Non-axisymmetric end wall transverse pressure distribution design method for weakening transverse flow and blade

Abstract

The invention relates to the field of non-axisymmetric end wall modeling design, in particular to a non-axisymmetric end wall transverse pressure distribution design method capable of weakening transverse flow and a blade, and the method comprises the steps that S10, the axial range of a non-axisymmetric end wall molded surface is limited in a region from 0-0.1 times of the axial chord length of the upstream of the front edge of the blade to 0-0.1 times of the axial chord length of the upstream of the tail edge of the blade; a transverse end wall profile control line is arranged at the position, 0.3-0.5 time of the axial chord length, of the downstream of the front edge; s20, calculating the transverse pressure gradient of the non-axisymmetric end wall at the profile control line based on a transverse flow model; s30, calculating the transverse distribution of the target static pressure of the non-axisymmetric end wall at the profile control line based on the transverse pressure gradient and the flow field result of the flat end wall cascade; and S40, the deformation amount of the non-axisymmetric end wall is calculated, so that the molded surface of the non-axisymmetric end wall continuously deforms to approach target static pressure distribution in the three-dimensional flow field solving process.

Description

Technical Field

[0001] The present disclosure relates to the field of non-axisymmetric end wall shape design, and in particular to a non-axisymmetric end wall lateral pressure distribution design method and a blade for weakening lateral flow. Background Art

[0002] The rapid development of machine learning and artificial intelligence has provided a new approach to the optimization process of non-axisymmetric endwall shaping that is completely independent of design experience. Simply by inputting a sample set into an automated optimization algorithm and giving the optimization objective function, the endwall shape corresponding to the optimal objective function value can be obtained. This method replaces the human analysis and judgment process with the training process of the model using an optimization algorithm, greatly simplifying the design process and removing the limitations of manual analysis on the design space and sample size, enabling the design of non-axisymmetric endwalls with more complex shapes. The rapid development of computational fluid dynamics tools and numerical optimization methods has greatly facilitated the shaping of non-axisymmetric endwalls, solving the problem of obtaining a better endwall shape from a very large design space in the absence of design experience.

[0003] However, a deep understanding of flow mechanisms is equally crucial in the design of non-axisymmetric endwalls. In the study of non-axisymmetric endwall shaping for compressors, some research has drawn on the idea of ​​reducing lateral pressure gradients in turbines by creating a concave suction surface and a convex pressure surface. It is believed that non-axisymmetric endwalls can also suppress corner separation by weakening lateral flow. Applying this understanding of flow mechanisms to the design of non-axisymmetric endwalls, thereby more easily and efficiently obtaining non-axisymmetric endwall profiles, remains an important issue. Summary of the Invention

[0004] To solve the above problems mentioned in the background technology, the present disclosure proposes a non-axisymmetric end wall lateral pressure distribution design method and blade that weakens the lateral flow, aiming to provide a method for improving the universal design features of the non-axisymmetric end wall flow in the end area of ​​the compressor blade.

[0005] According to one aspect of the present disclosure, a method for designing a non-axisymmetric end wall transverse pressure distribution for weakening transverse flow is provided, comprising the following steps: S10, limiting the axial range of the non-axisymmetric end wall profile to the region from 0-0.1 times the axial chord length upstream of the leading edge of the blade to 0-0.1 times the axial chord length upstream of the trailing edge, and setting a transverse end wall profile control line at a position 0.3-0.5 times the axial chord length downstream of the leading edge, wherein the axial chord length is the axial distance between the leading edge and the trailing edge of the blade; S20, Calculate the lateral pressure gradient of the non-axisymmetric end wall at the profile control line based on the lateral flow model S30, calculating the lateral distribution of the target static pressure of the non-axisymmetric end wall at the profile control line based on the lateral pressure gradient and the flow field result of the flat end wall cascade; S40. Calculate the deformation of the non-axisymmetric end wall based on the difference between the current static pressure value of the non-axisymmetric end wall at the profile control line and the target static pressure, thereby causing the non-axisymmetric end wall profile to continuously deform and approach the target static pressure distribution during the three-dimensional flow field solution process.

[0006] Optionally, the axial extent of the non-axisymmetric end wall profile is limited to a region from 0-0.1 times the axial chord length upstream of the leading edge of the blade to 0-0.1 times the axial chord length upstream of the trailing edge.

[0007] Optionally, a transverse end wall profile control line is provided at a position 0.3-0.5 times the axial chord length downstream of the leading edge.

