Supersonic turbine blade profile design method and system based on feature method

Abstract

The invention provides a supersonic turbine blade profile design method and system based on a feature method, and relates to the technical field of supersonic turbine blade profile design. According to the technical key points, a suction surface of the supersonic turbine blade is divided into a suction surface inlet transition section, a suction surface arc section and a suction surface outlet transition section, and a pressure surface is divided into a pressure surface inlet transition section, a pressure surface arc section and a pressure surface outlet transition section; based on a characteristic method, according to inlet parameters, outlet parameters and flow characteristic parameters of the supersonic turbine, multi-point coordinates on inlet transition section molded lines and outlet transition section molded lines of a suction surface and a pressure surface are solved in a stepping mode, and then transition section molded lines are obtained; and calculating according to the transition section molded line and the geometric characteristic parameters of the blade to obtain an arc section molded line. According to the method, efficient and accurate design of the supersonic turbine blade profile is achieved, high applicability is achieved, the design requirement of the supersonic turbine blade profile under the wide-range inlet Mach number working condition can be met, and reliable technical support is provided for supersonic turbine design.

Description

Technical Field

[0001] The present invention relates to the technical field of supersonic turbine blade profile design, and in particular to a supersonic turbine blade profile design method and system based on a characteristic method. Background Art

[0002] As thrust-to-weight ratios and efficiency requirements for aircraft engines and gas turbines continue to increase, supersonic turbines, due to their high energy density, have become a research hotspot. However, their complex flow environment (such as shock wave and expansion wave interactions, boundary layer separation, and high aerodynamic thermal loads) poses severe challenges to traditional blade design. Traditional empirical design methods or those based on potential flow theory struggle to accurately capture the nonlinear wave structure and shock wave losses in supersonic flows. Optimization methods that rely on high-precision computational fluid dynamics (CFD) face challenges such as high computational costs and complex parameter coupling. Summary of the Invention

[0003] Therefore, the present invention proposes a supersonic turbine blade design method and system based on the characteristic method to solve the problems of large CFD computing resource consumption, low accuracy of empirical design shock wave control and limited aerodynamic loss optimization in existing supersonic turbine blade design methods.

[0004] According to one aspect of the present invention, a supersonic turbine blade design method based on a characteristic method is proposed, the method comprising:

[0005] Obtain supersonic turbine inlet parameters, outlet parameters, flow characteristic parameters and blade geometric characteristic parameters;

[0006] The suction surface of the supersonic turbine blade is divided into a suction surface inlet transition section, a suction surface arc section and a suction surface outlet transition section, and the pressure surface is divided into a pressure surface inlet transition section, a pressure surface arc section and a pressure surface outlet transition section;

[0007] Based on the characteristic method, according to the supersonic turbine inlet parameters, outlet parameters, and flow characteristic parameters, the multi-point coordinates on the suction surface inlet transition section profile, the suction surface outlet transition section profile, the pressure surface inlet transition section profile, and the pressure surface outlet transition section profile are respectively solved step by step, thereby obtaining the suction surface inlet transition section profile, the suction surface outlet transition section profile, the pressure surface inlet transition section profile, and the pressure surface outlet transition section profile;

[0008] The suction surface arc segment profile is obtained by calculation based on the suction surface inlet transition section profile, the suction surface outlet transition section profile and the blade geometric characteristic parameters; the pressure surface arc segment profile is obtained by calculation based on the pressure surface inlet transition section profile, the pressure surface outlet transition section profile and the blade geometric characteristic parameters.

[0009] Furthermore, the supersonic turbine inlet parameters include the supersonic turbine inlet Mach number Mi , the export parameters include the turbine outlet Mach number M o ; Flow characteristic parameters include the exit Mach number M of the suction surface inlet transition section l and the outlet Mach number M of the pressure surface inlet transition section u ; Blade geometric characteristic parameters include supersonic turbine blade turning angle and blade thickness.

[0010] Furthermore, the process of step-by-step solving the coordinates of multiple points on the suction surface inlet transition section profile or the pressure surface inlet transition section profile based on the characteristic method and the supersonic turbine inlet parameters, outlet parameters, and flow characteristic parameters, and then obtaining the suction surface inlet transition section profile or the pressure surface inlet transition section profile includes:

[0011] Based on the characteristic method, a characteristic line equation of the isentropic expansion flow in the suction side inlet transition section or the pressure side inlet transition section is designed, and the characteristic line equation is solved to obtain the coordinates of multiple points on the characteristic line;

[0012] Based on the relationship between characteristic lines and Mach lines, the equations of multiple segments of Mach lines are determined according to the coordinates of multiple points on the characteristic lines;

[0013] Based on the relationship between the Mach line and the profile, the coordinates of multiple points on the profile are determined according to the multi-segment Mach line equation, and then the profile of the suction side inlet transition section or the pressure side inlet transition section is determined.

