Axisymmetric endwall shaping method, device, product, equipment and storage medium for supercritical carbon dioxide centrifugal compressor

Abstract

This application provides a method, apparatus, product, equipment, and storage medium for shaping the axisymmetric end wall of a supercritical carbon dioxide centrifugal compressor, relating to the field of supercritical carbon dioxide centrifugal compressor stabilization technology. The method achieves both ease of implementation and high efficiency, and improves the stabilization performance of supercritical carbon dioxide centrifugal compressors. The method comprises: dividing the area on the impeller casing of the centrifugal compressor where the axisymmetric end wall shaping is to be performed into N sub-areas along the axial direction; N ≥ 2; constructing an axisymmetric end wall shaping curve control function for each sub-area; one of the undetermined parameters of the function is the maximum shaping height Δ H max For each sub-area, determine the |Δ H max |; and determine the difference between Δ H max Other undetermined parameters except Δ H max Optimize and verify the centrifugal compressor before and after modeling.

Description

Technical Field

[0001] This application relates to the technical field of stability extension of supercritical carbon dioxide centrifugal compressors, and particularly to an axisymmetric endwall shaping method, device, product, equipment, and storage medium for supercritical carbon dioxide centrifugal compressors. Background Technique

[0002] As a key device for compressing and transporting gases in industrial production, the operating state of a centrifugal compressor is susceptible to various factors, such as gas flow rate, inlet pressure, temperature changes, etc. Under certain operating conditions, unstable phenomena such as rotating stall may occur in the centrifugal compressor, seriously affecting the performance of the centrifugal compressor.

[0003] Centrifugal compressor stability extension technology refers to a series of technical means aimed at improving the stable operating range of centrifugal compressors and avoiding unstable phenomena such as rotating stall. According to different implementation methods of the technology, these stability extension 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 stability extension, and at the same time, they are also accompanied by their own application challenges, which are specifically described as follows:

[0004] I. Active Control

[0005] The core of active control technology is to introduce external equipment to detect the internal flow state of the centrifugal compressor in real time, accurately locate the stall source. Once the stall source is detected, a disturbance wave opposite to the direction of the stall disturbance is induced to suppress the stall phenomenon. However, although active control has excellent stability extension performance in theory, its actual operation process is complex, the process details are cumbersome, and when integrating external equipment into a supercritical carbon dioxide centrifugal compressor, due to the compact structure of the centrifugal compressor, there are significant challenges in spatial layout and technology implementation.

[0006] When the temperature and pressure of carbon dioxide exceed its critical point (critical temperature 304.13K, i.e., 31.0°C; critical pressure 7.38MPa), it enters the supercritical state. A centrifugal compressor with supercritical carbon dioxide as the working medium is a supercritical carbon dioxide centrifugal compressor.

[0007] II. Passive Control

[0008] Compared with active control, passive control technology is more direct and easier to implement. It does not rely on external equipment, but adjusts the internal geometry or flow characteristics of the centrifugal compressor to achieve the purpose of stability extension. Common passive control technologies include casing treatment, endwall shaping, etc.

[0009] Casing treatment technology involves creating grooves, slits, or other special structures on the casing wall of a centrifugal compressor to alter the flow conditions within the compressor, significantly improving its stable operating range. However, while casing treatment can effectively increase stability, it also alters the optimal airflow path, resulting in reduced efficiency under designed operating conditions.

[0010] End wall molding technology, especially axisymmetric end wall molding technology, gives centrifugal compressors a certain degree of stability expansion capability while maintaining basically unchanged efficiency under design conditions. Specifically, axisymmetric end wall molding technology refers to the formation of an axisymmetric concave or convex structure on the casing or hub of the centrifugal compressor, so as to change the tip flow area within the molding area and achieve precise control of the internal flow field, thereby effectively suppressing the tip leakage flow, reducing the possibility of airflow separation and vortex formation, and thus suppressing the occurrence of rotating stall. However, in supercritical carbon dioxide centrifugal compressors, the "size effect" brought about by its compactness causes the centrifugal impeller to have a larger blade tip clearance. This larger blade tip clearance will aggravate the blade tip leakage flow in the centrifugal impeller, making the internal flow field characteristics more complex, and causing the centrifugal compressor to be more prone to rotating stall. However, the existing axisymmetric end wall shaping technology does not fully consider the complex flow characteristics of the internal flow field during the design process and is only applicable to small blade tip clearance scenarios. However, when faced with the large blade tip clearance scenario of a supercritical carbon dioxide centrifugal compressor, this technology is difficult to achieve fine control of the internal flow field, resulting in poor blade tip leakage flow suppression effect, which seriously restricts the improvement of the expansion stability performance of the centrifugal compressor.

