A method for designing a hypersonic carbon dioxide profile nozzle

Abstract

The present application relates to a kind of hypersonic carbon dioxide profile nozzle design method, belong to wind tunnel test field;Hypersonic carbon dioxide nozzle is set by expansion section, throat and contraction section three parts;Contraction section is determined by straight line plus circular arc curve;Expansion section is determined by circular arc curve and straight line;Smoothly connect the circular arc curve of contraction section and expansion section, i.e. get conical nozzle curve;The junction of contraction section and expansion section is throat;Nozzle throat diameter is by equivalent specific heat ratio and numerical calculation;Expansion section is determined by characteristic method and numerical correction;Contraction section is determined by straight line plus circular arc curve;The present application provides high-quality hypersonic wind tunnel test aerodynamic data for Mars reentry vehicle development, can simulate Mars flight environment.

Description

Technical Field

[0001] This invention belongs to the field of wind tunnel testing and relates to a design method for a hypersonic carbon dioxide profile nozzle. Background Technology

[0002] In hypersonic wind tunnel tests, the hypersonic nozzle is a core component for obtaining the required Mach number and Reynolds number parameters in the wind tunnel test section. For Mars reentry experiments using carbon dioxide as the test gas, a carbon dioxide profile nozzle needs to be designed to meet the experimental requirements. Carbon dioxide is a triatomic gas, and compared to air, its specific heat ratio varies significantly with temperature. The specific heat ratio differs in different temperature regions within the carbon dioxide nozzle flow field, placing high demands on wind tunnel testing capabilities and making nozzle design extremely challenging.

[0003] Hypersonic nozzle design has been developing for over 50 years; however, research on hypersonic carbon dioxide nozzle design is scarce. Existing tests have primarily involved changing the medium in existing air nozzles, resulting in insufficiently uniform flow fields. To obtain high-quality hypersonic carbon dioxide flow fields, further design work is needed to ensure excellent flow field quality, providing crucial support for the high-quality wind tunnel aerodynamic data required for Mars reentry vehicle development. Summary of the Invention

[0004] The technical problem solved by this invention is to overcome the shortcomings of the prior art and propose a design method for a hypersonic carbon dioxide profile nozzle, which provides high-quality hypersonic wind tunnel test aerodynamic data for the development of Mars reentry vehicles and can simulate the Mars flight environment.

[0005] The solution of the present invention is:

[0006] A method for designing a hypersonic carbon dioxide profile nozzle includes:

[0007] The hypersonic carbon dioxide nozzle is designed to consist of three parts: an expansion section, a throat, and a contraction section. The contraction section is defined by a straight line and a circular arc. The expansion section is defined by a circular arc and a straight line. The circular arc that smoothly connects the contraction section and the expansion section is the conical nozzle curve. The connection between the contraction section and the expansion section is the throat.

[0008] The nozzle throat diameter is calculated from the equivalent specific heat ratio and numerical values;

[0009] The expansion segment is determined by the characteristic method and numerical verification;

[0010] The contraction segment is determined by a straight line plus a circular arc curve.

[0011] In the aforementioned hypersonic carbon dioxide profile nozzle design method, the throat diameter is determined by the design Mach number Ma and the outlet area A and throat area A.* The ratio A / A * The total temperature T0 and total pressure P0 of the nozzle stagnation chamber determine that if the total temperature of the nozzle stagnation chamber is less than 1400K, carbon dioxide will not undergo a chemical reaction in the stagnation chamber.

[0012] In the aforementioned hypersonic carbon dioxide profile nozzle design method, a conical carbon dioxide nozzle is first designed, assuming a specific heat ratio of λ1, with an initial value of 1.25; the Mach number Ma and the exit area A and throat area A are then used to design the nozzle. * The ratio A / A * Relationship (1) determines the initial throat diameter A of the nozzle. *1 :

[0013]

[0014] Initial throat diameter A of the nozzle *1 The expansion section is designed with an export area A, and the maximum expansion angle of the expansion section is β; the value of β ranges from 8° to 16°.