[0014] Furthermore, the characteristic line equation of the isentropic expansion flow in the transition section of the suction surface inlet is designed as follows:

[0015]

[0016] Where, It represents the turning angle of the airflow during the isentropic expansion flow at the transition section of the suction surface inlet; R * represents the dimensionless radius of any point on the streamline, γ represents the gas specific heat ratio, f(R * ) represents a dimensionless radius function; R l * It represents the dimensionless radius of the inlet transition section of the suction surface; Indicates that R l * Substitute f(R * ) function;

[0017] The characteristic line equation of the isentropic expansion flow in the pressure surface inlet transition section is designed as follows:

[0018]

[0019] Where, R represents the turning angle of the airflow at the isentropic expansion flow in the transition section of the pressure surface inlet; u * It represents the dimensionless radius of the outlet of the transition section of the pressure surface inlet; Indicates that R u * Substitute f(R * ) function;

[0020] The characteristic line equation is solved using the Newton iteration method to obtain the dimensionless radius of each point on the characteristic line. The coordinates of the kth point on the characteristic line of the isentropic expansion flow in the transition section of the suction surface inlet are:

[0021]

[0022] Where, R represents the airflow turning angle of the kth section of the suction surface inlet transition section; k * The dimensionless radius of the kth point on the characteristic line of the isentropic expansion flow in the transition section of the suction surface inlet;

[0023] The coordinates of the jth point on the characteristic line of the isentropic expansion flow in the transition section of the pressure surface inlet are:

[0024]

[0025] Where, R represents the airflow turning angle of the jth section of the pressure surface inlet transition section; 2j * The dimensionless radius of the jth point on the characteristic line representing the isentropic expansion flow in the transition section of the pressure surface inlet.

[0026] Furthermore, the relationship between the characteristic line and the Mach line includes: the characteristic line intersects the Mach line, the slope direction of the Mach line is consistent with the flow direction of the airflow; the equation of the multi-segment Mach line is:

[0027]

[0028] Where m k represents the slope, which is the average flow direction of the airflow between the k+1th point and the kth point; x m,k * 、y m,k * represents the coordinates of the kth point on the Mach line; x k * 、y k * Represents the coordinates of the kth point on the feature line.

[0029] Furthermore, the relationship between the Mach line and the profile line includes: the direction of the profile line of the inlet transition section is parallel to the direction of the airflow velocity and intersects with the Mach line;

[0030] The equations of the infinitesimal straight lines of each segment of the inlet transition section profile are:

[0031]

[0032] Where, Indicates the slope of the straight line corresponding to the inlet transition section; x m,k+1 * y m,k+1 * represents the coordinates of the k+1th point on the Mach line; x s,k * 、y s,k * Indicates the coordinates of the kth point on the inlet transition section profile;

[0033] The intersection of the infinitesimal straight lines of each segment of the inlet transition section profile and the multi-segment Mach line equations is solved simultaneously to obtain the coordinates of multiple points on the suction surface inlet transition section profile or the pressure surface inlet transition section profile, and then determine the suction surface inlet transition section profile or the pressure surface inlet transition section profile.

[0034] Furthermore, the process of obtaining the suction surface arc segment profile or the pressure surface arc segment profile includes:

[0035] The suction surface arc segment turning angle is obtained by subtracting the airflow turning angle of the suction surface inlet transition section and the airflow turning angle of the suction surface outlet transition section from the supersonic turbine blade turning angle β; the reciprocal of the outlet Mach number of the suction surface inlet transition section is determined as the dimensionless radius of the suction surface arc segment; and the suction surface arc segment profile is determined according to the suction surface arc segment turning angle and the dimensionless radius of the suction surface arc segment;

[0036] The turning angle of the pressure surface arc section is obtained by subtracting the airflow turning angle of the pressure surface inlet transition section and the airflow turning angle of the pressure surface outlet transition section from the turning angle β of the supersonic turbine blade; the reciprocal of the outlet Mach number of the pressure surface inlet transition section is determined as the dimensionless radius of the pressure surface arc section; and the pressure surface arc section profile is determined based on the turning angle and the dimensionless radius of the pressure surface arc section.

[0037] Furthermore, the method also includes: using arc curves to design the leading edge section and trailing edge section of the supersonic turbine blade, and obtaining the tangent point coordinates of the leading edge section and trailing edge section curves of the blade with the suction surface and pressure surface based on the thickness of the supersonic turbine blade; under the conditions of two points on the determined arc and the arc radius, determining the curve equations of the leading edge section and trailing edge section, and then obtaining the leading edge section profile line and trailing edge section profile line.

[0038] According to another aspect of the present invention, a supersonic turbine blade profile design system based on a feature method is provided, the system comprising:

[0039] a parameter acquisition module configured to acquire supersonic turbine inlet parameters, outlet parameters, flow characteristic parameters, and blade geometric characteristic parameters;

[0040] A suction surface profile design module is configured to divide the suction surface of a supersonic turbine blade into a suction surface inlet transition section, a suction surface arc section, and a suction surface outlet transition section; based on a characteristic method, according to the supersonic turbine inlet parameters, outlet parameters, and flow characteristic parameters, the multi-point coordinates on the suction surface inlet transition section profile and the suction surface outlet transition section profile are respectively solved step by step to obtain the suction surface inlet transition section profile and the suction surface outlet transition section profile; the suction surface arc section profile is calculated based on the solved suction surface inlet transition section profile and the suction surface outlet transition section profile and the blade geometric characteristic parameters;

[0041] A pressure surface profile design module is configured to divide the pressure surface of a supersonic turbine blade into a pressure surface inlet transition section, a pressure surface arc section, and a pressure surface outlet transition section. Based on a characteristic method, according to the supersonic turbine inlet parameters, outlet parameters, and flow characteristic parameters, the multi-point coordinates on the pressure surface inlet transition section profile and the pressure surface outlet transition section profile are solved step by step to obtain the pressure surface inlet transition section profile and the pressure surface outlet transition section profile; the pressure surface arc section profile is calculated based on the solved pressure surface inlet transition section profile, the pressure surface outlet transition section profile, and the blade geometric characteristic parameters.

