Design method for large-size, wide-operating-condition, hypersonic, low-density contoured nozzle

Abstract

Disclosed is a design method for a large-size, wide-operating-condition, hypersonic, low-density contoured nozzle, relating to the field of low-density wind tunnel testing. During expansion of a low-density airflow in a nozzle, flow separation tends to occur between the airflow and the wall surface of the nozzle, and a thick boundary layer is formed midstream and downstream in the nozzle, suppressing airflow expansion and reducing the effective test area, resulting in a reduced effective test area and poor flow-field quality for conventional low-density nozzles. In the present invention, to address the difficulty of controlling low‑density hypersonic flow in the nozzle expansion section, and on the basis of different flow characteristics, a large-size, wide-operating-condition, low-density contoured nozzle can be changed into three different configurations, thus solving the problem of flow separation on the wall surface of the nozzle and effectively suppressing the growth of the boundary layer in the nozzle, while meeting wide-operating-condition requirements and reducing costs. The present invention significantly improves the flow-field quality of low-density contoured nozzles, expands the test area, and mitigates the problem of poor flow-field quality under off‑design conditions.

Description

A design method for a large-scale, wide-operating-mode hypersonic low-density profile nozzle

[0001] This application claims priority to the Chinese patent application filed with the China Patent Office on December 29, 2023, with application number 202311864491.X and invention name “A design method for a large-size, wide-operating-condition hypersonic low-density profile nozzle”, the entire contents of which are incorporated by reference into this application. Technical Field

[0002] The present invention belongs to the technical field of low-density wind tunnel engineering, and in particular relates to a design method for a large-size, wide-operating-condition hypersonic low-density profile nozzle. Background Art

[0003] When a hypersonic vehicle enters the atmosphere from space, at altitudes greater than 150 km, the air density reaches a sufficiently low value that only a few molecules collide with surfaces per unit time. When molecules are reflected from surfaces, they do not interact with subsequent molecules. At altitudes greater than 90 km, the no-slip boundary condition for viscous flow no longer holds, and the flow in the head region cannot be fully treated using the continuum assumption. Molecular kinematics methods must be employed to predict aerodynamic characteristics. Therefore, as a hypersonic vehicle enters the dense atmosphere from a thin atmosphere, the flow type undergoes a transition from free molecules, where individual molecules collide with surfaces, to a transitional form where slip plays a significant role, and finally to a continuum flow.

[0004] For a given problem, the Knudsen number is a criterion for determining the significance and extent of low-density effects. When the Knudsen number is less than 0.03, the flow is continuous; when the Knudsen number is greater than 0.03 and less than 0.1, it is in the transitional flow region; and when the Knudsen number is greater than 1, the effects of free molecular flow become prominent. Low-density effects are inherently unaffected by high Mach numbers. Simulating low-density effects on ground-based equipment requires a corresponding hypersonic low-density nozzle. However, profiled nozzles offer excellent flow field uniformity, but relevant technologies are currently lacking and urgently need to be developed.

[0005] Summary of the Invention

[0006] The technology of the present invention solves the problem: overcomes the shortcomings of the existing technology, provides a large-scale, wide-operating-condition hypersonic low-density profile nozzle design method, and provides a feasible idea for low-density nozzle design that has been verified by experiments.

[0007] In order to solve the above technical problems, the present invention discloses a design method for a large-scale, wide-operating-condition hypersonic low-density profile nozzle, comprising:

[0008] According to the Mach number Ma and the inviscid profile outlet diameter D of the nozzle to be designed, the throat diameter d of the nozzle to be designed is calculated.* ;

[0009] Based on the determined throat diameter d of the nozzle to be designed * , combined with the given semi-cone angle θ, an initial conical nozzle is designed; wherein the initial conical nozzle is composed of an expansion section and a contraction section smoothly connected; the contraction section of the initial conical nozzle adopts a shifted Witoszynski curve, a cubic curve, or a CQCQ curve;

[0010] Numerical simulation calculations are performed on the initial conical nozzle to determine the Knudsen number of the exit flow field of the initial conical nozzle.

