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SiC pyramidal core lattice sandwich panel
Applied Thermal Engineering 81 (2015) 10e17
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Research paper
Fabrication and heat transfer characteristics of C/SiC pyramidal core lattice sandwich panel Kai Wei a, Rujie He a, Xiangmeng Cheng a, Yongmao Pei a, Rubing Zhang b, *, Daining Fang a, ** a b
State Key Laboratory for Turbulence and Complex System, College of Engineering, Peking University, Beijing 100871, PR China Department of Mechanics, School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, PR China
h i g h l i g h t s Lightweight C/SiC lattice panel was firstly proposed and fabricated. Heat transfer properties of the C/SiC lattice panel were tested up to 1150 C. The heat insulation effect of C/SiC lattice panel achieved a peak value 90%. The equivalent conductivity of the C/SiC lattice panel increased with temperature.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 6 October 2014 Accepted 6 February 2015 Available online 14 February 2015
Lightweight C/SiC pyramidal core lattice sandwich panel was proposed and fabricated for potential applications as hot structure and thermal protection system (TPS). The heat transfer characteristics of C/ SiC lattice sandwich panel were measured from 600 to 1150 C through an aerodynamic heating simulation experimental system. Temperature distribution on the back surface of the lattice sandwich panel was obtained through periodical thermocouple assignment. Heat insulation effects under different temperatures were also investigated. Finally, a three dimensional finite element simulation model was built to calculate the heat transfer of the C/SiC lattice sandwich panel. The equivalent thermal conductivity of the C/SiC lattice sandwich panel varied from 1.98 to 4.95 W/(m C) when the front surface temperature increased from 600 to 1150 C. It is believed that these results can provide a foundational understanding on the heat transfer characteristics of C/SiC lattice sandwich panel. © 2015 Elsevier Ltd. All rights reserved.
Keywords: C/SiC lattice sandwich panel Heat transfer Finite element simulation Equivalent thermal conductivity
1. Introduction Reusable launch vehicle (RLV) and hypersonic vehicle have been extensively studied in the past decades [1]. It is found that one of the most important issues is the thermal protection system (TPS). The TPS protects the interior from high-speed aerodynamic heating and provides sufficient structural strength and stiffness to retain the aerodynamic shape [2]. Recent developments of thermal protection technology promote various new types of thermal protection system. Great efforts have been made to develop an efficient integrated TPS [3]. The key design of the integrated TPS is the
* Corresponding author. Tel.: þ86 1051684070. ** Corresponding author. Tel.: þ86 1062760322. E-mail addresses: [email protected] (R. (D. Fang).
Zhang),
http://dx.doi.org/10.1016/j.applthermaleng.2015.02.012 1359-4311/© 2015 Elsevier Ltd. All rights reserved.
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sandwich panel which acts as not only the main load bearing structure but also the thermal insulation material vessel [4]. Fortunately, lattice sandwich panels are found to exhibit integrated properties of lightweight natural instinct and high specific strength/stiffness [5,6]. Therefore, lattice sandwich panels are expected to be promising candidates for integrated TPS. However, up to now, only metal [7-9] and fiber reinforced resin matrix composite [10,11] lattice sandwich panels were reported. Wadley [7,8], Tian [9] developed several manufacture techniques to fabricate lattice core sandwich panels with aluminum, stainless steel nickel and copper. Fang [10] and Wu [11] reported an interweaving and hot compression molding method for fabricating the lattice sandwich panels with carbon and glass fiber reinforced resin matrix composites. Unfortunately, both the metal and fiber reinforced resin matrix composite lattice sandwich panels cannot be used for integrated TPS, owing to their low melting point and weak
K. Wei et al. / Applied Thermal Engineering 81 (2015) 10e17
oxidation resistance under high temperature environment. Recently, carbon fiber reinforced silicon carbide matrix composite (C/SiC) has been studied extensively due to its superior specific mechanical properties under elevated high temperature and thermal oxidative environment [12,13]. However, studies on the C/SiC lattice sandwich panel have never been reported. In addition, heat transfer properties play important roles on the hot structures. Many previous reports investigated the heat transfer of the sandwich structures with honeycomb [14,15] or foam core [16-18]. Swann and Pittman [14] developed a semi-empirical formula to predict the effective thermal conductivity of honeycomb sandwich panel. Zheng [15] measured the heat transfer properties of honeycomb sandwich panel up to 900 C. Zhu [16], Ye [17] and Kumar [18] developed the effective thermal conductivity of foam through theoretical modeling, experiments and numerical simulation, respectively. However, few studies focused on the heat transfer properties of lattice core sandwich panels, needless to say the heat transfer experiments of lattice sandwich panels under high temperature environments up to 1150 C. In this present work, C/SiC pyramidal core lattice sandwich panel was proposed and fabricated. The heat transfer properties of the as-prepared C/SiC lattice sandwich panel were evaluated from 600 to 1150 C. A three dimensional finite element simulation model was built to calculate the heat transfer of the C/SiC lattice sandwich panel. Finally, the equivalent thermal conductivity of the C/SiC lattice sandwich panel was successfully calculated under different front surface temperatures.
2. Fabrication and thermal experimental characterization The C/SiC pyramidal core sandwich panel was fabricated and the details of the process have been introduced in our previous work
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[19]. Fig. 1a gives a typical as-prepared C/SiC lattice sandwich panel. The unit cell is consisted of two face sheets and a pyramidal core, as shown in Fig. 1b. The dimensionless relative density r of the core can be given by [7]:
r¼
rC ¼ rS
p$d2 $l pffiffiffi 2 l$sinu$ 2$l$cosu
(1)
It characterizes the lightweight property of the lattice sandwich panel compared to its parent material. Where rC and rS are the densities of the pyramidal lattice core and parent material, respectively. d, l and u represent the diameter, length and inclined angle of the core rods, respectively. t is the thickness of the face sheet. In this study, t, d and l are 3.8, 2.0, and 18.5 mm, respectively. u is 45 . Thus the r is calculated to be 5.18%. Therefore, compared with bulk C/SiC core, the design of C/SiC lattice sandwich panel greatly reduces the relative density and finally realizes lightweight successfully. The microstructure of the cross section of the face sheet is illustrated in Fig. 2a. It is observed that the carbon fibers are covered with SiC (Fig. 2b). An infrared radiation heating system (School of Astronautics, Beijing University of Aeronautics and Astronautics, Beijing, China) was utilized to simulate aerodynamic heating processes on the front surface of the C/SiC pyramidal core sandwich panel. As shown in Fig. 3, a quartz infrared radiator was consisted of two staggered densely arrayed row quartz lamps. A reflector with a water cooling system was installed on back of the quartz lamps. Then, the infrared radiation was reflected to the specimen by the reflector during thermal tests. The C/SiC pyramidal core sandwich panel specimen (100 100 27 mm, containing 4 4 cells in-plane) was laid upright with its front surface faced to the quartz infrared radiator. The back surface of the specimen exchanged its heat through natural convection and radiation with the ambient environment. A porous ceramic adiabatic frame was fixed to the four sides of the specimen to reduce boundary heat dissipation. An automatic temperature control system was used for the aerodynamic thermal simulation experiment. The details of the control system, the control model and algorithm are described by Zheng [15]. This system is a sophisticated experimental system and has been used in many studies [20,21]. A K-type thermocouple was assigned to point-1 on the center of front surface of the C/SiC lattice sandwich panel, as shown in Fig. 4a. Inorganic high temperature glue named HN-767A (Haonian Glue Technology Co., Ltd., Tungkun, China) was used to bond the thermocouple on the surface of the C/SiC sandwich panel. Considering the periodic meso-structure of the pyramidal core configuration, two distinguishing point types were conducted, as illustrated in Fig. 4b. Type I meant the connection points of the four core rods to the face sheet, and Type II was denoted as the center point of the face sheet. Hence, point-2 and point-3~6 represented Type I and Type II points of the center unit cell, respectively. Point-7 belonged to Type I point of the adjacent unit cell. In the first 200 s, A maximum testing temperature of 600, 800, 1000 and 1150 C were conducted to simulate the severe aerodynamic heating, respectively. Then, an adequate loading time 1200 s was subsequently held to stabilize the heat transfer process. Finally, the temperature of the testing points were measured and evaluated. 3. Numerical simulation 3.1. Lattice sandwich panel model
Fig. 1. (a): C/SiC pyramidal core lattice sandwich panel. (b): The geometrical parameters of the unit cell.
