Structural Optimization of Structured Carbon-Based Energy-Storing Composite Materials Used in Space Vehicles

Abstract

The hot work environment of electronic components in the instrument cabin of spacecraft was researched, and a new thermal protection structure, namely graphite carbon foam, which is an impregnated phase-transition material, was adopted to implement the thermal control on the electronic components. We used the optimized parameters obtained from ANSYS to conduct 2D optimization, 3-D modeling and simulation, as well as the strength check. Finally, the optimization results were verified by experiments. The results showed that after optimization, the structured carbon-based energy-storing composite material could reduce the mass and realize the thermal control over electronic components. This phase-transition composite material still possesses excellent temperature control performance after its repeated melting and solidifying.

Keywords

Composite phase-transition material Graphite foam Optimization Spacecraft Thermal control

Introduction

The electronic components in the instrument cabin of spacecraft are becoming thinner and shorter, but the structural density of instrument cabin is rapidly increased. So, heat dissipation has become an important factor affecting the service life of electronic components. In order to avoid the failure caused by thermal stress and ensure reliability, the electronic components require effective thermal control structures to provide a stable thermal environment. Graphite carbon foam is an impregnated phase-transition material with light weight, high thermal conductivity and excellent thermal cycling stability, which could meet the requirement for stringent temperature range. And at the same time, its good thermal and electromagnetic properties can ensure the stable operation of electronic components. Shao et al used a phase-transition material in CCD camera and took advantage of its thermal coupling effect with the fins to conduct the heat load control, and finally the payload bay was verified through experiments (1). Kim et al studied the use of phase-transition materials in the intermittent instrument of spacecraft for thermal control, and calculations showed that the materials can effectively reduce the maximum temperature of the thermal control device and have the effect of peak clipping (2). Unfortunately, phase-transition materials have low thermal conductivity so that heat cannot be quickly transferred therein and they cannot effectively carry out temperature control over the equipment. Many scholars have tried various methods to carry out enhanced heat transfer for phase-transition materials, such as metal foam (3-4-5-6), graphite foam and others (7-8-9-10-11-12-13-14). The phase-transition material was impregnated in carbon graphite foam by Zhong et al (15) and the results showed that the thermal conductivity of the composite material enhanced about 300 times compared with before impregnation. They also found that the latent heat of the energy-storing composite material became larger with the increase of the content of phase-transition material. Li et al used an average model of porous media to establish a mathematical model of solid-liquid phase transition in the metal foam composite materials. The solid-liquid interfaces obtained at different times by numerical and experimental methods were compared and the results of both methods showed good agreement (15, 16). Because of the limited available space in the spacecraft, the heat of electronic components, the volume and mass of the control structure must be strictly controlled. To meet the temperature requirement, the optimization of structural parameters of carbon graphite foam is particularly important. In this paper, the pore size and porosity of the graphite carbon foam, the geometrical dimensions of the structured carbon-based composite energy-storing materials were optimized with ANSYS. We also established a three-dimensional heat transfer model to obtain the temperature distribution. Under the thermal coupling effect, we checked the strength of the composite material and designed experiments to validate the temperature distribution of the optimized structure.

Experimental procedure

Theoretical foundation

When the structured carbon-based composite material was conducted a two-dimensional optimal simulation, we used a porous media model based on the average volume theory (17). The governing equations of phase-transition heat transfer in porous media are as follows:

Continuity equation:

\frac{\partial (ρ u)}{\partial x} + \frac{\partial (ρ v)}{\partial y} = 0

Momentum equation:

\begin{array}{l} \frac{ρ}{ε} \frac{\partial u}{\partial t} + \frac{p}{ε^{2}} [\frac{\partial (u u)}{\partial x} + \frac{\partial (u v)}{\partial y}] = - \frac{\partial p}{\partial x} + \frac{μ}{ε} (\frac{\partial^{2} u}{\partial x^{2}} + \frac{\partial^{2} u}{\partial y^{2}}) \\ - (\frac{μ}{K} + \frac{p F}{K \frac{1}{2}} | u |) u \end{array}

\begin{array}{l} \frac{ρ}{ε} \frac{\partial v}{\partial t} + \frac{ρ}{ε^{2}} [\frac{\partial (u u)}{\partial y} + \frac{\partial (u v)}{\partial x}] = - \frac{\partial p}{\partial x} + \frac{μ}{ε} (\frac{\partial^{2} v}{\partial x^{2}} + \frac{\partial^{2} v}{\partial y^{2}}) \\ - (\frac{μ}{K} + \frac{ρ F}{K \frac{1}{2}} | v |) u + ρ g β_{f} (T_{f} - T_{m}) \end{array}

