Method of designing non-axisymmetric endwall pressure distribution to weaken crossflow and blade

Abstract

The present disclosure relates to the field of non-axisymmetric endwall shaping design, and particularly relates to a method for designing a non-axisymmetric endwall transverse pressure distribution weakening transverse flow and a blade, the method comprising: S10, limiting an axial range of a non-axisymmetric endwall profile to a region from 0-0.1 times an axial chord length upstream of a leading edge to 0-0.1 times an axial chord length upstream of a trailing edge, and setting a transverse endwall profile control line at a position of 0.3-0.5 times the axial chord length downstream of the leading edge; S20, calculating a transverse pressure gradient of the non-axisymmetric endwall at the profile control line based on a transverse flow model; S30, calculating a target transverse distribution of static pressure of the non-axisymmetric endwall at the profile control line based on the transverse pressure gradient and a flow field result of a flat endwall cascade; and S40, calculating a deformation amount of the non-axisymmetric endwall, so that the non-axisymmetric endwall profile is continuously deformed to approximate the target static pressure distribution in a three-dimensional flow field solving process.

Description

Technical Field

[0001] This disclosure relates to the field of non-axisymmetric endwall design, and more particularly to a design method and blade for non-axisymmetric endwall lateral pressure distribution that reduces lateral flow. Background Technology

[0002] The rapid development of machine learning and artificial intelligence has provided a new approach to optimizing non-axisymmetric endwall shapes, completely independent of design experience. Simply inputting a sample set into an automated optimization algorithm and providing the objective function yields the endwall shape corresponding to the optimal objective function value. This method replaces human analysis and judgment with the training process of the optimization algorithm, greatly simplifying the design process and removing the limitations of manual analysis on design space and sample size. It enables the design of more complex non-axisymmetric endwall shapes. The rapid development of computational fluid dynamics tools and numerical optimization methods has greatly facilitated non-axisymmetric endwall shaping, solving the problem of obtaining optimal endwall shapes from a very large design space when design experience is lacking.

[0003] However, a deep understanding of flow mechanisms is equally crucial in the design of non-axisymmetric endwalls. In the study of compressor non-axisymmetric endwall design, some research has drawn on the turbine approach of reducing the lateral pressure gradient by lowering the suction side and raising the pressure side, suggesting that non-axisymmetric endwalls can also suppress corner separation by weakening lateral flow. How to apply this understanding of flow mechanisms to the design of non-axisymmetric endwalls, thereby obtaining the non-axisymmetric endwall profile more conveniently and quickly, is an important question. Summary of the Invention

[0004] To address the aforementioned problems mentioned in the background art, this disclosure proposes a design method and blade for reducing the transverse pressure distribution on the non-axisymmetric endwall of the compressor blade, aiming to provide a method for improving the general design characteristics of the non-axisymmetric endwall of the compressor blade end region flow.

[0005] According to one aspect of this disclosure, a design method for mitigating the transverse pressure distribution at non-axisymmetric endwalls in transverse flow is provided, comprising the following steps:

[0006] S10. The axial range of the non-axisymmetric endwall profile is limited to the region from 0-0.1 times the axial chord length upstream of the leading edge to 0-0.1 times the axial chord length upstream of the trailing edge. A transverse endwall profile control line is set at a position 0.3-0.5 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.

[0007] S20. Calculate the transverse pressure gradient of the non-axisymmetric endwall at the profile control line based on the transverse flow model.

[0008] S30. Based on the lateral pressure gradient and the flow field results of the flat endwall blade cascade, calculate the lateral distribution of the target static pressure at the profile control line of the non-axisymmetric endwall.

[0009] S40. Calculate the deformation of the non-axisymmetric endwall based on the difference between the current static pressure value and the target static pressure at the profile control line of the non-axisymmetric endwall. This allows the profile of the non-axisymmetric endwall to continuously deform and approximate the target static pressure distribution during the three-dimensional flow field solution process.

[0010] Optionally, the axial range of the non-axisymmetric endwall profile is limited to the region from 0-0.1 times the axial chord length upstream of the leading edge to 0-0.1 times the axial chord length upstream of the trailing edge.

[0011] Optionally, a transverse endwall profile control line may be provided at a position 0.3-0.5 times the axial chord length downstream of the leading edge.

