A method for evaluating flow field uniformity of a slotted-wall test section of a supersonic wind tunnel

Abstract

A method for evaluating the flow field uniformity of a slotted wall test section of a supersonic wind tunnel belongs to the field of experimental aerodynamics. In order to quickly and efficiently evaluate the flow field uniformity of a slotted wall test section. The present invention calculates the wall boundary conditions of the slotted wall test section of a supersonic wind tunnel, divides the slotted wall test section into a characteristic line grid, and solves the aerodynamic parameters of the starting grid point on the wall; calculates the aerodynamic parameters and coordinates of the intersection of the right-extending characteristic line of the starting grid point on the wall extending upstream and the intersection point P of the test section inlet plane and the left-extending characteristic line emitted from point (0,0); calculates the aerodynamic parameters and coordinates of the intersection of the right-extending characteristic line emitted from point P and the left-extending characteristic line emitted from point (1,1) to point (5,5); calculates ( k , k ‑5) The right extension characteristic line from point ( k ‑5, k -5) Aerodynamic parameters and coordinates of the intersection of the left-extending characteristic line from point 1. The present invention has high calculation efficiency.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of experimental aerodynamics, and particularly relates to a flow field uniformity evaluation method for a slotted-wall test section of a supersonic wind tunnel. BACKGROUND

[0002] Advanced transonic wind tunnels at home and abroad all adopt slotted-wall test section forms, and the flow field quality of this type of test section is better than that of a hole-wall test section, but the slot profile of the slotted-wall test section needs to be carefully designed, and the slot profile of the slotted-wall test section directly determines the uniformity of the flow field of the test section. For the slotted-wall test section of a transonic wind tunnel, the test Mach number reaches Mach number 1.2 or 1.3 at the highest, and a larger Mach number can be achieved by a nozzle and a solid-wall test section. In order to obtain a uniform supersonic flow field without axial Mach number over-expansion, a large number of repeated wind tunnel test researches need to be carried out on various slot shapes, and the process of repeated tests is expensive in scientific research funds and needs a long time. Now CFD application has been very widely used, but simulating the slotted-wall test section is still a time-consuming and laborious work, especially in the design of the test section, a large amount of comparative analysis needs to be carried out on the slot profile. SUMMARY

[0003] The problem to be solved by the present application is to quickly and efficiently evaluate the flow field uniformity of the slotted-wall test section, and the present application provides a flow field uniformity evaluation method for a slotted-wall test section of a supersonic wind tunnel.

[0004] To achieve the above-mentioned purpose, the present application realizes the following technical scheme:

[0005] A flow field uniformity evaluation method for a slotted-wall test section of a supersonic wind tunnel, comprising the following steps:

[0006] S1. calculating the wall boundary conditions of the slotted-wall test section of the supersonic wind tunnel according to the total pressure drop through the longitudinal slotted-wall surface;

[0007] S2. performing characteristic line grid division on the slotted-wall test section of the supersonic wind tunnel, and solving the aerodynamic parameters of the starting grid point (5, 0) on the wall surface;

[0008] S3. calculating the aerodynamic parameters and coordinates of the intersection point of the right-stretching characteristic line emitted by the intersection P of the right-stretching characteristic line emitted by the starting grid point on the wall surface obtained in step S2 and the left-stretching characteristic line emitted by the (0, 0) point and extending upstream to the plane of the inlet of the test section according to the aerodynamic parameters of the starting grid point on the wall surface obtained in step S2;

[0009] S4. calculating the aerodynamic parameters and coordinates of the intersection point of the right-stretching characteristic line emitted by the P point and the left-stretching characteristic line emitted by the (1, 1) point to the (5, 5) point according to the aerodynamic parameters and coordinates obtained in steps S2 and S3;

[0010] S5, calculating the aerodynamic parameters and coordinates of the intersection point of the right stretching characteristic line from the (5, 0) point and the left stretching characteristic line from the (5, 0) point according to the aerodynamic parameters and coordinates obtained in steps S2, S3 and S4, k , k -5) point and the left stretching characteristic line from the (5, 0) point, k -5, k -5) point and the left stretching characteristic line from the (5, 0) point, k = 6 … n.

[0011] Further, the specific implementation method of step S1 includes the following steps:

[0012] S1.1, the expression of the total pressure drop across the longitudinally slotted wall surface is:

[0013] (1)

[0014] wherein, is the pressure difference between the inside and outside of the slotted wall test section, q is the dynamic pressure, is the flow angle, h is the slot center distance, is the first constant, is the second constant, is the third constant;

[0015] S1.2, the formula (1) is simplified, and the influences of the non-linear term and the first order term are integrated into the second order term to obtain the wall surface boundary condition of the slotted wall test section of the supersonic wind tunnel, and the expression is:

[0016] (2)

[0017] wherein, is the flow angle of the airflow relative to the wall surface, R is the geometric opening-closing ratio of the slotted wall, K is the coefficient considering the second order coefficient, jet and viscous effect factors, is the pressure coefficient;

