Supercritical carbon dioxide centrifugal compressor axial symmetry end wall modeling method and device, product, equipment and storage medium

Abstract

The invention provides a supercritical carbon dioxide centrifugal compressor axial symmetry end wall modeling method and device, a product, equipment and a storage medium, relates to the technical field of supercritical carbon dioxide centrifugal compressor stability extension, achieves the purposes that implementation is easy, high efficiency is achieved, and the stability extension performance of a supercritical carbon dioxide centrifugal compressor is improved. The method comprises the following steps of: dividing an area on a turbine casing of the centrifugal compressor, which is about to be subjected to axial symmetry end wall modeling, into N sub-areas along the axial direction; n > = 2; an axisymmetric end wall modeling curve control function is constructed for each sub-region; one of the undetermined parameters of the function is the maximum modeling height delta Hmax; for each sub-region, determining delta Hmax meeting the profile gradient requirement of the curve; other undetermined parameters except the delta Hmax are determined; the delta Hmax corresponding to the N sub-regions is optimized; and verifying the centrifugal compressor before and after molding.

Description

Technical Field

[0001] The present application relates to the technical field of supercritical carbon dioxide centrifugal compressor stabilization, and in particular to a method, device, product, equipment and storage medium for shaping the axisymmetric end wall of a supercritical carbon dioxide centrifugal compressor. Background Art

[0002] As a key equipment for compressing and transporting gas in industrial production, the operating status of centrifugal compressors is easily affected by many factors, such as gas flow, inlet pressure, temperature changes, etc. Under certain working conditions, centrifugal compressors may experience unstable phenomena such as rotational stall, which seriously affects the performance of the centrifugal compressors.

[0003] Centrifugal compressor stabilization technology refers to a series of technical means to improve the stable operating range of centrifugal compressors and avoid unstable phenomena such as rotational stall. According to different technical implementation methods, these stabilization technologies can be divided into two categories: active control and passive control. These two types of technologies have their own characteristics in achieving centrifugal compressor stabilization, and are also accompanied by their own application challenges, which are described in detail as follows: 1. Active Control The core of active control technology is to detect the flow state inside the centrifugal compressor in real time by introducing external equipment, accurately locate the stall source, and once the stall source is detected, induce a disturbance wave in the opposite direction of the stall disturbance to suppress the stall phenomenon. However, although active control has excellent stability expansion performance in theory, its actual operation process is complicated and the process details are cumbersome. In addition, when integrating external equipment into a supercritical carbon dioxide centrifugal compressor, due to the compact structure of the centrifugal compressor, it faces greater space layout and technical implementation difficulties.

[0004] When the temperature and pressure of carbon dioxide exceed its critical point (critical temperature 304.13K, i.e. 31.0℃; critical pressure 7.38MPa), it enters a supercritical state. A centrifugal compressor that uses carbon dioxide in a supercritical state as a working medium is called a supercritical carbon dioxide centrifugal compressor.

[0005] 2. Passive Control Compared with active control, passive control technology is more direct and easy to implement. It does not rely on external equipment, but achieves the purpose of stability by adjusting the internal geometry or flow characteristics of the centrifugal compressor. Common passive control technologies include casing treatment, end wall shaping, etc.

[0006] Among them, the casing treatment technology is to change the flow state inside the centrifugal compressor by making grooves, slits or other special structures on the casing wall of the centrifugal compressor, thereby significantly improving its stable working range. However, although casing treatment can effectively expand stability, it changes the optimal airflow path originally designed, so it will cause a decrease in efficiency under the designed working conditions.

[0007] The endwall shaping technology, especially the axisymmetric endwall shaping technology, endows the centrifugal compressor with a certain ability to expand the stable operating range while maintaining the efficiency under the design conditions basically unchanged. Specifically, the axisymmetric endwall shaping technology refers to forming an axisymmetric concave or convex structure at the casing or hub of the centrifugal compressor to change the tip passage area within the shaping region, thereby achieving precise control of the internal flow field, effectively suppressing the tip leakage flow, reducing the possibility of airflow separation and vortex formation, and further suppressing the occurrence of rotating stall. However, in a supercritical carbon dioxide centrifugal compressor, the "size effect" brought about by its compactness results in a relatively large tip clearance in the centrifugal impeller. This relatively large tip clearance will exacerbate the tip leakage flow within the centrifugal impeller, making the characteristics of the internal flow field more complex and causing the centrifugal compressor to be more prone to rotating stall. In the design process of the existing axisymmetric endwall shaping technology, the complex flow characteristics of the internal flow field are not fully considered, and it is only applicable to the scenario of a small tip clearance. When facing the scenario of a large tip clearance in a supercritical carbon dioxide centrifugal compressor, this technology is difficult to achieve refined control of the internal flow field, resulting in poor suppression effect of the tip leakage flow and severely restricting the improvement of the stable operating range expansion performance of the centrifugal compressor.

[0008] In summary, how to develop a stable operating range expansion technology that is easy to implement, efficient, and suitable for supercritical carbon dioxide centrifugal compressors has become an urgent problem to be solved in this field. Summary of the Invention

[0009] In view of the above problems, the present application provides an axisymmetric endwall shaping method, device, product, equipment, and storage medium for a supercritical carbon dioxide centrifugal compressor, taking into account both easy implementation and high efficiency, and improving the stable operating range expansion performance of the supercritical carbon dioxide centrifugal compressor. The specific solutions are as follows: The first aspect of the present application provides an axisymmetric endwall shaping method for a supercritical carbon dioxide centrifugal compressor, including: Dividing the region on the impeller casing of the supercritical carbon dioxide centrifugal compressor where axisymmetric endwall shaping is to be performed into N sub-regions along the axial direction; N≥2; Constructing an axisymmetric endwall shaping curve control function for each sub-region respectively; the function is used to describe the shape of the endwall shaping curve formed after performing axisymmetric endwall shaping on the sub-region, the curve is in the form of an equal-curvature circular arc, and the starting and ending points of the sub-region are the starting and ending points of the curve; the function contains multiple undetermined parameters, and one of the undetermined parameters is the maximum shaping height ΔH max ; For each sub-region, determining the absolute value |ΔH| of the maximum shaping height that satisfies the profile gradient requirement of the curve max|, the profile gradient requirement is set with the goal that the difference between the tip clearance at any point on the curve and the original tip clearance is within the allowable error range; and, according to the start and end point coordinates of the sub-region, determine the other undetermined parameters in the function except the maximum shaping height ΔH max other than; Taking the improvement of the isentropic efficiency η and the stall margin improvement ΔSMI as the optimization goals, on the basis of ensuring that the absolute value |ΔH max | meets the profile gradient condition, through experimental design, optimize the maximum shaping height ΔH corresponding to N sub-regions max to obtain N optimized maximum shaping heights ΔH max , and thus determine N functions with all parameters determined; Verify whether the isentropic efficiency η and the stall margin improvement ΔSMI are both within the target range after performing axisymmetric endwall shaping on the turbine casing according to the N functions; if not, adjust N and then execute the above steps again until both the isentropic efficiency η and the stall margin improvement ΔSMI are within the target range.