[0008] Optionally, in step S20, the lateral pressure gradient of the non-axisymmetric end wall at the profile control line is calculated using the following lateral flow model: , in, is the static pressure on the end wall, is the tangential coordinate, is the density, is the stream velocity, is the streamline curvature radius, the superscript and Represents the values ​​of two different relative heights. The subscripts FEW and NEW represent flat end walls and non-axisymmetric end walls, respectively. Where, the flow velocity and streamline curvature The definition is as follows: , , in, is the tangential velocity, is the axial velocity, is the airflow angle, defined as the angle between the stream velocity and the axial direction, is the rate of change of the airflow angle along the flow direction.

[0009] Optionally, in step S30, the lateral distribution of the target static pressure of the non-axisymmetric end wall at the profile control line is expressed as: , in, The non-axisymmetric end wall is in the tangential coordinate The target static pressure at is the static pressure on the end wall of the flat end wall cascade at the pressure surface, It is the tangential coordinate of the pressure surface of the blade at the profile control line.

[0010] Optionally, relative height It can be 0.01-0.02, relatively high According to another aspect of the present disclosure, there is also provided a blade having a non-axisymmetric end wall shape defined in the above method.

[0011] Optionally, the blade serves as a compressor blade.

[0012] Compared with the prior art, the beneficial effects of the present disclosure are: 1) The present disclosure can weaken the lateral secondary flow in the end region by reducing the lateral pressure gradient in the front section of the compressor blade passage, and reduce the flow loss caused by the secondary flow; 2) The present disclosure can weaken the lateral secondary flow in the compressor end region under different blade shapes and flow conditions.

[0013] 3) Compared with the numerical optimization method, the present invention does not require the establishment of a sample library, and the calculation amount is smaller. By setting the control line at a specific position and giving the static pressure coefficient change, the design process is simplified.

[0014] It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the disclosure.

[0015] Further features and aspects of the present disclosure will become apparent from the following detailed description of exemplary embodiments with reference to the attached drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] The accompanying drawings herein are incorporated into and constitute a part of the specification. These drawings illustrate embodiments consistent with the present disclosure and, together with the specification, are used to explain the technical solutions of the present disclosure.

[0017] Figure 1 A flow chart of a non-axisymmetric endwall design method for weakening cross flow is shown; Figure 2 A schematic diagram of the control of the non-axisymmetric end wall profile in an example of the present disclosure is shown; Figure 3 The end wall boundary layer streamlines of the flat end wall cascade with different heights in the embodiment of the present disclosure are shown; Figure 4 1 shows the spanwise velocity distribution of the flat endwall cascade at position P in an example of the present disclosure; Figure 5 The lateral distribution of static pressure of the flat end wall and the non-axisymmetric end wall in the examples of the present disclosure is shown; Figure 6 Shows a contour line cloud diagram of the non-axisymmetric end wall profile in an embodiment of the present disclosure; Figure 7 The spanwise distribution of the total pressure loss coefficient of the flat endwall cascade and the non-axisymmetric endwall cascade in the embodiment of the present disclosure is shown. DETAILED DESCRIPTION

[0018] Various exemplary embodiments, features, and aspects of the present disclosure will be described in detail below with reference to the accompanying drawings. The same reference numerals in the accompanying drawings represent elements with the same or similar functions. Although various aspects of the embodiments are shown in the accompanying drawings, the drawings are not necessarily drawn to scale unless otherwise indicated.

[0019] The word “exemplary” is used exclusively herein to mean “serving as an example, example, or illustration.” Any embodiment described herein as “exemplary” is not necessarily to be construed as preferred or advantageous over other embodiments.

[0020] The term "and / or" herein simply describes an association relationship between associated objects, indicating that three relationships can exist. For example, "A and / or B" can represent the existence of three situations: A alone, A and B simultaneously, and B alone. Furthermore, the term "at least one" herein refers to any combination of at least two of any one or more of a plurality of items. For example, "at least one of A, B, and C" can represent any one or more elements selected from the set consisting of A, B, and C.

[0021] In addition, numerous specific details are provided in the following detailed description to better illustrate the present disclosure. Those skilled in the art will appreciate that the present disclosure can be practiced without certain specific details. In some instances, methods, means, components, and circuits well known to those skilled in the art are not described in detail in order to highlight the main points of the present disclosure.

[0022] In order to make the purpose, technical solutions and advantages of the embodiments of the present disclosure clearer, the technical solutions in the embodiments of the present disclosure will be clearly and completely described below in conjunction with the drawings in the embodiments of the present disclosure. Obviously, the described embodiments are part of the embodiments of the present disclosure, not all the embodiments. Based on the embodiments in the present disclosure, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present disclosure.

