CN111275792A - New method for drawing axial surface streamline of mixed-flow water turbine - Google Patents
New method for drawing axial surface streamline of mixed-flow water turbine Download PDFInfo
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Abstract
The invention provides a new method for drawing axial surface streamline of a mixed flow turbine, which is divided into three steps, wherein the first step is to draw an equipotential line in a runner, the second step is to draw a streamline in the runner, and the third step is to check and correct the streamline. The theory of 'replacing curves with straight lines' and the principle of being perpendicular to the upper crown and the lower ring are adopted to draw equipotential lines, so that the equipotential lines meet the design requirements; and on the premise of drawing the equipotential lines, drawing the axial surface streamline by the principle that the streamline is vertical to the equipotential lines. By improving the axial surface streamline drawing method, the design process of the runner blade of the mixed-flow turbine can be optimized, and the influence of the experience of a designer on the axial surface streamline drawing quality is reduced.
Description
Technical Field
The invention belongs to the field of hydraulic mechanical engineering, and relates to a method for drawing axial surface streamline of mixed flow hydraulic machinery.
Background
The runner blade of the mixed-flow water turbine is a core component of the mixed-flow water turbine, has the function of realizing energy conversion, and has the working principle that the energy of water flow is converted into the power potential energy of rotating machinery, and the overall efficiency of the mixed-flow water turbine set is directly influenced by the quality of the performance. The blade is an important component of the runner, the design process comprises drawing a hydraulic calculation diagram, drawing a wood model diagram and three-dimensional modeling, and the design process has the defect in the aspect of an axial surface streamline drawing method. When the axial surface streamline is drawn according to the existing axial surface streamline drawing method, the quality of the drawn streamline for the first time directly influences the workload of the axial surface streamline correction, and the quality of the drawn streamline for the first time mainly depends on the experience of a designer and has the existence of an instability factor, so that the repeatability of the axial surface streamline correction is increased to a certain extent.
Disclosure of Invention
Aiming at the problems, the invention improves the method for drawing the axial surface streamline, provides a new method for drawing the axial surface streamline of the mixed-flow water turbine, and weakens the influence of the experience of a designer on the drawing quality of the axial surface streamline.
A new method for drawing axial surface streamline of mixed-flow water turbine is characterized in that: the method comprises the following steps:
1) drawing an equipotential line in the flow channel: the first equipotential line is a drawing vertical line taking a point K of an intersection point of the lower circular arc and the runner inlet section as a starting point; drawing in a straight curve-replacing manner from the second equipotential line, so that the equipotential lines are required to be perpendicular to the upper crown and the lower ring of the rotating wheel; and the equipotential lines should be smooth curves;
2) drawing a streamline in the flow channel: firstly, dividing points of an outlet and an inlet of a runner, and drawing a streamline by using a spline curve command in AutoCAD on the basis of finishing the division points of the inlet and the outlet of the runner, wherein the drawn streamline is vertical to an equipotential line and has the characteristic of smooth smoothness;
3) check and correct flow line: firstly, determining the intersection points of equipotential lines and flow lines on two sides by using a circle drawing method, drawing equipotential line groups by using a spline curve sequential connection method, and correcting the drawn flow lines and equipotential lines by using the flow equality between two adjacent flow surfaces as a theoretical basis.
Further, the drawing mode of "replacing song with straight" in the step 1) is as follows: the intersection point of the equipotential line and the lower ring is selected in an arc segment, two points A and B which are close to each other are selected at the position of the lower ring of the rotating wheel and connected, the two points A and B are marked as a straight line segment AB, the point C is used as a vertical line of the straight line segment AB, the point C at the midpoint of the straight line segment AB is used as the starting point of a spline curve, the equipotential line is drawn by using a spline curve fitting command along the direction of the vertical line of the straight line segment AB, after a plurality of fitting points, the drawn equipotential line is perpendicular to the crown of the rotating wheel, drawing of one equipotential line is completed, and the process is repeated to complete drawing of the rest equipotential lines.
