A method and system for shaping a full endwall periodic non-axisymmetric endwall

Abstract

The application provides a full end wall periodic non-axisymmetric end wall shaping method and system, which comprises the following steps: selecting an axial control point and a circumferential control point in the shaping range of a turbine end wall, determining non-adjustable control points at the channel inlet and the outlet circumferential position range, determining adjustable control points in one channel, selecting control points in other channels as follow-up control points, and mapping all non-adjustable control points and adjustable control points in the channel range selected as the adjustable control points into a rectangle; determining the amplitudes of all non-adjustable control points and adjustable control points mapped onto the rectangle, constructing a curved surface according to the amplitudes of all non-adjustable control points and adjustable control points, re-projecting the constructed curved surface into the shaping range of the turbine end wall, and obtaining a required full end wall periodic non-axisymmetric end wall shaping. The non-end shaping is more flexible in regulation and control, is helpful for improving the flow characteristics in front of the blade leading edge, improves the turbine end area thermal protection effect, and reduces the secondary flow loss.

Description

Technical Field

[0001] This invention belongs to the field of aero-gas turbine engine design technology, and particularly relates to a method and system for shaping a periodic non-axisymmetric endwall with full endwall. Background Technology

[0002] With the increasing demands for high performance and low emissions in aero-engines, turbine inlet temperatures are rising and becoming more uniformly distributed radially, resulting in increasingly higher thermal loads on the turbine endwalls. Furthermore, as the thrust-to-weight ratio increases, the turbine aerodynamic load also increases significantly, leading to more complex secondary flows and vortices in the turbine end region, thus causing significant aerodynamic losses. Modern turbine endwall design must consider the coordinated design of flow loss control and cooling enhancement. Therefore, turbine endwall cooling protection and flow control have become current research hotspots and challenges.

[0003] Non-axisymmetric endwall design has been extensively studied as a flow control method in the end region. The current mainstream non-axisymmetric turbine design method is the dual-control profile method. This method uses a half-cycle trigonometric function as the circumferential control line within the blade passage. A specific trigonometric function is constructed such that its half-cycle length is exactly equal to the blade pitch. The circumferential control line starts from the mid-arc line on one side of the blade passage and terminates at the mid-arc line on the other side. The peaks and troughs of the trigonometric function are located precisely on the mid-arc lines on both sides of the blade passage. Therefore, for a given axial position, only the amplitude on the mid-arc lines on both sides of the blade passage needs to be given to uniquely determine a corresponding trigonometric function. In the axial direction, a B-spline curve is used as the control line. By interpolating the amplitude of the circumferential control line, a uniquely determined axial control line can be obtained. Since the circumferential control line has different shaping amplitudes on the pressure side and suction side, the non-axisymmetric endwall surface obtained by shaping does not have periodicity in the circumferential direction. However, by giving the shaping amplitude of the leading and trailing edge positions as 0, it can be ensured that the parts of the endwall that cannot be spliced ​​by rotation are all located inside the blade. Therefore, the endwall shaping inside the blade passage can be achieved by cutting the endwall through the blade.

[0004] Current mainstream non-axisymmetric endwall design methods typically only allow for convex and concave shaping of the endwalls within the blade passage, making it difficult to shape the endwalls before the leading edge and after the trailing edge. Particularly in the leading edge region, the interaction between the leading-edge horseshoe vortex and the sealing-induced vortex leads to poor cooling in this area and increases secondary flow losses at the endwall. Furthermore, conventional non-axisymmetric endwall design methods usually employ pre-defined shape functions, resulting in limited design freedom and restrictive effectiveness in suppressing end-area losses. It is clear that traditional non-axisymmetric endwall design methods no longer meet the design requirements of current high aerodynamic and thermal load turbines. Summary of the Invention

[0005] To address the limitations of existing non-axisymmetric endwall design methods, which cannot perform non-axisymmetric design across the entire endwall area and have low design freedom, this invention provides a novel design method capable of non-axisymmetric design across the entire turbine endwall area. This method not only overcomes the limitations of traditional methods in performing non-axisymmetric endwall design across the entire endwall area, but also provides more flexible control over non-endwall design, more diverse design forms, and helps improve the flow characteristics in front of the blade leading edge. This, in turn, enhances the thermal protection effect of the turbine end area while reducing secondary flow losses.

