A high-temperature dielectric equivalent modeling method of a hypersonic vehicle radome

Abstract

The application belongs to the technical field of antenna covers, and particularly relates to a high-temperature dielectric equivalent modeling method of a hypersonic aircraft antenna cover. The application fully considers the complex temperature gradient distribution existing in the streamline antenna cover from the top to the bottom of the cover body, from the outer surface to the inner surface of the cover body and the like. Meanwhile, the change of the heat conductivity coefficient of the cover body material with temperature is also considered, so that the high-temperature dielectric equivalent model built by the application is more accurate. The application can accurately perform high-temperature dielectric equivalent modeling on the streamline antenna cover at any flight height in the atmosphere and at any high Mach number flight state before ablation, so as to make up for the lack of precision of the existing high-temperature dielectric equivalent modeling method of the streamline antenna cover, and further provide a basis for high-temperature electric performance calculation and design of the streamline antenna cover.

Description

Technical Field

[0001] This invention belongs to the field of radome technology, specifically relating to a high-temperature dielectric equivalent modeling method for hypersonic vehicle radomes. Background Technology

[0002] Hypersonic vehicles are aircraft that fly at speeds of Mach 5 or higher within or across the atmosphere. Under prolonged operating conditions, the streamlined radome at the very tip of a hypersonic vehicle is subjected to intense aerodynamic heating. This high temperature causes changes in the dielectric parameters of the radome material, leading to a deterioration in the radome's electrical performance and consequently affecting the guidance performance of the seeker antenna.

[0003] Testing the electrical performance of radomes under hypersonic conditions is generally difficult, making theoretical calculations essential. An accurate high-temperature dielectric equivalent model is key to performing high-temperature electrical performance calculations.

[0004] Currently, for high-temperature dielectric equivalent modeling of streamlined radomes, one approach involves partitioning the radome into sections and approximating them as locally planar radomes. Since planar radomes only exhibit a one-dimensional temperature gradient distribution from the inside out, while streamlined radomes have a more complex temperature distribution with gradients from top to bottom and from the outer to the inner surface, this method has significant errors. Another approach approximates the temperature gradient distribution from the outer to the inner surface as a linear distribution based on the surface temperature data. However, this differs significantly from the actual operating temperature distribution, also introducing errors. Furthermore, due to the large temperature variation range at high Mach numbers, these methods do not consider material property changes (i.e., thermal conductivity variations with temperature), leading to temperature calculation errors. Therefore, there is currently no accurate method for high-temperature dielectric equivalent modeling of streamlined radomes. Summary of the Invention

[0005] To address the aforementioned problems and shortcomings, and to overcome the lack of accuracy in existing high-temperature dielectric equivalent modeling methods for streamlined radomes, this invention provides a high-temperature dielectric equivalent modeling method for streamlined radomes of hypersonic vehicles. This method considers the changes in material properties caused by high temperatures when calculating the radome's temperature field, enabling high-temperature dielectric equivalent modeling of the radome at any flight altitude within the atmosphere and at any high Mach number before ablation. This provides a foundation for the calculation and design of the radome's high-temperature electrical performance.

[0006] A high-temperature dielectric equivalent modeling method for a streamlined radome of a hypersonic vehicle, the specific steps of which are as follows:

[0007] Step 1: Determine the material properties of the streamlined radome and the temperature field after aerodynamic heating reaches a steady state. The material properties of the radome are considered in terms of thermal conductivity. When the radome temperature varies over a large range, the thermal conductivity of the material will change with temperature. At zero angle of attack, aerodynamic heating creates temperature gradients primarily in two directions: from the top to the bottom of the radome, and from the outer surface to the inner surface. At a specific velocity, aerodynamic heating reaches a steady state of temperature very rapidly; therefore, the steady-state temperature field of the radome can be calculated using a two-dimensional steady-state thermal conductivity differential equation. In a Cartesian coordinate system, the bottom of the radome is located on the xoy plane, with its center point coinciding with the origin of the coordinate system, and the top of the radome faces the positive z-axis. For the radome cross-section on the yoz plane, the temperature distribution along the y and z axes is calculated, yielding the following formula for the thermal conductivity differential equation of the radome temperature field:

[0008]

[0009] Where λ is the thermal conductivity of the cover material; T is the temperature.