Energy equation – graphite foam carbon skeleton:

(1 - δ) {(ρ c)}_{s} \frac{\partial T_{s}}{\partial t} = k_{s e} (\frac{\partial^{2} T_{s}}{\partial x^{2}} + \frac{\partial^{2} T_{s}}{\partial y^{2}}) - h_{s f} a_{s f} (T_{s} - T_{f})

Energy equation – phase-transition materials:

\begin{array}{l} δ {(ρ c)}_{f} \frac{\partial T_{f}}{\partial t} + {(ρ c)}_{f} [u \frac{\partial T_{f f}}{\partial x} + v \frac{\partial T}{\partial y}] = K_{s e} (\frac{\partial^{2} T_{f}}{\partial x^{2}} + \frac{\partial^{2} T_{f}}{\partial y^{2}}) \\ + h_{s f} a_{s f} (T_{s} - T_{f}) - δ ρ L \frac{d f_{1}}{d t} \end{array}

where δ is the porosity of the porous medium;is a function of the liquid phase-transition material, here e = δ f₁; f₁ is the liquid-phase rate of the phase-transition material; K is the permeability of the porous medium, which is related to the porosity and pore size of carbon foam; F is the inertial resistance coefficient; k_se and k_fe are the effective thermal conductivities of the basic skeleton and phase-transition materials, respectively. This single-equation model assumes that the skeleton and the phase-transition material can reach a local thermal equilibrium, that is T_s = T_f = T, so the two energy equations can be combined into the following energy equation:

{(ρ c)}_{e f f} \frac{\partial T}{\partial t} = \nabla (k_{e f f} \nabla T) - ρ_{p c m} L δ \frac{d f_{1}}{d t}

where ${(ρ c)}_{e f f} = δ {(ρ c)}_{p c m} + (1 - δ)(ρ c)_{s}; k_{e f f}$ is the effective thermal conductivity of the composite material.

Modeling and optimization

Numerical simulation involves the grid independence and related issues of calculation step, for the four mesh sizes (Fig. 1).

Fig. 1

Different number grid of two-dimensional optimization model.

We conducted a simulation, taking the temperature of the hot end surface as the inspection object, and it can be seen from the results shown in Figure 2 that when the number of grids was raised about 25 times from 4489 to 110,889, the temperature of the hot end surface had no change. When saving computing resource was taken into account, we selected 4489 as the suitable number of two-dimensional grid models.

Fig. 2

Curve of hot end surface temperature.

For the correlation of the calculation step, we calculated in steps of 0.1 s and 1 s respectively, and made a comparison with the hot end surface temperature we had obtained, as shown in Figure 3. It can be seen that, after thinning the calculation step 10 times, the temperature value did not change. So we could use 1 s as a calculation step to conduct the optimization.

Fig. 3

Verify the correlation of calculation step.

For two-dimensional structure, there is only one direction to withstand heat, which may influence the final temperature distribution of hot end surface, while the other direction does not have any effect on the final result. Taking into account the subsequent computational complexity for the three-dimensional structure, we only highlight the length H in the direction of bearing heat flow. The hot work environment of electronic components in the instrument cabin of a spacecraft is taken as the calculation condition, and our two-dimensional optimization goal is that the surface temperature of the electronic components should be controlled below 343K and the calculation schematic diagram is shown in Figure 4.

Fig. 4

Schematic diagram of the two-dimensional optimization.

According to the production experiences of graphite carbon foam, we set the variation range of porosity and pore size as well as the material parameters in Tables I and II, wherein the heat flux is set to 10000 W/m², and working time is 120 s.

Table I

Performance parameters of graphite carbon foam

Thermal conductivity/ W/m.K	Porosity	Aperture/µm	The length direction of heat flow/mm
250	0.7-0.95	300-1000	5-25

Table II

Performance parameters of phase-transition material (paraffin)

Density/kg.m−3	Specific heat capacity/J.kg-1.K−1	Thermal conductivity/W.m−1.K−1	The phase transition temperature/°C	Latent heat/J.g−1
800	2850	0.15	60	200

Analysis of optimization results

We built a design space with DOE method, which has good space filling ability and is capable of forming uniform sample points from optimal Space-Filling Design. Adopting ANSYS to simulate the range of the parameters, the temperature changes of the hot end surfaces were obtained. In addition, using Response Surface to conduct fitting, which makes discrete space become continuous, the results can be optimized for solving extremum. The temperature of the hot end surface is shown in Figure 5, where the green dots are numerical results, and the red line is obtained by fitting the curve. It can be seen that the temperature distribution of the hot end surface is a direct proportion function and the temperature distribution is mainly below 350K, but the temperatures range from 332K to 423K still satisfies the requirements for the final temperature.

