WO2023078475A1 - 一种基于三维正交机织复合材料的高超音速飞行器前缘热防护设计方法 - Google Patents

一种基于三维正交机织复合材料的高超音速飞行器前缘热防护设计方法 Download PDF

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WO2023078475A1
WO2023078475A1 PCT/CN2023/070104 CN2023070104W WO2023078475A1 WO 2023078475 A1 WO2023078475 A1 WO 2023078475A1 CN 2023070104 W CN2023070104 W CN 2023070104W WO 2023078475 A1 WO2023078475 A1 WO 2023078475A1
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leading edge
mrve
thermal conductivity
temperature
composite material
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毛军逵
屠泽灿
赵陈伟
陈雄斌
简辉
韩省思
王飞龙
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南京航空航天大学
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/15—Vehicle, aircraft or watercraft design
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2113/00—Details relating to the application field
    • G06F2113/26—Composites
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/08—Thermal analysis or thermal optimisation

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  • the invention belongs to the technical field of engineering thermophysics, and in particular relates to a design method for thermal protection of the leading edge of a hypersonic aircraft based on a three-dimensional orthogonally woven composite material.
  • thermal protection structures In order to achieve cutting-edge thermal protection design, researchers have developed a variety of CMC-based thermal protection structures. Among these thermal protection structures, one is a passive thermal protection structure, represented by a sandwich structure, to achieve thermal insulation. The other is an active thermal protection structure, which is represented by the introduction of coolant (Ferrari L, Barbato M, Esser B, et al. Sandwich structured ceramic matrix composites with periodic cellular ceramic cores: an active cooled thermal protection for space vehicles. Composite Structures 2016;154:61-68).
  • coolant Ferrari L, Barbato M, Esser B, et al. Sandwich structured ceramic matrix composites with periodic cellular ceramic cores: an active cooled thermal protection for space vehicles. Composite Structures 2016;154:61-68.
  • the complex structure of sandwich structures poses challenges for material fabrication and component weight control.
  • the introduction of coolant will consume additional energy of the hypersonic vehicle, because the non-air cooling system needs to carry external coolant, which is a burden for the hypersonic vehicle. Therefore
  • the fiber structure in CMC has a significant impact on the temperature distribution of CMC components.
  • the fibers inside CMC can be woven into different structures, which directly determines the thermal conductivity of CMC.
  • various woven fibers with different thermal conductivity can be used in CMC. In particular, some fibers have ultrahigh thermal conductivity greater than 600 W/(m K).
  • Previous research Glass DE. Ceramic Matrix Composite (CMC) Thermal Protection Systems (TPS) and Hot Structures for Hypersonic Vehicles.
  • thermal protection fiber structure designs directly consider the woven structure of the entire leading edge according to the maximum temperature at the stagnation point.
  • the designed braided structure only considers the maximum temperature of the stagnation point, which can meet the requirements of thermal protection design.
  • a large amount of expensive high-thermal-conductive fibers is required, which ultimately increases the manufacturing cost of leading-edge components.
  • the heat flow distribution at the leading edge is uneven, which makes the design contribute a lot to the heat dissipation at the stagnation point, but too much to the heat dissipation in other areas. Therefore, it is of great significance to improve the efficiency of thermal protection design by considering the uneven distribution of heat flow at the leading edge and establishing a reasonable woven structure design.
  • the present invention is aimed at the thermal protection requirements of hypersonic leading edge components. Considering that the introduction of coolant in the current thermal protection design will consume the extra energy of the hypersonic aircraft, the present invention proposes a hypersonic composite material based on three-dimensional orthogonally woven composite materials. Design method for aircraft leading edge thermal protection. This method reduces the temperature of the leading edge components through the optimization of the macroscopic temperature field of the three-dimensional orthogonally woven ceramic matrix composite leading edge components and the collaborative design of the mesoscopic woven structure. Effectively reduce the leading edge temperature without cooling measures. First, a multivariate linear regression model is established to find the theoretically optimized heat conduction configuration of the leading edge, so that the temperature of the leading edge components can be effectively reduced.