[0010] Step 2: Determine the geometric region for calculation: Due to the symmetry of the streamlined radome, half of the radome wall cross section is taken as the geometric region for solving the heat conduction equation in Step 1.

[0011] Step 3: Determine the boundary conditions for the calculation: The streamlined radome's geometric region, as determined in Step 2, consists of four sides: the truncated boundary B1 at the center of the dome, the inner surface B2 of the radome, the bottom surface B3 of the radome, and the outer surface B4 of the radome (e.g., ...). Figure 2 As shown in the figure, there are a total of four boundary conditions.

[0012] a and B1 are assumed boundaries, not actual boundaries, therefore mandatory boundary conditions are required, expressed as:

[0013]

[0014] b and B2 are the inner surfaces of the radome. Due to the protective function of the radome, they are usually maintained at a low constant temperature, which is set here as T = 60℃.

[0015] c and B3 are the bottom of the radome, which can be approximated as a one-dimensional steady-state thermal boundary. The boundary conditions can be expressed as:

[0016]

[0017] d and B4 represent the outer surface of the radome, which is directly subjected to aerodynamic heating, representing a convective heat transfer boundary condition. Assuming the radome itself has no cooling and heat conduction to the outside is negligible, the boundary condition can be expressed as:

[0018]

[0019] ε is the emissivity of the cover material, σ is the Stephen-Boltzmann constant, and q a This refers to the heat flux density on the outer surface of the shield. After determining the flight speed and altitude, the local atmospheric parameters are obtained by consulting a standard atmospheric parameter table (the corresponding parameters are marked with subscripts "0"). ∞ The heat flux density on the outer surface of the cover is divided into stagnation point heat flux density q. a1 Heat flux density q in the stagnation zone a2 Heat flux density q in non-stationary regions a3 Stagnant heat flux density q a1 The simplified Lees formula is given as follows:

[0020]

[0021] Among them, R N The radius of the spherical head of the cover; at high temperatures, γ ∞ Take 1.4; γ is the specific heat of air at constant pressure, take γ = 1.4; heat flux density q in the stagnation region. a2 With stagnation heat flux density q a1 The relationship is represented as follows:

[0022]

[0023]

[0024] Where β is the angle between the radius line of the spherical head at the calculation point and the axis of the enclosure. In the non-stagnation region, the heat flux density is calculated based on the Ecker reference temperature method. First, the surface pressure coefficient is given by the Newtonian theory:

[0025]

[0026] Among them, Ma ∞ The Mach number of the incoming flow is represented, i.e., the flight speed; θ is the angle between the normal at the calculation point and the direction of the incoming flow. The airflow parameters after the shock wave are expressed as follows:

[0027]

[0028]

[0029]

[0030] Among them, P c ρ represents the pressure behind the shock wave. c θ represents the density after the shock wave. c This represents the shock wave angle. Based on this, the boundary layer parameters are expressed as follows:

[0031]

[0032]

[0033]

[0034]

[0035]

[0036]

[0037]

[0038] Among them, P δ ρ represents the boundary layer pressure. δ T represents the boundary layer density. δ Indicates the boundary layer temperature, ν δ h represents the boundary layer velocity. δ Ma represents the boundary enthalpy. δ h represents the boundary layer Mach number. s The total enthalpy is given. Finally, the heat flux density in the non-stagnation region of the outer surface of the shield is expressed as follows:

[0039]

[0040]

[0041]

[0042]

[0043]

[0044]

[0045]

[0046]

[0047] Among them, St * Represents the reference Stanton number; ρ * Reference airflow density; ν δ The velocity at the outer edge of the boundary layer; For reference specific heat at constant pressure, when the temperature is 550–2000 K, the coefficients in equation (22) are a0 = 874.687, a1 = 0.325431, and a2 = -2.07132 × 10⁻⁶. -5 a3 = -6.63386 × 10 -8 a4 = 2.66353 × 10 -11 When the temperature range is 273–550K, T r This represents the recovery temperature; α is the recovery coefficient, determined by the reference Prandtl number (denoted as Pr*) and the boundary layer state, with (Pr*) used for laminar flow. 1 / 2 Turbulent flow is represented by (Pr*). 1 / 3 .