[0018] Further, the specific implementation method of step S2 includes the following steps:

[0019] S2.1, the slotted wall test section of the supersonic wind tunnel is divided by characteristic line grid, the starting grid point on the wall surface is set as the (5, 0) point, the right stretching characteristic line of the starting grid point extends upward to the P point which intersects with the test section inlet plane, the coordinates of the P point are set as , and the number of the characteristic line grid point of the slotted wall test section of the supersonic wind tunnel is represented by (i, j), i is the left stretching characteristic line, and j is the right stretching characteristic line;

[0020] S2.2. Set the angle between the characteristic line extending right from point (5,0) and the wind tunnel axis to be , and thus the coordinates of point P are obtained The expression is:

[0021] (3)

[0022] in, for The Mach angle of the point, for The airflow angle at the point, for The horizontal coordinate of the point, for The horizontal axis, for The vertical coordinate of the point;

[0023] S2.3. Set the right extension characteristic line range angle from point P to , set the number of right-extending characteristic lines from point P to 6. In addition to the right-extending characteristic lines passing through points (0, 0) and (5, 0), the other right-extending characteristic lines from point P are 4. The 4 right-extending characteristic lines intersect the left-extending characteristic line from point (0, 0) at points (1, 0), (2, 0), (3, 0), and (4, 0);

[0024] S2.4. Assume that the Prandtl-Meyer flow assumption is valid within the distance from the test section entrance to point (5, 0). Then the Prandtl-Meyer angle at point (5, 0) is equal to the flow inclination angle, and the calculation formula is:

[0025] (4)

[0026] in, is the Prandtl-Meyer angle at (5, 0);

[0027] The Prandtl-Meyer angle is expressed as follows:

[0028] (5)

[0029] in, for The Prandtl-Meyer angle of a point, is the air specific heat ratio, for Mach angle of a point;

[0030] (6)

[0031] Where M is Mach number at a point;

[0032] The flow angle of the point is obtained according to the boundary condition formula, and the calculation formula is:

[0033] (7)

[0034] Then the The calculation formula is:

[0035] (8)

[0036] Wherein, is the ratio of the chamber pressure to the total pressure of the test section, is the Mach number of the point on the wall;

[0037] S2.5, according to formula 4-8, the geometric opening and closing ratio of the slotted wall of the (5, 0) point is given R And the coefficient K Then, the aerodynamic parameters , , , are solved.

[0038] Further, the specific implementation method of step S3 includes the following steps:

[0039] S3.1, set the intersection point of the right stretching characteristic line from the P point and the left stretching characteristic line from the (0, 0) point as (1, 0) point, (2, 0) point, (3, 0) point, (4, 0) point;

[0040] S3.2, the (1, 0) point, (2, 0) point, (3, 0) point, (4, 0) point obtained in step S3.1 meet the Prandtl-Meyer flow assumption, and the flow parameters and coordinates at the (0, 0) point are known, and the expression is:

[0041] (9)

[0042] S3.3, then for the (1, 0) point, set the characteristic lines from the P point and the (0, 0) point as straight lines, and the slope of the straight line between the (0, 0) and (1, 0) points is determined according to the average value of the characteristic angles And The expression is:

[0043] (10)

[0044] The expression of the slope of the straight line between the P point and the (1, 0) point is:

[0045] (11)

[0046] The coordinates of the (1, 0) point thus obtained satisfy the following expression:

[0047] (12)

[0048] (13)

[0049] S3.4, the (0, 0) point in step S3.3 is replaced by the (1, 0) point, the (2, 0) point, the (3, 0) point, the (1, 0) point in step S3.3 is replaced by the (2, 0) point, the (3, 0) point, the (4, 0) point, and the coordinates of the (2, 0) point, the (3, 0) point, the (4, 0) point are calculated;

[0050] S3.5, using the method of replacing the characteristic line with a straight line, the intersection point of the characteristic line from the (4, 0) point with the wall surface is the (5, 0) point, the updated abscissa of the (5, 0) point is calculated, the updated abscissa of the (5, 0) point is compared with the initial value, steps S3.1-S3.5 are repeated to enter a loop iteration, until the abscissa value of the (5, 0) point finally obtained is within the error allowable range of the value of the previous time, the aerodynamic parameters and coordinates of the intersection point of the left stretching characteristic line from the (0, 0) point are obtained.