[0006] To achieve the above objectives, in a first aspect, the present invention provides a method for shaping a periodic non-axisymmetric end wall with a full end wall, comprising the following steps: Step S1: Select axial control points and circumferential control points within the shape range of the turbine endwall. Determine non-adjustable control points near the inlet and outlet circumferential positions of the channel. Determine adjustable control points within one channel. Select control points in other channels as follow-up control points. Map all non-adjustable and adjustable control points within the channel range selected as adjustable control points into a rectangle. Step S2: Determine the amplitude of all non-adjustable and adjustable control points mapped onto the rectangle, and construct the surface based on the amplitude of all non-adjustable and adjustable control points; Step S3: Reproject the construction surface onto the appropriate shape range of the turbine endwall to obtain a periodic non-axisymmetric endwall shape that meets the requirements.

[0007] Furthermore, in S1, control points on four axial control lines near the channel inlet and outlet are selected as non-adjustable control points in the axial direction, and control points on five circumferential control lines, excluding those near the inlet and outlet, are selected as adjustable control points in the circumferential direction. The number of adjustable control points determines the degree of freedom of the non-end model; the remaining control points, excluding those shown on the circumferential control lines at the inlet and outlet, are follow-up control points.

[0008] Furthermore, the concave shape is larger near the suction surface of the blade, and there is an upward convex shape near the pressure surface of the blade at the leading edge of the blade passage, which extends outside the blade passage. There is also an upward convex shape near the trailing edge, with the shape extending outside the blade passage.

[0009] Furthermore, a comparative method is used to construct the surface, and the average total pressure loss coefficient of the surface obtained by constructing the surface using different methods is determined.

[0010] Furthermore, the NURBS method is used to construct the surface.

[0011] Furthermore, in S1, a point-to-point and line-to-line mapping method is adopted, where control points at corresponding positions are mapped to corresponding positions on the rectangle, and the arcs formed by connecting the control points on the original end wall correspond to the straight lines of the rectangle, with no change in the relative positions between the points.

[0012] Secondly, the present invention provides a modeling system for a periodic non-axisymmetric end wall with a full end wall, including a mapping module, a surface construction module, and a reprojection module; The mapping module is used to select axial and circumferential control points within the shape range of the turbine endwall, determine non-adjustable control points near the inlet and outlet circumferential positions of the channel, determine adjustable control points within one channel, select control points in other channels as follow-up control points, and map all non-adjustable and adjustable control points within the channel range selected as adjustable control points into a rectangle. The surface construction module is used to determine the amplitude of all non-adjustable and adjustable control points mapped onto the rectangle, and to construct the surface based on the amplitude of all non-adjustable and adjustable control points. The reprojection module is used to reproject the construction surface onto the appropriate shape range of the turbine endwall to obtain a periodic non-axisymmetric endwall shape that meets the requirements.

[0013] Thirdly, the present invention also provides a computer device, including a processor and a memory, wherein the memory is used to store a computer executable program, the processor reads part or all of the computer executable program from the memory and executes it, and the processor can realize the above-mentioned modeling method for periodic non-axisymmetric end walls of the entire end wall when executing part or all of the executable program.

[0014] Alternatively, a computer-readable storage medium may be provided, which stores a computer program that, when executed by a processor, enables the above-described method for modeling periodic non-axisymmetric endwalls with full endwalls.

[0015] Compared with the prior art, the present invention has at least the following beneficial effects: Based on NURBS surfaces, the present invention defines three types of control points: a non-adjustable control point with a fixed amplitude to ensure a smooth transition between the non-axisymmetric endwall shape and the front and rear endwalls of the blade channel; an adjustable control point whose amplitude can be freely adjusted within a given range to control and adjust the shape of the NURBS surface; and a follow-up control point whose amplitude is not zero but cannot be freely adjusted, and whose amplitude is determined by the adjustable control point. These control points are mainly used to ensure the periodicity of the non-axisymmetric endwall shape in the circumferential direction. Through the cooperation of the three control points, the periodicity of the non-axisymmetric endwall geometry in the circumferential direction is ensured. The non-axisymmetric endwall shape generated by this method can also achieve a smooth transition in the circumferential direction. This makes it possible to extend the endwall shape generation from the traditional dual-control profile method, which can only be generated within the blade channel, to the entire endwall range, thus achieving stronger end-area flow control capabilities. Attached Figure Description

