A design method for Laval nozzle with continuous curvature

Abstract

A curvature-continuous Laval nozzle design method belongs to the field of aerodynamic wind tunnel design technology. It involves specifying boundary conditions to ensure the curvature continuity of the nozzle's inviscid profile, designing the inviscid profile of the nozzle's diverging section using the characteristic grid method, determining the boundary layer displacement thickness at the nozzle throat and nozzle exit using empirical formulas and the Tucker method, expressing the boundary layer displacement thickness distribution along the nozzle throat to the nozzle exit using a fitting function combining a cubic curve and a straight line, and converting the boundary layer displacement thickness into a two-dimensional boundary layer displacement thickness based on the cross-sectional dimensions, superimposing the nozzle's inviscid profile and the corrected boundary layer displacement thickness, and adaptively generating the viscous profile of the nozzle's diverging section by controlling the nozzle exit height, and designing the nozzle's convergent section profile with continuous curvature at the throat using an nth-order polynomial function. This method is suitable for the design of flexible-wall nozzles and can more realistically simulate the supersonic flow field within the nozzle, thereby making the flow field at the nozzle exit more uniform.

Description

Technical Field

[0001] The invention relates to a design method for a Laval nozzle with continuous curvature, and belongs to the technical field of aerodynamic wind tunnel design. Background Art

[0002] The Laval nozzle is the primary instrument for establishing supersonic flow fields. Supersonic wind tunnel nozzles are primarily categorized as solid-wall and flexible-wall. Solid-wall nozzles are specifically calibrated to Mach numbers, requiring nozzle replacement for each Mach number change. This results in a large number of nozzles, but the efficiency of nozzle replacement is low, making them unsuitable for continuous wind tunnels. Today, mainstream supersonic wind tunnels generally use flexible-wall nozzles instead of solid-wall nozzles. The advantages of flexible-wall nozzles include a wide Mach number adjustment range, small Mach number intervals, a large number of profiles, high Mach number accuracy, and efficient nozzle profile replacement. However, because the curvature of the flexible plate is continuous, the curvature of the nozzle profile must also be continuous. Existing nozzle profile design methods primarily include analytical methods and the characteristic grid method. Laval nozzle design originated with Prandtl and Buseman, who first applied the characteristic grid method (MOC) to supersonic flow field evaluation in 1929. Building on this, Puckett (1946), Foelsch (1946), and Pinkel (1948) proposed various nozzle design methods based on the characteristic grid method. However, these methods suffered from curvature discontinuity, which caused characteristic lines to converge and disrupt the flow field. In 1949, Foelsch proposed an analytical design method for the Laval nozzle, which improved flow field uniformity but still did not meet the requirement for curvature continuity.

[0003] Various curvature-continuous nozzle profile design methods have been developed at home and abroad. In 1953, Riise proposed a semi-analytical and semi-characteristic grid method for flexible-wall nozzle design. The velocity and angle at the turning point are determined according to the radial flow assumption and flow conservation, and the characteristic grid is used on this basis. This method can ensure curvature continuity, but does not apply the transonic flow solution of the throat, that is, the HKL solution, and the nozzle flow field uniformity is general. In 1955, Sivells proposed an integral form of nozzle analytical design method, which also cannot apply the transonic flow solution of the throat, and the angle relationship between the turning point and the characteristic point is an assumed relationship. In 1978, Sivells proposed a nozzle design method based on the characteristic grid method, which also ensures the continuity of nozzle curvature. However, based on the radial flow assumption, it is necessary to specify the Mach number distribution on the centerline, which greatly affects the uniformity of the flow field at the outlet.

[0004] Therefore, it is urgent to propose a Laval nozzle design method with continuous curvature to solve the above technical problems. Summary of the Invention

[0005] The purpose of this invention is to develop a curvature-continuous Laval nozzle design method that allows the flexible plate to perfectly fit the nozzle profile, making it suitable for flexible-wall nozzle design. This method also uses the HKL solution as the inlet boundary condition for the characteristic grid at the throat, which can more realistically simulate the supersonic flow field within the nozzle, thereby making the flow field at the nozzle outlet more uniform. This invention is a curvature-continuous Laval nozzle design method with a design Mach number range of 1.15 to 5.0, meeting the profile design requirements of transonic wind tunnel flexible-wall nozzles. A brief overview of the invention is provided below to provide a basic understanding of certain aspects of the invention. It should be understood that this overview is not an exhaustive overview of the invention. It is not intended to identify key or important parts of the invention, nor is it intended to limit the scope of the invention.

[0006] The technical solution of the present invention:

[0007] A Laval nozzle design method with continuous curvature includes:

[0008] Step 1: Given the design Mach number and nozzle geometry parameters;

[0009] The design Mach number range is 1.15~5.0. The Mach number within this range is selected for nozzle design. In addition, the nozzle design requires a given nozzle outlet target height and the distance between the parallel walls of the nozzle, that is, the nozzle width.

[0010] Step 2: Create the boundary conditions of the curvature-continuous nozzle inviscid surface;

[0011] The inviscid surface of the nozzle is divided into three regions by four nodes, namely the throat, turning point A, characteristic point C and nozzle exit point;

[0012] The throat is the position of the profile closest to the axis, the turning point A is the point on the profile curve where the curvature is zero, and the characteristic point C is the point where the derivative of the right-extending characteristic function is zero;

[0013] The area between the sonic line k1 emitted from the throat and the right-extending characteristic line of the turning point is the initial expansion area Q1, the area between the right-extending characteristic line of the turning point and the right-extending characteristic line of the characteristic point is the semi-wave-absorptive area Q2, and the area between the right-extending characteristic line of the characteristic point and the left-extending characteristic line of the nozzle outlet is the complete wave-absorptive area Q3;

[0014] The angle between the flow direction and the axis of the nozzle flow field is defined as the airflow angle θ. The Mach angle μ is the angle between the boundary line of the local disturbance propagation and the incoming flow when the Mach number M ≥ 1. It is also the angle between the tangent line of the characteristic line and the flow direction, satisfying formula (1):

[0015] The formula for the Mach angle μ is:

[0016] Formula (1)

[0017] Where M is the Mach number, which is the ratio of the airflow speed to the local speed of sound;

[0018] Facing the flow direction, the characteristic line on the left is called the left-extending characteristic line, and the characteristic line on the right is called the right-extending characteristic line; the Prandtl-Meyer angle is a function of the Mach angle μ and satisfies formula (2):

[0019] Formula (2)

[0020] Where, is the specific heat ratio of air, at room temperature =1.4.