[0051] Further, the specific implementation method of step S4 includes the following steps:

[0052] S4.1, determining the aerodynamic parameters and coordinates of the characteristic points on the non-verification section axis;

[0053] S4.1.1, setting the points on the right stretching characteristic line and the points connected thereto to satisfy the following expression:

[0054] (14)

[0055] wherein, const is a constant;

[0056] the points on the left stretching characteristic line and the points connected thereto satisfy the following expression:

[0057] (15)

[0058] For the (2, 1) point, from equations (14) and (15), we have:

[0059] (16)

[0060] S4.1.2. Assume that point (i, j) is the intersection of two straight lines extending from the previous point on its left and right characteristic lines. The slopes of the left and right characteristic lines to point (i, j) satisfy the following expressions:

[0061] (17)

[0062] Then the left-extending characteristic line and the right-extending characteristic line of point (i, j) satisfy the following expressions:

[0063] (18)

[0064] Calculate the coordinates x(i, j) and y(i, j) of point (i, j);

[0065] S4.2. Calculate the aerodynamic parameters and coordinates of characteristic points (1, 1), (2, 2), (3, 3), (4, 4), and (5, 5) on the axis of the test section based on the aerodynamic parameters and coordinates of the characteristic points on the axis of the test section obtained in step S4.1.

[0066] S4.2.1. Set the flow inclination angles through points (1, 1), (2, 2), (3, 3), (4, 4), and (5, 5) to 0, and calculate the Prandtl-Meyer angle for the points on the axis of the test section using formula (14): :

[0067] (19)

[0068] in, i =1, 2, 3, 4, 5; then calculate the other aerodynamic parameters and coordinates of the left-extending characteristic line and the characteristic point on the axis of the test section according to equations (5), (6), (17), and (18);

[0069] S4.2.2 For the coordinates of a point on the wind tunnel axis, the value of the ordinate is zero. The value of the abscissa of the characteristic point can be calculated using equations (17) and (18).

[0070] Furthermore, the specific implementation method of step S5 includes the following steps:

[0071] S5.1, set on the wall ( k , k -5) points, ( k , k -5) points at ( k -5, k -5) on the left extended characteristic line, the following expression is satisfied:

[0072] (20)

[0073] wherein, k =6, 7, 8, 9…n; k k Prandtl-Meyer angle of the point (5) and boundary conditions satisfy (5)-(8) formula;

[0074] S5.2, assuming the abscissa value of the point (6, 1), the aerodynamic parameters of the abscissa of the point (6, 1) are obtained according to (20) formula, and then the new coordinate value of the point (6, 1) is solved by the left stretching characteristic line equation of the point (6, 1), and the iteration is repeated until the abscissa value of the point (6, 1) obtained finally and the value of the last time are in the error allowable range, the aerodynamic parameters and coordinate values of the point (6, 1) are obtained;

[0075] S5.3, according to the calculation process of steps S5.1 and S5.2, the aerodynamic parameters and coordinates of the points on the right stretching characteristic line from the point (6, 0) are calculated, and the corresponding aerodynamic parameters are obtained by (14), (15), (5), (6) formula, and the coordinate values of the characteristic points are obtained by (17), (18) formula;

[0076] S5.4, according to the calculation process of steps S5.1-S5.1, the aerodynamic parameters and coordinates of the characteristic grid points downstream of the right stretching characteristic line of the point (6, 1) are solved, and the calculation of all aerodynamic parameters and coordinates in the entire slotted wall test section is completed.

[0077] The beneficial effects of the application are:

[0078] The characteristic line method used in the flow field uniformity evaluation method of the slotted wall test section of the supersonic wind tunnel is a kind of verified and relatively reliable simulation method, and the advantage is that after the boundary condition is given, the required result is obtained in a very short time through program operation. However, the application of the characteristic line method is limited to the simulation of supersonic flow. In the state of empty wind tunnel without model, the characteristic line method can be applied to simulate the low supersonic flow in the two-dimensional slotted wall test section.

[0079] The flow field uniformity evaluation method of the slotted wall test section of the supersonic wind tunnel can exclude some slotted profiles with obvious poor effect, and retain better slotted profiles, so as to reduce the cost of CFD or wind tunnel test research. The slotted wall test section supersonic flow field uniformity evaluation method based on the characteristic line method is proposed, which can preliminarily analyze the flow field uniformity of different slotted profiles in the test section.

[0080] ​The method for evaluating the flow field uniformity of the slotted-wall test section of the supersonic wind tunnel has the advantages of simple operation and high calculation efficiency, can quickly evaluate the supersonic flow field quality of the slotted-wall test section, can be suitable for the aerodynamic design and optimization of the slot line of the slotted-wall test section, and can provide a large amount of comparative analysis data, thereby saving a large amount of calculation and time and cost for the design and selection of the test section. BRIEF DESCRIPTION OF DRAWINGS

[0081] Figure 1 A flow chart of the method for evaluating the flow field uniformity of the slotted-wall test section of the supersonic wind tunnel;

[0082] Figure 2 A test section characteristic line grid distribution schematic diagram of the method for evaluating the flow field uniformity of the slotted-wall test section of the supersonic wind tunnel;

[0083] Figure 3 A linear slotted profile and its distribution on the wallboard of the method for evaluating the flow field uniformity of the slotted-wall test section of the supersonic wind tunnel;