In Fig. 5, the model is consisted of two face sheets and pyramidal lattice core with 4 4 unit cells along the two in-plane directions.
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Fig. 2. (a): The SEM photograph of the cross-section for the face sheet. (b): EDS analysis.
linear hexahedral heat transfer element: DC3D8 (8-node linear heat transfer brick in Abaqus definition). Mesh quality was checked to avoid distortion and unreasonable ratio of the mesh side length. Mesh sensitivity analysis was performed with 5 different mesh sizes from 328,000 to 624,000. The analysis revealed that the results became accurate grid-independent under condition that more than 402,000 elements were used to mesh the model. This mesh size leaded to 4 and 100 meshes in the thickness and width directions of the face sheets. The core bars were meshed with 8, 30 and 60 meshes in the radial, angular and length directions, respectively. Finally, this mesh size was utilized in the following simulation. 3.2. Heat transfer process simulation Fig. 3. Schematic diagram of experimental setup.
Mesh sensitivity study is a necessary analysis to ensure that the numerical simulation results are grid-independent [22,23]. The geometrical model was meshed through the preprocessor of Abaqus. The core rods, up and down face sheets were meshed with
Various reports have studied the forced convection in the lattice core sandwich panels [24,25]. However, due to the complexity of the core geometry, the heat transfer mechanism of the lattice panel has never been reported till now. On the other hand, it is found that thermal conduction and thermal cavity radiation are the main heat processes in the lattice sandwich panel in our previous work [19].
Fig. 4. Temperature testing points arrangement of the specimen. Point-1 on the front surface and Point-2e7 on the back surface.
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Facet is a face of the element. Each facet is assumed to be isothermal and to have a uniform emissivity. The superscripts i and j represent different facets. εi, εj, Ti, Tj are the emissivities and temperatures of facet i and j. s is the StefaneBoltzmann constant, and Tz is the absolute zero on the temperature scale used. Fik is the viewfactor matrix and Ckj is the reflection matrix. All interior surfaces of the face sheets and the outside surfaces of the core rods are assumed to be gray bodies. The surface emissivity of the C/SiC has been widely studied [29]. It has been demonstrated that different heat treatment and surface morphology significantly affected the surface emissivity. In our study, ε ¼ 0.85 is therefore chosen for all surfaces on the C/SiC sandwich panel. 3.3. Boundary conditions
Fig. 5. Numerical simulation model.
Therefore, in the simulation procedure of heat transfer, the heat exchange by the thermal conduction and thermal cavity radiation are considered, as sketched in Fig. 5. Firstly, the heat flows from the upper face sheet along the rods and arrives at the down face sheet, which is described by three dimensional transient heat conduction equation as follows [26]:
vT v vT v vT v vT Ks þ Ks þ Ks rs c$ ¼ vt vx vx vy vy vz vz
(2)
where T is temperature, rs is density, Ks is thermal conductivity, and c is specific heat. t is time and x, y, z are the Cartesian coordinates. The gaseous conduction is in general several orders lower than the C/SiC and it is not included in this primary simulation model. The density of the C/SiC rs is 2.0 g/cm3. Zhang [27] reported a temperature dependent thermal diffusivity a(T) of the C/SiC. Based on the relationship of the a to rs, c and Ks: a(T) ¼ Ks(T)/rs$c(T), the specific heat c is chosen as a constant value of 1420 J/kg C. Hence, the temperature dependent thermal conductivity can be calculated and listed in Table 1. Besides, thermal cavity radiation conducts among the inner surfaces of the two face sheets and the outside surfaces of core rods. The radiation heat flux in the core of lattice sandwich panel qri for facet i is calculated via Eq. (3) [28].
qri ¼ s$εi
N X j¼1
εj
N X
1 Fik Ckj
Tj Tz
4
ðTi Tz Þ4
(3)
k¼1
Ckj ¼ dkj ð1 εi ÞFkj
(4)
Table 1 Temperature dependent thermal conductivity of C/SiC [27]. T ( C)
Ks (W/m C)
T ( C)
Ks (W/m C)
20 100 200 300 400 500 600
9.3 8.2 7.2 6.4 5.9 5.5 5.2
700 800 900 1000 1100 1200
5.0 4.9 4.8 4.7 4.6 4.5
A temperature boundary condition is loaded on the front surface of the C/SiC lattice sandwich panel since the front surface is heated through infrared radiation heating system. For the back surface, natural convection and radiation are the heat dissipation to the ambient environment. Newton's law of cooling is used to calculate the natural convection heat flux. The natural convection heat transfer coefficient of the C/SiC sandwich panel surface is calculated using an empirical correlation for natural convection for a vertical plate as shown in Eq. (5). This empirical correlation can be used over the whole range of Rayleigh number [30]. Where NmL is the Nusselt number, RaL is the Rayleigh number, and Pr is the Prandtl number.