[0011] When the Knudsen number of the outlet flow field is less than 0.03, the first strategy is used to reconstruct and optimize the initial conical nozzle profile to obtain the optimal nozzle profile.

[0012] When the Knudsen number of the outlet flow field is greater than 0.03 and less than 1, the second strategy is used to reconstruct and optimize the initial conical nozzle profile to obtain the optimal nozzle profile.

[0013] When the outlet flow field Knudsen number is greater than 1, the third strategy is used to reconstruct and optimize the initial conical nozzle profile to obtain the optimal nozzle profile.

[0014] In the above-mentioned large-scale wide-operating-condition hypersonic low-density profile nozzle design method, the throat diameter d of the nozzle to be designed is calculated based on the exit Mach number Ma and the inviscid profile exit diameter D of the nozzle to be designed. * ,include:

[0015] Determine the area A corresponding to the non-viscous profile outlet diameter D of the nozzle to be designed;

[0016] According to Ma and A, the throat area A of the nozzle to be designed is calculated * :

[0017] Where γ represents the specific heat ratio;

[0018] According to A * , calculate the throat diameter d of the nozzle to be designed * :

[0019] In the above-mentioned large-size, wide-operating-condition hypersonic low-density profile nozzle design method, 6°≤θ≤15°.

[0020] In the above-mentioned large-scale, wide-operating-mode hypersonic, low-density profile nozzle design method, when the exit flow field Knudsen number is less than 0.03, the first strategy is used to reconstruct and optimize the initial conical nozzle profile to obtain the optimal nozzle profile, including:

[0021] When the Knudsen number of the outlet flow field is less than 0.03, the initial conical nozzle profile is determined to be a continuous curve. The 7th to 9th degree Bézier curve is used to reconstruct the downstream area of ​​the nozzle throat along the outer streamline of the flow field. The throat point T is selected as the starting point of the Bézier curve, and the G1 point is selected as the end point of the Bézier curve. The slope upstream of the G1 point is calculated.

[0022] Based on the calculated slope upstream of point G1, draw a straight line to extend point G1 to point P1;

[0023] The wave-breaking area from point P1 to exit E1 is calculated using the analytical expression:

[0024] Among them, (x N1 ,y N1 ) represents a point on the P1E1 curve; r1 represents the source flow radius of point P1; θ P1 represents the airflow deflection angle at point P1; μ represents the Mach angle, θ1 represents the airflow deflection angle on the P1E1 curve;

[0025] Smoothly connect the TG1 curve, G1P1 curve and P1E1 curve to obtain the nozzle expansion section curve. After connecting the contraction section curve, the complete new nozzle profile is obtained.

[0026] Perform numerical simulation on the obtained complete new nozzle profile. If the Mach number deviation of the nozzle exit flow field determined by the numerical simulation does not meet the requirements, return to correct the Bézier curve, extend the distance of point G1, and iterate again until the obtained complete new nozzle profile meets the requirements.

[0027] In the aforementioned large-scale, wide-operating-mode hypersonic, low-density profile nozzle design method, when the exit flow field Knudsen number is greater than 0.03 and less than 1, the second strategy is used to reconstruct and optimize the initial conical nozzle profile to obtain the optimal nozzle profile, including:

[0028] When the Knudsen number of the outlet flow field is greater than 0.03 and less than 1, the nozzle profile is determined to be a discontinuous curve and the nozzle profile has two segments;

[0029] The starting point of the first curve is selected as the nozzle throat. The downstream area of ​​the nozzle throat is reconstructed along the outer streamline of the flow field using 7-9 degree Bézier curves. The throat point T is selected as the starting point of the Bézier curve, and the point G1 is selected as the end point of the Bézier curve.

[0030] Select point G2 as the starting point of the second curve segment. Point G2 satisfies the following conditions with point G1: point G2 is obtained by shifting point G1 downward by Δy1 along the y-axis, and the slope of point G2 is the same as that of point G1.