[0084] Figure 4 A nonlinear slotted profile and its distribution on the wallboard of the method for evaluating the flow field uniformity of the slotted-wall test section of the supersonic wind tunnel;

[0085] Figure 5 A test section core flow Mach number distribution diagram of M=1.05 of the method for evaluating the flow field uniformity of the slotted-wall test section of the supersonic wind tunnel;

[0086] Figure 6 A test section core flow Mach number distribution diagram of M=1.2 of the method for evaluating the flow field uniformity of the slotted-wall test section of the supersonic wind tunnel;

[0087] Figure 7 An axial Mach number distribution diagram on the wall of M=1.05 of the method for evaluating the flow field uniformity of the slotted-wall test section of the supersonic wind tunnel;

[0088] Figure 8 An axial Mach number distribution diagram on the wall of M=1.2 of the method for evaluating the flow field uniformity of the slotted-wall test section of the supersonic wind tunnel. DETAILED DESCRIPTION

[0089] In order to make the objects, technical solutions and advantages of the present application clearer, the present application will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application, i.e., the specific embodiments described are only a part of the embodiments of the present application, but not all the specific embodiments. The components of the specific embodiments of the present application generally described and shown in the accompanying drawings can be arranged and designed in various different configurations, and the present application can also have other embodiments.

[0090] Therefore, the detailed description of the specific embodiments of the present application provided below in the accompanying drawings is not intended to limit the scope of the claimed present application, but only represents selected specific embodiments of the present application. Based on the specific embodiments of the present application, all other specific embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0091] In order to further understand the inventive content, characteristics and effects of the present application, the following specific embodiments are exemplified, and the accompanying drawings are combined Figure 1 - the accompanying drawings Figure 8 The detailed description is as follows:

[0092] Specific embodiment one: a flow field uniformity evaluation method of a slotted wall test section of a supersonic wind tunnel, comprising the following steps:

[0093] S1, calculating the wall boundary conditions of the slotted wall test section of the supersonic wind tunnel according to the total pressure drop across the longitudinal slotted wall surface;

[0094] Further, the specific implementation method of step S1 comprises the following steps:

[0095] S1.1, the expression of the total pressure drop across the longitudinal slotted wall surface is:

[0096] (1)

[0097] wherein, is the pressure difference between the inside and outside of the slotted wall test section, q is the dynamic pressure, is the flow angle, h is the slot center distance, is the first constant, is the second constant, is the third constant;

[0098] S1.2, the influence of the nonlinear term and the first order term of the viscous effect is integrated into the second order term The simplified wall boundary condition of the slotted wall test section of the supersonic wind tunnel is obtained as follows: (2)

[0099] in, is the inclination angle of the airflow relative to the wall, R is the geometric opening and closing ratio of the slotted wall, K In order to comprehensively consider the coefficients including the secondary coefficient, jet and viscosity effect factors, is the pressure coefficient;

[0100] The results of the comparative study with the experimental results show that the value of K in the range of 0.8 to 0.9 is closest to the actual results;

[0101] S2. Perform characteristic line meshing on the slotted wall test section of the supersonic wind tunnel and calculate the aerodynamic parameters of the starting grid point (5,0) on the wall surface.

[0102] Furthermore, the specific implementation method of step S2 includes the following steps:

[0103] S2.1. Divide the slotted wall test section of the supersonic wind tunnel into a characteristic line grid. Set the starting grid point on the wall to (5, 0). The characteristic line to the right of the starting grid point extends upstream and intersects the test section entrance plane at point P. Set the coordinates of point P to , the number of the characteristic line grid points of the slotted wall test section of the supersonic wind tunnel is represented by (i, j), i is the left-extending characteristic line, and j is the right-extending characteristic line;

[0104] S2.2. Set the angle between the characteristic line extending right from point (5,0) and the wind tunnel axis to be , and thus the coordinates of point P are obtained The expression is:

[0105] (3)

[0106] in, for The Mach angle of the point, for The airflow angle at the point, for The horizontal coordinate of the point, for The horizontal axis, for The vertical coordinate of the point;

[0107] S2.3. Set the right extension characteristic line range angle from point P to , set the right stretch characteristic line number from P point for 6, in addition to the right stretch characteristic line of (0, 0) point and (5, 0) point, other 4 right stretch characteristic lines from P point, the -4 right stretch characteristic lines intersect with the left stretch characteristic line from (0, 0) point at (1, 0) point, (2, 0) point, (3, 0) point, (4, 0) point;

[0108] S2.4, set the distance range from the test section inlet to (5, 0) point to establish Prandtl-Meyer flow assumption, then the Prandtl-Meyer angle of (5, 0) point is equal to the flow angle, the calculation formula is obtained as follows:

[0109] (4)

[0110] Wherein, is the Prandtl-Meyer angle of (5, 0) point;

[0111] The Prandtl-Meyer angle is represented by the following formula:

[0112] (5)