[0010] In one possible implementation, the function is: f(z)=ΔH max sin(az + b)+r(z); where z is the coordinate of the curve on the axial coordinate axis; f(z) is the radius of the curve at the axial coordinate value of z; r(z) is the radius of the original turbine casing at the axial coordinate value of z; a and b are both constants; the undetermined parameters in the function include ΔH max , a and b.

[0011] In one possible implementation, determining the absolute value |ΔH max | of the maximum shaping height that meets the profile gradient requirement of the curve includes: Determine a |ΔH max / min(BO, CO) < 0.5 that meets the condition, as the absolute value |ΔH max | of the maximum shaping height that meets the profile gradient requirement of the curve; max |; Point B and point C are the start and end points of the curve respectively, and point O is the intersection point of the radial extension line of the maximum shaping height point and the original turbine casing surface; BO represents the distance between point B and point O, and CO represents the distance between point C and point O.

[0012] In one possible implementation, the verification of whether the isentropic efficiency η and the stall margin improvement ΔSMI are both within the target range after performing axisymmetric endwall shaping on the turbine casing according to the N functions includes: Through computer simulation technology, the axial symmetric end wall of the turbine casing is modeled according to N of the said functions, and the supercritical carbon dioxide centrifugal compressor after modeling is numerically simulated and analyzed to determine whether both the isentropic efficiency η and the improvement amount of stall margin ΔSMI are within the target range.

[0013] In a possible implementation, after numerically simulating and analyzing the supercritical carbon dioxide centrifugal compressor after modeling and determining that both the isentropic efficiency η and the improvement amount of stall margin ΔSMI are within the target range, it further includes: After manufacturing the supercritical carbon dioxide centrifugal compressor according to N of the said functions, the actual operating parameters of the supercritical carbon dioxide centrifugal compressor are collected and tested, and compared and analyzed with the actual operating parameters of the original supercritical carbon dioxide centrifugal compressor to determine whether both the isentropic efficiency η and the improvement amount of stall margin ΔSMI are within the target range.

[0014] In a possible implementation, before dividing the area on the turbine casing of the supercritical carbon dioxide centrifugal compressor where axial symmetric end wall modeling is to be performed into N sub-areas along the axial direction, it further includes: Through computer simulation technology, the operating characteristics of the supercritical carbon dioxide centrifugal compressor under different working conditions are numerically simulated and analyzed to determine the near-stall point of the supercritical carbon dioxide centrifugal compressor; according to the operating characteristics of the supercritical carbon dioxide centrifugal compressor at the near-stall point, an entropy production rate cloud map of any axial height section of the tip flow field of the supercritical carbon dioxide centrifugal compressor is generated, and the entropy production rate cloud map is output; the entropy production rate cloud map is one of the bases for determining the area where the axial symmetric end wall modeling is to be performed.

[0015] The second aspect of the present application provides an axial symmetric end wall modeling device for a supercritical carbon dioxide centrifugal compressor, including: An area division unit for dividing the area on the turbine casing of the supercritical carbon dioxide centrifugal compressor where axial symmetric end wall modeling is to be performed into N sub-areas along the axial direction; N≥2; A function construction unit for respectively constructing an axial symmetric end wall modeling curve control function for each sub-area; the function is used to describe the shape of the end wall modeling curve formed after performing axial symmetric end wall modeling on the sub-area, the curve is in the form of an equal-curvature circular arc and the start and end points of the sub-area are the start and end points of the curve; the function contains multiple undetermined parameters, and one of the undetermined parameters is the maximum modeling height ΔH max ; A parameter determination unit for determining, for each sub-area, the absolute value of the maximum modeling height |ΔH| that meets the profile gradient requirement of the curve max|, the profile gradient requirement is set with the goal that the difference between the tip clearance at any point on the curve and the original tip clearance is within the allowable error range; and, according to the starting and ending point coordinates of the sub-region, determine the other undetermined parameters in the function except the maximum profiling height ΔH max other than; The parameter optimization unit is used to take improving the isentropic efficiency η and the improvement amount of stall margin ΔSMI as the optimization goal. On the basis of ensuring that the absolute value of the maximum profiling height |ΔH max | meets the profile gradient condition, optimize the maximum profiling height ΔH corresponding to N sub-regions through experimental design max to obtain N optimized maximum profiling heights ΔH max , thereby determining N functions with all parameters determined; The verification and iteration unit is used to verify whether the isentropic efficiency η and the improvement amount of stall margin ΔSMI are both within the target range after performing axisymmetric endwall profiling on the turbomachine casing according to the N functions; if not, adjust N and then execute the above steps again until the isentropic efficiency η and the improvement amount of stall margin ΔSMI are both within the target range.

[0016] The third aspect of the present application provides a computer program product, including computer-readable instructions, which, when running on an electronic device, enable the electronic device to implement the axisymmetric endwall profiling method of a supercritical carbon dioxide centrifugal compressor according to the first aspect or any implementation manner of the first aspect.

[0017] The fourth aspect of the present application provides an electronic device, including at least one processor and a memory connected to the processor, wherein: The memory is used to store a computer program; The processor is used to execute the computer program so that the electronic device can implement the axisymmetric endwall profiling method of a supercritical carbon dioxide centrifugal compressor according to the first aspect or any implementation manner of the first aspect.