  • a design method for thermal protection of the leading edge of a hypersonic vehicle based on a three-dimensional orthogonally woven composite material comprising the following steps:
  • Step 1 Import the leading edge model into Comsol Multiphysics software, assign anisotropic thermophysical property parameters to the leading edge model and perform grid division, give heat flux boundary conditions to the outer surface of the leading edge model, and set temperature boundary conditions at the bottom to develop the temperature field The finite element calculation of the leading edge component under the initial conditions and the heat flux density field are obtained;
  • Step 2 According to the characteristics of the temperature field and heat flux density field obtained in Step 1, the leading edge structure is divided into different regions, and the leading edge heat dissipation model is obtained;
  • Step 3 Import the leading edge heat dissipation model obtained in step 2 into Comsol Multiphysics software, assign thermophysical parameters to different regions of the leading edge heat dissipation model, and repeat the operation of step 1, and at the same time make the thermophysical parameters within a certain range A set of data samples between the temperature of the leading edge and the thermal properties of the region at the corresponding temperature can be obtained;
  • Step 4 According to the data samples obtained in step 3 between the temperature of the front and the thermophysical properties of each region, a multivariate linear regression optimization model for the temperature of the front is established by means of linear regression. How to configure the thermal conductivity of each region in order to make the temperature of the leading edge components the lowest;
  • Step 5 According to the mesoscopic woven structure characteristics of the three-dimensional orthogonally woven material, a general calculation formula suitable for the calculation of the anisotropic thermal conductivity of the three-dimensional orthogonally woven ceramic matrix composite material with different weaving structures is established;
  • Step 6 According to the optimal thermal conductivity configuration obtained by the multivariable linear regression optimization model described in step 4, and the general calculation formula of thermal conductivity in geometric step 5, the material woven mesoscopic structure in different regions can be obtained to realize the thermal conductivity of the leading edge. Integrated co-design of shield design and material mesostructure to reduce the temperature of leading edge components;
  • the multivariate linear regression optimization model of the leading edge temperature is as follows:
  • T represents the maximum temperature of the leading edge
  • ⁇ represents the regression coefficient of each variable
  • ⁇ represents the residual error
  • En represents the n-dimensional identity matrix
  • X represents a matrix of variable values.
  • ⁇ 2 is the square difference.
  • T is the maximum temperature of the leading edge structure
  • ⁇ is the regression coefficient of the thermal conductivity of each region.
  • the general calculation formula for calculating the anisotropic thermal conductivity of different woven structures of the three-dimensional orthogonally woven ceramic matrix composite material is as follows:
  • ⁇ mrve,a ⁇ m v mrve,m + ⁇ f,a v mrve,f
  • D is the fiber diameter
  • L is the length of the representative unit.
  • the number of fibers in the X direction of the representative unit is: N xy ⁇ N xz
  • the number of fibers in the Y direction of the representative unit is: N yx ⁇ N yz
  • the number of fibers in the Z direction of the representative unit is: N zx ⁇ N zy
  • v mrve ,f represents the volume fraction of fibers in the unit cell
  • v mrve,m represents the volume fraction of the matrix in the unit cell
  • a represents the equivalent thermal conductivity of the unit cell in the axial direction
  • v mrve,m represents the transverse direction of the unit cell Equivalent thermal conductivity
  • ⁇ m represents the thermal conductivity of the fiber matrix, ⁇ p1,x , ⁇ p2,x , ⁇ p3,x , ⁇ p1,y , ⁇ p2, y , ⁇ p3,y
  • the present invention provides a thermal protection design method for the leading edge of a hypersonic aircraft based on three-dimensional orthogonally woven composite materials; first, a multivariable linear regression model is established to find the theoretically optimized heat conduction configuration of the leading edge, so that the temperature of the leading edge components was effectively reduced; secondly, a general calculation formula suitable for the calculation of the anisotropic thermal conductivity of different woven structures of three-dimensional orthogonally woven ceramic matrix composites was established, which is used to guide the mesoscopic weaving of three-dimensional orthogonally woven ceramic matrix composites.
  • the present invention reduces the temperature of the front part through the optimization of the macroscopic temperature field of the front part of the three-dimensional orthogonally woven ceramic matrix composite material and the collaborative design of the mesoscopic woven structure, and can effectively reduce the temperature of the front part without adding cooling measures.
  • the temperature of the leading edge realizes the design of the material of the leading edge part at the same time as the thermal protection design.
