CN115788908B - Bidirectional axial flow pump blade space coordinate design and construction method thereof - Google Patents
Bidirectional axial flow pump blade space coordinate design and construction method thereof Download PDFInfo
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Abstract
The invention discloses a bidirectional axial flow pump blade space coordinate design and a construction method thereof in the technical field of hydraulic engineering bidirectional axial flow pumps, wherein the bidirectional axial flow pump blade space coordinate design method comprises the following steps: the design of a bidirectional pump impeller; designing a plane two-dimensional airfoil and generating two-dimensional coordinates; generating three-dimensional rectangular coordinates of the bidirectional pump blade; the method for constructing the bidirectional axial flow pump blade comprises the following steps: generating space point coordinates; an airfoil space curved surface configuration; and (6) generating three-dimensional blades of the impeller. The invention can improve the energy performance and cavitation performance of the water pump, improve the efficiency, reduce the social resources such as manpower and material resources and the like and achieve the same drainage target.
Description
Technical Field
The invention belongs to the technical field of bidirectional axial flow pumps of hydraulic engineering, and particularly relates to a novel method for designing the space coordinates of bidirectional axial flow pump blades and a method for forming the bidirectional axial flow pump blades through space coordinate points.
Background
In the prior art, the bidirectional axial flow pump is reformed according to the horizontal axial flow pump, and aims to realize irrigation and drainage for bidirectional operation, and is mainly applied to coastal pump stations, farmland irrigation and tide experiments. The pump station is required to draw water and drain water at the same time, so that the reverse water pumping function is realized. The traditional pump station adopts a unidirectional axial flow pump to carry out reverse pumping, and the impeller wing profile is in an inverted arch state. A large number of experiments show that cavitation resistance of the impeller is related to a lift coefficient, and when the airfoil is in an inverted arch state, the pressure difference between the working surface and the back surface of the airfoil is large. The surface of the blade can generate serious flow removal, so that cavitation erosion and noise are generated on the blade, the energy performance and cavitation erosion performance of a pump unit of a pump station are seriously influenced, irreversible abrasion is also generated on the blade, and the safety of the pump station is endangered.
In order to meet the requirements of forward operation and reverse operation of a pump station, a bidirectional axial flow pump blade is required to be adopted for operation, and the novel space coordinate position method for constructing the blade is provided aiming at the bidirectional axial flow pump blade.
Disclosure of Invention
The invention aims to solve the problems of flow separation, cavitation erosion and the like of the blades of the traditional pump station during reverse rotation, and ensure the energy performance and cavitation erosion performance of the pump station unit during reverse operation. The main core of the invention is to provide a simpler three-dimensional coordinate method of the bidirectional pump vane.
One of the objects of the present invention is achieved by: a bidirectional axial flow pump blade space coordinate design method comprises the following steps:
step 1, designing a bidirectional pump impeller;
step 2, designing a plane two-dimensional airfoil and generating two-dimensional coordinates;
and 3, generating three-dimensional rectangular coordinates of the bidirectional pump blade.
As a further improvement of the present invention, the step 1 includes the steps of:
(1) Twisting the blade design; (2) a section airfoil profile change law; (3) correction of inlet attack angle; and (4) designing impeller parameters.
As a further improvement of the present invention, the step (1) of twisting the blade is designed to:
when the bidirectional pump impeller is designed, the model impeller is used as a basis, the diameter of the model impeller is 300mm, and the diameter of the hub and the diameter of the rim are determined according to the value of the hub ratio; after the hub diameter and the rim diameter are determined, 8 sections are linearly inserted in the middle, so that the impeller is divided into 10 sections for design;
the variable loop volume design is adopted:
V u (i)*(r(i) α +r(i) -α ) Constant =constant
Vu (i) is the component of the absolute velocity of the water flow of the ith section in the circumferential direction, and r (i) is the radius of the ith cylindrical section; alpha is a constant, the size of which takes a value between-1 and 1;
the change rule of the section airfoil profile in the step (2) is as follows:
dividing the impeller into 10 design sections from the hub to the rim, taking 0.3-0.5 l from the hub to the rim at the maximum camber position of the 10 section wing sections, taking 0.5l from the rim, taking 0.3l from the hub, and linearly changing the intermediate parameters;
the inlet attack angle correction in the step (3) is as follows:
when the bidirectional pump impeller is designed, the inlet attack angle delta alpha of the bidirectional pump impeller takes 0-4 degrees from the hub to the rim, the inlet attack angle of the middle section takes the change rule of a hyperbola, and the absolute value of the difference between the distances from the plane to two fixed points is a track with a fixed value;
the basic formula of the hyperbola is:
b 2 ＝2；
the impeller parameters in the step (4) are designed as follows:
the bi-directional pump impeller parameter design includes 4 design parameters, namely: the density of each section blade grid is l/t, wherein l represents the chord length, t represents the blade grid distance, the placement angle beta of each section airfoil, the camber F of each section and the thickness d of each section.
As a further improvement of the present invention, the α=1/2.
As a further improvement of the present invention, the step 2 includes the steps of:
(1) Wing section camber line design and coordinate expression; (2) airfoil coordinates.
