A design method for integrated end wall and suction surface of an axial flow compressor

Abstract

The present invention discloses a method for designing an integrated endwall-suction surface for an axial-flow compressor, comprising: S1: obtaining a disturbance surface mathematical model of the endwall-suction surface of the axial-flow compressor, the disturbance surface mathematical model comprising a first set of disturbance profile models and a second set of disturbance profile models; S2: linearly combining the first set of disturbance profile models and the second set of disturbance profile models to obtain a combined disturbance profile model; S3: obtaining a suction surface spatial mapping equation and an endwall spatial mapping equation based on the combined disturbance profile model, thereby achieving an integrated design of the endwall-suction surface of the axial-flow compressor. The method has strong modeling coverage, capable of completely covering the entire separation region; and its modeling continuity enables unified control of the full two-stage motion of the endwall secondary flow.

Description

Technical Field

[0001] The present invention relates to the technical field of impeller machinery, and in particular to a method for designing an integrated end wall-suction surface model of an axial flow compressor. Background Art

[0002] With the increase in compressor design load, end zone flow problems have become a prominent problem in compressors. Among them, corner zone separation is the main source of loss in the compressor end zone and will cause local flow blockage. The main reason for corner zone separation is the boundary layer of the annular wall. Since the centrifugal inertia force of the low-speed curved flow in the boundary layer cannot balance the centripetal force provided by the lateral pressure difference, the boundary layer flow migrates to the suction surface corner zone, forming a lateral secondary flow covering the end wall surface; the end wall secondary flow induces radial flow and flow separation in the suction surface corner zone, that is, corner zone separation. In order to suppress corner zone separation, a passive flow control scheme for end wall shaping is introduced. To ensure the shaping effect, 20-40 groups of uniformly distributed control points are often used in engineering applications to construct a braided surface, parameterize the end wall, and combine the surrogate model numerical optimization technology to obtain the optimal shaping design scheme.

[0003] Corner separation develops under the combined effects of secondary flows in the end wall, corner area, and suction surface areas. In particular, in recent years, the design of high-load, high-viscosity axial flow compressor channels often increases the intensity of the secondary flow on the end wall. After reaching the corner area, it usually climbs further along the suction surface, causing the secondary flow coverage area and the low-speed flow accumulation area in the corner area to extend to the low-span position of the compressor suction surface. Therefore, in addition to end wall shaping, the control of secondary flow in the corner area and suction surface may bring further performance improvements. However, in the existing joint shaping methods, the shaping methods of each part are relatively independent and are controlled according to their own existing experience or methods. On the one hand, this leads to poor shaping coverage and the inability to fully cover the entire separation area; on the other hand, it leads to poor shaping continuity: mechanical joint shaping cannot generate a continuous shaping surface direction, making it impossible to uniformly control the entire movement of the end wall secondary flow. Summary of the Invention

[0004] The present invention provides an axial flow compressor end wall-suction surface integrated modeling design method to overcome the above technical problems.

[0005] In order to achieve the above object, the technical solution of the present invention is:

[0006] A method for designing an integrated end wall and suction surface of an axial flow compressor comprises the following steps:

[0007] S1: Obtaining a disturbance surface mathematical model of the end wall-suction surface of the axial flow compressor, wherein the disturbance surface mathematical model includes a first set of disturbance surface models and a second set of disturbance surface models;

[0008] S2: linearly combining the first set of disturbance profile models and the second set of disturbance profile models to obtain a combined disturbance profile model;

[0009] S3: According to the combined disturbance profile model, a suction surface space mapping equation and an end wall space mapping equation are obtained to achieve an integrated design of the end wall and suction surface of the axial flow press.

[0010] Furthermore, the control equations of the first set of disturbance profile models are:

[0011]

[0012] in,

[0013] A1(ε)=cos 3 ((π(ε-(ε max +ε min ) / 2) / ε max -ε min )

[0014] F1(ξ)=sin(π(ξ-(ξ max +ξ min ) / 4) / (ξ max -ξ min ) / 2)

[0015] L(ξ)=(-cos(π×(ξ-ξ min ) / ξ min -ξ max )+1)

[0016] Where: e1 is the first set of disturbance surfaces; L(ξ) is the ξ-direction control function on the suction surface; F1(ξ) is the first ξ-direction control function on the end wall; A1(ε) is the first ε-direction control function; ε is the position coordinate in the ε direction of the standard space coordinate system; ξ is the position coordinate in the ξ direction of the standard space coordinate system; ε min is the minimum value in the ε direction in the standard space coordinate system; max is the maximum value in the ε direction in the standard space coordinate system, ξ min is the minimum value of the ξ direction in the standard space coordinate system; max is the maximum value in the ξ direction in the standard space coordinate system.