[0031] Calculate the slope upstream of point G1;

[0032] Based on the calculated slope upstream of point G1, draw a straight line to extend point G2 to point P2; the value of point P2 is determined by the source flow radius r2;

[0033] The wave-breaking zone from point P2 to exit E2 is calculated using the analytical expression:

[0034] Among them, (x N2 ,y N2 ) represents a point on the P2E2 curve; r2 represents the source flow radius of point P2; θ P2 represents the airflow deflection angle at point P2; θ2 represents the airflow deflection angle on the P2E2 curve;

[0035] Connect the contraction curve and TG1 curve, connect the G2P2 curve and P2E2 curve to obtain a complete new nozzle profile; among them, G1 and G2 are gap areas;

[0036] Perform numerical simulation on the obtained complete new nozzle profile. If the Mach number deviation of the nozzle exit flow field determined by the numerical simulation does not meet the requirements, return to the Bézier curve to correct it, extend the distance of point G1 or increase Δy1, and iterate again until the obtained complete new nozzle profile meets the requirements.

[0037] In the aforementioned large-scale, wide-operating-mode hypersonic, low-density profile nozzle design method, when the exit flow field Knudsen number is greater than 1, the third strategy is used to reconstruct and optimize the initial conical nozzle profile to obtain the optimal nozzle profile, including:

[0038] When the Knudsen number of the outlet flow field is greater than 1, the nozzle profile is determined to be a discontinuous curve, and the nozzle profile has three segments;

[0039] The starting point of the first curve is selected as the nozzle throat. The downstream area of ​​the nozzle throat is reconstructed along the outer streamline of the flow field using 7-9 degree Bézier curves. The throat point T is selected as the starting point of the Bézier curve, and the point G1 is selected as the end point of the Bézier curve.

[0040] Select point G2 as the starting point of the second curve segment, where point G2 satisfies the following conditions: point G1 is offset downward by Δy1 along the y-axis perpendicularly, and the slope of point G2 is the same as that of point G1.

[0041] Calculate the slope upstream of point G1;

[0042] Based on the calculated slope upstream of point G1, draw a straight line to extend point G2 to point P2; offset point P2 vertically downward along the y-axis by Δy2 to obtain point P3;

[0043] The wave-breaking zone from point P3 to exit E3 is calculated using the analytical expression:

[0044] Among them, (x N3 ,y N3 ) represents a point on the P3E3 curve; r3 represents the source flow radius of point P3; θ P3 represents the airflow deflection angle at point P3; θ3 represents the airflow deflection angle on the P3E3 curve;

[0045] Connect the contraction curve with the TG1 curve, the G2P2 curve, and the P3E3 curve to obtain a complete new nozzle profile; among them, G1 and G2 are gap areas, and P2 and P3 are gap areas;

[0046] Perform numerical simulation on the obtained complete new nozzle profile. If the Mach number deviation of the nozzle exit flow field determined by the numerical simulation does not meet the requirements, return to correct the Bézier curve, extend the distance of point G1 or increase Δy2 or Δy3, and iterate again until the obtained complete new nozzle profile meets the requirements.

[0047] In the above-mentioned large-size, wide-operating-condition hypersonic, low-density profile nozzle design method, the coordinate axis takes the vertical coordinate at the throat as the zero point as the coordinate origin, the x-axis is horizontal, and the positive direction is to the right, and the y-axis is vertical, and the positive direction is vertically upward.

[0048] In the above-mentioned large-scale wide-operating-condition hypersonic low-density profile nozzle design method, D=D0-δ0

[0049] Where D0 represents the actual diameter of the nozzle outlet, δ0 represents the actual boundary layer thickness; when the outlet flow field Knudsen number is less than 0.03, δ0 = δ ~ 1.2δ; when the outlet flow field Knudsen number is greater than 0.03 and less than 1, δ0 = 1.2δ ~ 1.4δ; when the outlet flow field Knudsen number is greater than 1, δ0 = 1.4δ ~ 1.6δ; δ represents the reference boundary layer thickness; x represents the axial distance from the source point, Re x is the streamwise Reynolds number at x.

[0050] In the above-mentioned large-size, wide-operating-condition hypersonic, low-density profile nozzle design method, when the exit flow field Knudsen number is greater than 0.03 and less than 1, the G2P2D0 segment can be moved in the vertical direction so that point G2 coincides with point G1; where point D0 is the nozzle exit position point.