[0011] In summary, how to develop an easy-to-implement, highly efficient and compatible stabilization technology for supercritical carbon dioxide centrifugal compressors has become an urgent problem to be solved in this field. Summary of the Invention

[0012] In view of the above problems, this application provides a method, device, product, equipment, and storage medium for shaping the axisymmetric end wall of a supercritical carbon dioxide centrifugal compressor, which balances ease of implementation and high efficiency, and improves the expansion stability performance of the supercritical carbon dioxide centrifugal compressor. The specific solution is as follows:

[0013] In a first aspect, the present application provides a method for shaping an axisymmetric end wall of a supercritical carbon dioxide centrifugal compressor, comprising:

[0014] The region on the impeller casing of the supercritical carbon dioxide centrifugal compressor where the axisymmetric end wall molding is to be performed is divided into N subregions along the axial direction; N ≥ 2;

[0015] 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 the axisymmetric endwall profiling of 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 profiling height ΔH max ;

[0016] For each sub-region, determine the absolute value |ΔH max | of the maximum profiling height that meets the profile gradient requirements of the curve, and 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 profiling height ΔH max ;

[0017] Taking the improvement of the isentropic efficiency η and the stall margin improvement ΔSMI as the optimization goal, on the basis of ensuring that the absolute value |ΔH max | of the maximum profiling height meets the profile gradient condition, optimize the maximum profiling height ΔH max corresponding to N sub-regions through experimental design, and obtain N optimized maximum profiling heights ΔH max , thereby determining N functions with all parameters determined;

[0018] Verify whether the isentropic efficiency η and the stall margin improvement ΔSMI are both within the target range after the axisymmetric endwall profiling of the turbine 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.

[0019] In one possible implementation, the function is:

[0020] f(z)=ΔH [[ID=…]] (The content of the ellipsis part needs to be completed according to the original text. Here, it seems that the original text has some incomplete or incorrect tags. Please check and correct it if necessary.) max sin(az + b)+r(z);

[0021] 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.

[0022] In one possible implementation, determining the absolute value |ΔH max | of the maximum profiling height that meets the profile gradient requirements of the curve includes:

[0023] Determine a value that satisfies ΔH max / The absolute value of ΔH where / min(BO, CO) < 0.5 max |, being the absolute value of the maximum profiling height that meets the profiling gradient requirement of the curve|ΔH max |;

[0024] Points B and C are respectively the starting and ending points of the curve, and point O is the intersection of the radial extension line of the maximum profiling height point and the original turbomachinery casing surface; BO represents the distance between point B and point O, and CO represents the distance between point C and point O.

[0025] In a possible implementation, after performing axisymmetric endwall profiling on the turbomachinery casing according to N of the functions, the verification of whether both the isentropic efficiency η and the stall margin improvement ΔSMI are within the target range includes:

[0026] Through computer simulation technology, perform axisymmetric endwall profiling on the turbomachinery casing according to N of the functions, and conduct numerical simulation analysis on the supercritical carbon dioxide centrifugal compressor after profiling to determine whether both the isentropic efficiency η and the stall margin improvement ΔSMI are within the target range.

[0027] In a possible implementation, after conducting numerical simulation analysis on the supercritical carbon dioxide centrifugal compressor after profiling and determining that both the isentropic efficiency η and the stall margin improvement ΔSMI are within the target range, it further includes:

[0028] After manufacturing the supercritical carbon dioxide centrifugal compressor according to N of the functions, collect and test the actual operating parameters of the supercritical carbon dioxide centrifugal compressor, and conduct comparative analysis with the actual operating parameters of the original supercritical carbon dioxide centrifugal compressor to determine whether both the isentropic efficiency η and the stall margin improvement ΔSMI are within the target range.

[0029] In a possible implementation, before dividing the area on the turbomachinery 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:

[0030] Through computer simulation technology, conduct numerical simulation analysis on 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 an entropy production rate contour map of any axial height section of the tip flow field of the supercritical carbon dioxide centrifugal compressor, and output the entropy production rate contour map; the entropy production rate contour map is one of the bases for determining the area where axisymmetric endwall profiling is to be performed.