[0017] Furthermore, the control equations of the second set of disturbance profile models are:

[0018]

[0019] Where, e2 is the second set of disturbance surfaces; k is the zeroing factor introduced to ensure that the disturbance surface does not change the average level of the ξ direction curve; minis the minimum value of the ξ direction in the standard space coordinate system; max is the maximum value in the ξ direction in the standard space coordinate system; A2(ε) is the second control function in the ε direction;

[0020] Among them, the second group of control functions A2(ε) to ε is a piecewise function that satisfies

[0021]

[0022] in

[0023]

[0024] Where: ε1 is the axial coordinate of the starting position of the disturbance, ε2 is the axial coordinate of the starting section of the disturbance, ε3 is the axial coordinate of the ending section of the disturbance, and ε4 is the axial coordinate of the ending position of the disturbance; σ0 is the coefficient of the starting position of the disturbance; σ1 is the proportional coefficient of the positioning coordinate point; σ2 is the proportional coefficient of the starting section of the disturbance; σ3 is the proportional coefficient of the ending section of the disturbance; ε min is the minimum value in the ε direction in the standard space coordinate system; max is the maximum value in the ε direction in the standard space coordinate system;

[0025]

[0026] in

[0027]

[0028] Where: ξ1 is the transverse coordinate of the starting point of the circumferential control curve, ξ2 is the transverse coordinate of the ending point of the circumferential control curve; σ l is the control variable at the starting point of the circumferential control curve, σ r is the control variable of the end point of the circumferential control curve; min is the minimum value of the ξ direction in the standard space coordinate system; max is the maximum value in the ξ direction in the standard space coordinate system.

[0029] Furthermore, the combined disturbance profile model is obtained as follows:

[0030] △R=l1e1+l2e2 (7)

[0031] Where: △R is the combined disturbance surface; l1 is the superposition weight of the first set of disturbance surfaces; l2 is the superposition weight of the second set of disturbance surfaces; e2 is the second set of disturbance surfaces; e1 is the first set of disturbance surfaces.

[0032] Furthermore, the suction surface space mapping equation is:

[0033]

[0034] Where: r is the radial coordinate in the compressor; z is the axial coordinate in the compressor; θ is the circumferential coordinate in the compressor; η is the position coordinate in the η direction of the standard space coordinate system; R h (z) is the radius position of the suction surface when the blade height is 30%; R + (z) is the radius position when the molding surface reaches the maximum molding height limit; R 0 (z) is the radius position of the end wall when not shaped; R - (z) is the radius position when the molding surface reaches the minimum molding height limit; TE is the axial coordinate of the frontal line; z LE is the axial coordinate of the caudal frontal line; θ s1 (z,ξ) is the circumferential angle coordinate corresponding to the maximum molding height line when the molding surface of the suction surface reaches the maximum molding height line; θ ss (z,ξ) is the circumferential angle coordinate of the suction surface; θ s2 (z,ξ) is the circumferential angle coordinate corresponding to the minimum molding height line when the molding surface of the suction surface reaches the minimum molding height line; ε min is the minimum value in the ε direction in the standard space coordinate system; max is the maximum value in the ε direction in the standard space coordinate system, ξ min is the minimum value of the ξ direction in the standard space coordinate system; max is the maximum value in the ξ direction in the standard space coordinate system; η max is the maximum value in the η direction in the standard space coordinate system.

[0035] Furthermore, the end wall space mapping equation is:

[0036]

[0037] Where: θ ps (z,ξ) is the circumferential angle coordinate of the pressure surface; θ + (z,ξ) is the circumferential angle positioning coordinate corresponding to the maximum limit position of the disturbance in the r direction of the end wall profile in the suction surface angle zone; θ - (z,ξ) is the circumferential angle positioning coordinate corresponding to the minimum limit position of the disturbance in the r direction of the end wall profile in the suction surface angle zone; ε min is the minimum value in the ε direction in the standard space coordinate system; max is the maximum value in the ε direction in the standard space coordinate system, ξ min is the minimum value of the ξ direction in the standard space coordinate system; max is the maximum value in the ξ direction in the standard space coordinate system; η max is the maximum value in the η direction in the standard space coordinate system.

