjugated with the inner conjugate profile section and the outer conjugate profile section on the dual rotor, and the shape of the outer conjugate profile section and the shape of the inner conjugate profile section are determined by the given dimensionless transient diameter definition and the given conjugate shape coefficient;
the circle centers of the top arc section and the valley arc section are both the center of the rotor and the central angle are equal (called as a top seal angle), the radius of the top arc section is equal to the radius of the rotor shape coefficient multiplied by the radius of the pitch circle, the radius of the valley arc section is equal to 2 multiplied by the radius of the pitch circle-the radius of the top arc section, and the rotor shape coefficient is equal to the radius of the top arc section/the radius of the pitch circle;
the structure can realize the maximization of the shape coefficient of the rotor and achieve the optimization of the lightweight effect of the pump, the base point is a known end point of a non-middle node on the inner conjugate profile section, and the vertex is a known end point on a non-top shaft on the top arc section;
the overall shape and the tip seal angle of the end face half-impeller profile structure are uniquely determined by the given dimensionless instantaneous diameter definition and the given rotor shape coefficient through the conjugate relation and the avoidance relation between the rotor auxiliary profiles; the dimensionless transient path definition is uniquely determined by a given conjugate contour segment curve type and a given conjugate shape coefficient; the overall size of the end face half-vane profile configuration is uniquely determined by a given pitch circle radius;
the axial half-vane profile is 7 helices starting at a given twist angle and seven points on the end face half-vane profile, respectively, in the rotor width direction (i.e. axial direction).
At present, although various flow pulsation coefficient calculation formulas are respectively given for different types of conjugate profile curves, integral calculation of micro-width theoretical flow in the thickness direction of a rotor cannot be avoided, if the micro-width theoretical flow is an easy-to-integrate function, a direct accurate integral method can be adopted, otherwise an indirect numerical calculation method is adopted, but programming and operation involved in the numerical calculation method and diversity of the types of the conjugate profile curves are not understood by general engineering technicians and are not universal.
Disclosure of Invention
The invention aims at the problems to be solved in the background art, and provides a simple and efficient general method for calculating the theoretical flow of the three-twisted-blade rotor pump and the flow pulsation coefficient of the three-twisted-blade rotor pump by using a high-shape construction method based on an end surface profile, taking the dimensionless instantaneous diameter of the end surface conjugate profile and the twisted blade angle of the axial profile as variables and using a dimensionless theoretical flow formula of a straight blade rotor to construct a dimensionless integral formula of the theoretical flow of the three-twisted-blade rotor pump, and using a fitting structure of the dimensionless theoretical flow.
In order to achieve the purpose, the technical solution of the invention is as follows:
a general calculation model of three torsion vane rotor pump flow pulsation coefficients is characterized in that:
Figure BDA0002918425910000031
a general calculation model of three torsion vane rotor pump flow pulsation coefficients is characterized in that: twisted blade rotor flow pulsation coefficient delta ([ xi ])b) The calculation of (a) can be simplified as:
Figure BDA0002918425910000032
the method for acquiring the universal calculation model of the pump flow pulsation coefficient of the three-twisted-blade rotor is characterized by comprising the following steps of: the method comprises the following steps:
s1, an accurate calculation method of the dimensionless theoretical flow of the three-twisted-blade rotor comprises the following steps:
the method comprises the following steps that (1) according to the theoretical flow of a three-twisted-blade rotor pump, the equivalent infinite micro theoretical flow corresponding to an axially infinite equivalent micro-width straight-blade rotor is formed by axially overlapping spiral lines, and the surfaces of a starting point, any point and an end point on each spiral line are defined as a starting end surface, an arbitrary section and a terminating end surface of the three-twisted-blade rotor respectively; defining the micro theoretical flow rate corresponding to the micro-width straight blade rotor at the initial end face as dQ0The corresponding dimensionless theoretical flow is q0At this time, the product is made by