[0051] In the above-mentioned large-size, wide-operating-condition hypersonic low-density profile nozzle design method, when the exit flow field Knudsen number is greater than 1, the P3D0 segment can move up and down along the vertical direction so that point P3 coincides with point P2.

[0052] The present invention has the following advantages:

[0053] This paper proposes a design method for a large-scale, wide-range hypersonic low-density profile nozzle, providing a feasible, experimentally verified approach to low-density profile nozzle design. This method not only significantly improves the optimization efficiency of low-density profile nozzles but also ensures a uniform flow field at varying low-density levels. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] FIG1 is a flowchart of a method for designing a large-scale, wide-operating-mode hypersonic, low-density profile nozzle according to an embodiment of the present invention;

[0055] FIG2 is a schematic diagram of a design of a large-scale low-density nozzle with a Knudsen number less than 0.03 according to an embodiment of the present invention;

[0056] FIG3 is a schematic diagram of a design of a large-size, low-density nozzle with a Knudsen number greater than 0.03 and less than 1 according to an embodiment of the present invention;

[0057] FIG4 is a schematic diagram of a design of a large-sized low-density nozzle with a Knudsen number greater than 1 in an embodiment of the present invention. DETAILED DESCRIPTION

[0058] In order to make the objectives, technical solutions and advantages of the present invention more clear, the embodiments disclosed in the present invention will be described in further detail below with reference to the accompanying drawings.

[0059] As shown in FIG1 , in this embodiment, the design method of the large-scale, wide-operating-mode hypersonic low-density profile nozzle includes:

[0060] Step 1: Calculate the throat diameter d of the nozzle to be designed based on the Mach number Ma and the inviscid profile outlet diameter D of the nozzle to be designed. * .

[0061] In this embodiment, d * The calculation process is as follows:

[0062] Determine the area A corresponding to the inviscid outlet diameter D of the nozzle to be designed;

[0063] According to Ma and A, the throat area A of the nozzle to be designed is calculated * :

[0064] Here, γ represents the specific heat ratio.

[0065] According to A *, calculate the throat diameter d of the nozzle to be designed * :

[0066] Step 2: Based on the determined throat diameter d of the nozzle to be designed * , combined with the given semi-cone angle θ, an initial conical nozzle is designed.

[0067] In this embodiment, the initial conical nozzle is formed by smoothly connecting an expansion section and a contraction section; the contraction section of the initial conical nozzle adopts a shifted Witoszynski curve, a cubic curve, or a CQCQ curve, wherein 6°≤θ≤15°.

[0068] Step 3: Perform numerical simulation calculations on the initial conical nozzle to determine the Knudsen number of the outlet flow field of the initial conical nozzle.

[0069] Step 4: When the Knudsen number of the outlet flow field is less than 0.03, the first strategy is used to reconstruct and optimize the initial conical nozzle profile to obtain the optimal nozzle profile.

[0070] In this embodiment, as shown in FIG2 , when the Knudsen number of the outlet flow field is less than 0.03, the initial conical nozzle profile is determined to be a continuous curve, and a 7th to 9th order Bézier curve is used to reconstruct the downstream region of the nozzle throat along the outer streamline of the flow field. Point T of the throat is selected as the initial point of the Bézier curve, and point G1 is selected as the end point of the Bézier curve. The slope upstream of point G1 is calculated.

[0071] Based on the calculated slope upstream of point G1, draw a straight line to extend point G1 to point P1.

[0072] The wave-breaking area from point P1 to exit E1 is calculated using the analytical expression:

[0073] Among them, (x N1 ,y N1 ) represents a point on the P1E1 curve; r1 represents the source flow radius of point P1; θ P1 represents the airflow deflection angle at point P1; μ represents the Mach angle, θ1 represents the airflow deflection angle on the P1E1 curve.

[0074] The nozzle expansion section curve is obtained by smoothly connecting the TG1 curve, G1P1 curve and P1E1 curve. After connecting the contraction section curve, a complete new nozzle profile is obtained.

[0075] Perform numerical simulation on the obtained complete new nozzle profile. If the Mach number deviation of the nozzle exit flow field determined by the numerical simulation does not meet the requirements, return to correct the Bézier curve, extend the distance of point G1, and iterate again until the obtained complete new nozzle profile meets the requirements.