[0031] The second aspect of the present application provides a device for axisymmetric endwall profiling of a supercritical carbon dioxide centrifugal compressor, including:

[0032] A region division unit for axially dividing the region on the impeller casing of a supercritical carbon dioxide centrifugal compressor where axisymmetric endwall profiling is to be performed into N sub-regions; N≥2;

[0033] A function construction unit for constructing an axisymmetric endwall profiling curve control function for each sub-region respectively; the function is used to describe the shape of the endwall profiling curve formed after performing axisymmetric endwall profiling on 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 ΔH max ;

[0034] A parameter determination unit for determining, for each sub-region, the absolute value |ΔH of the maximum profiling 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, based on the start and end point coordinates of the sub-region, determining the other undetermined parameters in the function except the maximum profiling height ΔH max ;

[0035] A parameter optimization unit for taking improving the isentropic efficiency η and the stall margin improvement ΔSMI as the optimization goal, on the basis of ensuring that the absolute value |ΔH max | satisfies the profile gradient condition, optimizing the maximum profiling height ΔH corresponding to the N sub-regions through experimental design max to obtain N optimized maximum profiling heights ΔH max and thus determining N functions with all parameters determined;

[0036] A verification and iteration unit for verifying whether the isentropic efficiency η and the stall margin improvement ΔSMI are both within the target range after performing axisymmetric endwall profiling on the impeller casing according to the N functions; if not, adjusting N and then executing the above steps again until both the isentropic efficiency η and the stall margin improvement ΔSMI are within the target range.

[0037] The third aspect of the present application provides a computer program product, including computer-readable instructions, which when running on an electronic device, cause the electronic device to implement the axisymmetric endwall profiling method for a supercritical carbon dioxide centrifugal compressor in the first aspect or any implementation manner of the first aspect.

[0038] The fourth aspect of the present application provides an electronic device, including at least one processor and a memory connected to the processor, where:

[0039] The memory is used to store a computer program;

[0040] The processor is used to execute the computer program, so that the electronic device can implement the method for the axisymmetric endwall shaping of a supercritical carbon dioxide centrifugal compressor according to the first aspect or any implementation manner of the first aspect.

[0041] The fifth aspect of the present application provides a computer storage medium, which carries one or more computer programs. When the one or more computer programs are executed by an electronic device, the electronic device can implement the method for the axisymmetric endwall shaping of a supercritical carbon dioxide centrifugal compressor according to the first aspect or any implementation manner of the first aspect.

[0042] By means of the above technical solutions, the present application innovatively combines the axisymmetric endwall shaping technology with the segmented shaping, and conducts a stability augmentation design for the impeller casing of a supercritical carbon dioxide centrifugal compressor. In the scenario of a large tip clearance of a supercritical carbon dioxide centrifugal compressor, this design not only gives full play to the advantages of easy implementation and high efficiency of the axisymmetric endwall shaping, but also precisely controls the flow characteristics of the tip flow field at different axial positions through segmented shaping, and finally achieves fine control of the internal flow field, effectively suppressing the tip leakage flow, significantly improving the stall margin of the supercritical carbon dioxide centrifugal compressor, and further greatly enhancing its stability augmentation performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Combined with the drawings and referring to the following specific embodiments, the above and other features, advantages and aspects of each embodiment of the present disclosure will become more obvious. Throughout the drawings, the same or similar reference numerals represent the same or similar elements. It should be understood that the drawings are schematic, and the original components and elements are not necessarily drawn to scale.

[0044] Figure 1 It is a flowchart of a method for the axisymmetric endwall shaping of a supercritical carbon dioxide centrifugal compressor provided by the present application;

[0045] 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;

[0046] Figure 3 It is Figure 2 a partially enlarged radial cross-sectional view at position A of the impeller in

[0047] Figure 4 It is a comparison diagram of an impeller casing before and after shaping provided by the present application; where 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;

[0048] Figure 5Schematic structural diagram of an axisymmetric endwall shaping device for a supercritical carbon dioxide centrifugal compressor provided by this application. Detailed implementation manners

[0049] The embodiments of this application provide a method, device, product, equipment and storage medium for axisymmetric endwall shaping of a supercritical carbon dioxide centrifugal compressor. It innovatively combines the axisymmetric endwall shaping technology with segmented shaping, and conducts a stability enhancement design for the impeller casing of the supercritical carbon dioxide centrifugal compressor. In the scenario of a large tip clearance of the 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 controls the flow characteristics of the tip flow field at different axial positions through segmented shaping, and finally realizes the refined control of the internal flow field, effectively suppressing the tip leakage flow, significantly improving the stall margin of the supercritical carbon dioxide centrifugal compressor, and further greatly enhancing its stability enhancement performance.