Figure BDA0002918425910000033
Obtaining the micro theoretical flow rate dQ corresponding to the micro-width straight blade rotor at any sectionzAnd its dimensionless theoretical flow qzComprises the following steps:
Figure BDA0002918425910000034
by dQzAnd the theoretical flow Q of the three-twisted-blade rotor and the dimensionless theoretical flow Q thereof are obtained by axial superposition of the spiral lines, namely integration in the width direction:
Figure BDA0002918425910000035
wherein, in the formula (1), the formula (2) and the formula (3), ω is the rotation angular velocity of the rotor, dz is the micro width, Ω is the instantaneous angle, ε is a given rotor shape coefficient, ρ is the instantaneous diameter, r is the pitch circle radius, ρ/r is a given dimensionless instantaneous diameter, and φ ═ π/6; xi is the stagger angle of any section relative to the top axis of the initial end face and is defined as a torsion anglebThe tip axis offset angle of the termination end face relative to the start end face is defined as a twisted blade angle;
s2, a fitting calculation method of the three-blade twisted rotor dimensionless theoretical flow is as follows:
from the constructive geometrical relationship of the outer and inner conjugate contour segments, q is known0(Ω) is symmetrical about Ω ═ Φ, then q is given0(omega) is fitted with the formula
Figure BDA0002918425910000041
In the formula, given the definition of ρ (Ω)/r, the fitting coefficient A, B, C is expressed by formula (1) corresponding to 5 groups q under ρ (0)/r, ρ (0.5 φ)/r, ρ (1.5 φ)/r, ρ (2 φ)/r0Data, uniquely determined by means of a method of fitting trend lines in EXCEL tables;
substituting the formula (4) into the formula (3) to obtain the dimensionless theoretical flow q (omega, xi) of the twisted blade rotorb) The piecewise fitting of (a) is:
Figure BDA0002918425910000042
s3, a general calculation method of flow pulsation coefficients of a three-twisted-blade rotor comprises the following steps:
the first derivative of formula (5) to Ω is equal to 0, resulting in q (Ω, ξ)b) In omega 0.5 xib、Ω＝φ+0.5ξbThe minimum value min (q) and the maximum value max (q) are obtained respectively, and the formula (5) shows
Figure BDA0002918425910000043
The dimensionless theoretical flow wave height corresponding to q is
Figure BDA0002918425910000051
From the formula (7) to xibIs equal to 0, to get Δ q (ξ)b) In xibWhen 2 phi is pi/3, a minimum value of 0 is obtained, in which case q (omega, 2 phi) is a constant value, and xi is setbSubstitution of formula (5) 2 phi pi/3 to obtain
Figure BDA0002918425910000052
The method is characterized in that the rotor is twisted or not to influence the infinite dimensionless theoretical flow q in the axial directionzThe mean value of (omega, xi) respectively, i.e. not following xibSo q (Ω, ξ) changesb) Q is an average value of0Average value of (Ω) ═ qzThe mean value of (Ω, ξ) is a constant value of q (Ω,2 Φ); then, the flow pulsation coefficient of the twisted blade rotor is defined as the theoretical flow wave height/the theoretical flow mean value
Figure BDA0002918425910000053
In the formula, xibWhen 2 phi is pi/3, the flow pulsation coefficient delta (2 phi) of the twisted blade rotor is 0, namely no flow pulsation; xibWhen the flow rate is equal to 0, the flow rate pulsation coefficient δ (0) of the twisted blade rotor is the flow rate pulsation coefficient of the straight blade rotor, and
Figure BDA0002918425910000054
s4, a simplified calculation method of twisted blade rotor flow pulsation coefficient:
through repeated trial calculation under different definitions of rho (omega)/r, the flow pulsation coefficient delta (xi) of the twisted blade rotorb) Along with twisting blade angle xibHas approximate negative linear relation, the flow pulsation coefficient delta (xi) of the twisted blade rotorb) Can be simplified into
Figure BDA0002918425910000055
Compared with the prior art, the invention has the following beneficial effects:
in the aspect of calculating twisted blade theoretical flow and flow pulsation coefficient thereof, a straight blade dimensionless theoretical flow fitting method is adopted, so that the complexity can be reduced into simplicity, and the difficulty can be reduced; thirdly, the simplest and most efficient general formula can be obtained, and the general formula is easy to be directly adopted by general engineering technicians.
Drawings
Other features, objects and advantages of the present invention will become more apparent upon reading of the following detailed description of non-limiting embodiments thereof, with reference to the accompanying drawings.
