A cyclic circle design method based on variable cross-sectional area distribution

Abstract

The application discloses a variable cross-sectional area distribution based circulating circle design method, which comprises the following steps: obtaining a given circulating circle outer ring; designing a circulating circle flow cross-sectional area distribution curve by using a Bezier curve, taking the flow cross-sectional area at an inlet as a standard, and taking the flow cross-sectional area at other positions as a relative cross-sectional area to obtain a circulating circle flow cross-sectional area distribution result; establishing a polar coordinate system and a rectangular coordinate system; and solving the inner ring coordinates of the circulating circle in the rectangular coordinate system according to the circulating circle flow cross-sectional area distribution result, and drawing an inner ring curve. The design method adopts a mode of fixing the circulating circle outer ring and changing the cross-sectional area distribution to design the inner ring, simultaneously realizes the circulating circle design with adjustable flow cross-sectional area distribution by using the Bezier curve, can separately design the circulating circle cross-sectional area distribution of different impellers, and realizes the variable cross-sectional area distribution design of the variable torque circulating circle.

Description

Technical Field

[0001] This invention relates to the field of fluid machinery circulating loop design technology, specifically to a circulating loop design method based on variable cross-sectional area distribution. Background Technology

[0002] In the design of circulating circles for turbine rotating machinery, the assumption of a constant cross-sectional area is often adopted to reduce volumetric losses in the flow channel. However, since the circulating circle of rotating machinery is essentially circular, and the cross-sectional area distribution can affect the blade surface load distribution, it will have different impacts on performance. Therefore, there is an urgent need to provide a new circulating circle design method. Summary of the Invention

[0003] This invention provides a circulating circle design method based on variable cross-sectional area distribution. This method designs the inner ring by fixing the outer ring of the circulating circle and changing the cross-sectional area distribution. At the same time, it uses Bézier curves to achieve an adjustable circulating circle design with adjustable flow cross-sectional area distribution. It can design the circulating circle cross-sectional area distribution of different impellers in multi-impeller hydraulic components such as hydraulic torque converters and hydraulic couplers separately, realize the variable cross-sectional area distribution design of the circulating circle of the torque converter, expand its design domain, provide new ways to improve its torque ratio and energy capacity, improve its flow performance, and facilitate the three-dimensional flow design of hydraulic components.

[0004] The present invention adopts the following specific technical solution:

[0005] A method for designing a cyclic circle based on variable cross-sectional area distribution, comprising the following steps:

[0006] Step 1: Obtain the given outer loop of the circular loop;

[0007] Step 2: Design the flow cross-sectional area distribution curve of the circulation circle using Bézier curves. The flow cross-sectional area distribution is based on the flow cross-sectional area at the inlet, and the flow cross-sectional area at other locations is characterized by relative cross-sectional areas to obtain the flow cross-sectional area distribution result of the circulation circle.

[0008] Step 3: Take the center point P of the outer loop of the circular loop. j Establish a polar coordinate system with the pole and any flow channel inlet as the polar diameter, and solve for the cross-sectional area of ​​the circulation circle. Establish a rectangular coordinate system ZOR with the rotation axis of the circulation circle as the horizontal axis Z, the perpendicular line between the pole and the rotation axis as the vertical axis R, and the intersection of the horizontal axis and the vertical axis as the origin O. Based on the distribution of the cross-sectional area of ​​the circulation circle obtained in step two, solve for the inner ring coordinates of the circulation circle in the rectangular coordinate system and draw the inner ring curve.

[0009] Furthermore, in step three, the flow cross-sectional area A(α) is calculated using the following formula:

[0010]

[0011] In the above formula, A0 is the cross-sectional area at the inlet, α is the polar angle at the curve position, A(α) is the flow cross-sectional area at the polar angle α, and P i Let i be the control points, i = 1, 2, ..., n+1;

[0012] basis function b i,n (α) is an nth-degree Bernstein polynomial, defined as:

[0013]

[0014] Furthermore, in step three, the coordinates of the inner loop of the repeating circle in the rectangular coordinate system are solved using the following formula:

[0015]

[0016] Where α is also the azimuth angle of vector P1P2 with the pump inlet as the starting position, |P1P2| is the length of vector P1P2, when the polar angle is α, the polar radius intersects the inner ring of the circulation circle at point P1 and intersects the outer ring at point P2, the annular area formed by the P1P2 line segment sweeping around the rotation axis is the flow cross-sectional area of ​​the circulation circle, R1 is the inner ring radius, and R2 is the outer ring radius.