[0050] Next, with reference to the accompanying drawings, a method for axisymmetric endwall shaping of a supercritical carbon dioxide centrifugal compressor provided by the embodiments of this application will be described in detail. As can be known to those of ordinary skill in the art, with the development of technology and the emergence of new scenarios, the technical solutions provided by the embodiments of this application are equally applicable to similar technical problems.

[0051] Terms such as "first", "second", etc. in the specification, claims and above-mentioned accompanying drawings of this application are used to distinguish similar objects, and do not have to be used to 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 distinction used when describing objects with the same attributes in the embodiments of this application. In addition, the terms "comprising" and "having" and any variations thereof are intended to cover non-exclusive inclusion, so that a process, method, system, product or equipment 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 processes, methods, products or equipment.

[0052] In addition, for the sake of easy understanding, the names of each direction are defined as follows:

[0053] Axial direction: along the axis direction of the cylinder;

[0054] Radial direction: along the radius direction of the cross-section (perpendicular to the axis);

[0055] Circumferential direction: around the axis direction of the cylinder (perpendicular to the axis and perpendicular to the cross-section radius at the same time).

[0056] See Figure 1 , a method for axisymmetric endwall shaping of a supercritical carbon dioxide centrifugal compressor proposed by the embodiments of this application includes:

[0057] 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.

[0058] Specifically, as Figure 2 shown in the schematic diagram of the impeller and diffuser structure of the supercritical carbon dioxide centrifugal compressor, in 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 channel 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 impeller casing 5 adopts an axisymmetric endwall design, which forms a closed and symmetric flow channel boundary around the impeller 2. By uniformly constraining the air flow, it reduces the circumferential flow non-uniformity and energy loss, and ensures the stable transmission of the gas; the hub 6 is the core support structure of the impeller 2 components (such as blades). On the one hand, it provides a stable installation and rotation basis for the impeller 2, and on the other hand, through a reasonable profile design, it optimizes the internal flow channel contour of the impeller 2, and cooperates with the impeller casing 5 to guide the gas to maintain a good flow pattern during the centrifugal acceleration process, reduce the separation and eddy current losses, and improve the overall aerodynamic performance and operation stability of the machine.

[0059] The axisymmetric endwall shaping technology is an easy-to-implement and high-efficiency centrifugal compressor stability enhancement technology. After determining the area on the impeller casing suitable for axisymmetric endwall shaping based on the rotating stall mechanism of the supercritical carbon dioxide centrifugal compressor, the embodiments of the present application divide 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 enhancement performance.

[0060] The larger the value of N, the finer the axisymmetric endwall shaping of the impeller casing, and more precise flow field regulation 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 regulation of the complex flow field, but also achieve a good balance between the design efficiency and the stability enhancement effect.

[0061] Step S02: Construct an axisymmetric endwall shaping curve control function for each sub-area respectively; the function is used to describe the shape of the endwall shaping curve formed after the axisymmetric endwall 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 。

[0062] Specifically, in the embodiments of the present application, for each sub-region, an axisymmetric endwall profile curve control function is constructed respectively. The axisymmetric endwall profile curve control function is a mathematical expression used to describe the shape of the endwall profile curve formed after performing axisymmetric endwall profiling on the sub-region, and can accurately determine the geometric characteristics of the endwall profile curve at different positions. By adjusting the parameters in the axisymmetric endwall profile curve control function, geometric attributes such as the curvature, slope, and height of the endwall profile curve can be flexibly changed, realizing the refined design of the endwall profile.

[0063] In the embodiments of the present application, the endwall 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 starting and ending points of the sub-region correspond to the starting and ending points of the endwall profile curve; the axisymmetric endwall 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 endwall profile curve in the radial direction relative to the original shape (i.e., the original turbine casing) when performing axisymmetric endwall profiling on the sub-region.

[0064] For example, the axisymmetric endwall profile curve control function of the sub-region can be designed as:

[0065] f(z)=ΔH max sin(az + b)+r(z) (1);

[0066] In formula (1), z is the coordinate of the endwall profile curve of the sub-region on the axial coordinate axis; f(z) is the radius of the endwall profile curve of the sub-region at the axial coordinate value of z, that is, the radius of the casing after axisymmetric endwall 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 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 the casing sinks 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; both a and b are constants. The undetermined parameters in formula (1) are ΔH max , a, and b.

