Method for establishing stream surface axis curvilinear coordinate system for describing complex fluid motion of turbomachinery

Abstract

This invention relates to a method for establishing a flow surface axis curve coordinate system to describe the complex fluid motion of turbine machinery. This coordinate system decomposes the complex flow within the turbine machinery into a main flow that achieves energy conversion and two secondary flows that dissipate energy. Simultaneously, by decomposing the forces acting on fluid particles within the turbine machinery into the a, b, and c axes, the relationship between forces and secondary flows is established, thereby revealing the mechanism of secondary flow generation and enabling direct solution of the secondary flow field and direct calculation of secondary flow energy loss. This changes the current practice of indirectly describing secondary flows. It achieves complete decomposition of complex flows and extracts secondary flows, and can be widely applied to various types of turbine machinery, including but not limited to pumps, water turbines, fans, and air compressors.

Description

Technical Field

[0001] This invention relates to a turbine machinery technology, and more particularly to a method for establishing a flow surface axis curve coordinate system to describe the complex fluid motion of a turbine machinery. Background Technology

[0002] In 1952, Professor Wu Zhonghua proposed two famous types of relative flow surfaces to address the hydrodynamic design problems of turbines, solving the mathematical description of the mainstream motion and ushering in the era of three-dimensional design for turbines. These two types of relative flow surfaces are S1 and S2. The S1 flow surface approximates a surface of revolution, while the S2 flow surface approximates a blade rib surface. The mainstream motion occurs along both S1 and S2 flow surfaces. Based on the S1 and S2 flow surfaces, an orthogonal curvilinear coordinate system (m,n,θ) describing the mainstream motion and a cylindrical coordinate system (r,θ,z) describing the blade geometry were established, as follows: Figure 1 The orthogonal curvilinear coordinate system and cylindrical coordinate system are shown (Wang Lixiang. Waterjet Propulsion Technology and Engineering Design [M]. Beijing: National Defense Industry Press, 2021).

[0003] Secondary flow is a common phenomenon in turbine machinery, existing in the boundary layer on the blade surface and the blade tip clearance region. It not only directly causes energy loss but also distorts the mainstream flow field, thereby reducing performance. Existing cylindrical coordinate systems (r, θ, z) and orthogonal curvilinear coordinate systems (m, n, θ) for turbine machinery cannot describe or characterize the secondary flow problem.

[0004] Secondary flow is the accompanying flow of the main motion, and its direction of motion is perpendicular to the main motion. Currently, for the secondary flow problem of turbine machinery, the secondary flow can only be analyzed from the perspective of the vortex of the main flow. The loss of secondary flow can only be indirectly evaluated from the perspective of entropy or vortex dissipation, which has low evaluation accuracy and incomplete understanding.

[0005] The two types of flow surfaces S1 and S2, which describe the main motion, cannot characterize the secondary flow within turbine machinery. CN114251129A proposes a third type of flow surface S3 to describe the secondary flow motion. This third type of flow surface, combined with numerical simulation technology, enables the reproduction, analysis, and quantitative evaluation of the secondary flow. However, it cannot be directly applied in mechanical design for calculating energy loss caused by the secondary flow and mitigating fault risks, thus limiting its widespread use. Summary of the Invention

[0006] To address the quantitative understanding of secondary flow in turbine machinery, a method for establishing a flow surface axis curve coordinate system to describe the complex fluid motion of turbine machinery is proposed. This method deeply reveals the mechanism of secondary flow in turbine machinery and can be directly used to characterize mathematical and physical models of secondary flow.

[0007] The technical solution of this invention is: a method for establishing a flow surface axis curve coordinate system to describe the complex fluid motion of turbine machinery, specifically including the following steps:

[0008] 1) In the cylindrical coordinate system (r, θ, z,) describing the blade geometry, take the middle meridional streamline m on the meridional surface of the turbine machine and draw the flow section line n in the middle of the blade. n is the intersection line of the S3 flow surface describing the secondary flow motion in the middle of the impeller passage and the meridional surface. The intersection point of the two lines m and n is taken as the origin O of the flow surface axis curve coordinate system.