[0076] Step 5: When the Knudsen number of the outlet flow field is greater than 0.03 and less than 1, the second strategy is used to reconstruct and optimize the initial conical nozzle profile to obtain the optimal nozzle profile.

[0077] In this embodiment, as shown in FIG3 , when the Knudsen number of the outlet flow field is greater than 0.03 and less than 1, the nozzle profile is determined to be a discontinuous curve, and the nozzle profile has two segments.

[0078] The starting point of the first curve segment is selected as the nozzle throat, and the 7th to 9th degree Bézier curve is used to reconstruct the downstream area of ​​the nozzle throat along the outer streamline of the flow field. The throat point T is selected as the initial point of the Bézier curve, and the G1 point is selected as the end point of the Bézier curve.

[0079] Select point G2 as the starting point of the second curve segment. Point G2 satisfies the following relationship with point G1: point G1 is offset downward by Δy1 along the y-axis, and the slope of point G2 is the same as that of point G1.

[0080] Calculate the slope upstream of point G1.

[0081] Based on the calculated slope upstream of point G1, a straight line is drawn to extend point G2 to point P2; the value of point P2 is determined by the source flow radius r2.

[0082] The wave-breaking zone from point P2 to exit E2 is calculated using the analytical expression:

[0083] Among them, (x N2 ,y N2 ) represents a point on the P2E2 curve; r2 represents the source flow radius of point P2; θ P2 represents the airflow deflection angle at point P2; θ2 represents the airflow deflection angle on the P2E2 curve.

[0084] Connect the contraction curve and the TG1 curve, and connect the G2P2 curve and the P2E2 curve to obtain a complete new nozzle profile; among them, G1 and G2 are gap areas.

[0085] Perform numerical simulation on the obtained complete new nozzle profile. If the Mach number deviation of the nozzle exit flow field determined by the numerical simulation does not meet the requirements, return to the Bézier curve to correct it, extend the distance of point G1 or increase Δy1, and iterate again until the obtained complete new nozzle profile meets the requirements.

[0086] Step 6: When the Knudsen number of the outlet flow field is greater than 1, the third strategy is used to reconstruct and optimize the initial conical nozzle profile to obtain the optimal nozzle profile.

[0087] In this embodiment, as shown in FIG4 , when the Knudsen number of the outlet flow field is greater than 1, the nozzle profile is determined to be a discontinuous curve, and the nozzle profile has three segments.

[0088] The starting point of the first curve segment is selected as the nozzle throat, and the 7th to 9th degree Bézier curve is used to reconstruct the downstream area of ​​the nozzle throat along the outer streamline of the flow field. The throat point T is selected as the initial point of the Bézier curve, and the G1 point is selected as the end point of the Bézier curve.

[0089] The starting point of the second curve segment is selected as point G2, where point G2 and point G1 satisfy the following conditions: the point G1 is offset downward by Δy1 along the vertical direction of the y-axis, and the slope of point G2 is the same as that of point G1.

[0090] Calculate the slope upstream of point G1.

[0091] Based on the calculated slope upstream of point G1, draw a straight line to extend point G2 to point P2; offset point P2 downward by Δy2 along the vertical direction of the y-axis to obtain point P3.

[0092] The wave-breaking zone from point P3 to exit E3 is calculated using the analytical expression:

[0093] Among them, (x N3 ,y N3 ) represents a point on the P3E3 curve; r3 represents the source flow radius of point P3; θ P3 represents the airflow deflection angle at point P3; θ3 represents the airflow deflection angle on the P3E3 curve.

[0094] The complete new nozzle profile is obtained by connecting the contraction section curve with the TG1 curve, the G2P2 curve and the P3E3 curve; among them, G1 and G2 are gap areas, and P2 and P3 are gap areas.

[0095] Perform numerical simulation on the obtained complete new nozzle profile. If the Mach number deviation of the nozzle exit flow field determined by the numerical simulation does not meet the requirements, return to correct the Bézier curve, extend the distance of point G1 or increase Δy2 or Δy3, and iterate again until the obtained complete new nozzle profile meets the requirements.