Further, in the step 1), the selection range of the number of the fitting points in the drawing process of each equipotential line is set to be 5-7 points including a starting point and an end point.
Further, in step 1), the number of drawn equipotential lines is 6-9.
Further, step 2) completes the drawing according to the following steps:
2.1) division point of the outlet and inlet of the first flow channel: equally dividing the inlet of the flow channel into n parts by using a constant number equal division command, and sequentially marking each node from the upper crown to the lower ring by using numbers 0, 1, 2, 3, … and n; the intersection point of an outlet straight line section EF of the lower ring of the rotating wheel and the extension line of the central axis is marked as an M point; selecting a radius drawing circle command, drawing a circle by taking an M point as a circle center and taking a straight line segment EM as a radius, recording the intersection point of the drawn circle and the central axis as an N point, taking a point E of a lower ring endpoint of the outlet of the runner as a vertical line of the central axis, recording the intersection point of the vertical line and the central axis as a point D, and recording the straight line segment between the point E and the point D as an outlet straight line segment ED; equally dividing the outlet straight-line segment ED into n parts by using a constant number equal division command, drawing a vertical line of the outlet straight-line segment ED through each node, wherein the vertical line corresponding to each node is equal to the circular arc segment
Each intersection point from the central axis to the outlet section of the lower ring is marked by numbers 1 ', 2', 3 ', … and (n-1)' in turn, and the number marks at the positions are in one-to-one correspondence with the number marks at the inlet;
2.2) drawing streamline: drawing a streamline by using a spline curve command in AutoCAD, drawing a spline curve which is sequentially vertical to each equipotential line by taking 1 point in divided points of a runner inlet as a starting point of the streamline, taking a finishing point of the spline curve as a 1 'point divided on the runner outlet corresponding to the selected starting point, and marking an intersection point of the spline curve and an outlet straight-line segment ED as 1'; drawing the remaining n-1 streamlines and sequentially marking the intersection points with the straight outlet line segment ED as 2 ', 3 ', … and (n-1) '; completing the drawing of the flow lineThen, the arc segment is deleted
And trimming the flow line by using a trimming command, wherein the trimming command mainly trims the arc section
And the line segments 1 ', 2' and 3 ', …, (n-1)', cut between the straight exit segment ED.
Further, the number of the drawn streamlines is 5, wherein the number of the drawn streamlines comprises an upper crown streamline and a lower ring streamline.
Further, the method for drawing the equipotential line group in step 3) specifically includes: initially determining the distances S of a group of equipotential lines on two sides to be 13, 13.2, 13.4, 13.6 and 13.8, selecting a radius circle drawing command, drawing a circle by taking the intersection point of the equipotential lines and the streamline as the center of a circle and taking S/2 as the radius; and after drawing the circle, sequentially connecting the intersection points of the circle and the streamline by using a spline curve.