[0113] Wherein, is the Prandtl-Meyer angle of (5, 0) point, is the specific heat ratio of air, , is the Mach angle of (5, 0) point;

[0114] (6)

[0115] Wherein, M is the Mach number of (5, 0) point;

[0116] The flow angle of (5, 0) point is obtained according to the boundary condition formula, and the calculation formula is as follows:

[0117] (7)

[0118] Then the calculation formula of is obtained as follows:

[0119] (8)

[0120] Wherein, is the ratio of the stagnation pressure to the total pressure of the test section, is the Mach number of the point on the wall;

[0121] S2.5, according to the formula 4-8, the geometric opening-closing ratio of the slotted wall of (5, 0) point is given R and the coefficient K ​​​​After that, the aerodynamic parameters of the initial grid points on the wall surface are solved 、 、 、 ;

[0122] S3, according to the aerodynamic parameters of the initial grid points on the wall surface obtained in step S2, the intersection point P of the right stretching characteristic line extending upstream from the initial grid point on the wall surface and the test section inlet plane is calculated, and the intersection point of the right stretching characteristic line emitted from the P point and the left stretching characteristic line emitted from the (0, 0) point is calculated. Aerodynamic parameters and coordinates of the intersection point;

[0123] Further, the specific implementation method of step S3 includes the following steps:

[0124] S3.1, set the intersection point of the right stretching characteristic line emitted from the P point and the left stretching characteristic line emitted from the (0, 0) point as (1, 0) point, (2, 0) point, (3, 0) point, (4, 0) point;

[0125] S3.2, the (1, 0) point, (2, 0) point, (3, 0) point, (4, 0) point obtained in step S3.1 meet the Prandtl-Meyer flow assumption, and the flow parameters and coordinates at the (0, 0) point are known, and the expression is:

[0126] (9)

[0127] S3.3, then for the (1, 0) point, set the characteristic lines emitted from the P point and the (0, 0) point as straight lines, and the slope of the straight line between the (0, 0) point and the (1, 0) point is determined according to the average value of the characteristic angles and , and the expression is:

[0128] (10)

[0129] The expression of the slope of the straight line between the P point and the (1, 0) point is:

[0130] (11)

[0131] Therefore, the coordinates of the (1, 0) point satisfy the following expression:

[0132] (12)

[0133] (13)

[0134] S3.4, replace the (0, 0) point in step S3.3 with (1, 0) point, (2, 0) point, (3, 0) point, replace the (1, 0) point in step S3.3 with (2, 0) point, (3, 0) point, (4, 0) point, calculate the coordinates of (2, 0) point, (3, 0) point, (4, 0) point;

[0135] S3.5, using the method of replacing the characteristic line with a straight line, the intersection point of the characteristic line from the (4, 0) point and the wall surface is the (5, 0) point, calculate the updated abscissa of the (5, 0) point, compare the obtained updated abscissa of the (5, 0) point with the initial value, repeat steps S3.1-S3.5 to enter a loop iteration, until the abscissa value of the (5, 0) point finally obtained and the value of the previous time are within the error allowable range, the aerodynamic parameters and coordinates of the intersection point of the left stretching characteristic line from the (0, 0) point are obtained;

[0136] S4, according to the aerodynamic parameters and coordinates obtained in steps S2 and S3, calculate the aerodynamic parameters and coordinates of the intersection point of the right stretching characteristic line from the P point and the left stretching characteristic line from the (1, 1) point to the (5, 5) point;

[0137] Further, the specific implementation method of step S4 includes the following steps:

[0138] S4.1, determine the aerodynamic parameters and coordinates of the characteristic points on the non-verification section axis;

[0139] S4.1.1, set the points on the right stretching characteristic line and the points connected thereto to satisfy the following expression:

[0140] (14)

[0141] wherein, const is a constant;

[0142] the points on the left stretching characteristic line and the points connected thereto satisfy the following expression:

[0143] (15)

[0144] For the (2, 1) point, from the equations (14) and (15), we have:

[0145] (16)

[0146] S4.1.2, assume that the point (i, j) is the intersection point of the two straight lines from the previous points on the left and right stretching characteristic lines, and the slopes of the left and right stretching characteristic lines to the point (i, j) satisfy the following expression:

[0147] (17)

[0148] Then the left-extending characteristic line and the right-extending characteristic line of point (i, j) satisfy the following expressions:

[0149] (18)

[0150] Calculate the coordinates x(i, j) and y(i, j) of point (i, j);

[0151] S4.2. Calculate the aerodynamic parameters and coordinates of the characteristic points (1, 1), (2, 2), (3, 3), (4, 4), and (5, 5) on the test section axis based on the aerodynamic parameters and coordinates of the characteristic points on the non-test section axis obtained in step S4.1.