[0016] Figure 1The diagram illustrates the distribution of NURBS surface control lines and control points for controlling the amplitude of the non-axisymmetric endwall in accordance with the present invention. Figure 2 To pass Figure 1 The geometric profile of the NURBS surface of the turbine endwall obtained by the non-axisymmetric endwall modeling method shown in the figure. Figure 3 To pass Figure 1 The amplitude distribution diagram of the NURBS three-dimensional surface of the end wall obtained by the non-axisymmetric end wall modeling method of the turbine is shown. Figure 4 This is a schematic diagram of the actual endwall and blade geometry obtained after adopting the full-endwall periodic non-axisymmetric endwall modeling method; Figure 5 This is a schematic diagram comparing the total pressure loss after non-end wall modeling using the full-end-wall periodic non-axisymmetric end-wall modeling method with the traditional dual-control profile method and spline surface method; Figure 6 This is a schematic diagram showing the difference in velocity vector between the non-axisymmetric endwall design at 10% blade height section of the turbine blade and the reference design after adopting the full-endwall periodic non-axisymmetric endwall modeling method. Detailed Implementation

[0017] To more intuitively demonstrate the objectives, technical solutions, and advantages of the present invention compared to traditional non-axisymmetric end-wall shaping methods, the present invention will be further described in detail below with reference to a specific embodiment and the accompanying drawings.

[0018] However, it is worth noting that the embodiments described below are only introductions to some implementations of this application, not all implementations. Similarly, the accompanying drawings are merely illustrative in nature and are intended to explain this application, not to limit it. All other implementations obtained by those skilled in the art within the scope of this application without inventive effort are within the protection scope of this application.

[0019] All terms used herein (including technical and scientific terms) have the meanings commonly understood by one of ordinary skill in the art, unless otherwise defined. It should be noted that the terms used herein should be interpreted in a manner consistent with the context of this specification, and not in an idealized or overly rigid manner.

[0020] According to some embodiments of the present invention, the turbine design includes an endwall profile and a plurality of turbine blades uniformly arranged circumferentially on the endwall profile. The space between two adjacent turbine blades is called a blade channel. One side of the blade channel is the pressure surface (PS) of one turbine blade, and the other side of the channel is the suction surface (SS) of another turbine blade.

[0021] According to some embodiments of the present invention, under certain operating conditions, when numerically calculating the turbine blade flow channel, the flow conditions near the endwall region of the blade channel and the total pressure loss at the outlet are obtained, along with the total pressure loss coefficient. The calculations include:

[0022] In the formula: p 0in The mainstream imported total pressure / Pa, p 0local The local total pressure is given in Pa. p in The mainstream imported static pressure is 100 Pa.

[0023] According to one embodiment of the present invention, a method for shaping a periodic non-axisymmetric end wall with full end walls is provided, comprising the following steps: Step S1: Within the styling range of the turbine endwall, select an appropriate number and location of axial and circumferential control points. The selection of control points should balance precision and economy, ensuring full coverage of the entire endwall design space to guarantee the freedom and accuracy of the design. Simultaneously, the increased complexity resulting from adding more control points should be assessed. Determine non-adjustable control points at suitable circumferential locations near the inlet and outlet of the turbine. Figure 1 As shown by the black dot, the adjustable control point is then determined within a channel, as follows. Figure 1 As shown by the hollow control point, control points in other channels are automatically selected as follow-up control points. All non-adjustable and adjustable control points within the selected adjustable control point range are mapped into a rectangle. The mapping method uses a point-to-point, line-to-line mapping approach; that is, control points at corresponding positions are mapped to corresponding positions on the rectangle, and the arcs formed by connecting the control points on the original end walls correspond to the straight lines of the rectangle, ensuring that the relative positions between the points do not change.