[0021] Assume that there is a left-extending characteristic function ψ in the nozzle - (x) and the right-extended characteristic function ψ + (x), right-extended characteristic function ψ + (x) is the eigenvalue ψ on the characteristic line + The function of the relative x-coordinate is half the sum of the function v(x) of the Prandtl-Meyer angle v on the right characteristic line relative to the x-coordinate and the function θ(x) of the airflow angle θ relative to the x-coordinate, ψ + (x)=(ν(x)+θ(x)) / 2; left-stretched characteristic function ψ - (x) is the eigenvalue ψ on the characteristic line - The function of the relative x-coordinate is half the difference between the function v(x) of the Prandtl-Meyer angle v on the left characteristic line relative to the x-coordinate and the function θ(x) of the airflow angle θ relative to the x-coordinate, ψ - (x) = (ν(x) - θ(x)) / 2;

[0022] The following relationship is satisfied on the right extended characteristic line:

[0023] Formula (3)

[0024] Where, (i, j) represents the intersection of the i-th right-extending characteristic line and the j-th left-extending characteristic line, i=1,2,3..., j=1,2,3...;

[0025] The following relationship is satisfied on the left extended characteristic line:

[0026] Formula (4)

[0027] therefore,

[0028] Formula (5)

[0029] Formula (6)

[0030] The aerodynamic parameters in the inviscid surface area of ​​the nozzle satisfy the following equations:

[0031] Compatibility equation:

[0032] Formula (7)

[0033] Right now Formula (8)

[0034] In addition to the above formulas (7) and (8), the following boundary conditions are met at the throat initial right extension characteristic line, nozzle axis, initial expansion zone Q1 profile, turning point, characteristic point, semi-absent zone Q2 profile, complete absent zone Q3 profile, and nozzle exit:

[0035] Step 2.1, right extension characteristic line of transonic solution at the throat

[0036] The velocity of the characteristic line at the initial right extension from the throat is the analytical transonic solution, which is the HKL solution determined by the method of Hall, Kliegel, and Levine.

[0037] Hall R -1 The series expansion of the power gives the exact solution for the flow in this region. R is the radius of curvature of the throat expressed in terms of the throat half-height. For the initial expansion section of the cubic curve, the expression for R is (9):

[0038] Formula (9)

[0039] In the formula is the x-coordinate of the inflection point A of the inviscid surface, is the inclination angle of the inflection point A of the inviscid surface, It is the half height of the throat of the non-viscous profile;

[0040] Kliegel and Levine replaced R with S, satisfying the following relationship:

[0041] R -1 =S -1 +S -2 +S -3 +... Formula (10)

[0042] Where S = R + 1. Similarly, the series expansion of S also gives the exact transonic solution in the throat region, resulting in a velocity curve with a known Mach number, coordinates, and flow angle. This curve serves as the starting point of the characteristic line or the inlet boundary condition of the characteristic grid.

[0043] The calculation steps of HKL transonic solution are as follows:

[0044] Step 2.11, longitudinal velocity distribution u:

[0045] Formula (11)

[0046] Where γ=1.4, x is the distance in the x direction relative to the throat point of the inviscid surface, and y is the distance in the y direction relative to the throat point of the inviscid surface;

[0047] Step 2.12, transverse velocity distribution v:

[0048] Formula (12)

[0049] Where γ=1.4, x is the distance in the x direction relative to the throat point of the inviscid surface, and y is the distance in the y direction relative to the throat point of the inviscid surface;

[0050] Step 2.2, boundary conditions of the initial expansion zone Q1;

[0051] The airflow angle on the nozzle axis is zero, and the left extension characteristic function value is the same as the right extension characteristic function value; the surface design of the initial expansion area Q1 adopts a cubic polynomial or a quartic polynomial;

[0052] Formula (13)

[0053] Where h t is the half height of the throat of the non-viscous profile, x a is the horizontal coordinate of the turning point A, θ a is the turning angle, that is, the inclination angle of the profile at the turning point A to the nozzle axis;

[0054] Assuming that the flow at the turning point A is radial spring flow, x a 、y a According to the one-dimensional pipe flow conservation relationship, the expression is as follows:

[0055] Formula (14)

[0056] Step 2.3, boundary conditions at turning point A;

[0057] The curvature at the turning point A is zero, so the derivative of the airflow angle is zero, and the derivatives of the left-extending characteristic function and the right-extending characteristic function with respect to the horizontal coordinate of the profile are both zero. a ) / dx=0, from this we can know:

[0058] Formula (15)

[0059] Step 2.4, boundary conditions on the half-effective wave region and characteristic point C;

[0060] The right-extending characteristic function on the profile in the semi-absorptive zone Q2 is a quadratic polynomial of the profile's horizontal coordinate, ψ + (x)=ax2 +bx+c, a, b, c and X c There are 4 unknown quantities in total, and the turning point A is known to have a value of + (X a ) and dψ + (X a ) / dx, dψ on the feature point C + (X c ) / dx=0 and ψ + (X c )=ν out / 2, there are 4 known conditions in total, and the solution is ψ + (x) and the abscissa Xc of the feature point C;

[0061] The right extension characteristic function value of the characteristic point C is a constant, that is, half of the Prandtl-Meyer angle of the nozzle exit Mach number, ψ + (x)=ν out / 2=const, the derivative of the airflow angle at the characteristic point C with respect to the horizontal coordinate is equal to the negative value of the derivative of the left-extended characteristic function with respect to the horizontal coordinate;

[0062] Formula (16)

[0063] Step 2.5, boundary conditions of the completely wave-breaking zone Q3;

[0064] The left-extending characteristic function value on the Q3 profile in the complete wave-breaking zone is equal to the left-extending characteristic value on the right-extending characteristic line at the characteristic point C;

[0065] The left extension characteristic function value ψ at the nozzle exit point - (X out ) is the Prandtl-Meyer angle ν at the tube exit Mach number out Half of ψ - (X out )=ν out / 2=const, so we can see

[0066] Formula (17).

[0067] Step 3: Generate a curvature-continuous inviscid nozzle profile based on the feature grid method;

[0068] Based on the boundary conditions of the curvature-continuous nozzle inviscid surface created in step 2, the nozzle inviscid surface is solved by the characteristic grid method. After the boundary layer displacement thickness correction is performed on the nozzle inviscid surface, the nozzle viscous surface is obtained.

