Aerodynamic design method for molded surface curve near throat of laminar flow supersonic velocity nozzle

Abstract

The invention discloses an aerodynamic design method for a molded surface curve near a throat of a laminar flow supersonic nozzle, and relates to the field of aerodynamic design of supersonic equipment. Determining key point coordinates of the spray pipe; determining an initial section curve; determining a subsonic velocity shrinkage curve; determining a boundary layer exhaust seam lip curve of the boundary layer exhaust seam; according to the method, the requirement of a model supersonic boundary layer natural transition test on the laminar flow supersonic spray pipe can be met, the aerodynamic design and verification difficulty of the profile curve near the throat of the laminar flow supersonic spray pipe is reduced, and the design quality is improved.

Description

Technical Field

[0001] This invention relates to the field of aerodynamic design of supersonic equipment, and more specifically, to an aerodynamic design method for the profile curve near the throat of a laminar supersonic nozzle. Background Technology

[0002] A wind tunnel supersonic nozzle (or simply nozzle) is a meticulously designed Laval nozzle, mainly composed of three parts: a converging section for airflow acceleration, a throat for transonic airflow, and a termination section for regulating the uniformity of airflow space. It is the key section for achieving uniform supersonic test airflow in a supersonic wind tunnel. In a wind tunnel, the upstream boundary layer of the nozzle is turbulent. Conventional nozzles, lacking boundary layer re-lamination measures, cause turbulent noise generated by the supersonic boundary layer within the nozzle to radiate along the Mach line to the downstream test airflow, resulting in test airflow noise that is 1 to 2 orders of magnitude higher than that of the flight environment. In wind tunnel testing, the location of the natural transition on the test model surface occurs much earlier than in actual flight.

[0003] To improve the simulation accuracy of the natural transition of the boundary layer under supersonic conditions, the supersonic flow region of the nozzle needs to achieve laminar boundary layer flow. A necessary condition for this is to achieve re-laminarization of the boundary layer upstream of the throat. Setting a boundary layer extraction slot upstream of the throat is an effective means to achieve re-laminarization. The upstream flow passes through the lip of the extraction slot, expelling the original boundary layer flow from the nozzle. At the same time, a new laminar boundary layer flow is formed inside the lip of the extraction slot, and the flow continues to accelerate to sonic speed through the subsonic contraction section before entering the throat section.

[0004] Currently, the downstream profile curve design of supersonic nozzles in wind tunnels generally employs the analytical method based on the fountain assumption, while the upstream profile curve is typically designed using bicubic, quintic, or other multiple contraction curves. However, for supersonic nozzles with an upstream boundary layer containing an extraction slot, the aerodynamic design of the profile near the throat—between the extraction slot lip and the downstream inflection point—lacks a systematic and effective design method. The main challenges include suppressing the separated bubble and supersonic flow near the extraction slot lip, shortening the axial length of the subsonic contraction section downstream of the extraction slot lip, and meeting the high requirements for uniform flow at the throat inlet. These challenges are also contradictory. This results in significant design difficulty, requiring repeated verification through computational fluid dynamics simulations and even experiments, leading to long design cycles and even design failures. Summary of the Invention

[0005] The purpose of this invention is to solve the above problems, reduce the difficulty of design and verification, improve the design quality, and meet the requirements of laminar supersonic nozzles for the natural transition test of the supersonic boundary layer in 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... TOnce the initial design conditions are transformed into geometric parameter constraints, the solution equations for each curve are established to achieve a precise mapping between aerodynamic targets, geometric parameters, and curve shapes, thus avoiding the disconnect between geometry and aerodynamics.

[0014] The curve selection method of this invention specifically resolves the contradictions of traditional design. Elliptical curves suppress separation bubbles and meet the requirements for shortening, while multiple curves ensure the uniformity of the flow field and reduce the trial-and-error space. The parameterized design logic is fixed, eliminating the need for blind adjustments based on experience and reducing trial costs. The segmented coupling design allows for the independent verification of individual curve segments, and parameter modifications do not require the reconstruction of the entire model, reducing simulation iterations and rework and improving verification efficiency. The surface curve has smooth curvature characteristics throughout the entire region, ensuring a uniform flow field gradient, suppressing turbulence and separation, and ensuring the stability of the laminar boundary layer. The fixed design logic ensures the consistency and repeatability of results, reducing quality fluctuations caused by experience differences.