[0018] The fifth aspect of the present application provides a computer storage medium, which carries one or more computer programs, and when the one or more computer programs are executed by an electronic device, the electronic device can implement the axisymmetric endwall profiling method of a supercritical carbon dioxide centrifugal compressor according to the first aspect or any implementation manner of the first aspect.

[0019] With the above technical solution, the present application innovatively combines the axisymmetric endwall shaping technology with segmented shaping, and conducts a stability enhancement design for the impeller casing of a supercritical carbon dioxide centrifugal compressor. In the scenario of a large tip clearance in a supercritical carbon dioxide centrifugal compressor, this design not only gives full play to the advantages of easy implementation and high efficiency of axisymmetric endwall shaping, but also precisely regulates the flow characteristics of the tip flow field at different axial positions through segmented shaping, ultimately achieving refined control of the internal flow field, effectively suppressing tip leakage flow, significantly improving the stall margin of the supercritical carbon dioxide centrifugal compressor, and thus greatly enhancing its stability enhancement performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] In combination with the accompanying drawings and with reference to the following specific embodiments, the above and other features, advantages, and aspects of the various embodiments of the present disclosure will become more apparent. Throughout the drawings, the same or similar reference numerals denote the same or similar elements. It should be understood that the drawings are schematic, and the original elements and components are not necessarily drawn to scale.

[0021] Figure 1 It is a flowchart of a method for shaping the axisymmetric endwall of a supercritical carbon dioxide centrifugal compressor provided by the present application; Figure 2 It is a schematic structural diagram of an impeller and a diffuser of a supercritical carbon dioxide centrifugal compressor provided by the present application; Figure 3 is Figure 2 a partially enlarged view of the radial cross-section at location A of the impeller in Figure 4 It is a comparison diagram of the impeller casing before and after shaping provided by the present application; among them, Figure 4 (a) is a radial cross-sectional view of the impeller casing before shaping; Figure 4 (b) is a radial cross-sectional view of the impeller casing after shaping; Figure 5 It is a schematic structural diagram of a device for shaping the axisymmetric endwall of a supercritical carbon dioxide centrifugal compressor provided by the present application. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0022] The embodiments of the present application provide a method, device, product, equipment, and storage medium for shaping the axisymmetric endwall of a supercritical carbon dioxide centrifugal compressor, which innovatively combines the axisymmetric endwall shaping technology with segmented shaping, and conducts a stability enhancement design for the impeller casing of a supercritical carbon dioxide centrifugal compressor. In the scenario of a large tip clearance in a supercritical carbon dioxide centrifugal compressor, this design not only gives full play to the advantages of easy implementation and high efficiency of axisymmetric endwall shaping, but also precisely regulates the flow characteristics of the tip flow field at different axial positions through segmented shaping, ultimately achieving refined control of the internal flow field, effectively suppressing tip leakage flow, significantly improving the stall margin of the supercritical carbon dioxide centrifugal compressor, and thus greatly enhancing its stability enhancement performance.

[0023] The following will, in conjunction with the accompanying drawings, first elaborate on an axisymmetric endwall shaping method for a supercritical carbon dioxide centrifugal compressor provided by an embodiment of the present application. Those of ordinary skill in the art will understand that with the development of technology and the emergence of new scenarios, the technical solutions provided by the embodiments of the present application are equally applicable to similar technical problems.

[0024] The terms "first", "second", etc. in the specification, claims, and the above-mentioned accompanying drawings of the present application are used to distinguish similar objects and do not necessarily describe a specific order or sequence. It should be understood that such terms can be interchanged under appropriate circumstances, which is only a way of distinguishing objects with the same attributes when describing the embodiments of the present application. In addition, the terms "include" and "have" and any variations thereof are intended to cover non-exclusive inclusion, so that a process, method, system, product, or device including a series of units does not have to be limited to those units, but may include other units not clearly listed or inherent to these process, method, product, or device.

[0025] In addition, for ease of understanding, the following are the definitions of the names of each direction: Axial direction: along the axis direction of the cylinder; Radial direction: along the radius direction of the cross-section (perpendicular to the axis); Circumferential direction: around the axis direction of the cylinder (perpendicular to the axis and perpendicular to the cross-section radius at the same time).

[0026] See Figure 1 , an axisymmetric endwall shaping method for a supercritical carbon dioxide centrifugal compressor proposed by an embodiment of the present application includes: Step S01: Divide the area on the impeller casing of the supercritical carbon dioxide centrifugal compressor where axisymmetric endwall shaping is to be performed into N sub-areas along the axial direction, where N≥2, and then proceed to step S02.

[0027] Specifically, as Figure 2Schematic diagram of the impeller and diffuser structure of the shown supercritical carbon dioxide centrifugal compressor. Inside the supercritical carbon dioxide centrifugal compressor, gas is introduced from the impeller inlet 1, and obtains kinetic energy under the action of the centrifugal force generated by the high-speed rotation of the impeller 2; after the gas flows out of the impeller 2, it enters the diffuser 3, and the flow passage of the diffuser 3 gradually expands, converting the kinetic energy of the gas into pressure energy, and finally discharging from the diffuser outlet 4. The turbine casing 5 adopts an axisymmetric end wall design, which forms a closed and symmetric flow passage boundary around the impeller 2. By uniformly restricting the air flow, the circumferential flow non-uniformity and energy loss are reduced, ensuring the stable transmission of the gas; the hub 6 is the core support structure of the impeller 2 assembly (such as blades). On the one hand, it provides a stable installation and rotation basis for the impeller 2. On the other hand, through a reasonable profile design, the internal flow passage contour of the impeller 2 is optimized, and in cooperation with the turbine casing 5, it guides the gas to maintain a good flow pattern during the centrifugal acceleration process, reducing separation and eddy current losses, and improving the overall aerodynamic performance and operation stability of the machine.