[0069] Step 3.1, calculation of the flow field parameters of the initial expansion section and turning point A. In the initial expansion section, a series of left-extending characteristic lines are issued from the inlet boundary condition. The inlet boundary condition is the right-extending characteristic line of the transonic solution at the throat. These characteristic lines are reflected in the form of right-extending characteristic lines after hitting the initial expansion section profile curve, and are reflected in the form of left-extending characteristic lines after hitting the nozzle centerline E1. This process is repeated until the left-extending characteristic line reaches the turning point A. Formulas (1) to (8) are used to solve the flow field parameters in this area. The flow field parameters at the turning point A need to be given by interpolation calculation, and the turning point A is obtained by linear regression. value;

[0070] Step 3.2, calculate the flow field parameters of the partial wave-breaking area and the characteristic point C. The known condition is that the turning point A and , boundary conditions of feature point C: and , a total of 4 known conditions, assuming a polynomial function ,a,b,c and There are 4 unknown quantities in total, and the solution is The expression and the horizontal coordinate of the characteristic point C Then, from some nodes on the right-extending characteristic line where the turning point A is located, a left-extending characteristic line is sent to the profile of the semi-wave-breaking region Q2. The flow field parameters other than the vertical coordinate y of the profile are solved using formulas (1) to (8). The solution of the vertical coordinate y can be obtained by linear interpolation, as shown in the following formula:

[0071] Formula (18)

[0072] The flow field parameters inside the semi-wave-breaking region Q2 are still solved using formulas (1) to (8);

[0073] Step 3.3, calculation of flow field parameters in the complete wave-breaking zone Q3, the left-extending characteristic lines from all nodes on the right-extending characteristic line before the characteristic point C are projected onto the profile, and the right-extending characteristic line is no longer reflected, and the boundary conditions are met on the profile. and , using formulas (1) to (8) and (17), calculate all flow field parameters on the surface.

[0074] Step 4, calculating the curvature-continuous boundary layer displacement thickness distribution;

[0075] In the process of solving the inviscid surface, the Mach number distribution on the surface is obtained, and the boundary layer displacement thickness at the throat is estimated using an empirical formula. On this basis, the boundary layer displacement thickness at the turning point of the nozzle inviscid surface and the nozzle exit is calculated using the Tucker method. The boundary layer displacement thickness distribution is represented by a fitting curve composed of a cubic polynomial curve and a straight line. The boundary layer displacement thickness is converted into a two-dimensional boundary layer displacement thickness according to the cross-sectional dimensions.

[0076] Step 5, adaptively generating a nozzle expansion portion profile with continuous curvature;

[0077] Assuming the nozzle inviscid surface outlet height, the inviscid surface throat height is calculated based on one-dimensional pipe flow theory. This inviscid throat height is used as the initial value to calculate the nozzle inviscid surface and boundary layer displacement thickness distribution. The calculated value of the nozzle outlet height is obtained by superimposing the inviscid surface and boundary layer displacement thickness:

[0078] Formula (19).

[0079] Where, is the nozzle non-stick surface outlet height, is the displacement thickness of the boundary layer at the nozzle inviscid surface outlet, is the inclination angle of the non-stick surface at the nozzle outlet;

[0080] Since there is a deviation between the calculated value of the nozzle exit height and the target nozzle exit height, the nozzle exit target height and the boundary layer displacement thickness are used to inversely solve the exit height of the inviscid surface. The inviscid surface throat height and the nozzle profile are recalculated based on this height, and the calculated value of the nozzle exit height is obtained again. The above process is iterated until the calculated value of the nozzle exit height is consistent with the target nozzle exit height.

[0081] Step 6: Generate a nozzle contraction profile with continuous curvature at the throat.

[0082] Preferably, step 6 includes:

[0083] Based on step 5, after determining the height and curvature of the nozzle inlet, according to the above conditions, an n-order polynomial curve with continuous profile curvature and monotonic slope is used to obtain a subsonic profile curve that meets the above boundary conditions; the n-order polynomial curve is as follows:

[0084] Formula (20)

[0085] Where h t is the half-height of the throat, h in is the nozzle inlet half height, l c is the axial length of the subsonic profile, a, b, c are unknown coefficients, and their values ​​are different at different design Mach numbers. n is 4 or 5.

[0086] The present invention has the following beneficial effects:

[0087] 1. The present invention adopts a contraction curve that ensures the continuity of the profile curvature, a non-viscous profile boundary condition, and a boundary layer displacement thickness distribution function, which is suitable for the design of flexible-wall nozzles;

[0088] 2. The Laval nozzle design method with continuous curvature of the present invention has the advantages of a wide Mach number range, excellent nozzle flow field uniformity, and adjustable nozzle proportions and dimensions;

[0089] 3. The present invention is easy to implement, has high nozzle profile production efficiency, can generate a large number of profiles in a short time, and has broad development prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0090] Figure 1 It is a schematic diagram of the nozzle area division of the present invention;

[0091] Figure 2 This is a working principle diagram of the non-stick nozzle profile design of the present invention;

[0092] Figure 3 is a schematic diagram of characteristic lines at a certain point in the nozzle flow field of the present invention; DETAILED DESCRIPTION

[0093] To make the objectives, technical solutions, and advantages of the present invention more clearly apparent, the present invention is described below using specific embodiments shown in the accompanying drawings. However, it should be understood that these descriptions are merely illustrative and are not intended to limit the scope of the present invention. In addition, in the following description, descriptions of well-known structures and technologies are omitted to avoid unnecessary confusion of the concepts of the present invention.

[0094] The connections referred to in this invention are categorized as fixed and removable. Fixed connections (i.e., non-removable connections) include, but are not limited to, conventional fixed connection methods such as hemming, rivet connections, adhesive connections, and welding. Removable connections include, but are not limited to, conventional removable methods such as threaded connections, snap connections, pin connections, and hinge connections. When a specific connection method is not explicitly specified, it is assumed that at least one existing connection method can achieve the desired function. Persons skilled in the art may select the connection as needed. For example, welding may be selected for fixed connections, and hinges may be selected for removable connections.

[0095] Specific implementation method 1: Combination Figure 1-Figure 3This embodiment describes a method for designing a Laval nozzle with continuous curvature. The Laval nozzle profile includes a nozzle convergence surface and a nozzle divergence surface, wherein the divergence surface is a composite of the nozzle's inviscid surface and a viscous boundary layer. This method ensures that the nozzle convergence surface, the inviscid surface of the divergence portion, and the boundary layer displacement thickness distribution all maintain curvature continuity.

