Design and analysis of thermal protection and load-bearing integrated structure of the telescopic wing

Abstract

A novel three-layer integrated structure was designed to meet the thermal-insulation and load-bearing requirements of high-speed telescopic wing aircraft. The structure consists of heat shield layer, load-bearing skeleton, and pyramid lattice structure filled with aerogel to achieve the insulation function. Sensitivity analysis of the design parameters and optimal design of the integrated structure was carried out, and the structure was optimized by using response surface method. Compared to the initial structure, the optimized structure has an equivalent thermal conductivity of 0.0276, reduced by 40%, and a relative density of $685.5 kg / m^{3}$ , reduced by 3.7%. And it has a thermal conductivity that is over 20% lower than that of ceramic insulating tiles. Then, the integrated structure was regarded as a homogeneous plate, and the equivalent mechanical and thermal parameters were determined and verified by simulation and experimental results. The equivalence error was controlled within 10%. Finally, a simulation model of the telescopic wing was established. The result shows that the maximum deformation under 20 kPa surface pressure is 3.96 mm. The temperature resistance of the structure surface is up to 1500°C, and the wing internal temperature is controlled within 200°C after 1200 s of thermal loading. The results verified that the integrated structure meets the requirement of a high-speed telescopic wing.

Keywords

Telescopic wing thermal insulation-bearing integration lattice structure force/thermal coupling analysis

Introduction

In order to improve flight efficiency, maneuverability, and multi-task adaptability, aircraft should have a larger flight envelope, and its wings should adapt to complex flight tasks with the best aerodynamic shape.¹ Fixed-wing aircraft are unable to translate into several geometrical shapes to meet different missions. There are many existing morphing wing concepts, such as variable-wing sweep, variable span, and chord morphing.^2–5 Among them, the span morphing concepts have been studied and explored for several decades abroad and are one of the main development directions of morphing wing aircraft technology. When the moving panel extends outside the fixed panel, the aspect ratio increases accordingly, which can improve the whole aircraft’s lift-drag ratio and the aircraft’s endurance performance. Therefore, the telescopic wing can effectively change its aerodynamic characteristics, adapt to different flight states, and meet a variety of mission requirements.

Many existing studies focus on the innovative deformation mechanism, which is designed to realize the deformation function of UAVs.^6–8 However, during the long, high-speed flight, the maximum heat flux of the leading edge of the wing can reach $100 W / c m^{2}$ .⁹ Severe aerodynamic heating will cause surface temperature increases drastically. As a result, the outer surface of the skin needs to withstand a high temperature of nearly 2000 K. Meanwhile, the aerodynamic load borne by the skin can reach 20 kPa in high-speed environment. Since the fixed panel is hollow inside to accommodate the moving panel, there is no spar or rib to support the skin. Therefore, the telescopic wing structure requires the ability of thermal protection and load-bearing simultaneously.Thermal protection has become one of the bottleneck problems restricting high-speed aircraft development.¹¹ At present, the thermal protection system of high-speed aircraft is mainly divided into active,^12,13 semi-active,^14,15 and passive type.^16,17 Active and semi-active cooling techniques have excellent thermal protection performance, but the relatively complex structure and unsatisfactory reusability preclude their application to the telescopic wing. Passive thermal protection by the material and structure itself to withstand and insulate heat. For example, fiber insulation mats, ceramic matrix composite thermal protection system (TPS), metal TPS, etc., have been widely studied and applied. The thermal protection system has gradually developed from a single-functional component to a multi-functional integration to enable the aircraft to obtain more payload and design space. Integrated thermal protection system (ITPS), which includes load-bearing and thermal protection functions, has received attention due to its high structural efficiency.^18,19 The key advantage of ITPS is that the sandwich structure can be used as the bearing structure and container of the thermal insulation filler material.²⁰ Since it has high porosity and the mesostructure can be optimized, lattice structure can achieve higher specific strength/stiffness.²¹ And its application scenario includes jet blast deflector,²² reusable launch vehicles,²³ hypersonic vehicles,²⁴ etc. Metal and resin-based fiber composite lattice structures have been designed and analyzed extensively.^25–27 Figure 1 shows core structures in sandwich panels, includes honeycomb,²⁸ tetrahedral,²⁹ pyramidal,^30,31 Kagome,²² woven textile, etc. At low relative density, pyramidal lattices are competitive with honeycombs because slender columns have superior buckling resistance to thin sheets.³² Figure 2 shows the normalized strength variation with relative density for cellular metals.

Figure 1.

