A method for aerodynamic design of profile curve near the throat of laminar supersonic nozzle

Abstract

The application discloses a laminar flow supersonic nozzle throat vicinity profile curve aerodynamic design method, relates to the field of supersonic equipment aerodynamic design, and comprises the following steps: giving a design nozzle initial design condition; determining nozzle key point coordinates; determining an initial section curve; determining a subsonic contraction curve; determining a boundary layer bleed slot boundary layer bleed slot lip curve; and giving throat vicinity profile curve coordinates. The method can meet the requirements of a model supersonic boundary layer natural transition test on a laminar flow supersonic nozzle, reduces the difficulty of laminar flow supersonic nozzle throat vicinity profile curve aerodynamic design and verification, and improves the design quality.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of aerodynamic design of supersonic equipment, in particular, to an aerodynamic design method for a profile curve near a throat of a laminar supersonic nozzle. BACKGROUND

[0002] The supersonic nozzle of a wind tunnel is a Laval nozzle with a carefully designed profile, mainly composed of a converging section for accelerating airflow, a throat section for airflow at transonic speed, and a termination section for adjusting spatial uniformity of airflow. It is a key section for achieving uniform supersonic test airflow in a supersonic wind tunnel. In the wind tunnel, the boundary layer upstream of the nozzle is turbulent flow. The conventional nozzle does not use boundary layer re-laminarization measures, and the turbulent noise generated by the supersonic boundary layer in the nozzle will be radiated along the Mach line to the downstream test airflow, resulting in a noise of the test airflow that is 1-2 orders of magnitude higher than that in the flight environment. In the wind tunnel test, the position of natural transition on the surface of the test model is greatly advanced compared with that in real flight.

[0003] In order to improve the simulation accuracy of the natural transition of the boundary layer of the model in a supersonic state, the boundary layer flow in the supersonic flow region of the nozzle needs to be in a laminar state, and the necessary condition is to achieve boundary layer re-laminarization upstream of the throat. Setting a boundary layer bleed slot upstream of the throat is an effective means to achieve re-laminarization. The original boundary layer flow is discharged from the nozzle through the lip of the boundary layer bleed slot of the upstream airflow, and a laminar boundary layer flow is reformed inside the lip of the boundary layer bleed slot, which continues to accelerate through the subsonic converging section to the speed of sound and enters the throat section.

[0004] At present, the profile curve design downstream of the throat of the supersonic nozzle of the wind tunnel is generally designed by using the analytical method of the fountain flow assumption, and the profile curve upstream of the throat is generally designed by using a double-cubic or quintic multiple converging curve. However, for the design of the supersonic nozzle with a boundary layer containing a bleed slot upstream of the throat, there is a lack of systematic and effective design method for the profile near the throat between the lip of the boundary layer bleed slot upstream of the throat and the turning point downstream of the throat. The main problems include suppression of separation bubbles near the lip of the boundary layer bleed slot and supersonic flow, shortening design of the axial length of the subsonic converging section downstream of the lip of the boundary layer bleed slot, and high requirement of flow uniformity at the inlet of the throat. There are design contradictions among them. This results in great difficulty in design, long design cycle due to repeated verification through computational fluid simulation or even test, and even failure of the design result. SUMMARY

[0005] The present application aims to solve the above problems, reduce the design and verification difficulty, improve the design quality, and meet the requirements of the laminar supersonic nozzle for the natural transition test of the supersonic boundary layer of the model.

[0006] To achieve the above-mentioned objectives, this invention provides an aerodynamic design method for the profile curve near the throat of a laminar supersonic nozzle, the method comprising:

[0007] Step S01: Given the initial design conditions for the nozzle, including the nozzle exit design Mach number Ma. T , nozzle exit half height y T The ratio of the radius of curvature of the larynx to the half-height of the larynx, R C / y C Maximum expansion angle θ of the nozzle A , semi-major axis a1 of the boundary layer evacuation joint lip ellipse, semi-minor axis b1 of the boundary layer evacuation joint lip ellipse, and inclination angle θ1 of the major axis of the boundary layer evacuation joint lip ellipse.

[0008] Step S02: Based on the initial design conditions of the nozzle, determine the coordinates of key points C and A. Point C is the location of the nozzle throat wall, and point A is the turning point of the nozzle expansion section.

[0009] Step S03: The initial segment curve adopts multiple curve design. The front and rear endpoints of the initial segment curve are point C and point A, respectively. Based on the initial design conditions of the nozzle and the coordinates of point C and point A, the solution equation of the initial segment curve is constructed.