[0015] In the above-mentioned hypersonic carbon dioxide profile nozzle design method, when the equation of the converging section arc curve is:

[0016]

[0017] In the formula, C1 is a coefficient;

[0018] R c The radius of curvature of the larynx;

[0019] x is the coordinate of the contracted segment;

[0020] r * Let A be the radius of the larynx, and let A be the area of ​​the larynx. * Calculated;

[0021] Then the intersection point X of the above circular arc curve and the contraction segment a for:

[0022]

[0023] θ a The radius of the contracted straight line is 25°-50°.

[0024] In the above-mentioned hypersonic carbon dioxide profile nozzle design method, the Navier-Stokes equations are solved, and the designed carbon dioxide conical nozzle is numerically simulated to obtain the specific heat ratio of the nozzle flow field, the nozzle exit Mach number, and the Pitot pressure; the specific heat ratio of the nozzle flow field and the exit Mach number are analyzed.

[0025] In the aforementioned hypersonic carbon dioxide profile nozzle design method, claims 3 to 5 are iterated, and the value of the comparative heat ratio is modified according to the actual situation. A new carbon dioxide conical nozzle is regenerated, and numerical calculations are performed until the deviation between the designed Mach number and the calculated Mach number is less than 0.1, thus obtaining the nozzle throat radius r. n and specific heat ratio λ n .

[0026] In the aforementioned hypersonic carbon dioxide profile nozzle design method, the expansion section profile is designed using the method of characteristics. The specific heat ratio used in the method of characteristics is λ. n The nozzle throat radius is r n .

[0027] In the above-mentioned hypersonic carbon dioxide profile nozzle design method, when designing the nozzle using the method of characteristics, the characteristic line equations and compatibility relations are written in the form of finite difference equations. The position coordinates of the grid points are determined by the difference equations of the characteristic lines, and the flow parameters on the grid points are determined by the difference equations of the compatibility relations. For a supersonic steady, irrotational, axisymmetric ideal gas, the characteristic line equations and compatibility equations are divided into two parts: right-handed and left-handed. Given point 1, and the parameters at points 1 and 2, the left-handed characteristic line emanating from point 1 intersects the right-handed characteristic line emanating from point 2 at point 3.

[0028] In the above-mentioned hypersonic carbon dioxide profile nozzle design method, the right-hand characteristic line and compatibility relationship are as follows:

[0029]

[0030]

[0031] In the formula, ψ is Prandtmeyer angle;

[0032] θ is the airflow deflection angle;

[0033] μ is the Mach angle;

[0034] x and y are coordinate points;

[0035] The subscripts 1, 2, and 3 represent point 1, point 2, and point 3, respectively.

[0036] Δζ is the compensation amount, Δζ=(x3-x2)secβ;

[0037] β is the angle between the right-moving feature line and x;

[0038] The left-hand characteristic lines and their compatibility relationships are as follows:

[0039]

[0040]

[0041] Where Δζ is the compensation amount, Δζ=(x3-x1)secα;

[0042] α is the angle between the left-side feature line and x;

[0043] After calculating the inviscid profile of the nozzle using the method of characteristics, the KAMAN momentum integral equation method is then selected for boundary layer correction to complete the initial design of the expansion section profile.

[0044] In the aforementioned hypersonic carbon dioxide profile nozzle design method, combining claims 3, 4, and 6, a contraction section is designed and smoothly connected to the expansion section of claim 9. Numerical calculations are then performed. The design is complete when the deviation between the calculated nozzle exit Mach number and the designed Mach number is less than 0.1; otherwise, the throat radius r is adjusted when the deviation is greater than or equal to 0.1. n The design is completed by iterating through claims 6 to 9 until the deviation between the calculated nozzle exit Mach number and the designed Mach number is less than 0.1.