[0067] 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 starting and ending point coordinates of the sub-region, determine the parameters in the function other than the maximum profiling height ΔH maxOther undetermined parameters other than those outside.

[0068] Specifically, refer to Figure 3 , Figure 3 is Figure 2 The partial enlarged view of the radial section at point A of the impeller in . In this partial enlarged view, the dotted line L1 is the original casing curve of the turbine; the solid line L2 is the casing curve after shaping, that is, the end wall shaping curve formed after the axisymmetric end wall shaping; the distance between the top of the 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 shaping curve of a sub-region, the phase difference between points B and C is 180°, P max point is the maximum shaping height point; P max The intersection point of the radial extension line of point and the original casing surface of the turbine is point O.

[0069] To ensure that the tip clearance remains basically unchanged before and after shaping, the maximum shaping 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:

[0070] ΔG = ΔH max / min(BO, CO) (2);

[0071] 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.

[0072] When conducting DOE (Design of Experiments) experiments, the number of segments N divided by the end wall shaping is corresponding to N factors. This is because: the shaping of each sub-region can be adjusted and controlled independently, and the change of each segment may have an impact on 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 shaping height ΔH max as the key variable, two levels of positive and negative are set, corresponding to the two shaping 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 tip profile of the blade 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 impact 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.

[0073] The profile gradient can be understood as the slope of the surface of the turbine casing or the profile curve of the blade tip 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 that the requirement of constant tip clearance is met. This is because: a smaller profile gradient means that the change of the surface curve of the turbine casing is relatively gentle. In this case, according to the above adjustment method where the profile of the blade tip adapts to the shape of the casing, it is relatively easy to maintain the stability of the tip clearance; if the profile gradient is too large, the change of the surface curve of the turbine casing is too drastic. When adjusting the height of the blade tip 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 cause large fluctuations in the tip clearance, thus affecting the performance of the supercritical carbon dioxide centrifugal compressor.

[0074] In addition, since the starting and ending point coordinates of the sub-region are known, other undetermined parameters in the control function of the axisymmetric end wall 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.

[0075] 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 |ΔH max | satisfies the profile gradient condition, optimize the maximum profile height ΔH max corresponding to N sub-regions through DOE experiments, and obtain N optimized maximum profile heights ΔH max , thereby determining N functions with all parameters determined.

[0076] 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 under 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 end wall profile of the turbine casing.

[0077] Among them, the isentropic efficiency η is an index that measures the effectiveness of a supercritical carbon dioxide centrifugal compressor in converting the input mechanical energy into gas pressure energy and kinetic energy. 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 of the supercritical carbon dioxide centrifugal compressor during the gas compression process, 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.

[0078] The calculation formula for the isentropic efficiency η is as follows:

[0079] (3);

[0080] In formula (3), h 01 is the total enthalpy at the inlet of the supercritical carbon dioxide centrifugal compressor, h 02 is the total enthalpy at the outlet of the supercritical carbon dioxide centrifugal compressor, and h 02s is the isentropic outlet total enthalpy of the supercritical carbon dioxide centrifugal compressor.

[0081] The stall margin refers to the safety margin of a supercritical carbon dioxide centrifugal compressor during operation, which is the distance from the occurrence of stall. 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 amount ΔSMI is used to measure the change in the stall margin of the supercritical carbon dioxide centrifugal compressor relative to before through certain design improvement or optimization measures. A positive value of ΔSMI indicates that the stall margin has been improved, meaning that the supercritical carbon dioxide centrifugal compressor can operate stably within a wider range of operating conditions and is not prone to stall, thereby improving the reliability and stability of the operation of the supercritical carbon dioxide centrifugal compressor.

[0082] The calculation formula for the stall margin improvement amount ΔSMI is as follows:

[0083] (4);

[0084] In formula (4), π NS and π a,NS respectively represent the total pressure ratios of the supercritical carbon dioxide centrifugal compressor before and after modification at the near-stall point; m NS and m a,NS respectively represent the mass flow rates of the supercritical carbon dioxide centrifugal compressor before and after modification at the near-stall point.

[0085] See Figure 4 , Figure 4 is the comparison diagram of the radial cross-sections of the impeller casing 5 before and after modeling. 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 a radial cross-sectional view of the impeller casing obtained after DOE experimental optimization and axisymmetric end wall modeling according to N functions. Figure 4 Only N=5 (i.e., divided into five sub-areas N1 to N5) is taken as an example for illustration.

[0086] Step S05: Verify whether the isentropic efficiency η and the stall margin improvement ΔSMI are both within the target range after the impeller casing is axially symmetrically shaped according to the N functions; if so, the shaping is considered complete and the current round of control is terminated; if not, proceed to step S06.