Example of sandwich panels cored.¹⁰

Figure 2.

Normalized strength variation with relative density for cellular metals.³²

Focus on the design requirements of high-speed telescopic wing aircraft, and this paper researched a novel three-layer thermal-protect and load-bearing integrated structure combining a lightweight lattice structure and aerogel insulation layer. And structural parameters such as pillar diameter and pillar angle were analyzed and optimized. The theoretical derivation and simulation analysis of the mechanical and thermal properties of the structure was carried out, and experimental verification was carried out. The structure was homogenized and equivalent to a simplified FEA model, and thermal structurall coupled simulations of the telescopic wing system were completed to verify the effectiveness of the integrated structure. The flow chart of methodology is shown in Figure 3.

Figure 3.

Flow chart of methodology.

Integrated structure design of thermal insulation and bearing capacity for telescopic wing

Configuration design of telescopic wing of high-speed aircraft

Based on the given aerodynamic shape, the telescopic wing of high-speed aircraft is designed, shown in Figure 4. The telescopic wing is driven in parallel by multiple motors, and the ball screw is used for linear transmission. Several guide rails are arranged inside the fixed panel of the telescopic wing, and the ball screw nut is connected to the telescopic wing. The ball screw nut can drive the telescopic wing to move straight along the guide rail and extend or withdraw the moving panel. In addition, load-bearing and thermal-protection structures are designed for thermal and aerodynamic load. In the current aviation industry, the aircraft wing is generally designed as a “skeleton + skin” thin-walled stiffened structure. This load-bearing structure has a high utilization efficiency of materials, can greatly reduce the weight of the wing structure, and to a certain extent, avoid the wing buckling instability caused by structural failure. However, under the contraction state, the fixed panel needs to accommodate the moving panel internally, resulting in the existence of cavities in the structure, and the wing beam and wing ribs cannot be arranged. And the skin structure should not be thin to avoid a large step on the skin surface which affect the aerodynamic performance dramatically.

Figure 4.

Schematic diagram of telescopic wing.

Regarding thermal load, during the long-term flight of high-speed aircraft, the friction between the wing surface and the high-speed airflow will produce a violent aerodynamic heating effect, which will cause the wing surface of the aircraft to heat up sharply. If it is not blocked, heat will be quickly transmitted to the cabin and the wing to produce a high-temperature environment of thousands of degrees Celsius, leading to the failure and destruction of most of the internal components, resulting in catastrophic consequences. Therefore, it is necessary to carry the appropriate thermal protection structure and materials on the aircraft’s surface to effectively protect the internal components. Therefore, the telescopic wing’s surface needs to have light weight, high efficiency, high-temperature resistance, and low thermal conductivity. It is necessary to design a thermal protection composite structure with thermal insulation and bearing integration.

Design of thermal-protect and load-bearing integrated structure

The lattice structure with low density, high specific strength and stiffness, and good design ability is applied to the lightweight thermal protection system of high-speed aircrafts. The thermal-protection and load-bearing integrated structure is shown in Figure 5.

Figure 5.

The structure of the pyramid lattice filled aerogel sandwich plate.

In the non-oxidizing environment, Carbon/Carbon(C/C) composites are composite materials composed of carbon fibers and matrix phases, which can maintain structural strength at 2800°C. The structure made of C/C composites not only has high specific strength, high specific modulus, and low thermal expansion coefficient but also has a series of properties required by heat protection, such as heat shock and ablative resistance. C/C composite material is coated on the wing outer surface so that the aircraft’s wing can bear the severe aerodynamic heat/force load in a high-speed environment. However, due to the good thermal conductivity of C/C composites, high heat transfer on the surface leads to high internal temperature, so it is necessary to block the heat transfer of C/C composites. A light thermal insulation aromatic heterocyclic polymer nanofiber aerogel was selected as the filling material.³³ Tables 1 and 2 lists the parameters for the selected materials.

Table 1.

Mechanical properties of C/C composite material.

Density	Poisson’s ratio	Elastic modulus	Thermal conductivity
$1900 kg / m^{3}$	0.25	$40 GPa$	$0.462 W / m \cdot k$

Table 2.

Mechanical properties of C/C composite material.

Density	Poisson’s ratio	Elastic modulus	Thermal conductivity
$10.1 kg / m^{3}$	0.25	$0.25 MPa$	$0.013 W / m \cdot k$

Analysis of bearing capacity of integrated insulation layer

Analysis of compressive and shear modulus of structure

Figure 6 shows the schematic diagram of the designed C/C quadrilateral pyramid lattice structure. The lattice is filled with thermal insulation aerogel material. In the figure, $d$ is the diameter of a single column; $l$ is the length of a single column; $θ$ is the pillar inclination Angle; $h$ is the lattice height; $t_{1}$ and $t_{2}$ are respectively the thickness of the upper and lower panels; $B$ is the length of a single cell; $H$ is the total thickness.