0 NmL
B ¼ @0:825 þ
12 0:387RaL 1 þ ð0:492=PrÞ
9=16
C 8=27 A
qrad ¼ εs Tb4 Ta4
(5)
(6)
The radiation heat flux is calculated by Eq. (6). Where ε and Tb are the surface emissivity and temperature of the back surface, respectively. Ta is the ambient temperature. Additionally, to simulate the insulation effects of the porous ceramic adiabatic frame, adiabatic boundaries are assigned to the four sides of the model. 4. Results and discussion 4.1. Temperature evolution and distribution The measured temperature of test-point 1 and the preset control curve are compared in Fig. 6. The preset control temperature curves and the measured temperatures of the test-pint 1 almost coincide with each other, which reveal a very high control and measurement accuracy of temperature of the system. Owing to the cellular meso-structure of the lattice sandwich panel and the low thermal conductivity of the C/SiC, the temperatures of the back surface Tb (testing points-2e7) gradually increase in the first 200 s, showing a hysteresis relative to the loading temperature. After the hysteresis stage, the heat transfer process accelerates to achieve stable state as the temperature of the front surface Tf keep as the target temperature. The final temperature difference DT ¼ T1 T2 (where T1 and T2 are the temperature of point-1 and point-2) is marked in Fig. 6. With the max loading temperature increases from 600 to 1150 C, the temperature difference DT expands from 130.4 to 207.6 C. The final temperature values of the testing points on back surface are summarized in Fig. 7. Compared to the max loading temperature, the final temperatures shows little difference with each other. The reason for this near homogeneous temperature
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K. Wei et al. / Applied Thermal Engineering 81 (2015) 10e17
Fig. 6. Temperature history of the testing points.
distribution is attributed to the finally stabilized in-plane heat transfer of the back face sheet. As shown in Fig. 8, debonding damage in the back face sheet appears. Since the face sheets are 2D weaving C/SiC, the incompatible thermal deformation between the matrix and fibers leads to significant debonding. The core rods also suffer ablation. Excessively large thermal deformation of the TPS in high temperature environment will lead to the undesirable change of aerodynamic shape and flight trajectory of hypersonic vehicles. However, the front face sheet of the C/SiC sandwich panel only slightly deform and flex after 1150 C thermal testing. Therefore, it is demonstrated that the C/SiC sandwich panel can be used as the sandwich structure of the integrated TPS under high temperature environment.
Fig. 7. The final stable temperatures of the testing points on back surface.
4.2. Heat insulation effect In order to describe the thermal heat insulation effect, heat insulation effect J is defined as:
J¼
T1 T2 100% T1
(7)
The heat insulation effect J with the testing loading time is illustrated in Fig. 9. Due to the cellular meso-structure of the lattice sandwich panel and the low thermal conductivity of C/SiC, the C/ SiC lattice sandwich panel has low thermal diffusivity. At the severe heating in the initial stage, the low thermal diffusivity limits the temperature acceleration on the back surface, resulting in large temperature difference and high heat insulation effect. Consequently, a peak value around 90% is observed at 150 s. Afterward, the temperature difference gradually becomes much smaller with the heating process further proceeding, and the heat insulation effect also decreases and stabilizes at about 20%. So, the C/SiC lattice sandwich panel exhibits high heat insulation effect at the beginning of the high temperature loading and considerable insulation effect at the stabilized stage. This finding provides an important
Fig. 8. Thermal damage of the specimen after experiments.
K. Wei et al. / Applied Thermal Engineering 81 (2015) 10e17
Fig. 9. Heat insulation effect J of C/SiC lattice sandwich panel.
experimental data for the potential application as the hot structures.
4.3. Numerical simulation results Fig. 10 shows the typical temperature distribution of the overall C/SiC sandwich panel and its back surface. According to Fig. 11, the numerical calculated temperature curves show the same evolution tendency with the experiments and there is always a negative temperature difference between the numerical and experimental results. The detailed final temperature of the back surface Tb and relative errors are listed in Table 2. The relative error decreased
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Fig. 11. Back surface temperature in simulation and experiments for different front surface temperature: 600e1150 C.
with the front surface temperature Tf increased. When Tf ¼ 600 C, the calculated Tb is 12% lower than the measured value. However, the error decreases to 10.1% when Tf ¼ 800 C. With Tf increases to 1000e1150 C, the relative errors are only 5.0e6.0%, indicating that the calculated temperature is very closed to the measured results. These results can be understand as follow. In the experiments, the total heat flux qExp can be decomposed as:
qExp ¼ qc;s þ qc;gas þ qr þ qconv
(8)
Where the qc,s and qc,gas are the heat flux due to the thermal conduction of the C/SiC and the gas in the core of the C/SiC sandwich panel, respectively. qr and qconv are the heat flux generated by the
Fig. 10. The temperature distribution of (a): the C/SiC lattice sandwich panel, (b): back surface (front surface temperature was 600 C, t ¼ 1200 s).
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Table 2 Comparison of back surface temperature between experiments and simulation. Front surface temperature ( C)
Back surface temperature (experimental measured) ( C)
Back surface temperature (numerical calculated) ( C)
Error (%)
600 800 1000 1150
461.1 651.0 821.5 943.3
405.7 585.0 772.2 896.1
12.0 10.1 6.0 5.0
thermal cavity radiation and convection in the core, respectively. In our primary simulation model, only the thermal conduction of C/ SiC and thermal cavity radiation in the core are considered as the main heat exchange procedures. The total heat flux in simulation qSim is:
qSim ¼ qc;s þ qr
(9)
So, the systematical lower deviation of the simulation results to the experiments is resulted from the ignorance of qc,gas and qconv. The stable heat flux qc,s and qc,gas can be broad estimated according to the Fourier's law. qconv can be estimated based on the Newton's law of cooling. The radiation heat flux qr can be estimated according to the radiation of two infinite parallel panels. The expressions are as follow:
qc;s Ks $ Tf Tb
(10)
qc;gas Kgas $ Tf Tb
(11)
qconv h$ Tf Tb
(12)
qr
s$ε 4 $ Tf Tb4 ¼ r$ Tf Tb 2ε
s$ε 3 $ Tf þ Tb3 r¼ 2ε
(13) 5. Conclusions
(14)
where the Tf and Tb are the temperatures of front and back surfaces. h is the convective heat transfer coefficient. ε is surface emissivity. The relative difference of the qSim and qExp can be calculated as follow:
qExp qSim qc;gas þ qconv Kgas þ h ¼ qExp qc;s þ qc;gas þ qr þ qconv Ks þ Kgas þ r þ h
transfer of lattice sandwich panels. qc,gas and qconv should not be ignored when the loading temperature on the front surface Tf is not high. While with Tf is higher than 1150 C, the deviation of Tb is no more than 5%. A simplified numerical simulation model for the C/ SiC lattice sandwich panel which contains the main heat transfer processes can give relative precise (relative error is less than 5%) temperature results forTf 1150 C. We hope these findings will provide significant reference to the studies of the heat transfer mechanism in lattice sandwich panels. The detailed and systematical theoretical and experimental studies of the gas conduction and natural convection in the core of the lattice sandwich panels are in the progress of our further work. Fig. 12 shows the equivalent thermal conductivity of the C/SiC lattice sandwich panel. Keq increases from 1.98 to 4.95 W/(m C) when Tf increases from 600 to 1150 C, indicating a strong temperature dependence of the equivalent thermal conductivity. Even though the thermal conductivity Ks of C/SiC decreases with temperature as listed in Table 1, while the surface emissivity increases significantly and the thermal cavity radiation in the C/SiC lattice sandwich panel is quartic dependent on temperature as mentioned before. The cavity thermal radiation becomes the dominant heat transfer process and accelerates heat transfer rapidly in high temperature. Therefore, even with the same temperature difference between the front and the back surfaces, the higher temperature environment results in larger heat flux and equivalent thermal conductivity. Based on this analysis, the reduction of the thermal cavity radiation in C/SiC lattice sandwich panel will significantly raise the heat insulation effect and reduce the equivalent thermal conductivity. The C/SiC lattice sandwich panel is expected to be used as the integrated TPS. The insulation materials such as saffil fibers filled in the pore of the lattice will block the thermal cavity radiation. Reduction of the surface emissivity will be another effective approach to weaken the thermal cavity radiation.