[0015] Preferably, the coordinates of point C are (0, y). C The coordinates of point A are (x, y). A y A ), where y C The laryngeal half-height is calculated as follows:

[0016] ;

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

[0018] ;

[0019] Ma A The Mach number at point A is calculated as follows:

[0020] ;

[0021] 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.

[0022] Preferably, the equation for solving the initial segment curve is:

[0023] ;

[0024] Where (x3, y3) are the coordinates of any point on the initial curve segment, 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 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] in, for exist The value is m, where m is the semi-suppression zone constant.

[0051] Preferably, the coordinates of the center point of the boundary layer extraction joint lip curve are (x O1 y O1 The boundary layer venting joint lip curve intersects the subsonic contraction curve at point B. The equation for solving the boundary layer venting joint lip curve is:

[0052] ;

[0053] 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.

[0054] Preferably, the center point coordinates (x) of the boundary layer extraction joint lip curve O1 y O1 The calculation method for ) is as follows:

[0055] ;

[0056] 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.

[0057] Preferably, the range of values ​​for θ1 is: This reduces the risk of supersonic flow near the lip of the boundary layer evacuation seam and poor flow uniformity near the throat.

[0058] One or more technical solutions provided by this invention 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 extraction lip curve, 2-subsonic contraction curve, 3-initial section curve, 4-termination section curve, 5-low-speed contraction curve, 6-upper inner wall of boundary layer extraction pipe, 7-lower inner wall of boundary layer extraction pipe, 8-nozzle outlet section, 9-contraction section inlet section, 10-throat section, point T is the nozzle expansion section outlet wall point, point D is the lower end point of the boundary layer extraction lip throat, point E is the upper end point of the boundary layer extraction lip throat, and point F is the contraction section inlet wall point. Detailed Implementation

[0072] To better understand the above-mentioned objectives, features, and advantages of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, where there is no conflict, the embodiments of the present invention and the features thereof can be combined with each other.

[0073] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and therefore the scope of protection of the invention is not limited to the specific embodiments disclosed below.

[0074] Example 1;

[0075] To meet the requirements of laminar supersonic nozzles for natural transition tests of the supersonic boundary layer in models, reduce the difficulty of aerodynamic design and verification of the profile curve near the throat of laminar supersonic nozzles, and improve design quality, this invention provides an aerodynamic design method for the profile curve near the throat of laminar supersonic nozzles.

[0076] The profile curves near the nozzle throat include the boundary layer extraction lip curve, the subsonic contraction curve, and the initial segment curve, which are connected in sequence. The boundary layer extraction lip curve and the subsonic contraction curve, and the subsonic contraction curve and the initial segment curve intersect at points B and C respectively. The curves before and after the intersection points B and C should satisfy the first-order and second-order continuity.

[0077] The present invention provides an aerodynamic design method for the profile curve near the throat of a laminar supersonic nozzle, comprising: providing initial design conditions for the nozzle; determining the coordinates of key points of the nozzle; determining the initial segment curve; determining the subsonic contraction curve; determining the boundary layer extraction lip curve; and providing the coordinates of the profile curve near the throat.

[0078] The boundary layer extraction joint lip curve is an elliptical curve with semi-major and semi-minor axes a1 and b1, respectively. The coordinates of the ellipse center O1 are (x...). O1 y O1 The major axis makes an angle θ with the x-axis of the coordinate system, and any point (x1, y1) on the elliptic curve should satisfy the equation of the curve:

[0079] (1)

[0080] Where x1 takes values ​​in the range of x B Let B be the x-coordinate of the intersection point B of the boundary layer evacuation lip curve and the subsonic contraction curve.