Figure 6.

Pyramid lattice composite structure and its parameters.

The pyramid lattice composite structure mainly withstands the surface load caused by the pressure difference between the upper and lower wing surfaces of the aircraft, as shown in Figure 7. Therefore, this paper mainly considers the compressive stiffness of the lattice structure. The total thickness of the integrated structure $H$ is the main sensitive parameter to be considered, which is selected as 20 mm here.

Figure 7.

Force analysis of single pyramid lattice pillar under pressure load.

The relative density of the pyramid lattice structure can be derived:

ρ' = \frac{l π d^{2}}{B^{2} h} = \frac{π d^{2}}{\sin θ {(\sqrt{2} l \cos θ)}^{2}}

(1)

Let the elastic modulus of the fiber column be $E$ , According to the Hooke’s law,³⁴

Δ l = \frac{Fl}{EA}, Δ l = Δ h \sin θ

(2)

And then,

F_{a} = EA \frac{Δ l}{l} = \frac{1}{4} π d^{2} E \frac{Δ h \sin θ}{l}

(3)

$F_{t}$ can be obtained by the deflection formula of the cantilever beam³⁴

\begin{matrix} F_{t} = \frac{3 EI Δ σ_{m} ax}{l^{3}} = \frac{3 E π d^{4}}{64 l^{3}} Δ h \cos θ \end{matrix}

(4)

\begin{matrix} F = F_{a} \sin θ + F_{t} \cos θ \\ = \frac{π E d^{2} Δ h}{4 l} (\sin^{2} θ + \frac{3}{16} {(\frac{d}{l})}^{2} \cos^{2} θ) \end{matrix}

(5)

The compressive modulus of the corresponding lattice structure in the Z direction can be expressed as:

\begin{matrix} \begin{matrix} E_{z} = \frac{4 F}{S ε_{z}} = \frac{π E d^{2}}{{(\sqrt{2} l \cos θ)}^{2}} (\sin^{3} θ + \frac{3}{16} {(\frac{d}{l})}^{2} \cos^{2} θ \sin θ) \end{matrix} \end{matrix}

(6)

It can be seen in Figure 8 that the equivalent compressive modulus of the lattice cell increases with the increase of pillar inclination angle and pillar diameter.

Figure 8.

Relationship between pillar diameter, pillar angle and the z-axis compressive modulus of the pyramid lattice.

The shear modulus of the lattice structure is analyzed theoretically by the energy method.³⁵ Each pillar of the pyramid structure is symmetrical. It is assumed that the shear load direction of the parallel panel is at an angle of 45° with the X and Y axes. $F_{x}$ is the force along the X-axis, and the displacement $δ x$ and shear deformation angle $γ_{x} z$ are shown in Figure 9. The relationship between strain energy $V$ and $F_{x}$ is as follows:

F_{x} = \frac{dV}{dx}

(7)

Figure 9.

Shear diagram of pyramid lattice structure.

Strain energy $V_{a}$ generated by axial deformation of single column is as follows:

V_{a} = \frac{EA Δ a^{2}}{2 l}

(8)

Where, $E$ is the compressive modulus of the column and $A$ is the cross-sectional area of a single column, and $Δ a = Δ x \cos θ$ , $Δ s = Δ x \sin θ$ . Strain energy generated by lateral displacement is as follows:

V_{s} = \frac{6 EI Δ s^{2}}{l^{3}} = \frac{3 π E d^{3} Δ s^{2}}{32 l^{3}}

(9)

At then, the strain energy of pyramid cell is as follows:

\begin{matrix} V = 2 (V_{s} + V_{a}) \\ = \frac{EA Δ a^{2}}{2 l} + \frac{3 π E d^{3} Δ s^{2}}{32 l^{3}} \\ = 2 \frac{Δ x^{2}}{2} [\frac{EA \cos^{2} θ}{l} + \frac{3 π E d^{3} \sin^{2} θ}{64 l^{3}}] \end{matrix}

(10)

Substitute equation (10) into equation (7) to get:

\begin{matrix} F_{x} = \frac{dV}{dx} = K_{x} Δ x \\ = 2 [\frac{EA \cos^{2} θ}{l} + \frac{3 π E d^{3} \sin^{2} θ}{64 l^{3}}] Δ x \end{matrix}