[0010] Step S04: The subsonic contraction curve adopts an elliptic curve design. The front and rear endpoints of the subsonic contraction curve are point B and point C, respectively. Based on the initial design conditions of the nozzle and the coordinates of point C, the solution equation of the subsonic contraction curve is constructed.

[0011] Step S05: The boundary layer extraction slot lip curve is designed using an elliptical curve. Based on the initial design conditions of the nozzle and the coordinates of point B, the solution equation for the boundary layer extraction slot lip curve is constructed.

[0012] Step S06: Based on the solution equations of the initial segment curve, the subsonic contraction curve, and the boundary layer extraction lip curve, and their corresponding value ranges, obtain the discrete coordinates of the initial segment curve, the subsonic contraction curve, and the boundary layer extraction lip curve. Draw the contour coordinate curve based on the discrete coordinates of the curves to complete the aerodynamic design of the surface curve near the nozzle throat.

[0013] The core principles of this invention include: Segmented curve coupling design: The initial segment uses multiple curves to adapt to the airflow expansion requirements from the throat (point C) to the inflection point (point A) of the expansion segment, ensuring a stable flow field; the subsonic contraction segment and the boundary layer extraction lip both use elliptical curves, utilizing their continuous and smooth curvature characteristics to achieve short-distance uniform contraction, suppress lip separation, and ensure laminar flow generation; the three curves are coupled through the coordinates of key points (B, C, A) to form a coherent aerodynamic profile. Parametric drive: The nozzle exit Mach number Ma... TThe initial design conditions are converted into geometric parameter constraints, the solving equations of the curves are established, the accurate mapping of the aerodynamic target-geometric parameter-curve shape is realized, and the disconnection between geometry and aerodynamics is avoided.

[0014] The curve selection of the application resolves the traditional design contradictions, the elliptic curve suppresses the separation bubble and meets the shortening demand, the multiple curves guarantee the uniformity of the flow field and reduce the trial and error space, the parameterized design logic is fixed, the experience-based blind adjustment is not needed, the trial and error cost is reduced, the segmented coupling design can verify the single curve, the parameter modification does not need to reconstruct the whole model, the simulation iteration and rework are reduced, the verification efficiency is improved, the surface curve has the curvature smoothness in the whole region, the flow field gradient is uniform, the turbulence and separation are suppressed, and the laminar boundary layer is stable, the fixed design logic ensures the consistency and repeatability of the results, and the quality fluctuation caused by the experience difference is reduced.

[0015] Preferably, the coordinates of point C are (0, y C ), and the coordinates of point A are (x A , y A ), wherein y C is the half height of the throat, and the calculation method is as follows:

[0016] ;

[0017] The calculation method of y A is as follows:

[0018] ;

[0019] Ma A is the Mach number at point A, and the calculation method is as follows:

[0020] ;

[0021] , wherein is the Prandtl-Meyer angle corresponding to the Mach number Ma A , and is the Prandtl-Meyer angle corresponding to the Mach number Ma T , and B is the angle of the full-damping zone of the nozzle, and the root() function is used to represent the root.

[0022] Preferably, the solving equation of the initial segment curve is as follows:

[0023] ;

[0024] , wherein (x3, y3) are the coordinates of any point on the initial segment curve, the value range of x3 is , the inclination angle of point C is 0, the inclination angle of point A is A , and the curvature radius R AThe value is 0, where n is the initial curve degree and x is the x-axis. A Let A be the x-coordinate of point A. The initial segment curve's ordinate y3 is a function of its abscissa x3;

[0025] x A The calculation method is as follows:

[0026] ;

[0027] Among them, y A Let be the ordinate of point A;

[0028] laryngeal curvature radius R C The calculation method is as follows:

[0029] .

[0030] Preferably, to improve the uniformity of the throat flow, the axial pipe length of the initial section curve is controlled to increase the pressure gradient along the flow direction on the wall, thereby improving the stability of the boundary layer flow in the initial section. This method uses R... C / y C Designed to satisfy 3≤R C / y C ≤8, to ensure that the boundary layer evacuation joint lip curve and subsonic contraction curve have solutions, R C satisfy:

[0031] .

[0032] Preferably, the inclination angle of point B is θ. B The radii of curvature at points B and C are the same as those at the initial segment curve and the boundary layer venting lip curve, respectively. The equation for solving the subsonic contraction curve is:

[0033] ;

[0034] Where (x2, y2) are the coordinates of any point on the subsonic contraction curve, a2 is the semi-major axis of the subsonic contraction curve ellipse, and b2 is the semi-minor axis of the subsonic contraction curve ellipse.