[0045] The advantages of this invention compared to the prior art are:

[0046] (1) Based on the characteristic line method and combined with numerical simulation, this invention considers the influence of the total temperature of the nozzle chamber on the heat ratio, and the flow field quality of the designed hypersonic carbon dioxide nozzle can achieve excellent indicators.

[0047] (2) This invention can provide high-quality hypersonic wind tunnel test aerodynamic data for the development of Mars reentry vehicles and can simulate the Mars flight environment. Attached Figure Description

[0048] Figure 1 This is a schematic diagram of the hypersonic carbon dioxide profile nozzle of the present invention;

[0049] Figure 2 This is a schematic diagram showing the relationship between the position and angle of the feature line method of the present invention;

[0050] Figure 3 This is a flowchart illustrating the design process of the carbon dioxide profile nozzle of this invention. Detailed Implementation

[0051] The present invention will be further described below with reference to the embodiments.

[0052] This invention provides a design method for hypersonic carbon dioxide nozzle profiles. Based on the characteristic line method and combined with numerical simulation, and considering the influence of the total temperature and specific heat ratio of the nozzle stagnation chamber, the designed hypersonic carbon dioxide nozzle achieves excellent flow field quality. This invention can provide high-quality hypersonic wind tunnel aerodynamic data for the development of Mars reentry vehicles and can simulate the Martian flight environment.

[0053] The design method for hypersonic carbon dioxide profile nozzles includes the following steps:

[0054] The hypersonic carbon dioxide nozzle is designed to consist of three parts: an expansion section, a throat, and a contraction section. The contraction section is defined by a straight line and a circular arc; the expansion section is defined by a circular arc and a straight line. A smooth connection between the contraction and expansion sections via a circular arc results in the conical nozzle profile. The junction of the contraction and expansion sections forms the throat. Figure 1 As shown.

[0055] The nozzle throat diameter is calculated from the equivalent specific heat ratio and numerical values.

[0056] The expansion segment is determined by the characteristic method and numerical verification.

[0057] The contraction segment is determined by a straight line plus a circular arc curve.

[0058] The throat diameter is determined by the design Mach number Ma and the outlet area A and the throat area A. * The ratio A / A * The total temperature T0 and total pressure P0 of the nozzle stagnation chamber determine that if the total temperature of the nozzle stagnation chamber is less than 1400K, carbon dioxide will not undergo a chemical reaction in the stagnation chamber.

[0059] First, design a carbon dioxide conical nozzle, assuming a specific heat ratio of λ1, with an initial value of 1.25; then, consider the Mach number Ma, the outlet area A, and the throat area A... * The ratio A / A * Relationship (1) determines the initial throat diameter A of the nozzle. *1 :

[0060]

[0061] Initial throat diameter A of the nozzle *1 The expansion section is designed with an export area A, and the maximum expansion angle of the expansion section is β; the value of β ranges from 8° to 16°.

[0062] When the equation of the circular arc curve of the contraction segment is:

[0063]

[0064] In the formula, C1 is a coefficient;

[0065] R c The radius of curvature of the larynx;

[0066] x is the coordinate of the contracted segment;

[0067] r * Let A be the radius of the larynx, and let A be the area of ​​the larynx. * Calculated;

[0068] Then the intersection point X of the above circular arc curve and the contraction segment a for:

[0069]

[0070] θ a The radius of the contracted straight line is 25°-50°.

[0071] Solving the Navier-Stokes equations, numerical simulations were performed on the designed carbon dioxide conical nozzle to obtain the specific heat ratio of the nozzle flow field, the nozzle exit Mach number, and the Pitot pressure; the specific heat ratio of the nozzle flow field and the exit Mach number were analyzed.