(11)

Similarly, on the Y-axis, the lattice structure also has a coefficient $K_{y}$ . Due to the symmetry of the pyramid structure designed in this paper, $K_{x} = K_{y} = K$ and the shear modulus can be obtained and calculated.

\begin{matrix} G = \frac{F}{S γ} = \frac{\sqrt{F_{x}^{2} + F_{y}^{2}}}{B^{2} \frac{\sqrt{Δ x^{2} + Δ y^{2}}}{h}} = \frac{K \sqrt{Δ x^{2} + Δ y^{2}}}{B^{2} \frac{\sqrt{Δ x^{2} + Δ y^{2}}}{h}} = \frac{Kh}{B^{2}} \end{matrix}

(12)

Simulation and theoretical verification

The accuracy of the theoretical model is verified by static structural FEA analysis. First, a 4 × 4 pyramid lattice structure with an inclination angle of 45° and a single column diameter of 3.2 mm is established. The compressive modulus and shear modulus of the lattice structure are obtained by $E_{z} = \frac{σ}{ε}$ and $G = \frac{F}{S γ}$ , where $σ$ is the pressure load on the upper surface. And $ε = \frac{Δ h}{h}$ , $Δ h$ is the deformation of upper surface. Since the panel edge is not supported by a pyramid lattice, the deformation in the middle of the panel is selected, as shown in Figure 10.

Figure 10.

Deformation cloud diagram of compressive and shear deformation.

The comparison of simulation results and theoretical results is shown in Table 3. The simulation value is slightly larger than the theoretical result, and the error of compressive modulus and shear modulus are both less than 10%.

Table 3.

Mechanical properties of composite lattice structures.

Parameter	Theoretical value (MPa)	Simulation value (MPa)	Error (%)
Compressive modulus	568.39	615.38	8.3
Shear modulus	284.04	300.06	5.6

The following is a compression test to further verify the theory analysis of the pyramid lattice structure. According to the ASTM D638M measurement standard, the compression performance of the 3D printing 4 × 4-pyramid lattice test sample was measured, and the lattice structure unit was printed together with the tensile test sample, as shown in Figure 11.

Figure 11.

Tensile test sample and 4 × 4 lattice structural unit 3D printed sample.

Instron universal material testing machine was used to carry out tensile tests on the specimens. According to the test results, the elastic modulus and tensile strength of the specimens were calculated as 2211 and 76.9 MPa, respectively. The photocured materials were isotropic.

The static compression test of the 4 × 4-pyramid lattice structure was conducted in accordance with ASTM C365-05 standard. The loading speed was set at 0.4 mm/min, the sample size was 113 mm × 113 mm × 20 mm, and the deformation curve of the specimen was obtained, as shown in Figure 12.

Figure 12.

Loading deformation curve of 3D printed dot matrix test parts.

Considering the bearing area and combined with the loading deformation curve of the 3D printing lattice test piece, it can be concluded that the compressive modulus of the sample under the pressure load is 28.58 MPa. By substituting the structure parameters and elastic modulus of photocured material into equation (6), the theoretical result is obtained, and the compressive modulus of the structure is 31.23 MPa with an error of 8.5%. The reason why the test value is less than the theoretical value is mainly due to the low dimensional accuracy and manufacturing defects of the lattice structure.

Thermal insulation performance analysis of integrated thermal insulation layer

Calculation of structural thermal conductivity

The following is a quantitative calculation of the thermal conductivity based on the thermal resistance method. As shown in Figure 13, the thermal resistance $R_{2}$ of the integrated structure is composed of four lattice pillar and aerogel. $R_{2}$ is connected in series with panel thermal resistance $R_{1}$ and $R_{3}$ . The thermal resistance of the single column $R_{0}$ , filled aerogel $R_{f}$ , and upper panel $R_{1}$ and lower panel $R_{3}$ are respectively expressed as:

\begin{matrix} {\begin{matrix} R_{0} = \frac{H - 2 t}{λ_{s} \cdot A_{0}} \\ R_{f} = \frac{H - 2 t}{λ_{f} \cdot (A - 4 A_{0})} \\ R_{1} = \frac{t}{λ_{s} \cdot A}, R_{3} = \frac{t}{λ_{d} A} \end{matrix} \end{matrix}

(13)