FIG. 1 is a configuration of a three twisted pair of lobes rotor and half lobe end profile;
FIG. 2 is a configuration of half-lobe end profile of a three twist lobe rotor;
FIG. 3 is a torsional angle relationship of rotor profiles on a starting end face, arbitrary cross-section, and a terminating end face;
FIG. 4 is a dimensionless theoretical flow position relationship of a straight-bladed rotor with three micro-widths in the width direction;
FIG. 5 is a non-dimensional theoretical flow curve of a circular arc straight blade rotor and a fitting curve thereof;
FIG. 6 is a non-dimensional theoretical flow curve for an example of a circular arc twisted blade rotor;
FIG. 7 is a flow pulsation coefficient curve for an example of a circular twisted blade rotor;
FIG. 8 is a flow pulsation coefficient curve for an involute twisted vane rotor example;
FIG. 9 is a graph of flow pulsation coefficient for an exemplary cycloidal twisted lobe rotor;
wherein: o, rotor center, r, pitch circle radius, 01, top arc segment, 12, outer avoidance profile segment, 23, outer conjugate profile segment, 34, inner conjugate profile segment, 45, inner avoidance profile segment, 56, valley arc segment, O0, top axis, O6, valley axis, 1, vertex, 3, middle node, 4, base point, 7, top node, 8, instant node, 9, valley node, O3, middle axis, phi pi/6, alpha, top seal angle, omega, instant angle, rho, instant diameter, epsilon0Conjugate shape coefficient, epsilon, rotor shape coefficient, b, rotor width, z, axial distance from any section to initial end face, delta, flow pulsation coefficient of twisted-blade rotor, xibTwisted leaf angle, xi, twisted angle, q0Dimensionless theoretical flow at the starting end face, qzThe dimensionless theoretical flow of any section, and the dimensionless theoretical flow of the twisted blade rotor.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
A three-twisted-blade rotor pair aimed at by a general calculation method for pump flow pulsation coefficients of a three-twisted-blade rotor has a body rotor completely the same as a dual rotor, and is therefore collectively referred to as a twisted-blade rotor, as shown in fig. 1; the half-vane profile of the twisted vane rotor is a basic profile of the twisted vane rotor profile, and each half-vane profile comprises two parts, namely an end face half-vane profile and an axial half-vane profile. The end surface half impeller profile is composed of a top arc section 01 at the outer side of a pitch circle, an outer avoidance profile section 12, an outer conjugate profile section 23, and seven-point six-section end-to-end connection of an inner conjugate profile section 34, an inner avoidance profile section 45 and a valley arc section 56 at the inner side of the pitch circle, wherein the seven-point six-section end-to-end connection is 0, 1, 2, 3, 4, 5, 6 and 7. The head and tail points 0 and 6 of the end surface half impeller profile are respectively positioned on an end surface top symmetric axis (called a top axis for short) of the impeller profile and an end surface valley symmetric axis (called a valley axis for short) crossing the impeller profile, the included angle between the top axis and the valley axis is pi/3, the intersection point is a rotor center O, the intersection points of the top axis O0 and the valley axis O6 and a pitch circle are respectively a top node 7 and a valley node 9, the intersection point 3 of the end surface half impeller profile and the pitch circle is a middle point on a pitch arc between the top node 7 and the valley node 9 and is called a middle node, and the connecting line of the middle node 3 and the rotor center O is a middle axis O3 of the end surface half impeller profile as shown in FIG. 2;
any point 8 on the pitch arc between the top node 7 and the valley node 9 is called an instantaneous node, the normal distance from the instantaneous node 8 to the inner and outer conjugate profile sections 234 is an instantaneous diameter rho (omega), the instantaneous diameter rho (omega)/the pitch radius r is a dimensionless instantaneous diameter, the central angle omega of the pitch arc between the instantaneous node 8 and the valley node 9 is an instantaneous angle, and the conjugate shape coefficient epsilon of the inner and outer conjugate profile sections is an instantaneous angle0Is a dimensionless instantaneous path p (2 phi)/r +1 at the top node, phi pi/6, as shown in fig. 2;
the outer conjugate contour section 23 and the inner conjugate contour section 34 are respectively conjugated with the inner conjugate contour section 34 and the outer conjugate contour section 23 on the dual rotor, and the shape of the outer conjugate contour section 23 and the shape of the inner conjugate contour section 34 are defined by the dimensionless instantaneous diameter rho (omega)/r and the given conjugate shape coefficient epsilon0Unique determination;
the centers of the top arc segment 01 and the valley arc segment 56 are both the rotor center O and the central angle α are equal (called as a top seal angle), the radius of the top arc segment is equal to the rotor shape coefficient epsilon x the pitch circle radius r, the radius of the valley arc segment is equal to (2-epsilon) r, and the rotor shape coefficient epsilon is equal to the top arc segment radius/pitch circle radius r, as shown in fig. 2;
the outer avoidance profile section 12 and the inner avoidance profile section 45 are avoidance profile sections which just avoid the base point 4 and the peak 1 of the profile on the dual rotor respectively, the structure can realize the maximization of the shape coefficient of the rotor and the optimization of the lightweight effect of the pump, the base point 4 is the known endpoint 4 of the non-middle node on the inner conjugate profile section 34, and the peak 1 is the known endpoint 1 on the non-top shaft on the top arc section;
the overall shape and the tip seal angle alpha of the end face half-impeller profile structure are defined by a dimensionless instantaneous diameter rho (omega)/r and a given rotor shape coefficient epsilonThe conjugate relation and the avoidance relation between the outlines are uniquely determined; the dimensionless instant diameter ρ (Ω)/r defines the curve type defined by a given conjugate profile segment 23 or 34 and a given conjugate shape coefficient ε0And (4) uniquely determining. The overall size of the end face half-vane profile configuration is uniquely determined by a given pitch radius r;
the axial half impeller profile is along the width direction (axial direction) of the rotor and takes a twisted blade angle as xibAnd seven points of 0, 1, 2, 3, 4, 5, 6 and 7 on the profile of the end face half impeller are respectively 7 spiral lines of which the starting points are.