As a further improvement of the present invention, the airfoil camber line design and coordinates of the step (1) are expressed as:
the two-way pump camber line wing profile adopts a bilateral symmetry wing profile, the unilateral camber line adopts a quadratic function curve derived based on a circular arc curve and a Ru-Kovus base curve, and a curve equation is as follows:
x 2 +Ay 2 +Bx+Cy＝0
wherein A, B, C is a constant, and the design of the impeller of the bidirectional pump is that timeB＝2，C＝1；
Airfoil camber line coordinates: the abscissa of the airfoil camber line is denoted x (ss); the ordinate yc= [ yc1, yc2] of the airfoil camber line, wherein yc1 (ss) represents the ordinate value of the ss-th point on the left side of the camber line, yc1 represents the array of the ordinate of the ss-th point on the left side of the camber line, yc2 (ss) represents the ordinate value of the ss-th point on the right side of the camber line, yc2 represents the array of the ordinate of the ss-th point on the right side of the camber line, yc represents the array of the ordinate of all points of the whole camber line; represented by different ycs according to different positions; determining the coordinate of the ss-th point of the airfoil camber line as (x (ss), yc (ss)) according to the ordinate yc (ss) and the abscissa x (ss) of the airfoil camber line;
the coordinate arrangement expression of the camber line is as follows:
when x (ss) is less than or equal to g, the ordinate of the camber line is solved by adopting the following formula:
yc1(ss)＝F(i)/g^2*(2*g*(x(ss)/l(i)-(x(ss)/l(i))^2)
the ordinate of the camber line is solved using the following formula when x (ss) > g:
yc2(ss)＝F(i)/(1-g)^2*((1-2*g)+2*g*(x(ss)/l(i)-(x(ss)/l(i))^2)
wherein x (ss) is the abscissa value of the ss point on the wing section, i represents the section number of the impeller from the hub to the rim; SS represents the number of discrete points taken on the airfoil curve; g represents the maximum camber position of the section airfoil, and the maximum camber position is 0.3 l-0.5 l from the hub to the rim;
the wing profile coordinates of the step (2) are:
coordinates of each point of the airfoil curve: the variation relationship between airfoil thickness and chord length is as follows:
d (i) represents the maximum thickness of the ith airfoil section, l (i) is the airfoil length of the ith section, m, n are indices, and the relationship is m+n=2; yt (ss) represents the thickness calculation result required to be increased or decreased on the camber basis for that point with the abscissa x (ss), and yt represents the thickness calculation array required to be increased or decreased for all points;
according to the change rule of the airfoil thickness curve and the coordinate of the airfoil camber line, the upper airfoil ordinate of the two-way pump airfoil is obtained as follows: yr1=yc-yt; the ordinate of the lower wing of the two-way pump wing is yr2=yc+yt; obtaining airfoil curve coordinates (x (ss), yr (ss)); wherein yr1 (ss) represents the ordinate value of the ss point of the upper wing, yr1 represents the array of the ordinate of the ss point of the upper wing, yr2 (ss) represents the ordinate value of the ss point of the lower wing, and yr2 represents the array of the ordinate of the ss point of the lower wing;
the two-dimensional coordinates of the airfoil profile obtained above are coordinates obtained by taking the chord length as the horizontal position, and when the bidirectional pump airfoil profile is designed, the chord length is converted into the position with the setting angle, and after the chord length is converted into the setting angle, the conversion formula of the coordinates of the corresponding points is as follows:
upper airfoil abscissa conversion formula:
Xr1(ss)＝x(ss)*cosd(β(i))-yr1(ss)*sind(β(i))
upper airfoil ordinate conversion formula:
Yr1(ss)＝x(ss)*sind(β(i))+yr1(ss)*cosd(β(i))
the lower airfoil abscissa conversion formula:
Xr2(ss)＝x(ss)*cosd(β(i))-yr2(ss)*sind(β(i))
the lower airfoil ordinate conversion formula:
Yr2(ss)＝x(ss)*sind(β(i))+yr2(ss)*cosd(β(i))
obtaining two-dimensional airfoil coordinates (Xr (ss), yr (ss)) of the airfoil with the ith section after rotating by an angle beta (i) through the conversion of the formula;
the plane coordinates of the two-dimensional wing profile of the bi-directional pump are obtained, the plane wing profile coordinates are converted into cylindrical wing profile coordinates, and the arc coordinates theta of each coordinate point of the section where the plane wing profile is located are obtained through formula calculation;
upper airfoil arc coordinates θ1=xr1/(r (i))/pi (). 180;
the lower airfoil arc coordinate θ2=xr2/(r (i))/pi (). 180;
wherein r (i) is the radial radius of the coordinate point from the impeller origin O, namely the radius of the ith section, pi () is the expression of a constant pi;
and obtaining the arc coordinates (theta, yr) of the two-dimensional airfoil.