Further, the specific method for correcting the streamline and the equipotential lines in the step 3) is as follows:
on the basis of completing the drawing of the equipotential line group, breaking the streamline and the equipotential line from each intersection point of the streamline and the equipotential line by using a break-at-point command in the AutoCAD; for the distance between a straight line segment or two points, measuring the length of the straight line segment or the distance between the two points by adopting linear marking, and for a curve segment, inputting a list command to check the length of the curve segment; sequentially measuring the length delta Lm of each section of the middle axial plane streamline, the length delta b of the equipotential center line between adjacent two axial plane streamlines and the distance R from the intersection point of the streamlines and the equipotential lines to the central axis, wherein the distance R between the middle point of the equipotential center line between the adjacent two axial plane streamlines and the central axis is the average value of the R at the end point of the equipotential center line;
automatically programming by using MATLAB, finishing the automatic correction process of the drawn streamline through for circulation, outputting the reasonable length delta Lm of each section of the middle axial plane streamline, the length delta b of the equipotential center line between the adjacent two axial plane streamlines and the distance r between the midpoint of the equipotential center line between the adjacent two axial plane streamlines and the central axis, and drawing the equipotential center line into an AutoCAD graph;
bases for autonomous programming with MATLABThe content is as follows: and finishing the correction calculation of the axial surface streamline by using the for loop body statement. According to the measured original data, calculating the error value delta, and judging whether the error value delta meets the requirement, if not, correcting delta b for the length of the equipotential central line between the adjacent two axial flow lines by means of the error value delta, namely: Δ bCorrectionΔ b × (1- δ), and the difference Δ b × δ between the correction value and the original data is averaged and added to the length Δ b of the equipotential center lines of the remaining segments, where Δ b: length of equipotential median line between adjacent two axial flow lines; the length delta Lm of the middle axial surface streamline and the distance r between the midpoint of the equipotential center line and the central axis between the adjacent two axial surface streamlines can be calculated by a similarity conversion method through a formula (5) and a formula (6);
rcorrection＝(R2-R1)×(1-δ)+R1(5)
ΔLmCorrection＝ΔLm×(1-δ) (6)
In the above formula: Δ bCorrection: Δ b after correction value adjustment of Δ b obtained by reference calculation;
R1，R2: the distance from the intersection point of the equipotential center line and the axial surface streamline to the central axis;
the criterion to be followed in the process of correcting the axial surface streamline is as follows:
the length of the equipotential center line is not changed, i.e.: Δ b1+Δb2+Δb3+Δb4＝const；
The length delta b of the equipotential median line between the adjacent two axial flow lines satisfies the relation of decreasing from the upper crown to the lower ring, namely: Δ b1>Δb2>Δb3>Δb4；
The length delta Lm of each section of the intermediate axial surface streamline satisfies the sequentially decreasing relation from the upper crown to the lower ring, namely: delta Lm1>ΔLm2>ΔLm3>ΔLm4。
Compared with the existing design method, the invention has the advantages that:
the novel method for drawing the axial surface streamline of the mixed-flow water turbine adopts the idea of 'directly replacing a curve' and the principle of being perpendicular to an upper crown and a lower ring to draw an equipotential line, so that the equipotential line meets the design requirement; on the premise of drawing the equipotential lines, the axial surface streamline is drawn by means of the principle that the streamline is perpendicular to the equipotential lines, so that the influence of experience of a designer on the drawing quality of the axial surface streamline is weakened.
Drawings
Fig. 1 is an equipotential line drawing by adopting the new method for drawing the axial surface streamline of the francis turbine.
Fig. 2 is a flow channel inlet and outlet distribution diagram drawn by the new method for drawing the axial surface streamline of the mixed-flow water turbine.
Fig. 3 is an axial surface streamline diagram drawn by the new method for drawing the axial surface streamline of the francis turbine.
Fig. 4 is an axial surface streamline diagram corrected by the new method for drawing the axial surface streamline of the francis turbine.
Fig. 5 is an enlarged view of a C equipotential line group in the new method for drawing the axial surface streamline of the mixed-flow water turbine.
Detailed Description
The invention will be further described with reference to the following figures and specific examples, but the scope of the invention is not limited thereto.
The invention relates to a new method for drawing axial surface streamline of a mixed-flow water turbine, which is characterized by comprising the following steps: the method comprises the steps of drawing an equipotential line in a flow channel in three steps, drawing a streamline in the flow channel in the second step, and checking and correcting the streamline in the third step. Spline curve fitting, constant number dividing, radius drawing, trimming, deleting, breaking in points, marking, list and other commands are used in AutoCAD software to complete drawing of streamline and equipotential lines.
The invention relates to a novel method for drawing axial surface streamline of a mixed-flow water turbine, which specifically comprises the following steps.