  • Figure 1 is a schematic diagram of the leading edge model and boundary conditions
  • Fig. 2 is a schematic diagram of the material structure and the partition of the leading edge before the temperature field optimization of the leading edge. Among them: (a) Schematic diagram of the material structure before the temperature field of the leading edge is not optimized, (b) Schematic diagram of the partition of the leading edge;
  • Figure 3 is a schematic diagram of the temperature field at the leading edge, (a) a schematic diagram of the temperature field at the leading edge without optimization, and (b) a schematic diagram of the temperature field at the leading edge after optimization;
  • Fig. 4 is the optimization schematic diagram of multiple linear regression temperature field
  • Fig. 5 is a schematic diagram of the weaving structure of a three-dimensional woven composite material
  • Fig. 6 is a schematic diagram of the weaving structure in each area of the leading edge after optimization
  • Figure 7 is the temperature distribution curve on the leading edge characteristic line before and after optimization.
  • the thermal protection design method for the leading edge of a hypersonic vehicle based on three-dimensional orthogonal woven composite materials is described.
  • the heat flux on the surface is 500W/m 2 , and at the same time, considering the heat radiation from the front surface to the environment, the surface emissivity ⁇ is 0.9, and the ambient temperature T ⁇
  • the same three-dimensional orthogonal woven composite material is used for the entire leading edge structure, as shown in Fig. 2(a).
  • the calculation of the temperature field at the leading edge mainly uses the steady-state solid heat transfer module in Comsol Multiphysics software. Through the calculation, the distribution of the temperature field at the leading edge before optimization can be obtained. As shown in Figure 3(a), the head and two shoulders of the leading edge High temperatures occur, especially in the head region up to 2800K.
  • the leading edge is divided into six regions as shown in Figure 2(b) during the optimization of the leading edge temperature field .
  • ⁇ z can vary from 100W/(m ⁇ K) to 150W/(m ⁇ K), and the thermal conductivity variable is brought into the following multivariable linear regression temperature optimization model to obtain the optimal heat conduction of each region Coefficient configuration in which the leading edge has the lowest temperature.