(15)
We can find that r is cubic dependence of the temperature. With Tf increases, the thermal cavity radiation in the sandwich panel accelerates rapidly. Moreover, the surface emissivity of the C/SiC increases significantly with the temperature increment [29]. These two main reasons enable the cavity thermal radiation to be the dominant heat transfer process in C/SiC lattice sandwich panel in high temperature environment. Similar conclusion is also found in our previous work [19]. The r increases quickly and lead to rapid increase of the qr compared to other heat fluxes. Therefore, the proportion of the qr in the total heat flux rises significantly with Tf increase, indicating the proportion of qc,gas and qconv decreases correspondingly. Ultimately, the influence of the underestimation of the gas conduction and natural convection decreases which leads to smaller relative error. This conclusion has been demonstrated since the relative error of Tb in simulation and experiments decreases from 12.0% to 5.0% with Tf increase from 600 to 1150 C. The deviation of the simulation and experiments exactly reveals the role of the gas conduction and natural convection in heat
In this study, C/SiC pyramidal core lattice sandwich panel was proposed and fabricated. The heat transfer properties of the asprepared C/SiC lattice sandwich panel were experimental tested from 600 to 1150 C. A numerical simulation model was built to calculate the heat transfer of the C/SiC lattice sandwich panel. Main results are listed as follow: (1) C/SiC lattice sandwich panel was fabricated by interweaving process and chemical vapor infiltration (CVI). The relative
Fig. 12. Equivalent thermal conductivity Keq of C/SiC lattice sandwich panel.
K. Wei et al. / Applied Thermal Engineering 81 (2015) 10e17
(2)
(3)
(4)
(5)
density of the as-prepared sandwich panel is only 5.18%, indicating that lightweight characteristic is realized successfully. The heat insulation effect of C/SiC lattice sandwich panel achieves a peak value around 90% at 150 s and stabilized at a value of about 20%. The front face sheet of the C/SiC sandwich panel only slightly deforms and flexes after high temperature of 1150 C thermal testing, primarily demonstrated that the C/SiC sandwich panel can be used as the sandwich structure for integrated TPS in high temperature environment. The equivalent thermal conductivity of the C/SiC lattice sandwich panel varies from 1.98 to 4.95 W/(m C) when the front surface temperature increases from 600 to 1150 C. Thermal cavity radiation is the dominant heat transfer process in high temperature. The numerical simulation model for the C/SiC lattice sandwich panel which contained the main heat transfer processes could give relative precise (relative error was less than 5%) temperature simulation results for high temperature environment.
Acknowledgements This work was supported by National Natural Science Foundation of China under grants (Nos. 11402003, 11227801 and 90816025) and the National Basic Research Program of China (Nos. G2010CB832701, 2011CB610303 and 2011CB606105). The authors would like to acknowledge Prof. Dafang Wu and Prof. Bing Pan from Beijing University of Aeronautics and Astronautics, PR China. References [1] T.A. Parthasarathy, M.D. Petry, M.K. Cinibulk, T. Mathur, M.R. Gruber, Thermal and oxidation response of UHTC leading edge samples exposed to simulated hypersonic flight conditions, J. Am. Ceram. Soc. 96 (2013) 907e915. [2] K. Wei, R.J. He, X.M. Cheng, R.B. Zhang, Y.M. Pei, D.N. Fang, Fabrication and mechanical properties of lightweight ZrO2 ceramic corrugated core sandwich panels, Mater. Des. 64 (2014) 91e95. [3] G. David, Ceramic matrix composite (CMC) thermal protection systems (TPS) and hot structures for hypersonic vehicles, in: AIAA 2008-2682, 15th AIAA International Space Planes and Hypersonic Systems and Technologies Conference, Ohio, 2008. [4] S.K. Bapanapalli, O.M. Martinez, C. Gogu, B.V. Sankar, R.T. Haftka, M.L. Blosser, Analysis and design of corrugated-core sandwich panels for thermal protection systems of space vehicles, in: AIAA 2008-2682, 47th Structures, Structural Dynamics, and Materials Conference, Newport, Rhode Island, 2006. [5] A. Vigliotti, D. Pasini, Mechanical properties of hierarchical lattices, Mech. Mater. 62 (2013) 32e43. [6] H.L. Fan, F.H. Meng, W. Yang, Sandwich panels with Kagome lattice cores reinforced by carbon fibers, Compos. Struct. 81 (2007) 533e539. [7] H.N. Wadley, Multifunctional periodic cellular metals, Philos. Trans. R. Soc. A 364 (2006) 31e68. [8] H.N. Wadley, A.G. Evans, Fabrication and structural performance of periodic cellular metal sandwich structures, Compos. Sci. Technol. 63 (2003) 2331e2343. [9] J. Tian, T. Kim, T.J. Lu, H.P. Hodson, D.T. Queheillalt, D.J. Sypeck, H.N. Wadley, The effects of topology upon fluid-flow and heat-transfer within cellular copper structures, Int. J. Heat Mass Transf. 47 (2004) 3171e3186. [10] H. Fan, L. Yang, F. Sun, D. Fang, Compression and bending performances of carbon fiber reinforced lattice-core sandwich composites, Compos. Part A Appl. Sci. Manuf. 52 (2013) 118e125. [11] B. Wang, G.Q. Zhang, Q.L. He, L. Ma, L.Z. Wu, J.C. Feng, Mechanical behavior of carbon fiber reinforced polymer composite sandwich panels with 2-D lattice truss cores, Mater. Des. 55 (2014) 591e596. [12] S.W. Li, Z.D. Feng, Y.S. Liu, W.B. Yang, W.H. Zhang, L.F. Cheng, Microstructural evolution of coating-modified 3D C/SiC composites after annealing in wet oxygen at different temperatures, Corros. Sci. 52 (2010) 2837e2845. [13] X.C. Liu, L.F. Cheng, L.T. Zhang, N. Dong, S.J. Wu, Z.X. Meng, Tensile properties and damage evolution in a 3D C/SiC composite at cryogenic temperatures, Mater. Sci. Eng. A 528 (2011) 7524e7528. [14] R.T. Swann, C.M. Pittman, Analysis of Effective Thermal Conductivities of Honeycomb-core and Corrugated-core Sandwich Panels, April 1961. NASA Technical Note D-714.