[0038] Beneficial effects: The present invention provides an integrated modeling design method for the end wall and suction surface of an axial flow compressor. By linearly combining the first set of disturbance surface models and the second set of disturbance surface models, a combined disturbance surface model is obtained. The modeling has strong coverage and can completely cover the entire separation area. The continuity of the modeling can uniformly control the entire movement of the secondary flow of the end wall. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following is a brief introduction to the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0040] Figure 1 Flowchart of the integrated design method for the end wall and suction surface of an axial flow compressor in an embodiment of the present invention;

[0041] Figure 2 is a definition diagram of a first group of disturbance profile models in an embodiment of the present invention;

[0042] Figure 3 is a definition diagram of a second group of disturbance profile models in an embodiment of the present invention;

[0043] Figure 4 Schematic diagram of a weighted superposition method of a group disturbance profile model in an embodiment of the present invention;

[0044] Figure 5a Schematic diagram of the spatial coordinate system mapping relationship of the combined disturbance profile in an embodiment of the present invention;

[0045] Figure 5b Schematic diagram of the combined disturbance profile after modeling mapping in an embodiment of the present invention;

[0046] Figure 6 Optimization design flow chart in an embodiment of the present invention;

[0047] Figure 7 is a total pressure loss distribution diagram of the molding result in an embodiment of the present invention;

[0048] Figure 8a : is a distribution diagram of the total pressure loss coefficient at 0.5C downstream of the trailing edge in an embodiment of the present invention;

[0049] Figure 8b This is a diagram of axial dense flow distribution at 0.5C downstream of the trailing edge in an embodiment of the present invention;

[0050] Figure 9aThe limiting streamlines and static pressure coefficient cloud diagram of the suction surface and end wall of the OP1 prototype cascade in an embodiment of the present invention;

[0051] Figure 9b OP1Case1 is the limit streamline and static pressure coefficient cloud diagram of the suction surface and end wall in the embodiment of the present invention;

[0052] Figure 10a The limiting streamlines and static pressure coefficient cloud diagram of the suction surface and end wall of the OP2 prototype cascade in an embodiment of the present invention;

[0053] Figure 10b 1 is the limiting streamline and static pressure coefficient cloud diagram of the suction surface and end wall of OP2Case1 in the embodiment of the present invention. DETAILED DESCRIPTION

[0054] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0055] This embodiment provides an axial flow compressor end wall-suction surface integrated modeling design method, such as Figure 1 As shown, the following steps are included:

[0056] S1: Obtaining a disturbance surface mathematical model of the end wall-suction surface of the axial flow compressor, wherein the disturbance surface mathematical model includes a first set of disturbance surface models and a second set of disturbance surface models;

[0057] Specifically, this embodiment first establishes a standard space coordinate system, {(ε,ξ,η)|ε∈[ε min ,ε max ],ξ∈[ξ min ,ξ max ],η∈[-η max ,η max ]}, whose coordinate axes correspond to the axial, transverse and radial directions of the axial flow compressor channel respectively; wherein ε represents the coordinate of the axial direction of the axial flow compressor channel, that is, the position coordinate of the standard space coordinate system in the ε direction; ξ represents the coordinate of the transverse direction of the axial flow compressor channel, that is, the position coordinate of the standard space coordinate system in the ξ direction; η represents the coordinate of the radial direction of the axial flow compressor channel; to obtain the disturbance surface mathematical model of the axial flow compressor end wall-suction surface, the disturbance surface mathematical model includes a first group of disturbance profile models and a second group of disturbance profile models;

[0058] Preferably, the control equations of the first set of disturbance profile models are:

[0059]

[0060] in,

[0061] A1(ε)=cos 3 ((π(ε-(ε max +ε min ) / 2) / ε max -ε min )

[0062] F1(ξ)=sin(π(ξ-(ξ max +ξ min ) / 4) / (ξ max -ξ min ) / 2)

[0063] L(ξ)=(-cos(π×(ξ-ξ min ) / ξ min -ξ max )+1)

[0064] Where: e1 is the first set of disturbance surfaces; L(ξ) is the ξ-direction control function on the suction surface; F1(ξ) is the first ξ-direction control function on the end wall; A1(ε) is the first ε-direction control function; ε is the position coordinate in the ε direction of the standard space coordinate system; ξ is the position coordinate in the ξ direction of the standard space coordinate system; ε min is the minimum value in the ε direction in the standard space coordinate system; max is the maximum value in the ε direction in the standard space coordinate system, ξ min is the minimum value of the ξ direction in the standard space coordinate system; max is the maximum value in the ξ direction in the standard space coordinate system;

[0065] Specifically, the ε-direction first control function A1(ε)=cos 3 ((π(ε-(ε max +ε min ) / 2) / ε max -ε min ) as the ξ-direction control function F1(ξ)=sin(π(ξ-(ξ max +ξ min ) / 4) / (ξ max -ξ min ) / 2) and

[0066] L(ξ)=(-cos(π×(ξ-ξ min ) / ξ min -ξ max )+1), the maximum position of the disturbance fluctuation in the ε direction is fixed at 50%. Figure 2 As shown, the first set of perturbation profile models will construct slopes in the ε and ξ directions in the standard geometric space.