  • T represents the maximum temperature of the leading edge
  • ⁇ represents the regression coefficient of each variable
  • ⁇ represents the residual error
  • En represents the n-dimensional identity matrix
  • X represents a matrix of variable values.
  • ⁇ 2 is the square difference.
  • the schematic diagram of the woven structure of the three-dimensional orthogonal braided composite is shown in Fig. 5.
  • the material consists of woven fibers in three directions and a matrix material.
  • the thermal conductivity obtained by the optimized model is brought into the general calculation formula applicable to the calculation of the anisotropic thermal conductivity of different woven structures of three-dimensional orthogonally woven ceramic matrix composites established by the present invention, as follows: the material of each region can be obtained
  • the number of fibers in the three weaving directions is shown in Table 1.
  • ⁇ mrve,a ⁇ m v mrve,m + ⁇ f,a v mrve,f
  • ⁇ RVE,x is the thermal conductivity of the three-dimensional orthogonal material along the X direction
  • ⁇ RVE,y is the thermal conductivity of the three-dimensional orthogonal material along the Y direction
  • ⁇ RVE,z is the thermal conductivity of the three-dimensional orthogonal material along the Z direction.
  • the temperature of the leading edge components can be effectively reduced without introducing cooling measures, especially in the head region, and the temperature of the leading edge can be reduced by about 300K at most. around the temperature.

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Abstract

一种基于三维正交机织复合材料的高超音速飞行器前缘热防护设计方法，属于工程热物理技术领域，可以在不增加冷却措施的情况下有效降低前缘温度。该方法首先建立多变量线性回归模型，寻找前缘的理论优化导热配置，使得前缘部件温度得到有效降低；其次建立了适用于三维正交机织陶瓷基复合材料不同机织结构各向异性导热系数计算的通用计算公式，用于指导三维正交机织陶瓷基复合材料的介观机织结构；最后将多变量线性回归模型得到的优化结果与通用公式直接结合，设计出不同区域所需的介观机织结构，实现了前缘宏观温度优化与三维正交机织陶瓷基复合材料介观机织结构的协同设计。

Description

一种基于三维正交机织复合材料的高超音速飞行器前缘热防护设计方法 技术领域
本发明属于工程热物理技术领域，特别涉及一种基于三维正交机织复合材料的高超音速飞行器前缘热防护设计方法。
背景技术
随着高超声速飞行器以高马赫数飞行时，动能在前缘驻点处转化为内能，使头部区域温度急剧升高(Bull JD,Rasky DJ,Tran HK,et al.Material Response of Diboride Matrix Composites to Low Pressure Simulated Hypersonic Flows.NASA CP-3235 1994；Part 2(5):653-673.)。由于高超声速飞行器存在严重的气动加热，飞行器前缘的材料必须满足热防护要求。与传统材料相比，陶瓷基复合材料(CMC)具有优异的耐温性和高温力学性能，在高超声速应用中具有显著优势。然而，CMC在超高温(>2000K)环境中的氧化使其力学性能迅速下降。因此，热防护设计对高超音速带CMC前缘的安全稳定工作具有重要意义。