[0023] The disclosed embodiment proposes a design method for a non-axisymmetric end wall lateral pressure distribution that weakens lateral flow, such as Figure 1 As shown, the following steps are included: S10, limiting the axial range of the non-axisymmetric end wall profile to the region from 0-0.1 times the axial chord length upstream of the leading edge of the blade to 0-0.1 times the axial chord length upstream of the trailing edge, and setting a transverse end wall profile control line at a position 0.3-0.5 times the axial chord length downstream of the leading edge, wherein the axial chord length is the axial distance between the leading edge and the trailing edge of the blade; S20, calculating the lateral pressure gradient of the non-axisymmetric end wall at the profile control line according to the lateral flow model; S30, calculating the lateral distribution of the target static pressure of the non-axisymmetric end wall at the profile control line based on the lateral pressure gradient and the flow field result of the flat end wall cascade; S40. Calculate the deformation of the non-axisymmetric end wall based on the difference between the current static pressure value of the non-axisymmetric end wall at the profile control line and the target static pressure, thereby causing the non-axisymmetric end wall profile to continuously deform and approach the target static pressure distribution during the three-dimensional flow field solution process.

[0024] Based on the above steps, the disclosed embodiment can reduce the lateral pressure gradient in the front section of the compressor blade passage to weaken the lateral secondary flow in the end region and reduce the flow losses caused by the secondary flow. It can also weaken the lateral secondary flow in the compressor end region under different blade shapes and flow conditions. The following is a detailed description of the feasible implementation methods of the steps: S10, limiting the axial range of the non-axisymmetric end wall profile to the region from 0-0.1 times the axial chord length upstream of the leading edge of the blade to 0-0.1 times the axial chord length upstream of the trailing edge, and setting a transverse end wall profile control line at a position 0.3-0.5 times the axial chord length downstream of the leading edge, wherein the axial chord length is the axial distance between the leading edge and the trailing edge of the blade; Among them, the compressor blades shown in Table 1 below can be used to perform non-axisymmetric end wall shaping, and the end wall profile control is as follows: Figure 2 As shown, the profile range covers the axial direction from the upstream of the blade leading edge 0.1 times the axial chord length ( ) to the area 0.1 times the axial chord length upstream of the trailing edge. A transverse endwall profile control line is set at a position 0.3 times the axial chord length downstream of the leading edge. Here, the axial chord length refers to the axial distance between the leading and trailing edges of the blade.

[0025] Table 1 Blade parameters

[0026] S20, calculating the lateral pressure gradient of the non-axisymmetric end wall at the profile control line according to the lateral flow model; The lateral flow model is expressed as: , in, is the static pressure on the end wall, is the tangential coordinate, is the density, is the stream velocity, is the streamline curvature radius, the superscript and Represents the values ​​of two different relative heights. The subscripts FEW and NEW represent flat end walls and non-axisymmetric end walls, respectively. Where, the flow velocity and streamline curvature The definition is as follows: , , in, is the tangential velocity, is the axial velocity, is the airflow angle, defined as the angle between the stream velocity and the axial direction, is the rate of change of the airflow angle along the flow direction.

[0027] The above process can be Figure 3 and Figure 4 To understand, Figure 3 Figure 2 shows five streamlines A, B, C, D, and E at different heights in the boundary layer of the endwall of a flat endwall cascade. All of the streamlines pass through the tangential position P on the profile control line, and the velocity magnitudes when passing through position P are as follows: Figure 4 As shown. Among them, streamline A is at a relatively high position At this point, streamline E is at a relatively high position. The non-axisymmetric end wall lateral pressure gradient calculated by the above lateral flow model makes the streamline curvature of streamline A when passing through position P equal to the streamline curvature of streamline E when passing through position P, thereby weakening the lateral flow.

[0028] S30. Based on the lateral pressure gradient and the flow field results of the flat end wall cascade, the lateral distribution of the target static pressure of the non-axisymmetric end wall at the profile control line is calculated using the following formula: , in, The non-axisymmetric end wall is in the tangential coordinate The target static pressure at is the static pressure on the end wall of the flat end wall cascade at the pressure surface, It is the tangential coordinate of the pressure surface of the blade at the profile control line.

[0029] like Figure 5 As shown, the above formula makes the static pressure of the non-axisymmetric end wall at the pressure surface equal to that of the flat end wall, while the static pressure of the end wall at the suction surface is higher than that of the flat end wall, thereby reducing the lateral pressure difference on both sides.

[0030] S40, calculate the deformation of the non-axisymmetric end wall according to the difference between the current static pressure value of the non-axisymmetric end wall at the profile control line and the target static pressure, so that the non-axisymmetric end wall profile is continuously deformed and approaches the target static pressure distribution during the three-dimensional flow field solution process, and finally generate Figure 6Compared to numerical optimization methods, the method in the embodiment of the present disclosure does not require the establishment of a sample library, has a smaller computational workload, and simplifies the design process by setting control lines at specific locations and specifying the static pressure coefficient variation.