Where $λ_{s}$ is the thermal conductivity of the C/C composite on the upper panel, $λ_{d}$ is the thermal conductivity of the superalloy on the lower panel, and $λ_{f}$ is the thermal conductivity of the aerogel. $A$ and $A_{0}$ are the cross-sectional areas of heat conduction of an integrated structural cell and a single column, respectively. According to the parallel relation of thermal resistance:

1 / R = \sum_{i = 1}^{N} 1 / R_{i}

(14)

$R_{2}$ can be expressed as:

R_{2} = \frac{l \sin θ}{λ_{f} (A - 4 A_{0}) + 4 λ_{s} A_{0}}

(15)

And then, the equivalent thermal conductivity of the integrated structure can be expressed as:

λ_{equ} = λ_{s} [\frac{{(\sqrt{2} l \cos θ)}^{2} \sin θ}{π d^{2} + \frac{λ_{f}}{λ_{s}} ({(\sqrt{2} 1 \cos θ)}^{2} \sin θ - π d^{2})}]

(16)

Figure 13.

Thermal resistance of C/C pyramidal lattice filled aerogel structure.

The thermal insulation equivalent performance of the structure

The heat transfer process is highly nonlinear, and it is difficult to establish and solve an accurate theoretical model of heat transfer. In most engineering applications, equivalent thermal conductivity is used to measure the thermal insulation performance of composite structures. The integrated lattice structure is equivalent to homogeneous material, and the total heat flow of the structure can be expressed by Fourier thermal conductivity law as follows:

Q_{t} = λ_{equ} A_{equ} \frac{Δ T}{H}

(17)

Where $Q_{t}$ is the heat flow in the direction of heat transmission; $A_{equ}$ is the equivalent area perpendicular to the direction of heat transmission; $H$ is the lattice thickness of heat insulation layer; $Δ T$ is the temperature difference between the upper and lower surfaces of the lattice sandwich structure; $λ_{equ}$ is the equivalent thermal conductivity.

As shown in Figure 14, an integrated lattice structure composed of pyramid lattice filled with aerogel was established, with a lattice inclination angle of 45° and a single column diameter of d = 3.2 mm. Through ANSYS steady-state thermal finite element simulation, the average heat flux of the integrated lattice structure in 1 s is obtained when $Δ T$ is 1°C. The equivalent thermal conductivity of the integrated lattice structure at different temperatures can be calculated by equation (17).

Figure 14.

Heat flux cloud of composite structural unit at 1500°C (aerogels hidden).

The equivalent density is $80.168 kg / m^{3}$ . The thermal conductivity obtained by simulation is shown in Table 4. And the error of the simulation and theoretical results of the integrated structure’s equivalent thermal conductivity is lower than 5%. It can be concluded that the equivalent theory in this paper is feasible.

Table 4.

Equivalent thermal conductivity of integrated thermal insulation structure.

Temperature (°C)	Theoretical thermal conductivity (W/m K)		Error (%)
25	0.0289	0.0282	2.4
200	0.0231	0.0224	3.0
1000	0.0154	0.0147	4.5
1500	0.0153	0.0146	4.6
2000	0.0152	0.0145	4.6%

Thermal insulation performance test verification

The insulation performance test of integrated structural units was conducted with alternative materials. High purity graphite plates with 3 and 5 mm thickness were selected for the upper and lower panels, granular silica aerogel was selected for filling materials. Stainless steel 3D printed parts with a single column diameter of 3.2 mm and structure height of 20 mm were selected for the lattice, and secondary polishing was carried out. The stepped aluminum silicate insulation box was designed according to the size of 2 × 2 lattice units at different incline angles, as shown in Figure 15. And the thermal property of these materials are shown in Table 5.

Figure 15.

Schematic diagram of heat insulation performance test bench design.

Table 5.

Thermal property of test meterials.

	316L stainless steel	Graphite plate	Silica aerogel
Thermal conductivity (W/m K)	13.5	151	0.021

Since the used thermal conductivity of the integrated structure used in the test was much higher than that of aluminum silicate plate (≤0.07 W/(m K)). And the contact area between the upper panel and the box is far less than the equivalent heat transfer area measured in the test. As a result, aluminum silicate box is able to avoid the influence of the external environment.

Firstly, heat the graphite plate of the upper panel to 350°C, and use the thermocouple to measure the temperature changes over time at the center of the undersurface. The influence of aerogel on the heat insulation performance can be observed by comparing the experiment result of a pyramid lattice(no aerogel) with integrated structure(filled with aerogel). Then, a transient thermal simulation was conducted to verify the accuracy of the experiment results.