为了实现前沿的热防护设计，研究人员开发了多种基于CMC的热防护结构。在这些热防护结构中，一种是被动热防护结构，以夹层结构为代表，以实现隔热。另一种是主动热保护结构，其表现为引入冷却剂(Ferrari L,Barbato M,Esser B,et al.Sandwich structured ceramic matrix composites with periodic cellular ceramic cores:an active cooled thermal protection for space vehicles.Composite Structures 2016；154:61-68)。然而，夹层结构的复杂结构给材料制造和构件重量控制带来了挑战。冷却剂的引入将消耗高超声速飞行器的额外能量，因为非空气冷却系统需要携带外部冷却剂，这对高超声速飞行器来说是一个负担。因此，迫切需要在不引入额外挑战的情况下实现热防护设计。
除了上述宏观热结构外，CMC中的纤维结构对CMC部件的温度分布有重大影响。一方面，CMC内部的纤维可以编织成不同的结构，这直接决定了CMC的导热性。另一方面，具有不同导热性的各种机织纤维可用于CMC。特别是，一些纤维的超高导热系数大于600W/(m K)。先前的研究(Glass DE.Ceramic Matrix Composite(CMC)Thermal Protection Systems(TPS)and Hot Structures for Hypersonic Vehicles.15th AIAA International Space Planes and Hypersonic Systems and Technologies Conference:AIAA；2008)已经证明，具有高导热纤维的合理编 织结构将有助于前缘结构散热，避免部件过热，从而避免对高超音速飞行器造成额外负担。因此，采用这种方法进行热防护设计是有利的。
目前大多数的热防护纤维结构设计都是根据停滞点的最高温度直接考虑整个前缘的机织结构。所设计的编织结构只考虑了驻点的最高温度，可以满足热防护设计的要求。然而，基于这种设计，需要大量昂贵的高导热纤维，这最终会增加前沿组件的制造成本。同时，前缘热流分布不均匀，这使得设计对驻点处的散热贡献很大，但对其他区域的散热贡献过大。因此，考虑前缘热流分布不均匀的特点，建立合理的机织结构设计，对提高热防护设计的效率具有重要意义。
为了找到合理的前缘机织结构设计，需要确定具有不同机织结构的CMC的热导率值。目前，有一种方法可以估算三维正交编织CMC的热导率([18]
Lee SE,Yoo JS,Kang JH,et al.Prediction of the thermal conductivities of four-axial non-woven composites.Composite Structures 2009；89(2):262-269.)，但它适用于特定的三维正交编织结构。如果机织结构发生变化，则很难通过调整导热系数计算来获得相应结构的导热系数。因此，迫切需要建立一种有效的通用三维正交机织CMC导热系数计算方法。
发明内容
本发明针对高超音速前缘部件热防护的需求，考虑到目前热防护设计中冷却剂的引入将消耗高超声速飞行器的额外能，本发明提出了一种基于三维正交机织复合材料的高超音速飞行器前缘热防护设计方法，该方法通过三维正交机织陶瓷基复合材料前缘部件的宏观温度场优化和介观机织结构的协同设计来降低了前缘部件的温度，可以在不增加冷却措施的情况下有效降低前缘温度。首先，建立多变量线性回归模型，寻找前缘的理论优化导热配置，使得前缘部件温度得到有效降低。其次，建立了适用于三维正交机织陶瓷基复合材料不同机织结构各向异性导热系数计算的通用计算公式，用于指导三维正交机织陶瓷基复合材料的介观机织结构。最后，将多变量线性回归模型得到的优化结果与通用公式直接结合，设计出不同区域所需的介观机织结构，实现了前沿宏观温度优化与三维正交机织陶瓷基复合材料介观机织结构的协同设计。
为实现上述目的，本发明采用的技术方案为：
一种基于三维正交机织复合材料的高超音速飞行器前缘热防护设计方法，包括以下步骤：
步骤一：将前缘模型导入Comsol Multiphysics软件，对前缘模型进行各向异性热物性参数赋值并进行网格划分，对前缘模型外表面给热流密度边界条件，底部给定温边界条件开展温度场的有限元计算，获得初始条件下前缘部件的温度场以及热流密度场；
步骤二：根据步骤一中获取的温度场以及热流密度场特征，将前缘结构划分为不同的区域，得到前缘热疏导模型；
步骤三：将步骤二得到的前缘热疏导模型导入Comsol Multiphysics软件，对所述前缘热疏导模型不同区域进行热物性参数赋值，并重复步骤一的操作，同时使得热物性参数在一定范围内变化，即可得到一组前缘温度与对应温度下区域热物性之间的数据样本；
步骤四：根据步骤三得到的前缘温度与各区域热物性之间的数据样本，通过线性回归的方法，建立起前缘温度多变量线性回归优化模型，通过该模型可以得到在一定导热系数范围内，每个区域导热系数该如何配置，才能使得前缘部件温度最低；
步骤五：根据三维正交机织材料的介观机织结构特征，建立一个适用于三维正交机织陶瓷基复合材料不同机织结构各向异性导热系数计算的通用计算公式；
步骤六：根据步骤四中所述多变量线性回归优化模型得到的最优导热系数配置，几何步骤五的导热系数通用计算公式，即可得到不同区域的材料机织介观结构，实现前缘热防护设计和材料介观结构的一体化协同设计，以降低前缘部件的温度；
所述步骤四中，前缘温度多变量线性回归优化模型如下式：
Figure PCTCN2023070104-appb-000001
Figure PCTCN2023070104-appb-000002
ε＝(ε 1 ... ε n) T
β＝(β 0 β 1 ... β m) T＝(β 0 ... β xx-i β yy-i βz z-i ...) T,i＝1,2,...,6
