NUMERICAL SIMULATION ON THERMAL CONTACT RESISTANCE OF PRACTICAL SOLID SURFACES

Transcription

1 Proceedings of the Asian Conference on Thermal Sciences 2017, 1st ACTS March 26-30, 2017, Jeju Island, Korea ACTS-P00642 NUMERICAL SIMULATION ON THERMAL CONTACT RESISTANCE OF PRACTICAL SOLID SURFACES Yan-Jun Dai, Jian-Jun Gou, Xing-Jie Ren, Fan Bai, Wen-Quan Tao * Key Laboratory of Thermo-Fluid Science and Engineering of MOE, School of Energy and Power Engineering, Xi an Jiaotong University, Xi an, Shaanxi , China Presenting Author: daiyanjun@stu.xjtu.edu.cn * Corresponding Author: wqtao@mail.xjtu.edu.cn ABSTRACT This paper raised an approach to predict thermal contact resistance (TCR) of two practical solid surfaces under high temperature and high pressure. The real surface topography of each specimen suraface was measured by a surface profiler named Bruker Contour GT-K 3D Optical Microscope. The numerical contact model was generated in ANSA according to the data of surface topography from the microscope and the simulation was implemented with software ABAQUS. Based on the elastic-plastic constitutive equations of the specimen and three-dimensional steady state heat conduction theory, finite element analysis of contact model was performed with ABAQUS in the light of sequential coupling method. The studied specimen pairs are Ti-6Al-4V Ti-6Al-4V with two different roughness. To verify the accuracy of the method, the simulated results from ABAQUS were compared with the experimental results under the same boundary conditions. And they are in good agreement with each other. This method can be used to predict TCR in different pressure, temperature and roughness in the engineering application. KEYWORDS: Thermal contact resistance, Simulation, Roughness, High temperature, High pressure. 1. INTRODUCTION Thermal contact conductance (TCC), which is the reciprocal of thermal contact resistance (TCR), is a key factor on the thermal protection system design in the aerospace engineering. For example, the magnitude of the TCR must be figured out to predict the thermally induced stresses between the outer layer material and structure of aerodynamically heated supersonic flight vehicles. During the past decades, numerous experimental measurements and theoretical study have been conducted to determine the TCR between various materials. One of the most adoptive theoretical thermal contact conductance models was developed by Cooper, Mikic, and Yovanovich (CMY) for isotropic surfaces deforming plastically[1]. Madhusudana experimentally studied the effect of heat losses to the surroundings and analyzed the accuracy in TCC experiments[2]. Ding and Wang experimentally investigated the TCC of stainless steel-gfrp interface under vacuum environment[3]. Zhang et al. established a high-precision instrumentation to measure TCR using reversible heat flux[4]. Liu et al. conducted the high temperature TCR between high thermal conductivity C/C material and Inconel 600[5]. Choi and Kim [6]carried out experiment on TCR between metals below 100K. Meanwhile, a lot of numerical simulation work have been implemented on TCR. Black analyzed and predicted the constriction resistance for contact between rough engineering surfaces[7]. Cui et al. carried out the multiscale simulation of thermal contact resistance in electronic packaging[8]. Verma and Mazumder extracted TCC of metal-metal contacts from scale-resolved direct numerical simulation[9]. Zou et al. developed a random number model based on fractal geometry to calculate the TCC[10]. Murashov and Panin numerically simulated the contact heat transfer problem with work hardened rough surfaces[11]. All the above mentioned numerical simulation are based on the fractal or other methods, not on the practical surfaces. 1

2 In this paper, we adopt a white light interference microscope to measure the rough surfaces of the specimen pair Ti-6Al-4V Ti-6Al-4V, and the coordinates of the roughness are used to generate the numerical model. Then the commercial software ABAQUS are employed to implement the TCR calculation. Besides,TCR of 12 cases with different temperatures and loading pressures are experimentally measured based on 1-D steady state heat flux method. The numerical results agree very well with the experimental results with the same boundary condition of all the cases. 2.1 COMPUTATIONAL REGION 2. NUMERICAL MODAL Fig. 1(a) shows the computational region including the two specimens. And the size of the real specimens used in the experiment are illustrated in Fig. 1(b). Each specimen is 48mm in diameter and 48mm in height. In order to reduce the computational complexity, only the blue box region is selected as the computational region. Fig. 1(a) The computational region Fig. 1(b) The size of the specimens 2.2 ROUGH SURFACES The surface topography of the two surfaces are measured by a microscope (Bruker 3D Contour GT-K) with the vertical resolution 0.1nm. Fig. 3 shows the microscope and Fig. 4 shows the measurement system. The measured data can be imported to ANSA to reconstruct its 3-D morphology by self-written program with Python. Fig.5 shows the surface topography of the upper surface and the lower surface TC4 pair. The mean absolute deviation R a and standard deviation Rq of the roughness of the lower Ti specimen are and 31.49μm, for the upper Ti specimen are and 17.95μm. The computational region of each specimen has about 28,165 data points. Fig. 3 Bruker 3D Contour GT-k Fig. 4 Surface topography measurement system 2