[0031] In this embodiment, Figure 7 The spanwise distribution of the total pressure loss coefficient for the prototype cascade and the non-axisymmetric endwall cascade is given. The non-axisymmetric endwall reduces the lateral secondary flow by reducing the lateral pressure gradient, resulting in a reduction in the total pressure loss within the span height range below 12% of the end region.

[0032] As another aspect of the embodiments of the present disclosure, there is also provided a non-axisymmetric end wall shape as defined in the above embodiment method.

[0033] As an optional embodiment, the blade serves as a compressor blade.

[0034] Those skilled in the art will understand that in the above-mentioned non-axisymmetric end wall lateral pressure distribution design method and system for weakening lateral flow in a specific embodiment, the writing order of each step does not mean a strict execution order and constitutes any limitation on the implementation process. The specific execution order of each step should be determined by its function and possible internal logic.

[0035] The flow charts and block diagrams in the accompanying drawings show the possible architecture, functions and operations of the systems, methods and computer program products according to multiple embodiments of the present disclosure. In this regard, each box in the flow chart or block diagram can represent a part of a module, program segment or instruction, and the part of the module, program segment or instruction contains one or more executable instructions for realizing the prescribed logical function. In some alternative implementations, the functions marked in the box can also occur in a sequence different from that marked in the accompanying drawings. For example, two consecutive boxes can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each box in the block diagram and / or flow chart, and the combination of the boxes in the block diagram and / or flow chart can be implemented by a dedicated hardware-based system that performs the prescribed function or action, or can be implemented by a combination of dedicated hardware and computer instructions.

[0036] While various embodiments of the present disclosure have been described above, the above descriptions are illustrative, non-exhaustive, and not intended to be limiting of the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments. The terminology used herein is selected to best explain the principles of the embodiments, their practical applications, or technical improvements to existing technologies, or to enable others skilled in the art to understand the embodiments disclosed herein.

Claims

1. A design method for the non-axisymmetric end wall lateral pressure distribution to weaken lateral flow, characterized in that: The steps include: S10, limiting the axial range of the non-axisymmetric end wall profile to the region from 0-0.1 times the axial chord length upstream of the leading edge of the blade to 0-0.1 times the axial chord length upstream of the trailing edge, and setting a transverse end wall profile control line at a position 0.3-0.5 times the axial chord length downstream of the leading edge, wherein the axial chord length is the axial distance between the leading edge and the trailing edge of the blade; S20, calculating the lateral pressure gradient of the non-axisymmetric end wall at the profile control line according to the lateral flow model; S30, calculating the lateral distribution of the target static pressure of the non-axisymmetric end wall at the profile control line based on the lateral pressure gradient and the flow field result of the flat end wall cascade; S40. Calculate the deformation of the non-axisymmetric end wall based on the difference between the current static pressure value of the non-axisymmetric end wall at the profile control line and the target static pressure, thereby causing the non-axisymmetric end wall profile to continuously deform and approach the target static pressure distribution during the three-dimensional flow field solution process.

2. The method according to claim 1, characterized in that The axial extent of the non-axisymmetric end wall profile is limited to the region from 0.1 times the axial chord length upstream of the leading edge of the blade to 0.1 times the axial chord length upstream of the trailing edge.

3. The method according to claim 1, characterized in that A transverse end wall profile control line is set at a position 0.3 times the axial chord length downstream of the leading edge.

4. The method according to claim 1, wherein In step S20, the lateral pressure gradient of the non-axisymmetric end wall at the profile control line is calculated using the following lateral flow model: ， in, is the static pressure on the end wall, is the tangential coordinate, is the density, is the stream velocity, is the streamline curvature radius, the superscript and Represents the values ​​of two different relative heights. The subscripts FEW and NEW represent flat end walls and non-axisymmetric end walls, respectively. Where, the flow velocity and streamline curvature The definition is as follows: ， ， in, is the tangential velocity, is the axial velocity, is the airflow angle, defined as the angle between the stream velocity and the axial direction, is the rate of change of the airflow angle along the flow direction.

5. The method according to claim 1, characterized in that In step S30, the lateral distribution of the target static pressure of the non-axisymmetric end wall at the profile control line is expressed as: ， in, The non-axisymmetric end wall is in the tangential coordinate The target static pressure at is the static pressure on the end wall of the flat end wall cascade at the pressure surface, It is the tangential coordinate of the pressure surface of the blade at the profile control line.

6. The method according to claim 5, characterized in that Relative height Take 0.01-0.02, relatively high Take 0.05-0.

06.

7. A blade, characterized in that: Having a non-axisymmetric end wall shape as defined in the method according to any one of claims 1 to 6.

8. The blade according to claim 7, characterized in that The blades serve as compressor blades.

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