[0035] and The calculation method is as follows:

[0036] ;

[0037] Among them, R C The radius of curvature of the throat is denoted as ... The semi-major axis of the subsonic contraction curve ellipse about The function, The semi-minor axis of the subsonic contraction curve ellipse about The function;

[0038] The coordinates of point B (x) B y B The calculation method for ) is as follows:

[0039] ;

[0040] in, Let x be the x-coordinate of point B. B About function, Let y be the ordinate of point B. B About function.

[0041] Preferably, the method further includes:

[0042] When θ B =θ1, obtain Minimum design value ,when At that time, obtain Maximum design value The calculation method is as follows:

[0043] ;

[0044] based on and To obtain the range of values ​​for the axial length of the subsonic contraction curve. Check whether the axial length range of the subsonic contraction curve meets the design requirements. If not, adjust the relevant parameters.

[0045] Preferably, in order to balance accelerating the airflow velocity and reducing the axial length of the boundary layer flow downstream of the boundary layer extraction lip, this method designs θ B The range of values ​​is When θ B Value When, θ B Corresponding vector BC argument The calculation method is as follows:

[0046] ;

[0047] in, For θ B Lower limit of value, for Regarding θ B function, y C It is halfway up the larynx;

[0048] The calculation method is as follows:

[0049] ;

[0050] Wherein, In The value is a half-wave constant, and m is a half-wave constant.

[0051] Preferably, the coordinate of the center point of the boundary layer suction slot lip curve is (x O1 , y O1 ), the boundary layer suction slot lip curve intersects with the subsonic contraction curve at point B, and the solving equation of the boundary layer suction slot lip curve is as follows:

[0052] ;

[0053] Wherein, θ is a surface tangent direction angle, and the value range is , θ B is the inclination angle of point B, is a function of the horizontal coordinate x1 of the suction slot lip curve with respect to θ, is a function of the vertical coordinate y1 of the suction slot lip curve with respect to θ.

[0054] Preferably, the calculation method of the coordinate of the center point of the boundary layer suction slot lip curve (x O1 , y O1 ) is as follows:

[0055] ;

[0056] Wherein, is an elliptical center horizontal coordinate x O1 of the boundary layer suction lip curve with respect to θ B , is an elliptical center vertical coordinate y O1 of the boundary layer suction lip curve with respect to θ B , is a function of the horizontal coordinate x B of point B with respect to θ B , is a function of the vertical coordinate y B of point B with respect to θ B , and θ B is the inclination angle of point B.

[0057] Preferably, the value range of θ1 is , so as to reduce the risk of causing supersonic flow near the boundary layer suction slot lip and causing poor flow uniformity near the throat.

[0058] The one or more technical solutions provided by the application have at least the following technical effects or advantages: ​

[0059] The design method provided by this invention can complete the surface profile curve near the throat between the boundary layer extraction lip and the nozzle inflection point of a laminar supersonic nozzle by controlling geometric parameters with clear physical meaning. The method is easy to implement and highly practical.

[0060] The design method provided by this invention ensures that the upstream and downstream radii of curvature are consistent at the throat position, which can effectively solve the problem of poor flow field uniformity caused by mismatch of curvature radii in conventional nozzle design.

[0061] The design method provided by this invention uses the ratio of the throat curvature radius to the throat half-height as a design input parameter. This parameter can be used to control the axial length of the initial section of the nozzle, effectively shortening the axial length of this section and improving the stability of the laminar boundary layer of the nozzle.

[0062] The design method provided by this invention uses the curve inclination angle at the intersection of the extraction slit lip curve and the subsonic contraction curve as a design parameter, and provides an optimal method for this parameter, effectively solving the design problem of the contradiction between the requirement for short axial length of the upstream curve of the throat and high flow field uniformity at the throat position. Attached Figure Description

[0063] The accompanying drawings, which are provided to further illustrate embodiments of the invention and constitute a part of this invention, are not intended to limit the scope of the invention.

[0064] Figure 1 This is a schematic diagram of the design method of the present invention;

[0065] Figure 2 A two-dimensional schematic diagram of the aerodynamic profile of a nozzle containing boundary layer extraction;

[0066] Figure 3 This is a schematic diagram of the initial segment curve;

[0067] Figure 4 This is a schematic diagram of the subsonic contraction curve;

[0068] Figure 5 A schematic diagram of the lip curve of the boundary layer evacuation joint.

[0069] Figure 6 A schematic diagram of the curve design results near the throat;

[0070] Figure 7 For β BC ~θ B Schematic diagram of the curve.