Fig. 5

The temperature profile of the hot end surface.

Figure 6 shows the flow rate distribution of the melted phase-transition material due to the action of heat impact in a two-dimensional model. Figure 7 shows the impact force of melted phase-transition material acting on the graphite carbon foam. As the temperature increases, the fluid flowing rate increases, also leading to a stronger impact on the graphite carbon foam, the obtained fitted curves are a direct proportion function.

Fig. 6

Distribution of fluid flowing rate.

Fig. 7

Fluid pressure distribution for carbon foam

To determine the optimal results, the influencing trend on the hot end surface temperature by pore size, porosity and thickness H of graphite carbon foam was inspected.

Figure 8 shows the temperature affecting curves of the graphite carbon foam thickness on the hot end surface. As can be seen, when the porosity is relatively fixed, the hot end surface temperature decreases with the carbon foam thickness. Within the first 10-20 mm, the temperature drops rapidly, due to the enhanced heat transfer of graphite carbon foam, which makes the phase-transition material melt to absorb heat and hence reduce the temperature by 95%. While within the foam thickness range from 20 mm to 30 mm, the temperature decrease is only 5%, which suggests the need for the optimization of the thickness.

Fig. 8

Curve of thickness on the hot end surface temperature when the porosity is different.

Figure 9 shows the process that the hot end surface temperature first decreased and then increased with the increase of porosity when the thickness is relatively constant. It is because the porosity affects the volume that the phase-transition material can be filled in and hence the effective thermal conductivity of graphite foam carbon. As the porosity increases, the phase-transition material increases and results in an increase in heat absorption, so the hot end surface temperature decreases. Consequently, the heat cannot be validly transferred since the effective thermal conductivity of the graphite carbon foam reduces after the porosity decreases to a certain extent, resulting in a temperature rise on the hot end surface. Figure 8 shows that, at a thickness of about 20 mm, the hot end surface temperature will reach its extremum, and at this moment, the porosity is about 0.84, just at the inflection point of Figure 9B.

Fig. 9

Curve of porosity on the hot end surface temperature when the thickness is different.

Figure 10 shows that the pore size cannot affect the thermal boundary temperature, because when the porosity is fixed, the pore size and the number of pores have opposite changing trends. Combining all these factors, we obtained Figure 11, which shows a three-dimensional affecting trend.

Fig. 10

Influence of different aperture for thermal boundary temperature.

Fig. 11

Influence trends of porosity and thickness for hot end surface temperatures.

Based on the above analysis, the extreme values are set as follows:

\begin{array}{l} \min ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ H \\ s e e k p o r o s i t y = 0.84; \\ \max T e m p a t u r e o n h o t b o u n d a r y \leq 343 K \end{array}

We obtained optimal results through the multi-objective genetic algorithm, as shown in Figure 12. When the porosity is 0.86, the thickness of the carbon graphite foam impregnated in phase-transition material is 8.42 mm, which could meet the requirements of electronic components for hot work environment.

Fig. 12

Dimensional optimization results of graphite carbon foam.

Using the results obtained by optimizing three-dimensional modeling, the temperature distribution was calculated as shown in Figure 13. It can be seen from the figure that the optimized results and the three-dimensional temperature cloud picture are identical, but irregular boundary caused by gravity effect can be seen from Figure 13B.

Fig. 13

Comparative distribution of temperature field of carbon graphite foam.

Figure 7 shows that the maximum pressure applied on the graphite carbon foam by the melted phase-transition material is 3 Pa. In view of saving computing resource and ignoring this pressure with respect to the strength of graphite carbon foam, only the stress, strain and the maximum deformation caused by the temperature were studied. It can be seen from Figure 14 that the maximum stress occurred on the hot face, reaching up to 0.0297 MPa; the maximum value appeared at the ligaments, and we obtained the strength of carbon graphite foam 3.3 MPa according to the carbon graphite foam density (0.36 g/cm³) and the fitting formula of strength. Obviously, the results can meet the strength requirements because the structure was not destroyed. Since the hot end surface of graphite carbon foam is close to the electronic components, we fixed the hot end surface and got the maximum deformation, which is at the other side and its value is 0.0099 mm. Relative to the size of carbon graphite foam, it could meet the conditions required.

