18 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS ON EFFECTIVE THERMAL CONDUCTIVITY OF SUPER ALLOY HONEYCOMB CORE IN SANDWICH STRUCTURES J. Zhao 1 *, Z.H. Xie 1 , L. Li 2 , W. Li 1 , J. Tian 1 1 College of Astronautics, Northwestern Polytechnical University Xi’an, China, 2 Aircraft Strength Research Institute of China, Xi’an, China * Corresponding author( zhaojian.net@ gmail.edu.cn) Keywords : Honeycomb core, sandwich, effective thermal conductivity, finite element method q is the heat flux along the thickness direction, λ is 1 General Introduction The Honeycomb core sandwich structures are the effective thermal conductivity of the specimen, widely used in aerospace applications due to their dT / dx is the temperature gradient in the thickness high specific strength and specific stiffness, good direction. While the thermal equilibrium is achieved, thermal insulation and vibration absorption q equals to the total heat flux dissipated from the capabilities, etc. A typical sandwich panel consists outer face, i.e. the summation of thermal radiation of three layers: two thin and stiff face sheets and a flux and thermal convection flux. lightweight core (Fig.1). In many cases, heat transfer The radiation heat flux can be obtained according to analysis is necessary for the design of sandwich Stefan-Boltzmann’s Law: structures. Due to the discontinuity of honeycomb = εσ − cores, heat transfer modes in sandwich structures 4 4 q ( T T ) (2) r 1 a usually include heat conduction, heat radiation and ε is the emissivity of the specimen upper face, σ is heat convection and are quite complex. Modeling a detailed sandwich structure in thermal analysis is Stefan-Boltzmann constant, T is the ambient a very difficult, extremely costly and sometimes even temperature. impossible in real engineering applications. It is The thermal convection between the specimen upper commonly expected that a discontinuous honeycomb face and the ambient air can be regarded as natural core can be replaced as a continuum with effective convection problem in infinite space, as can be macroscopic thermal parameters, such as thermal computed according to the experimental correlation conductivity and specific thermal capacity. This formula for natural convection in infinite space. The paper mainly focuses on the experimental and simplified equations are adopted to calculate the heat numerical methods to determine the macroscopic transfer of natural convection in infinite space [1]: effective thermal conductivities of honeycomb cores. = Pr) n N C Gr ( (3) u 2 Experimental Methods α Δ 3 g tl = The effective thermal conductivities of honeycomb (4) Gr υ 2 sandwich structure specimen at different temperatures were measured using static test method. N is the Nusselt number. Gr is the Grashof number, As shown in Fig.2, in the test, the specimen was u α is the volume expansion coefficient, Δ is the t placed on a heating plate, surrounded by zirconia temperature difference between upper face and fiber insulations; upper face of the specimen was environment, υ is the kinematic viscosity coefficient exposed in air. The heat dissipated from the upper under reference temperature, l is the reference length, face was in two forms: thermal radiation and thermal g is the gravity acceleration. convection. According to Fourier’s Law, the heat For the heated isothermal horizontal surface facing flux along the thickness direction is: upward, the experimental correlations which has dT been used extensively for the Nusselt number can be = − λ q (1) dx given as [1]:
acquisition computer, as shown in Fig.3, high- ⎧ = ≤ ≤ ⎪ 1/4 4 7 N 0.54( Gr Pr) ,10 Gr Pr 10 velocity thermo couples were utilized to measure the ⎨ u (5) = ≤ ≤ surface temperatures of the both sides of the ⎪ 1/3 7 11 ⎩ N 0.15( Gr Pr) ,10 Gr Pr 10 u specimen. The honeycomb core sandwich structure specimen was made of super alloy Hastelloy X, its λ dimensions are illustrated in Fig.4. A standard = f h N (6) u specimen of same surface condition with the l specimen upper surface was manufactured to λ l is the characteristic length, is the thermal measure its emissivity, the result is 0.54; the inner f conductivity of fluid at reference temperature, h is surface of the core cavity undergoes sufficient oxidization, its emissivity is 0.85 [2]. the thermal transfer coefficient for thermal convective heat transfer. 3 Theoretical Model According to Newton’s Law of Cooling, the Complex thermal transfer modes exist in the convective heat flux can be given as follows: honeycomb core cavity when it is heated, including = − q h T ( T ) (7) heat conduction of cell foils, conduction and c 1 a convection of gas, thermal radiation between Thus, the total heat flux dissipated from the upper different surfaces. surface to environment can be calculated by The Swann and Pittman semi-empirical model has summing Eq.2 and Eq.7. With the temperatures of been utilized as a standard in aerospace industry to the both sides of the specimen be obtained, the total predict the effective thermal conductivity of thermal conductivity of the sandwich structure can honeycomb core panels [3,4]. Swann and Pittman be derived from Eq.1; moreover, the conductivity of analyzed the combined heat transfer problem of honeycomb core itself can be derived using thermal honeycomb sandwich structure using finite resistance analysis method. difference method, developed a semi-empirical Total thermal resistance of the honeycomb sandwich model for computing radiation heat transfer in the is: core cavity. Moreover, Swann and Pittman − developed an parallel thermal network model to T T = 2 1 R (8) compute the effective thermal conductivity of the q o honeycomb sandwich structure [5]: The upper face sheet, honeycomb core and lower Δ Δ ⎛ ⎞ A A = + − + face sheet of the sandwich structure can be treated as ⎜ ⎟ k k k 1 k (10) e f g ⎝ ⎠ r A A series connection for heat transfer. According to the principle of superimposition of thermal resistance in Where k is the effective thermal conductivity, it is a series, total thermal resistance of the sandwich e function of honeycomb core geometries and material structure equals to summation of the resistance of thermal properties; k , k and k are the thermal the three parts: f g r conductivities contributed by the constitutive foil t t t = + + 1 c 2 R material, the gas in the core cavity and the radiation (9) λ λ λ Δ respectively; is the ratio of the cross-section m c m A / A area of solid core to the entire honeycomb core. t , 2 t , c t are the thicknesses of the upper face sheet, 1 The thermal conductivity of gas can be obtained honeycomb core and lower face sheet respectively, from: λ is the thermal conductivity of the face sheets, is m * the effective thermal conductivity of the honeycomb k = ( ) g k ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ core itself. g − α γ λ (11) 2 2 1 ⎜ ⎟⎜ ⎟⎜ ⎟ + 1 2 ⎝ ⎠⎝ The experimental system consists of high ⎠⎝ ⎠ α γ + 1 P L r c temperature heater, thyristor control system, PSI multi-channel temperature scanning valve and data
Recommend
More recommend