[0071] Wherein, 1 - boundary layer suction slot lip curve, 2 - subsonic contraction curve, 3 - initial section curve, 4 - terminal section curve, 5 - low-speed contraction curve, 6 - upper inner wall of boundary layer suction pipe, 7 - lower inner wall of boundary layer suction pipe, 8 - nozzle exit section, 9 - contraction section inlet section, 10 - throat section, point T is the nozzle expansion section exit wall point, point D is the boundary layer suction slot throat lower end point, point E is the boundary layer suction slot throat upper end point, and point F is the contraction section inlet wall point. DETAILED DESCRIPTION

[0072] In order to enable the above-mentioned objects, features and advantages of the present application to be more clearly understood, the present application will be further described below with reference to the drawings and specific embodiments. It should be noted that the embodiments of the present application and the features in the embodiments can be combined with each other without conflict.

[0073] In the following description, a large number of specific details are set forth in order to facilitate a thorough understanding of the present application, but the present application can also be implemented in other ways different from the scope described herein, and therefore the scope of protection of the present application is not limited by the specific embodiments disclosed below.

[0074] Embodiment one;

[0075] In order to meet the requirements of the model supersonic boundary layer natural transition test on the laminar supersonic nozzle, reduce the difficulty of aerodynamic design and verification of the throat profile curve near the laminar supersonic nozzle, and improve the design quality, the present application provides an aerodynamic design method for the throat profile curve near the laminar supersonic nozzle.

[0076] The nozzle throat profile curve comprises a boundary layer suction slot lip curve, a subsonic contraction curve and an initial section curve connected in sequence, the boundary layer suction slot lip curve and the subsonic contraction curve, and the subsonic contraction curve and the initial section curve intersect with points B and C in sequence, and the front and rear curves at the intersection points B and C should satisfy the first and second order continuity.

[0077] The aerodynamic design method for the throat profile curve near the laminar supersonic nozzle of the present application comprises: giving the initial design conditions of the designed nozzle; determining the coordinates of the key points of the nozzle; determining the initial section curve; determining the subsonic contraction curve; determining the boundary layer suction slot boundary layer suction slot lip curve; and giving the coordinates of the throat profile curve.

[0078] Wherein, the boundary layer suction slot lip curve is an elliptic curve, the semi-major axis and the semi-minor axis are a1 and b1 respectively, the elliptic center O1 coordinate position is (x O1 , y O1 ), the angle between the major axis and the x-axis of the coordinate system is θ, and any point (x1, y1) on the elliptic curve should satisfy the curve equation:

[0079] ; (1)

[0080] wherein x1 is in the range of , x B is the abscissa of the intersection point B of the boundary layer bleed slot lip curve and the subsonic contraction curve.

[0081] wherein the subsonic contraction curve is an elliptic curve, the semi-major axis and semi-minor axis of which are a2 and b2 respectively, and the center O2 of the elliptic curve is located at (0, y C +b2), and any point (x2, y2) on the elliptic curve should satisfy the curve equation:

[0082] ; (2)

[0083] wherein x2 is in the range of , y C is the throat half-height.

[0084] wherein the initial segment curve is a multiple curve, which is an n-th curve, and any point (x3, y3) on the curve should satisfy the curve equation:

[0085] ; (3)

[0086] wherein x3 is in the range of , x A is the abscissa of the turning point where the convex curve downstream of the nozzle throat turns into a concave curve.

[0087] In an alternative embodiment, the throat curve can be solved according to given nozzle design conditions and control parameters, and the specific steps include:

[0088] Step S01: Given the initial design conditions of the design nozzle.

[0089] The initial design conditions of the nozzle include: the design Mach number Ma T at the nozzle outlet, the nozzle outlet half-height y T , the ratio of the throat curvature radius R C to the throat half-height y C , the maximum expansion angle θ A of the nozzle, the semi-major axis a1 of the boundary layer bleed slot lip elliptic curve, the semi-minor axis b1 of the boundary layer bleed slot lip elliptic curve, and the inclination angle θ1 of the major axis of the boundary layer bleed slot lip elliptic curve.

[0090] Step S02: Determine the coordinates of the key points of the nozzle.

[0091] Taking the center point O of the nozzle throat as the origin and the center line of the nozzle as the x-axis, a rectangular coordinate system is established. The key points include the nozzle throat wall position point C (0, y C ), the nozzle expansion segment turning point A (xA , y A ).