[0152] S4.2.1. Set the flow inclination angles through points (1, 1), (2, 2), (3, 3), (4, 4), and (5, 5) to 0, and calculate the Prandtl-Meyer angle for the points on the axis of the test section using formula (14): :

[0153] (19)

[0154] in, i =1, 2, 3, 4, 5; then calculate the other aerodynamic parameters and coordinates of the left-extending characteristic line and the characteristic point on the axis of the test section according to equations (5), (6), (17), and (18);

[0155] S4.2.2 For the coordinates of points on the wind tunnel axis, the value of the ordinate is zero. The value of the abscissa of the characteristic point can be calculated using equations (17) and (18);

[0156] S5. Calculate ( k , k -5) point and the right extension characteristic line ( k -5, k -5) The aerodynamic parameters and coordinates of the intersection of the left-extending characteristic line from point 1, k =6……n;

[0157] Furthermore, the specific implementation method of step S5 includes the following steps:

[0158] S5.1, set on the wall ( k , k -5) points, ( k , k -5) points at ( k -5, k-5) point on the left stretch characteristic line satisfies the following expression:

[0159] (20)

[0160] wherein, k =6, 7, 8, 9…n; k , k Prandtl-Meyer angle of the (5) point and the boundary conditions satisfy (5)-(8) formula;

[0161] S5.2, assuming the abscissa value of the (6, 1) point, the aerodynamic parameters of the abscissa of the (6, 1) point are calculated according to (20) formula, and then the new coordinate value of the (6, 1) point is calculated through the left stretch characteristic line equation of the (6, 1) point, and the iteration is repeated until the abscissa value of the (6, 1) point obtained finally and the value of the last time are in the error allowable range, the aerodynamic parameters and coordinate values of the (6, 1) point are obtained;

[0162] S5.3, according to the calculation process of steps S5.1 and S5.2, the aerodynamic parameters and coordinates of the points on the right stretch characteristic line from the (6, 0) point are calculated, the corresponding aerodynamic parameters are calculated by (14), (15), (5), (6) formula, and the coordinate values of the characteristic points are calculated by (17), (18) formula;

[0163] S5.4, according to the calculation process of steps S5.1-S5.1, the aerodynamic parameters and coordinates of the characteristic grid points downstream of the (6, 1) point right stretch characteristic line are solved, and the calculation of all aerodynamic parameters and coordinates in the entire slotted wall test section is completed.

[0164] Further, the slotted wall test section is a test section form of the transonic wind tunnel, and an excellent slotted wall test section can establish a high-quality wind tunnel flow field. The slotted wall test section design and the rapid evaluation of the supersonic flow field quality are one of the important projects of the wind tunnel design. The characteristic line method and the slotted wall test section supersonic tunnel wall boundary condition are adopted in the present application to simulate the supersonic flow field of the slotted wall test section, to obtain the interference of the test section wall slot profile on the test section flow field, so as to rapidly and efficiently evaluate the design quality of the slotted wall test section, and also can be used for screening better slotted wall design scheme.

[0165] The drawings of the specification are further described as follows:

[0166] One kind of slot type line is that the opening-closing ratio R linearly changes from 0 to 6%, see Figure 3 ; another is that the opening-closing ratio R nonlinearly changes from 0 to 6%, see Figure 4 ;

[0167] The opening-closing ratio R of the linear slotted type line satisfies the linear relationship formula:

[0168] ;

[0169] in, X For slotted seams X coordinate, L is the axial length of the slot;

[0170] The opening and closing ratio R of the nonlinear slotted slit satisfies the polynomial:

[0171] ;

[0172] The core flow Mach number distribution of the test section for the linear slotted profile and the nonlinear slotted profile when M=1.05 is shown in Figure 5 The core flow Mach number distribution of the test section for the linear slotted profile and the nonlinear slotted profile when M=1.2 is shown in Figure 6 The axial Mach number distribution on the test section wall of the linear slotted profile and the nonlinear slotted profile when M=1.05 is shown in Figure 7 The axial Mach number distribution on the test section wall of the linear slotted profile and the nonlinear slotted profile when M=1.2 is shown in Figure 8 By comparing and analyzing the core flow and the wall axial Mach number distribution uniformity of the two slotted profile test sections, it can be found that the airflow acceleration of the nonlinear slotted profile is faster than that of the linear slotted profile, but the flow field uniformity of the nonlinear slotted profile is reduced.

[0173] It should be noted that relational terms such as "first" and "second" are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of additional identical elements in the process, method, article, or apparatus comprising the element.

[0174] Although the present application has been described with reference to the specific embodiments thereof, it should be understood by those skilled in the art that various changes can be made and equivalents can be substituted for elements thereof without departing from the scope of the present application. In particular, various features and aspects of the present application can be used individually or in any combination depending on the specific application and implementation. Therefore, it is expressly intended that the specific embodiments of the present application both as set forth and including any equivalents thereof should not limit the present application or scope of the claims herein, but rather the overall scope of pertaining solely to the methods and the articles of manufacture specifically recited in the following claims.