[0087] Step S06: Adjust the size of N, and then return to step S01.

[0088] In summary, the embodiment of the present application innovatively combines the axisymmetric end wall molding technology with the segmented molding technology, and performs a stabilization design for the impeller casing of a supercritical carbon dioxide centrifugal compressor, taking into account both ease of implementation and high efficiency, and is suitable for compact structural models, which can significantly improve the stabilization performance of the supercritical carbon dioxide centrifugal compressor.

[0089] In one possible implementation, verifying whether the isentropic efficiency η and the stall margin improvement ΔSMI are both within a target range after the impeller casing is axisymmetrically shaped according to N functions includes: using computer simulation technology, axisymmetrically shaped the impeller casing end wall according to the N functions, and performing numerical simulation analysis on the supercritical carbon dioxide centrifugal compressor after the shaping to determine whether the isentropic efficiency η and the stall margin improvement ΔSMI are both within the target range.

[0090] Specifically, through this function-based axisymmetric end wall shaping combined with numerical simulation analysis, performance can be evaluated in advance before actual manufacturing, avoiding repeated modifications due to unreasonable design, thereby shortening the R&D cycle. At the same time, accurately judging whether the isentropic efficiency η and stall margin improvement ΔSMI are within the target range will help to adjust the design in a timely manner, reduce the number of unnecessary experiments, reduce R&D costs, quickly determine the design scheme that meets performance requirements, and further improve R&D efficiency.

[0091] In a possible implementation, after performing numerical simulation analysis on the shaped supercritical carbon dioxide centrifugal compressor 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, on one hand, the computer simulation is used to quickly evaluate the design feasibility and shorten the R & D cycle, and on the other hand, the real working condition data is obtained through the actual machine testing to ensure the engineering practicability of the optimization scheme; this verification method combining theory and practice can effectively reduce the design risk and accurately verify the improvement effect of the axisymmetric endwall shaping 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.

[0092] Based on any of the above-provided axisymmetric endwall shaping 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 shaping is to be performed into N sub-regions along the axial direction, it further includes: through computer simulation technology, performing numerical simulation analysis on 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 cloud map of any axial height section of the tip flow field of the supercritical carbon dioxide centrifugal compressor, and outputting the entropy production rate cloud map. The entropy production rate cloud map provides a core reference basis for researchers to determine the area where axisymmetric endwall shaping is to be performed.

[0093] 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 like rotational speed, flow rate, inlet and outlet pressures, etc. 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 ability 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.

[0094] By continuously adjusting the operating conditions of the supercritical carbon dioxide centrifugal compressor and simulating, 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 airflow separation occur, approaching but not yet reaching the stall state. That is, 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.

[0095] The entropy production rate is a physical quantity that measures the 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, airflow 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.

[0096] The flow condition at the tip has an important impact on the overall performance of the supercritical carbon dioxide centrifugal compressor. Analyzing the cross-section of the 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 tip flow field is selected to draw an entropy production rate contour map, which graphically shows the distribution of the entropy production rate on the cross-section of the 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 tip flow field.

[0097] Based on the energy loss distribution of the tip flow field, researchers determine the rotating stall mechanism of the supercritical carbon dioxide centrifugal compressor, and then determine the flow channel area where the source of the energy loss is located; the end wall covering the flow channel area is used as the area for axially symmetric end wall shaping.

[0098] In addition, corresponding to the above method embodiments, see Figure 5 , the embodiments of this application also provide a device for axially symmetric end wall shaping of a supercritical carbon dioxide centrifugal compressor, including:

[0099] A region division unit 100, configured to divide the region on the impeller casing of the supercritical carbon dioxide centrifugal compressor where axially symmetric end wall shaping is to be performed into N sub-regions along the axial direction; N≥2;

[0100] A function construction unit 200 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 starting and ending points of the sub-region are the starting and ending points of the curve; the function includes multiple undetermined parameters, and one of the undetermined parameters is the maximum profiling height ΔH. max ;

[0101] A parameter determination unit 300 is configured to, for each sub-region, determine the absolute value |ΔH| of the maximum profiling height that satisfies 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, based on the starting and ending point coordinates of the sub-region, determine the other undetermined parameters in the function except for the maximum profiling height ΔH. max |, and, based on the starting and ending point coordinates of the sub-region, determine the other undetermined parameters in the function except for the maximum profiling height ΔH. max outside.