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Nomenclature r: relative density of the lattice core (%) rc: density of pyramidal lattice core (kg/m3) rs: density of C/SiC (kg/m3) d: diameter of the core rod (m) l: length of the core rod (m) t: thickness of the face sheet (m) u: inclined angle of the core rod ( ) T: temperature ( C) c: specific heat of C/SiC (J/kg C) Ks: thermal conductivity of C/SiC (W/m C) ε: surface emissivity a: thermal diffusion coefficient (m2/s) t: time (S) qr: radiation heat flux of facet (W/m2) s: StefaneBoltzmann constant F: viewfactor matrix C: reflection matrix NmL: Nusselt number RaL: Rayleigh number Pr: Prandtl number qrad: radiation heat flux of back surface (W/m2) Tb: temperature of back surface ( C) Ta: ambient temperature ( C) Tf: temperature of front surface ( C) DT: temperature difference ( C) J: heat insulation effect (%) qExp: total heat flux of C/SiC sandwich panel in experiments (W/m2) qSim: total heat flux of C/SiC sandwich panel in simulation (W/m2) qc,s: heat flux of thermal conduction of C/SiC (W/m2) qc,gas: heat flux of thermal conduction of gas (W/m2) qr: heat flux of thermal cavity radiation (W/m2) qconv: heat flux of convection in the core (W/m2) h: convective heat transfer coefficient (W/m2 C) Keq: equivalent thermal conductivity of the C/SiC lattice sandwich panel (W/m C)
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Research paper
Fabrication and heat transfer characteristics of C/SiC pyramidal core lattice sandwich panel Kai Wei a, Rujie He a, Xiangmeng Cheng a, Yongmao Pei a, Rubing Zhang b, *, Daining Fang a, ** a b
State Key Laboratory for Turbulence and Complex System, College of Engineering, Peking University, Beijing 100871, PR China Department of Mechanics, School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, PR China
h i g h l i g h t s Lightweight C/SiC lattice panel was firstly proposed and fabricated. Heat transfer properties of the C/SiC lattice panel were tested up to 1150 C. The heat insulation effect of C/SiC lattice panel achieved a peak value 90%. The equivalent conductivity of the C/SiC lattice panel increased with temperature.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 6 October 2014 Accepted 6 February 2015 Available online 14 February 2015
Lightweight C/SiC pyramidal core lattice sandwich panel was proposed and fabricated for potential applications as hot structure and thermal protection system (TPS). The heat transfer characteristics of C/ SiC lattice sandwich panel were measured from 600 to 1150 C through an aerodynamic heating simulation experimental system. Temperature distribution on the back surface of the lattice sandwich panel was obtained through periodical thermocouple assignment. Heat insulation effects under different temperatures were also investigated. Finally, a three dimensional finite element simulation model was built to calculate the heat transfer of the C/SiC lattice sandwich panel. The equivalent thermal conductivity of the C/SiC lattice sandwich panel varied from 1.98 to 4.95 W/(m C) when the front surface temperature increased from 600 to 1150 C. It is believed that these results can provide a foundational understanding on the heat transfer characteristics of C/SiC lattice sandwich panel. © 2015 Elsevier Ltd. All rights reserved.
Keywords: C/SiC lattice sandwich panel Heat transfer Finite element simulation Equivalent thermal conductivity
1. Introduction Reusable launch vehicle (RLV) and hypersonic vehicle have been extensively studied in the past decades [1]. It is found that one of the most important issues is the thermal protection system (TPS). The TPS protects the interior from high-speed aerodynamic heating and provides sufficient structural strength and stiffness to retain the aerodynamic shape [2]. Recent developments of thermal protection technology promote various new types of thermal protection system. Great efforts have been made to develop an efficient integrated TPS [3]. The key design of the integrated TPS is the
* Corresponding author. Tel.: þ86 1051684070. ** Corresponding author. Tel.: þ86 1062760322. E-mail addresses: [email protected] (R. (D. Fang).
Zhang),
http://dx.doi.org/10.1016/j.applthermaleng.2015.02.012 1359-4311/© 2015 Elsevier Ltd. All rights reserved.
[email protected]
sandwich panel which acts as not only the main load bearing structure but also the thermal insulation material vessel [4]. Fortunately, lattice sandwich panels are found to exhibit integrated properties of lightweight natural instinct and high specific strength/stiffness [5,6]. Therefore, lattice sandwich panels are expected to be promising candidates for integrated TPS. However, up to now, only metal [7-9] and fiber reinforced resin matrix composite [10,11] lattice sandwich panels were reported. Wadley [7,8], Tian [9] developed several manufacture techniques to fabricate lattice core sandwich panels with aluminum, stainless steel nickel and copper. Fang [10] and Wu [11] reported an interweaving and hot compression molding method for fabricating the lattice sandwich panels with carbon and glass fiber reinforced resin matrix composites. Unfortunately, both the metal and fiber reinforced resin matrix composite lattice sandwich panels cannot be used for integrated TPS, owing to their low melting point and weak
K. Wei et al. / Applied Thermal Engineering 81 (2015) 10e17
oxidation resistance under high temperature environment. Recently, carbon fiber reinforced silicon carbide matrix composite (C/SiC) has been studied extensively due to its superior specific mechanical properties under elevated high temperature and thermal oxidative environment [12,13]. However, studies on the C/SiC lattice sandwich panel have never been reported. In addition, heat transfer properties play important roles on the hot structures. Many previous reports investigated the heat transfer of the sandwich structures with honeycomb [14,15] or foam core [16-18]. Swann and Pittman [14] developed a semi-empirical formula to predict the effective thermal conductivity of honeycomb sandwich panel. Zheng [15] measured the heat transfer properties of honeycomb sandwich panel up to 900 C. Zhu [16], Ye [17] and Kumar [18] developed the effective thermal conductivity of foam through theoretical modeling, experiments and numerical simulation, respectively. However, few studies focused on the heat transfer properties of lattice core sandwich panels, needless to say the heat transfer experiments of lattice sandwich panels under high temperature environments up to 1150 C. In this present work, C/SiC pyramidal core lattice sandwich panel was proposed and fabricated. The heat transfer properties of the as-prepared C/SiC lattice sandwich panel were evaluated from 600 to 1150 C. A three dimensional finite element simulation model was built to calculate the heat transfer of the C/SiC lattice sandwich panel. Finally, the equivalent thermal conductivity of the C/SiC lattice sandwich panel was successfully calculated under different front surface temperatures.