Claims

1. A method for evaluating the flow field uniformity of a slotted-wall test section of a hypersonic wind tunnel, characterized by: It comprises the following steps: S1, calculating the wall boundary condition of the slotted wall test section of the supersonic wind tunnel according to the total pressure drop across the longitudinal slotted wall surface; S2, performing characteristic line grid division on the slotted wall test section of the supersonic wind tunnel, and solving the aerodynamic parameters of the starting grid point (5, 0) on the wall surface; S3, calculating the aerodynamic parameters and coordinates of the intersection point of the right-stretching characteristic line from the intersection point P of the right-stretching characteristic line from the starting grid point on the wall surface and the left-stretching characteristic line from the (0, 0) point according to the aerodynamic parameters of the starting grid point on the wall surface obtained in step S2; S4, calculating the aerodynamic parameters and coordinates of the intersection point of the right-stretching characteristic line from the (1, 1) point to the left-stretching characteristic line from the (5, 5) point according to the aerodynamic parameters and coordinates obtained in steps S2 and S3; S5. Calculate ( k , k -5) point and the right extension characteristic line ( k -5, k -5) The aerodynamic parameters and coordinates of the intersection of the left-extending characteristic line from point 1, k =6……n.

2. The method of claim 1, wherein, The specific implementation method of step S1 comprises the following steps: S1.1, the expression of the total pressure drop across the longitudinal slotted wall surface is: (1) wherein, is the pressure difference between the inside and outside of the slotted wall test section, q is the dynamic pressure, is the angle of the gas flow, h is the slot center distance, is the first constant, is the second constant, is the third constant; S1.2, Simplify equation (1) and combine the influence of the nonlinear term of viscous effect and the first order term to the second order term , the simplified boundary condition of the slotted wall test section of supersonic wind tunnel is obtained, which is expressed as: (2) wherein, is the angle of the gas flow relative to the wall, R is the geometric opening-closing ratio of the slotted wall, K is a coefficient that takes into account the quadratic coefficient, the jet effect factor and the viscous effect factor, is the pressure coefficient.

3. The method of evaluating the flow field uniformity of a slotted-wall test section of a supersonic wind tunnel according to claim 1 or 2, characterized in that, The specific implementation method of step S2 comprises the following steps: S2.1, the characteristic line grid of the slotted wall test section of the supersonic wind tunnel is divided, the starting grid point on the wall is set as (5, 0) point, the right stretching characteristic line of the starting grid point extends upstream, intersects with the test section inlet plane at P point, the coordinates of P point are set as , the number of the characteristic line grid point of the slotted wall test section of the supersonic wind tunnel is represented by (i, j), i is the left stretching characteristic line, and j is the right stretching characteristic line; S2.2, the angle between the (5, 0) point right stretch characteristic line and the wind tunnel axis is set to , the coordinates of the P point are obtained The expression of (3) wherein is the Mach angle of the point, is the flow angle of the point, is the abscissa of the point, is the abscissa of the point, is the ordinate of the point; S2.3, set the right stretch characteristic line range angle from P point as , set the right stretch characteristic line number from P point as 6, in addition to the right stretch characteristic line passing through (0, 0) point and (5, 0) point, other right stretch characteristic line from P point is 4, and the 4 right stretch characteristic lines intersect with the left stretch characteristic line from (0, 0) point at (1, 0), (2, 0), (3, 0), (4, 0) points; S2.4, setting the Prandtl-Meyer flow assumption to be established in the distance range from the test section inlet to the (5, 0) point, so that the Prandtl-Meyer angle of the (5, 0) point is equal to the flow inclination angle, and the calculation formula is: (4) wherein is the Prandtl-Meyer angle at the point (5, 0). The Prandtl-Meyer angle is represented by the following formula: (5) wherein, is Prandtl-Meyer angle at the point, is the air specific heat ratio, is Mach angle at the point; (6) where M is Mach number of the point; The flow angle of the point is obtained according to the boundary condition formula, and the calculation formula is: (7) Then, we obtain The calculation formula is: (8) wherein is the ratio of the chamber pressure to the total pressure in the test section, is the Mach number at the point on the wall; S2.5, the geometric opening-closing ratio of the slotted wall at the (5, 0) point is given according to formulas 4-8 R and the coefficient K After that, the aerodynamic parameters , , , are solved.