[0028] The axisymmetric end wall shaping technology is an easy-to-implement and high-efficiency centrifugal compressor stability-enhancing technology. After determining the area on the turbine casing suitable for axisymmetric end wall shaping based on the rotating stall mechanism of the supercritical carbon dioxide centrifugal compressor, the embodiment of the present application divides this area into N (N≥2) sub-areas along the axial direction, so as to carry out refined shaping design and performance optimization for the flow field characteristics of each sub-area, better adapt to the size characteristics of compact models, and improve the stability-enhancing performance.

[0029] The larger the value of N, the finer the axisymmetric end wall shaping of the turbine casing, and more precise flow field control can be achieved. However, an increase in the value of N also means a higher complexity of the shaping design and optimization. Therefore, the value of N needs to be comprehensively weighed (for example, N is taken as 5 to 8), which can not only meet the precise control of the complex flow field, but also achieve a good balance between design efficiency and stability-enhancing effect.

[0030] Step S02: Construct an axisymmetric end wall shaping curve control function for each sub-area respectively; the function is used to describe the shape of the end wall shaping curve formed after the axisymmetric end wall shaping of the sub-area. The curve is in the form of an equal-curvature circular arc, and the start and end points of the sub-area are the start and end points of the curve; the function contains multiple undetermined parameters, and one of the undetermined parameters is the maximum shaping height ΔH max 。

[0031] Specifically, in the embodiments of the present application, for each sub-region, an axisymmetric end-wall profile curve control function is respectively constructed. The axisymmetric end-wall profile curve control function is a mathematical expression used to describe the shape of the end-wall profile curve formed after performing axisymmetric end-wall profiling on the sub-region, and can accurately determine the geometric features of the end-wall profile curve at different positions. By adjusting the parameters in the axisymmetric end-wall profile curve control function, geometric attributes such as the curvature, slope, and height of the end-wall profile curve can be flexibly changed, realizing the refined design of the end-wall profile.

[0032] In the embodiments of the present application, the end-wall profile curve of the sub-region is designed as a curve in the form of an equal-curvature circular arc (i.e., a curve with a constant curvature throughout an arc). The start and end points of the sub-region correspond to the start and end points of the end-wall profile curve; the axisymmetric end-wall profile curve control function of the sub-region contains multiple undetermined parameters, and one of the undetermined parameters is the maximum profiling height ΔH. max The maximum profiling height ΔH max refers to the maximum height change of the end-wall profile curve in the radial direction relative to the original shape (i.e., the original turbine casing) when performing axisymmetric end-wall profiling on the sub-region.

[0033] For example, the axisymmetric end-wall profile curve control function of the sub-region can be designed as: f(z)=ΔH max sin(az + b)+r(z) (1); In formula (1), z is the coordinate of the end-wall profile curve of the sub-region on the axial coordinate axis; f(z) is the radius of the end-wall profile curve of the sub-region at the axial coordinate value of z, that is, the radius of the casing after axisymmetric end-wall profiling at the axial coordinate value of z; the initial value of the maximum profiling height ΔH max can be assigned as N times the original tip clearance. If ΔH max takes a positive value, it means that the casing bulges upward (i.e., the casing surface bulges upward at the corresponding position), and if ΔH max takes a negative value, it means that the casing concaves downward (i.e., the casing surface sinks downward at the corresponding position); r(z) is the radius of the original turbine casing at the axial coordinate value of z; a and b are both constants. The undetermined parameters in formula (1) are ΔH max , a, and b.

[0034] Step S03: For each sub-region, determine the absolute value |ΔH max | of the maximum profiling height that satisfies the profile gradient requirement of the curve. The profile gradient requirement is set with the goal that the difference between the tip clearance at any point on the curve and the original tip clearance is within the allowable error range; and, according to the start and end point coordinates of the sub-region, determine the other undetermined parameters in the function except for the maximum profiling height ΔH max .

[0035] Specifically, referring to Figure 3 , Figure 3 is Figure 2 a partial enlarged view of the radial section at point A of the impeller in . In this partial enlarged view, the dashed line L1 is the original casing curve; the solid line L2 is the casing curve after profiling, that is, the end wall profiling curve formed after axisymmetric end wall profiling; the distance between the top of blade 7 and the inner wall of the casing is called the tip clearance h, the solid line L3 is the leading edge of the blade, and the solid line L4 is the trailing edge of the blade. Points B and C are the starting and ending points of the end wall profiling curve of a sub-region, and the phase difference between points B and C is 180°, P max point is the maximum profiling height point; the radial extension line of P max point intersects the original casing surface at point O.

[0036] To ensure that the tip clearance remains basically unchanged before and after profiling, the maximum profiling height ΔH max should satisfy the profile gradient constraint condition. When the profile gradient value ΔG is less than 0.5, it can be considered that the design requirement of unchanged tip clearance is met. The profile gradient is: ΔG = ΔH max / min(BO, CO) (2); In formula (2), BO represents the distance between point B and point O, CO represents the distance between point C and point O, and min(BO, CO) represents the smaller value of BO and CO.

[0037] When conducting DOE (Design of Experiments) experiments, the number of segments N of the end wall profiling is corresponded to N factors. This is because: the profiling of each sub-region can be adjusted and controlled independently, and the change of each segment may affect the performance of the entire end wall. Therefore, each segment is regarded as an independent factor to study its effect on the experimental results. Taking the maximum profiling height ΔH max as the key variable, two levels, one positive and one negative, are set, corresponding to the two profiling states of the casing concave and convex respectively. When the casing is concave or convex, it is necessary to keep the height of the tip clearance basically unchanged, that is, it is necessary to adapt the blade tip profile to the shape of the casing, and the height of the corresponding position blade will change with the change of the casing surface. This is because: the tip clearance has an important influence on the performance of the supercritical carbon dioxide centrifugal compressor. If the tip clearance changes too much, it may lead to an increase in leakage flow, thereby reducing the efficiency and performance of the compressor.