[0092] wherein y C is the throat half-height, which can be calculated according to the flow conservation:

[0093] ; (4)

[0094] wherein the turning point A ordinate y A can be calculated according to the analytical design method of supersonic nozzle fountain flow:

[0095] ; (5)

[0096] wherein Ma A is the Mach number at the turning point A, which is solved by the following equation:

[0097] ; (6)

[0098] wherein is the Prandtl-Meyer angle corresponding to the Mach number Ma A , is the Prandtl-Meyer angle corresponding to the Mach number Ma T :

[0099] ; (7)

[0100] wherein θ B is the total damping zone angle of the nozzle, and is taken as , wherein the proportional factor s takes a value range of .

[0101] wherein m is a half-damping zone constant, and is taken as 1.

[0102] Step S03: determining an initial segment curve.

[0103] The initial segment curve is designed by using a multiple curve, and the front and rear endpoints are points C and A respectively, the inclination angle at point C is 0, the inclination angle at point A is θ A , and the curvature radius R A at point A is 0. Wherein the multiple curve refers to that the highest degree n in the polynomial of the curve equation is not limited to an integer, but is a real number greater than 2. The purpose is to solve the problem that the ratio of the throat curvature radius to the throat half-height is too large and the adjustment range is limited in the current conventional multiple curve design, which leads to the difficulty in further shortening the initial segment axial design length.

[0104] Thus, the equation of the curve is:

[0105] ; (8)

[0106] wherein (x3, y3) is the coordinate of any point on the initial curve, wherein x3 ranges from 0 to L .

[0107] wherein n is the degree of the initial curve, and n ranges from 1 to 5 .

[0108] wherein the x-coordinate of point A is x A is calculated as:

[0109] ; (9)

[0110] wherein according to the equation of the initial curve, the curvature radius R C of the curve at the throat position can be obtained:

[0111] ; (10)

[0112] Preferably, the ratio of R C to y C should not be lower than 3 to improve the uniformity of the flow at the throat; preferably, the ratio of R C to y C should not be higher than 8 to control the axial length of the initial curve, improve the streamwise pressure gradient along the wall, and thus improve the stability of the boundary layer flow of the initial curve, and delay the position of the boundary layer transition of the nozzle.

[0113] wherein R C can be adjusted according to the parameters n and θ A , and R A increases with n and decreases with θ

[0114] Preferably, in order to meet the adjustment range of R C , the parameter n is preferably adjusted, and n can be inversely solved according to the design requirements of R C .

[0115] wherein in order to ensure that the boundary layer bleed slot lip curve and the subsonic contraction curve have solutions, R C should satisfy:

[0116] ; (11)

[0117] If not, the conditions can be met by adjusting the design parameters n, θ A , θ1, a1 and b1.

[0118] Step S04: determining the subsonic contraction curve.

[0119] The subsonic contraction curve is designed as an elliptical curve, the short axis of which coincides with the y-axis, and the front and rear endpoints are points B and C, respectively, and the inclination angle at point B is θ BAt points B and C, the radii of curvature coincide with the initial segment curve and the boundary layer extraction lip curve, respectively. Therefore, the equation of this curve is:

[0120] (12)

[0121] Where (x2, y2) are the coordinates of any point on the subsonic contraction curve.

[0122] The purpose of designing the subsonic contraction curve as an elliptical curve is: 1. To propose an aerodynamic profile design method that is completely controlled by specific and physically significant parameters such as the throat curvature radius, the suction lip inclination angle, and the thickness. The profile design process is simple and reliable. 2. To ensure that the profile curve from the suction lip to the initial section maintains curvature continuity, avoiding boundary layer disturbances caused by curvature discontinuities and preventing premature boundary layer transition within the nozzle.

[0123] Where a2 is the semi-major axis of the subsonic contraction curve ellipse, and b2 is the semi-minor axis of the subsonic contraction curve ellipse, based on the design parameter θ. B calculate:

[0124] (13)

[0125] Wherein, the coordinates of point B (x B y B According to the design parameter θ B calculate:

[0126] (14)

[0127] Where, respectively when θ B =θ1、 At that time, obtain Minimum design value and maximum design value .

[0128] (15)

[0129] Based on this, the range of values ​​for the axial length of the subsonic contraction curve is obtained. And check whether it meets the design requirements for the axial length range of the subsonic contraction curve. If it does not meet the requirements, adjust the throat curvature radius y. C , Lip angle during suction and the boundary layer bleed slot lip ellipse curve semi-major axis a1 is adjusted. Wherein, the nozzle boundary layer transition position is related to the streamwise distance from the bleed slot lip leading edge point, with the lengthening of the subsonic contraction curve circumferential length, the relative position of the transition position in the nozzle expansion section will be relatively advanced, forming the effective test area size to be reduced. Therefore, the subsonic contraction curve axial length should be reduced as much as possible, and the specific reduction amount of the subsonic contraction curve axial length can be determined according to the actual situation, and the embodiment of the present application does not make corresponding limitation and elaboration.