[0009] 2) Rotate the meridional streamline m around the axis z to form the S1 flow surface, and take the blade arch surface as the S2 flow surface;

[0010] 3) Unfold the S1 flow surface. In the channel formed by the two adjacent blades, the intersection of the S2 flow surface and the S1 flow surface in the middle is the main flow streamline. This streamline is taken as the a-axis of the flow surface axis curve coordinate system. The intersection of the S3 flow surface and the S1 flow surface passing through the origin O is the b-axis of the flow surface axis curve coordinate system.

[0011] 4) Expand the S3 flow surface passing through the origin O. The intersection lines of the S1 flow surface, the S2 flow surface and the S3 flow surface are the two coordinate axes b and c of the flow surface axis curve coordinate system.

[0012] Furthermore, the b-axis and c-axis are orthogonal to the a-axis, and the b-axis and c-axis are quasi-orthogonal. The b-axis and c-axis respectively describe the secondary flow in the normal direction of the S2 flow surface and the S1 flow surface.

[0013] A flow field solution method using the flow surface axis curve coordinate system is proposed. Based on the flow surface axis curve coordinate system, the real-time rotational centrifugal force, streamline bending centrifugal force, Coriolis force, viscous force and pressure of the fluid micro-particles in the turbine are decomposed into the three axes a, b and c of the flow surface axis curve coordinate system. The relationship between force and motion is established. The relationship between force and motion in the a-axis direction is the main flow field of energy conversion, and the corresponding force and motion in the b-axis and c-axis directions at the same time is the secondary flow field of energy loss.

[0014] The beneficial effects of this invention are as follows: This invention describes a method for establishing a flow surface axis curve coordinate system for the complex fluid motion of turbine machinery. Through this coordinate system, the complex flow within the turbine machinery is decomposed into the main flow that achieves energy conversion and two secondary flow flows that consume energy. Simultaneously, by decomposing the forces acting on fluid particles within the turbine machinery into the a, b, and c axes, the relationship between forces and secondary flows is established, thereby revealing the mechanism of secondary flow generation and enabling direct solution of the secondary flow field and direct calculation of secondary flow energy loss, thus changing the current situation of indirect description of secondary flows. It achieves complete decomposition of complex flows and extracts secondary flows, and can be widely applied to various types of turbine machinery, including but not limited to pumps, water turbines, fans, and air compressors. Attached Figure Description

[0015] Figure 1 This is a schematic diagram of an orthogonal curvilinear coordinate system and a cylindrical coordinate system;

[0016] Figure 2 This is a schematic diagram of streamline m on the meridional surface of the turbine machinery of the present invention;

[0017] Figure 3 This is a diagram of the a-axis and b-axis of the cross-sectional axis coordinate system on the S1 flow surface of the present invention;

[0018] Figure 4 This is a diagram of the b-axis and c-axis of the surface axis curve coordinate system on the S3 surface of the present invention. Detailed Implementation

[0019] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0020] This invention provides a flow surface axis curve coordinate system (a, b, c) based on flow surfaces S1, S2, and S3. In this system, the three coordinate axes are a, b, and c. The a-axis describes the main flow motion, while the b and c axes describe the secondary flows in the normal directions of the S2 and S1 flow surfaces, respectively. The b and c axes are orthogonal to the a-axis, and the b and c axes are quasi-orthogonal. This flow surface axis curve coordinate system enables a complete description of the complex flow field (including secondary flows) in turbine machinery.

[0021] The method for establishing a flow surface axis curve coordinate system to describe the complex fluid motion of turbine machinery includes the following steps:

[0022] 1) such as Figure 2 The schematic diagram of streamline m on the meridional surface of the turbine is shown. In the cylindrical coordinate system (r,θ,z,) describing the geometry of the blade, the middle meridional streamline m is taken on the meridional surface inside the turbine. The flow section line n in the middle of the blade is drawn. n is the intersection line of the S3 flow surface describing the secondary flow motion in the middle of the impeller passage and the meridional surface. The intersection point of the two lines m and n is taken as the origin O of the flow surface axis curve coordinate system.