[0081] The subsonic contraction curve is an elliptic curve with semi-major and semi-minor axes a2 and b2, respectively. The coordinates of the ellipse center O2 are (0, y). C +b2), any point (x2, y2) on the elliptic curve should satisfy the equation of the curve:

[0082] (2)

[0083] Where x2 takes values ​​in the range of y C It is halfway up the larynx.

[0084] The initial segment curve is a polynomial curve, specifically an nth-degree curve, and any point (x3, y3) on the curve should satisfy the curve equation:

[0085] (3)

[0086] Where x3 takes values ​​in the range of x A The x-coordinate is the inflection point where the convex curve in the downstream of the nozzle throat turns into a concave curve.

[0087] In one optional implementation, the throat curve can be obtained based on given nozzle design conditions and control parameters, specifically including the following steps:

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

[0089] Initial nozzle design conditions include: 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.

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

[0091] A rectangular coordinate system is established with the nozzle throat center point O as the origin and the nozzle centerline as the x-axis. Key points include the nozzle throat wall location point C(0, y). C ), nozzle expansion section inflection point A (x)A y A ).

[0092] Among them, y C That is, the throat half-height, which can be calculated based on the principle of flow conservation:

[0093] (4)

[0094] Where the ordinate of the turning point A is y A It can be calculated using the analytical design method for supersonic jet streams:

[0095] (5)

[0096] Among them, Ma A The Mach number at inflection point A is obtained by solving the following equation:

[0097] (6)

[0098] in, Mach number Ma A The corresponding Plantmeyer angle, Mach number Ma T The corresponding Prandmeier angle:

[0099] (7)

[0100] Where, θ B For the nozzle's full bleed-out zone angle, take The scaling factor s takes values ​​ranging from 1 to 10. .

[0101] Where m is the semi-suppression region constant, which is taken as 1.

[0102] Step S03: Determine the initial segment curve.

[0103] The initial curve segment uses a multiple curve design, with its endpoints at points C and A, respectively. The inclination angle at point C is 0°, and the inclination angle at point A is θ. A The radius of curvature R of point A A The value is 0. Here, a polynomial curve refers to a curve equation where the highest degree n is not limited to an integer, but is a real number greater than 2. Its purpose is to address the problem in current conventional polynomial curve designs where the ratio of throat curvature radius to throat half-height is too large and the adjustment range is limited, making it difficult to further shorten the axial design length of the initial segment.

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

[0105] (8)

[0106] Where (x3, y3) are the coordinates of any point on the initial segment of the curve, and the range of values ​​for x3 is... .

[0107] Where n is the degree of the initial curve segment, and its value range is... .

[0108] Where, the x-coordinate of point A is x A The calculation is as follows:

[0109] (9)

[0110] Based on the equation of the initial segment curve, the radius of curvature R of the curve at the throat position can be obtained. C :

[0111] (10)

[0112] Preferred, R C With y C The ratio should not be less than 3 to improve the uniformity of throat flow; preferably, R C With y C The ratio should not exceed 8 in order to control the axial tube length of the initial section curve, increase the pressure gradient along the flow direction on the wall, thereby improving the stability of the boundary layer flow in the initial section and delaying the transition position of the nozzle boundary layer.

[0113] Among them, R C Based on parameters n and θ A Adjustments are made as n increases and as θ increases. A Decreasing.

[0114] Preferably, in order to satisfy R C The adjustment range is preferably adjusted based on parameter n, which can be determined according to R. C The design requires solving for the value of n in reverse.

[0115] Among them, to ensure that the boundary layer evacuation joint lip curve and the subsonic contraction curve have solutions, R C Should meet:

[0116] (11)

[0117] If this is not satisfied, it can be addressed by adjusting n and θ. A Design parameters such as θ1, a1, and b1 are used to meet the conditions.

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

[0119] The subsonic contraction curve is designed as an elliptic curve, with its minor axis coinciding with the y-axis. Its endpoints are points B and C, respectively, and its 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 The semi-major axis a1 of the elliptical curve of the boundary layer extraction lip is adjusted. The transition position of the nozzle boundary layer is related to the flow distance from the leading edge of the extraction lip. As the circumferential length of the subsonic contraction curve increases, the relative position of the transition position in the nozzle expansion section will be advanced, resulting in a smaller effective test area. Therefore, the axial length of the subsonic contraction curve should be minimized as much as possible. The specific reduction in the axial length of the subsonic contraction curve can be determined according to the actual situation; this embodiment of the invention does not impose corresponding limitations or elaborate on this.