[0042] Furthermore, in the suction surface profile design module and the pressure surface profile design module, based on the characteristic method, according to the supersonic turbine inlet parameters, outlet parameters, and flow characteristic parameters, the process of step-by-step solving the multi-point coordinates on the suction surface inlet transition section profile, the suction surface outlet transition section profile, the pressure surface inlet transition section profile, and the pressure surface outlet transition section profile includes:

[0043] Based on the characteristic method, a characteristic line equation of the isentropic expansion flow in the transition section is designed, and the characteristic line equation is solved to obtain the coordinates of multiple points on the characteristic line;

[0044] Based on the relationship between characteristic lines and Mach lines, the equations of multiple segments of Mach lines are determined according to the coordinates of multiple points on the characteristic lines;

[0045] Based on the relationship between the Mach line and the profile line, the coordinates of multiple points on the profile line are determined according to the multi-segment Mach line equation.

[0046] The beneficial technical effects of the present invention are:

[0047] The present invention proposes a supersonic turbine blade design method and system based on the characteristic method. Based on the physical modeling of the characteristic line method of complete gas steady isentropic flow, the supersonic flow field parameters and the blade geometric curvature are explicitly associated by constructing a characteristic line network, thereby realizing efficient and accurate design of the supersonic turbine blade.

[0048] The present invention regulates the flow state of the supersonic airflow through the isentropic constraints of compression waves and expansion waves (i.e., formulas (4) and (5)), thereby realizing isentropic expansion, isentropic compression and flow steering of the supersonic airflow, thereby effectively suppressing aerodynamic losses and optimizing the flow structure. The parameterized characteristic line method has high design applicability and can meet the supersonic turbine blade design requirements for a wide range of inlet Mach number conditions.

[0049] The present invention combines theoretical rigor with engineering practicality. While ensuring the orderly distribution of compression waves and expansion waves, it significantly shortens the design cycle and provides reliable theoretical and technical support for the rapid design of supersonic turbines. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] The above and other objects, features and advantages of the exemplary embodiments of the present invention will become readily apparent by reading the following detailed description with reference to the accompanying drawings, in which several embodiments of the present invention are shown by way of example and not limitation, in which:

[0051] Figure 1 Schematic diagram of a supersonic turbine blade profile calculation model in an embodiment of the present invention;

[0052] Figure 2 This is a flow chart of a supersonic turbine blade design method based on a feature method according to an embodiment of the present invention;

[0053] Figure 3 is a distribution diagram of the Mach number on the surface of the turbine blade in an embodiment of the present invention;

[0054] Figure 4 Schematic diagram of dimensionless calculation of the transition section profile of the suction surface inlet in an embodiment of the present invention;

[0055] Figure 5 Schematic diagram of dimensionless calculation of the pressure surface inlet transition section profile in an embodiment of the present invention;

[0056] Figure 6 Schematic diagram of the supersonic turbine blade structure designed in an embodiment of the present invention. DETAILED DESCRIPTION

[0057] The principles and spirit of the present invention will be described below with reference to several exemplary embodiments. It should be understood that these embodiments are provided solely to enable those skilled in the art to better understand and implement the present invention, and are not intended to limit the scope of the present invention in any way. Rather, these embodiments are provided to make this disclosure more thorough and complete, and to fully convey the scope of the present disclosure to those skilled in the art.

[0058] It is known to those skilled in the art that the embodiments of the present invention may be implemented as a system, apparatus, device, method, or computer program product. Therefore, the present disclosure may be specifically implemented in the following forms, namely: complete hardware, complete software (including firmware, resident software, microcode, etc.), or a combination of hardware and software. It should be understood that any number of elements in the accompanying drawings is for illustration and not limitation, and any nomenclature is for distinction only and does not have any limiting meaning.

[0059] The Method of Characteristics (MOC) analyzes the physical propagation path of supersonic flow by solving the characteristic line network of hyperbolic partial differential equations, thereby systematically constructing a mapping relationship between blade curvature and flow parameters. This method generates the initial blade profile through characteristic line interpolation. Combined with shock wave control strategies (such as isentropic compression surface design), it can effectively optimize shock wave morphology and reduce total pressure loss, while also taking into account aerodynamic stability in the transonic transition region. In addition, the characteristic method can be integrated with optimization tools such as genetic algorithms and adjoint equations to further achieve adaptive blade profile generation under multi-objective constraints, providing a solution that combines theoretical rigor with engineering practicality for the efficient design of supersonic turbines.

[0060] In response to the problems of large CFD computing resource consumption, low accuracy of empirical design shock wave control, and limited aerodynamic loss optimization in existing supersonic turbine blade design methods, the present invention proposes a supersonic turbine blade design method and system based on the characteristic method, that is, a supersonic turbine blade characteristic design method based on complete gas steady isentropic flow, which realizes the controllable and orderly distribution of compression waves and expansion wave systems through explicit mapping of characteristic lines to geometric curvatures, and can quickly and accurately solve and draw the profile lines of the two-dimensional turbine blade pressure surface and suction surface under a given inlet airflow Mach number.