[0024] Step S2: Determine the magnitudes of the control points mapped onto the rectangle using a suitable method and construct the NURBS surface based on the magnitudes of each control point. A p-th degree NURBS curve is defined as shown in Equation 1: (1) In the formula: u is the independent variable of the curve, C is the curve amplitude corresponding to the position of u, Pi is the control point, w is the weight factor, and N is the p-th order B-spline basis function defined on the node vector U, as shown in Equations 2 and 3: (2) (3) U is a node vector, which is a monotonically non-decreasing sequence of real numbers, and its expression is shown in the following equation.

[0025] (4) Step S3: Reproject the NURBS surface generated based on the control points mapped into the rectangle back into the appropriate shape range of the turbine endwall to obtain a full-endwall periodic non-axisymmetric endwall shape that meets the requirements.

[0026] In this embodiment, by Figure 1 As shown, control points on four axial control lines near the inlet and outlet of the channel were selected as non-adjustable control points, which ensured that the non-axisymmetric endwall shape could smoothly transition at the front and rear endwalls of the blade channel.

[0027] In this embodiment, as Figure 1 As shown, control points numbered 1 to 5 on the circumferential control lines, excluding those near the inlet and outlet, were selected as adjustable control points. The number of adjustable control points determines the degree of freedom of the non-end model.

[0028] In this embodiment, as Figure 1 As shown, the remaining control points, except for the circumferential control lines near the inlet and outlet, such as those shown in 1'~5', are follow-up control points. The follow-up control points ensure that the non-end shape can smoothly transition in the circumferential direction, so that the end wall shape can be extended from the traditional blade channel interior to the full end wall shape.

[0029] According to some embodiments of the present invention, when the blade passage is non-axisymmetrically shaped, the range of its shaping amplitude variation generally does not exceed 10% of the blade height.

[0030] Figure 3 This is a schematic diagram of the end-wall design obtained using a full-end-wall periodic non-axisymmetric end-wall design method.

[0031] Figure 4 It is a schematic diagram of a three-dimensional endwall model obtained by using a full-endwall periodic non-axisymmetric endwall modeling method.

[0032] According to some embodiments of the present invention, such as Figure 3 and Figure 4 As shown, its endwall design is not limited to the inside of the blade channel, but can also be made outside the blade channel. There is also a large-scale concave design in the middle of the blade channel, but the concave range is larger near the suction surface of the blade. There is a large-scale convex design on the leading edge of the blade channel near the pressure surface of the blade, and the convex design extends outside the blade channel. At the same time, there is a small-scale convex design near the trailing edge, and the design range also extends outside the blade channel.

[0033] To demonstrate the advantages of the full-end-wall periodic non-axisymmetric end-wall design method, non-axisymmetric end-wall optimization was carried out for the GE-E3 airfoil and channel. Experiments and numerical simulations were conducted to compare the reference unoptimized model, the dual-control profile method optimization model, the spline surface method optimization model, and the full-end-wall periodic method optimization model.

[0034] Figure 5 This is a comparison of the circumferential average distribution of the total pressure loss coefficient at the outlet along the blade height for the four models tested.

[0035] exist Figure 6 In the diagram, Ref represents the reference design, 2Curve represents the dual-control profile method, Surf represents the spline surface method, and NURBS represents the full end-wall modeling method based on NURBS surfaces. Combined with... Figure 5 As shown in Table 1, the non-axisymmetric endwall design significantly shifts the lower channel vortex position upwards and significantly reduces the total pressure loss coefficient at the lower channel vortex position. The non-axisymmetric endwall design generated by the NURBS method has the largest reduction in lower channel vortex position loss, followed by the non-axisymmetric endwall generated by the spline surface method, while the endwall design generated by the dual-control profile method has the smallest reduction. The non-axisymmetric endwall design also thickens the boundary layer near the lower endwall, increasing the boundary layer loss near the lower endwall. The non-axisymmetric endwall design generated by the spline surface method has the largest increase in lower endwall boundary layer loss, followed by the endwall design generated by the NURBS method, while the non-axisymmetric endwall generated by the dual-control profile method has the smallest increase. Furthermore, the wake loss and upper channel vortex loss also differ among different models. The dual-control endwall design method can reduce the area-average total pressure loss coefficient at the cascade exit section by 7.8%, while the spline surface endwall design method can reduce the area-average total pressure loss coefficient by 11.4%. The full endwall design method based on NURBS surfaces provides the highest improvement in aerodynamic performance, with its area-average total pressure loss coefficient reduced by 12.4% relative to the reference design.