[0102] A parameter optimization unit 400 is configured to use improving the isentropic efficiency η and the stall margin improvement ΔSMI as the optimization goal. On the basis of ensuring that the absolute value |ΔH| of the maximum profiling height satisfies the profile gradient condition, optimize the maximum profiling height ΔH corresponding to N sub-regions through DOE experiments to obtain N optimized maximum profiling heights ΔH, thereby determining N functions with all parameters determined. max |, and on the basis of ensuring that the absolute value |ΔH| of the maximum profiling height satisfies the profile gradient condition, optimize the maximum profiling height ΔH corresponding to N sub-regions through DOE experiments to obtain N optimized maximum profiling heights ΔH. max to obtain N optimized maximum profiling heights ΔH. max , thereby determining N functions with all parameters determined.

[0103] A verification and iteration unit 500 is configured to verify whether the isentropic efficiency η and the stall margin improvement ΔSMI are both within the target range after axisymmetric endwall profiling of the turbomachinery 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.

[0104] This device takes into account both ease of implementation and high efficiency, and is suitable for compact structures, improving the stability extension performance of the supercritical carbon dioxide centrifugal compressor.

[0105] In an embodiment of the present application, an electronic device is further provided. 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 supercritical carbon dioxide centrifugal compressor axisymmetric endwall profiling methods.

[0106] In an embodiment of the present application, there is also provided a computer program product including computer-readable instructions. When the computer-readable instructions run on an electronic device, the electronic device is enabled to implement any of the axial symmetry endwall shaping methods of a supercritical carbon dioxide centrifugal compressor provided in the embodiments of the present application.

[0107] In an embodiment of the present application, there is also provided a computer-readable storage medium. 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 is enabled to implement any of the axial symmetry endwall shaping methods of a supercritical carbon dioxide centrifugal compressor provided in the embodiments of the present application.

[0108] In addition, it should be noted that the device embodiments described above are only illustrative. The units described as separate components may or may not be physically separated, and 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 attached drawings of the device embodiments provided in the present application, the connection relationship between the modules indicates that they have a communication connection, which can be specifically implemented as one or more communication buses or signal lines.

[0109] 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, and of course, it can also be implemented by dedicated hardware including dedicated 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, etc. However, for the present application, in more cases, software program implementation is a better implementation method. 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, etc., and includes several instructions to enable 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.

[0110] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware or any combination thereof. When implemented by software, it can be implemented in whole or in part in the form of a computer program product.

[0111] 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 the present 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 via wired (such as coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (such as infrared, wireless, microwave, etc.) means. 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 a data center that includes one or more integrated available media. The available medium may be a magnetic medium (such as a floppy disk, a hard disk, a magnetic tape), an optical medium (such as a DVD), or a semiconductor medium (such as a solid state disk (SSD)).

[0112] The foregoing description of the disclosed embodiments enables those skilled in the art to implement or use the present application. Various modifications to these embodiments will be readily 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 the present application. Therefore, the embodiments of the present application will not be limited to the embodiments shown herein, but will be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for shaping the axisymmetric end wall of a supercritical carbon dioxide centrifugal compressor, characterized in that: include: The region on the impeller casing of a supercritical carbon dioxide centrifugal compressor where axisymmetric end wall shaping is to be performed is divided into N subregions along the axial direction. N≥2； A control function for the axisymmetric end wall shaping curve is constructed for each sub-region; the function is used to describe the shape of the end wall shaping curve formed after the axisymmetric end wall shaping of the sub-region is performed. The curve is in the form of an arc of constant curvature 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, one of which is the maximum shaping height Δ H max ; For each sub-area, determine the absolute value of the maximum molding height |Δ H max The profile gradient requirement is set based on 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 coordinates of the starting and ending points of the sub-region, the function excluding the maximum profile height Δ is determined. H max Other undetermined parameters besides To improve isentropic efficiency η and stall margin improvement Δ SMI As the optimization goal, the absolute value of the maximum molding height |Δ H max |On the basis of satisfying the gradient condition of the molding line, the maximum molding height Δ corresponding to N sub-areas is experimentally designed. H max Optimize and obtain N optimized maximum modeling heights Δ H max , thereby determining N functions with all parameters determined; Verify that after the impeller casing is axially symmetrically shaped according to N of the above functions, the isentropic efficiency η and stall margin improvement Δ SMI Are they all within the target range? If not, adjust N and execute the above steps again until the isentropic efficiency is η and stall margin improvement Δ SMI All are within the target range.