As a further improvement of the invention, the three-dimensional rectangular coordinates of the bidirectional pump blade in the step 3 are generated as follows:
according to the two-dimensional arc coordinates (theta, yr) of each section of the airfoil, obtaining the three-dimensional rectangular coordinates of each section of the bi-directional pump blade through formula transformation; the transformation formula is as follows:
X(ss)＝r(i)*sindθ(ss)；
Y(ss)＝r(i)*cosdθ(ss)；
Z(ss)＝Yr(ss)；
and obtaining three-dimensional coordinates (X, Y, Z) on any airfoil section of the bi-directional pump blade according to the formula.
The invention also aims to provide a method for constructing the bidirectional axial flow pump blade.
The purpose of the invention is realized in the following way: a method of constructing a bi-directional axial flow pump blade, comprising the steps of:
step a, generating space point coordinates;
step b, constructing an airfoil space curved surface;
and c, generating three-dimensional blades of the impeller.
As a further improvement of the invention, the space point coordinates of the step a are three-dimensional rectangular coordinates of the bidirectional pump blade;
the wing section space curved surface structure in the step b is as follows:
the design of the wing profile is carried out by selecting 10 different design sections from the hub to the rim according to linear variation,
generating space point coordinates, namely selecting 20-30 points from an upper airfoil and a lower airfoil on any design section to generate points, conducting round guiding treatment on 2% of the positions close to the top end of the airfoil aiming at the chord length l of different airfoil sections, taking one point every 5% of the positions close to the front end 20% of the airfoil, and taking one point every 10% of the positions in 20% -50% of the middle section of the airfoil, namely 20-30 points can be obtained on one airfoil section; then generating space points on the rest airfoil sections according to the steps, and finally generating an airfoil profile by carrying out fitting curve through sweeping of the datum points;
the three-dimensional impeller blade in the step c is generated as follows:
and (3) carrying out impeller curved surface construction in three-dimensional modeling software, wherein points on 10 working surfaces are connected in one-to-one correspondence along the axial direction to generate curves, the smooth curved surfaces constructed by the curves are the working surfaces, and meanwhile, the obtained points on 10 different airfoil section are connected in the radial direction, namely, the generation of the blade width in the popular sense is carried out, so that the bidirectional axial flow pump blade construction is completed.
The method of the invention is mainly divided into two parts, wherein the first part is designed for the space coordinates of the blade, and mainly provides a method for generating the space point coordinates of the bidirectional pump blade. The method comprises three modules: the device comprises an impeller design module, a planar two-dimensional airfoil design and two-dimensional coordinate generation module and a two-way pump blade three-dimensional rectangular coordinate generation module. The second part is a method for constructing a bidirectional axial flow pump blade, and the second part comprises: and (3) generating space point coordinates, constructing an airfoil space curved surface, and generating the impeller three-dimensional blade.
The blades generated by the method are uniformly and symmetrically welded around the hub on the same horizontal line. The wing profiles at different positions of the blade are in inverted V-shaped central symmetry, and the thickness of the wing profile at the middle position is in function change favorable for energy performance and cavitation performance.
In the blade space coordinate design method, the bidirectional impeller is mainly designed by: 1. the design of the twisted blade 2, the change rule of the section airfoil 3, the correction of the inlet attack angle 4 and the design of impeller parameters, and the basic shape of the two-dimensional airfoil is determined. And then carrying out planar two-dimensional airfoil design and two-dimensional coordinate generation, wherein the method mainly comprises the following steps: 1. the airfoil camber line design and coordinate expression 2, airfoil coordinates and transformation thereof generate a two-dimensional airfoil arc coordinate expression form. And finally, generating the bidirectional pump impeller blade by a bidirectional pump blade three-dimensional rectangular coordinate generation method.
The method for constructing the impeller blade of the bidirectional axial flow pump comprises the steps of generating a curved surface by an axial curve, generating a curved surface by a radial curve and generating an integral blade. The method comprises the following steps:
1. and connecting the points on the working surface in a one-to-one correspondence manner along the axial direction to generate curves, wherein the smooth curved surface constructed by the curves is the working surface.
2. The radial direction of points on different airfoil sections is connected, namely the generation of the blade width in a popular sense.
Compared with the prior art, the invention has the beneficial effects that: the novel axial flow pump vane space coordinate design and the construction method thereof are provided, the design and construction method is novel and unique, the principle is simple, the designed impeller meets the operation requirement, and the front edge of the impeller vane is reduced in the process of reverse operation. Along with the requirements of river-crossing water-transferring engineering, pump station updating and reconstruction and urban infrastructure in recent years, especially urban infrastructure, urban water supply and urban drainage become necessary, the novel design and construction method provided by the invention can improve the energy performance and cavitation performance of the water pump, improve the efficiency, and reduce the social resources such as manpower and material resources and the like to achieve the same drainage target.
Drawings
FIG. 1 is a flow chart of a two-way axial flow pump vane space coordinate design.
FIG. 2 is a schematic cross-sectional view of a double circular arc symmetrical airfoil.
Fig. 3 is a planar infinite cascade diagram.
Fig. 4 is a graph of airfoil coordinate points.
FIG. 5 is an airfoil of a different design section.
FIG. 6 is a graph of spatial coordinate points and line locations of airfoil sections of different sections.
FIG. 7 is a schematic diagram of a bi-directional pump vane.