According to the experiment results of the thermocouple, the heating rate of the back temperature surface of the pyramid lattice without filling the aerogels is significantly higher than that of the back temperature surface of the integrated structure. It can be concluded that the structural design of the integrated structure can achieve the heat insulation effect. Through the comparison between the experiment and simulation, it can be seen that under the same thermal loading condition, the measured temperature in the experiment is significantly less than the simulation value in the first 200 s. In practice, the contact gap generally exists between the contact surfaces and heat transfer is realized through heat radiation and heat convection of the air in the contact gap, which will lead to low equivalent thermal conductivity in the initial stage of heat transfer.

In order to reduce the influence of contact thermal resistance on the experiment results, the copper plate was heated to provide a stable heat source with the upper surface. Heat the copper plate to 600°C and keep heating it so that it is dynamically stable at 600ºC as the heat source of the upper panel. Based on the above experimental devices, the heat insulation experiment of 35°, 45°, and 55° lattice inclination angle is conducted. The emissivity of the graphite plate was measured by the thermal imager at 0.98 and the ambient temperature was set at 26.1°C. By considering heat dissipation from the upper surface to the environment and applying the alternative material parameters to the simulation model, the simulation result is obtained, as shown in Table 6. And the temperature simulation results (upper) and experiment results (lower) on the back of the integrated structure with different inclination angles are shown in Figure 16.

Table 6.

Thermal insulation test of 25° lattice filled aerogel integrated structure.

Time/s	Experiment result/°C	Simulation result/°C	Error (%)
0	26.1	26.1	/
200	28.8	34.4	67.5
300	32.0	39.6	56.3
400	35.8	43.5	44.3
500	39.5	46.9	35.6
600	42.6	49.6	29.8
700	45.4	51.8	24.9

Figure 16.

Experiment and simulation result with different tilt angles: (a) temperature of undersurface in simulation result and (b) temperature of undersurface in experiment result.

According to the experiment and simulation, the temperature on the back of the integrated structure in the first 200 s of the test is greatly different from the simulation value due to the contact thermal resistance. With the increase of the structure temperature, the effect of contact thermal resistance decreases, and the experiment value gradually approaches the simulation value. At last, the experiment results are still less than the simulation value, but the error drops to less than 10% at 800 s. There are two main reasons for this result: firstly, in addition to heat radiation heat, there is also heat dissipation caused by heat convection with the air will affect the structural temperature; secondly, the wall of the aluminum silicate box container will also lose part of the heat. As a result, it is feasible to equivalent the integrated structure to homogeneous material and the error is within the allowable range.

Integrated structural response surface optimization

Response surface optimization is a process of obtaining the optimal combination of structural parameters by utilizing non-linear fitting on stress, deformation, and heat transfer data obtained through multiple simulations and experiments on the integrated structure under different structural parameters. The process flow is illustrated in Figure 3.

Parametric model establishment and finite element analysis

An integrated structure with 3 × 3 cells is parametrically modeled by SolidWorks and interfaced with ANSYS Workbench. According to the structural parameters shown in Figure 5, several structural parameters that affect its mechanical properties are listed in Table 7. And the total thickness H sets as 20 mm.

Table 7.

Design parameters in parametric model.

Thickness of upper panel	Thickness of lower panel	Pillar angle	Pillar diameter
$t_{1} / mm$	$t_{2} / mm$	$α / °$	$d / mm$

Solid 187 elements were selected for meshing with a tetrahedron element type in order to adapt to complex structure. The meshed parameters model with 137,613 nodes and 97,218 elements is shown in Figure 17. And the average element quality is 0.85.

Figure 17.

Parameterized structure meshing result.

The wing surface is subject to external aerodynamic and thermal loads during flight, with an internal skeleton providing support. The focus is on its compressive stiffness and thermal conductivity. Therefore, in finite element analysis, the bottom surface of the lower panel is considered as a fixed constraint, while the top surface bears a pressure of 20 kPa. In structural static thermal analysis, the temperature of the top surface of the upper panel is set at 1100°, and the temperature of the bottom surface of the lower panel is set at 100°, with the thermal conductivity analyzed by measuring the heat flux.

Parameter sensitivity analysis

Using the parameter correlation module, the influence of design parameters on the maximum deformation, maximum stress, and heat flux of the structure was analyzed, and their relative sensitivity was compared. The sensitivity column chart is shown in Figure 18, which indicates that the thickness of the upper panel (P25), pillar angle (P27), and pillar diameter (P26) have a significant impact on the output results. These three parameters were selected as variables for the subsequent DOE and response surface fitting. The thickness of the lower panel (P31) had a trial impact and was therefore ignored in the optimization process.