2. Fabrication and thermal experimental characterization The C/SiC pyramidal core sandwich panel was fabricated and the details of the process have been introduced in our previous work
11
[19]. Fig. 1a gives a typical as-prepared C/SiC lattice sandwich panel. The unit cell is consisted of two face sheets and a pyramidal core, as shown in Fig. 1b. The dimensionless relative density r of the core can be given by [7]:
r¼
rC ¼ rS
p$d2 $l pffiffiffi 2 l$sinu$ 2$l$cosu
(1)
It characterizes the lightweight property of the lattice sandwich panel compared to its parent material. Where rC and rS are the densities of the pyramidal lattice core and parent material, respectively. d, l and u represent the diameter, length and inclined angle of the core rods, respectively. t is the thickness of the face sheet. In this study, t, d and l are 3.8, 2.0, and 18.5 mm, respectively. u is 45 . Thus the r is calculated to be 5.18%. Therefore, compared with bulk C/SiC core, the design of C/SiC lattice sandwich panel greatly reduces the relative density and finally realizes lightweight successfully. The microstructure of the cross section of the face sheet is illustrated in Fig. 2a. It is observed that the carbon fibers are covered with SiC (Fig. 2b). An infrared radiation heating system (School of Astronautics, Beijing University of Aeronautics and Astronautics, Beijing, China) was utilized to simulate aerodynamic heating processes on the front surface of the C/SiC pyramidal core sandwich panel. As shown in Fig. 3, a quartz infrared radiator was consisted of two staggered densely arrayed row quartz lamps. A reflector with a water cooling system was installed on back of the quartz lamps. Then, the infrared radiation was reflected to the specimen by the reflector during thermal tests. The C/SiC pyramidal core sandwich panel specimen (100 100 27 mm, containing 4 4 cells in-plane) was laid upright with its front surface faced to the quartz infrared radiator. The back surface of the specimen exchanged its heat through natural convection and radiation with the ambient environment. A porous ceramic adiabatic frame was fixed to the four sides of the specimen to reduce boundary heat dissipation. An automatic temperature control system was used for the aerodynamic thermal simulation experiment. The details of the control system, the control model and algorithm are described by Zheng [15]. This system is a sophisticated experimental system and has been used in many studies [20,21]. A K-type thermocouple was assigned to point-1 on the center of front surface of the C/SiC lattice sandwich panel, as shown in Fig. 4a. Inorganic high temperature glue named HN-767A (Haonian Glue Technology Co., Ltd., Tungkun, China) was used to bond the thermocouple on the surface of the C/SiC sandwich panel. Considering the periodic meso-structure of the pyramidal core configuration, two distinguishing point types were conducted, as illustrated in Fig. 4b. Type I meant the connection points of the four core rods to the face sheet, and Type II was denoted as the center point of the face sheet. Hence, point-2 and point-3~6 represented Type I and Type II points of the center unit cell, respectively. Point-7 belonged to Type I point of the adjacent unit cell. In the first 200 s, A maximum testing temperature of 600, 800, 1000 and 1150 C were conducted to simulate the severe aerodynamic heating, respectively. Then, an adequate loading time 1200 s was subsequently held to stabilize the heat transfer process. Finally, the temperature of the testing points were measured and evaluated. 3. Numerical simulation 3.1. Lattice sandwich panel model
Fig. 1. (a): C/SiC pyramidal core lattice sandwich panel. (b): The geometrical parameters of the unit cell.
In Fig. 5, the model is consisted of two face sheets and pyramidal lattice core with 4 4 unit cells along the two in-plane directions.
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Fig. 2. (a): The SEM photograph of the cross-section for the face sheet. (b): EDS analysis.
linear hexahedral heat transfer element: DC3D8 (8-node linear heat transfer brick in Abaqus definition). Mesh quality was checked to avoid distortion and unreasonable ratio of the mesh side length. Mesh sensitivity analysis was performed with 5 different mesh sizes from 328,000 to 624,000. The analysis revealed that the results became accurate grid-independent under condition that more than 402,000 elements were used to mesh the model. This mesh size leaded to 4 and 100 meshes in the thickness and width directions of the face sheets. The core bars were meshed with 8, 30 and 60 meshes in the radial, angular and length directions, respectively. Finally, this mesh size was utilized in the following simulation. 3.2. Heat transfer process simulation Fig. 3. Schematic diagram of experimental setup.
Mesh sensitivity study is a necessary analysis to ensure that the numerical simulation results are grid-independent [22,23]. The geometrical model was meshed through the preprocessor of Abaqus. The core rods, up and down face sheets were meshed with
Various reports have studied the forced convection in the lattice core sandwich panels [24,25]. However, due to the complexity of the core geometry, the heat transfer mechanism of the lattice panel has never been reported till now. On the other hand, it is found that thermal conduction and thermal cavity radiation are the main heat processes in the lattice sandwich panel in our previous work [19].
Fig. 4. Temperature testing points arrangement of the specimen. Point-1 on the front surface and Point-2e7 on the back surface.
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Facet is a face of the element. Each facet is assumed to be isothermal and to have a uniform emissivity. The superscripts i and j represent different facets. εi, εj, Ti, Tj are the emissivities and temperatures of facet i and j. s is the StefaneBoltzmann constant, and Tz is the absolute zero on the temperature scale used. Fik is the viewfactor matrix and Ckj is the reflection matrix. All interior surfaces of the face sheets and the outside surfaces of the core rods are assumed to be gray bodies. The surface emissivity of the C/SiC has been widely studied [29]. It has been demonstrated that different heat treatment and surface morphology significantly affected the surface emissivity. In our study, ε ¼ 0.85 is therefore chosen for all surfaces on the C/SiC sandwich panel. 3.3. Boundary conditions
Fig. 5. Numerical simulation model.