[0130] Where, θ B For design parameters, the allowed value range is: When θ B Take the lower limit value At that time, the intersection point B of the subsonic contraction curve and the boundary layer extraction lip curve is located at the vertex of the major axis of the ellipse of the subsonic contraction curve; when θ B When the upper limit value θ1 is taken, the intersection point B is located at the vertex of the minor axis of the ellipse of the boundary layer extraction lip curve.

[0131] Preferably, the design parameter θ B The range of values ​​is This is to balance accelerating the airflow and reducing the axial length of the boundary layer flow downstream of the boundary layer extraction lip. Wherein, when θ B When the upper limit θ1 is taken, the intersection point B of the subsonic contraction curve and the initial segment curve is located at the vertex of the minor axis of the ellipse of the boundary layer extraction lip curve. At this time, the axial length of the subsonic contraction curve is the shortest, which is beneficial to improving the boundary layer stability at the throat position and delaying the boundary layer transition position in the nozzle expansion section; when θ B Value At that time, the absolute value of the argument of the corresponding vector BC for The maximum value within the range indicates that the airflow accelerates the fastest within the subsonic contraction curve range, which helps to reduce the Mach number of the airflow near the lip of the boundary layer extraction slot and avoid repeated changes between subsonic and supersonic speeds in the vicinity.

[0132] Wherein, the argument of vector BC The calculation is as follows:

[0133] (16)

[0134] in, This can be solved numerically, specifically by:

[0135] (17)

[0136] Step S05: Determine the lip curve of the boundary layer evacuation joint.

[0137] The boundary layer evacuation joint lip curve adopts an elliptical curve design, with its center located at (x... O1 y O1 The major axis makes an angle θ1 with the x-axis, and intersects the subsonic contraction curve at point B. Therefore, the equation of this curve is:

[0138] (18)

[0139] In this section of the curve, the y-coordinate corresponding to the x-coordinate has multiple values ​​near the lip. Therefore, using the surface tangent direction angle θ as a parameter, the curve equation is expressed in parametric form as follows:

[0140] (19)

[0141] Where θ takes values ​​in the range of .

[0142] Specifically, θ1 should not be too small, otherwise it may lead to supersonic flow near the lip of the boundary layer extraction slit; θ1 should not be too large, otherwise it may lead to poor flow uniformity near the throat. Preferably, the range of θ1 is... .

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

[0144] Preferably, the elliptic ratio represented by a1 should be no less than twice that of b1 to optimize the pressure distribution downstream of the stagnation point at the boundary layer venting lip, avoid the formation of leading-edge separation bubbles, and prevent premature boundary layer transition.

[0145] Among them, the coordinates of the ellipse center of the boundary layer extraction joint lip curve (x O1 y O1 The calculation is as follows:

[0146] (20)

[0147] Step S06: Give the coordinates of the surface curve near the throat.

[0148] Based on the given equations and ranges of values ​​for each curve segment, provide the discrete coordinates of the curve and plot the contour coordinate curve.

[0149] Please refer to Figures 1-7 ,like Figure 2A wind tunnel employs a two-dimensional supersonic nozzle with boundary layer extraction. The nozzle profile near the throat comprises three segments along the flow direction: the boundary layer extraction lip curve, the subsonic contraction curve, and the initial segment curve. These segments intersect at points B and C, respectively. To determine the coordinates of each point and the curve profile, a rectangular coordinate system is established with the nozzle throat cross-section center O as the origin and the nozzle centerline as the x-axis. The nozzle exit design Mach number is [Ma]. T =3.0, nozzle exit half height y T =150mm, the ratio of the laryngeal curvature radius to the half-height of the laryngeal passage R C / y C =5, maximum nozzle expansion angle θ A =12°, semi-major axis a1=1mm, semi-minor axis b1=3mm, and major axis inclination angle θ1=-15°.