Figure 18.

Parameter sensitivity of structure.

Design of experiments and response surface fitting

The DOE method reflects the relationship between input and output variables as reasonably as possible through a finite number of experiments. Due to its complex non-linear relationship, the central composite design (CCD) method was used for the response surface design of experiments. Afterwards, results from structures with different parameters were analyzed by Workbench. And the response relationship between the different parameters and output variables was obtained by response surface fitting.

Figure 19 shows the relationship between pillar angle, pillar diameter, and equivalent thermal conductivity. When the pillar angle is small, the thermal conductivity decreases first and then increases as the pillar diameter increases. When the pillar angle is large, the thermal conductivity increases with the increase in pillar diameter.

Figure 19.

Relationship between pillar angle, pillar diameter, and equivalent thermal conductivity.

Figure 20 shows the relationship between pillar angle, pillar diameter, and maximum structural deformation. When the pillar angle is large, the structural deformation is small, and the influence of the pillar diameter is minimal. When the pillar angle is small, the structural deformation increases with decreasing pillar diameter.

Figure 20.

Relationship between pillar angle, pillar diameter, and structure max deformation.

Also, results show that the maximum equivalent stress increase as the pillar angle decreases. And the or all parameter combinations, the equivalent stress of the structure is less than 10 MPa.

Optimization and result analysis

The structural optimization objective is to optimize the thermal conductivity while meeting the strength and stiffness requirements and enhance its insulation properties. Therefore, the maximum stress of the structure is constrained to be less than 10 MPa, the maximum deformation is less than 0.1 mm, and the minimum thermal flux of the structure is used as the objective function. The two optimal parameter combinations obtained are shown in Table 8.

Table 8.

Optimization result.

Optimization result	1	2	Origin
$t_{1} (mm)$	4.4	4.7	3
$d (mm)$	4	4	5
$α (^{°})$	34.6°	33.4°	45°
Maximum deformation $(μ m)$	1.42	1.25	0.79
Average heat flux $(W / m m^{2})$	0.00138	0.00141	0.00231
Relative density $(kg / m^{3})$	685.5	714.9	711.6

Since result 1 has the lowest average heat flux and relative density, take this parameter set as the optimal design parameter setting. Table 1 shows that the equivalent thermal conductivity of the structure is reduced by 40% compared to before optimization, and the relative density is reduced by 3.7%. Table 9 provides the parameters of the insulation ceramic tiles and insulation layers, and it can be seen that the thermal conductivity of the integrated structure is reduced by more than 20% compared to the insulation ceramic tiles while ensuring the load-bearing capacity.

Table 9.

Thermal property of the insulation ceramic tiles.

	Average heat flux $(W / m m^{2})$	Relative density $(kg / m^{3})$
Proposed integrate structure	0.0276	685.5
LI-900	0.036	144
LI-2200	0.052	352
AETB-8	0.064	128

Simulation analysis of telescopic wing structure

The designed load-bearing skeleton structure of the telescopic wing is composed of C/C composite thermal protection layer, integrated structure with pyramid lattice and aerogel, wing ribs, and wing spar. The cantilever guide rail is used as the guide support structure of the telescopic wing. The schematic diagram of the telescopic wing is shown in Figure 21.

Figure 21.

Schematic diagram of a telescopic wing.

Under the action of thermal load, the temperature inside the wing changes greatly and the temperature field distribution is uneven. The thermal stress and deformation will affect the bearing capacity of the airfoil. The thermal structural coupled simulation is applied in pressure vessel,³⁶ strucutre thermal vibration,³⁷ brake pads,^38–41 and so on. Most of the above analyses are strong coupling analysis of the interaction between heat conduction and structural motion deformation. Due to the complex structure of the whole wing, the weak coupling analysis, which is carried out separately from the temperature field analysis and structural analysis, is applied in this section to verify the bearing capacity and insulation capacity of the wing surface under the action of thermal and mechanical loads. The integrated structure was equivalent to a homogeneous material. The fixed panel end face was set as fixed supports, and the friction coefficient between the telescopic moving panel and the guide rail was set as 0.1. And the friction coefficient contact surface between the moving panel and the fixed panel is set as 0.3.

Thermo-mechanical coupling simulation of telescopic wing

Firstly, the equivalent telescopic wing model was imported into ANSYS for finite element transient thermal simulation analysis, and Solid186 element was used to mesh the wing. According to the environmental temperature data of high speed aircraft, the thermal load of 1800°C was loaded on the leading edge of the wing, 1500°C on the upper and lower surface, 600°C on the trailing edge, and the loading time was set as 1200 s. Regardless of the thermal load on the moving panel, its thermal load was set as adiabatic. The simulation result is shown in Figure 22.