[0012] Optionally, in step S20, the lateral pressure gradient of the non-axisymmetric endwall at the profile control line is calculated using the following lateral flow model:

[0013] ,

[0014] in, It is the static pressure on the end wall. It is a tangential coordinate. It's density. It is the flow velocity. It is the streamline radius of curvature, superscript. and These represent values ​​at two different relative elevations. The subscripts FEW and NEW represent flat end walls and non-axisymmetric end walls, respectively.

[0015] In the formula, the flow velocity is... and streamline curvature The definition is as follows:

[0016] ,

[0017] ,

[0018] in, It is the tangential velocity. It is the axial velocity. It is the airflow angle, defined as the angle between the flow velocity and the axial direction. It is the rate of change of the airflow angle along the flow direction.

[0019] Optionally, in step S30, the lateral distribution of the target static pressure at the profile control line of the non-axisymmetric end wall is expressed as follows:

[0020] ,

[0021] in, Is the non-axisymmetric end wall in tangential coordinates The target static pressure at that location. It is the endwall static pressure of the flat-endwalled blade cascade at the pressure surface. It is the tangential coordinate of the airfoil pressure surface at the profile control line.

[0022] Optionally, relative height A value of 0.01-0.02 is acceptable, representing a relative expansion. The value can be 0.05-0.06. According to another aspect of this disclosure, a blade having the non-axisymmetric endwall shape defined in the above method is also provided.

[0023] Optionally, the blade is a compressor blade.

[0024] Compared to the prior art, the beneficial effects of this disclosure are as follows:

[0025] 1) This 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.

[0026] 2) This disclosure can reduce the lateral secondary flow in the compressor end region under different blade shapes and flow conditions.

[0027] 3) Compared with numerical optimization methods, this disclosure does not require the establishment of a sample library, has a smaller computational load, and simplifies the design process by setting control lines at specific locations and giving the static pressure coefficient variation.

[0028] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit this disclosure.

[0029] Other features and aspects of this disclosure will become clear from the following detailed description of exemplary embodiments with reference to the accompanying drawings. Attached Figure Description

[0030] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this disclosure and, together with the specification, serve to illustrate the technical solutions of this disclosure.

[0031] Figure 1 A flowchart illustrating a non-axisymmetric endwall design method to mitigate transverse flow is shown.

[0032] Figure 2 A schematic diagram of non-axisymmetric endwall profile control in an example of this disclosure is shown;

[0033] Figure 3 The endwall boundary layer streamlines of the flat-endwalled blade cascade at different spans are shown in the examples of this disclosure;

[0034] Figure 4 The spanwise velocity distribution of the flat-endwalled blade cascade at position P is shown in an example of this disclosure;

[0035] Figure 5 The lateral distribution of static pressure on the flat-end wall and the non-axisymmetric end wall in an example of this disclosure is shown;

[0036] Figure 6 The non-axisymmetric endwall profile contour map of this embodiment is shown;

[0037] Figure 7 The spanwise distribution of the total pressure loss coefficient of flat-endwall blade cascades and non-axisymmetric endwall blade cascades in embodiments of this disclosure is shown. Detailed Implementation

[0038] Various exemplary embodiments, features, and aspects of this disclosure will now be described in detail with reference to the accompanying drawings. The same reference numerals in the drawings denote elements that have the same or similar functions. Although various aspects of the embodiments are shown in the drawings, they are not necessarily drawn to scale unless specifically indicated otherwise.

[0039] The term “exemplary” as used herein means “serving as an example, embodiment, or illustration.” Any embodiment illustrated herein as “exemplary” is not necessarily to be construed as superior to or better than other embodiments.

[0040] In this document, the term "and / or" is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent three cases: A alone, A and B simultaneously, and B alone. Furthermore, the term "at least one" in this document means any combination of at least two of any one or more elements. For example, including at least one of A, B, and C can mean including any one or more elements selected from the set consisting of A, B, and C.

[0041] Furthermore, to better illustrate this disclosure, numerous specific details are set forth in the following detailed description. Those skilled in the art will understand that this disclosure can be practiced without certain specific details. In some instances, methods, means, components, and circuits well known to those skilled in the art have not been described in detail in order to highlight the main points of this disclosure.