[0036] Table 1 Average Total Pressure Loss Coefficient at the Outlet Section

[0037] Figure 6 Comparison of velocity difference streamline distribution at 10% blade height section in a numerical simulation model using a full-endwall periodic non-end-wall modeling method.

[0038] The velocity difference vector is the difference between the velocity vector of the non-axisymmetric endwall design on this cross section and the velocity vector of the reference design on this cross section, derived from... Figure 6It can be seen that for the full-endwall periodic non-end-shaped model, the velocity difference vector in the middle of the blade passage points to the blade pressure surface side, indicating that the non-axisymmetric endwall shaping suppresses the transverse flow in the blade passage. Furthermore, since the range of the non-axisymmetric endwall shaping is extended to outside the blade passage, the velocity difference changes significantly before and after the blade passage.

[0039] The present invention can also provide a periodic non-axisymmetric end wall with full end wall, which is designed using the above-mentioned modeling method for a periodic non-axisymmetric end wall with full end wall.

[0040] In summary, this invention fully considers the latest design requirements for non-axisymmetric endwalls in the turbine end region. This invention provides a method for shaping a periodic non-axisymmetric endwall across the entire endwall, comprising the following steps: Within the turbine endwall's design range, axial and circumferential control points are selected. Non-adjustable control points are determined near the inlet and circumferential outlet of the passageway. Adjustable control points are determined within one passageway, and control points in other passageways are selected as follow-up control points. All non-adjustable and adjustable control points within the selected adjustable control point range are mapped onto a rectangle. The amplitudes of all non-adjustable and adjustable control points mapped onto the rectangle are determined, and a surface is constructed based on these amplitudes. The constructed surface is then reprojected onto the turbine endwall's intended design range, resulting in a compliant, periodic, non-axisymmetric endwall design. This method, based on periodic NURBS surfaces, is a comprehensive non-axisymmetric endwall design approach that can perform smooth non-axisymmetric design on the entire endwall region, including the interior of the blade passageway and the area before the leading edge and after the trailing edge. The non-axisymmetric endwalls designed using this method offer high design freedom and a large design space, playing a crucial role in endwall loss suppression and cooling enhancement.

[0041] Example 2: Based on the technical concept of the method, the present invention provides a modeling system for a periodic non-axisymmetric end wall with full end wall, including a mapping module, a surface construction module, and a reprojection module; The mapping module is used to select axial and circumferential control points within the shape range of the turbine endwall, determine non-adjustable control points near the inlet and outlet circumferential positions of the channel, determine adjustable control points within one channel, select control points in other channels as follow-up control points, and map all non-adjustable and adjustable control points within the channel range selected as adjustable control points into a rectangle. The surface construction module is used to determine the amplitude of all non-adjustable and adjustable control points mapped onto the rectangle, and to construct the surface based on the amplitude of all non-adjustable and adjustable control points. The reprojection module is used to reproject the construction surface onto the appropriate shape range of the turbine endwall to obtain a periodic non-axisymmetric endwall shape that meets the requirements.

[0042] On the other hand, the present invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, enables the modeling method for periodic non-axisymmetric endwalls with full endwalls as described in the present invention.

[0043] The present invention can also provide a computer device, including a processor and a memory, wherein the memory is used to store a computer executable program, the processor reads the computer executable program from the memory and executes it, and the processor can realize the modeling method of the periodic non-axisymmetric end wall of the whole end wall described in the present invention when executing the computer executable program.

[0044] The computer device may be a laptop, a desktop computer, or a workstation.

[0045] The processor can be a central processing unit (CPU), a graphics processing unit (GPU), a digital signal processor (DSP), an application-specific integrated circuit (ASIC), or an off-the-shelf programmable gate array (FPGA).

[0046] The memory described in this invention can be an internal storage unit of a laptop, desktop computer, or workstation, such as memory or hard disk; or it can be an external storage unit, such as a portable hard disk or flash memory card.

[0047] Computer-readable storage media can include computer storage media and communication media. Computer storage media includes volatile and non-volatile, removable and non-removable media implemented using any method or technology for storing information such as computer-readable instructions, data structures, program modules, or other data. Computer-readable storage media can include: read-only memory (ROM), random access memory (RAM), solid-state drives (SSDs), or optical discs, etc. Random access memory can include resistive random access memory (ReRAM) and dynamic random access memory (DRAM).