[0048] μ * For the reference air viscosity coefficient, in equation (24), β S = 1.458 × 10⁻⁶ kg·m -1 ·s -1 ·K -1 / 2 S = 110.4K; k * T is the thermal conductivity of air. * Considering temperature as a parameter, for laminar flow:

[0049] T * =0.19T r +0.23T δ +0.58T (27)

[0050] For turbulent flow:

[0051] T * =0.22T r +0.28T δ +0.5T (28)

[0052] For laminar flow, the surface friction coefficient is... Blasius coefficient of friction, expressed as:

[0053]

[0054] For turbulent flow, when 5×10 5 <Re * <10 7 hour, The Prandtl friction coefficient is used.

[0055]

[0056] When Re * >10 7 hour, The Schultz-Grunow friction coefficient is used;

[0057]

[0058] In equations (29)-(31), Re * For reference to the Reynolds number, it is represented as:

[0059]

[0060] Where l represents the distance from the stagnation point along the surface of the cover to the calculation point.

[0061] After determining the boundary conditions B1, B2, B3, and B4 in steps 4 and 3, perform aerodynamic heating and two-dimensional steady-state temperature field calculations for the enclosure (e.g., using MATLAB coding).

[0062] Step 5: Based on the temperature field calculation results from Step 4, and combined with the temperature variation curves of the dielectric constant and loss tangent of the radome material, the radome is divided into layers. This yields the dielectric constant, loss tangent, and coordinates of the layer boundaries for each layer. Since temperature exhibits a gradient distribution, and dielectric parameters generally increase with increasing temperature, the dielectric parameters of each layer also show a gradient distribution, and the thickness of each layer is not constant.

[0063] Step 6: Using the layer coordinates and dielectric parameters of each layer obtained in Step 5, import the layer coordinate data into 3D modeling software to establish a variable thickness gradient dielectric layer model. Then, import the model into electromagnetic simulation software and input the dielectric parameters of each layer to complete the high-temperature dielectric equivalent modeling.

[0064] In summary, this invention fully considers the complex temperature gradient distribution that exists in the streamlined radome from top to bottom and from the outer surface to the inner surface. Simultaneously, it also considers the change in thermal conductivity of the radome material with temperature, making the high-temperature dielectric equivalent modeling method of this invention more accurate. This invention can accurately perform high-temperature dielectric equivalent modeling for streamlined radomes at any flight altitude within the atmosphere and at any high Mach number before ablation, overcoming the accuracy deficiencies of existing high-temperature dielectric equivalent modeling methods for streamlined radomes, and thus providing a foundation for the calculation and design of the high-temperature electrical performance of streamlined radomes. Attached Figure Description

[0065] Figure 1 This is a top view of the target radome in the embodiment.

[0066] Figure 2 This is a schematic diagram of the geometric region used for calculating the heat conduction equation in an example.

[0067] Figure 3 This is a graph showing the change in dielectric parameters of the cover material with temperature, as illustrated in the example.

[0068] Figure 4 The temperature distribution calculation results are for the example.

[0069] Figure 5 This is a model of the variable thickness gradient dielectric layer of the target radome in the embodiment;

[0070] Figure 6 This is a flowchart of the present invention;

[0071] Figure 7 This is a schematic diagram of β. Detailed Implementation

[0072] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0073] This embodiment uses Figure 1 The target radome shown is analyzed and modeled at four different flight speeds.

[0074] Step 1: Taking a tangential oval radome as an example, such as... Figure 1 As shown, the cover material is silicon nitride ceramic with a porosity of 46% and an emissivity of 0.6. For silicon nitride ceramic, in equation (1), its thermal conductivity λ is a function of temperature T and porosity P, where the relationship between thermal conductivity λ and porosity P is expressed as:

[0075]

[0076] The functional relationship between thermal conductivity λ and temperature T is as follows:

[0077] λ0 = 43.03e -T / 495.59 +15.64

[0078] This invention allows for the setting of material properties based on the different materials used in the cover.

[0079] Step 2: Determine the geometric region for calculating the heat conduction equation. Based on the contour of the enclosure, perform dense coordinate sampling on the geometric region. Figure 2 The extracted geometric region used for calculation;

[0080] Step 3: Determine boundary conditions, set the flight altitude to 20km, and the local atmospheric parameters are as follows: T ∞ =230K, P ∞ =5.4672×10 3 Pa, ρ ∞ =0.0879kg / m 3 ,ν ∞ = 295.0491 m / s. Flight speeds were set to Mach 5, Mach 6, Mach 6.5, and Mach 7. Boundary conditions were determined based on actual flight parameters to flexibly adapt to the aircraft's potentially varying flight altitude and speed.