The method for acquiring the universal calculation model of the pump flow pulsation coefficient of the three-twisted-blade rotor is characterized by comprising the following steps of: the method comprises the following steps:
step one, accurate calculation method of dimensionless theoretical flow of twisted blade rotor
The theoretical flow of the three-twisted-blade rotor pump is equivalent to the infinite micro theoretical flow corresponding to the axial infinite equivalent micro-width straight blade rotor and is formed by axially overlapping along a spiral line. The surfaces of the starting point, any point and the end point on the spiral line are called the starting end surface, any section and the ending end surface of the twisted blade rotor respectively, as shown in fig. 3.
Let the micro-theoretical flow rate corresponding to the micro-width straight blade rotor at the initial end face be dQ0The corresponding dimensionless theoretical flow is q0As shown in fig. 4. At this time by
Figure BDA0002918425910000081
Obtaining the micro theoretical flow rate dQ corresponding to the micro-width straight blade rotor at any sectionzAnd its dimensionless theoretical flow qzIs composed of
Figure BDA0002918425910000082
As shown in fig. 4.
By dQzThe theoretical flow Q of the twisted blade rotor and the dimensionless theoretical flow Q thereof are obtained after the integration in the width direction along the axial superposition of the spiral lines
Figure BDA0002918425910000083
In the formulas (1) to (3), ω is the rotation angular velocity of the rotor, dz is the micro width, Ω is the instantaneous angle, ε is a given rotor shape coefficient, ρ is the instantaneous diameter, r is the pitch circle radius, ρ/r is a given dimensionless instantaneous diameter, and φ ═ π/6; xi is the stagger angle of any section relative to the apical axis of the initial end face, called twist angle, xibThe tip end face is offset from the tip axis of the start end face by an angle, referred to as the twisted blade angle.
Step two, fitting calculation method of dimensionless theoretical flow of twisted blade rotor
The calculation of q in formula (3) involves q in formula (1)0If q is integral0For easy integration function, the precise integration method can be directly adopted, otherwise, q is adopted0The method of fitting first and integrating later (called as fitting integration method) is easy to calculate and is universal, and the fitting integration method is uniformly adopted in the invention.