[0017] Furthermore, in the rectangular coordinate system ZOR, the axis of rotation is the Z-axis and all the recurring circles lie on the positive half of the R-axis. Therefore, yj>0, y>0, and Rj>0 always hold true. Thus, formula (3) can be simplified to:

[0018]

[0019] Beneficial effects:

[0020] The circulation circle design method of this invention, based on a given outer ring of the circulation circle, uses Bézier curves to design the cross-sectional area distribution curve of the circulation circle, calculates the coordinates of the inner ring and the cross-sectional area of ​​the circulation circle, and plots the inner ring curve based on the inner ring coordinates, thus enabling the design of the inner ring given the outer ring. This design method allows for independent design of the cross-sectional area distribution in the circulation circle design, and allows for Bézier curve-based design of the cross-sectional area distribution, achieving designs including linear, expansion, contraction, and expansion / contraction types. Furthermore, different impellers can have their cross-sectional areas designed individually, thus allowing for the individual design of impeller characteristics using different cross-sectional area distribution types, ultimately improving the overall hydraulic performance of the hydraulic components. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of the outer ring structure of the circular loop;

[0022] Figure 2 The structure is a circular flow cross-sectional area distribution structure.

[0023] Figure 3 This is a schematic diagram of the flow channel cross-section of a hydraulic torque converter;

[0024] Figure 4 A schematic diagram of the design result for the cyclic circle;

[0025] Figures 5a-5c The cross-sectional area distribution and its circular design structure are shown in the typical embodiment;

[0026] Figure 6 This is the result of the cross-sectional area distribution of a typical torque converter;

[0027] Figure 7 The design result of the circulation circle for a typical torque converter. Detailed Implementation

[0028] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0029] This embodiment provides a method for designing a cyclic circle based on a variable cross-sectional area distribution. The method includes the following steps:

[0030] Step 1: Obtain the outer loop of the given repeating circle; the outer loop of the repeating circle is as follows: Figure 1 As shown;

[0031] Step two: Design the flow cross-sectional area distribution curve of the circulation circle using Bézier curves. The flow cross-sectional area distribution is based on the flow cross-sectional area at the inlet, and the flow cross-sectional areas at other locations are characterized by relative cross-sectional areas. Without loss of generality, this embodiment uses the most commonly used equal cross-sectional area distribution as an example for design, so the distribution result is as follows: Figure 2 As shown; the distribution of the cross-sectional area of ​​the circulating circle is obtained;

[0032] Step 3: The inner and outer rings of the circulation circle of the hydraulic torque converter are approximately circular. Based on this, a method for representing the cross-sectional area of ​​the circulation circle based on the polar coordinate system approximation is established, such as... Figure 3 As shown, take the center point P of the outer loop of the circular ring. jEstablish a polar coordinate system with the pole and any flow channel inlet as the polar diameter; establish a rectangular coordinate system ZOR with the rotation axis of the circulation circle as the horizontal axis Z, the perpendicular line between the pole and the rotation axis as the vertical axis R, and the intersection of the horizontal and vertical axes as the origin O; when the polar angle is α, its polar diameter intersects the inner ring of the circulation circle at point P1 and the outer ring at point P2. The annular area formed by the line segment P1P2 sweeping around the rotation axis Z of the circulation circle is the flow cross-sectional area A(α) of the circulation circle. The schematic diagram of its flow channel cross-section is shown below. Figure 3 As shown, the cross-sectional area of ​​the circulating circle is thus calculated, and a function distribution curve A(α) based on the polar angle α and the cross-sectional area A can be established. For the complete circulating circle of the torque converter, given that its basic parameters such as the circulating circle width, circulating circle diameter, and circulating circle outer ring are determined, considering the center point P... j (Z j ,R j Furthermore, the circle perpendicular to the axis of rotation should evenly divide the cross-sectional area of ​​the outer ring of the circular circle to ensure the rationality of the distribution of the inner and outer rings, while also ensuring the maximum design domain. Therefore, let Z... j R is the center in the width direction of the circular loop, and radially upwards. j Designed as follows:

[0033]

[0034] Among them, D max D is the diameter of the cyclic circle. min This is the minimum diameter of the outer ring of the circular loop;

[0035] In step three above, when calculating the cross-sectional area of ​​the circulating circle, the cross-sectional area A(α) is calculated using the following formula:

[0036]

[0037] In the above formula, A0 is the cross-sectional area at the inlet, α is the polar angle at the curve position, A(α) is the flow cross-sectional area at the polar angle α, and P i Let i be the control points, i = 1, 2, ..., n+1;

[0038] basis function b i,n (α) is an nth-degree Bernstein polynomial, defined as:

[0039]

[0040] Based on the flow cross-sectional area distribution of the circulation circle obtained in step two, the inner ring coordinates of the circulation circle in the rectangular coordinate system are calculated. The following formula is used to calculate the inner ring coordinates of the circulation circle in the rectangular coordinate system, and the inner ring curve is plotted, as follows. Figure 4 As shown,

[0041]

[0042] Where α is also the azimuth angle of vector P1P2 with the pump inlet as the starting position, |P1P2| is the length of vector P1P2, when the polar angle is α, the polar radius intersects the inner ring of the circulation circle at point P1 and intersects the outer ring at point P2, the annular area formed by the P1P2 line segment sweeping around the rotation axis is the flow cross-sectional area of ​​the circulation circle, R1 is the inner ring radius, and R2 is the outer ring radius.

[0043] For a circular circle in a ZOR rectangular coordinate system, if its axis of rotation is on the Z-axis and all circular circles lie on the positive half of the R-axis, then yj>0, y>0, and Rj>0 always hold true. Therefore, the formula for the cross-sectional area can be simplified to:

[0044]

[0045] Typical examples include the design results of circular circles with uniform cross-sectional area distribution, expansion-contraction distribution with initial increase followed by decrease, and expansion distribution, as shown below. Figure 5a , Figure 5b as well as Figure 5c As shown.

[0046] Typical embodiments also include this method for fitting and designing existing circular cross-sectional areas. Figure 6 This is the result of the cross-sectional area distribution of a certain torque converter, while Figure 7 The design of its circulating circle reveals that the cross-sectional area of ​​the torque converter is not uniformly distributed. Because its guide wheel is a straight circulating circle, it exhibits a typical shrinking-expanding tube-type cross-sectional area distribution, decreasing first and then increasing. The pump wheel has a nearly uniform distribution, and the turbine also approximates a shrinking-expanding tube cross-sectional area distribution.

[0047] The aforementioned circulating circle design method, based on a given outer ring of the circulating circle, utilizes Bézier curves to design the cross-sectional area distribution curve of the circulating circle, calculates the coordinates of the inner ring and the cross-sectional area of ​​the circulating circle, and plots the inner ring curve based on the inner ring coordinates. This allows for the design of the inner ring given the outer ring. The design method of this invention enables independent design of the cross-sectional area distribution in the circulating circle design. Furthermore, the cross-sectional area distribution of the circulating circle can be designed based on Bézier curves, achieving cross-sectional area distribution designs including straight-line, expansion, contraction, and expansion / contraction types. In addition, different impellers can have their cross-sectional areas designed individually, thus allowing for the individual design of impeller characteristics using different cross-sectional area distribution types, ultimately improving the overall hydraulic performance of the hydraulic components.

[0048] Based on the properties of Bézier curves, second-order Bézier curves can be used to achieve the design of cross-sectional area distributions of linear, flow channel expansion, and flow channel contraction types. Third-order or even higher-order Bézier curves can also be used to achieve the design of cross-sectional area distributions of flow channel expansion, flow channel contraction, flow channel expansion-contraction, and other types, thereby realizing the rational design of different impeller surface loads and ultimately improving the comprehensive hydraulic performance of hydraulic components.