其中T表示前缘最高温度，β表示各变量的回归系数，ε为残差，En为n介单位矩阵。X表示变量值矩阵。σ 2为平方差。
表1 各变量回归系数值
Figure PCTCN2023070104-appb-000003
其中T为前缘结构最高温度，β为各区域导热系数的回归系数。
所述步骤五中，三维正交机织陶瓷基复合材料不同机织结构各向异性导热系数计算的通用计算公式，如下式：
Figure PCTCN2023070104-appb-000004
v mrve,m＝1-v mrve,f
λ mrve,a＝λ mv mrve,m+λ f，av mrve,f
Figure PCTCN2023070104-appb-000005
λ p1,x＝λ mrve,a
λ p2,x＝λ mrve,t
λ p3,x＝λ m
Figure PCTCN2023070104-appb-000006
λ p1,y＝λ mrve,t
λ p2,y＝λ mrve,a
λ p3,y＝λ m
Figure PCTCN2023070104-appb-000007
Figure PCTCN2023070104-appb-000008
λ p1,z＝λ mrve,t
λ p2,z＝λ mrve,t
λ p3,z＝λ m
Figure PCTCN2023070104-appb-000009
Figure PCTCN2023070104-appb-000010
λ p4,x＝λ mrve,a
λ p5,x＝λ mrve,t
λ p6,x＝λ m
Figure PCTCN2023070104-appb-000011
λ p4,y＝λ mrve,t
λ p5,y＝λ mrve,t
λ p6,y＝λ m
Figure PCTCN2023070104-appb-000012
Figure PCTCN2023070104-appb-000013
λ p4,z＝λ mrve,t
λ p5,z＝λ mrve,a
λ p6,z＝λ m
Figure PCTCN2023070104-appb-000014
Figure PCTCN2023070104-appb-000015
Figure PCTCN2023070104-appb-000016
Figure PCTCN2023070104-appb-000017
Figure PCTCN2023070104-appb-000018
其中：D为纤维直径，L为代表单元的长度。代表单元X方向上的纤维数目为：N xy×N xz,代表单元Y方向上的纤维数目为：N yx×N yz,代表单元Z方向上的纤维数目为：N zx×N zy，v mrve,f表示单胞单元中纤维的体积分数，v mrve,m表示单胞单元中基体的体积分数，λ mrve,a表示单胞轴向的等效导热系数，v mrve,m表示单胞的横向等效导热系数，λ m表示纤维的基体的导热系数，λ p1,x、λ p2,x、λ p3,x、λ p1,y、λ p2,y、λ p3,y、λ p1,z、λ p2,z、λ p3,z分别表示典型代表单元中层I区域p1、p2、p3沿X、Y、Z3个方向的等效导热系数，λ I,x、λ I,y、λ I,z分别表示典型代表单元中层I沿X、Y、Z3个方向的等效导热系数，λ p4,x、λ p5,x、λ p5,x、λ p4,y、λ p5,y、λ p6,y、λ p4,z、λ p5,z、λ p6,z分别表示典型代表单元中层II区域p4、p5、p6沿X、Y、Z3个方向的等效导热系数，λ II,x、λ II,y、λ II,z分别表示典型代表单元中层II沿X、Y、Z3个方向的等效导热系数，λ RVE,x为三维正交材料沿X方向的导热系数，λ RVE,y为三维正交材料沿Y方向的导热系数，λ RVE,z为三维正交材料沿Z方向的导热系数。
有益效果：本发明提供了一种基于三维正交机织复合材料的高超音速飞行器前缘热防护设计方法；首先建立多变量线性回归模型，寻找前缘的理论优化导热配置，使得前缘部件温度得到有效降低；其次建立了适用于三维正交机织陶瓷基复合材料不同机织结构各向异性导热系数计算的通用计算公式，用于指导三维正 交机织陶瓷基复合材料的介观机织结构；最后将多变量线性回归模型得到的优化结果与通用公式直接结合，设计出不同区域所需的介观机织结构，实现了前沿宏观温度优化与三维正交机织陶瓷基复合材料介观机织结构的协同设计。本发明通过三维正交机织陶瓷基复合材料前缘部件的宏观温度场优化和介观机织结构的协同设计来降低了前缘部件的温度，能够可以在不增加冷却措施的情况下有效降低前缘温度，在热防护设计的同时实现了对前缘部件材料的设计。
附图说明
图1为前缘模型及边界条件示意图；
图2为前缘未温度场优化前材料结构以及前缘分区示意图。其中：(a)前缘温度场未优化前材料结构示意图，(b)前缘分区示意图；
图3为前缘温度场示意图，(a)前缘未优化温度场示意图，(b)前缘优化后温度场示意图；
图4为多元线性回归温度场优化示意图；
图5为三维机织复合材料机织结构示意图；
图6为优化后前缘各区域机织结构示意图；
图7为优化前后前缘特征线上温度分布曲线。
具体实施方式
下面结合附图和具体实施例对本发明作更进一步的说明。
实施例1
以某高超音速飞行器前缘为例阐述基于三维正交机织复合材料的高超音速飞行器前缘热防护设计方法，如图1所示，前缘结构的几何特征以及计算边界条件；前缘主要由两部分组成：激波针和肩部；激波针驻点区域为半球形，直径Ds＝50mm，冲击波针的长度Ls＝75mm，前缘的长度Ll＝300mm，前缘宽度Wl＝250mm，前缘高度Hl＝85mm，驻点区域具有最强的气动加热，热通量5000KW/m2，肩部区域的热通量为3000KW/m 2，前缘底部设置为恒温边界，T＝293.15K，其他表面的热通量为500W/m 2，同时，考虑了前缘表面对环境的热辐射，表面发射率ε为0.9，环境温度为T ∞是293.15K。