[0038] The profile gradient can be understood as the slope of the turbomachinery casing surface or the blade tip contour curve at a certain position, which reflects the rate of change of the curve. When the profile gradient is less than 0.5, it is considered to meet the requirement of constant tip clearance. The reason is as follows: a smaller profile gradient means that the change of the turbomachinery casing surface curve is relatively gentle. In this case, according to the above adjustment method where the blade tip contour adapts to the casing shape, it is relatively easy to maintain the stability of the tip clearance; if the profile gradient is too large, the change of the turbomachinery casing surface curve is too drastic. When adjusting the blade tip height to adapt to the change of the casing shape, it is very difficult to accurately ensure that the tip clearance remains unchanged all the time, which may lead to large fluctuations in the tip clearance, thus affecting the performance of the supercritical carbon dioxide centrifugal compressor.

[0039] In addition, since the start and end point coordinates of the sub-region are known, other undetermined parameters in the control function of the axisymmetric endwall profile curve can be determined accordingly except for the maximum profile height ΔH max For example, it is known that Figure 3 the coordinates of points B and C in [reference] and the phase difference between points B and C is 180°. Substitute the coordinates of points B and C into Equation (1), and use the phase difference relationship between these two points to first find the parameter a, and then substitute the coordinates of point B or point C into Equation (1) to solve for the parameter b.

[0040] Step S04: Taking the improvement of the isentropic efficiency η and the stall margin improvement ΔSMI as the optimization objectives, on the basis of ensuring that the absolute value of the maximum profile height |ΔH max | meets the profile gradient condition, optimize the maximum profile height ΔH max corresponding to N sub-regions through DOE experiments to obtain N optimized maximum profile heights ΔH max , and thus determine N functions with all parameters determined.

[0041] Specifically, the DOE experiment first designs multiple groups of different ΔH max parameter combinations around the maximum profile height ΔH max of each sub-region within the value range of |ΔH max | limited by the profile gradient condition; obtains the isentropic efficiency η and stall margin improvement ΔSMI data for each group of ΔH max parameters through simulation or experiment; conducts comparative analysis on the data based on the optimization objectives, and screens out the ΔH max parameter combinations that meet the profile gradient requirements and can achieve the optimization objectives, thereby determining all the parameters of N functions and completing the precise optimization of the axisymmetric endwall profile of the turbomachinery casing.

[0042] Among them, the isentropic efficiency η is an index to measure the effective degree of converting the input mechanical energy into gas pressure energy and kinetic energy by a supercritical carbon dioxide centrifugal compressor. It represents the degree to which the actual compression process approaches the ideal isentropic compression process. The higher the isentropic efficiency η, the smaller the energy loss during the gas compression process by the supercritical carbon dioxide centrifugal compressor, the higher the operating efficiency, and the more effectively it can convert electrical energy or other forms of energy into the pressure increase of the gas, thereby reducing the operating cost and improving the overall performance of the system.

[0043] The calculation formula for the isentropic efficiency η is as follows: (3); In formula (3), h 01 is the total enthalpy at the inlet of the supercritical carbon dioxide centrifugal compressor, and h 02 is the total enthalpy at the outlet of the supercritical carbon dioxide centrifugal compressor, and h 02s is the isentropic total enthalpy at the outlet of the supercritical carbon dioxide centrifugal compressor.

[0044] The stall margin refers to the safety margin from the occurrence of stall during the operation of a supercritical carbon dioxide centrifugal compressor. Stall is an unstable flow phenomenon inside the supercritical carbon dioxide centrifugal compressor, which will lead to a decline in the performance of the supercritical carbon dioxide centrifugal compressor or even damage. The stall margin improvement ΔSMI is used to measure the change in the stall margin of the supercritical carbon dioxide centrifugal compressor relative to before through a certain design improvement or optimization measure. A positive value of ΔSMI indicates an increase in the stall margin, meaning that the supercritical carbon dioxide centrifugal compressor can operate stably within a wider range of operating conditions, is not prone to stall, and thus improves the reliability and stability of the operation of the supercritical carbon dioxide centrifugal compressor.

[0045] The calculation formula for the stall margin improvement ΔSMI is as follows: (4); In formula (4), π NS and π a,NS respectively represent the total pressure ratios at the near-stall point before and after the modification of the supercritical carbon dioxide centrifugal compressor; m NS and m a,NS respectively represent the mass flow rates at the near-stall point before and after the modification of the supercritical carbon dioxide centrifugal compressor.

[0046] See Figure 4 , Figure 4 is the comparison diagram of the radial cross-section of the impeller casing 5 before and after shaping. The left figure, namely Figure 4 (a) is the radial cross-section diagram of the original impeller casing; the right figure, namely Figure 4 (b) is the radial cross-section diagram of the impeller casing obtained after being optimized by the DOE experiment and axially symmetric end wall shaping according to N said functions.Figure 4 Only take N = 5 (i.e., divided into five sub-regions N1 to N5) as an example for illustration.

[0047] Step S05: Verify whether both the isentropic efficiency η and the improvement amount ΔSMI of the stall margin are within the target range after performing axisymmetric endwall shaping on the compressor casing according to the N functions; if so, consider the shaping completed and end this round of control; if not, proceed to step S06.

[0048] Step S06: Adjust the value of N, and then return to step S01.

[0049] In summary, the embodiments of the present application innovatively combine the axisymmetric endwall shaping technology with segmented shaping, perform a stability enhancement design for the compressor casing of a supercritical carbon dioxide centrifugal compressor, take into account ease of implementation and high efficiency, and are suitable for compact-structured models, which can significantly improve the stability enhancement performance of the supercritical carbon dioxide centrifugal compressor.

[0050] In a possible implementation, verifying whether both the isentropic efficiency η and the improvement amount ΔSMI of the stall margin are within the target range after performing axisymmetric endwall shaping on the compressor casing according to the N functions includes: through computer simulation technology, performing axisymmetric endwall shaping on the compressor casing according to the N functions, and performing numerical simulation analysis on the supercritical carbon dioxide centrifugal compressor after shaping, to determine whether both the isentropic efficiency η and the improvement amount ΔSMI of the stall margin are within the target range.

[0051] Specifically, through this method of performing axisymmetric endwall shaping based on functions and combining numerical simulation analysis, it is possible to pre-evaluate the performance before actual manufacturing, avoid repeated modifications caused by unreasonable designs, thereby shortening the R & D cycle. At the same time, accurately determining whether the isentropic efficiency η and the improvement amount ΔSMI of the stall margin are within the target range helps to adjust the design in a timely manner, reduce unnecessary experimental times, lower the R & D cost, quickly determine a design solution that meets the performance requirements, and further improve the R & D efficiency.