Firstly, drawing an equipotential line in a flow channel: after the cross section area of the flow channel is checked to be correct, the equipotential lines are drawn by using a spline curve command in AutoCAD. The starting point of the first equipotential line is selected at the K point of the intersection point of the lower ring arc and the inlet section of the flow channel, and the inlet of the flow channel is a straight line section, so that the K point is crossed to form a perpendicular line of the straight line section of the inlet. From the second equipotential line, the intersection point of the equipotential line and the lower ring is generally selected to be in a circular arc section, and the equipotential line is drawn by using the idea of 'replacing a curve with straight' in order to ensure that the equipotential line can be perpendicular to the lower ring of the rotating wheel. The implementation process of the idea of "replacing song with song" will be described with reference to fig. 1. Optionally selecting two points A and B close to each other at the position of the lower ring of the rotating wheel, connecting the two points A and B, marking as a straight line segment AB, wherein the center point is a point C, and drawing a perpendicular line of the straight line segment AB through the point C. The process of drawing equipotential lines will be described with reference to the equipotential lines drawn by the new method of drawing axial flow lines in fig. 1. And taking the point C of the midpoint of the straight line segment AB as the starting point of the spline curve, drawing an equipotential line by using a spline curve fitting command along the direction of the perpendicular line of the straight line segment AB, and after passing through a plurality of fitting points, enabling the drawn equipotential line to be perpendicular to the crown of the rotating wheel. The above process is repeated, the remaining equipotential lines are drawn, and the equipotential lines are marked with a, b, c, d, e, and f in sequence from the entrance.
The number of the equipotential lines directly influences the correction result of the streamline, the number of the equipotential lines is large, the correction result of the streamline is relatively accurate, the streamline is closer to the streamline in the actual flow, and when the number of the equipotential lines exceeds 9, the accuracy of the streamline correction result is improved to a limited extent; if the number of equipotential lines is too small, the correction result for the streamline is not ideal, and the error in the calculation of the axial flow velocity and the wrap angle is amplified. In order to ensure that the streamline correction result is ideal and the error of subsequent design is reduced, the number of the equipotential lines is determined to be 6-9 equipotential lines by referring to the existing design method. The fitting points are points which are set for finely adjusting the curve to enable the curve to meet the requirements, the drawing difficulty is increased due to too many fitting points, the drawing difficulty is difficult to achieve due to too few fitting points, and the selection range of the number of the fitting points is set to be 5-7 points including a starting point and an end point from the aspects of considering both the drawing difficulty and the curve quality.
The drawn equipotential lines must be perpendicular to the upper crown and lower ring of the wheel; and the equipotential lines are smooth curves, and if the uneven part appears, the equipotential lines can be adjusted through the fitting points to be smooth. Because the flow situation at the circular arc of the lower ring of the rotating wheel is complex, in order to ensure the actual flow situation, the starting point of the equipotential line should be optimal in a direction perpendicular to the circular arc of the lower ring of the rotating wheel.
Before drawing the axial surface streamline, the division of the outlet and the inlet of the runner is carried out. The process of dividing the inlet and outlet of the flow channel will be described with reference to the flow line drawing method of axial plane of the attached figure 2. The process of flow entry pointing is described below, using a constant number equal division command to divide the flow entry equally into 4, each node from the upper crown to the lower ring being labeled with the numbers 0, 1, 2, 3 and 4 in sequence. The process of flow channel exit tapping is described below, where the straight exit segment EF of the lower ring of the wheel and the central axis are extended to intersect, and the intersection point is marked with M. Selecting a radius circle drawing command, drawing a circle by taking the point M as the center of a circle and taking the straight line segment EM as the radius, recording the intersection point of the circle M and the central axis as the point N, taking the point E of the lower ring endpoint of the outlet of the runner as the vertical line of the central axis, taking the intersection point of the vertical line and the central axis as the point D, and recording the straight line segment between the point E and the point D as the straight line segment ED of the outlet. Dividing the outlet straight line section ED into 4 parts by using a constant number dividing command, drawing a vertical line of the outlet straight line section ED through each node, wherein the vertical line corresponding to each node is equal to the circular arc section
There are intersections, each intersection from the central axis to the outlet section of the lower ring is marked with a number 1 ', 2 ' and 3 ' in turn, and the number marking at this location needs to correspond one-to-one to the number marking at the inlet.