[0061] like Figure 1As shown, the present invention divides the suction surface of the supersonic turbine blade into a straight line segment (BE segment and GJ segment), a suction surface inlet transition segment (AB segment), a suction surface arc segment (AF segment) and a suction surface outlet transition segment (FG segment), and the pressure surface is divided into a pressure surface inlet transition segment (CD segment), a pressure surface arc segment (CH segment) and a pressure surface outlet transition segment (HI segment); the straight line segment on the suction surface does not affect the gas flow characteristics, so it does not need to be designed and solved, while the other parts of the profile need to be solved and calculated using the characteristic line method.

[0062] Therefore, the embodiment of the present invention provides a supersonic turbine blade design method based on the characteristic method, such as Figure 2 As shown, the method includes:

[0063] First, obtain the supersonic turbine inlet parameters, outlet parameters, flow characteristic parameters and blade geometric characteristic parameters;

[0064] Then, the suction surface of the supersonic turbine blade is divided into a suction surface inlet transition section, a suction surface arc section and a suction surface outlet transition section, and the pressure surface is divided into a pressure surface inlet transition section, a pressure surface arc section and a pressure surface outlet transition section; based on the characteristic method, according to the supersonic turbine inlet parameters, outlet parameters and flow characteristic parameters, the multi-point coordinates on the suction surface inlet transition section profile line, the suction surface outlet transition section profile line, the pressure surface inlet transition section profile line and the pressure surface outlet transition section profile line are respectively solved step by step, and then the suction surface inlet transition section profile line, the suction surface outlet transition section profile line, the pressure surface inlet transition section profile line and the pressure surface outlet transition section profile line are obtained;

[0065] Then, the suction surface arc segment profile is obtained by calculation based on the obtained suction surface inlet transition section profile, suction surface outlet transition section profile and blade geometric characteristic parameters; the pressure surface arc segment profile is obtained by calculation based on the solved pressure surface inlet transition section profile, pressure surface outlet transition section profile and blade geometric characteristic parameters.

[0066] In this embodiment, the supersonic turbine inlet parameters include the supersonic turbine inlet Mach number M i , the export parameters include the turbine outlet Mach number M o ; Flow characteristic parameters include the exit Mach number M of the suction surface inlet transition section l and the outlet Mach number M of the pressure surface inlet transition section u ; The blade geometric characteristic parameters include the supersonic turbine blade turning angle β and blade thickness δ.

[0067] like Figure 3 As shown in the figure, the suction side inlet transition section and the pressure side inlet transition section convert the given uniform incoming flow into vortex flow, and the suction side inlet transition section converts the inlet Mach number M i Increase to the exit Mach number M of the transition section of the suction surface inlet l; The pressure surface inlet transition section will inlet Mach number M i Reduce the exit Mach number M of the pressure surface inlet transition section u ; The Mach number of the airflow on the arc section of the suction surface and the arc section of the pressure surface remains unchanged, achieving flow turning and maintaining vortex flow. Theoretically, since the Euler equation for binary steady isentropic supersonic flow is a hyperbolic differential equation, the flow characteristics upstream are independent of the downstream parameters, so the flow field can be solved using a step-by-step characteristic line method. In the characteristic method design, the flow in the flow field is controlled to satisfy the isentropic flow of the binary Euler equation to minimize the loss. During the calculation process, the flow field is decomposed into multiple small areas, and the flow characteristics in each area are considered constant. Adjacent areas are divided by characteristic lines, Mach lines or physical boundaries.

[0068] Based on the above principles, Figure 4 As shown, the suction surface inlet transition section profile of the supersonic turbine blade is composed of a series of straight line segments, and the process of obtaining the suction surface inlet transition section profile is as follows.

[0069] First, according to the turbine inlet Mach number M i and the exit Mach number M of the suction surface inlet transition section l , calculate the Prandtl-Meyer expansion angle v at the turbine inlet respectively i and the Prandtl-Meyer expansion angle v at the inlet transition section outlet of the suction surface l , the calculation formula of the Prandtl-Meyer expansion angle is as follows:

[0070]

[0071] Where, γ is the gas specific heat ratio; M * Indicates the speed factor.

[0072] Since the product of the velocity V and the streamline radius R in the eddy current field is a constant, the critical velocity V is used. cr The product of V and R is dimensionless by the radius r* of the sonic line:

[0073]

[0074] Where R * Represents the dimensionless radius. Equation (2) is valid for any point in the eddy current field.

[0075] Speed ​​factor M * The relationship with the Mach number M is as follows:

[0076]

[0077] According to the turbine inlet Mach number M in the input parameters i and the exit Mach number M of the suction surface inlet transition sectionl The inlet velocity factor M of the suction surface inlet transition section can be obtained by formula (3): i * and the outlet velocity factor M of the suction surface inlet transition section l * ; Then, the dimensionless radius R of the inlet transition section of the suction surface is obtained by formula (2): i * and the dimensionless radius R of the outlet l * .

[0078] The inlet transition section passes through the The flow turning angle of each microelement is calculated in a step-by-step manner. Since the airflow is an isentropic expansion flow at the inlet transition section, the flow turning angle is The dimensionless radius R of any point on the streamline * The following relationship is satisfied:

[0079]

[0080] C in formula (4) represents a constant; f(R * ) represents a dimensionless radius function. For the characteristic line of the expansion flow in the transition section of the suction surface inlet, in formula (4) Take the "+" sign and click k max+1 (x * =0,y * =R * l ) is on the characteristic line, so the characteristic line equation satisfies:

[0081]

[0082] Where R l * It represents the dimensionless radius of the inlet transition section of the suction surface; Indicates that R l * Substitute f(R * ) function.