Therefore, in the simulation procedure of heat transfer, the heat exchange by the thermal conduction and thermal cavity radiation are considered, as sketched in Fig. 5. Firstly, the heat flows from the upper face sheet along the rods and arrives at the down face sheet, which is described by three dimensional transient heat conduction equation as follows [26]:
vT v vT v vT v vT Ks þ Ks þ Ks rs c$ ¼ vt vx vx vy vy vz vz
(2)
where T is temperature, rs is density, Ks is thermal conductivity, and c is specific heat. t is time and x, y, z are the Cartesian coordinates. The gaseous conduction is in general several orders lower than the C/SiC and it is not included in this primary simulation model. The density of the C/SiC rs is 2.0 g/cm3. Zhang [27] reported a temperature dependent thermal diffusivity a(T) of the C/SiC. Based on the relationship of the a to rs, c and Ks: a(T) ¼ Ks(T)/rs$c(T), the specific heat c is chosen as a constant value of 1420 J/kg C. Hence, the temperature dependent thermal conductivity can be calculated and listed in Table 1. Besides, thermal cavity radiation conducts among the inner surfaces of the two face sheets and the outside surfaces of core rods. The radiation heat flux in the core of lattice sandwich panel qri for facet i is calculated via Eq. (3) [28].
qri ¼ s$εi
N X j¼1
εj
N X
1 Fik Ckj
Tj Tz
4
ðTi Tz Þ4
(3)
k¼1
Ckj ¼ dkj ð1 εi ÞFkj
(4)
Table 1 Temperature dependent thermal conductivity of C/SiC [27]. T ( C)
Ks (W/m C)
T ( C)
Ks (W/m C)
20 100 200 300 400 500 600
9.3 8.2 7.2 6.4 5.9 5.5 5.2
700 800 900 1000 1100 1200
5.0 4.9 4.8 4.7 4.6 4.5
A temperature boundary condition is loaded on the front surface of the C/SiC lattice sandwich panel since the front surface is heated through infrared radiation heating system. For the back surface, natural convection and radiation are the heat dissipation to the ambient environment. Newton's law of cooling is used to calculate the natural convection heat flux. The natural convection heat transfer coefficient of the C/SiC sandwich panel surface is calculated using an empirical correlation for natural convection for a vertical plate as shown in Eq. (5). This empirical correlation can be used over the whole range of Rayleigh number [30]. Where NmL is the Nusselt number, RaL is the Rayleigh number, and Pr is the Prandtl number.
0 NmL
B ¼ @0:825 þ
12 0:387RaL 1 þ ð0:492=PrÞ
9=16
C 8=27 A
qrad ¼ εs Tb4 Ta4
(5)
(6)
The radiation heat flux is calculated by Eq. (6). Where ε and Tb are the surface emissivity and temperature of the back surface, respectively. Ta is the ambient temperature. Additionally, to simulate the insulation effects of the porous ceramic adiabatic frame, adiabatic boundaries are assigned to the four sides of the model. 4. Results and discussion 4.1. Temperature evolution and distribution The measured temperature of test-point 1 and the preset control curve are compared in Fig. 6. The preset control temperature curves and the measured temperatures of the test-pint 1 almost coincide with each other, which reveal a very high control and measurement accuracy of temperature of the system. Owing to the cellular meso-structure of the lattice sandwich panel and the low thermal conductivity of the C/SiC, the temperatures of the back surface Tb (testing points-2e7) gradually increase in the first 200 s, showing a hysteresis relative to the loading temperature. After the hysteresis stage, the heat transfer process accelerates to achieve stable state as the temperature of the front surface Tf keep as the target temperature. The final temperature difference DT ¼ T1 T2 (where T1 and T2 are the temperature of point-1 and point-2) is marked in Fig. 6. With the max loading temperature increases from 600 to 1150 C, the temperature difference DT expands from 130.4 to 207.6 C. The final temperature values of the testing points on back surface are summarized in Fig. 7. Compared to the max loading temperature, the final temperatures shows little difference with each other. The reason for this near homogeneous temperature
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Fig. 6. Temperature history of the testing points.
distribution is attributed to the finally stabilized in-plane heat transfer of the back face sheet. As shown in Fig. 8, debonding damage in the back face sheet appears. Since the face sheets are 2D weaving C/SiC, the incompatible thermal deformation between the matrix and fibers leads to significant debonding. The core rods also suffer ablation. Excessively large thermal deformation of the TPS in high temperature environment will lead to the undesirable change of aerodynamic shape and flight trajectory of hypersonic vehicles. However, the front face sheet of the C/SiC sandwich panel only slightly deform and flex after 1150 C thermal testing. Therefore, it is demonstrated that the C/SiC sandwich panel can be used as the sandwich structure of the integrated TPS under high temperature environment.
Fig. 7. The final stable temperatures of the testing points on back surface.
4.2. Heat insulation effect In order to describe the thermal heat insulation effect, heat insulation effect J is defined as:
J¼
T1 T2 100% T1
(7)
The heat insulation effect J with the testing loading time is illustrated in Fig. 9. Due to the cellular meso-structure of the lattice sandwich panel and the low thermal conductivity of C/SiC, the C/ SiC lattice sandwich panel has low thermal diffusivity. At the severe heating in the initial stage, the low thermal diffusivity limits the temperature acceleration on the back surface, resulting in large temperature difference and high heat insulation effect. Consequently, a peak value around 90% is observed at 150 s. Afterward, the temperature difference gradually becomes much smaller with the heating process further proceeding, and the heat insulation effect also decreases and stabilizes at about 20%. So, the C/SiC lattice sandwich panel exhibits high heat insulation effect at the beginning of the high temperature loading and considerable insulation effect at the stabilized stage. This finding provides an important
Fig. 8. Thermal damage of the specimen after experiments.
K. Wei et al. / Applied Thermal Engineering 81 (2015) 10e17
Fig. 9. Heat insulation effect J of C/SiC lattice sandwich panel.
experimental data for the potential application as the hot structures.
4.3. Numerical simulation results Fig. 10 shows the typical temperature distribution of the overall C/SiC sandwich panel and its back surface. According to Fig. 11, the numerical calculated temperature curves show the same evolution tendency with the experiments and there is always a negative temperature difference between the numerical and experimental results. The detailed final temperature of the back surface Tb and relative errors are listed in Table 2. The relative error decreased
15
Fig. 11. Back surface temperature in simulation and experiments for different front surface temperature: 600e1150 C.
with the front surface temperature Tf increased. When Tf ¼ 600 C, the calculated Tb is 12% lower than the measured value. However, the error decreases to 10.1% when Tf ¼ 800 C. With Tf increases to 1000e1150 C, the relative errors are only 5.0e6.0%, indicating that the calculated temperature is very closed to the measured results. These results can be understand as follow. In the experiments, the total heat flux qExp can be decomposed as:
qExp ¼ qc;s þ qc;gas þ qr þ qconv
(8)
Where the qc,s and qc,gas are the heat flux due to the thermal conduction of the C/SiC and the gas in the core of the C/SiC sandwich panel, respectively. qr and qconv are the heat flux generated by the
Fig. 10. The temperature distribution of (a): the C/SiC lattice sandwich panel, (b): back surface (front surface temperature was 600 C, t ¼ 1200 s).