From the constructive geometrical relationship of the outer and inner conjugate contour segments, q is known0(Ω) is symmetrical about Ω ═ Φ, then q is given0(omega) is fitted with the formula
Figure BDA0002918425910000091
In the formula, given the definition of ρ (Ω)/r, the fitting coefficient A, B, C is expressed by formula (1) corresponding to 5 groups q under ρ (0)/r, ρ (0.5 φ)/r, ρ (1.5 φ)/r, ρ (2 φ)/r0Data, uniquely determined by means of a method of fitting trend lines in EXCEL tables;
substituting the formula (4) into the formula (3) to obtain the dimensionless theoretical flow q (omega, xi) of the twisted blade rotorb) Is fitted to
Figure BDA0002918425910000092
Step three, general calculation method of twisted blade rotor flow pulsation coefficient
The first derivative of formula (5) to Ω is equal to 0, resulting in q (Ω, ξ)b) In omega 0.5 xib、Ω＝φ+0.5ξbThe minimum value min (q) and the maximum value max (q) are obtained respectively, and the formula (5) shows
Figure BDA0002918425910000093
The dimensionless theoretical flow wave height corresponding to q is
Figure BDA0002918425910000094
From the formula (7) to xibIs equal to 0, to get Δ q (ξ)b) In xibWhen 2 phi is pi/3, a minimum value of 0 is obtained, in which case q (omega, 2 phi) is a constant value, and xi is setbSubstitution of formula (5) 2 phi pi/3 to obtain
Figure BDA0002918425910000105
The method is characterized in that the rotor is twisted or not to influence the infinite dimensionless theoretical flow q in the axial directionzThe mean value of (omega, xi) respectively, i.e. not following xibSo q (Ω, ξ) changesb) Q is an average value of0Average value of (Ω) ═ qzThe average value of (Ω, ξ) is a constant value of q (Ω,2 Φ). Then, the flow pulsation coefficient of the twisted blade rotor is defined as the theoretical flow wave height/the theoretical flow mean value
Figure BDA0002918425910000101
In the formula, xibWhen 2 phi is pi/3, the flow pulsation coefficient delta (2 phi) of the twisted blade rotor is 0, namely no flow pulsation; xibWhen the flow rate is equal to 0, the flow rate pulsation coefficient δ (0) of the twisted blade rotor is the flow rate pulsation coefficient of the straight blade rotor, and
Figure BDA0002918425910000102
step four, embodiment of twisted blade rotor flow pulsation coefficient calculation
Example of an embodiment of the conjugated contour section 23 is, for example, a curve of the type using circular arcs and e ═ e-01.47, at this time
Figure BDA0002918425910000103
The formula (1) and the formula (11) correspond to 5 groups q under the condition that omega is 0, 0.5 phi, 1.5 phi and 2 phi0(omega) data obtained by means of the method of "insert → graph → dot plot → increase of trend line" in the EXECL table
Figure BDA0002918425910000104
Then a-0.8098, B-1.0371, C-0.4721.
Q obtained by the formula (1)0Exact curves and q from formula (b)0(Ω) fitting the curve, as shown in fig. 5, wherein the fitting accuracy is very high.
ξbDimensionless theoretical flow q (omega, xi) of circular arc twisted blade rotor under 0, 0.5 phi, 1.5 phi and 2 phib) As shown in fig. 6. Although q is0The (omega) has a serious nonlinear relation with the change of omega, but the twisted blade rotor flow pulsation coefficient delta (xi) obtained by the formula (9)b) But has an approximately negative linear change law as shown in fig. 7.
Step five, simplified calculation method of twisted blade rotor flow pulsation coefficient
By trial and error under different definitions of rho (omega)/r, the example epsilon is epsilon0When the flow pulsation coefficient of the involute twisted blade rotor is 1.47, the corresponding a is 0, B is-0.8057 and C is 1.1609 as shown in fig. 8; epsilon0The flow pulsation coefficient of the trochoidal twisted blade rotor with 1.5 and 1.6 lower epsilon is shown in fig. 9, and when corresponding a is 0.3155, B is 0.9983 and C is 1.6, the flow pulsation coefficient delta (xi) of the twisted blade rotor is obtainedb) Along with twisting blade angle xibHas approximate negative linear relation, the flow pulsation coefficient delta (xi) of the twisted blade rotorb) Can be simplified into
Figure BDA0002918425910000111
While there have been shown and described what are at present considered the fundamental principles and essential features of the invention and its advantages, it will be apparent to those skilled in the art that the invention is not limited to the details of the foregoing exemplary embodiments, but is capable of other specific forms without departing from the spirit or essential characteristics thereof. The present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein.