Detailed Description
Example 1
The following describes the space coordinate design method of the bidirectional axial flow pump vane according to the present embodiment in detail with reference to fig. 1-7.
FIG. 1 is a flow chart of the present invention, briefly summarizing the flow of designing the spatial bidirectional axial flow pump blade. In fig. 2, l is the airfoil chord length of the bidirectional axial flow pump blade, F is the airfoil camber, d is the thickness value of each section, and different circle centers are smoothly connected by using a bezier curve to form a curve, which is named as an airfoil bone line. Fig. 3 shows a plurality of airfoils, collectively called a cascade, having identical cross-sections and obtained by cutting an impeller of an axial flow pump by means of a cylindrical surface. Fig. 4 is a graph of airfoil coordinate points. Fig. 5 is a cross-sectional view of a hypothetical construction at 10 different radial locations. FIG. 6 is a graph of spatial coordinate points and airfoil shaped lines generated by sweeping a reference point that exhibits a dense at both ends and sparse at the middle. Fig. 7 is a schematic view of the impeller after completion of the construction of the wheelspace curve.
The method for designing the space coordinates of the bidirectional axial flow pump blade in the embodiment comprises the following steps:
step 1, designing a bidirectional pump impeller:
(1) Twisted blade design:
the bidirectional pump impeller is designed based on a model impeller with the diameter of 300mm, and the diameter of the hub and the diameter of the rim are determined according to the value of the hub ratio. After the hub diameter and the rim diameter are determined, 8 sections are linearly inserted in the middle, so that the impeller is divided into 10 sections for design;
the component speed of the absolute speed of the bidirectional axial flow pump in the circumferential direction is an important speed parameter for designing a space twisted blade, and the cavitation performance and the energy performance of the bidirectional axial flow pump are considered, and based on forced vortex and free vortex flow patterns, the variable-annular-quantity design method is adopted:
V u (i)*(r(i) α +r(i) -α ) =constant; this formula means that the numerical products of the different sections are equal,i.e. constant; the constant is inconsistent when different impeller designs are performed, and the constant takes a value of 6 when the invention is implemented;
vu (i) is the component of the absolute velocity of the water flow of the ith section in the circumferential direction, and r (i) is the radius of the ith cylindrical section; alpha is a constant, the size of the constant can take a value between-1 and 1, and when alpha takes 1, the constant-circulation flow type, namely free vortex flow is adopted; when alpha takes-1, it is a forced vortex flow pattern. Both have advantages and disadvantages, the cavitation performance and the energy performance of the water pump impeller are considered, the twisting shape of the water pump impeller is improved by adopting a relative variable-loop design method, meanwhile, the hydraulic efficiency of the impeller is improved as much as possible, and a more excellent design effect meeting the design requirement can be obtained when alpha=1/2;
(2) Profile airfoil profile variation law:
the traditional axial flow pump design divides the impeller into a plurality of sections from the hub to the rim, and then designs design parameters of different sections, and then selects or loads the same airfoil according to the design parameters of the impeller. All the different sections of the axial flow pump impeller design are loaded with the same airfoil data. The bidirectional pump impeller is a special symmetrical impeller, so that cavitation performance and water pump efficiency are both considered. Based on earlier research, the maximum camber position of the airfoil is known to have a great influence on cavitation performance and efficiency of the water pump. The maximum camber position can theoretically take any value of 0 to 1, but in the actual value process, the value is generally 0.3 to 0.6, and the smaller the value is, the higher the efficiency of the water pump is; the larger the value, the better the cavitation performance of the water pump. The maximum camber position of the wing section of different sections of the same axial flow pump impeller is a certain fixed value. The design of the bidirectional pump impeller adopts a method of changing the position of the maximum camber to consider both the efficiency and cavitation performance of the water pump, namely, when the bidirectional pump is designed, the impeller is divided into 10 design sections from a hub to a rim, 0.3-0.5 l of the maximum camber position of the 10 section wing profile is taken from the hub to the rim, and 0.5l of the rim is taken in consideration of the clearance vortex cavitation of the tip of the water pump; in order to give consideration to the shape of the blade and improve the efficiency of the water pump, 0.3l of the hub is taken, and the middle parameters are changed linearly;
(3) Correction of inlet attack angle:
conventional axial flow pump designs are considered to be 0, or a constant angle of attack (e.g., Δα=0.5) is added during the design process. The three-dimensional diagram of the bidirectional pump is symmetrical and is influenced by the wing profile, the symmetrical wing profile or the flat wing profile is generally adopted, and the inlet attack angle is not suitable for 0 or equal attack angle. Through the preliminary study of the invention, when the bidirectional pump impeller is designed, the inlet attack angle delta alpha of the bidirectional pump impeller should be 0-4 degrees from the hub to the rim, the inlet attack angle of the middle section takes the change rule of a hyperbola, and the absolute value of the difference between the distances from the plane to two fixed points is a track with a fixed value.