[0096] This embodiment provides boundary conditions to ensure the curvature continuity of the nozzle's inviscid profile, and designs the inviscid profile of the nozzle's diverging section using the characteristic grid method. The boundary layer displacement thickness at the nozzle throat and nozzle outlet is determined using empirical formulas and the Tucker method. A fitting function combining a cubic curve and a straight line is used to express the boundary layer displacement thickness distribution along the nozzle throat to the nozzle outlet. The boundary layer displacement thickness is then converted into a two-dimensional boundary layer displacement thickness based on the cross-sectional dimensions. The nozzle's inviscid profile and the corrected boundary layer displacement thickness are superimposed, and the viscous profile of the nozzle's diverging section is adaptively generated by controlling the nozzle outlet height. An nth-order polynomial function is used to design the nozzle's convergent section profile with continuous curvature at the throat, as follows:

[0097] Step 1: Given the design Mach number and nozzle geometry parameters;

[0098] The design Mach number range is 1.15 to 5.0, and nozzle design can be performed within this range. Furthermore, nozzle design requires a target nozzle exit height and the distance between the nozzle parallel walls (i.e., nozzle width).

[0099] Step 2: Create the boundary conditions of the curvature-continuous nozzle inviscid surface;

[0100] The inviscid surface of the nozzle is divided into three regions by four nodes, namely the throat, turning point A, characteristic point C and nozzle exit point;

[0101] The throat is the position of the profile closest to the axis, the turning point A is the point on the profile curve where the curvature is zero, and the characteristic point C is the point where the derivative of the right-extending characteristic function is zero;

[0102] The area between the sonic line k1 emitted from the throat and the right-extending characteristic line of the turning point is the initial expansion area Q1. The area between the right-extending characteristic line of the turning point and the right-extending characteristic line of the characteristic point C is the semi-absentation area Q2. The area between the right-extending characteristic line of the characteristic point C and the left-extending characteristic line of the nozzle exit is the complete absentation area Q3.

[0103] The angle between the flow direction and the axis of the nozzle flow field is defined as the airflow angle θ. The Mach angle μ is the angle between the boundary line of the local disturbance propagation and the incoming flow when the Mach number M ≥ 1. It is also the angle between the tangent line of the characteristic line and the flow direction, satisfying formula (1):

[0104] The formula for the Mach angle μ is:

[0105] Formula (1)

[0106] Where M is the Mach number, which is the ratio of the airflow speed to the local speed of sound;

[0107] Facing the flow direction, the characteristic line on the left is called the left-extending characteristic line, and the characteristic line on the right is called the right-extending characteristic line; the Prandtl-Meyer angle v is a function of the Mach angle μ and satisfies formula (2):

[0108] Formula (2)

[0109] Where, is the specific heat ratio of air, at room temperature =1.4.

[0110] Assume that there is a left-extending characteristic function ψ in the nozzle - (x) and the right-extended characteristic function ψ + (x), right-extended characteristic function ψ + (x) is the eigenvalue ψ on the characteristic line + The function of the relative x-coordinate is half the sum of the function v(x) of the Prandtl-Meyer angle v on the right characteristic line relative to the x-coordinate and the function θ(x) of the airflow angle θ relative to the x-coordinate, ψ + (x)=(ν(x)+θ(x)) / 2; left-stretched characteristic function ψ - (x) is the eigenvalue ψ on the characteristic line - The function of the relative x-coordinate is half the difference between the function v(x) of the Prandtl-Meyer angle v on the left characteristic line relative to the x-coordinate and the function θ(x) of the airflow angle θ relative to the x-coordinate, ψ - (x) = (ν(x) - θ(x)) / 2;

[0111] The following relationship is satisfied on the right extended characteristic line:

[0112] Formula (3)

[0113] Where, (i, j) represents the intersection of the i-th right-extending characteristic line and the j-th left-extending characteristic line, i=1,2,3..., j=1,2,3...;

[0114] The following relationship is satisfied on the left extended characteristic line:

[0115] Formula (4)

[0116] therefore,

[0117] Formula (5)

[0118] Formula (6)

[0119] The aerodynamic parameters in the inviscid surface area of ​​the nozzle satisfy the following equations:

[0120] Compatibility equation:

[0121] Formula (7)

[0122] Right now Formula (8)

[0123] In addition to the above formulas (7) and (8), the following boundary conditions are met at the throat initial right extension characteristic line, nozzle axis, initial expansion zone Q1 profile, turning point A, characteristic point C, semi-absorptive zone Q2 profile, full-absorptive zone profile, and nozzle outlet:

[0124] Step 2.1, right-extend the characteristic line of the transonic solution at the throat;

[0125] The velocity of the characteristic line at the initial right extension from the throat is the analytical transonic solution, which is the HKL solution determined by the method of Hall, Kliegel, and Levine.

[0126] Hall R -1 The series expansion of the power gives the exact solution for the flow in this region. R is the radius of curvature of the throat expressed in terms of the throat half-height. For the initial expansion section of the cubic curve, the expression for R is (9):

[0127] Formula (9)

[0128] In the formula is the x-coordinate of the inflection point A of the inviscid surface, is the inclination angle of the inflection point A of the inviscid surface, It is the half height of the throat of the non-viscous profile;

[0129] Kliegel and Levine replaced R with S, satisfying the following relationship:

[0130] R -1 =S -1 +S -2 +S -3 +... Formula (10)

[0131] Where S = R + 1. Similarly, the series expansion of S also gives the exact transonic solution in the throat region, resulting in a velocity curve with a known Mach number, coordinates, and flow angle. This curve serves as the starting point of the characteristic line or the inlet boundary condition of the characteristic grid.