[0083] Assume that the suction surface inlet transition section is divided into k max The step increment of the Prandtl-Meyer expansion angle corresponding to each infinitesimal straight line segment is Δv, and its value can be calculated by the following formula:

[0084]

[0085] The corresponding kth segment (k ranges from 1 to k max ) is:

[0086]

[0087] Where, v i represents the Prandtl-Meyer expansion angle at the turbine inlet; v l represents the Prandtl-Meyer expansion angle at the outlet of the inlet transition section of the suction surface; It represents the airflow turning angle of the k+1th section of the suction surface inlet transition section.

[0088] According to equations (1), (5), (6) and (8), we can get the k-th point The relationship with Δv satisfies the following formula:

[0089]

[0090] For each k value, the dimensionless radius of the point on the characteristic line can be solved by Newton iteration method (i.e., iteratively solving equation (5)). Then the coordinates of the kth point on the characteristic line are:

[0091]

[0092] Where, R represents the airflow turning angle of the kth section of the suction surface inlet transition section; k * The dimensionless radius of the kth point on the characteristic line representing the isentropic expansion flow in the transition section of the suction surface inlet.

[0093] In this embodiment, the points on the characteristic line and the points on the inlet transition section profile are established through the Mach line. Therefore, based on the solution of the characteristic line equation, the recursive relationship of the Mach line is further solved to determine the points on the inlet transition section profile.

[0094] The points on the solved characteristic line are also on the Mach line (that is, the characteristic line intersects the Mach line), and the slope of the Mach line is consistent with the flow direction. First, the average flow angle between points k+1 and k is used to solve the slope of the Mach line in this area:

[0095]

[0096] Where, Mach angle μ k for:

[0097]

[0098] Among them, M k is the Mach number at the kth point on the characteristic line.

[0099] The Mach line equation is:

[0100]

[0101] Where x m,k * 、y m,k * represents the coordinates of the kth point on the Mach line; x k * 、y k * Represents the coordinates of the kth point on the feature line.

[0102] After obtaining the Mach line equation, since the direction of the suction surface inlet transition section profile is parallel to the airflow velocity direction and intersects with the Mach line, the slope of the straight line corresponding to the inlet transition section is for:

[0103]

[0104] In the above formula, the value of k ranges from k=1 to k=k max .

[0105] The equations of the infinitesimal straight lines of each segment of the inlet transition section profile are:

[0106]

[0107] Where x m,k+1 * 、y m,k+1 * represents the coordinates of the k+1th point on the Mach line; x s,k * 、y s,k * Indicates the coordinates of the kth point on the inlet transition section profile.

[0108] The coordinates of the intersection of two straight lines (i.e. a certain Mach line and a certain inlet transition section profile) can be solved as:

[0109]

[0110] The coordinates of the intersection points of the straight lines on the inlet transition section are from k=k max Solve step by step until k=1, and k=k max hour,

[0111] In this embodiment, the design of the suction surface outlet transition section profile is the same as that of the suction surface inlet transition section profile. The difference is that the characteristic method is used according to the above process from k=1 to k=k max Step-by-step solution, the airflow from the suction surface Mach number M l Through a series of isentropic compression waves, the airflow reaches the exit Mach number M of the suction surface exit transition section. o , that is, the turbine inlet Mach number M iand the exit Mach number M of the suction surface inlet transition section l Replaced by the inlet Mach number M of the suction surface outlet transition section l and the exit Mach number M of the suction surface exit transition section o , and for formula (4) Take the “-” sign and the Mach angle in formula (13) takes a positive value, that is:

[0112]

[0113] The rest of the calculation process is the same and will not be repeated here.

[0114] In this embodiment, for the design of the arc section profile of the suction surface, according to equations (2) and (3), since the radius does not change and the flow velocity does not change, the arc section only provides the turning of the airflow without changing the airflow velocity. The Mach number of the airflow on the arc section is always equal to the outlet Mach number M of the inlet transition section of the suction surface. l , so the dimensionless radius of the arc segment can be determined as:

[0115]

[0116] The arc profile can be determined by simply determining the angle of the arc segment. c It can be obtained by subtracting the inlet transition section airflow turning angle and the outlet transition section airflow turning angle from the given turbine blade turning angle β, that is:

[0117] β c =β-(|v l -v i |+|v l -v o |) (21)

[0118] The outlet Prandtl-Meyer expansion angle v of the outlet transition section is o The turbine outlet Mach number M is input o The solution of equation (1) is: and the arc segment turning angle β c Determine the arc segment profile of the suction surface.

[0119] In this embodiment, Figure 5 As shown, the pressure surface inlet transition section profile of the supersonic turbine blade is composed of a series of straight line segments, and the process of obtaining the pressure surface inlet transition section profile is as follows.

[0120] The inlet Mach number is M i The airflow isentropically compressed and decelerated to the input pressure surface Mach number M uThe specific calculation process is the same as the design process of the suction surface inlet transition section profile. The difference is that in the flow compression process, the "-" sign is used in equation (4), so the characteristic line equation of equation (6) is rewritten as:

[0121]

[0122] Where, R represents the turning angle of the airflow at the isentropic expansion flow in the transition section of the pressure surface inlet; u * It represents the dimensionless radius of the outlet of the transition section of the pressure surface inlet; Indicates that R u * Substitute f(R * ) function.