[0072] Iterate through formulas (1) to (3), modify the heat ratio value according to the actual situation, regenerate a new carbon dioxide conical nozzle, and perform numerical calculations until the deviation between the designed Mach number and the calculated Mach number is less than 0.1, and obtain the nozzle throat radius r. n and specific heat ratio λ n .

[0073] The expansion section profile is designed using the method of characteristics, with a specific heat ratio of λ. n The nozzle throat radius is r n .

[0074] When designing nozzles using the method of characteristics, the characteristic line equations and compatibility relations are written in finite difference form. The position coordinates of the grid points are determined by the difference equations of the characteristic lines, and the flow parameters at the grid points are determined by the difference equations of the compatibility relations. For an ideal gas with supersonic steady, irrotational, axisymmetric flow, the characteristic line equations and compatibility equations are divided into right-hand and left-hand parts. Given point 1, and the parameters at points 1 and 2, the left-hand characteristic line emanating from point 1 intersects the right-hand characteristic line emanating from point 2 at point 3. A schematic diagram of the three points is shown below. Figure 2 As shown.

[0075] The right-hand characteristic lines and their compatibility relationships are as follows:

[0076]

[0077]

[0078] In the formula, ψ is Prandtmeyer angle;

[0079] θ is the airflow deflection angle;

[0080] μ is the Mach angle;

[0081] x and y are coordinate points;

[0082] The subscripts 1, 2, and 3 represent point 1, point 2, and point 3, respectively.

[0083] Δζ is the compensation amount, Δζ=(x3-x2)secβ;

[0084] β is the angle between the right-moving feature line and x;

[0085] The left-hand characteristic lines and their compatibility relationships are as follows:

[0086]

[0087]

[0088] Where Δζ is the compensation amount, Δζ=(x3-x1)secα;

[0089] α is the angle between the left-side feature line and x;

[0090] After calculating the inviscid profile of the nozzle using the method of characteristics, the KAMAN momentum integral equation method is then selected for boundary layer correction to complete the initial design of the expansion section profile.

[0091] Combining formulas (1) to (3), design the contraction section and smoothly connect it with the expansion sections of formulas (4) to (7). Then perform numerical calculations. When the deviation between the calculated nozzle exit Mach number and the design Mach number is less than 0.1, the design is completed. When the deviation between the calculated nozzle exit Mach number and the design Mach number is greater than or equal to 0.1, change the throat radius r. n The process is iterated until the deviation between the calculated nozzle exit Mach number and the design Mach number is less than 0.1, at which point the design is complete.

[0092] Example

[0093] Overall design process as follows Figure 3 As shown.

[0094] Step 1: Determine the design parameters, including the nozzle exit Mach number, nozzle exit diameter and nozzle inlet diameter, and the total temperature and total pressure of the nozzle stagnation chamber.

[0095] Step 2: The hypersonic carbon dioxide nozzle consists of three parts: the expansion section, the throat, and the contraction section. The diameter of the nozzle throat is determined by the equivalent specific heat ratio and numerical calculation, the expansion section is determined by the characteristic method and numerical calibration, and the contraction section is determined by a straight line plus a circular arc curve.

[0096] Step 3: The nozzle throat diameter is determined by the design Mach number Ma and the exit area A and throat area A. * The ratio A / A * The total temperature T0 and total pressure P0 of the nozzle stagnation chamber determine that if the total temperature of the nozzle stagnation chamber is less than 1400K, carbon dioxide will not undergo a chemical reaction in the stagnation chamber.

[0097] Step 4: Design a carbon dioxide conical nozzle, assuming a specific heat ratio of λ1 (the initial value of λ1 is 1.25), based on the Mach number Ma and the outlet area A and throat area A.* The ratio A / A * Relationship (1) determines the initial throat diameter A of the nozzle. *1 .

[0098]

[0099] The initial throat diameter A of the nozzle *1 The expansion section of the conical nozzle is designed with an outlet area A. The maximum expansion angle of the conical nozzle is β, and the value of β ranges from 8 to 16°.