Claims (3)

1. A general calculation model of three torsion vane rotor pump flow pulsation coefficients is characterized in that:
Figure FDA0002918425900000011
。
2. the universal calculation model for pump flow pulsation coefficient of three-twisted-blade rotor as claimed in claim 1, wherein: twisted blade rotor flow pulsation coefficient delta ([ xi ])b) The calculation of (a) can be simplified as:
Figure FDA0002918425900000012
。
3. a method for obtaining a universal calculation model of a three-twisted-blade rotor pump flow pulsation coefficient is characterized by comprising the following steps: the method comprises the following steps:
s1, an accurate calculation method of the dimensionless theoretical flow of the three-twisted-blade rotor comprises the following steps:
the method comprises the following steps that (1) according to the theoretical flow of a three-twisted-blade rotor pump, the equivalent infinite micro theoretical flow corresponding to an axially infinite equivalent micro-width straight-blade rotor is formed by axially overlapping spiral lines, and the surfaces of a starting point, any point and an end point on each spiral line are defined as a starting end surface, an arbitrary section and a terminating end surface of the three-twisted-blade rotor respectively; defining the micro theoretical flow rate corresponding to the micro-width straight blade rotor at the initial end face as dQ0The corresponding dimensionless theoretical flow is q0At this time, the product is made by
Figure FDA0002918425900000013
Obtaining the micro theoretical flow rate dQ corresponding to the micro-width straight blade rotor at any sectionzAnd its dimensionless theoretical flow qzComprises the following steps:
Figure FDA0002918425900000014
by dQzAnd the theoretical flow Q of the three-twisted-blade rotor and the dimensionless theoretical flow Q thereof are obtained by axial superposition of the spiral lines, namely integration in the width direction:
Figure FDA0002918425900000015
wherein, in the formula (1), the formula (2) and the formula (3), ω is the rotation angular velocity of the rotor, dz is the micro width, Ω is the instantaneous angle, ε is a given rotor shape coefficient, ρ is the instantaneous diameter, r is the pitch circle radius, ρ/r is a given dimensionless instantaneous diameter, and φ ═ π/6; xi is the stagger angle of any section relative to the top axis of the initial end face and is defined as a torsion anglebThe tip axis offset angle of the termination end face relative to the start end face is defined as a twisted blade angle;
s2, a fitting calculation method of the three-blade twisted rotor dimensionless theoretical flow is as follows:
from outer conjugate profile section and inner conjugate wheelConstructive geometry of the profile, knowing q0(Ω) is symmetrical about Ω ═ Φ, then q is given0(omega) is fitted with the formula
Figure FDA0002918425900000021
In the formula, given the definition of ρ (Ω)/r, the fitting coefficient A, B, C is expressed by formula (1) corresponding to 5 groups q under ρ (0)/r, ρ (0.5 φ)/r, ρ (1.5 φ)/r, ρ (2 φ)/r0Data, uniquely determined by means of a method of fitting trend lines in EXCEL tables;
substituting the formula (4) into the formula (3) to obtain the dimensionless theoretical flow q (omega, xi) of the twisted blade rotorb) The piecewise fitting of (a) is:
Figure FDA0002918425900000022
s3, a general calculation method of flow pulsation coefficients of a three-twisted-blade rotor comprises the following steps:
the first derivative of formula (5) to Ω is equal to 0, resulting in q (Ω, ξ)b) In omega 0.5 xib、Ω＝φ+0.5ξbThe minimum value min (q) and the maximum value max (q) are obtained respectively, and the formula (5) shows
Figure FDA0002918425900000023
The dimensionless theoretical flow wave height corresponding to q is
Figure FDA0002918425900000024
From the formula (7) to xibIs equal to 0, to get Δ q (ξ)b) In xibWhen 2 phi is pi/3, a minimum value of 0 is obtained, in which case q (omega, 2 phi) is a constant value, and xi is setbSubstitution of formula (5) 2 phi pi/3 to obtain
Figure FDA0002918425900000031
The method is characterized in that the rotor is twisted or not to influence the infinite dimensionless theoretical flow q in the axial directionzThe mean value of (omega, xi) respectively, i.e. not following xibSo q (Ω, ξ) changesb) Q is an average value of0Average value of (Ω) ═ qzThe mean value of (Ω, ξ) is a constant value of q (Ω,2 Φ); then, the flow pulsation coefficient of the twisted blade rotor is defined as the theoretical flow wave height/the theoretical flow mean value
Figure FDA0002918425900000032
In the formula, xibWhen 2 phi is pi/3, the flow pulsation coefficient delta (2 phi) of the twisted blade rotor is 0, namely no flow pulsation; xibWhen the flow rate is equal to 0, the flow rate pulsation coefficient δ (0) of the twisted blade rotor is the flow rate pulsation coefficient of the straight blade rotor, and
Figure FDA0002918425900000033
s4, a simplified calculation method of twisted blade rotor flow pulsation coefficient:
through repeated trial calculation under different definitions of rho (omega)/r, the flow pulsation coefficient delta (xi) of the twisted blade rotorb) Along with twisting blade angle xibHas approximate negative linear relation, the flow pulsation coefficient delta (xi) of the twisted blade rotorb) Can be simplified into
Figure FDA0002918425900000034
。
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