3 (a)up-inner-surface Fig. 5 Surface topography (b)down-inner-surface 2.4 NUMERICAL METHOD AND BOUNDARY CONDITIONS The finite element method is used in this paper for both mechanical contact analysis and heat transfer analysis. Sequential coupling algorithm is adopted to solve the thermomechanical coupled problem. C3D8 linear element is used to solve the mechanics problem while DC3D8 is the corresponding thermal model element to solve the diffusive heat transfer problem. The model contains 1,778,432 hexahedral elements and 1,858,890 nodes. The boundary conditions for the mechanical contact problem can be describe as: Up-surface: ux uy 0, p p0 Down-surface: u u u 0 where u x, directions. u y p 0, u z x y z Up-round and Down-round: u u 0 represent displacement in x, y, z directions respectively. represents the pressure measured by the pressure sensor. The boundary conditions for the heat transfer problem can be described as: Up-surface: T T where T represents the temperature, temperature of down-surface. 3.1 CONTACT ANALYSIS Down-surface: T T down Up-round and Down-round: q 0 T up up x y represents the temperature of up-surface, 3.RESULTS AND DISCUSSION p represents the pressure in z T down represents the Fig. 6 shows the real contact area distribution under the loading pressures of , , , , 0.3, 4.65, 7.78, 12MPa respectively. The conclusion can be drawn that the real contact area increases with the loading pressure increases. Fig. 7 shows the stress distribution of contact surface under pressures of 4.65, 7.78, 12.08MPa respectively. We can see that with the increase of loading pressure, the contact stress increases. 3.2 THERMAL ANALYSIS In this paper, 12 cases are simulated (under pressures of 4.65, 7.78, MPa at the heating temperature of 400,500,600,700 resprectively). Fig. 8 shows the temperature contours of the up-inner-surface (the 3

4 Fig. 6 The real contact area distribution under different loading pressures Fig.7 Proportion of real contact area and stress distribution under different loading pressures upper three figures) and the down-inner-surface (the lower three figures) under different pressures at the heating temperature of 400. With the increase of loading pressure, the average temperature difference between up-inner-surface and down-inner-surface decreases under the pressure range investigated. 3.3 COMPARISON WITH EXPERIMENTAL RESULTS To verify the accuracy of the method, the simulated results from ABAQUS are compared with the experimental results under the same boundary conditions and the results are listed in table 1. We can see that the maximum deviation is 9.5% while 75% results' deviation is within 5%. This numerical method has high accuracy. 4. CONCLUSIONS This paper raised an approach to predict thermal contact resistance (TCR) of two practical solid surfaces under high temperature and high pressure. The surface topography of contact surfaces are measured by a 4

5 surface profiler and used to establish a numerical model to investigate the contact mechanical deformation and heat transfer. Then the TCR can be obtained. The numerical results indicate: 1. The present method can be adopted to predict the TCR between rough contact surfaces very well. 2. The thermal contact resistance decreases with the increase of the pressure in the study temperature range. 3. The thermal contact resistance decreases slowly with the increase of the temperature under the study pressure range. Pressure(MPa) Table 1. Comparison of numerical results with experimental results Heating temperature( ) TCR(Exp.) (m 2 K/W) TCR(Num.) (m 2 K/W) Difference (%) Fig. 8 Contact surfaces temperature distribution under different loading pressures 5

6 ACKNOWLEDGMENT This study is supported by the Key Project of International Joint Research of National Nature Science Foundation of China ( ). REFERENCE [1] M.G. Cooper, B.B. Mikic and M.M Yovanovich., Thermal contactnconductance, Int. J. Heat Transfer 12(1969) [2] C.V. Madhusudana, Accuracy in thermal contact conductance experiments - The effect of heat losses to the surroundings, Int. Com. Heat Mass Transfer 27(2000) [3] C.Ding, R. Wang, Thermal contact conductance of stainless steel-gfrp interface under vacuum environment. Exp.Thermal Fluid Science. 42(2012) 1-5. [4] P. Zhang, Y.M. Xuan, Q. Li,A high-precision instrumentation of measuring thermal contact resistance using reversible heat flux. Exp.Thermal Fluid Science. 54(2014) [5] D.H. Liu, Y. Luo, X. Shang, Experimental investigation of high temperature thermal contact resistance between high thermal conductivity C/C material and Inconel 600. Int. J. Heat Mass Transfer 80(2015) [6] Y.S. Choi, M.S. Kim. Experiments on thermal contact conductance between metals below 100 K, AIP Conference Proceedings. 1573(2014) [7] A.F. Black, V. Singhal, S.V. Garimella Analysis and prediction of constriction resistance for contact between rough engineering surfaces. J. Thermophysics Heat Transfer. 18(2004) [8] T.F. Cui, Q. Li, Y.M. Xuan, P. Zhang, Multiscale simulation of thermal contact resistance in electronic packaging. Int. J. Thermal Sciences. 83(2014) [9] N.N. Verma, S. Mazumder Extraction of thermal contact conductance of metal metal contacts from scale-resolved direct numerical simulation. Int. J. Heat Mass Transfer. 94(2016) [10] M.Q. Zou, B.M. Yu, J.C. Cai, P. Xu Fractal model for thermal contact conductance. J. Heat Transfer-Transactions of the ASME. 130(2008) [11] M.V. Murashov, S.D. Panin, Numerical modelling of contact heat transfer problem with work hardened rough surfaces. Int. J. Heat Mass Transfer 90(2015)