Fig. 14

Strength check of three-dimensional graphite carbon foam.

Results and discussion

In order to verify the correctness of the simulation results, an electric heating plate as the heat source was used to simulate the electronic components in work conditions. We used the temperature detecting device and temperature acquisition module to measure the temperature with a measuring time of 120 s, and the experimental platform is shown in Figure 15.

Fig. 15

Experimental platform.

In Figure 15, mark 1 denotes the transformer to supply power for the electric heating film; mark 2 denotes the electric heating plates and graphite carbon foam impregnated with paraffin; the size of the composite energy-storing material was prepared in accordance with the optimization results, as shown in Figure 16. Since we could not determine whether or not the optimal results are correct before the experiment, we reserved an allowance and let the size of the composite material be 10 mm. Mark 3 denotes DAM-3039F, a data acquisition module, working at 24 V supplied by transformer 4. We collect the hot end temperature from the software in the computer so the measured temperature is relatively accurate. When the temperature detecting wire plugs into the composite material, its specific location is shown in Figure 17. In the experiment, when the power is on, the heating plate temperature is stable after 2 min; after heating for 120 s, the morphology of the composite is shown in Figures 18 and 19.

Fig. 16

Composite energy storage materials.

Fig. 17

The relative position of the temperature measurement line.

Fig. 18

The composite energy storage materials after absorbing.

Fig. 19

Composite energy storage materials heat before and after.

Figure 18 shows the partially melted composite material after heating. You can see the border of this part is close to 8.5 mm, and the edges show an inclined state. Compared with Figure 13B, we can see that the numerical simulation and experimental results agreed very well, which validates the optimization results. The temperature curves are shown in Figures 20 and 21. The temperature curve of hot end surface obtained by numerical simulation is shown in Figures 22 and 23.

Fig. 20

The temperature of the hot end face is measured by experimental platform.

Fig. 21

The temperature of the hot end face for an enlarged view.

Fig. 22

The temperature of the hot end face for numerical simulation.

Fig. 23

The temperature of the hot end face for an enlarged view.

When we compare Figures 20 and 22, it can be seen that the hot end surface temperature curves measured from the experimental platform and obtained from numerical simulation have the same variation tendency, and the difference of 2°C is the error due to the experiments. But the experimentally measured highest temperature is lower than the set maximum temperature 70°C. From the enlarged pictures it can be seen that there exist temperature differences at different locations. The highest temperature is at position 1, while the lowest temperature is at position 4. This is because the phase-transition material was affected by gravity and viscosity during the process of absorbing heat and melting, which not only makes the melt boundary form a curved shape, but also results in different temperatures at different locations. It can be seen from Figure 23 that there exist temperature difference due to different positions by comparing with the numerical simulation results.

Conclusions

In this paper, the composite module used in the temperature control over the electronic components in spacecraft instrument cabin was studied, and the optimal size was obtained through the multi-objective genetic algorithm. The finite element software was used to calculate its three-dimensional temperature field and the strength was checked out at the same time. In order to verify the simulation results, we used experimental platform to measure the hot end surface temperature, and the results were compared with the simulation results, so the following conclusions can be drawn:

(1)

When using the energy-storing composite materials for thermal control over the electronic components in spacecraft instrument cabin, the porosity of the carbon skeleton of the graphite foam and the duration of withstanding heat are the main factors influencing the temperature of hot end surface, and the pore size has almost no effect;

(2)

We obtained the optimal size of the energy-storing composite materials through a multi-objective genetic algorithm, and ANSYS was used to simulate the three-dimensional temperature field. When the strength was checked, we found that the brittle graphite foam carbon was not damaged;

(3)

We measured the temperature of hot end surface by the self-built experiment platform and compared with numerical simulation results. The temperatures of hot end surface of energy-storing material were different at different locations, and the highest temperature was on the top surface of the material. The experimental results verified the optimization result within an allowable error range, and could meet the working conditions required.

Footnotes

Financial support: No grants or funding have been received for this study.

Conflict of interest: None of the authors has financial interest related to this study to disclose.

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