[0023] 2) Rotate the meridional streamline m around the axis z to form the S1 flow surface, and take the blade arch surface (the blade mid-surface) as the S2 flow surface;

[0024] 3) such as Figure 3 The diagram shows the a-axis and b-axis of the surface axis curve coordinate system for the S1 flow surface. When the S1 flow surface is unfolded, the intersection of the S2 flow surface and the S1 flow surface in the middle of the channel formed by the two adjacent blades is the main flow streamline. This streamline is taken as the a-axis of the surface axis curve coordinate system, with the origin in the middle. The intersection of the S3 flow surface and the S1 flow surface passing through point O is the b-axis of the surface axis curve coordinate system. The tangents of curves a and b at point O are perpendicular to each other.

[0025] 4) such as Figure 4The diagram shows the b-axis and c-axis of the surface axis curve coordinate system for the S3 flow surface. Expanding the S3 flow surface passing through point O, the intersection lines of the S1 flow surface, the S2 flow surface, and the S3 flow surface are the two coordinate axes b and c of the surface axis curve coordinate system, respectively.

[0026] Through the above steps, the coordinate system of the flow surface axis curve was established. The a-axis represents the main flow motion, and the b and c axes represent the secondary flow motions perpendicular to the S2 and S1 flow surfaces, respectively.

[0027] The flow surface axis curve coordinate system decomposes the complex fluid motion within a turbine into mainstream motion and secondary flow, with the mainstream motion realizing energy conversion. Secondary flow not only consumes energy and reduces efficiency but also degrades flow field quality and induces vibration and noise. Based on the flow surface axis curve coordinate system, the rotational centrifugal force, streamline bending centrifugal force, Coriolis force, viscous force, and pressure acting on fluid particles within the turbine are decomposed into three axes (a, b, and c), establishing the relationship between force and motion. This reveals the influence mechanism of various forces within the fluid machinery on the mainstream and two secondary flows, and enables the solution of the complex flow field, obtaining the secondary flow velocity. Thus, for the first time, the solution for secondary flow energy and a complete description of the secondary flow are achieved.

[0028] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.

Claims

1. A method for establishing a flow surface axis curve coordinate system to describe the complex fluid motion of turbine machinery, characterized in that, Specifically, the steps include the following: 1) In the cylindrical coordinate system describing the blade geometry ( r , θ , z, In the process, the middle meridional streamline m is taken on the meridional surface inside the turbine, and the flow section line n is drawn in the middle of the blade. n is the intersection line of the S3 flow surface describing the secondary flow motion in the middle of the impeller passage and the meridional surface. The intersection point of the two lines m and n is taken as the origin O of the flow surface axis curve coordinate system. 2) Rotate the meridional streamline m around the axis z to form the S1 flow surface, and take the blade arch surface as the S2 flow surface; 3) Unfold the S1 flow surface. In the channel formed by the two adjacent blades, the intersection of the S2 flow surface and the S1 flow surface in the middle is the main flow streamline. This streamline is taken as the a-axis of the flow surface axis curve coordinate system. The intersection of the S3 flow surface and the S1 flow surface passing through the origin O is the b-axis of the flow surface axis curve coordinate system. 4) Expand the S3 flow surface passing through the origin O. The intersection lines of the S1 flow surface, the S2 flow surface and the S3 flow surface are the two coordinate axes b and c of the flow surface axis curve coordinate system.

2. The method for establishing a flow surface axis curve coordinate system to describe the complex fluid motion of turbine machinery according to claim 1, characterized in that, The b-axis and c-axis are orthogonal to the a-axis, and the b-axis and c-axis are quasi-orthogonal. The b-axis and c-axis respectively describe the secondary flow in the normal direction of the S2 flow surface and the S1 flow surface.

3. A method for solving flow fields using a flow surface axis curve coordinate system, characterized in that, According to claim 2, the method for establishing a flow surface axis curve coordinate system to describe the complex fluid motion of a turbine is to establish a flow surface axis curve coordinate system, decompose the real-time rotational centrifugal force, streamline bending centrifugal force, Coriolis force, viscous force and pressure on the fluid micro-particles in the turbine into the three axes a, b and c of the flow surface axis curve coordinate system, and establish the relationship between force and motion. The relationship between force and motion in the a-axis direction is the main flow field of energy conversion, and the corresponding force and motion relationships in the b-axis and c-axis directions at the same time are the secondary flow fields of energy loss.

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