[0123] If the Mach angle takes a positive value, equation (13) can be rewritten as:

[0124]

[0125] The coordinates of the intersection points of the straight line segments on the pressure surface inlet transition section are from j=j max Solve step by step until j=1, and j=j max hour,

[0126] The coordinates of the jth point on the characteristic line of the isentropic expansion flow in the transition section of the pressure surface inlet are:

[0127]

[0128] Where, R represents the airflow turning angle of the jth section of the pressure surface inlet transition section; 2j * The dimensionless radius of the jth point on the characteristic line representing the isentropic expansion flow in the transition section of the pressure surface inlet.

[0129] In this embodiment, the calculation methods of the pressure surface arc transition section and the pressure surface outlet transition section profiles are consistent with the aforementioned suction surface arc transition section and the suction surface outlet transition section profiles, and are not repeated here.

[0130] Since the complete turbine blade profile also includes a leading edge segment and a trailing edge segment, they are not directly solved in the above-mentioned solution calculation. Instead, they are directly generated by inputting the blade profile geometric parameters after determining the suction surface and pressure surface profiles. Therefore, they are not directly given in the calculation model schematic. In this embodiment, preferably, the blade profile leading edge segment and trailing edge segment are described by circular arc curves. Under the conditions of the calculated blade profile suction surface and pressure surface profiles, and given the thickness of the supersonic turbine blade, the position coordinates of the tangent points of the blade leading edge segment and trailing edge segment curves with the blade profile suction surface and pressure surface can be obtained; under the conditions of the two points on the determined arc and the arc radius, the curve equations of the leading edge segment and trailing edge segment can be further determined, and the supersonic turbine blade profile leading edge and trailing edge curve profiles can be further obtained.

[0131] It should be noted that the gas flow in the region is limited to the direction of the wall through the structural design. The designed supersonic turbine blade structure is as follows Figure 6 shown.

[0132] In this embodiment, optionally, MATLAB software programming is used to achieve parameter acquisition and profile generation of each part of the supersonic turbine blade profile.

[0133] An embodiment of the present invention proposes a method for designing the suction and pressure surface profiles of a supersonic turbine based on a characteristic method. The method calculates the pressure surface profile and the suction surface profile by inputting five parameters, namely, the turbine inlet Mach number, the suction surface transition section outlet Mach number, the pressure surface transition section outlet Mach number, the turbine outlet Mach number, and the blade turning angle, and solves the coordinates of the points on the inlet transition section and the outlet transition section profiles in a step-by-step manner; then, the arc segment profile is calculated with the end point of the inlet transition section and the starting point of the outlet transition section as the arc segment end points and the calculated dimensionless radius and arc angle; the coordinates and arc segment profile of each point on the inlet transition section and the outlet transition section profile of the suction and pressure surfaces of the supersonic turbine blade are obtained; the points on the inlet transition section and the outlet transition section are connected by straight lines, and the arc segment profile is drawn, thereby completing the design of the pressure and suction surface profiles of the two-dimensional blade.

[0134] The embodiment of the present invention further provides a supersonic turbine blade design system based on a feature method, the system comprising:

[0135] a parameter acquisition module configured to acquire supersonic turbine inlet parameters, outlet parameters, flow characteristic parameters, and blade geometric characteristic parameters;

[0136] A suction surface profile design module is configured to divide the suction surface of a supersonic turbine blade into a suction surface inlet transition section, a suction surface arc section, and a suction surface outlet transition section; based on a characteristic method, according to the supersonic turbine inlet parameters, outlet parameters, and flow characteristic parameters, the multi-point coordinates on the suction surface inlet transition section profile and the suction surface outlet transition section profile are respectively solved step by step to obtain the suction surface inlet transition section profile and the suction surface outlet transition section profile; the suction surface arc section profile is calculated based on the solved suction surface inlet transition section profile and the suction surface outlet transition section profile and the blade geometric characteristic parameters;

[0137] A pressure surface profile design module is configured to divide the pressure surface of a supersonic turbine blade into a pressure surface inlet transition section, a pressure surface arc section, and a pressure surface outlet transition section. Based on a characteristic method, according to the supersonic turbine inlet parameters, outlet parameters, and flow characteristic parameters, the multi-point coordinates on the pressure surface inlet transition section profile and the pressure surface outlet transition section profile are solved step by step to obtain the pressure surface inlet transition section profile and the pressure surface outlet transition section profile; the pressure surface arc section profile is calculated based on the solved pressure surface inlet transition section profile, the pressure surface outlet transition section profile, and the blade geometric characteristic parameters.

[0138] In this embodiment, preferably, in the suction surface profile design module and the pressure surface profile design module, based on the characteristic method, according to the supersonic turbine inlet parameters, outlet parameters, and flow characteristic parameters, the process of step-by-step solving the multi-point coordinates on the suction surface inlet transition section profile, the suction surface outlet transition section profile, the pressure surface inlet transition section profile, and the pressure surface outlet transition section profile respectively includes:

[0139] Based on the characteristic method, a characteristic line equation of the isentropic expansion flow in the transition section is designed, and the characteristic line equation is solved to obtain the coordinates of multiple points on the characteristic line;

[0140] Based on the relationship between characteristic lines and Mach lines, the equations of multiple segments of Mach lines are determined according to the coordinates of multiple points on the characteristic lines;

[0141] Based on the relationship between the Mach line and the profile line, the coordinates of multiple points on the profile line are determined according to the multi-segment Mach line equation.