[0052] In a possible implementation, after numerically simulating and analyzing the supercritical carbon dioxide centrifugal compressor after profiling, and determining that both the isentropic efficiency η and the improvement amount of stall margin ΔSMI are within the target range, it further includes: after manufacturing the supercritical carbon dioxide centrifugal compressor according to the N functions, collecting and testing the actual operating parameters of the supercritical carbon dioxide centrifugal compressor, and comparing and analyzing them with the actual operating parameters of the original supercritical carbon dioxide centrifugal compressor to determine whether both the isentropic efficiency η and the improvement amount of stall margin ΔSMI are within the target range. Thus, through the double verification of numerical simulation and actual testing, it not only uses computer simulation to quickly evaluate the design feasibility and shorten the R & D cycle, but also obtains real operating condition data through actual machine testing to ensure the engineering practicability of the optimization plan; this verification method combining theory and practice can effectively reduce the design risk and accurately verify the improvement effect of the axisymmetric endwall profiling technology on the isentropic efficiency η and the improvement amount of stall margin ΔSMI of the supercritical carbon dioxide centrifugal compressor, providing a reliable basis for the industrial application of the technology.

[0053] Based on any of the above-provided axisymmetric endwall profiling methods for supercritical carbon dioxide centrifugal compressors, before dividing the area on the impeller casing of the supercritical carbon dioxide centrifugal compressor where axisymmetric endwall profiling is to be performed into N sub-regions along the axial direction, it further includes: through computer simulation technology, numerically simulating and analyzing the operating characteristics of the supercritical carbon dioxide centrifugal compressor under different working conditions to determine the near-stall point of the supercritical carbon dioxide centrifugal compressor; according to the operating characteristics of the supercritical carbon dioxide centrifugal compressor at the near-stall point, generating an entropy production rate contour map of any axial height section of the tip flow field of the supercritical carbon dioxide centrifugal compressor, and outputting the entropy production rate contour map. The entropy production rate contour map provides a core reference basis for researchers to determine the area where axisymmetric endwall profiling is to be performed.

[0054] Specifically, computer simulation technology is a method of using a computer to establish a mathematical model to simulate the actual physical process. When studying the supercritical carbon dioxide centrifugal compressor, due to its complex actual operating conditions, high direct experimental costs and long cycles, through computer simulation technology, different working conditions are set, such as parameters such as rotational speed, flow rate, inlet and outlet pressures. These parameters are substituted into the mathematical model describing the internal fluid flow and energy conversion of the supercritical carbon dioxide centrifugal compressor, and the powerful computing power of the computer is used to solve the equations to obtain the distributions of physical quantities such as internal pressure, velocity, and temperature of the supercritical carbon dioxide centrifugal compressor under different working conditions, and then analyze its operating characteristics.

[0055] By continuously adjusting the operating conditions of the supercritical carbon dioxide centrifugal compressor and performing simulations, the near-stall point of the supercritical carbon dioxide centrifugal compressor is found. The near-stall point is a key operating condition point during the operation of the supercritical carbon dioxide centrifugal compressor. Near this point, the performance of the supercritical carbon dioxide centrifugal compressor begins to become unstable, and phenomena such as air flow separation occur, approaching but not yet reaching the stall state. That is to say, the near-stall point refers to the critical point where the supercritical carbon dioxide centrifugal compressor is close to stalling but has not completely stalled during operation, and can also be called the stall critical point.

[0056] The entropy production rate is a physical quantity that measures the degree of irreversibility of a thermodynamic process. In the flow field inside the supercritical carbon dioxide centrifugal compressor, due to the existence of irreversible factors such as viscous friction, air flow impact, and heat transfer, the generation of entropy will occur. The greater the entropy production rate at any point, the higher the degree of irreversibility at that point, which also means a greater energy loss.

[0057] The flow condition at the blade tip has an important impact on the overall performance of the supercritical carbon dioxide centrifugal compressor. Analyzing the cross-section of the blade tip flow field can provide an important reference for understanding the flow and energy loss inside the entire supercritical carbon dioxide centrifugal compressor. For this reason, in the embodiments of this application, a cross-section at any axial height of the blade tip flow field is selected to draw the entropy production rate contour map. The entropy production rate contour map graphically shows the distribution of the entropy production rate on the cross-section of the blade tip flow field. By observing information such as the color and contour lines of the entropy production rate contour map, researchers can clearly see the magnitude and change trend of the entropy production rate at different positions, thereby helping researchers quickly understand the energy loss distribution of the blade tip flow field.

[0058] Based on the energy loss distribution of the blade tip flow field, researchers determine the rotating stall mechanism of the supercritical carbon dioxide centrifugal compressor, and then determine the flow passage area where the source of the energy loss is located; the end wall covering the flow passage area is used as the area to be subjected to axisymmetric end wall shaping.

[0059] In addition, corresponding to the above method embodiments, see Figure 5 , the embodiments of this application also provide a device for axisymmetric end wall shaping of a supercritical carbon dioxide centrifugal compressor, including: A region division unit 100 for dividing the region to be subjected to axisymmetric end wall shaping on the turbine casing of the supercritical carbon dioxide centrifugal compressor into N sub-regions along the axial direction; N≥2; A function construction unit 200 for respectively constructing an axisymmetric end wall shaping curve control function for each sub-region; the function is used to describe the shape of the end wall shaping curve formed after axisymmetric end wall shaping of the sub-region, the curve is in the form of an equal-curvature circular arc and the start and end points of the sub-region are the start and end points of the curve; the function contains multiple undetermined parameters, and one of the undetermined parameters is the maximum shaping height ΔHmax ; A parameter determination unit 300, which is used to determine, for each sub-region, the absolute value |ΔH max | of the maximum modeling height that meets the profile gradient requirements of the curve, where the profile gradient requirements are set with the goal that the difference between the tip clearance at any point on the curve and the original tip clearance is within the allowable error range; and, according to the starting and ending point coordinates of the sub-region, determine the other undetermined parameters in the function except the maximum modeling height ΔH max ; A parameter optimization unit 400, which is used to take improving the isentropic efficiency η and the stall margin improvement ΔSMI as the optimization goal, and on the basis of ensuring that the absolute value |ΔH max | meets the profile gradient condition, optimize the maximum modeling height ΔH corresponding to N sub-regions through DOE experiments max to obtain N optimized maximum modeling heights ΔH max , thereby determining N functions with all parameters determined; A verification and iteration unit 500, which is used to verify whether the isentropic efficiency η and the stall margin improvement ΔSMI are both within the target range after performing axisymmetric endwall modeling on the turbomachinery casing according to the N functions; if not, adjust N and then execute the above steps again until the isentropic efficiency η and the stall margin improvement ΔSMI are both within the target range.