[0067] Preferably, the control equations of the second set of disturbance profile models are:

[0068]

[0069] Where, e2 is the second set of disturbance surfaces; k is the zeroing factor introduced to ensure that the disturbance surface does not change the average level of the ξ direction curve; min is the minimum value of the ξ direction in the standard space coordinate system; max is the maximum value in the ξ direction in the standard space coordinate system; A2(ε) is the second control function in the ε direction;

[0070] Among them, the second group of control functions A2(ε) to ε is a piecewise function that satisfies

[0071]

[0072] in

[0073]

[0074] Where: ε1 is the axial coordinate of the starting position of the disturbance, ε2 is the axial coordinate of the starting section of the disturbance, ε3 is the axial coordinate of the ending section of the disturbance, and ε4 is the axial coordinate of the ending position of the disturbance; σ0 is the coefficient of the starting position of the disturbance; σ1 is the proportional coefficient of the positioning coordinate point; σ2 is the proportional coefficient of the starting section of the disturbance; σ3 is the proportional coefficient of the ending section of the disturbance; ε min is the minimum value in the ε direction in the standard space coordinate system; max is the maximum value in the ε direction in the standard space coordinate system;

[0075] Specifically, the ε-direction second control function A2(ε) of the second set of disturbance profile models in this embodiment is actually defined by four sets of control variables (σ0, σ1, σ2, σ3): σ0 is the disturbance starting position coefficient, which together with σ1 specifies the axial control points (ε2,1) and (ε3,1); σ2 and σ3 are the disturbance starting segment proportional coefficient and the ending segment proportional coefficient, respectively, which are used to determine the starting point and ending control points (ε1,0) and (ε4,0), thereby adjusting the starting and ending segment slopes of the configuration, as shown in FIG. Figure 3 The control equations of the climbing section (ε1<ε<ε2) and the downhill section (ε3<ε<ε4) are constructed using cubic spline interpolation functions with boundary conditions, and the boundary slope is set to 0 to ensure a smooth connection between the disturbed and undisturbed parts.

[0076] The ξ-direction disturbance function is composed of two sets of position control variables (σ l ,σ r), control the perturbation configuration, the specific definition is:

[0077]

[0078] in

[0079]

[0080] Where: ξ1 is the transverse coordinate of the starting point of the circumferential control curve, ξ2 is the transverse coordinate of the ending point of the circumferential control curve; σ l is the control variable at the starting point of the circumferential control curve, σ r is the control variable of the end point of the circumferential control curve; min is the minimum value of the ξ direction in the standard space coordinate system; max is the maximum value in the ξ direction in the standard space coordinate system;

[0081] Specifically, in this embodiment, F(ξ) increases monotonically in the interval [ξ1, ξ2]. In addition, k in formula (2) is a zeroing factor introduced to ensure that the disturbance surface does not change the average level of the ξ direction curve. By adjusting formula (2) ξ∈[(ξ max +ξ min ) / 2,ξ max ]Integrate it to 0 and you can get the value of k. Figure 3 As shown, the second group of disturbance profile models has the function of controlling the slope of the disturbance profile structure at a certain position and with a certain slope.

[0082] S2: Linearly combine the first set of disturbance profile models and the second set of disturbance profile models to obtain a combined disturbance profile model, as shown in the attached figure. Figure 4 As shown,

[0083] Preferably, the combined disturbance profile model is obtained as follows:

[0084] △R=l1e1+l2e2 (7)

[0085] Where: △R is the combined disturbance surface; l1 is the superposition weight of the first set of disturbance surfaces; l2 is the superposition weight of the second set of disturbance surfaces;

[0086] Specifically, the combined disturbance profile model is composed of the first group of disturbance profile models and the second group of disturbance profile models, which can meet the needs of axial flow compressor flow channel control angle zone separation. The first group of disturbance profiles only needs one control parameter l1, and the second group of disturbance profiles only needs seven control parameters σ0, σ1, σ2, σ3, σ l , σ r , l2, so the superimposed surface control only needs 8 parameters, compared with the traditional method of using compiled curved surfaces to control the end wall and suction surface modeling, it significantly saves control parameters and reduces the optimization design cycle.

[0087] S3: According to the combined disturbance profile model, a suction surface space mapping equation and an end wall space mapping equation are obtained to achieve an integrated design of the end wall and suction surface of the axial flow press.

[0088] Specifically, the disturbance amount of the combined disturbance profile model obtained by equation (7) in the standard space is mapped to the axial flow compressor end wall-suction surface (axial flow compressor blade). Figure 5a As shown, when ε=ε min and ε=ε max When ξ=ξ, they correspond to the leading and trailing edge lines respectively; when ξ=ξ min ,ξ=(ξ max +ξ min ) / 2 and ξ=ξ max When , they correspond to the starting height line of the suction surface, the suction surface side of the end wall, and the pressure surface side of the end wall, that is, ξ∈[ξ min ,(ξ max +ξ min ) / 2] is the suction surface shaping area, ξ∈[(ξ max +ξ min ) / 2,ξ max ] is the end wall molding area.