[0130] Wherein, θ B is a design parameter, and the allowed value range is When θ B takes the lower limit value , the intersection point B of the subsonic contraction curve and the boundary layer bleed slot lip curve is located at the ellipse long axis vertex of the subsonic contraction curve; when θ B takes the upper limit value θ1, the intersection point B is located at the ellipse short axis vertex of the boundary layer bleed slot lip curve.

[0131] Preferably, the design parameter θ B takes the value range , so as to take into account the acceleration speed of the airflow and the reduction of the axial length of the boundary layer flow downstream of the boundary layer bleed slot lip. Wherein, when θ B takes the upper limit value θ1, the intersection point B of the subsonic contraction curve and the initial section curve is located at the ellipse short axis vertex of the boundary layer bleed slot lip curve, at this time the axial length of the subsonic contraction curve is the shortest, which is beneficial to improve the stability of the boundary layer at the throat position and delay the transition position of the boundary layer in the nozzle expansion section; when θ B takes the value , the absolute value of the amplitude angle of the vector BC is , which is the maximum value in the range , at this time the airflow acceleration speed in the range of the subsonic contraction curve is the fastest, which is beneficial to reduce the airflow Mach number near the boundary layer bleed slot lip and avoid the repeated change of subsonic and supersonic speed near it.

[0132] Wherein, the amplitude angle of the vector BC is calculated as:

[0133] ; (16)

[0134] Wherein, can be solved by numerical method, and the specific calculation is:

[0135] ; (17)

[0136] Step S05: determining the boundary layer bleed slot lip curve.

[0137] The lip curve of the boundary layer bleed slot is designed as an elliptic curve, the center of which is located at (x O1 , y O1 ), the angle between the long axis and the x axis is θ1, and the elliptic curve intersects with the subsonic contraction curve at point B. Thus, the equation of the curve is obtained as follows:

[0138] ; (18)

[0139] wherein the y coordinate corresponding to the x coordinate near the lip of the curve has multiple values. Therefore, the curve equation is expressed in a parameter form with the surface tangent direction angle θ as the parameter:

[0140] ; (19)

[0141] wherein the value range of θ is .

[0142] wherein θ1 should not be too small, otherwise supersonic flow near the lip of the boundary layer bleed slot is prone to occur; θ1 should not be too large, otherwise poor flow uniformity near the throat is prone to occur. Preferably, the value range of θ1 is .

[0143] Preferably, the thickness of the lip of the boundary layer bleed slot represented by b1 should be as small as possible (not more than 5% of the half height y C of the throat) under the conditions of structural strength and machining precision, so as to reduce the influence range of the stagnation point of the lip of the boundary layer bleed slot, thereby reducing the axial design length of the subsonic contraction curve.

[0144] Preferably, the elliptic ratio represented by a1 should be not less than 2 times of b1, so as to optimize the pressure distribution downstream of the stagnation point of the lip of the boundary layer bleed slot, and avoid the occurrence of leading edge separation bubbles, which leads to early transition of the boundary layer.

[0145] wherein the center coordinates (x O1 , y O1 ) of the elliptic curve of the lip curve of the boundary layer bleed slot are calculated as follows:

[0146] ; (20)

[0147] Step S06: giving the profile curve coordinates near the throat.

[0148] According to the given curve equation and value range of each segment, the discrete coordinates of the curve are given, and the profile coordinate curve is drawn.

[0149] Please refer to Figures 1-7 , for example Figure 2, a certain wind tunnel adopts a two-dimensional supersonic nozzle with boundary layer suction, wherein the profile curve near the throat includes three curve segments of a boundary layer suction slot lip curve, a subsonic contraction curve and an initial segment curve along the flow direction, and the first and last of which intersect at points B and C, respectively. In order to determine the coordinates of each point and curve profile, a rectangular coordinate system is established with the center O of the throat section of the nozzle as the origin and the center line of the nozzle as the x-axis. The design Mach number Ma T =3.0 at the nozzle exit, the half height y T =150mm at the nozzle exit, the ratio of the throat curvature radius R C / y C =5, the maximum expansion angle θ A =12° of the nozzle, the half long axis a1=1mm of the boundary layer suction slot lip ellipse curve, the half short axis b1=3mm of the boundary layer suction slot lip ellipse curve, and the long axis inclination angle θ1=-15° of the boundary layer suction slot lip ellipse curve.