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Table 2 Comparison of back surface temperature between experiments and simulation. Front surface temperature ( C)
Back surface temperature (experimental measured) ( C)
Back surface temperature (numerical calculated) ( C)
Error (%)
600 800 1000 1150
461.1 651.0 821.5 943.3
405.7 585.0 772.2 896.1
12.0 10.1 6.0 5.0
thermal cavity radiation and convection in the core, respectively. In our primary simulation model, only the thermal conduction of C/ SiC and thermal cavity radiation in the core are considered as the main heat exchange procedures. The total heat flux in simulation qSim is:
qSim ¼ qc;s þ qr
(9)
So, the systematical lower deviation of the simulation results to the experiments is resulted from the ignorance of qc,gas and qconv. The stable heat flux qc,s and qc,gas can be broad estimated according to the Fourier's law. qconv can be estimated based on the Newton's law of cooling. The radiation heat flux qr can be estimated according to the radiation of two infinite parallel panels. The expressions are as follow:
qc;s Ks $ Tf Tb
(10)
qc;gas Kgas $ Tf Tb
(11)
qconv h$ Tf Tb
(12)
qr
s$ε 4 $ Tf Tb4 ¼ r$ Tf Tb 2ε
s$ε 3 $ Tf þ Tb3 r¼ 2ε
(13) 5. Conclusions
(14)
where the Tf and Tb are the temperatures of front and back surfaces. h is the convective heat transfer coefficient. ε is surface emissivity. The relative difference of the qSim and qExp can be calculated as follow:
qExp qSim qc;gas þ qconv Kgas þ h ¼ qExp qc;s þ qc;gas þ qr þ qconv Ks þ Kgas þ r þ h
transfer of lattice sandwich panels. qc,gas and qconv should not be ignored when the loading temperature on the front surface Tf is not high. While with Tf is higher than 1150 C, the deviation of Tb is no more than 5%. A simplified numerical simulation model for the C/ SiC lattice sandwich panel which contains the main heat transfer processes can give relative precise (relative error is less than 5%) temperature results forTf 1150 C. We hope these findings will provide significant reference to the studies of the heat transfer mechanism in lattice sandwich panels. The detailed and systematical theoretical and experimental studies of the gas conduction and natural convection in the core of the lattice sandwich panels are in the progress of our further work. Fig. 12 shows the equivalent thermal conductivity of the C/SiC lattice sandwich panel. Keq increases from 1.98 to 4.95 W/(m C) when Tf increases from 600 to 1150 C, indicating a strong temperature dependence of the equivalent thermal conductivity. Even though the thermal conductivity Ks of C/SiC decreases with temperature as listed in Table 1, while the surface emissivity increases significantly and the thermal cavity radiation in the C/SiC lattice sandwich panel is quartic dependent on temperature as mentioned before. The cavity thermal radiation becomes the dominant heat transfer process and accelerates heat transfer rapidly in high temperature. Therefore, even with the same temperature difference between the front and the back surfaces, the higher temperature environment results in larger heat flux and equivalent thermal conductivity. Based on this analysis, the reduction of the thermal cavity radiation in C/SiC lattice sandwich panel will significantly raise the heat insulation effect and reduce the equivalent thermal conductivity. The C/SiC lattice sandwich panel is expected to be used as the integrated TPS. The insulation materials such as saffil fibers filled in the pore of the lattice will block the thermal cavity radiation. Reduction of the surface emissivity will be another effective approach to weaken the thermal cavity radiation.
(15)
We can find that r is cubic dependence of the temperature. With Tf increases, the thermal cavity radiation in the sandwich panel accelerates rapidly. Moreover, the surface emissivity of the C/SiC increases significantly with the temperature increment [29]. These two main reasons enable the cavity thermal radiation to be the dominant heat transfer process in C/SiC lattice sandwich panel in high temperature environment. Similar conclusion is also found in our previous work [19]. The r increases quickly and lead to rapid increase of the qr compared to other heat fluxes. Therefore, the proportion of the qr in the total heat flux rises significantly with Tf increase, indicating the proportion of qc,gas and qconv decreases correspondingly. Ultimately, the influence of the underestimation of the gas conduction and natural convection decreases which leads to smaller relative error. This conclusion has been demonstrated since the relative error of Tb in simulation and experiments decreases from 12.0% to 5.0% with Tf increase from 600 to 1150 C. The deviation of the simulation and experiments exactly reveals the role of the gas conduction and natural convection in heat
In this study, C/SiC pyramidal core lattice sandwich panel was proposed and fabricated. The heat transfer properties of the asprepared C/SiC lattice sandwich panel were experimental tested from 600 to 1150 C. A numerical simulation model was built to calculate the heat transfer of the C/SiC lattice sandwich panel. Main results are listed as follow: (1) C/SiC lattice sandwich panel was fabricated by interweaving process and chemical vapor infiltration (CVI). The relative
Fig. 12. Equivalent thermal conductivity Keq of C/SiC lattice sandwich panel.
K. Wei et al. / Applied Thermal Engineering 81 (2015) 10e17
(2)
(3)
(4)
(5)
density of the as-prepared sandwich panel is only 5.18%, indicating that lightweight characteristic is realized successfully. The heat insulation effect of C/SiC lattice sandwich panel achieves a peak value around 90% at 150 s and stabilized at a value of about 20%. The front face sheet of the C/SiC sandwich panel only slightly deforms and flexes after high temperature of 1150 C thermal testing, primarily demonstrated that the C/SiC sandwich panel can be used as the sandwich structure for integrated TPS in high temperature environment. The equivalent thermal conductivity of the C/SiC lattice sandwich panel varies from 1.98 to 4.95 W/(m C) when the front surface temperature increases from 600 to 1150 C. Thermal cavity radiation is the dominant heat transfer process in high temperature. The numerical simulation model for the C/SiC lattice sandwich panel which contained the main heat transfer processes could give relative precise (relative error was less than 5%) temperature simulation results for high temperature environment.
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Nomenclature r: relative density of the lattice core (%) rc: density of pyramidal lattice core (kg/m3) rs: density of C/SiC (kg/m3) d: diameter of the core rod (m) l: length of the core rod (m) t: thickness of the face sheet (m) u: inclined angle of the core rod ( ) T: temperature ( C) c: specific heat of C/SiC (J/kg C) Ks: thermal conductivity of C/SiC (W/m C) ε: surface emissivity a: thermal diffusion coefficient (m2/s) t: time (S) qr: radiation heat flux of facet (W/m2) s: StefaneBoltzmann constant F: viewfactor matrix C: reflection matrix NmL: Nusselt number RaL: Rayleigh number Pr: Prandtl number qrad: radiation heat flux of back surface (W/m2) Tb: temperature of back surface ( C) Ta: ambient temperature ( C) Tf: temperature of front surface ( C) DT: temperature difference ( C) J: heat insulation effect (%) qExp: total heat flux of C/SiC sandwich panel in experiments (W/m2) qSim: total heat flux of C/SiC sandwich panel in simulation (W/m2) qc,s: heat flux of thermal conduction of C/SiC (W/m2) qc,gas: heat flux of thermal conduction of gas (W/m2) qr: heat flux of thermal cavity radiation (W/m2) qconv: heat flux of convection in the core (W/m2) h: convective heat transfer coefficient (W/m2 C) Keq: equivalent thermal conductivity of the C/SiC lattice sandwich panel (W/m C)