[0042] To make the objectives, technical solutions, and advantages of the embodiments of this disclosure clearer, the technical solutions of the embodiments of this disclosure will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of this disclosure, but not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of this disclosure without creative effort are within the scope of protection of this disclosure.

[0043] This disclosure proposes a design method for mitigating the non-axisymmetric endwall lateral pressure distribution in transverse flow, such as... Figure 1 As shown, it includes the following steps:

[0044] S10. The axial range of the non-axisymmetric endwall profile is limited to the region from 0-0.1 times the axial chord length upstream of the leading edge to 0-0.1 times the axial chord length upstream of the trailing edge. A transverse endwall profile control line is set at a position 0.3-0.5 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.

[0045] S20. Calculate the transverse pressure gradient of the non-axisymmetric endwall at the profile control line based on the transverse flow model.

[0046] S30. Based on the lateral pressure gradient and the flow field results of the flat endwall blade cascade, calculate the lateral distribution of the target static pressure at the profile control line of the non-axisymmetric endwall.

[0047] S40. Calculate the deformation of the non-axisymmetric endwall based on the difference between the current static pressure value and the target static pressure at the profile control line of the non-axisymmetric endwall. This allows the profile of the non-axisymmetric endwall to continuously deform and approximate the target static pressure distribution during the three-dimensional flow field solution process.

[0048] Based on the above steps, the embodiments of this disclosure can weaken the lateral secondary flow in the end region by reducing the lateral pressure gradient in the leading section of the compressor blade passage, 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 feasible implementation methods in the steps are described in detail below:

[0049] S10. The axial range of the non-axisymmetric endwall profile is limited to the region from 0-0.1 times the axial chord length upstream of the leading edge to 0-0.1 times the axial chord length upstream of the trailing edge. A transverse endwall profile control line is set at a position 0.3-0.5 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.

[0050] Among them, compressor blades as shown in Table 1 below can be used for non-axisymmetric endwall design, and the endwall profile can be controlled as follows: Figure 2 As shown, the profile extends axially over a distance of 0.1 times the axial chord length from the upstream edge of the blade leading edge. The region extending from the leading edge to 0.1 times the axial chord length upstream of the trailing edge. A transverse endwall profile control line is established 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.

[0051] Table 1 Blade Parameters

[0052]

[0053] S20. Calculate the transverse pressure gradient of the non-axisymmetric endwall at the profile control line based on the transverse flow model.

[0054] The lateral flow model is expressed as follows:

[0055] ,

[0056] in, It is the static pressure on the end wall. It is a tangential coordinate. It's density. It is the flow velocity. It is the streamline radius of curvature, superscript. and These represent values ​​at two different relative elevations. The subscripts FEW and NEW represent flat end walls and non-axisymmetric end walls, respectively.

[0057] In the formula, the flow velocity is... and streamline curvature The definition is as follows:

[0058] ,

[0059] ,

[0060] in, It is the tangential velocity. It is the axial velocity. It is the airflow angle, defined as the angle between the flow velocity and the axial direction. It is the rate of change of the airflow angle along the flow direction.

[0061] The above process can be achieved through Figure 3 and Figure 4 To understand, Figure 3 The diagram shows five streamlines A, B, C, D, and E at different elevation positions within the boundary layer of the endwall of the flat-endwall blade cascade. All of these streamlines pass through a tangential position P on the profile control line, and the velocity magnitude at position P is as follows: Figure 4 As shown. Streamline A is located at a relatively high position. At that point, streamline E is located at a relatively high position. The non-axisymmetric endwall lateral pressure gradient calculated using the above lateral flow model makes the streamline curvature of streamline A at position P equal to that of streamline E at position P, thereby weakening the lateral flow.

[0062] S30. Based on the lateral pressure gradient and the flow field results of the flat-endwall blade cascade, the lateral distribution of the target static pressure at the profile control line of the non-axisymmetric endwall is calculated using the following formula:

[0063] ,

[0064] in, Is the non-axisymmetric end wall in tangential coordinates The target static pressure at that location. It is the endwall static pressure of the flat-endwalled blade cascade at the pressure surface. It is the tangential coordinate of the airfoil pressure surface at the profile control line.

[0065] 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.