The basic formula of the hyperbola is:
in the practice of the present invention,b 2 =2. The hub is 0 degree, the rim is 4 degrees, and the attack angle of the middle section shows hyperbolic rule change according to the distance between the hub and the rim, so that the blade placing angle of the rim can be increased, and the distortion degree of the bidirectional pump impeller is improved;
(4) Impeller parameter design:
the bi-directional pump impeller parameter design includes 4 design parameters, namely: the density of each section blade cascade (l/t), where l represents the chord length, t represents the cascade distance, the airfoil setting angle (β) for each section, the camber (F) for each section and the thickness value (d) for each section.
The cascade density is one of the parameters that has a great influence on the performance of the bidirectional axial flow pump blade, and the airfoil performance of each cylindrical surface depends on whether the selection of l/t is proper or not. Too large l/t, increased friction coefficient, necessarily reduced hydraulic efficiency; too small a l/t, the impeller's power capability decreases and the thickness ratio increases, which requires an increase in airfoil camber or setting angle, so the choice of l/t is very important.
On the premise of considering efficiency and cavitation performance, the l/t value at the rim can be selected according to the table 1, and the l/t value at the hub can be selected according to the following: (l/t) h ＝(1.3～1.5)(l/t) t
Wherein (l/t) h Represents the density of the blade grid at the hub (l/t) t Representing the cascade density l/t taken at the rim. For the density l/t of the blade cascade of each airfoil section in the middle, each section from the hub to the rim changes along with the distance from the hub to the rim according to a linear rule, so that the lift coefficient is ensured to be in an optimal range.
TABLE 1
The airfoil setting angle beta of each section blade can be as follows:
where u=pi nD/60, n is the axial pump speed, D is the impeller diameter, v u2 For radial velocity component of airfoil section exit velocity, v m The axial component speed of the airfoil section outlet speed can be determined by an outlet speed triangle. w (w) m The geometrical average value of the relative flow velocity of the liquid at the inlet of the blade grid and the relative flow velocity of the outlet of the blade grid is calculated according to the formula. Thus, the relative flow angle beta of each airfoil section can be calculated 1 The relative flow angle plus a certain attack angle delta alpha is the placement angle beta of the airfoil, namely: beta=beta 1 +Δα。
The maximum thickness of the blade at the hub is as follows:
wherein D is the diameter of the impeller, H is the lift, and k is the material coefficient.
The relative thickness of the blades at the hub is usually d/l=0.09-0.12, the thickness of the blades at the rim is determined by the process conditions, and the thickness of the blades at the rim should be as thin as possible, and the relative thickness is usually d/l=0.02-0.05. The thickness of the inner wing shape of each section from the hub to the rim changes according to a linear rule along with the distance from the hub to the rim. The schematic cross-section of the double-arc symmetrical wing profile is shown in figures 2 and 3;
step 2, plane two-dimensional airfoil design and two-dimensional coordinate generation:
(1) Airfoil camber line design and coordinate expression:
the two-way pump camber line airfoil profile adopts a bilateral symmetry airfoil profile, the single-side camber line gives consideration to cavitation performance and energy performance, a quadratic function curve is strictly derived based on a circular arc curve and a Ru-Koff-base curve, and a curve equation is as follows:
x 2 +Ay 2 +Bx+Cy＝0
the design curve equation of the axial flow pump for the bidirectional pump is as above, wherein A, B, C is a constant, and the impeller of the bidirectional pump is designedB＝2，C＝1。
Airfoil camber line coordinates: the abscissa of the airfoil camber line is denoted x (ss); the ordinate yc= [ yc1, yc2] of the airfoil camber line, wherein yc1 (ss) represents the ordinate value of the ss point on the left side of the camber line, yc1 represents the ordinate array of the ss point on the left side of the camber line, yc2 (ss) represents the ordinate value of the ss point on the right side of the camber line, yc2 represents the ordinate array of the ss point on the right side of the camber line, yc represents the ordinate array of all points of the whole camber line (including left and right sides). Fig. 4 is seen in detail with different yc representations in different positions; the coordinates of the ss-th point of the camber line of the airfoil can be determined as (x (ss), yc (ss)) according to the ordinate yc (ss) and the abscissa x (ss) of the camber line of the airfoil.
The coordinate arrangement expression of the camber line is as follows:
when x (ss) is less than or equal to g, the ordinate of the camber line is solved by adopting the following formula:
yc1(ss)＝F(i)/g^2*(2*g*(x(ss)/l(i)-(x(ss)/l(i))^2)
the ordinate of the camber line is solved using the following formula when x (ss) > g:
yc2(ss)＝F(i)/(1-g)^2*((1-2*g)+2*g*(x(ss)/l(i)-(x(ss)/l(i))^2)
wherein x (ss) is the abscissa value of the ss point on the wing section, i represents the section number of the impeller from the hub to the rim; SS represents the number of discrete points taken on the airfoil curve; g represents the maximum camber position of the section airfoil, and the maximum camber position is 0.3 l-0.5 l from the hub to the rim.