[0100] If the converging section of the conical nozzle uses a straight line plus a circular curve, see the design drawing. Figure 1 ,

[0101] The equation of a circular arc curve can be expressed as:

[0102]

[0103] In the formula, the intersection point of the above circular arc curve and the contraction segment is:

[0104]

[0105] Where C1 is a coefficient, Rc is the radius of curvature of the larynx, x is the coordinate of the constriction segment, θa is the radius of the straight line of the constriction segment, and the angle is 25–50°. r* is the radius of the larynx, which is determined by the area A of the larynx. * Calculated.

[0106] By smoothly connecting the contraction and expansion curves, a conical nozzle curve is obtained.

[0107] Step 5: Solve the Navier-Stokes equations and numerically simulate the designed carbon dioxide conical nozzle to obtain flow field parameters such as the specific heat ratio, nozzle exit Mach number, and Pitot pressure. Analyze the specific heat ratio and exit Mach number of the nozzle flow field.

[0108] Step 6: Iterate through steps 4 and 5, modify the heat ratio value, regenerate a new carbon dioxide conical nozzle, and perform numerical calculations until the deviation between the designed Mach number and the calculated Mach number is less than 0.1, thus obtaining the nozzle throat radius r. n and specific heat ratio λ n .

[0109] Step 7: Design the carbon dioxide nozzle profile using the method of characteristics. The specific heat ratio used in the method of characteristics is the specific heat ratio λ. n .

[0110] Step 8: When designing the nozzle using the method of characteristics, write the characteristic line equations and compatibility relations in finite difference form. The position coordinates of the grid points are determined by the difference equations of the characteristic lines, and the flow parameters at the grid points are determined by the difference equations of the compatibility relations. For a supersonic, steady, irrotational, axisymmetric ideal gas, the characteristic line equations and compatibility equations are divided into right-hand and left-hand parts. Given the parameters at points 1 and 2, the left-hand characteristic line emanating from point 1 intersects the right-hand characteristic line emanating from point 2 at point 3. (See...) Figure 2

[0111] Right-hand characteristic lines and compatibility relationships:

[0112]

[0113]

[0114] Where ψ is Prandtl-Meyer angle, θ is airflow deflection angle, μ is Mach angle, x and y are coordinate points, and subscripts 1 and 2 represent different coordinate points, Δζ = (x3-x2)secβ, and β is the angle between the traverse line and the x-axis.

[0115] Left-side characteristic lines and compatibility relationships:

[0116]

[0117]

[0118] Where Δζ=(x3-x1)secα, and α is the angle between the eigenline and the x-axis.

[0119] After calculating the inviscid profile of the nozzle using the method of characteristics, the KAMAN momentum integral equation method is then selected for boundary layer correction to complete the initial design of the expansion section profile.

[0120] Step 9: Combining Steps 4 and 6, design the nozzle profile contraction section and smoothly connect it with the expansion section from Step 8. Then perform numerical calculations. If the deviation between the calculated nozzle exit Mach number and the design Mach number is less than 0.1, the design is complete. If the deviation between the calculated nozzle exit Mach number and the design Mach number is greater than 0.1, change the throat radius rn and iterate through Steps 6 to 8 until the deviation between the calculated nozzle exit Mach number and the design Mach number is less than 0.1, and the design is complete.

[0121] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solutions of the present invention by utilizing the methods and techniques disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and alterations 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 protection scope of the technical solutions of the present invention.