[0150] On the basis of the above given design conditions, the profile curve near the throat of the nozzle is aerodynamically designed by using the scheme of the present application, and the results are given.

[0151] Among the profile curve near the throat, the boundary layer suction slot lip curve (see Figure 3 ) and the subsonic contraction curve (see Figure 4 ) are elliptical curves, and the initial segment curve (see Figure 5 ) is a multiple curve.

[0152] According to the flow conservation, the throat half height y C can be obtained:

[0153] ;

[0154] According to the nozzle fountain analytical design method, under the condition that the half wave suppression zone angle is θ B =2°, i.e. s=1 / 6, the Mach number of the turning point A is:

[0155] ;

[0156] And the longitudinal coordinate y A of the turning point A is:

[0157] ;

[0158] According to the ratio of the throat curvature radius R C / y C =5, the throat curvature radius R C =177.114mm can be obtained. Checking its compliance requirements shows that the design condition can ensure that the boundary layer suction slot lip curve and the subsonic contraction curve have solutions.

[0159] According to the initial segment curve, the radius of curvature R at the throat is C The calculation formula can obtain the initial segment curve order n = 2.146, and obtain the initial segment curve equation:

[0160] ;

[0161] Wherein the x-coordinate of point A is x A :

[0162] ;

[0163] The curve is drawn in the rectangular coordinate system as shown in Figure 6 .

[0164] In the range of θ B allowable value range , calculate , and draw curve as shown in Figure 7 , In the value interval of θ B , there is an extreme value. The extreme value position is obtained by numerical method, which is taken as the design value of θ B .

[0165] Thus, the half long axis a2 of the subsonic contraction ellipse curve is 25.994 mm, the half short axis b2 is 3.815 mm, and the coordinates (x B , y B ) of the end point B are (-25.862, 38.853) mm; and the equation of the ellipse curve is obtained:

[0166] ;

[0167] The curve is drawn in the rectangular coordinate system as shown in Figure 6 .

[0168] The center coordinates (x O1 , y O1 ) of the ellipse curve of the lip of the boundary layer suction slot are (-23.069, 38.485) mm, and thus the equation of the ellipse curve is obtained:

[0169] ;

[0170] The curve is drawn in the rectangular coordinate system as shown in Figure 6 .

[0171] The coordinates of the throat near the profile curve are summarized as Table 1. Table 1 is the coordinate table of the throat near the profile curve.

[0172] Table 1

[0173]

[0174]

[0175] While the preferred embodiments of the application have been described, additional variations and modifications can be made to these embodiments by those skilled in the art once they have the benefit of the present disclosure without departing from the spirit and scope of the application. Accordingly, it is intended that the appended claims include all such modifications and variations as fall within the scope of the present application.

[0176] It is apparent that those skilled in the art can, without departing from the spirit and scope of the application, make various changes and modifications of the application. Thus, it is intended that the present application cover all modifications and variations of this application provided they come within the scope of the appended claims and their equivalents.

Claims

1. A method of aerodynamic design of a profile curve in the vicinity of a throat of a laminar ultrasonic nozzle, characterized in that, The method includes: Step S01: Given the initial design conditions of the nozzle, the initial design conditions of the nozzle include: the design Mach number Ma T of the nozzle outlet, the half-height y T of the nozzle outlet, the ratio R C / y C of the throat curvature radius and the throat half-height, the maximum expansion angle θ A of the nozzle, the semi-major axis a1 of the boundary layer bleed slot lip elliptic curve, the semi-minor axis b1 of the boundary layer bleed slot lip elliptic curve, and the inclination angle θ1 of the boundary layer bleed slot lip elliptic curve; Step S02: Based on the initial design conditions of the nozzle, determine the coordinates of key points C and A. Point C is the location of the nozzle throat wall, and point A is the turning point of the nozzle expansion section. Step S03: The initial segment curve adopts multiple curve design. The front and rear endpoints of the initial segment curve are point C and point A, respectively. Based on the initial design conditions of the nozzle and the coordinates of point C and point A, the solution equation of the initial segment curve is constructed. Step S04: The subsonic contraction curve adopts an elliptic curve design. The front and rear endpoints of the subsonic contraction curve are point B and point C, respectively. Based on the initial design conditions of the nozzle and the coordinates of point C, the solution equation of the subsonic contraction curve is constructed. Step S05: The boundary layer extraction slot lip curve is designed using an elliptical curve. Based on the initial design conditions of the nozzle and the coordinates of point B, the solution equation for the boundary layer extraction slot lip curve is constructed. Step S06: Based on the solution equations of the initial segment curve, the subsonic contraction curve, and the boundary layer extraction slot lip curve, and their corresponding value ranges, obtain the discrete coordinates of the initial segment curve, the subsonic contraction curve, and the boundary layer extraction slot lip curve. Draw the contour coordinate curve based on the discrete coordinates of the curves to complete the aerodynamic design of the surface curve near the nozzle throat. The angle of point B is θ B The solving equation of the subsonic contraction curve is: ； Wherein, (x2, y2) is the coordinates of any point on the subsonic contraction curve, a2 is the semi-major axis of the subsonic contraction curve ellipse, b2 is the semi-minor axis of the subsonic contraction curve ellipse, With The calculation method is: ； wherein R C is the throat radius of curvature, is the subsonic convergent curve ellipse semi-major axis is the function of , is the subsonic convergent curve ellipse semi-minor axis is the function of . The coordinates (x B , y B ) of point B are calculated as follows: ； in, Let x be the x-coordinate of point B. B About function, Let y be the ordinate of point B. B About function; The coordinate of the center point of the boundary layer bleed slot lip curve is (x O1 , y O1 ), the boundary layer bleed slot lip curve intersects with the subsonic contraction curve at point B, and the solving equation of the boundary layer bleed slot lip curve is: ； Where θ is the surface tangent direction angle, and its value ranges from 0 to 1. θ B Let B be the angle of inclination. Let x1 be the abscissa of the air extraction lip curve as a function of θ. The vertical coordinate y1 of the air extraction lip curve is a function of θ.