[0142] It should be noted that the function of the supersonic turbine blade profile design system based on the feature method described in this embodiment can be described by the aforementioned supersonic turbine blade profile design method based on the feature method. For the parts not described in detail in the system embodiment, please refer to the above method embodiment.

[0143] Although the spirit and principles of the present invention have been described with reference to several specific embodiments, it should be understood that the present invention is not limited to the specific embodiments disclosed, and the division into various aspects does not mean that the features of these aspects cannot be combined to benefit. Such division is only for the convenience of expression. The present invention is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.

Claims

1. A supersonic turbine blade design method based on the characteristic method, characterized in that: include: Obtain supersonic turbine inlet parameters, outlet parameters, flow characteristic parameters and blade geometric characteristic parameters; The suction surface of the supersonic turbine blade is divided into a suction surface inlet transition section, a suction surface arc section and a suction surface outlet transition section, and the pressure surface is divided into a pressure surface inlet transition section, a pressure surface arc section and a pressure surface outlet transition section; Based on the characteristic method, according to the supersonic turbine inlet parameters, outlet parameters, and flow characteristic parameters, the multi-point coordinates on the suction surface inlet transition section profile, the suction surface outlet transition section profile, the pressure surface inlet transition section profile, and the pressure surface outlet transition section profile are respectively solved step by step, thereby obtaining the suction surface inlet transition section profile, the suction surface outlet transition section profile, the pressure surface inlet transition section profile, and the pressure surface outlet transition section profile; The suction surface arc segment profile is obtained by calculation based on the suction surface inlet transition section profile, the suction surface outlet transition section profile and the blade geometric characteristic parameters; the pressure surface arc segment profile is obtained by calculation based on the pressure surface inlet transition section profile, the pressure surface outlet transition section profile and the blade geometric characteristic parameters.

2. The supersonic turbine blade design method based on the characteristic method according to claim 1, characterized in that: The supersonic turbine inlet parameters include the supersonic turbine inlet Mach number M i , the export parameters include the turbine outlet Mach number M o ; Flow characteristic parameters include the exit Mach number M of the suction surface inlet transition section l and the outlet Mach number M of the pressure surface inlet transition section u ; Blade geometric characteristic parameters include supersonic turbine blade turning angle and blade thickness.

3. The method for designing a supersonic turbine blade profile based on the characteristic method according to claim 2, characterized in that: The process of step-by-step solving the coordinates of multiple points on the suction surface inlet transition section profile or the pressure surface inlet transition section profile based on the characteristic method according to the supersonic turbine inlet parameters, outlet parameters, and flow characteristic parameters, and then obtaining the suction surface inlet transition section profile or the pressure surface inlet transition section profile includes: Based on the characteristic method, a characteristic line equation of the isentropic expansion flow in the suction side inlet transition section or the pressure side inlet transition section is designed, and the characteristic line equation is solved to obtain the coordinates of multiple points on the characteristic line; Based on the relationship between characteristic lines and Mach lines, the equations of multiple segments of Mach lines are determined according to the coordinates of multiple points on the characteristic lines; Based on the relationship between the Mach line and the profile, the coordinates of multiple points on the profile are determined according to the multi-segment Mach line equation, and then the profile of the suction side inlet transition section or the pressure side inlet transition section is determined.

4. The method for designing a supersonic turbine blade profile based on the characteristic method according to claim 3, characterized in that: The characteristic line equation of the isentropic expansion flow in the transition section of the suction surface inlet is designed as follows: Where, It represents the turning angle of the airflow during the isentropic expansion flow at the transition section of the suction surface inlet; R * represents the dimensionless radius of any point on the streamline, γ represents the gas specific heat ratio, f(R * ) represents a dimensionless radius function; R l * It represents the dimensionless radius of the inlet transition section of the suction surface; Indicates that R l * Substitute f(R * ) function; The characteristic line equation of the isentropic expansion flow in the transition section of the pressure surface inlet is designed as follows: Where, R represents the turning angle of the airflow at the isentropic expansion flow in the transition section of the pressure surface inlet; u * It represents the dimensionless radius of the outlet of the transition section of the pressure surface inlet; Indicates that R u * Substitute f(R * ) function; The characteristic line equation is solved using the Newton iteration method to obtain the dimensionless radius of each point on the characteristic line. The coordinates of the kth point on the characteristic line of the isentropic expansion flow in the transition section of the suction surface inlet are: Where, R represents the airflow turning angle of the kth section of the suction surface inlet transition section; k * The dimensionless radius of the kth point on the characteristic line of the isentropic expansion flow in the transition section of the suction surface inlet; The coordinates of the jth point on the characteristic line of the isentropic expansion flow in the transition section of the pressure surface inlet are: Where, R represents the airflow turning angle of the jth section of the pressure surface inlet transition section; 2j * The dimensionless radius of the jth point on the characteristic line representing the isentropic expansion flow in the transition section of the pressure surface inlet.