(2) Airfoil coordinates:
coordinates of each point of the airfoil curve: after the coordinates of the camber line of the airfoil are obtained, a certain airfoil thickness can be added or subtracted on the basis of the ordinate of the camber line, and the coordinates of an upper curve and a lower curve of the airfoil can be obtained. However, since the thickness of the airfoil is variable, the thickness variation trend of the airfoil is first determined. The variation relationship between airfoil thickness and chord length (abscissa) of the present invention is as follows:
d (i) represents the maximum thickness of the i-th airfoil section, l (i) is the airfoil length of the i-th section, m, n are indices, and the relationship is m+n=2. yt (ss) represents the thickness calculation result required to be increased or decreased on the camber basis for that point with the abscissa x (ss), and yt represents the thickness calculation array required to be increased or decreased for all points.
According to the change rule of the airfoil thickness curve and the coordinate of the airfoil camber line, the upper airfoil ordinate of the two-way pump airfoil (figure 4) is obtained as follows: yr1=yc-yt; the lower airfoil ordinate of the two-way pump airfoil (fig. 4) is yr2=yc+yt. Further, airfoil curve coordinates (x (ss), yr (ss)) were obtained. Wherein yr1 (ss) represents the ordinate value of the ss point of the upper wing, yr1 represents the array of the ordinate of the ss point of the upper wing, yr2 (ss) represents the ordinate value of the ss point of the lower wing, and yr2 represents the array of the ordinate of the ss point of the lower wing.
The two-dimensional coordinates of the airfoil curve obtained above are coordinates obtained by taking the chord length as a horizontal position, and when the bidirectional pump airfoil is designed, the chord length is also required to be converted into a position with a certain setting angle by converting the horizontal position into a conversion formula of coordinates of corresponding points after the horizontal position is converted into a certain setting angle:
upper airfoil abscissa conversion formula:
Xr1(ss)＝x(ss)*cosd(β(i))-yr1(ss)*sind(β(i))
upper airfoil ordinate conversion formula:
Yr1(ss)＝x(ss)*sind(β(i))+yr1(ss)*cosd(β(i))
the lower airfoil abscissa conversion formula:
Xr2(ss)＝x(ss)*cosd(β(i))-yr2(ss)*sind(β(i))
the lower airfoil ordinate conversion formula:
Yr2(ss)＝x(ss)*sind(β(i))+yr2(ss)*cosd(β(i))
through the conversion of the formula, the two-dimensional airfoil coordinates (Xr (ss), yr (ss)) of the ith section airfoil after the rotation of beta (i) angle can be obtained, and the two-dimensional airfoil coordinate point schematic diagram is shown in figure 4.
The plane coordinates of the two-dimensional airfoil of the bi-directional pump are obtained through the steps, and the plane airfoil coordinates are converted into cylindrical airfoil coordinates. Firstly, calculating the arc coordinate theta of each coordinate point of the section by a formula.
Upper airfoil arc coordinates θ1=xr1/(r (i))/pi (). 180;
the lower airfoil arc coordinate θ2=xr2/(r (i))/pi (). 180;
where r (i) is the radial radius of the coordinate point from the impeller origin O, i.e., the radius of the ith section, pi () is the expression of a constant pi.
Thus, the arc coordinates (θ, yr) of the two-dimensional airfoil can be obtained.
Step 3, generating three-dimensional rectangular coordinates of the bidirectional pump blade:
and according to the two-dimensional arc coordinates (theta, yr) of each section of the airfoil, obtaining the three-dimensional rectangular coordinates of each section of the bi-directional pump blade through formula transformation. The transformation formula is as follows:
X(ss)＝r(i)*sindθ(ss)；
Y(ss)＝r(i)*cosdθ(ss)；
Z(ss)＝Yr(ss)；
thus, according to the formula, the three-dimensional coordinates (X, Y, Z) on any airfoil section of the bi-directional pump blade can be obtained.
Example 2
The method for constructing the bidirectional axial flow pump blade of the embodiment comprises the following steps:
step a, generating space point coordinates;
step b, constructing an airfoil space curved surface;
and c, generating three-dimensional blades of the impeller.
The generation of the space point coordinates in the step a is the three-dimensional rectangular coordinates of the bi-directional pump blade generated in the step 3 in the embodiment 1.
The wing-shaped space curved surface structure of the step b is as follows:
the design sections are divided from the hub to the rim by the wing-shaped space curved surface structure, in general, the more wing-shaped sections are obtained, the more accurate the blade design is, and 6-10 wing-shaped sections are generally considered according to engineering practice.
And selecting 20-30 points on the upper airfoil and the lower airfoil of a certain design section to generate points by a first part space point generation method. Considering that the impeller is not easy to flow off at the top of the blade when rotating, aiming at the chord length l of different airfoil sections, the position close to the top 2% of the airfoil is rounded, and at the same time, the position close to the front 20% of the airfoil adopts one point at each interval of 5%, and the middle section of the airfoil adopts one point at each interval of 10% of 20% -50%, so that 20-30 points can be obtained on one airfoil section. And similarly, generating space points on the rest airfoil sections according to the method, and finally generating an airfoil profile by fitting a curve through sweeping a datum point, wherein each airfoil section is shown in fig. 5 and 6.