[0060] This device takes into account both ease of implementation and high efficiency, and is adapted to compact models, improving the stability extension performance of the supercritical carbon dioxide centrifugal compressor.

[0061] An electronic device is also provided in an embodiment of the present application. The electronic device in the embodiment of the present application may include, but is not limited to, fixed terminals such as mobile phones, laptop computers, PDAs (Personal Digital Assistants), PADs (Tablet Computers), desktop computers, etc. The electronic device includes at least one processor and a memory connected to the processor, where: the memory is used to store a computer program; the processor is used to execute the computer program so that the electronic device can implement any one of the above-mentioned axisymmetric endwall modeling methods for supercritical carbon dioxide centrifugal compressors.

[0062] A computer program product is also provided in an embodiment of the present application, including computer-readable instructions, which when running on an electronic device, enable the electronic device to implement any one of the axisymmetric endwall modeling methods for supercritical carbon dioxide centrifugal compressors provided in the embodiment of the present application.

[0063] In an embodiment of the present application, a computer-readable storage medium is further provided. The storage medium carries one or more computer programs. When the one or more computer programs are executed by an electronic device, the electronic device can implement any of the axisymmetric endwall shaping methods of the supercritical carbon dioxide centrifugal compressor provided in the embodiments of the present application.

[0064] In addition, it should be noted that the device embodiments described above are merely illustrative. The units described as separation components may or may not be physically separated. The components shown as units may or may not be physical units, that is, they may be located in one place or distributed to multiple network units. Some or all of the modules can be selected according to actual needs to achieve the purpose of the solution of this embodiment. In addition, in the accompanying drawings of the device embodiments provided in the present application, the connection relationships between modules indicate that they have communication connections, which can be specifically implemented as one or more communication buses or signal lines.

[0065] Through the description of the above embodiments, those skilled in the art can clearly understand that the present application can be implemented by means of software plus necessary general hardware. Of course, it can also be implemented by dedicated hardware including application-specific integrated circuits, dedicated CPUs, dedicated memories, dedicated components, etc. Generally, functions completed by computer programs can be easily implemented by corresponding hardware, and the specific hardware structures for implementing the same function can also be various, such as analog circuits, digital circuits or dedicated circuits. However, for the present application, software program implementation is a better implementation method in more cases. Based on such an understanding, the technical solution of the present application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. The computer software product is stored in a readable storage medium, such as a floppy disk, USB flash drive, mobile hard disk, ROM, RAM, magnetic disk or optical disc of a computer, and includes several instructions for causing a computer device (which can be a personal computer, training device, or network device, etc.) to execute the methods described in various embodiments of the present application.

[0066] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware or any combination thereof. When implemented using software, it can be implemented in whole or in part in the form of a computer program product.

[0067] The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, they generate, wholly or partly, the processes or functions described in the embodiments of this application. The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable devices. The computer instructions may be stored in a computer-readable storage medium, or transmitted from one computer-readable storage medium to another. For example, the computer instructions may be transmitted from one website, computer, training device, or data center to another website, computer, training device, or data center by wire (such as coaxial cable, optical fiber, digital subscriber line (DSL)) or wirelessly (such as infrared, wireless, microwave, etc.). The computer-readable storage medium may be any available medium that can be stored by a computer, or a data storage device such as a training device or data center that includes one or more integrated available media. The available medium may be a magnetic medium (such as a floppy disk, hard disk, magnetic tape), an optical medium (such as a DVD), or a semiconductor medium (such as a solid state disk (SSD)), etc.

[0068] The above description of the disclosed embodiments enables those skilled in the art to implement or use this application. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the embodiments of this application. Therefore, the embodiments of this application will not be limited to the embodiments shown herein, but rather will be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. An axisymmetric endwall shaping method for a supercritical carbon dioxide centrifugal compressor, characterized in that, Comprising: Dividing the region on the impeller casing of the supercritical carbon dioxide centrifugal compressor where axisymmetric endwall shaping is to be performed into N sub-regions along the axial direction; N≥2； Construct an axisymmetric endwall profile curve control function for each sub-region respectively; the function is used to describe the shape of the endwall profile curve formed after axisymmetric endwall profiling of the sub-region, the curve is in the form of an equal-curvature circular arc and the start and end points of the sub-region are the start and end points of the curve; the function contains multiple undetermined parameters, and one of the undetermined parameters is the maximum profiling height Δ H max ; For each sub-region, determine the absolute value |Δ H max | of the maximum profiling height that meets the profile gradient requirements of the curve, where the profile gradient requirements are set with the goal that the difference between the tip clearance at any point on the curve and the original tip clearance is within the allowable error range; and, based on the start and end point coordinates of the sub-region, determine the other undetermined parameters in the function except for the maximum profiling height Δ H max ; To improve the isentropic efficiency η and the improvement amount Δ of the stall margin SMI As the optimization objectives, on the basis of ensuring that the absolute value |Δ H max | meets the profile gradient condition, through experimental design, the maximum profile height Δ corresponding to N sub-regions H max is optimized to obtain N optimized maximum profile heights Δ H max , and N functions with all parameters determined are thus determined; Verify that after the axisymmetric endwall of the turbine casing is shaped according to the N functions, the isentropic efficiency η and the improvement amount Δ SMI of the stall margin are both within the target range; If not, adjust N and then execute the above steps again until the isentropic efficiency η and the improvement amount Δ SMI of the stall margin are both within the target range.