Claims

1. A method for designing a hypersonic carbon dioxide profile nozzle, characterized in that: include: The hypersonic carbon dioxide nozzle is designed to consist of three parts: an expansion section, a throat, and a contraction section; the contraction section is defined by a straight line plus a circular arc curve. The expansion section is defined by a circular arc and a straight line; the circular arc that smoothly connects the contraction section and the expansion section yields the conical nozzle curve; the connection between the contraction section and the expansion section is the throat. The nozzle throat diameter is calculated from the equivalent specific heat ratio and numerical values; The throat diameter is determined by the design Mach number Ma and the outlet area A and the throat area A. ratio The total temperature T0 and total pressure P0 of the nozzle stagnation chamber determine that when the total temperature of the nozzle stagnation chamber is less than 1400K, carbon dioxide in the stagnation chamber will not undergo a chemical reaction. First, design a carbon dioxide conical nozzle, assuming a specific heat ratio of... , The initial value is 1.25; determined by the Mach number Ma and the exit area. With larynx area ratio Relationship (1) determines the initial throat diameter of the nozzle. : （1） Initial throat diameter of nozzle and export area Design the expansion segment, the maximum expansion angle of the expansion segment is: ; The value range is 8°-16°; When the equation of the circular arc curve of the contraction segment is: （2） In the formula, For coefficients; The radius of curvature of the larynx; The coordinates of the contracted segment; The radius of the larynx is given by the area of ​​the larynx. Calculated; The intersection point of the above circular arc curve and the straight line of the contraction segment for: （3） The angle is half the angle of the contracted straight line, ranging from 25° to 50°; Solve the Navier-Stokes equations and numerically simulate the designed carbon dioxide conical nozzle to obtain the specific heat ratio of the nozzle flow field, the Mach number at the nozzle exit, and the Pitot pressure; analyze the specific heat ratio of the nozzle flow field and the Mach number at the exit. Iterate through formulas (1) to (3), modify the heat ratio value according to the actual situation, regenerate a new carbon dioxide conical nozzle, and perform numerical calculations until the deviation between the designed Mach number and the calculated Mach number is less than 0.1, and obtain the nozzle throat radius. and specific heat ratio ; The expansion segment is determined by the method of characteristics and numerical verification; The expansion section profile is designed using the method of characteristics. The specific heat ratio used in the method of characteristics is... The nozzle throat radius is .

2. The hypersonic carbon dioxide profile nozzle design method according to claim 1, characterized in that: When designing nozzles using the method of characteristics, the characteristic line equations and compatibility relations are written in the form of finite difference equations. The position coordinates of the grid points are determined by the difference equations of the characteristic lines, and the flow parameters at the grid points are determined by the difference equations of the compatibility relations. For an ideal gas with supersonic steady, irrotational, axisymmetric flow, the characteristic line equations and compatibility equations are divided into right-hand and left-hand parts. Given the parameters at points 1 and 2, the left-hand characteristic line emanating from point 1 intersects the right-hand characteristic line emanating from point 2 at point 3.

3. The hypersonic carbon dioxide profile nozzle design method according to claim 2, characterized in that: The right-hand characteristic lines and their compatibility relationships are as follows: （4） （5） In the formula, For Pruntmeyer Point; This refers to the airflow deflection angle; Mach angle; , Let the coordinates be the points; The subscripts 1, 2, and 3 represent point 1, point 2, and point 3, respectively. For compensation amount, ; For right-moving feature lines and The included angle; The left-hand characteristic lines and their compatibility relationships are as follows: （6） （7） in, For compensation amount, ; For left-side feature lines and The included angle; After calculating the inviscid profile of the nozzle using the method of characteristics, the KAMAN momentum integral equation method is then selected for boundary layer correction to complete the initial design of the expansion section profile.

4. The hypersonic carbon dioxide profile nozzle design method according to claim 3, characterized in that: The contraction section is designed using formulas (1) to (3) and smoothly connected to the expansion section using formulas (4) to (7). Numerical calculations are then performed. The design is complete when the deviation between the calculated nozzle exit Mach number and the designed Mach number is less than 0.

1. The throat radius is changed when the deviation is greater than or equal to 0.

1. The process is iterated until the deviation between the calculated nozzle exit Mach number and the design Mach number is less than 0.1, at which point the design is complete.

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