[0096] In this embodiment, the inviscid profile outlet diameter D of the nozzle to be designed can be determined based on the actual nozzle outlet diameter D0 and the actual boundary layer thickness δ0: D = D0 - δ0. Furthermore, the actual boundary layer thickness δ0 and the reference boundary layer thickness δ satisfy the following conditions: when the outlet flow field Knudsen number is less than 0.03, δ0 = δ ~ 1.2δ; when the outlet flow field Knudsen number is greater than 0.03 and less than 1, δ0 = 1.2δ ~ 1.4δ; when the outlet flow field Knudsen number is greater than 1, δ0 = 1.4δ ~ 1.6δ; reference boundary layer thickness. Furthermore, x represents the axial distance from the source point, Re x is the streamwise Reynolds number at x.

[0097] In this embodiment, when the Knudsen number of the outlet flow field is greater than 0.03 and less than 1, the G2P2D0 segment can be moved vertically so that point G2 coincides with point G1. When the Knudsen number of the outlet flow field is greater than 1, the P3D0 segment can be moved vertically up and down so that point P3 coincides with point P2. Point D0 is the nozzle exit location.

[0098] In this embodiment, if If the calculated value of L is greater than r1, reduce Ma until the calculated value of L is less than r1.

[0099] In this embodiment, when the Knudsen number of the outlet flow field is greater than 1, the slope on the left side of point G1 is the same as the slope on the right side of point G2, and the slope on the left side of point P2 is the same as the slope on the right side of point P3, so that when the airflow flows through, no disturbance caused by inconsistent geometric slopes occurs.

[0100] In this embodiment, the gap Δy1 between points G1 and G2 is smaller than the thickness of the airflow boundary layer there; the gap Δy2 between points P2 and P3 is smaller than the thickness of the airflow boundary layer there, ensuring that the disturbance caused by the curve discontinuity is inside the boundary layer.

[0101] In this embodiment, the Bézier curve is a combination of the position vectors of the characteristic polygon vertices and the Bernstein basis function, and the 7th to 9th order Bézier curves are selected to reconstruct the downstream curve of the nozzle throat. The first two vertices ensure the continuity of the parameters of the initial point and the first and second order derivatives, the last three points ensure the continuity of the parameters of the end point and the first and second order derivatives, and the other points are used to control the shape of the curve.

[0102] It should be noted that the coordinate axes described in this embodiment are: the vertical coordinate at the throat is the zero point as the coordinate origin, the x-axis is the horizontal direction, the positive direction is to the right, and the y-axis is the vertical direction, the positive direction is vertically upward.

[0103] In summary, the design method for a large-scale hypersonic low-density profile nozzle proposed in this paper provides a feasible, experimentally verified approach to low-density profile nozzle design. This method not only significantly improves the optimization efficiency of low-density profile nozzles but also ensures a uniform flow field at varying low-density levels.

[0104] Although the present invention has been disclosed above in terms of preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art may make possible changes and modifications to the technical solutions of the present invention by using the methods and technical contents disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the scope of protection of the technical solutions of the present invention.

[0105] The contents not described in detail in the specification of the present invention belong to the common knowledge of professionals in this field.

Claims

1. A design method for a large-size, wide-operating-condition, hypersonic, low-density profile nozzle, characterized in that, Including: Based on the exit Mach number Ma of the nozzle to be designed and the exit diameter D of the inviscid profile, the throat diameter d of the nozzle to be designed is calculated * ; Based on the determined throat diameter d of the nozzle to be designed * , in combination with the given half-cone angle θ, design an initial conical nozzle; wherein, the initial conical nozzle is smoothly connected by an expansion section and a contraction section; the contraction section of the initial conical nozzle adopts a shifted Witoszynski curve, a cubic curve or a CQCQ curve; Performing numerical simulation calculations on the initial conical nozzle to determine the Knudsen number of the outlet flow field of the initial conical nozzle; When the Knudsen number of the outlet flow field is less than 0.03, adopting the first strategy to reconstruct and optimize the profile of the initial conical nozzle to obtain the optimal nozzle profile; When the Knudsen number of the outlet flow field is greater than 0.03 and less than 1, adopting the second strategy to reconstruct and optimize the profile of the initial conical nozzle to obtain the optimal nozzle profile; When the Knudsen number of the outlet flow field is greater than 1, adopting the third strategy to reconstruct and optimize the profile of the initial conical nozzle to obtain the optimal nozzle profile.