2. The method for shaping the axisymmetric end wall of a supercritical carbon dioxide centrifugal compressor according to claim 1, wherein The function is: f ( z ) = Δ H max sin(a z + b ) + r ( z ); Among them, z is the coordinate of the curve on the axial coordinate axis; f ( z ) is the radius of the curve at the axial coordinate value of z ; r ( z ) is the radius of the original turbine casing at the axial coordinate value of z ; a and b are both constants; the undetermined parameters in the function include Δ H max , a, and b.

3. The method for axisymmetric endwall shaping of a supercritical carbon dioxide centrifugal compressor according to claim 1, wherein Determine the absolute value of the maximum styling height |Δ H max | that meets the profile gradient requirements of the curve, including: Determine a Δ that satisfies H max / min(BO, CO) < 0.5 for |Δ H max |, and use it as the absolute value of the maximum styling height |Δ H max | that meets the profile gradient requirements of the curve; Point B and point C are respectively the starting and ending points of the curve, and point O is the intersection point of the radial extension line of the maximum shaping height point and the original impeller casing surface; BO represents the distance between point B and point O, and CO represents the distance between point C and point O.

4. The method for shaping the axisymmetric end wall of a supercritical carbon dioxide centrifugal compressor according to claim 1, 2 or 3, characterized in that The verification is to check whether the isentropic efficiency η and the improvement amount Δ of the stall margin SMI are both within the target range after performing axisymmetric endwall shaping on the compressor casing according to the N functions, including: Through computer simulation technology, the axisymmetric endwall of the turbine casing is modeled according to the N functions, and the supercritical carbon dioxide centrifugal compressor after modeling is numerically simulated and analyzed to judge the isentropic efficiency η and the improvement amount Δ SMI of the stall margin are both within the target range.

5. The method for axisymmetric endwall shaping of a supercritical carbon dioxide centrifugal compressor according to claim 4, wherein After performing numerical simulation analysis on the supercritical carbon dioxide centrifugal compressor after shaping to determine the isentropic efficiency η and the improvement amount Δ SMI of the stall margin are both within the target range, it further includes: After manufacturing the supercritical carbon dioxide centrifugal compressor according to the N functions, collect and test the actual operating parameters of the supercritical carbon dioxide centrifugal compressor, and compare and analyze them with the actual operating parameters of the original supercritical carbon dioxide centrifugal compressor to judge the isentropic efficiency η and the improvement amount Δ SMI of the stall margin are both within the target range.

6. The method for axisymmetric endwall shaping of a supercritical carbon dioxide centrifugal compressor according to claim 1, wherein Before dividing the region on the impeller casing of the supercritical carbon dioxide centrifugal compressor where axisymmetric endwall shaping is to be performed into N sub-regions along the axial direction, it further includes: Through computer simulation technology, numerically simulate and analyze the operating characteristics of the supercritical carbon dioxide centrifugal compressor under different working conditions to determine the near-stall point of the supercritical carbon dioxide centrifugal compressor; according to the operating characteristics of the supercritical carbon dioxide centrifugal compressor at the near-stall point, generate the entropy production rate cloud map on any axial height section of the tip flow field of the supercritical carbon dioxide centrifugal compressor, and output the entropy production rate cloud map; the entropy production rate cloud map is one of the bases for determining the region where axisymmetric endwall shaping is to be performed.

7. An axisymmetric endwall shaping device for a supercritical carbon dioxide centrifugal compressor, characterized in that, Comprising: A region division unit for dividing the region on the impeller casing of the supercritical carbon dioxide centrifugal compressor where axisymmetric endwall shaping is to be performed into N sub-regions along the axial direction; N≥2； A function construction unit is configured to separately construct an axisymmetric endwall profile curve control function for each sub-region; the function is used to describe the shape of the endwall profile curve formed after axisymmetric endwall profiling of the sub-region, the curve is in the form of an equal-curvature circular arc, and the start and end points of the sub-region are the start and end points of the curve; the function includes a plurality of undetermined parameters, and one of the undetermined parameters is the maximum profiling height Δ H max ; A parameter determination unit, which is used to determine, for each sub-region, the absolute value |Δ H max | of the maximum profiling height that meets the profile gradient requirement of the curve, where the profile gradient requirement is set with the goal that the difference between the tip clearance at any point on the curve and the original tip clearance is within the allowable error range; and, according to the start and end point coordinates of the sub-region, determine other undetermined parameters in the function except for the maximum profiling height Δ H max ; A parameter optimization unit for improving the isentropic efficiency η and the improvement amount Δ of the stall margin SMI as the optimization objectives, on the basis of ensuring that the absolute value |Δ H max | satisfies the camber line gradient condition, through experimental design, the maximum camber height Δ corresponding to N sub-regions H max is optimized to obtain N optimized maximum camber heights Δ H max , and thereby N functions with all parameters determined are determined; Verification and iteration unit, used to verify whether the isentropic efficiency η and the improvement amount Δ SMI of the stall margin are both within the target range after performing axisymmetric endwall shaping on the turbine casing according to N of the said functions; If not, adjust N and then execute the above steps again until the isentropic efficiency η and the improvement amount of the stall margin Δ SMI are both within the target range.

8. A computer program product, characterized in that, Including computer-readable instructions, when the computer-readable instructions run on an electronic device, enabling the electronic device to implement the axisymmetric endwall shaping method of the supercritical carbon dioxide centrifugal compressor as described in any one of claims 1 to 6.

9. An electronic device, characterized in that, Including at least one processor and a memory connected to the processor, wherein: The memory is used to store a computer program; The processor is used to execute the computer program so that the electronic device can implement the axisymmetric endwall shaping method of the supercritical carbon dioxide centrifugal compressor as described in any one of claims 1 to 6.

10. A computer storage medium, characterized in that, The storage medium carries one or more computer programs, and when the one or more computer programs are executed by an electronic device, enabling the electronic device to implement the axisymmetric endwall shaping method of the supercritical carbon dioxide centrifugal compressor as described in any one of claims 1 to 6.

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