Secondly, drawing a streamline in the flow channel: and on the basis of finishing the division of the inlet and the outlet of the runner, drawing the streamline by using a spline curve command in the AutoCAD. The process of drawing axial flow lines is described with reference to fig. 3. Because the flow line and the equipotential lines have the characteristic of being perpendicular to each other, 1 point in the points divided by the inlet of the flow channel is selected as the starting point of the flow line, a spline curve which is sequentially perpendicular to each equipotential line is drawn, the ending point is the 1' point divided on the outlet of the flow channel corresponding to the selected starting point, and the flow line and the equipotential lines are divided into two pointsThe intersection point of the straight line section ED and the outlet is marked as 1'; drawing the remaining two flow lines according to the method, and sequentially marking the intersection points of the flow lines and the straight line section ED as 2 'and 3'; after the streamline is drawn, the arc segment needs to be deleted
And trimming the flow line by using a trimming command, wherein the trimming command mainly trims the arc section
And the line segments 1 ' 1 ", 2 ' 2" and 3 ' 3 "cut between the straight outlet segments ED.
A streamline is a hypothetical curve that exists within a flow field and represents the flow conditions within the flow field at a given time. Because the design of the runner blade of the francis turbine adopts a binary design theory of omega being 0, the drawn streamline is perpendicular to the equipotential line, and the streamline has the characteristic of smoothness and smoothness. For the concave-convex part of the streamline, the streamline can be smoothened by adjusting the vertical position of the streamline and the equipotential line. A large number of practices prove that when the number of the flow lines is more than 5, the precision improvement of the mixed flow turbine runner blade design is very limited, and a large amount of time is consumed in the process of correcting the flow lines; therefore, the number of the streamline is selected to be 5, wherein the number comprises an upper crown streamline and a lower ring streamline.
Before checking and correcting the axial streamline, drawing equipotential line groups is performed, and therefore the drawing process of the equipotential line groups is described with reference to fig. 4. Because the equipotential line group generally comprises three equipotential lines, the distances from the equipotential lines on the two sides to the middle equipotential line are equal, and the equipotential line group presents the shape of a bell mouth from the lower ring to the upper crown, the intersection point of the equipotential lines on the two sides and the streamline is determined by using a circle drawing method, and the equipotential line group is drawn by using a method of sequentially connecting spline curves. The distances S of a group of equipotential lines on two sides are initially determined to be 13, 13.2, 13.4, 13.6 and 13.8, a radius circle drawing command is selected, the intersection point of the equipotential lines and the streamline is used as the center of a circle, and S/2 is used as the radius circle drawing command. And after drawing the circle, sequentially connecting the intersection points of the circle and the streamline by using a spline curve.
Since the preliminarily drawn streamline may have a large error, the drawn streamline needs to be checked and corrected, and the checking and correction of the streamline is performed based on the following theory. Because axial flow is a potential flow, the flow between two adjacent flow surfaces is required to be equal, namely:
ΔQ＝const (1)
the flow between two adjacent flow surfaces is:
ΔQ＝2πrΔbVm (2)
and:
Vm＝ΔΦ/ΔLm(3；
as for the same group of adjacent equipotential lines, Δ Φ is const, Δ Q is equal, and it is understood from equations (1), (2), and (3) that:
rΔb/ΔLm＝const(4)
in the formula: Δ b: length of equipotential median line between adjacent two axial flow lines;
Δ Q: flow between two adjacent axial surface streamlines;
Δ Φ: potential differences of equipotential lines on two sides in the equipotential line group;
r: the distance between the midpoint of the equipotential center line and the central axis between the adjacent two axial flow lines;
Δ Lm: length of mid-axial surface streamlines of each segment.