[0089] Preferably, the suction surface space mapping equation is:

[0090]

[0091] Where: r is the radial coordinate in the compressor; z is the axial coordinate in the compressor; θ is the circumferential coordinate in the compressor; η is the position coordinate in the η direction of the standard space coordinate system (i.e., radial coordinate); R h (z) is the radius position of the suction surface when the blade height is 30%; R + (z) is the radius position when the molding surface reaches the maximum molding height limit; R 0 (z) is the radius position of the end wall when not shaped; R - (z) is the radius position when the molding surface reaches the minimum molding height limit; TE is the axial coordinate of the frontal line; z LE is the axial coordinate of the caudal frontal line; θ s1 (z,ξ) is the circumferential angle coordinate corresponding to the maximum molding height line when the molding surface of the suction surface reaches the maximum molding height line; θ ss (z,ξ) is the circumferential angle coordinate of the suction surface; θ s2 (z,ξ) is the circumferential angle coordinate corresponding to the minimum molding height line when the molding surface of the suction surface reaches the minimum molding height line; ε min is the minimum value in the ε direction in the standard space coordinate system; maxis the maximum value in the ε direction in the standard space coordinate system, ξ min is the minimum value of the ξ direction in the standard space coordinate system; max is the maximum value in the ξ direction in the standard space coordinate system; η max is the maximum value in the η direction in the standard space coordinate system;

[0092] Specifically, since the channel profile changes with the axis coordinate z, R h (z), R + (z), R - (z) and R 0 (z) are all functions of z; θ ss (z,ξ) represents the circumferential angle coordinates of the pressure surface and the suction surface, θ s1 (z,ξ),θ s2 (z,ξ) represents the circumferential angle coordinates corresponding to the maximum and minimum shaping height lines of the suction surface. Since the blade has a twist, θ s1 (z,ξ),θ s2 (z,ξ) and θ ss (z,ξ) are functions of z and ξ;

[0093] In another embodiment of the present invention, the cylindrical coordinate system corresponding to the modeling method needs to be replaced with the Cartesian coordinate system commonly used for the cascade because the modeling object is a plane cascade (if applied to compressor modeling, the compressor coordinate parameters are directly substituted without replacement). The specific relationship is: R h (z) represents the radius position of the suction surface shape at 30% blade height, and the x coordinate at 30% blade height position is brought into the cascade, R + (z), R - (z) represents the radius position when the modeling surface reaches the maximum and minimum modeling height limits, R 0 (z) represents the radius position of the end wall when not shaped, and the corresponding x coordinates are brought into the cascade; since the channel profile changes with the axis coordinate z, R h (z), R + (z), R - (z) and R 0 (z) are all functions of z; θ ss (z,ξ) represents the circumferential angle coordinates of the pressure surface and the suction surface, θ s1 (z,ξ),θ s2 (z,ξ) represents the circumferential angle coordinates corresponding to the maximum and minimum shaping height lines of the suction surface. The corresponding y coordinates are brought into the cascade. Since the blade has a twist, θ s1 (z,ξ),θ s2 (z,ξ) and θ ss (z,ξ) are functions of z and ξ; z TE、z LE Represents the axial coordinates of the leading edge frontal line and the trailing edge frontal line, and the z coordinates of the leading edge frontal line and the trailing edge frontal line are included in the cascade.

[0094] Preferably, the end wall space mapping equation is:

[0095]

[0096] Where: θ ps (z,ξ) is the circumferential angle coordinate of the pressure surface; θ + (z,ξ) is the circumferential angle positioning coordinate corresponding to the maximum limit position of the disturbance in the r direction of the end wall profile in the suction surface angle zone; θ - (z,ξ) is the circumferential angle positioning coordinate corresponding to the minimum limit position of the disturbance in the r direction of the end wall profile in the suction surface angle zone; ε min is the minimum value in the ε direction in the standard space coordinate system; max is the maximum value in the ε direction in the standard space coordinate system, ξ min is the minimum value of the ξ direction in the standard space coordinate system; max is the maximum value in the ξ direction in the standard space coordinate system; η max is the maximum value in the η direction in the standard space coordinate system;

[0097] Specifically, in one embodiment of the present invention, the cylindrical coordinate system corresponding to the modeling method has a mapping effect as shown in the attached figure. Figure 5b shown.

[0098] Specifically, the modeling mapping in S3 sets the compressor end wall and suction surface area coordinate system to (r, θ, z), and makes the leading edge and trailing edge lines of the compressor correspond to ε = ε in the standard modeling space respectively. min 、ε=ε max Correspondingly, the starting height line of the suction surface of the channel, the suction surface side of the end wall and the pressure surface side of the end wall are min ,ξ=(ξ max +ξ min ) / 2, ξ=ξ max The mapping area covers the suction surface, the entire end wall, and the corner area connecting the suction surface and the end wall, realizing the integrated control of the motion of the boundary layer near the wall.

