Zhong Chen,Vince Rodriguez, November 2013
I. INTRUDUCTION In the heating process of microwave absorbers under incident electromagnetic waves, two disciplines of physics are intertwined, i.e., electromagnetic waves behavior governed by Maxwell’s equations and heat transfer process dictated by laws of thermodynamics. The power density in the absorbers due to the electromagnetic .eld is given by p= s|E|2 =2po0 o ' f|E|2 (1) where, E is the total electric .eld (V/m) in the material, s is electrical conductivity of the material (S/m), o0 is the free space permittivity (8.854 × 10-12 F/m), o' is the imaginary part of the relative dielectric constant, and f is the frequency in Hz. This is point form of the Joule’s law, and is well understood by RF engineers. The EM behavior of the polyurethane absorbers can be numerically computed. The EM .eld acts as the heating source, and its distribution in the absorber can provide a good indication on the locations of hot spots. Polyurethane foam is an excellent insulator, so the conductive heat loss may be minimal. The heat exchanges can be reasonably described by radiation and convection transfers. Radiation takes place in the form of EM wave, mainly in the infrared region. The net power transferred from a body to the surroundings is described by Stefan-Boltzmann’s law [1], prad = osA(T4 -T04 ) (2) where A is the surface area, T is the surface temperature of the radiation body in K, and T0 is the ambient temperature in K. Unfortunately, the conventional symbols used in heat transfer s and o are not the same as those in Eq. (1). s here is the emissivity or emission coef.cient, and is de.ned as the ratio of the actual radiation emitted and the radiation that would be from a black body. o in Eq. (2) is the Stefan-Boltzmann constant (5.67 × 10-8 W/m2 K4 ). The context in the paper should make it clear which symbols the authors are referring to. Otherwise, we will make explicit references. The convective heat transfer is due to the motion of air surrounding the absorbers. Two forms can take place, naturally or by forced air. The relationship is described by Newton’s law of cooling [1]: pconv = hA(T -T0 ) (3) where h is the convection heat transfer coef.cient in (W/m-2 K-1 ). h is often treated as a constant, although it can be a function of the temperature. Eq. (3) assumes that the ambient air is abundant, and is taken to be constant. This is a reasonable assumption, because the heating is typically con.ned to a small localized area in a relatively large anechoic chamber. Combining the two mechanisms of heat transfer, the total heat loss is given by p= osA(T4 -T4 )+ hA(T -T0 ) (4) 0 It is possible to solve for the temperatures from coupled Maxwell’s and heat transfer equations. Realistic results require accurate electrical and thermal properties of the materials. It is often a non-trivial process to obtain the material properties in and of itself. Careful validation is warranted before we can have full con.dence in the results. In this paper, we adopt a measurement approach instead. We conduct a series of experiments to measure the temperature both on the surface of the absorbers using an infrared imaging camera, and internally using thermocouple probes inserted into the absorbers. Temperature pro.les versus applied E .eld are experimentally established. From the measured data, we curve .t to Eq. (4) or other mathematical functions. These functions are useful to calculate results at other .eld levels, e.g., extrapolating to a higher .eld where measurement results cannot be readily obtained. II. FIELD DISTRIBUTION INSIDE THE ABSORBERS Numerical analysis was performed using Ansys HFSS, a commercially available Finite Elements software package. As it was described in [2], symmetry is taken advantage of, so only one quarter of the pyramidal absorber is solved. The quarter pyramid is located inside a square cross section prism that bounds the computational domain. The structure is fed using a port located on the top of the geometry and the side boundaries of the domain are set as perfect electric conductor (PEC) or perfect magnetic conductor (PMC). The base is modeled as PEC. This is exactly the same approach taken in [2]. The structure of a CRV-23PCL-4 is analyzed at 12.4 GHz, the same frequency as used in the measurements. The resulting .eld is extracted at one plane. The plane is one of the two orthogonal planes that cut the pyramid in 4 sections. Fig. 1 shows the .eld distribution at 12.4 GHz. The curvature of the absorber pro.le has been added for clarity. The results are an approximation. The permittivity of the material is assumed to be fairly constant from 6 GHz to 12 GHz. The