[0048] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings. It should be noted that implementations not illustrated or described in the drawings or the main text of the specification are forms known to those skilled in the art and are not described in detail. Furthermore, the definitions of the components described above are not limited to the various specific structures, shapes, or methods mentioned in the embodiments, and those skilled in the art can easily modify or substitute them.

Claims

1. A method for shaping a periodic, non-axisymmetric end wall, characterized in that, Includes the following steps: Step S1: Select axial control points and circumferential control points within the shape range of the turbine endwall. Determine non-adjustable control points near the inlet and outlet circumferential positions of the channel. Determine adjustable control points within one channel. Select control points in other channels as follow-up control points. Map all non-adjustable and adjustable control points within the channel range selected as adjustable control points into a rectangle. Step S2: Determine the amplitude of all non-adjustable and adjustable control points mapped onto the rectangle, and construct the surface based on the amplitude of all non-adjustable and adjustable control points; Step S3: Reproject the construction surface onto the appropriate shape range of the turbine endwall to obtain a periodic non-axisymmetric endwall shape that meets the requirements.

2. The method for shaping a periodic non-axisymmetric end wall according to claim 1, characterized in that, In S1, control points on four axial control lines near the inlet and outlet of the channel are selected as non-adjustable control points in the axial direction, and control points on five circumferential control lines, excluding those near the inlet and outlet, are selected as adjustable control points in the circumferential direction. The number of adjustable control points determines the degree of freedom of the non-end model; the remaining control points, excluding those shown on the circumferential control lines at the inlet and outlet, are follow-up control points.

3. The method for shaping a periodic, non-axisymmetric end wall according to claim 1, characterized in that, The concave shape is greater near the suction surface of the blade, and there is an upward convex shape at the leading edge of the blade passage near the pressure surface of the blade, which extends outside the blade passage. There is also an upward convex shape near the trailing edge, with the shape extending outside the blade passage.

4. The method for shaping a periodic non-axisymmetric end wall according to claim 1, characterized in that, The surface is constructed using a comparative method, and the average total pressure loss coefficient of the surface is determined based on the different methods used to construct the surface.

5. The method for shaping a periodic non-axisymmetric end wall according to claim 4, characterized in that, The NURBS method is used to construct the surface.

6. The method for shaping a periodic non-axisymmetric end wall according to claim 1, characterized in that, In S1, a point-to-point and line-to-line mapping method is adopted. The control points at corresponding positions are mapped to the corresponding positions of the rectangle. The arcs formed by connecting the control points on the original end walls correspond to the straight lines of the rectangle. The relative positions between the points do not change.

7. A periodic non-axisymmetric end wall with a full end wall, characterized in that, The design was based on the modeling method of the periodic non-axisymmetric end wall of the full end wall as described in any one of claims 1-6.

8. A modeling system for a periodic, non-axisymmetric endwall, characterized in that, This includes a mapping module, a surface construction module, and a reprojection module; The mapping module is used to select axial and circumferential control points within the shape range of the turbine endwall, determine non-adjustable control points near the inlet and outlet circumferential positions of the channel, determine adjustable control points within one channel, select control points in other channels as follow-up control points, and map all non-adjustable and adjustable control points within the channel range selected as adjustable control points into a rectangle. The surface construction module is used to determine the amplitude of all non-adjustable and adjustable control points mapped onto the rectangle, and to construct the surface based on the amplitude of all non-adjustable and adjustable control points. The reprojection module is used to reproject the construction surface onto the appropriate shape range of the turbine endwall to obtain a periodic non-axisymmetric endwall shape that meets the requirements.

9. A computer device, characterized in that, It includes a processor and a memory, the memory being used to store a computer-executable program, the processor reading part or all of the computer-executable program from the memory and executing it, and the processor executing part or all of the computed executable program is able to implement the modeling method of the periodic non-axisymmetric endwall of all endwalls as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, A computer-readable storage medium stores a computer program that, when executed by a processor, enables the modeling method for a periodic non-axisymmetric endwall as described in any one of claims 1-7.

Images