未优化前，整个前缘结构都使用的同一种三维正交机织复合材料，如图2(a)所示。在该机制结构下材料3个方向上的导热系数λx＝λ ν＝λz＝176W/(m·K)。前缘 温度场计算主要采用Comsol Multiphysics软件中的稳态固体传热模块，通过计算可以得到未优化前，前缘温度场分布，如图3(a)所示，前缘的头部和两肩出现高温，尤其在头部区域温度高达2800K。
根据未优化前的前缘温度场分布，在前缘温度场优化时将前缘划分为如图2(b)所示的6个区域，在优化时每个区域的导热系数λx、λ ν、λz可以在100W/(m·K)达150W/(m·K)之间变化，将导热系数变量带入到如下的多变量线性回归温度优化模型中，即可得到每个区域的最优导热系数配置，在该配置下前缘具有最低温度。
Figure PCTCN2023070104-appb-000019
Figure PCTCN2023070104-appb-000020
ε＝(ε 1 ... ε n) T
β＝(β 0 β 1 ... β m) T＝(β 0 ... β xx-i β yy-i βz z-i ...) T,i＝1,2,...,6
Figure PCTCN2023070104-appb-000021
其中T表示前缘最高温度，β表示各变量的回归系数，ε为残差，En为n介单位矩阵。X表示变量值矩阵。σ 2为平方差。
多变量线性回归温度优化模型下每个区域导热系数变化与前缘温度的关系如图4所示，多变量线性回归温度优化模型给出的每个区域导热系数配置如表1所示：
表1 每个区域导热系数配置
Figure PCTCN2023070104-appb-000022
Figure PCTCN2023070104-appb-000023
三维正交编织复合材料的机织结构示意图，如图5所示。材料由三个方向上的机织纤维和基体材料组成。为了制造出满足各个区域所需导热系数的三维正交复合材料，则需要调整材料三个方向上的纤维数目比。将优化模型得到的导热系数带入到本发明建立的适用于三维正交机织陶瓷基复合材料不同机织结构各向异性导热系数计算的通用计算公式，如下式：即可得到每个区域材料在三个编织方向上的纤维数目，如表1所示。
Figure PCTCN2023070104-appb-000024
v mrve,m＝1-v mrve,f
λ mrve,a＝λ mv mrve,m+λ f，av mrve,f
Figure PCTCN2023070104-appb-000025
λ p1,x＝λ mrve,a
λ p2,x＝λ mrve,t
λ p3,x＝λ m
Figure PCTCN2023070104-appb-000026
λ p1,y＝λ mrve,t
λ p2,y＝λ mrve,a
λ p3,y＝λ m
Figure PCTCN2023070104-appb-000027
Figure PCTCN2023070104-appb-000028
λ p1,z＝λ mrve,t
λ p2,z＝λ mrve,t
λ p3,z＝λ m
Figure PCTCN2023070104-appb-000029
Figure PCTCN2023070104-appb-000030
λ p4,x＝λ mrve,a
λ p5,x＝λ mrve,t
λ p6,x＝λ m
Figure PCTCN2023070104-appb-000031
λ p4,y＝λ mrve,t
λ p5,y＝λ mrve,t
λ p6,y＝λ m
Figure PCTCN2023070104-appb-000032
Figure PCTCN2023070104-appb-000033
λ p4,z＝λ mrve,t
λ p5,z＝λ mrve,a
λ p6,z＝λ m
Figure PCTCN2023070104-appb-000034
Figure PCTCN2023070104-appb-000035
Figure PCTCN2023070104-appb-000036
Figure PCTCN2023070104-appb-000037
Figure PCTCN2023070104-appb-000038
其中：λ RVE,x为三维正交材料沿X方向的导热系数，λ RVE,y为三维正交材料沿Y方向的导热系数，λ RVE,z为三维正交材料沿Z方向的导热系数。
综上即实现前缘宏观温度优化与三维正交机织陶瓷基复合材料介观机织结构的协同设计，整个前缘在传热优化后不同区域的材料机织结构如图6所示，其中区域1为前缘激波针的半球区，区域2为前缘激波针的圆柱区域，区域3为激波针与肩部的连接区域，区域4为前缘两侧的肩部区域，区域5为两肩部区域的中间区域，区域6为前缘的底部区域。从图7前缘特征线上的温度分布曲线可以看出，基于本发明方法可以在不引入冷却措施的情况下有效降低前缘部件的温度， 尤其在头部区域，最多可以减低前缘约300K左右的温度。
以上所述仅是本发明的优选实施方式，应当指出：对于本技术领域的普通技术人员来说，在不脱离本发明原理的前提下，还可以做出若干改进和润饰，这些改进和润饰也应视为本发明的保护范围。

Claims (3)

  1. 一种基于三维正交机织复合材料的高超音速飞行器前缘热防护设计方法，其特征在于，包括以下步骤：
    步骤一：将前缘模型导入Comsol Multiphysics软件，对前缘模型进行各向异性热物性参数赋值并进行网格划分，对前缘模型外表面给热流密度边界条件，底部给定温边界条件开展温度场的有限元计算，获得初始条件下前缘部件的温度场以及热流密度场；
    步骤二：根据步骤一中获取的温度场以及热流密度场特征，将前缘结构划分为不同的区域，得到前缘热疏导模型；