[0150] Based on the above-mentioned design conditions, the aerodynamic design of the surface curve near the nozzle throat is carried out using the scheme of this application, and the results are given.

[0151] In the surface curve near the throat, the boundary layer evacuation lip curve (see...) Figure 3 ) and subsonic contraction curve (see Figure 4 The curve is an elliptic curve, and the initial segment of the curve (see...) Figure 5 () is a polynomial curve.

[0152] Based on flow conservation, the throat half-height y can be obtained. C :

[0153] ;

[0154] Based on the analytical design method of jet streams, the angle in the semi-wave-damping zone is θ. B =2°, that is, under the condition that s=1 / 6, the Mach number of the inflection point A is:

[0155] ;

[0156] And obtain the ordinate y of the turning point A. A :

[0157] ;

[0158] Based on the ratio of the radius of curvature at the larynx to the half-height of the larynx, R... C / y C =5, and the radius of curvature R of the larynx can be obtained. C =177.114mm. Check that it conforms to... The requirements indicate that the design conditions can ensure that the boundary layer evacuation joint lip curve and the subsonic contraction curve have solutions.

[0159] Based on the initial segment curve, the radius of curvature R at the throat is... C The calculation formula yields the initial curve degree n = 2.146, and the equation of the initial curve segment is obtained:

[0160] ;

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

[0162] ;

[0163] Plot the curve in a rectangular coordinate system as follows: Figure 6 As shown.

[0164] In θ B Allowed value range Inside, calculation and draw Curves Figure 7 As shown, In θ B The interval contains extreme values. The locations of these extreme values ​​can be determined numerically. , as θ B Design value.

[0165] Therefore, the semi-major axis a2 = 25.994 mm, the semi-minor axis b2 = 3.815 mm, and the coordinates of endpoint B (x) of the subsonic contracting elliptic curve are obtained. B y B The equation of the elliptic curve segment is obtained as follows: (-25.862, 38.853) mm.

[0166] ;

[0167] Plot the curve in a rectangular coordinate system as follows: Figure 6 As shown.

[0168] The center coordinates (x) of the boundary layer evacuation joint lip ellipse O1 y O1 The equation of the elliptic curve segment is obtained from the given equation: (-23.069, 38.485) mm.

[0169] ;

[0170] Plot the curve in a rectangular coordinate system as follows: Figure 6 As shown.

[0171] The coordinates of the surface curves near the throat are obtained by summarizing the curves of each segment, as shown in Table 1. Table 1 is a table of coordinates of the surface curves near the throat.

[0172] Table 1

[0173]

[0174]

[0175] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the invention.

[0176] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. An aerodynamic design method for the profile curve near the throat of a laminar supersonic nozzle, characterized in that, The method includes: 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. 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 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.

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 The coordinates of point A are (x, y). A y A ), where y C The laryngeal half-height is calculated as follows: ； y A The calculation method is as follows: ； Ma A The Mach number at point A is calculated as follows: ； 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 curve segment, 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 method is as follows: ； Among them, y A Let be the ordinate of point A; laryngeal curvature radius R C The calculation method is 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 satisfy: 。 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 angle of inclination 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: ； 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. and The calculation method is as follows: ； 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; The coordinates of point B (x) B y B The calculation method for ) is 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.

6. The aerodynamic design method for the profile curve near the throat of a laminar supersonic nozzle according to claim 5, 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.

7. The aerodynamic design method for the profile curve near the throat of a laminar supersonic nozzle according to claim 5, 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.

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 coordinates of the center point of the boundary layer evacuation joint lip curve are (x O1 y O1 The boundary layer venting joint lip curve intersects the subsonic contraction curve at point B. The equation for solving the boundary layer venting joint 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.

9. The aerodynamic design method for the profile curve near the throat of a laminar supersonic nozzle according to claim 8, characterized in that, The coordinates of the center point of the boundary layer evacuation joint lip curve (x O1 y O1 The calculation method for ) 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.

10. 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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