[0099] In this embodiment, an integrated shape design is completed for the compressor blade cascade, and a total of 8 variables are used to control the shape changes of the suction surface and the end wall surface.

[0100] An embodiment of the present invention combining the axial flow compressor end wall-suction surface integrated modeling design method with numerical optimization technology is as follows: Figure 6 .

[0101] The research object is the compressor blade cascade, whose geometric parameters are derived from the end section of the last stage stator of a high-load compressor. According to the conclusions of previous studies on compressor blade cascades, when the total pressure loss coefficient under the two working conditions of the design point and the large angle of attack point is reduced, the performance of the remaining angles of attack distributed within the two working conditions will also be improved. Therefore, this example takes the total pressure loss coefficient of the outlet under the two working conditions of the design point (OP1, i = 0°) and the large angle of attack point (OP2, i = +4°) as the optimization variable to carry out multi-objective optimization, where i represents the inlet airflow angle;

[0102] Eight variables are used to control the shape change of the end wall and suction surface. First, 56 suction surface and end wall joint modeling samples are generated by random sampling of the eight parameter variables. Then, the CFD method is used to simulate them and the total pressure loss coefficient (defined as ω) of each model at OP1 and OP2 is obtained. o1 and ω o2 ), together with the sample variables, constitute the initial database used for optimization. Finally, the ISIGHT software is used to control the optimization process. Figure 6 As shown in Figure 1, the optimization process proceeds through a two-layer loop. The inner loop first utilizes a radial basis function neural network model as a surrogate model for CFD calculations and uses the aforementioned database to train the neural network. Finally, a genetic algorithm (NSGA-II) is used to find the minimum total pressure loss coefficient. Each genetic iteration uses the surrogate model to estimate and select 20 optimal solutions. The outer loop verifies the 20 optimal solutions selected by the inner iteration through CFD simulation and adds the results to the database. The optimization process stops when convergence is reached or when the outer iteration exceeds 20 steps.

[0103] Figure 7 The multi-objective optimization results are shown. The horizontal axis represents the global loss coefficient for each sample at OP2, while the vertical axis represents the global loss coefficient for OP1. Diamonds represent prototype data, triangles represent initial database samples, and dots represent intermediate solutions during the optimization process. Based on the coordinate axis orientation, the sample near the lower left corner of the figure effectively controls loss at both OP1 and OP2.

[0104] exist Figure 7 Select Case 1 with the best control effect for analysis. Figure 8a and 8b The total pressure loss coefficient (ω) and axial density ratio (AVDR) along the blade span distribution between the prototype blade cascade and Case 1 are compared. For OP1 and OP2, Figure 8aThe combined shaping of the suction surface and endwall reduces the total pressure loss coefficient ω, with a maximum reduction of 0.08 from the hub to 30% of the blade height. This indicates that shaping significantly suppresses the development of corner separation. Furthermore, the AVDR curve shows a decrease at the mid-blade and an increase at the blade root, gradually approaching 1. This indicates that the combined shaping eliminates end-zone blockage caused by corner separation.

[0105] Regarding the influence of the flow field, the first thing to look at is the OP2 prototype blade. Figure 9a It can be seen from the limiting streamline that, on the one hand, the boundary layer at the front end of the channel separates, forming a serious separation vortex (the vortex core is located at the vortex point F2). On the other hand, the gap between the reattachment line (RL1) from the incoming flow to the leading edge and the separation line (SL2) emitted from the saddle point (S2) at the leading edge of the adjacent blade is small. It can be inferred from these two situations that the separation vortex completely blocks the channel entrance near the blade end wall. The end wall secondary flow located downstream of the separation line SL3 in the figure is emitted from the pressure surface, and flows to the front end of the end wall under the action of the adverse pressure gradient, forming a reverse flow near the suction surface angle area. After the end wall shaping is applied, Figure 9b The extreme streamlines show that the flow field near the suction surface and the leading edge of the end wall has been significantly improved. The reason for this improvement is that the upslope shape eliminates the corner separation and channel blockage in this area, and the airflow can smoothly enter the blade channel under the adverse pressure gradient. For OP1, Figure 10a The prototype's separation vortex point (F2) is shown, along with the reverse flow between F2 and the suction surface. Compared to the separation vortex position of OP2, the separation vortex core F2 of OP1 appears further downstream and closer to the suction surface, without significant blockage at the front end of the passage. Therefore, the impact of corner separation on OP1 is primarily in the middle and rear portion of the blade passage. Figure 10b It can be seen that although the effect of the combined shaping on the OP1 flow field is not as significant as that of OP2, the essential difference is not significant. Moreover, since the front of the channel in this working condition is unobstructed, the specific flow improvement brought about by the upslope along the flow direction can be more clearly shown. The upslope shaping along the flow direction accelerates the end wall boundary layer along the flow direction, thereby delaying the starting point of the reverse flow to 0.5Ca, and ultimately eliminating the separation vortex point F2 at the front of the channel. The end wall on the suction side of the rear part of the blade channel is raised, which enhances the lateral local pressure gradient, forcing the secondary flow of the end wall in this area to accelerate and drive it to the suction surface.