    步骤三：将步骤二得到的前缘热疏导模型导入Comsol Multiphysics软件，对所述前缘热疏导模型不同区域进行热物性参数赋值，并重复步骤一的操作，同时使得热物性参数在一定范围内变化，即可得到一组前缘温度与对应温度下区域热物性之间的数据样本；
    步骤四：根据步骤三得到的前缘温度与各区域热物性之间的数据样本，通过线性回归的方法，建立起前缘温度多变量线性回归优化模型，通过该模型可以得到在一定导热系数范围内，每个区域导热系数该如何配置，才能使得前缘部件温度最低；
    步骤五：根据三维正交机织材料的介观机织结构特征，建立一个适用于三维正交机织陶瓷基复合材料不同机织结构各向异性导热系数计算的通用计算公式；
    步骤六：根据步骤四中所述多变量线性回归优化模型得到的最优导热系数配置，几何步骤五的导热系数通用计算公式，即可得到不同区域的材料机织介观结构，实现前缘热防护设计和材料介观结构的一体化协同设计，以降低前缘部件的温度。
  2. 根据权利要求1所述的基于三维正交机织复合材料的高超音速飞行器前缘热防护设计方法，其特征在于，步骤四中前缘温度多变量线性回归优化模型如下式：
    Figure PCTCN2023070104-appb-100001
    Figure PCTCN2023070104-appb-100002
    ε＝(ε 1 … ε n) T
    β＝(β 0 β 1 … β m) T＝(β 0 … β xx-i β yy-i β zz-i …) T,i＝1,2,…,6
    其中T表示前缘最高温度，β表示各变量的回归系数，ε为残差，En为n介单位矩阵。X表示变量值矩阵。σ 2为平方差。
    表1各变量回归系数值
    Figure PCTCN2023070104-appb-100003
    其中T为前缘结构最高温度，β为各区域导热系数的回归系数。
  3. 根据权利要求1所述的基于三维正交机织复合材料的高超音速飞行器前缘热防护设计方法，其特征在于，步骤五中三维正交机织陶瓷基复合材料不同机织结构各向异性导热系数计算的通用计算公式，如下式：
    Figure PCTCN2023070104-appb-100004
    v mrve,m＝1-v mrve,f
    λ mrve,a＝λ mv mrve,m+λ f，av mrve,f
    Figure PCTCN2023070104-appb-100005
    λ p1,x＝λ mrve,a
    λ p2,x＝λ mrve,t
    λ p3,x＝λ m
    Figure PCTCN2023070104-appb-100006
    λ p1,y＝λ mrve,t
    λ p2,y＝λ mrve,a
    λ p3,y＝λ m
    Figure PCTCN2023070104-appb-100007
    Figure PCTCN2023070104-appb-100008
    λ p1,z＝λ mrve,t
    λ p2,z＝λ mrve,t
    λ p3,z＝λ m
    Figure PCTCN2023070104-appb-100009
    Figure PCTCN2023070104-appb-100010
    λ p4,x＝λ mrve,a
    λ p5,x＝λ mrve,t
    λ p6,x＝λ m
    Figure PCTCN2023070104-appb-100011
    λ p4,y＝λ mrve,t
    λ p5,y＝λ mrve,t
    λ p6,y＝λ m
    Figure PCTCN2023070104-appb-100012
    Figure PCTCN2023070104-appb-100013
    λ p4,z＝λ mrve,t
    λ p5,z＝λ mrve,a
    λ p6,z＝λ m
    Figure PCTCN2023070104-appb-100014
    Figure PCTCN2023070104-appb-100015
    Figure PCTCN2023070104-appb-100016
    Figure PCTCN2023070104-appb-100017
    Figure PCTCN2023070104-appb-100018
    其中：D为纤维直径，L为代表单元的长度。代表单元X方向上的纤维数目为：N xy×N xz,代表单元Y方向上的纤维数目为：N yx×N yz,代表单元Z方向上的纤维数目为：N zx×N zy，v mrve,f表示单胞单元中纤维的体积分数，v mrve,m表示单胞单元中基体的体积分数，λ mrve,a表示单胞轴向的等效导热系数，v mrve,m表示单胞的横向等效导热系数，λ m表示纤维的基体的导热系数，λ p1,x、λ p2,x、λ p3,x、λ p1,y、λ p2,y、λ p3,y、λ p1,z、λ p2,z、λ p3,z分别表示典型代表单元中层I区域p1、p2、p3沿X、Y、Z3个方向的等效导热系数，λ I,x、λ I,y、λ I,z分别表示典型代表单元中层I沿X、Y、Z3个方向的等效导热系数，λ p4,x、λ p5,x、λ p5,x、λ p4,y、λ p5,y、λ p6,y、λ p4,z、λ p5,z、λ p6,z分别表示典型代表单元中层II区域p4、p5、p6沿X、Y、Z3个方向的等效导热系数，λ II,x、λ II,y、λ II,z分别表示典型代表单元中层II沿X、Y、Z3个方向的等效导热系数，λ RVE,x为三维正交材料沿X方向的导热系数，λ RVE,y为三维正交材料沿Y方向的导热系数，λ RVE,z为三维正交材料沿Z方向的导热系数。
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