[0049] The key point of the above-mentioned circulating circle design method is to introduce cross-sectional area distribution design into the circulating circle design of multi-impeller rotating machinery such as hydraulic torque converters or hydraulic couplings; on this basis, a method for calculating the flow cross-sectional area of ​​the circulating circle is proposed; and the flow cross-sectional area distribution curve is designed or optimized based on the Bezier curve, which can improve the load on the surface of different impeller blades, thereby improving the overall hydraulic performance of its hydraulic components.

[0050] In general, in the design of expander-contractor tubes or contraction-expanderor tubes, to ensure that diffusion losses and rotation losses are not too large, the ratio of the maximum cross-sectional area to the minimum cross-sectional area, i... A It is generally advisable to control it between 1.00 and 1.30. The inlet cross-sectional area A of the pump impeller is used as a reference. P.in For reference, relative cross-sectional area data at different positions of the blades can be extracted. Taking a torque converter with a circulating circle diameter of 310mm as an example, under the design domain where the ratio of the pump impeller and turbine relative to the pump impeller inlet area does not exceed 1.0±0.15 and the guide wheel is 1.0±0.10, the flow field characteristics and performance characteristics of the torque converter are predicted and verified using computational fluid dynamics methods. The pump impeller torque index can be improved by 18.5%, and the starting torque ratio is also improved by 3.4%. It can be seen that the difference in cross-sectional area distribution has a significant impact on the performance of the torque converter.

[0051] Obviously, those skilled in the art can make various modifications and variations to the embodiments of the present invention without departing from the spirit and scope of the invention. Therefore, if these modifications and variations fall within the scope of the claims of the present invention and their equivalents, the present invention also intends to include these modifications and variations.

Claims

1. A method for designing a cyclic circle based on variable cross-sectional area distribution, characterized in that, Includes the following steps: Step 1: Obtain the given outer ring of the turbine rotating mechanical circulation circle; Step 2: Design the flow cross-sectional area distribution curve of the circulation circle using Bézier curves. The flow cross-sectional area distribution is based on the flow cross-sectional area at the inlet, and the flow cross-sectional area at other polar angle positions is characterized by relative cross-sectional area to obtain the flow cross-sectional area distribution result of the circulation circle. Step 3: Take the center point P of the outer loop of the circular loop. j Establish a polar coordinate system with the pole and any flow channel inlet as the polar diameter, and solve for the cross-sectional area of ​​the circulation circle. Establish a rectangular coordinate system ZOR with the rotation axis of the circulation circle as the horizontal axis Z, the perpendicular line between the pole and the rotation axis as the vertical axis R, and the intersection of the horizontal and vertical axes as the origin O. Based on the distribution of the cross-sectional area of ​​the circulation circle obtained in step two, solve for the inner ring coordinates of the circulation circle in the rectangular coordinate system and draw the inner ring curve. The cross-sectional area A of the flow is calculated using the following formula ( α ): （1）； In the above formula, A0 is the cross-sectional area at the entrance. α Let A be the polar angle of the curve's position. α ( ) is the polar angle α The cross-sectional area of ​​the flow at point P i As control points, i =1, 2, ..., n+1; basis functions b i,n (α) is an nth-degree Bernstein polynomial, defined as: （2）； The coordinates of the inner loop of the repeating circle in the rectangular coordinate system are solved using the following formula: （3）； in, α It is also the azimuth angle of vector P1P2 starting from the pump wheel inlet, where |P1P2| is the length of vector P1P2 and the polar angle is... α The polar radius intersects the inner ring of the circulation circle at point P1 and the outer ring at point P2. The annular area formed by the line segment P1P2 sweeping around the rotation axis is the cross-sectional area of ​​the circulation circle. R1 is the radius of the inner ring and R2 is the radius of the outer ring.

2. The method for designing a circular loop as described in claim 1, characterized in that, In the rectangular coordinate system ZOR, the axis of rotation is the Z-axis and all the repeating circles lie on the positive half of the R-axis. yj >0、 y >0、R j If 0 is always true, then formula (3) can be simplified to: （4）。

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