[0066] S40. Calculate the deformation of the non-axisymmetric endwall based on the difference between the current static pressure value and the target static pressure at the profile control line. This allows the non-axisymmetric endwall profile to continuously deform during the three-dimensional flow field solution process, approximating the target static pressure distribution, ultimately generating... Figure 6 The end wall profile is shown. Compared to numerical optimization methods, the method in this embodiment does not require the establishment of a sample library, has a smaller computational load, and simplifies the design process by setting control lines at specific locations and specifying the variation in the static pressure coefficient.

[0067] In this embodiment, Figure 7 The spanwise distribution of the total pressure loss coefficient for both the prototype blade cascade and the non-axisymmetric endwall blade cascade is presented. The non-axisymmetric endwall weakens the transverse secondary flow by reducing the transverse pressure gradient, thereby reducing the total pressure loss in the spanwise region below 12% of the end height.

[0068] As another aspect of the present disclosure, a non-axisymmetric endwall shape having the method defined in the above embodiments is also provided.

[0069] As an alternative embodiment, the blade is a compressor blade.

[0070] Those skilled in the art will understand that, in the above-described design method and system for weakening transverse flow through non-axisymmetric endwall transverse pressure distribution in specific embodiments, the order in which each step is written does not imply a strict execution order and does not constitute any limitation on the implementation process. The specific execution order of each step should be determined by its function and possible internal logic.

[0071] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present disclosure. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of an instruction containing one or more executable instructions for implementing a specified logical function. In some alternative implementations, the functions marked in the blocks may occur in a different order than those shown in the drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, may be implemented using a dedicated hardware-based system that performs the specified function or action, or using a combination of dedicated hardware and computer instructions.

[0072] The various embodiments of this disclosure have been described above. These descriptions are exemplary and not exhaustive, nor are they limited to 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 chosen to best explain the principles, practical application, or technical improvements to the technology in the market, or to enable others skilled in the art to understand the embodiments disclosed herein.

Claims

1. A design method for reducing non-axisymmetric endwall lateral pressure distribution in transverse flow, characterized in that, Includes the following steps: S10. The axial range of the non-axisymmetric endwall profile is limited to the region from 0-0.1 times the axial chord length upstream of the leading edge to 0-0.1 times the axial chord length upstream of the trailing edge. A transverse endwall profile control line is set at a position 0.3-0.5 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 transverse pressure gradient of the non-axisymmetric endwall at the profile control line based on the transverse flow model. S30. Based on the lateral pressure gradient and the flow field results of the flat endwall blade cascade, calculate the lateral distribution of the target static pressure at the profile control line of the non-axisymmetric endwall. The lateral distribution of the target static pressure at the profile control line of the non-axisymmetric endwall is expressed as follows: ， in, Is the non-axisymmetric end wall in tangential coordinates The target static pressure at that location. It is the endwall static pressure of the flat-endwalled blade cascade at the pressure surface. It is the tangential coordinate of the airfoil pressure surface at the profile control line; S40. Calculate the deformation of the non-axisymmetric endwall based on the difference between the current static pressure value and the target static pressure at the profile control line of the non-axisymmetric endwall. This allows the profile of the non-axisymmetric endwall to continuously deform and approximate 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 range of the non-axisymmetric endwall profile is limited to the region from 0.1 times the axial chord length upstream of the leading edge 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 endwall 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, characterized in that, In step S20, the lateral pressure gradient of the non-axisymmetric endwall at the profile control line is calculated using the following lateral flow model: ， in, It is the static pressure on the end wall. It is a tangential coordinate. It's density. It is the flow velocity. It is the streamline radius of curvature, superscript. and These represent values ​​at two different relative elevations. The subscripts FEW and NEW represent flat end walls and non-axisymmetric end walls, respectively. In the formula, the flow velocity is... and streamline curvature The definition is as follows: ， ， in, It is the tangential velocity. It is the axial velocity. It is the airflow angle, defined as the angle between the flow velocity and the axial direction. It is the rate of change of the airflow angle along the flow direction.

5. The method according to claim 4, characterized in that, Relative exhibition height Take a value of 0.01-0.02, relative expansion height Take a value of 0.05-0.

06.

6. A blade, characterized in that, It has a non-axisymmetric endwall shape as defined in the method of any one of claims 1-5.

7. The blade according to claim 6, characterized in that, The blades are compressor blades.

Images