purpose of the numerical analysis is to check the expected .eld distribution in the pyramid, which we can use to compare with the infrared (IR) images of the absorbers taken during the measurements. Fig. 1. Electric Field distribution at 12.4 GHz The .eld distribution data shows that most of the .eld exists on the upper third of the pyramid. It also shows that there is a region of high .eld existing in the valleys between the pyramids. The surface temperature pro.le from the IR pictures shows that this is an real phenomena. On the other hand, the .eld is higher at the very tip of the absorber. Measurements from the IR images seem to contradict this result. This can be explained. Since the tip is smaller, it cools faster to the surrounding ambient temperature. III. EXPERIMENTAL SETUP AND DATA Experiments were performed on ETS-Lindgren CRV-23PCL-8, and CRV-23PCL-4 absorbers at 12.4 GHz. Both types are 23” long from tips to bases. A piece has a base size of 2’ × 2’. A CRV-23PCL-8 piece consists of 8×8=64 pyramids, whereas a CRV-23PCL-4 piece consists of 4×4=16 pyramids. The two types are designed to have similar RF performances, but the CRV-23PCL-8 is made of slender pyramids to facilitate better heat transfers to the surroundings [2]. The absorbers are mounted on a particle board with metallic backings, and are placed in front a Ku band horn antenna with a circular aperture (the gain is approximately 20 dBi). A 300W ampli.er is used, and the power to the antenna is monitored through a 40 dB directional coupler connected to a power meter. The test setup is shown in Fig. 2. The ambient temperature is at 23.C. Fig. 2. Test setup using a conical horn antenna to illuminate the absorbers As a .rst step, a 200 V/m .eld is generated by leveling to a calibrated electric .eld probe. The distance from the probe to the antenna is 30”. At this distance, near .eld coupling is assumed neglegible, and the incident wave uniform (numerical simulation also validated these assumptions). The power needed to generate 200 V/m .eld is recorded. Next, the .eld probe is replaced with the absorbers under test. The tips of the absorbers are placed at the same distance (30”) from the antenna. Other .eld strengths can be leveled by scaling from the power for 200 V/m. A. Surface Temperature Figs. 3 and 4 show two examples of the infrared images taken after the temperature reached equilibrium under a constant 700 V/m CW at f=12.4 GHz for the two types of absorbers described earlier. There is no forced air.ow during the measurement. Table 1 summarizes the resulting temperatures on the absorber surfaces at different .eld levels. Tests were performed on two .nishes of otherwise identical CRV-23PCL-8 absorbers, i.e., fully covered with rubberized paint, or with latex paint. The data indicates that the paint has minimal effects on absorber temperatures. Table 1 also lists data for the wider CRV-23PCL-4 absorbers (with latex paint). B. Internal Temperature of the Absorber recorded by Thermocouples Three thermocouples are inserted in the CRV-23PCL-8 which are painted with rubberized coating. They are inserted at distances of 4”, 6”, and 8” from the tip of the pyramid, as illustrated in Fig. 5. Fig. 6 shows the temperatures measured by the three sensors. The temperatures at 8” from the tip are consistently higher than at other locations. There is a gap in the data at 700 V/m because RF power was turned off brie.y. Internal temperature reached 115 .C under 1.7 kW/m2 Fig. 3. Infrared camera image for incident electric .eld of 700 V/m. The absorber is the slender CRV-23PCL-8. Fig. 4. Infrared camera image for incident electric .eld of 700 V/m. The absorber is the wider CRV-23PCL-4. (800 V/m). Since the maximum allowed temperature for the polyurethane foam material is 125 .C, the incident power density is recommended to stay less than 1.7 kW/m2 for CRV-23PCL-8 absorbers mounted vertically and with natural convection in a 23.C room. After the temperature reached equilibrium under 800 V/m, additional air.ow was introduced by turning on a 6” diameter fan at 45” in front of the absorbers. The air.ow rate was measured to be approximately 80 ft/min at this distance. Note that this is a rather moderate air.ow, which can arise naturally from air-conditioning vents in a chamber. As shown in Fig. 6, the internal temperature quickly dropped to 102.C from 115.C. TABLE I MAXIMUM SURFACE TEMPERATURE RECORDED BY THE IR CAMERA (AT EQUILIBRIUM). T0 =23. C. E Power CRV-23PCL-8 CRV-23PCL-8 CRV-23PCL-4 (V/m) Density rubberized latex (. C) rubberized (kW/m2 ) (. C) (. C) 200 0.11 24 300 0.24 28 360 0.34 30 400 0.42 35 36 43 500 0.66 41 50 600 0.95 54 67 700 1.30 63 82