The three-dimensional impeller blade in the step c is generated as follows:
according to the design, 10 working surfaces and non-working surfaces are obtained, and because the information of the working surfaces and the non-working surfaces is known, the position information of each airfoil section is also known, so that the impeller curved surface structure can be carried out in three-dimensional modeling software, wherein the three-dimensional modeling software is UG, the points on the 10 working surfaces are connected in a one-to-one correspondence manner along the axial direction in the UG to generate curves, and the smooth curved surface formed by the curves is the working surface. Meanwhile, the points on the 10 different airfoil sections obtained above are connected in the radial direction, namely, the generation of the blade width in the popular sense is carried out, so that the space coordinate design and the construction method of the bidirectional axial flow pump blade are completely completed, and the figure 7 is a schematic diagram of the bidirectional pump blade generated according to the steps of the invention.
Claims (3)
1. The method for designing the space coordinates of the bidirectional axial flow pump blade is characterized by comprising the following steps:
step 1, designing a bidirectional pump impeller;
the step 1 comprises the following steps:
(1) Twisting the blade design; (2) a section airfoil profile change law; (3) correction of inlet attack angle; (4) impeller parameter design;
the step (1) of twisting the blade is designed as follows:
when the bidirectional pump impeller is designed, the model impeller is used as a basis, the diameter of the model impeller is 300mm, and the diameter of the hub and the diameter of the rim are determined according to the value of the hub ratio; after the hub diameter and the rim diameter are determined, 8 sections are linearly inserted in the middle, so that the impeller is divided into 10 sections for design;
the variable loop volume design is adopted:
V u (i)*(r(i) α +r(i) -α ) Constant =constant
Vu (i) is the component of the absolute velocity of the water flow of the ith section in the circumferential direction, and r (i) is the radius of the ith cylindrical section; alpha is a constant, and the size of the alpha is between-1 and 1;
the change rule of the section airfoil profile in the step (2) is as follows:
dividing the impeller into 10 design sections from the hub to the rim, taking 0.3-0.5 l from the hub to the rim at the maximum camber position of the 10 section wing sections, taking 0.5l from the rim, taking 0.3l from the hub, and linearly changing the intermediate parameters;
the inlet attack angle correction in the step (3) is as follows:
when the bidirectional pump impeller is designed, the inlet attack angle delta alpha of the bidirectional pump impeller takes 0-4 degrees from the hub to the rim, the inlet attack angle of the middle section takes the change rule of a hyperbola, and the absolute value of the difference between the distances from the plane to two fixed points is a track with a fixed value;
the basic formula of the hyperbola is:
b 2 ＝2；
the impeller parameters in the step (4) are designed as follows:
the bi-directional pump impeller parameter design includes 4 design parameters, namely: the density of each section blade grid is l/t, wherein l represents chord length, t represents blade grid distance, each section airfoil profile setting angle beta, each section camber F and each section thickness value d;
step 2, designing a plane two-dimensional airfoil and generating two-dimensional coordinates;
the step 2 comprises the following steps:
(1) Wing section camber line design and coordinate expression; (2) airfoil coordinates;
the airfoil camber line design and coordinate expression in the step (1) are as follows:
the two-way pump camber line wing profile adopts a bilateral symmetry wing profile, the unilateral camber line adopts a quadratic function curve derived based on a circular arc curve and a Ru-Kovus base curve, and a curve equation is as follows:
x 2 +Ay 2 +Bx+Cy＝0
wherein A, B, C is a constant, and the design of the impeller of the bidirectional pump is that timeB＝2，C＝1；
Airfoil camber line coordinates: the abscissa of the airfoil camber line is denoted x (ss); the ordinate yc= [ yc1, yc2] of the airfoil camber line, wherein yc1 (ss) represents the ordinate value of the ss-th point on the left side of the camber line, yc1 represents the array of the ordinate of the ss-th point on the left side of the camber line, yc2 (ss) represents the ordinate value of the ss-th point on the right side of the camber line, yc2 represents the array of the ordinate of the ss-th point on the right side of the camber line, yc represents the array of the ordinate of all points of the whole camber line; represented by different ycs according to different positions; determining the coordinate of the ss-th point of the airfoil camber line as (x (ss), yc (ss)) according to the ordinate yc (ss) and the abscissa x (ss) of the airfoil camber line;
the coordinate arrangement expression of the camber line is as follows:
when x (ss) is less than or equal to g, the ordinate of the camber line is solved by adopting the following formula:
yc1(ss)＝F(i)/g^2*(2*g*(x(ss)/l(i)-(x(ss)/l(i))^2)
the ordinate of the camber line is solved using the following formula when x (ss) > g:
yc2(ss)＝F(i)/(1-g)^2*((1-2*g)+2*g*(x(ss)/l(i)-(x(ss)/l(i))^2)
wherein x (ss) is the abscissa value of the ss point on the wing section, i represents the section number of the impeller from the hub to the rim; ss represents the number of discrete points taken on the airfoil curve; g represents the maximum camber position of the section airfoil, and the maximum camber position is 0.3 l-0.5 l from the hub to the rim;
the wing profile coordinates of the step (2) are:
coordinates of each point of the airfoil curve: the variation relationship between airfoil thickness and chord length is as follows:
d (i) represents the maximum thickness of the ith airfoil section, l (i) is the airfoil length of the ith section, m, n are indices, and the relationship is m+n=2; yt (ss) represents the thickness calculation result required to be increased or decreased on the camber basis for that point with the abscissa x (ss), and yt represents the thickness calculation array required to be increased or decreased for all points;
according to the change rule of the airfoil thickness curve and the coordinate of the airfoil camber line, the upper airfoil ordinate of the two-way pump airfoil is obtained as follows: yr1=yc-yt; the ordinate of the lower wing of the two-way pump wing is yr2=yc+yt; obtaining airfoil curve coordinates (x (ss), yr (ss)); wherein yr1 (ss) represents the ordinate value of the ss point of the upper wing, yr1 represents the array of the ordinate of the ss point of the upper wing, yr2 (ss) represents the ordinate value of the ss point of the lower wing, and yr2 represents the array of the ordinate of the ss point of the lower wing;
the two-dimensional coordinates of the airfoil profile obtained above are coordinates obtained by taking the chord length as the horizontal position, and when the bidirectional pump airfoil profile is designed, the chord length is converted into the position with the setting angle, and after the chord length is converted into the setting angle, the conversion formula of the coordinates of the corresponding points is as follows:
upper airfoil abscissa conversion formula:
Xr1(ss)＝x(ss)*cosd(β(i))-yr1(ss)*sind(β(i))
upper airfoil ordinate conversion formula:
Yr1(ss)＝x(ss)*sind(β(i))+yr1(ss)*cosd(β(i))
the lower airfoil abscissa conversion formula:
Xr2(ss)＝x(ss)*cosd(β(i))-yr2(ss)*sind(β(i))
the lower airfoil ordinate conversion formula:
Yr2(ss)＝x(ss)*sind(β(i))+yr2(ss)*cosd(β(i))
obtaining two-dimensional airfoil coordinates (Xr (ss), yr (ss)) of the airfoil with the ith section after rotating by an angle beta (i) through the conversion of the formula;
the plane coordinates of the two-dimensional wing profile of the bi-directional pump are obtained, the plane wing profile coordinates are converted into cylindrical wing profile coordinates, and the arc coordinates theta of each coordinate point of the section where the plane wing profile is located are obtained through formula calculation;
upper airfoil arc coordinates θ1=xr1/(r (i))/pi (). 180;
the lower airfoil arc coordinate θ2=xr2/(r (i))/pi (). 180;
wherein r (i) is the radial radius of the coordinate point from the impeller origin O, namely the radius of the ith section, pi () is the expression of a constant pi;
obtaining arc coordinates (theta, yr) of the two-dimensional airfoil;
step 3, generating three-dimensional rectangular coordinates of the bidirectional pump blade;
and 3, generating three-dimensional rectangular coordinates of the bidirectional pump blade as follows:
according to the two-dimensional arc coordinates (theta, yr) of each section of the airfoil, obtaining the three-dimensional rectangular coordinates of each section of the bi-directional pump blade through formula transformation; the transformation formula is as follows:
X(ss)＝r(i)*sindθ(ss)；
Y(ss)＝r(i)*cosdθ(ss)；
Z(ss)＝Yr(ss)；
and obtaining three-dimensional coordinates (X, Y, Z) on any airfoil section of the bi-directional pump blade according to the formula.
2. The method for designing the space coordinates of the blades of the bidirectional axial flow pump according to claim 1, wherein α=1/2.
3. A method of constructing a bi-directional axial flow pump vane space coordinate design method as defined in claim 2, comprising the steps of:
step a, generating space point coordinates;
step b, constructing an airfoil space curved surface;
step c, generating three-dimensional blades of the impeller;
the space point coordinates in the step a are three-dimensional rectangular coordinates of the bidirectional pump blade;
the wing section space curved surface structure in the step b is as follows:
the design of the wing profile is carried out by selecting 10 different design sections from the hub to the rim according to linear variation,
generating space point coordinates, namely selecting 20-30 points from an upper airfoil and a lower airfoil on any design section to generate points, conducting round guiding treatment on 2% of the positions close to the top end of the airfoil aiming at the chord length l of different airfoil sections, taking one point every 5% of the positions close to the front end 20% of the airfoil, and taking one point every 10% of the positions in 20% -50% of the middle section of the airfoil, namely 20-30 points can be obtained on one airfoil section; then generating space points on the rest airfoil sections according to the steps, and finally generating an airfoil profile by carrying out fitting curve through sweeping of the datum points;
the three-dimensional impeller blade in the step c is generated as follows:
and (3) carrying out impeller curved surface construction in three-dimensional modeling software, wherein points on 10 working surfaces are connected in one-to-one correspondence along the axial direction to generate curves, the smooth curved surfaces constructed by the curves are the working surfaces, and meanwhile, the obtained points on 10 different airfoil section are connected in the radial direction, namely, the generation of the blade width in the popular sense is carried out, so that the bidirectional axial flow pump blade construction is completed.
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| CN103696983A (en) * | 2013-12-31 | 2014-04-02 | 江苏大学 | Method for optimally designing impellers of bidirectional axial flow pumps |
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