[0106] The modeling results of this embodiment are compared with the modeling results obtained by the traditional optimization method in the early stage. The main parameters are shown in Table 2. In the early traditional optimization method, the suction surface and the end wall are parameterized into Bezier surfaces according to the experience of internal flow problems, and the transition is performed using an 8-parameter trigonometric function combination function surface at the intersection corner area. The traditional method used as the comparison group is consistent with the current application experience in terms of parameterized geometric modeling; when actually applied to optimization design, its process is the same as that of the present invention (i.e. Figure 6 The process shown here simply replaces the "endwall-suction surface integrated modeling method" with a traditional parametric approach. Clearly, the integrated modeling design approach of this invention offers significant advantages in both design time and computational workload. A comparison of the final application results reveals that under design conditions, the integrated suction surface and endwall modeling optimization method described herein achieves superior results. Under stall conditions, the difference between the two approaches is comparable, demonstrating that the new approach can effectively manage the corner separation of multiple localized secondary flows.

[0107] Table 2 Comparison of modeling design effects

[0108]

[0109] It is worth noting that although the modeling method of this invention was developed for compressors, it can also be directly applied to planar blade cascades after a simple coordinate system transformation of the modeling results. The main reason for using a linear blade cascade for the validation study is that it retains the high-load environment of the compressor blade tip, and the contradictions of the corner zone problem are consistent with the compressor; while it is not affected by specific factors such as blade twist and boundary layer tilt. Therefore, the control effects and conclusions related to corner zone separation obtained are more universal.

[0110] Therefore, this embodiment optimizes the shape design of a high-load axial compressor blade cascade according to the design optimization method described in the content of the invention, and verifies its effect by numerical simulation.

[0111] The geometric parameters and aerodynamic parameters of the high-load axial compressor prototype cascade are shown in Table 1

[0112] Table 1 Geometric and aerodynamic parameters of high-load axial compressor prototype cascade

[0113]

[0114] Beneficial effects: The present invention provides an integrated modeling design method for the end wall and suction surface of an axial flow compressor. By linearly combining the first set of disturbance surface models and the second set of disturbance surface models, a combined disturbance surface model is obtained. The modeling has strong coverage and can completely cover the entire separation area. The continuity of the modeling can uniformly control the entire movement of the secondary flow of the end wall.

[0115] The present invention's integrated endwall-suction surface design method for axial-flow compressors requires only eight control parameters for surface shaping, limiting the number of control parameters and reducing optimization design cycles. The resulting suction surface continuously changes with the endwall, enabling the construction of various integrated suction surface and endwall structures that enhance compressor aerodynamic performance. This direct correlation between parameters, shaping geometry, and secondary flow control ensures that the new method not only manages angular separation control of multiple localized secondary flows but also facilitates analysis and integration of effective flow control methods based on optimization results.

[0116] This invention is widely applicable to common single-stage axial-flow compressors and can be integrated with conventional optimization design platforms. It can achieve integrated control of the compressor endwall, suction surface secondary flow, and corner separation structure using a relatively small number of control parameters, with parameter changes directly linked to the secondary flow control method. Therefore, employing the integrated endwall and suction surface design method developed in this invention within conventional optimization design processes can effectively control corner separation and improve compressor performance, while significantly accelerating optimization convergence and shortening the design cycle. It also facilitates the analysis and integration of effective flow control methods from optimization results, accumulating empirical data based on flow control for subsequent designs.

[0117] The above specific description further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above description is only a specific embodiment of the present invention, which is used to explain the present invention and is not used to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