5. The method for designing a supersonic turbine blade profile based on the characteristic method according to claim 4, characterized in that: The relationship between the characteristic line and the Mach line includes: the characteristic line intersects the Mach line, and the slope direction of the Mach line is consistent with the flow direction of the airflow; the equation of the multi-segment Mach line is: Where m k represents the slope, which is the average flow direction of the airflow between the k+1th point and the kth point; x m,k * 、y m,k * represents the coordinates of the kth point on the Mach line; Represents the coordinates of the kth point on the feature line.

6. The method for designing a supersonic turbine blade profile based on the characteristic method according to claim 5, characterized in that: The relationship between the Mach line and the profile line includes: the direction of the profile line of the inlet transition section is parallel to the direction of the airflow velocity and intersects with the Mach line; The equations of the infinitesimal straight lines of each segment of the inlet transition section profile are: Where, Indicates the slope of the straight line corresponding to the inlet transition section; x m,k+1 * y m,k+1 * represents the coordinates of the k+1th point on the Mach line; x s,k * 、y s,k * Indicates the coordinates of the kth point on the inlet transition section profile; The intersection of the infinitesimal straight lines of each segment of the inlet transition section profile and the multi-segment Mach line equations is solved simultaneously to obtain the coordinates of multiple points on the suction surface inlet transition section profile or the pressure surface inlet transition section profile, and then determine the suction surface inlet transition section profile or the pressure surface inlet transition section profile.

7. The method for designing a supersonic turbine blade profile based on the characteristic method according to claim 6, characterized in that: The process of obtaining the suction surface arc segment profile or the pressure surface arc segment profile comprises: The suction surface arc segment turning angle is obtained by subtracting the airflow turning angle of the suction surface inlet transition section and the airflow turning angle of the suction surface outlet transition section from the supersonic turbine blade turning angle β; the reciprocal of the outlet Mach number of the suction surface inlet transition section is determined as the dimensionless radius of the suction surface arc segment; and the suction surface arc segment profile is determined according to the suction surface arc segment turning angle and the dimensionless radius of the suction surface arc segment; The turning angle of the pressure surface arc section is obtained by subtracting the airflow turning angle of the pressure surface inlet transition section and the airflow turning angle of the pressure surface outlet transition section from the turning angle β of the supersonic turbine blade; the reciprocal of the outlet Mach number of the pressure surface inlet transition section is determined as the dimensionless radius of the pressure surface arc section; and the pressure surface arc section profile is determined based on the turning angle and the dimensionless radius of the pressure surface arc section.

8. The method for designing a supersonic turbine blade profile based on the characteristic method according to claim 7, characterized in that: The method also includes: using circular arc curves to design the leading edge section and trailing edge section of the supersonic turbine blade, and obtaining the coordinates of the tangent points of the leading edge section and trailing edge section curves with the suction surface and pressure surface of the blade based on the thickness of the supersonic turbine blade; under the conditions of two points on the arc and the arc radius, determining the curve equations of the leading edge section and the trailing edge section, and then obtaining the leading edge section profile line and the trailing edge section profile line.

9. A supersonic turbine blade design system based on the feature method, characterized in that: include: a parameter acquisition module configured to acquire supersonic turbine inlet parameters, outlet parameters, flow characteristic parameters, and blade geometric characteristic parameters; A suction surface profile design module is configured to divide the suction surface of a supersonic turbine blade into a suction surface inlet transition section, a suction surface arc section, and a suction surface outlet transition section; based on a characteristic method, according to the supersonic turbine inlet parameters, outlet parameters, and flow characteristic parameters, the multi-point coordinates on the suction surface inlet transition section profile and the suction surface outlet transition section profile are respectively solved step by step to obtain the suction surface inlet transition section profile and the suction surface outlet transition section profile; the suction surface arc section profile is calculated based on the solved suction surface inlet transition section profile and the suction surface outlet transition section profile and the blade geometric characteristic parameters; A pressure surface profile design module is configured to divide the pressure surface of a supersonic turbine blade into a pressure surface inlet transition section, a pressure surface arc section, and a pressure surface outlet transition section. Based on a characteristic method, according to the supersonic turbine inlet parameters, outlet parameters, and flow characteristic parameters, the multi-point coordinates on the pressure surface inlet transition section profile and the pressure surface outlet transition section profile are solved step by step to obtain the pressure surface inlet transition section profile and the pressure surface outlet transition section profile; the pressure surface arc section profile is calculated based on the solved pressure surface inlet transition section profile, the pressure surface outlet transition section profile, and the blade geometric characteristic parameters.

10. A supersonic turbine blade design system based on feature method according to claim 9, characterized in that: In the suction surface profile design module and the pressure surface profile design module, based on the characteristic method, according to the supersonic turbine inlet parameters, outlet parameters, and flow characteristic parameters, the process of step-by-step solving the multi-point coordinates on the suction surface inlet transition section profile, the suction surface outlet transition section profile, the pressure surface inlet transition section profile, and the pressure surface outlet transition section profile respectively includes: Based on the characteristic method, a characteristic line equation of the isentropic expansion flow in the transition section is designed, and the characteristic line equation is solved to obtain the coordinates of multiple points on the characteristic line; Based on the relationship between characteristic lines and Mach lines, the equations of multiple segments of Mach lines are determined according to the coordinates of multiple points on the characteristic lines; Based on the relationship between the Mach line and the profile line, the coordinates of multiple points on the profile line are determined according to the multi-segment Mach line equation.

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