2. The design method of the large-size, wide-operating-condition, hypersonic, low-density profile nozzle according to claim 1, characterized in that According to the exit Mach number Ma of the nozzle to be designed and the exit diameter D of the inviscid profile, the throat diameter d of the nozzle to be designed is calculated * , including: Determining the area A corresponding to the diameter D of the inviscid profile outlet of the nozzle to be designed; According to Ma and A, the throat area A of the nozzle to be designed is calculated * : Where γ represents the specific heat ratio; According to A * , the throat diameter d of the nozzle to be designed is calculated * :

3. The design method of a large-size, wide-operating-condition, hypersonic, low-density profile nozzle according to claim 1, characterized in that, 6° ≤ θ ≤ 15°.

4. The design method of the large-size, wide-operating-condition, hypersonic, low-density profile nozzle according to claim 1, characterized in that When the Knudsen number of the outlet flow field is less than 0.03, adopting the first strategy to reconstruct and optimize the profile of the initial conical nozzle to obtain the optimal nozzle profile, including: When the Knudsen number of the outlet flow field is less than 0.03, determining that the profile of the initial conical nozzle is a continuous curve, and using a 7-9th degree Bézier curve to reconstruct the downstream area of the nozzle throat along the outer streamline of the flow field, selecting the throat T point as the initial point of the Bézier curve and the G1 point as the end point of the Bézier curve, and calculating the slope upstream of the G1 point; Based on the calculated slope upstream of the G1 point, drawing a straight line to extend the G1 point to the P1 point; Using an analytical expression, calculate the wave dissipation area from point P1 to point E1 at the outlet: Among them, (x N1 , y N1 ) represents the point on the P1E1 curve; r1 represents the source flow radius of point P1; θ P1 represents the air flow deflection angle of point P1; μ represents the Mach angle, θ1 represents the airflow deflection angle on the P1E1 curve; Smoothly connecting the TG1 curve, the G1P1 curve, and the P1E1 curve to obtain the nozzle expansion section curve, and after connecting the contraction section curve, obtaining the complete new nozzle profile; Performing numerical simulation on the obtained complete new nozzle profile. If the Mach number deviation of the nozzle outlet flow field determined according to the numerical simulation does not meet the requirements, then return to correct the Bézier curve, extend the distance of the G1 point, and perform iteration again until the obtained complete new nozzle profile meets the requirements.

5. The design method of a large-size, wide-operating-condition, hypersonic, low-density profile nozzle according to claim 4, characterized in that When the Knudsen number of the outlet flow field is greater than 0.03 and less than 1, adopting the second strategy to reconstruct and optimize the profile of the initial conical nozzle to obtain the optimal nozzle profile, including: When the Knudsen number of the outlet flow field is greater than 0.03 and less than 1, determining that the nozzle profile is a discontinuous curve and the nozzle profile has 2 segments; Selecting the starting point of the first segment curve as the nozzle throat and using a 7-9th degree Bézier curve to reconstruct the downstream area of the nozzle throat along the outer streamline, selecting the throat T point as the initial point of the Bézier curve and the G1 point as the end point of the Bézier curve; Selecting the starting point of the second segment curve as the G2 point; where the relationship between the G2 point and the G1 point is: the point obtained by shifting the G1 point vertically downward along the y-axis by Δy1 is the G2 point, and the slope of the G2 point is the same as the slope of the G1 point; Calculating the slope upstream of the G1 point; Based on the calculated slope upstream of the G1 point, drawing a straight line to extend the G2 point to the P2 point; where the value of the P2 point is determined by the source radius r2; Using the analytical expression, the wave dissipation area from point P2 to point E2 at the outlet is calculated: Among them, (x N2 , y N2 ) represents the point on the P2E2 curve; r2 represents the source flow radius of point P2; θ P2 represents the air flow deflection angle of point P2; θ2 represents the air flow deflection angle on the P2E2 curve; Connecting the contraction section curve and the TG1 curve, connecting the G2P2 curve and the P2E2 curve to obtain the complete new nozzle profile; where G1 and G2 are the gap areas; Perform numerical simulation on the obtained complete new nozzle profile. If the Mach number deviation of the nozzle outlet flow field determined according to the numerical simulation does not meet the requirements, return to correct the Bézier curve, extend the distance of point G1 or increase Δy1, and perform iteration again until the obtained complete new nozzle profile meets the requirements.