[0132] The calculation steps of HKL transonic solution are as follows:

[0133] Step 2.11, longitudinal velocity distribution u:

[0134] Formula (11)

[0135] Where γ=1.4, x is the distance in the x direction relative to the throat point of the inviscid surface, and y is the distance in the y direction relative to the throat point of the inviscid surface;

[0136] Step 2.12, transverse velocity distribution v:

[0137] Formula (12)

[0138] Where γ=1.4, x is the distance in the x direction relative to the throat point of the inviscid surface, and y is the distance in the y direction relative to the throat point of the inviscid surface;

[0139] Step 2.2, boundary conditions of the initial expansion zone Q1;

[0140] The airflow angle on the nozzle axis is zero, and the left extension characteristic function value is the same as the right extension characteristic function value; the surface design of the initial expansion area Q1 adopts a cubic polynomial or a quartic polynomial;

[0141] Formula (13)

[0142] Where h t is the half height of the throat of the non-viscous profile, x a is the horizontal coordinate of the turning point A, θ a is the turning angle, that is, the inclination angle of the profile at the turning point A to the nozzle axis;

[0143] Assuming that the flow at the turning point A is radial spring flow, x a 、y a According to the one-dimensional pipe flow conservation relationship, the expression is as follows:

[0144] Formula (14)

[0145] Step 2.3, boundary conditions at turning point A;

[0146] The curvature at the turning point A is zero, so the derivative of the airflow angle is zero, and the derivatives of the left-extending characteristic function and the right-extending characteristic function with respect to the horizontal coordinate of the profile are both zero. a ) / dx=0, from this we can know:

[0147] Formula (15)

[0148] Step 2.4, boundary conditions on the half-effective wave region and characteristic point C;

[0149] The right-extending characteristic function on the profile in the semi-absorptive zone Q2 is a quadratic polynomial of the profile's horizontal coordinate, ψ + (x)=ax 2 +bx+c, a, b, c and X c There are 4 unknown quantities in total, and the ψ of the turning point A is known + (X a ) and dψ + (X a ) / dx, dψ on the feature point C + (X c ) / dx=0 and ψ + (X c )=ν out / 2, there are 4 known conditions in total, and the solution is ψ + (x) and the abscissa Xc of the feature point C;

[0150] The right extension characteristic function value of the characteristic point C is a constant, that is, half of the Prandtl-Meyer angle of the nozzle exit Mach number, ψ + (x)=ν out / 2=const, the derivative of the airflow angle at the characteristic point C with respect to the horizontal coordinate is equal to the negative value of the derivative of the left-extended characteristic function with respect to the horizontal coordinate;

[0151] Formula (16)

[0152] Step 2.5, boundary conditions of the completely wave-breaking zone Q3;

[0153] The left-extending characteristic function value on the Q3 profile in the complete wave-breaking zone is equal to the left-extending characteristic value on the right-extending characteristic line at the characteristic point C;

[0154] The left extension characteristic function value ψ at the nozzle exit point - (X out ) is the Prandtl-Meyer angle ν at the tube exit Mach number out Half of ψ - (X out )=ν out / 2=const, so we can see

[0155] Formula (17).

[0156] Step 3: Generate a curvature-continuous inviscid nozzle profile based on the feature grid method;

[0157] Based on the boundary conditions of the curvature-continuous nozzle inviscid surface created in step 2, the nozzle inviscid surface is solved by the characteristic grid method. After the boundary layer displacement thickness correction is performed on the nozzle inviscid surface, the nozzle viscous surface is obtained.

[0158] Step 3.1, calculation of the flow field parameters of the initial expansion section and turning point A. In the initial expansion section, a series of left-extending characteristic lines are issued from the inlet boundary condition. The inlet boundary condition is the right-extending characteristic line of the transonic solution at the throat. These characteristic lines are reflected in the form of right-extending characteristic lines after hitting the initial expansion section profile curve, and are reflected in the form of left-extending characteristic lines after hitting the nozzle centerline E1. This process is repeated until the left-extending characteristic line reaches the turning point A. Formulas (1) to (8) are used to solve the flow field parameters in this area. The flow field parameters at the turning point A need to be given by interpolation calculation, and the turning point A is obtained by linear regression. value;

[0159] Step 3.2, calculate the flow field parameters of the partial wave-breaking area and the characteristic point C. The known condition is that the turning point A and , boundary conditions of feature point C: and , a total of 4 known conditions, assuming a polynomial function ,a,b,c and There are 4 unknown quantities in total, and the solution is The expression and the horizontal coordinate of the characteristic point C Then, from some nodes on the right-extending characteristic line where the turning point A is located, a left-extending characteristic line is sent to the profile of the semi-wave-breaking region Q2. The flow field parameters other than the vertical coordinate y of the profile are solved using formulas (1) to (8). The solution of the vertical coordinate y can be obtained by linear interpolation, as shown in the following formula:

[0160] Formula (18)

[0161] The flow field parameters inside the semi-wave-breaking region Q2 are still solved using formulas (1) to (8);

[0162] Step 3.3, calculation of flow field parameters in the complete wave-breaking zone Q3, the left-extending characteristic lines from all nodes on the right-extending characteristic line before the characteristic point C are projected onto the profile, and the right-extending characteristic line is no longer reflected, and the boundary conditions are met on the profile. and , using formulas (1) to (8) and (17), calculate all flow field parameters on the surface.

[0163] Step 4, calculating the curvature-continuous boundary layer displacement thickness distribution;

[0164] First, calculate the boundary layer displacement thickness at the throat, then calculate the boundary layer displacement thickness at the nozzle turning point and nozzle exit. The specific method is as follows:

[0165] Step 4.1, calculate the boundary layer displacement thickness at the throat

[0166] The boundary layer displacement thickness at the throat is calculated using the following empirical formula.

[0167] Formula (19.2)

[0168] Where h t is the half-height of the throat of the inviscid profile, T0 is the total temperature, r t is the radius of curvature at the throat, ν am is based on the reference temperature T am The kinematic viscosity coefficient.

[0169] Step 4.2, calculation method of boundary layer displacement thickness along the nozzle

[0170] The boundary layer displacement thickness along the nozzle is calculated by Tucker method.

[0171] The principle of Tucker method for calculating boundary layer displacement thickness is as follows:

[0172] The momentum integral equation for a shock-free, steady, compressible viscous flow is as follows:

[0173] Formula (19.3)

[0174] Converted into the following form:

[0175] Formula (19.4)

[0176] Where, , f is the ratio of the boundary layer momentum thickness to the boundary layer thickness , g is the ratio of boundary layer displacement thickness to boundary layer thickness , H is the ratio of g to f .