And correcting the axial surface streamline through the value of the corrected delta b, correcting the position of the axial surface streamline and the corresponding equipotential line group according to the corrected value so as to obtain a second approximate axial surface streamline network, and repeatedly performing the calculation until the calculation meets the requirement.
The third step is checking and correcting the streamline: the process of correcting the axial flow line will be described with reference to fig. 4 and 5. On the basis of finishing the drawing of the equipotential line group, in order to facilitate the measurement of each parameter, an interruption-to-point command in AutoCAD is used for interrupting the streamline and the equipotential line from each intersection point of the streamline and the equipotential line. For a straight line segment or the distance between two points, the length of the straight line segment or the distance between two points is measured by adopting a linear label, and for a curve segment, a list command is input to check the length of the curve segment. Sequentially measuring the length delta Lm of each section of the middle axial plane streamline, the length delta b of the equipotential center line between the adjacent two axial plane streamlines and the distance R from the intersection point of the streamlines and the equipotential lines to the central axis, wherein the distance R between the middle point of the equipotential center line between the adjacent two axial plane streamlines and the central axis is the average value of the R at the end points of the equipotential center lines. On the basis of completing the measurement of original data, MATLAB is used for autonomous programming, the automatic correction process of drawn streamlines is completed through for circulation, the reasonable length delta Lm of each section of middle axial plane streamlines, the length delta b of equipotential center lines between adjacent two axial plane streamlines and the distance r between the midpoint of the equipotential center lines between the adjacent two axial plane streamlines and the central axis are output, and the equipotential center lines are drawn into an AutoCAD graph, so that errors caused in the process of repeatedly adjusting the streamlines are reduced.
The basic content of autonomous programming with MATLAB is: and finishing the correction calculation of the axial surface streamline by using the for loop body statement. According to the measured original data, calculating the error value delta, and judging whether the error value delta meets the requirement, if not, correcting delta b for the length of the equipotential central line between the adjacent two axial flow lines by means of the error value delta, namely: Δ bCorrectionAnd equally dividing the difference value delta b x delta between the corrected value and the original data to be added to the length delta b of the equipotential center lines of the rest sections, wherein the length delta Lm of the middle axial surface streamline and the distance r between the middle point of the equipotential center line and the center axis between the adjacent two axial surface streamlines can be calculated by a similarity conversion method through a formula (5) and a formula (6).
Formula (5) and formula (6) are illustrated by taking an enlarged view of the equipotential line group of the new method C drawn by the axial surface streamline in the attached figure 5 as an example:
rcorrection＝(R2-R1)×(1-δ)+R1(5)
ΔLmCorrection＝ΔLm×(1-δ) (6)
In the above formula: Δ bCorrection: Δ b after correction value adjustment of Δ b obtained by reference calculation;
R1，R2: the distance from the intersection point of the equipotential center line and the axial surface streamline to the central axis;
the criterion to be followed in the process of correcting the axial surface streamline is as follows:
the length of the equipotential lines is not changed. Namely: Δ b1+Δb2+Δb3+Δb4＝const。
The length delta b of the equipotential median line between the adjacent two axial flow lines satisfies the relation of decreasing from the upper crown to the lower ring. Namely: Δ b1>Δb2>Δb3>Δb4。
The length delta Lm of each section of the middle axial surface streamline satisfies the relation of decreasing from the upper crown to the lower ring. Namely: delta Lm1>ΔLm2>ΔLm3>ΔLm4。
The present invention is not limited to the above-described embodiments, and any obvious improvements, substitutions or modifications can be made by those skilled in the art without departing from the spirit of the present invention.