Figure 22.

Wing thermal load simulation result.

The simulation results show that the temperature inside the fixed panel after 1200 s can be controlled below 200°C, which meets the normal working environment temperature of the components inside the fixed wing.

Then, the above transient thermal simulation results as well as the material mechanical parameters are imported into ANSYS static analysis module. The simulation time step is set to be consistent with transient thermal analysis, and 20 kPa pressure is loaded on the wing’s upper surface. Through thermal structural coupled simulation, the stress and deformation cloud diagram of the skeleton structure and the telescopic wing system are obtained and are shown in Figures 23 and 24.

Figure 23.

Stress cloud diagram of fixed wing bearing skeleton.

Figure 24.

Stress and deformation cloud diagram of thermo-mechanical coupling simulation of the telescopic wing.

The simulation results show that in terms of structural stress, the maximum stress value of the fixed panel skeleton is 648.24 MPa. The stress at the contact area between the fixed panel and the moving panel is small. As a result, the moving panel does not squeeze the contact area greatly in the moving process, which can effectively reduce the driving force of the telescopic wing. In terms of structural deformation, the maximum deformation at the contact area is 3.96 mm, and the maximum deformation of the telescopic wing system is 5.6 mm at the wingtip of the moving panel.

Conclusion

In this research, a telescopic wing construction was proposed, and a thermal-protect and load-bearing integrated structure was designed. The conclusions from the present study is as follows:

(1) The equivalent compression modulus and shear modulus of the integrated structure are deduced theoretically, and the finite element simulation and experimental verification are carried out. Based on Fourier’s law of thermal conductivity and thermal resistance, the equivalent heat transfer characteristics of the integrated heat insulation structure are derived. The error of theoretical calculation and finite element simulation is less than 5%. The heat transfer performance of the integrated structure is verified experimentally by using alternative materials, and the accuracy of the heat transfer theory and simulation in this paper is verified within the allowed error range. The force and thermal characteristics of the integrated structure were equivalent to homogeneous material, and the equivalence error was controlled within 10%.

(2) Parameter sensitivity analysis was conducted using Workbench, and the structural parameters were optimized using the response surface method. Compared to the initial structure, the optimized structure has an equivalent thermal conductivity of 0.0276, reduced by 40%, and a relative density of 685.5 kg/m³, reduced by 3.7%. While maintaining its load-bearing capacity, the optimized structure has a thermal conductivity that is more than 20% lower than that of the ceramic insulating tiles.

(3) The thermal structural coupled simulation model of the telescopic wing system was established. The thermal insulation performance and mechanical load performance of the telescopic wing system were analyzed. The result demonstrates that maximum deformation under 20 kPa surface pressure is 3.96 mm. The temperature resistance of the structure surface is up to 1500°C, and the wing internal temperature is controlled within 200°C after 1200 s of thermal loading. The results show that the integrated structure can meet the requirement of high-speed telescopic wing. And the proposed structure can also be applied in reusable launch vehicles, hypersonic vehicles, and other high-speed morphing wings.

In the future, we will consider the force distribution on the wing surface and explore the design method of the sandwich structure. Thermal expansion leads to high contact force between fixed and moving parts, which increases the friction force or gets stuck. As a result, although the thermal expansion is trivial in a single cell, it has a great effect on the wing and should be investigated.

Footnotes

Appendix

$ρ'$ relative density of the integrated structure

$E$ elastic modulus of structure

$d$ diameter of column

$B$ width of single cell

$h$ thickness of single cell

$θ$ angle of column

$l$ length of column

$t 1$ thickness of top panel

$t 2$ thickness of bottom panel

$Ez$ compressive modulus

$G$ shear modulus

$R 0, R 1, R 2, R 3$ thermal resistance of sandwich structure

$Rf$ thermal resistance of fulfilled aerogel

$λ_{s}, λ_{f}$ thermal conductivity

$λ_{equ}$ equivalent thermal conductivity

Handling Editor: Chenhui Liang

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors gratefully acknowledge the support of National Natural Science Foundation of China (NNSFC) through grant nos. 52192631 and 52105013, China Postdoctoral Science Foundation(2023T160168), and Self-Planned Task (no. SKLRS202202C) of State Key Laboratory of Robotics and System (HIT).

ORCID iDs

Hongwei Guo

Chunfeng Li

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