6. The design method of a large-size, wide-operating-condition, hypersonic, low-density profile nozzle according to claim 5, characterized in that When the Knudsen number of the outlet flow field is greater than 1, adopt the third strategy to reconstruct and optimize the profile of the initial conical nozzle to obtain the optimal nozzle profile, including: When the Knudsen number of the outlet flow field is greater than 1, it is determined that the nozzle profile is a discontinuous curve and the nozzle profile has 3 segments; Select the starting point of the first segment of the curve as the nozzle throat, and use a 7-9th order Bézier curve to reconstruct the downstream area of the nozzle throat along the outer streamline of the flow field. Select the throat point T as the starting point of the Bézier curve and point G1 as the end point of the Bézier curve; Select the starting point of the second segment of the curve as point G2. Among them, the relationship between point G2 and point G1 is: the point obtained by offsetting point G1 vertically downward along the y-axis by Δy1 is point G2, and the slope of point G2 is the same as the slope of point G1; Calculate the slope upstream of point G1; Based on the calculated slope upstream of point G1, draw a straight line so that point G2 is extended to point P2; offset point P2 vertically downward along the y-axis by Δy2 to obtain point P3; Using an analytical expression, the wave dissipation area from point P3 to point E3 at the outlet is calculated: Among them, (x N3 , y N3 ) represents a point on the P3E3 curve; r3 represents the source flow radius of point P3; θ P3 represents the air flow deflection angle of point P3; θ3 represents the air flow deflection angle on the P3E3 curve; Connect the contraction section curve and the TG1 curve, and the G2P2 curve and the P3E3 curve to obtain the complete new nozzle profile; among them, G1 and G2 are the gap areas, and P2 and P3 are the gap areas; Perform numerical simulation on the obtained complete new nozzle profile. If the Mach number deviation of the nozzle outlet flow field determined according to the numerical simulation does not meet the requirements, return to correct the Bézier curve, extend the distance of point G1 or increase Δy2 or increase Δy3, and perform iteration again until the obtained complete new nozzle profile meets the requirements.

7. The design method of a large-size, wide-operating-condition, hypersonic, low-density profile nozzle according to claim 6, characterized in that The coordinate axes take the zero point of the ordinate at the throat as the coordinate origin, the x-axis is the horizontal direction with the positive direction to the right, and the y-axis is the vertical direction with the positive direction vertically upward.

8. The design method of a large-size, wide-operating-condition, hypersonic, low-density profile nozzle according to claim 6, characterized in that D = D0 - δ0 where D0 represents the actual diameter of the nozzle exit, and δ0 represents the actual boundary layer thickness; when the Knudsen number of the exit flow field is less than 0.03, δ0 = δ~1.2δ; when the Knudsen number of the exit flow field is greater than 0.03 and less than 1, δ0 = 1.2δ~1.4δ; when the Knudsen number of the exit flow field is greater than 1, δ0 = 1.4δ~1.6δ; δ represents the reference boundary layer thickness; x represents the axial distance measured from the source point, and Re x is the streamwise Reynolds number at x.

9. The design method of the large-size wide-operating-condition hypersonic low-density profile nozzle according to claim 5, characterized in that When the Knudsen number of the outlet flow field is greater than 0.03 and less than 1, the G2P2D0 segment can be moved vertically so that point G2 coincides with point G1; among them, point D0 is the nozzle outlet position point.

10. The design method of a large-size, wide-operating-condition, hypersonic, low-density profile nozzle according to claim 6, characterized in that When the Knudsen number of the outlet flow field is greater than 1, the P3D0 segment can be moved vertically up and down so that point P3 coincides with point P2.

Images