Claims (8)
1. A new method for drawing axial surface streamline of mixed-flow water turbine is characterized in that: the method comprises the following steps:
1) drawing an equipotential line in the flow channel: the first equipotential line is a drawing vertical line taking a point K of an intersection point of the lower circular arc and the runner inlet section as a starting point; drawing in a straight curve-replacing manner from the second equipotential line, so that the equipotential lines are required to be perpendicular to the upper crown and the lower ring of the rotating wheel; and the equipotential lines should be smooth curves;
2) drawing a streamline in the flow channel: firstly, dividing points of an outlet and an inlet of a runner, and drawing a streamline by using a spline curve command in AutoCAD on the basis of finishing the division points of the inlet and the outlet of the runner, wherein the drawn streamline is vertical to an equipotential line and has the characteristic of smooth smoothness;
3) check and correct flow line: firstly, determining the intersection points of equipotential lines and flow lines on two sides by using a circle drawing method, drawing equipotential line groups by using a spline curve sequential connection method, and correcting the drawn flow lines and equipotential lines by using the flow equality between two adjacent flow surfaces as a theoretical basis.
2. The new method for drawing axial surface streamline of francis turbine according to claim 1, which is characterized in that: the drawing mode of 'replacing koji with straight' in the step 1) is as follows: the intersection point of the equipotential line and the lower ring is selected in an arc segment, two points A and B which are close to each other are selected at the position of the lower ring of the rotating wheel and connected, the two points A and B are marked as a straight line segment AB, the point C is used as a vertical line of the straight line segment AB, the point C at the midpoint of the straight line segment AB is used as the starting point of a spline curve, the equipotential line is drawn by using a spline curve fitting command along the direction of the vertical line of the straight line segment AB, after a plurality of fitting points, the drawn equipotential line is perpendicular to the crown of the rotating wheel, drawing of one equipotential line is completed, and the process is repeated to complete drawing of the rest equipotential lines.
3. The new method for drawing axial surface streamline of francis turbine according to claim 2, which is characterized in that: in the step 1), the selection range of the number of fitting points in the drawing process of each equipotential line is set to be 5-7 points including a starting point and an end point.
4. The new method for drawing axial surface streamline of francis turbine according to claim 2, which is characterized in that: in the step 1), the number of drawn equipotential lines is 6-9.
5. The new method for drawing axial surface streamline of francis turbine according to claim 2, which is characterized in that: step 2) finishing the drawing according to the following steps:
2.1) division point of the outlet and inlet of the first flow channel: equally dividing the inlet of the flow channel into n parts by using a constant number equal division command, and sequentially marking each node from the upper crown to the lower ring by using numbers 0, 1, 2, 3, … and n; the intersection point of an outlet straight line section EF of the lower ring of the rotating wheel and the extension line of the central axis is marked as an M point; selecting a radius drawing circle command, drawing a circle by taking an M point as a circle center and taking a straight line segment EM as a radius, recording the intersection point of the drawn circle and the central axis as an N point, taking a point E of a lower ring endpoint of the outlet of the runner as a vertical line of the central axis, recording the intersection point of the vertical line and the central axis as a point D, and recording the straight line segment between the point E and the point D as an outlet straight line segment ED; equally dividing the outlet straight-line segment ED into n parts by using a constant number equal division command, drawing a vertical line of the outlet straight-line segment ED through each node, wherein the vertical line corresponding to each node is equal to the circular arc segment
Each intersection point from the central axis to the outlet section of the lower ring is marked by numbers 1 ', 2', 3 ', … and (n-1)' in turn, and the number marks at the positions are in one-to-one correspondence with the number marks at the inlet;
2.2) drawing streamline: drawing a streamline by using a spline curve command in AutoCAD, drawing a spline curve which is sequentially vertical to each equipotential line by taking 1 point in divided points of a runner inlet as a starting point of the streamline, taking a finishing point of the spline curve as a 1 'point divided on the runner outlet corresponding to the selected starting point, and marking an intersection point of the spline curve and an outlet straight-line segment ED as 1'; drawing the remaining n-1 streamlines and sequentially marking the intersection points with the straight outlet line segment ED as 2 ', 3 ', … and (n-1) '; after the streamline is drawn, the arc segment needs to be deleted
And trimming the flow line by using a trimming command, wherein the trimming command mainly trims the arc section
And the line segments 1 ', 2' and 3 ', …, (n-1)', cut between the straight exit segment ED.