[0177] Assume that the velocity pattern in the boundary layer is exponentially distributed as follows:

[0178] Formula (19.5)

[0179] Then use the boundary layer thickness , boundary layer displacement thickness , boundary layer momentum thickness Substituting the definition of into the expressions of f and g, we get

[0180] Formula (19.6)

[0181] Formula (19.7)

[0182] For a wide range of Reynolds numbers, the velocity parameter N=7 is selected as the standard value. The relationship given by Tucker is

[0183] Formula (19.8)

[0184] Can be calculated according to the following formula

[0185] Formula (19.9)

[0186] Friction coefficient The expression is as follows

[0187] Formula (19.10)

[0188] In the formula ,therefore

[0189] Formula (19.11)

[0190] Substituting the expressions of parameters g, f, and N into the momentum integral equation, we get the new expression of the momentum equation as follows:

[0191] Formula (19.12)

[0192] in,

[0193] Formula (19.13)

[0194] Formula (19.14)

[0195] Formula (19.15)

[0196] In order to take into account the correction of wave system and boundary layer interference, the displacement boundary layer thickness is used After correction, for the pressure gradient, the integral solution of the momentum equation on the integral interval (a, b) is as follows:

[0197] Formula (19.16)

[0198] Where,

[0199] Formula (19.18)

[0200] Formula (19.19)

[0201] Formula (19.20)

[0202] Given the coordinates Xa, Mach number Ma, and boundary layer displacement thickness of point a, And the coordinates Xb and Mach number Mb of point b, calculate the boundary layer displacement thickness at point b The above formula is used to calculate the boundary layer displacement thickness at each point along the nozzle.

[0203] The slope and curvature of the boundary layer thickness curve are continuous, and the boundary layer displacement thickness from the throat to the turning point is approximately expressed by a cubic polynomial:

[0204] Formula (19.21)

[0205] In the formula is the horizontal coordinate of the turning point of the inviscid surface, is the boundary layer displacement thickness at the turning point A calculated by the Tucker method.

[0206] The boundary layer displacement thickness from the turning point to the nozzle exit basically shows a linear growth law. The boundary layer displacement thickness from the turning point to the nozzle exit is expressed by the linear relationship:

[0207] Formula (19.22)

[0208] is the boundary layer displacement thickness at the nozzle exit calculated by the Tucker method.

[0209] The displacement thickness of the boundary layer parallel to the wall is converted to the profile wall using the following formula.

[0210] Formula (19.23)

[0211] Where w is half the distance between the parallel walls and Y(x) is the half height of the nozzle cross section.

[0212] Step 5, adaptively generating a nozzle expansion portion profile with continuous curvature;

[0213] Assuming the nozzle has no sticky surface outlet height , is the target value of the nozzle outlet half height. The inviscid profile throat height is calculated based on the one-dimensional pipe flow theory. , as follows:

[0214] Formula (19.24.)

[0215] Where specific heat ratio .

[0216] Using this inviscid throat height as the initial value, the first round of nozzle inviscid profile and boundary layer displacement thickness distribution is calculated according to steps 3 and 4. The nozzle inviscid profile and boundary layer displacement thickness are superimposed according to the following formula to obtain the coordinates (X, Y) of the nozzle profile along the path:

[0217] Formula (19.25)

[0218] Where x and y are the coordinates of the non-bonded surface, is the inclination angle of the non-stick surface. From this, we can know that the calculated value of the nozzle outlet height is as follows:

[0219] Formula (19)

[0220] Where, is the nozzle non-stick surface outlet height, is the displacement thickness of the boundary layer at the nozzle inviscid surface outlet, is the inclination angle of the non-stick surface at the nozzle outlet;

[0221] Since there is a deviation between the calculated nozzle exit height and the nozzle exit target height, it is necessary to use the nozzle exit target height and the boundary layer displacement thickness to inversely solve the inviscid surface exit height.

[0222] Formula (19.26)

[0223] The inviscid profile throat height and nozzle profile are recalculated based on this inviscid profile outlet height, and the calculated nozzle outlet height is obtained again. The above process is repeated until the calculated nozzle outlet height is consistent with the target nozzle outlet height.

[0224] Step 6: Generate a nozzle contraction profile with continuous curvature at the throat.

[0225] Based on step 5, after determining the height and curvature of the nozzle inlet, according to the above conditions, an n-order polynomial curve that satisfies the surface curvature continuity and monotonic slope is used to obtain a subsonic surface curve that meets the above boundary conditions. The n-order polynomial curve is as follows:

[0226] Formula (20)

[0227] Where h t is the half-height of the throat, h in is the nozzle inlet half height, l c is the axial length of the subsonic profile, a, b, c are unknown coefficients, and their values ​​are different at different design Mach numbers. n is 4 or 5.

[0228] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or combinations thereof.

[0229] Unless otherwise specifically stated, the relative arrangement of the parts and steps, the numerical expressions and the numerical values ​​set forth in these embodiments do not limit the scope of the present invention. At the same time, it should be understood that, for ease of description, the sizes of the various parts shown in the drawings are not drawn according to the actual proportional relationship. The techniques, methods and equipment known to those of ordinary skill in the relevant art may not be discussed in detail, but where appropriate, the techniques, methods and equipment should be considered as part of the authorization specification. In all examples shown and discussed here, any specific values ​​should be interpreted as being merely exemplary and not as limiting. Therefore, other examples of the exemplary embodiments may have different values. It should be noted that similar numbers and letters represent similar items in the following figures, and therefore, once an item is defined in one figure, it does not need to be further discussed in subsequent figures.

[0230] In the description of the present invention, it should be understood that the directions or positional relationships indicated by directional words such as "front, back, up, down, left, right", "horizontal, vertical, perpendicular, horizontal" and "top, bottom" are usually based on the directions or positional relationships shown in the accompanying drawings. They are only for the convenience of describing the present invention and simplifying the description. Unless otherwise specified, these directional words do not indicate or imply that the device or element referred to must have a specific direction or be constructed and operated in a specific direction. Therefore, they cannot be understood as limiting the scope of protection of the present invention; the directional words "inside and outside" refer to the inside and outside relative to the outline of each component itself.

[0231] For ease of description, spatially relative terms such as "above", "above", "on the upper surface of", "above", etc. may be used herein to describe the spatial positional relationship of a device or feature to other devices or features as shown in the figures. It should be understood that spatially relative terms are intended to include different orientations of the device in use or operation in addition to the orientation described in the figures. For example, if the device in the drawings is inverted, the device described as "above other devices or structures" or "above other devices or structures" will be positioned as "below other devices or structures" or "below other devices or structures". Thus, the exemplary term "above" can include both "above" and "below". The device can also be positioned in other different ways (rotated 90 degrees or in other orientations), and the spatially relative descriptions used here are interpreted accordingly.