4. The method of claim 3, wherein the method further comprises: The specific implementation method of step S3 comprises the following steps: S3.1, setting the intersection point of the right-stretching characteristic line from the (0, 0) point and the left-stretching characteristic line from the (0, 0) point as the (1, 0) point, the (2, 0) point, the (3, 0) point and the (4, 0) point; S3.2, the (1, 0) point, the (2, 0) point, the (3, 0) point and the (4, 0) point obtained in step S3.1 satisfy the Prandtl-Meyer flow assumption, the flow parameters and coordinates of the (0, 0) point are known, and the expression is: (9) S3.3, then for the (1, 0) point, the characteristic line emitted by the P point and the (0, 0) point is a straight line, the slope of the straight line between the (0, 0) and (1, 0) points is determined according to the average value of the characteristic angles and , the expression is as follows: (10) The expression of the slope of the straight line between the (1, 0) point and the (0, 0) point is: (11) Therefore, the coordinates of the (1, 0) point satisfy the following expression: （12） （13） S3.4, replacing the (0, 0) point in step S3.3 with the (1, 0) point, the (2, 0) point and the (3, 0) point, and replacing the (1, 0) point in step S3.3 with the (2, 0) point, the (3, 0) point and the (4, 0) point, and calculating the coordinates of the (2, 0) point, the (3, 0) point and the (4, 0) point; S3.5, using the method of replacing the characteristic line with a straight line, the intersection point of the characteristic line from the (4, 0) point and the wall surface is the (5, 0) point, and the updated x-coordinate of the (5, 0) point is calculated, and the updated x-coordinate of the (5, 0) point is compared with the initial value, and steps S3.1-S3.5 are repeated to enter a loop iteration until the x-coordinate value of the (5, 0) point obtained finally is within the error allowable range of the previous value, and the aerodynamic parameters and coordinates of the intersection point of the left-stretching characteristic line from the (0, 0) point are obtained.

5. The method of evaluating the flow field uniformity of a slotted-wall test section of a supersonic wind tunnel according to claim 4, wherein The specific implementation method of step S4 comprises the following steps: S4.1, determining the aerodynamic parameters and coordinates of the characteristic points on the non-test section axis; S4.1.1, setting the points on the right-stretching characteristic line and the points connected thereto to satisfy the following expression: (14) wherein const is a constant; The point on the left stretching characteristic line and the point connected therewith satisfy the following expression: (15) For the point (2, 1), the expressions (12) and (13) can be obtained: (16) S4.1.2, assuming that the point (i, j) is the intersection point of two straight lines emitted from the previous points on the left stretching characteristic line and the right stretching characteristic line of the point (i, j), the slopes of the left stretching characteristic line and the right stretching characteristic line to the point (i, j) satisfy the following expression: (17) The left stretching characteristic line and the right stretching characteristic line of the point (i, j) satisfy the following expression: (18) The coordinates x(i, j) and y(i, j) of the point (i, j) are calculated; S4.2, the aerodynamic parameters and the coordinates of the characteristic points (1, 1), (2, 2), (3, 3), (4, 4) and (5, 5) on the test section axis are calculated according to the aerodynamic parameters and the coordinates of the characteristic points on the non-test section axis obtained in step S4.

1. S4.2.1, set the flow angle of the flow passing through the (1, 1) point, (2, 2) point, (3, 3) point, (4, 4) point, (5, 5) point to 0, and calculate the Prandtl-Meyer angle of the point on the test section axis by using formula (14) : （19） wherein, i = 1, 2, 3, 4, 5; then according to formula (5), formula (6), formula (17), formula (18) to calculate the left stretch characteristic line emitted by the point on the test section axis and other aerodynamic parameters and coordinates of the characteristic point on the test section axis; S4.2.2, for the coordinates of the points on the wind tunnel axis, the value of the longitudinal coordinate is zero, and the value of the transverse coordinate of the characteristic point can be obtained from the expressions (15) and (16).

6. The method of evaluating the flow field uniformity of a slotted-wall test section of a supersonic wind tunnel according to claim 5, wherein The specific implementation method of step S5 includes the following steps: S5.1, setting a point on the wall surface k , k -5) point, k , k -5) point on the left stretching characteristic line issued from the point k -5, k -5) point satisfies the following expression: (20) wherein, k = 6, 7, 8, 9... n; k , k -5) Prandtl-Meyer angle of the point and the boundary conditions satisfy (5)-(8) equations; S5.2, assuming the value of the transverse coordinate of the point (6, 1), the aerodynamic parameters of the assumed transverse coordinate of the point (6, 1) are calculated according to the expression (20), and then the new coordinate value of the assumed point (6, 1) is calculated through the left stretching characteristic line equation of the assumed point (6, 1), and the iteration is repeated until the final value of the transverse coordinate of the point (6, 1) is within the error allowable range of the previous value, and the aerodynamic parameters and the coordinate value of the point (6, 1) are obtained; S5.3, according to the calculation process of steps S5.1 and S5.2, the aerodynamic parameters and the coordinates of the points on the right stretching characteristic line emitted from the point (6, 0) are calculated, the corresponding aerodynamic parameters are calculated through the expressions (12), (13), (5) and (6), and the coordinate values of the characteristic points are calculated through the expressions (15) and (16); S5.4, according to the calculation process of steps S5.1-S5.1, the aerodynamic parameters and the coordinates of the characteristic grid points downstream of the right stretching characteristic line of the point (6, 1) are calculated, and the calculation of all the aerodynamic parameters and the coordinates in the entire slotted wall test section is completed.

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