6. The new method for drawing axial surface streamline of francis turbine according to claim 5, which is characterized in that: the number of the drawn streamline is 5, wherein the number comprises an upper crown streamline and a lower ring streamline.
7. The new method for drawing axial surface streamline of francis turbine according to claim 5, which is characterized in that: the method for drawing the equipotential line group in the step 3) specifically comprises the following steps: initially determining the distances S of a group of equipotential lines on two sides to be 13, 13.2, 13.4, 13.6 and 13.8, selecting a radius circle drawing command, drawing a circle by taking the intersection point of the equipotential lines and the streamline as the center of a circle and taking S/2 as the radius; and after drawing the circle, sequentially connecting the intersection points of the circle and the streamline by using a spline curve.
8. The new method for drawing axial surface streamline of francis turbine according to claim 7, which is characterized in that: the specific method for correcting the streamline and the equipotential lines in the step 3) comprises the following steps:
on the basis of completing the drawing of the equipotential line group, breaking the streamline and the equipotential line from each intersection point of the streamline and the equipotential line by using a break-at-point command in the AutoCAD; for the distance between a straight line segment or two points, measuring the length of the straight line segment or the distance between the two points by adopting linear marking, and for a curve segment, inputting a list command to check the length of the curve segment; sequentially measuring the length delta Lm of each section of the middle axial plane streamline, the length delta b of the equipotential center line between adjacent two axial plane streamlines and the distance R from the intersection point of the streamlines and the equipotential lines to the central axis, wherein the distance R between the middle point of the equipotential center line between the adjacent two axial plane streamlines and the central axis is the average value of the R at the end point of the equipotential center line;
automatically programming by using MATLAB, finishing the automatic correction process of the drawn streamline through for circulation, outputting the reasonable length delta Lm of each section of the middle axial plane streamline, the length delta b of the equipotential center line between the adjacent two axial plane streamlines and the distance r between the midpoint of the equipotential center line between the adjacent two axial plane streamlines and the central axis, and drawing the equipotential center line into an AutoCAD graph;
the basic content of autonomous programming with MATLAB is: and finishing the correction calculation of the axial surface streamline by using the for loop body statement. According to the measured original data, calculating the error value delta, and judging whether the error value delta meets the requirement, if not, correcting delta b for the length of the equipotential central line between the adjacent two axial flow lines by means of the error value delta, namely: Δ bCorrectionΔ b × (1- δ), and the difference Δ b × δ between the correction value and the original data is averaged and added to the length Δ b of the equipotential center lines of the remaining segments, where Δ b: length of equipotential median line between adjacent two axial flow lines; the length delta Lm of the middle axial surface streamline and the distance r between the midpoint of the equipotential center line and the central axis between the adjacent two axial surface streamlines can be calculated by a similarity conversion method through a formula (5) and a formula (6);
rcorrection＝(R2-R1)×(1-δ)+R1(5)
ΔLmCorrection＝ΔLm×(1-δ) (6)
In the above formula: Δ bCorrection: Δ b after correction value adjustment of Δ b obtained by reference calculation;
R1，R2: the distance from the intersection point of the equipotential center line and the axial surface streamline to the central axis;
the criterion to be followed in the process of correcting the axial surface streamline is as follows:
the length of the equipotential center line is not changed, i.e.: Δ b1+Δb2+Δb3+Δb4＝const；
The length delta b of the equipotential median line between the adjacent two axial flow lines satisfies the relation of decreasing from the upper crown to the lower ring, namely: Δ b1>Δb2>Δb3>Δb4；
The length delta Lm of each section of the intermediate axial surface streamline satisfies the sequentially decreasing relation from the upper crown to the lower ring, namely: delta Lm1>ΔLm2>ΔLm3>ΔLm4。
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