[0118] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for designing an integrated end wall and suction surface of an axial flow compressor, characterized in that: The steps include: S1: Obtaining a disturbance surface mathematical model of the end wall-suction surface of the axial flow compressor, wherein the disturbance surface mathematical model includes a first set of disturbance surface models and a second set of disturbance surface models; The governing equations of the first set of disturbance profile models are: in, A1(ε)=cos 3 ((p(e-(e max +e min ) / 2) / e max -e min ) F1(ξ)=sin(π(ξ-(ξ max +ξ min ) / 4) / (ξ max -x min ) / 2) L(ξ)=(-cos(π×(ξ-ξ min ) / ξ min -x max )+1) Where: e1 is the first set of disturbance surfaces; L(ξ) is the ξ-direction control function on the suction surface; F1(ξ) is the first ξ-direction control function on the end wall; A1(ε) is the first ε-direction control function; ε is the position coordinate in the ε direction of the standard space coordinate system; ξ is the position coordinate in the ξ direction of the standard space coordinate system; ε min is the minimum value in the ε direction in the standard space coordinate system; max is the maximum value in the ε direction in the standard space coordinate system, ξ min is the minimum value of the ξ direction in the standard space coordinate system; max is the maximum value in the ξ direction in the standard space coordinate system; The governing equations of the second set of disturbance profile models are: Where, e2 is the second set of disturbance surfaces; k is the zeroing factor introduced to ensure that the disturbance surface does not change the average level of the ξ direction curve; min is the minimum value of the ξ direction in the standard space coordinate system; max is the maximum value in the ξ direction in the standard space coordinate system; A2(ε) is the second control function in the ε direction; Among them, the second group of control functions A2(ε) to ε is a piecewise function that satisfies in Where: ε1 is the axial coordinate of the starting position of the disturbance, ε2 is the axial coordinate of the starting section of the disturbance, ε3 is the axial coordinate of the ending section of the disturbance, and ε4 is the axial coordinate of the ending position of the disturbance; σ0 is the coefficient of the starting position of the disturbance; σ1 is the proportional coefficient of the positioning coordinate point; σ2 is the proportional coefficient of the starting section of the disturbance; σ3 is the proportional coefficient of the ending section of the disturbance; ε min is the minimum value in the ε direction in the standard space coordinate system; max is the maximum value in the ε direction in the standard space coordinate system; in Where: ξ1 is the transverse coordinate of the starting point of the circumferential control curve, ξ2 is the transverse coordinate of the ending point of the circumferential control curve; σ l is the control variable at the starting point of the circumferential control curve, σ r is the control variable of the end point of the circumferential control curve; min is the minimum value of the ξ direction in the standard space coordinate system; max is the maximum value in the ξ direction in the standard space coordinate system; S2: linearly combining the first set of disturbance profile models and the second set of disturbance profile models to obtain a combined disturbance profile model; The combined disturbance profile model is obtained as follows: △R=l1e1+l2e2 (7) Where: △R is the combined disturbance surface; l1 is the superposition weight of the first set of disturbance surfaces; l2 is the superposition weight of the second set of disturbance surfaces; e2 is the second set of disturbance surfaces; e1 is the first set of disturbance surfaces; S3: According to the combined disturbance profile model, a suction surface space mapping equation and an end wall space mapping equation are obtained to achieve an integrated design of the end wall and suction surface of the axial flow press.

2. The method for designing an integrated end wall and suction surface of an axial flow compressor according to claim 1, characterized in that: The suction surface space mapping equation is: Where: r is the radial coordinate in the compressor; z is the axial coordinate in the compressor; θ is the circumferential coordinate in the compressor; η is the position coordinate in the η direction of the standard space coordinate system; R h (z) is the radius position of the suction surface when the blade height is 30%; R + (z) is the radius position when the molding surface reaches the maximum molding height limit; R 0 (z) is the radius position of the end wall when not shaped; R - (z) is the radius position when the molding surface reaches the minimum molding height limit; TE is the axial coordinate of the frontal line; z LE is the axial coordinate of the caudal frontal line; θ s1 (z,ξ) is the circumferential angle coordinate corresponding to the maximum molding height line when the molding surface of the suction surface reaches the maximum molding height line; θ ss (z,ξ) is the circumferential angle coordinate of the suction surface; θ s2 (z,ξ) is the circumferential angle coordinate corresponding to the minimum molding height line when the molding surface of the suction surface reaches the minimum molding height line; ε min is the minimum value in the ε direction in the standard space coordinate system; max is the maximum value in the ε direction in the standard space coordinate system, ξ min is the minimum value of the ξ direction in the standard space coordinate system; max is the maximum value in the ξ direction in the standard space coordinate system; η max is the maximum value in the η direction in the standard space coordinate system.

3. The method for designing an integrated end wall and suction surface of an axial flow compressor according to claim 1, characterized in that: The end wall space mapping equation is: Where: θ ps (z,ξ) is the circumferential angle coordinate of the pressure surface; θ + (z,ξ) is the circumferential angle positioning coordinate corresponding to the maximum limit position of the disturbance in the r direction of the end wall profile in the suction surface angle zone; θ - (z,ξ) is the circumferential angle positioning coordinate corresponding to the minimum limit position of the disturbance in the r direction of the end wall profile in the suction surface angle zone; ε min is the minimum value in the ε direction in the standard space coordinate system; ε max is the maximum value in the ε direction in the standard space coordinate system, ξ min is the minimum value of the ξ direction in the standard space coordinate system; max is the maximum value in the ξ direction in the standard space coordinate system; η max is the maximum value in the η direction in the standard space coordinate system.

Images