[0232] It should be noted that the terms "first," "second," and the like in the specification and claims of this application and the accompanying drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or precedence. It should be understood that the terms used in this manner are interchangeable where appropriate, so that the embodiments of the present application described herein can be implemented in an order other than that illustrated or described herein.

[0233] It should be noted that in the above embodiments, as long as the technical solutions are not contradictory, they can be permuted and combined. Those skilled in the art can exhaust all possibilities based on the mathematical knowledge of permutations and combinations. Therefore, the present invention will no longer describe the technical solutions after permutations and combinations one by one, but it should be understood that the technical solutions after permutations and combinations have been disclosed by the present invention.

[0234] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A method for designing a Laval nozzle with continuous curvature, characterized in that: include: Step 1: Given the design Mach number and nozzle geometry parameters; Step 2: Create the boundary conditions of the curvature-continuous nozzle inviscid surface; Step 3: Generate a curvature-continuous inviscid nozzle profile based on the feature grid method; Step 4, calculating the curvature-continuous boundary layer displacement thickness distribution; Step 5, adaptively generating a nozzle expansion portion profile with continuous curvature; Step 6: Generate a nozzle contraction profile with continuous curvature at the throat; The step 2 includes: The inviscid surface of the nozzle is divided into three regions by four nodes, namely the throat, turning point A, characteristic point C and nozzle exit point; The throat is the position of the profile closest to the axis, the turning point A is the point on the profile curve where the curvature is zero, and the characteristic point C is the point where the derivative of the right-extending characteristic function is zero; The area between the sonic line k1 emitted from the throat and the right-extending characteristic line of the turning point is the initial expansion area Q1. The area between the right-extending characteristic line of the turning point and the right-extending characteristic line of the characteristic point C is the semi-absentation area Q2. The area between the right-extending characteristic line of the characteristic point C and the left-extending characteristic line of the nozzle exit is the complete absentation area Q3. The initial right extension characteristic line of the throat satisfies the following boundary conditions: Step 2.1, right-extend the characteristic line of the transonic solution at the throat; The velocity of the characteristic line at the initial right extension from the throat is the analytical transonic solution, which is the HKL solution determined by the method of Hall, Kliegel, and Levine. Hall R -1 The series expansion of the power gives the exact solution for the flow in this region. R is the radius of curvature of the throat expressed in terms of the throat half-height. For the initial expansion section of the cubic curve, the expression for R is (9): Formula (9) In the formula is the x-coordinate of the inflection point A of the inviscid surface, is the inclination angle of the inflection point A of the inviscid surface, It is the half height of the throat of the non-viscous profile; Kliegel and Levine replaced R with S, satisfying the following relationship: R -1 =S -1 +S -2 +S -3 +... Formula (10) Where S = R + 1. Similarly, the series expansion of S also gives an exact solution for the transonic speed in the throat region, resulting in a velocity curve with a known Mach number, coordinates, and flow angle. This curve serves as the starting point of the characteristic line or the inlet boundary condition of the characteristic grid.

2. The method for designing a Laval nozzle with continuous curvature according to claim 1, characterized in that: The step 1 comprises: The design Mach number range is 1.15~5.

0. The Mach number within this range is selected for nozzle design. In addition, the nozzle design requires a given nozzle outlet target height and the distance between the parallel walls of the nozzle, that is, the nozzle width.

3. The method for designing a Laval nozzle with continuous curvature according to claim 1, characterized in that: The angle between the flow direction and the axis of the nozzle flow field is defined as the airflow angle θ. The Mach angle μ is the angle between the boundary line of the local disturbance propagation and the incoming flow when the Mach number M ≥ 1. It is also the angle between the tangent line of the characteristic line and the flow direction, satisfying formula (1): The formula for the Mach angle μ is: Formula (1) Where M is the Mach number, which is the ratio of the airflow speed to the local speed of sound; Facing the flow direction, the characteristic line on the left is called the left-extending characteristic line, and the characteristic line on the right is called the right-extending characteristic line; the Prandtl-Meyer angle v is a function of the Mach angle μ and satisfies formula (2): Formula (2) Where, is the specific heat ratio of air, at room temperature =1.4; Assume that there is a left-extending characteristic function ψ in the nozzle - (x) and the right-extended characteristic function ψ + (x), right-extended characteristic function ψ + (x) is the eigenvalue ψ on the characteristic line + The function of the relative x-coordinate is half the sum of the function v(x) of the Prandtl-Meyer angle v on the right characteristic line relative to the x-coordinate and the function θ(x) of the airflow angle θ relative to the x-coordinate, ψ + (x)=(ν(x)+θ(x)) / 2; left-stretched characteristic function ψ - (x) is the eigenvalue ψ on the characteristic line - The function of the relative x-coordinate is half the difference between the function v(x) of the Prandtl-Meyer angle v on the left characteristic line relative to the x-coordinate and the function θ(x) of the airflow angle θ relative to the x-coordinate, ψ - (x) = (ν(x) - θ(x)) / 2; The following relationship is satisfied on the right extended characteristic line: Formula (3) Where, (i, j) represents the intersection of the i-th right-extending characteristic line and the j-th left-extending characteristic line, i=1,2,3..., j=1,2,3...; The following relationship is satisfied on the left extended characteristic line: Formula (4) therefore, Formula (5) Formula (6) The aerodynamic parameters in the inviscid surface area of ​​the nozzle satisfy the following equations: Compatibility equation: Formula (7) Right now Formula (8) In addition to the above formulas (7) and (8), the following boundary conditions are met at the nozzle axis, the initial expansion zone Q1 surface, the turning point A, the characteristic point C, the semi-absorptive zone Q2 surface, the full-absorptive zone surface, and the nozzle outlet: The calculation steps of HKL transonic solution are as follows: Step 2.11, longitudinal velocity distribution u: Official (11) Where γ=1.4, x is the distance in the x direction relative to the throat point of the inviscid surface, and y is the distance in the y direction relative to the throat point of the inviscid surface; Step 2.12, transverse velocity distribution v: Formula (12) Where γ=1.4, x is the distance in the x direction relative to the throat point of the inviscid surface, and y is the distance in the y direction relative to the throat point of the inviscid surface; Step 2.2, boundary conditions of the initial expansion zone Q1; The airflow angle on the nozzle axis is zero, and the left extension characteristic function value is the same as the right extension characteristic function value; the surface design of the initial expansion area Q1 adopts a cubic polynomial or a quartic polynomial; Official (13) Where h t is the half height of the throat of the non-viscous profile, x a is the horizontal coordinate of the turning point A, θ a is the turning angle, that is, the inclination angle of the profile at the turning point A to the nozzle axis; Assuming that the flow at the turning point A is radial spring flow, x a 、y a According to the one-dimensional pipe flow conservation relationship, the expression is as follows: Official (14) Step 2.3, boundary conditions at turning point A; The curvature at the turning point A is zero, so the derivative of the airflow angle is zero, and the derivatives of the left-extending characteristic function and the right-extending characteristic function with respect to the horizontal coordinate of the profile are both zero. a ) / dx=0, from this we can know: Official (15) Step 2.4, boundary conditions on the half-effective wave region and characteristic point C; The right-extending characteristic function on the profile in the semi-absorptive zone Q2 is a quadratic polynomial of the profile's horizontal coordinate, ψ + (x)=ax 2 +bx+c, a, b, c and X c There are 4 unknown quantities in total, and the turning point A is known to have a value of + (X a ) and dψ + (X a ) / dx, dψ on the feature point C + (X c ) / dx=0 and ψ + (X c )=ν out / 2, there are 4 known conditions in total, and the solution is ψ + (x) and the abscissa Xc of the feature point C; The right extension characteristic function value of the characteristic point C is a constant, that is, half of the Prandtl-Meyer angle of the nozzle exit Mach number, ψ + (x)=ν out / 2=const, the derivative of the airflow angle with respect to the horizontal coordinate at the characteristic point C is equal to the negative value of the derivative of the left-extended characteristic function with respect to the horizontal coordinate; Official (16) Step 2.5, boundary conditions of the completely wave-breaking zone Q3; The left-extending characteristic function value on the Q3 profile in the complete wave-breaking zone is equal to the left-extending characteristic value on the right-extending characteristic line at the characteristic point C; The left extension characteristic function value ψ at the nozzle exit point - (X out ) is the Prandtl-Meyer angle ν at the tube exit Mach number out Half of ψ - (X out )=ν out / 2=const, so we can see Official (17).