2. The aerodynamic design method for the profile curve near the throat of a laminar supersonic nozzle according to claim 1, characterized in that, The coordinates of point C are (0, y C ), and the coordinates of point A are (x A , y A ), wherein y C is the throat half-height, and the calculation method is as follows: ； y A The calculation method is as follows: ； Ma A Ma is the Mach number at point A, calculated as: ； in, Mach number Ma A The corresponding Plantmeyer angle, Mach number Ma T The corresponding Prandtmeyer angle, θ B Let be the angle of the nozzle's full bleed-out zone. The root() function is used to find the root.

3. The aerodynamic design method for the profile curve near the throat of a laminar supersonic nozzle according to claim 1, characterized in that, The equation for solving the initial segment curve is: ； Where (x3, y3) are the coordinates of any point on the initial segment of the curve, and the range of x3 is: The angle of inclination of point C is 0, and the angle of inclination of point A is θ. A The radius of curvature R of point A A The value is 0, where n is the initial curve degree and x is the x-axis. A Let A be the x-coordinate of point A. The initial segment curve's ordinate y3 is a function of its abscissa x3; x A The calculation is as follows: ； where y A is the ordinate of point A; throat curvature radius R C is calculated as follows: 。 4. The aerodynamic design method for the profile curve near the throat of a laminar supersonic nozzle according to claim 1, characterized in that, 3≤R C / y C ≤8, R C satisfies: 。 5. The aerodynamic design method for the profile curve near the throat of a laminar supersonic nozzle according to claim 1, characterized in that, The method further includes: When θ B =θ1, obtain Minimum design value ,when At that time, obtain Maximum design value The calculation method is as follows: ； based on and To obtain the range of values ​​for the axial length of the subsonic contraction curve. Check whether the axial length range of the subsonic contraction curve meets the design requirements. If not, adjust the relevant parameters.

6. The aerodynamic design method for the profile curve near the throat of a laminar supersonic nozzle according to claim 1, characterized in that, θ B The range of values ​​is When θ B Value When, θ B Corresponding vector BC argument The calculation method is as follows: ； in, For θ B Lower limit of value, for Regarding θ B function, y C It is halfway up the larynx; The calculation method is as follows: ； in, for exist The value of , where m is the semi-suppression zone constant.

7. The aerodynamic design method for the profile curve near the throat of a laminar supersonic nozzle according to claim 1, characterized in that, The calculation of the center point coordinate (x O1 , y O1 ) of the boundary layer bleed slot lip curve is as follows: ； in, x is the x-coordinate of the center of the ellipse of the boundary layer extraction lip curve. O1 Regarding θ B The function, The ordinate of the center of the boundary layer extraction lip curve ellipse is y. O1 Regarding θ B The function, Let x be the x-coordinate of point B. B Regarding θ B function, Let y be the ordinate of point B. B Regarding θ B function, θ B Let be the angle of inclination of point B.

8. The aerodynamic design method for the profile curve near the throat of a laminar supersonic nozzle according to claim 1, characterized in that, The range of values ​​for θ1 is: .

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