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

3. The method for shaping the axisymmetric end wall of a supercritical carbon dioxide centrifugal compressor according to claim 1, characterized in that: Determine the absolute value of the maximum molding height |Δ that meets the profile gradient requirements of the curve H max |, including: Determine a solution that satisfies Δ H max / min(BO,CO)<0.5|Δ H max |, as the absolute value of the maximum molding height that meets the profile gradient requirement of the curve |Δ H max |; Point B and point C are the starting and ending points of the curve respectively, and point O is the intersection of the radial extension line of the maximum molding 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 that after the impeller casing is axially symmetrically shaped according to N functions, the isentropic efficiency η and stall margin improvement Δ SMI Are all within target ranges, including: Through computer simulation technology, the impeller casing is shaped into an axisymmetric end wall according to N functions, and the supercritical carbon dioxide centrifugal compressor after the shape is numerically simulated and analyzed to determine the isentropic efficiency. η and stall margin improvement Δ SMI Are they all within the target range? 5. The method for shaping the axisymmetric end wall of a supercritical carbon dioxide centrifugal compressor according to claim 4, characterized in that: The numerical simulation analysis of the supercritical carbon dioxide centrifugal compressor after modeling was carried out to determine the isentropic efficiency η and stall margin improvement Δ SMI Once all are within the target range, it also includes: After manufacturing a supercritical carbon dioxide centrifugal compressor according to N functions, the actual operating parameters of the supercritical carbon dioxide centrifugal compressor are collected and tested, and compared with the actual operating parameters of the original supercritical carbon dioxide centrifugal compressor to determine the isentropic efficiency. η and stall margin improvement Δ SMI Are they all within the target range? 6. The method for shaping the axisymmetric end wall of a supercritical carbon dioxide centrifugal compressor according to claim 1, characterized in that: Before dividing the region on the impeller casing of the supercritical carbon dioxide centrifugal compressor where the axisymmetric end wall shaping is to be performed into N subregions along the axial direction, the method 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; based on the operating characteristics of the supercritical carbon dioxide centrifugal compressor at the near-stall point, an entropy generation rate cloud map on any axial height cross-section of the blade tip flow field of the supercritical carbon dioxide centrifugal compressor is generated, and the entropy generation rate cloud map is output; the entropy generation rate cloud map is one of the bases for determining the area where the axisymmetric end wall shaping is to be performed.

7. A supercritical carbon dioxide centrifugal compressor axisymmetric end wall molding device, characterized in that: include: A region division unit is used to divide the region on the impeller casing of the supercritical carbon dioxide centrifugal compressor where axisymmetric end wall shaping is to be performed into N subregions along the axial direction; N≥2； A function construction unit is used to construct 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 the axisymmetric end wall shaping of the sub-region is performed, the curve is in the form of a circular arc of constant curvature 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, one of which is the maximum shaping height Δ H max ; A parameter determination unit is used to determine, for each sub-area, the absolute value of the maximum molding height |Δ H max The profile gradient requirement is set based on 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 coordinates of the starting and ending points of the sub-region, the function excluding the maximum profile height Δ is determined. H max Other undetermined parameters besides Parameter optimization unit to improve isentropic efficiency η and stall margin improvement Δ SMI As the optimization goal, the absolute value of the maximum molding height |Δ H max |On the basis of satisfying the gradient condition of the molding line, the maximum molding height Δ corresponding to N sub-areas is experimentally designed. H max Optimize and obtain N optimized maximum modeling heights Δ H max , thereby determining N functions with all parameters determined; Verification and iteration unit, used to verify the isentropic efficiency after the impeller casing is axially symmetrically shaped according to N functions. η and stall margin improvement Δ SMI Are they all within the target range? If not, adjust N and execute the above steps again until the isentropic efficiency is η and stall margin improvement Δ SMI All are within the target range.

8. A computer program product, characterized in that The method comprises computer-readable instructions, which, when executed on an electronic device, enable the electronic device to implement the method for shaping the axisymmetric end wall of a supercritical carbon dioxide centrifugal compressor as claimed in any one of claims 1 to 6.

9. An electronic device, characterized in that: comprising at least one processor and a memory connected to the processor, wherein: The memory is used to store computer programs; The processor is used to execute the computer program so that the electronic device can implement the axisymmetric end wall shaping method of a 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, which, when executed by an electronic device, enable the electronic device to implement the method for shaping the axisymmetric end wall of a supercritical carbon dioxide centrifugal compressor as described in any one of claims 1 to 6.

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