[0081] Step 4: After determining the relevant parameters of the boundary conditions, perform temperature field calculations. The temperature field results are as follows: Figure 4 As shown, the results clearly demonstrate the temperature gradient distribution of the enclosure from top to bottom and from the outer surface to the inner surface during aircraft operation, providing a good foundation for accurate layered modeling in the next step.

[0082] Step 5: Obtain the dielectric parameters of each layer and the layer coordinates based on the temperature variation curve of the radome material.

[0083] Step 6: Based on the layered coordinate data, create a variable thickness gradient medium layer in 3D modeling software (such as SolidWorks). The model for different speeds is shown below. Figure 5 As shown, the model is then imported into electromagnetic simulation software, where the dielectric parameters of each layer are input to complete the dielectric equivalent model.

[0084] As can be seen from the above embodiments, this invention fully considers the complex temperature gradient distribution that exists in the streamlined radome from top to bottom and from outer to inner surfaces. Simultaneously, it also considers the change in thermal conductivity of the radome material with temperature, making the high-temperature dielectric equivalent modeling method of this invention more accurate. This invention can accurately perform high-temperature dielectric equivalent modeling for streamlined radomes at any flight altitude within the atmosphere and at any high Mach number before ablation, overcoming the accuracy deficiencies of existing high-temperature dielectric equivalent modeling methods for streamlined radomes, and thus providing a foundation for the calculation and design of the high-temperature electrical performance of streamlined radomes.