4. The method for designing a Laval nozzle with continuous curvature according to claim 3, characterized in that: The step 3 includes: Based on the boundary conditions of the curvature-continuous nozzle inviscid surface created in step 2, the nozzle inviscid surface is solved by the characteristic grid method. After the boundary layer displacement thickness correction is performed on the nozzle inviscid surface, the nozzle viscous surface is obtained. Step 3.1, calculation of the flow field parameters of the initial expansion section and turning point A. In the initial expansion section, a series of left-extending characteristic lines are issued from the inlet boundary condition. The inlet boundary condition is the right-extending characteristic line of the transonic solution at the throat. These characteristic lines are reflected in the form of right-extending characteristic lines after hitting the initial expansion section profile curve, and are reflected in the form of left-extending characteristic lines after hitting the nozzle centerline E1. This process is repeated until the left-extending characteristic line reaches the turning point A. Formulas (1) to (8) are used to solve the flow field parameters in this area. The flow field parameters at the turning point A need to be given by interpolation calculation, and the turning point A is obtained by linear regression. value; Step 3.2, calculate the flow field parameters of the partial wave-breaking area and the characteristic point C. The known condition is that the turning point A and , boundary conditions of feature point C: and , a total of 4 known conditions, assuming a polynomial function ,a,b,c and There are 4 unknown quantities in total, and the solution is The expression and the horizontal coordinate of the characteristic point C Then, from some nodes on the right-extending characteristic line where the turning point A is located, a left-extending characteristic line is sent to the profile of the semi-wave-breaking region Q2. The flow field parameters other than the vertical coordinate y of the profile are solved using formulas (1) to (8). The solution of the vertical coordinate y can be obtained by linear interpolation, as shown in the following formula: Official (18) The flow field parameters inside the semi-wave-breaking region Q2 are still solved using formulas (1) to (8); Step 3.3, calculation of flow field parameters in the complete wave-breaking zone Q3, the left-extending characteristic lines from all nodes on the right-extending characteristic line before the characteristic point C are projected onto the profile, and the right-extending characteristic line is no longer reflected, and the boundary conditions are met on the profile. and , using formulas (1) to (8) and (17), calculate all flow field parameters on the surface.

5. The method for designing a Laval nozzle with continuous curvature according to claim 4, characterized in that: The step 4 comprises: In the process of solving the inviscid surface, the Mach number distribution on the surface is obtained, and the boundary layer displacement thickness at the throat is estimated using an empirical formula. On this basis, the boundary layer displacement thickness at the turning point A of the nozzle inviscid surface and the nozzle exit is calculated using the Tucker method. The boundary layer displacement thickness distribution is represented by a fitting curve composed of a cubic polynomial curve and a straight line. The boundary layer displacement thickness is converted into a two-dimensional boundary layer displacement thickness according to the cross-sectional dimensions.

6. The method for designing a Laval nozzle with continuous curvature according to claim 5, characterized in that: The step 5 comprises: Assuming the nozzle inviscid surface outlet height, the inviscid surface throat height is calculated based on one-dimensional pipe flow theory. This inviscid throat height is used as the initial value to calculate the nozzle inviscid surface and boundary layer displacement thickness distribution. The calculated value of the nozzle outlet height is obtained by superimposing the inviscid surface and boundary layer displacement thickness: Official (19) Where, is the nozzle non-stick surface outlet height, is the displacement thickness of the boundary layer at the nozzle inviscid surface outlet, is the inclination angle of the non-stick surface at the nozzle outlet; Since there is a deviation between the calculated value of the nozzle exit height and the target nozzle exit height, the nozzle exit target height and the boundary layer displacement thickness are used to inversely solve the exit height of the inviscid surface. The inviscid surface throat height and the nozzle profile are recalculated based on this height, and the calculated value of the nozzle exit height is obtained again. The above process is iterated until the calculated value of the nozzle exit height is consistent with the target nozzle exit height.

7. The method for designing a Laval nozzle with continuous curvature according to claim 6, characterized in that: The step 6 comprises: Based on step 5, after determining the height and curvature of the nozzle inlet, according to the above conditions, an n-order polynomial curve with continuous profile curvature and monotonic slope is used to obtain a subsonic profile curve that meets the above boundary conditions; the n-order polynomial curve is as follows: Official (20) Where h t is the half-height of the throat, h in is the nozzle inlet half height, l c is the axial length of the subsonic profile, a, b, c are unknown coefficients, and their values ​​are different at different design Mach numbers. n is 4 or 5.

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