Claims

1. A high-temperature dielectric equivalent modeling method for a streamlined radome of a hypersonic vehicle, characterized in that, The specific steps are as follows: Step 1: Determine the material properties of the streamlined radome and the temperature field after aerodynamic heating reaches a steady state. The thermal conductivity of the material is taken into account. The steady-state temperature field of the radome is calculated using the two-dimensional steady-state thermal conductivity differential equation: In a spatial rectangular coordinate system, the bottom of the radome is located on the xoy plane, and the center point of the bottom coincides with the origin of the coordinate system. The top of the radome faces the positive z-axis. For the radome cross-section on the yoz plane, the temperature distribution along the y and z axes is calculated, and the thermal conductivity differential equation for the radome temperature field is obtained as follows: (1) Where λ is the thermal conductivity of the cover material; T is the temperature; Step 2: Determine the geometric region for calculation: Due to the symmetry of the streamlined radome, half of the radome wall cross section is taken as the geometric region for solving the heat conduction equation in Step 1. Step 3: Determine the boundary conditions for the calculation: The geometric region of the streamlined radome determined in step 2 consists of four sides, namely the truncated boundary B1 of the center of the sphere, the inner surface of the radome B2, the bottom surface of the radome B3, and the outer surface of the radome B4. Therefore, there are a total of four boundary conditions. a and B1 are assumed boundaries, not actual boundaries, therefore mandatory boundary conditions are required, expressed as: (2) b and B2 are the inner surfaces of the radome. Due to the protective function of the radome, the temperature here is set to T=60℃. c and B3 are the bottom of the radome, which can be approximated as a one-dimensional steady-state thermal boundary. The boundary conditions can be expressed as: (3) P is porosity; d and B4 represent the outer surface of the radome, which is directly subjected to aerodynamic heating, and are convective heat transfer boundary conditions. If the radome itself has no cooling and heat conduction to the outside is negligible, the boundary conditions can be expressed as: (4) ε is the emissivity of the cover material, σ is the Stephen-Boltzmann constant, and q a The heat flux density is the outer surface of the shield. After determining the flight speed and altitude, the local atmospheric parameters are obtained by consulting the standard atmospheric parameter table, with the corresponding parameters marked with subscripts. ∞ The heat flux density on the outer surface of the shield is divided into stagnation point heat flux density q. a1 Heat flux density q in the stagnation zone a2 Heat flux density q in non-stationary regions a3 ; Stagnant heat flux density q a1 The simplified Lees formula is given as follows: (5) Among them, R N The radius of the spherical head of the cover; at high temperatures, γ ∞ Take 1.4; γ is the specific heat of air at constant pressure, take γ=1.4; heat flux density q in the stagnation region. a2 With stagnation heat flux density q a1 The relationship is represented as follows: (6) (7) Where β is the angle between the radius line of the spherical head at the calculation point and the axis of the enclosure; in the non-stagnation region, the heat flux density is calculated based on the Ecker reference temperature method; firstly, the surface pressure coefficient is given by the Newtonian theory: (8) Among them, Ma ∞ The Mach number of the incoming flow is represented, i.e., the flight speed; θ is the angle between the normal at the calculation point and the direction of the incoming flow; the airflow parameters after the shock wave are expressed as follows: (9) (10) (11) Among them, P c ρ represents the pressure behind the shock wave. c θ represents the density after the shock wave. c The shock wave angle is represented; based on this, the boundary layer parameters are expressed as follows: (12) (13) (14) (15) (16) (17) (18) Among them, P δ ρ represents the boundary layer pressure. δ T represents the boundary layer density. δ Indicates the boundary layer temperature, ν δ h represents the boundary layer velocity. δ Ma represents the boundary enthalpy. δ h represents the boundary layer Mach number. s The total enthalpy; finally, the heat flux density in the non-stagnation zone on the outer surface of the shield is expressed as follows: (19) (20) (21) (22) (23) (24) (25) (26) Among them, St * Represents the reference Stanton number; ρ * Reference airflow density; ν δ The velocity at the outer edge of the boundary layer; For reference specific heat at constant pressure, when the temperature is 550~2000K, the coefficients in equation (22) are a0=874.687, a1=0.325431, a2=-2.07132×10 -5 a3 = -6.63386 × 10 -8 a4 = 2.66353 × 10 -11 When the temperature range is 273~550K, =1018.2 J / (kg·K); T r This represents the recovery temperature; α is the recovery coefficient, determined by the reference Prandtl number (Pr*) and the boundary layer state, with (Pr*) used for laminar flow. 1 / 2 Turbulent flow is represented by (Pr*). 1 / 3 μ * For the reference air viscosity coefficient, in equation (24), β S =1.458×10⁻⁶ kg·m -1 ·s -1 ·K -1 / 2 S=110.4K; k * T is the thermal conductivity of air. * Considering temperature as a parameter, for laminar flow: (27) For turbulent flow: (28) For laminar flow, the surface friction coefficient is... Blasius coefficient of friction, expressed as: (29) For turbulent flow, when 5×10 5 <Re * <10 7 hour, The Prandtl friction coefficient is used. (30) When Re * >10 7 hour, The Schultz-Grunow friction coefficient is used; (31) In equations (29)-(31), Re * For reference to the Reynolds number, it is represented as: (32) Where l represents the distance from the stagnation point along the surface of the enclosure to the calculation point; After the boundary conditions of B1, B2, B3 and B4 in steps 4 and 3 are determined, the aerodynamic heating and two-dimensional steady-state temperature field calculation of the cover are performed. Step 5: Based on the temperature field calculation results in Step 4, and combined with the temperature variation curves of the dielectric constant and loss tangent of the radome material, the radome is divided into layers. This yields the dielectric constant, loss tangent, and coordinates of the boundary lines of each layer. Since the temperature exhibits a gradient distribution, the dielectric parameters generally increase with increasing temperature. Therefore, the dielectric parameters of each layer also exhibit a gradient distribution, and the thickness of each layer is not constant. Step 6: Using the layer coordinates and dielectric parameters of each layer obtained in Step 5, import the layer coordinate data into 3D modeling software to establish a variable thickness gradient dielectric layer model. Then, import the model into electromagnetic simulation software and input the dielectric parameters of each layer to complete the high-temperature dielectric equivalent modeling.

2. The high-temperature dielectric equivalent modeling method for the streamlined radome of a hypersonic vehicle as described in claim 1, characterized in that: In step 4, MATLAB coding is used to perform pneumatic heating and two-dimensional steady-state temperature field calculation of the cover.

3. The high-temperature dielectric equivalent modeling method for the streamlined radome of a hypersonic vehicle as described in claim 1, characterized in that: In step 1, the cover material is silicon nitride ceramic with a porosity of 46% and an emissivity of 0.

6. For silicon nitride ceramic, in equation (1), its thermal conductivity λ is a function of temperature T and porosity P, where the relationship between thermal conductivity λ and porosity P is expressed as: The functional relationship between thermal conductivity λ and temperature T is as follows: 。

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