Comparing 2-D Conduction Experiments with Simulation

Transcription

1 Comparing 2-D Conduction Experiments with Simulation Introduction Simulation techniques are often used in industry as a beneficial part in the development process whether an engineer or scientist is designing a prototype component, studying the interaction of two systems or developing a process. After using the tool simple2d, you should be aware of the power of simulation. By using simple2d in Example 3, you were able to look at the 2-D conduction of a system at various boundary conditions quickly. Simulation allows the user to set up a framework that describes a physical system and make changes to parameters of interest to study the behavior of the system. An alternative approach to simulation is physical experimentation. Physical experiments, however, require a physical representation of the system to be tested. Often the physical representation of the system is more costly to construct than simulating it numerically. Because various computational tools (e.g. MapleSim, Matlab/Simulink, ANSYS Fluent) are now available to engineers and experimentation is often costly, simulation techniques are becoming increasingly more popular in both industry and academia. Experiment 1 The simple system for we will test consists of one aluminum block oriented so the bottom face of the block is in direct contact with a hot plate (simulating a fixed temperature boundary condition) while the remaining edges are exposed to a room temperature environment (22.22 C) at atmospheric pressure ( kpa). We will look at the temperature gradient across one face of the block. Figure 1 shows the set up for Experiment 1. Isometric View Front View 2 cm 6 cm 6 cm Top View Figure 1: Plain aluminum block atop the hot plate

2 We would like to study the temperature gradient across the 6 cm x 6 cm face of the block. By insulating the two 6 cm x 6 cm surfaces with high temperature silicon insulation we will transform the 3-D block into a 2-D system. Figure 2 shows the aluminum block with the high temperature silicon insulation attached with custom brackets. The brackets were place so as to not contact the aluminum block. Figure 2: Insulated aluminum block atop hotplate A network of T-type thermocouples were attached to the face of the block with 1 cm spacing in the both the x and y direction using epoxy. Figure 3 shows the aluminum block with the thermocouples attached. Figure 3: Plain aluminum block with thermocouples atop the hot plate

3 J-B KWIK two-part epoxy was the original choice for attaching thermocouples to the block face. However, the use of J-B KWIK did not always result in ample contact between the thermocouples and block face. After numerous attempts to obtain good contact at the thermocouple/block surface interface, J-B KWIK was substituted with OB-101 from Omega at certain nodes. The J-B KWIK and OB-101 appear in black and white respectively in Figure 3. During the first initial testing phases of this experiment it was found that the bottom face of the aluminum block and top surface of the hotplate were not in good contact creating a high contact resistance. An aluminum plate was placed between aluminum block and hotplate to alleviate complications due to the contact resistance. A thermal epoxy was applied to interface between the top surface of the aluminum plate and the bottom surface of the aluminum block. With the aluminum plate serving as an additional layer between the hot plate and block; the hot plate would be heated to a temperature sufficient enough to allow the top surface of the aluminum plate to reach the desired fixed temperature boundary condition for the experiment. Figure 4 illustrates the experimental set up used in Experiment 1. Conducting Experiment 1 Figure 4: Experimental set up used in Experiment 1 With the experimental setup complete; the block was placed atop the hotplate. The experiment began by adjusting the hotplate surface temperature so the aluminum plate temperature between the block and hotplate is correct for the fixed temperature boundary condition. Three different temperatures (50 C, 75 C and 100 C) were tested as the fixed temperature boundary condition. The data was read into a manageable digital file by using a data acquisition system.

4 Experiment 1 Result Figure 5 illustrates the nodal locations with red dots and the location of the fixed temperature boundary condition with a yellow line Figure 5: Nodal locations Figure 6 shows the data for experiment 1 at each case tested (50 C, 75 C and 100 C). The cells of each grid highlighted in red correspond to the red dots on the aluminum block shown in Figure 5. The cells highlighted in yellow correspond the fixed temperature boundary edge. The temperature of the fixed temperature boundary condition was fixed using a hot plate. The temperatures shown in the yellow cells were measured using T-type thermocouples. The accuracy of the temperature display of the hot plate versus the actual average temperature of the center of the hot plate is ± 5.0 C. Fixed Edge 50 C (49.89 C) Fixed Edge 75 C (74.56 C) Fixed Edge 100 C (97.73 C) Figure 6: Nodal temperatures for experiment 1 with fixed edge temperatures 50 C, 75 C and 100 C

5 Simulating Experiment 1 A more in-depth (than simple2d) script was written using the finite difference methodology in Matlab to predict the nodal temperatures in experiment 1 as accurately as possible. In simple2d, the user supplies a convection coefficient as an educated guess. The main difference between the simulation of Experiment 1 and simple2d is that the convection coefficients of the left, right and top edge are calculated in the simulation of Experiment 1 using the methodology described in the How to Calculate the Free Convection Coefficient document. Additionally, the thermal conductivity of the block is not considered constant but as a function of temperature. Calculating the convection coefficient for each node on the aluminum block exposed to ambient air introduces additional complexity in the simulation. The simulation script for Experiment 1 requires the nodal spacing, ambient temperature and the temperature of the fixed temperature boundary condition. Figures 7-9 show the nodal temperature for comparison of the experiment and simulation. Experiment Simulated Free Convection Coefficients (W/m 2 C) Figure 7: Experiment, simulated nodal temperatures and convection coefficients where the fixed temperature boundary 50 C Experiment Simulated Free Convection Coefficients (W/m 2 C) Figure 8: Experiment, simulated nodal temperatures and convection coefficients where the fixed temperature boundary 75 C

6 Experiment Simulated Free Convection Coefficients (W/m 2 C) Figure 9: Experiment, simulated nodal temperatures and convection coefficients where the fixed temperature boundary 100 C The average absolute difference between experimental and simulated nodal temperatures was found to be 0.24 C with a minimum and maximum difference found to be 0.01 C and 0.53 C. The simulation over-predicted the nodal temperature 83.33% of the time. Infrared Images The nodal temperatures were observed using a Mikron M7815 thermal imaging camera. Figures show a thermal image of Experiment 1 where the fixed temperature 50 C, 75 C and 100 C. An observant reader may wonder why only the nodes appear to be at an elevated temperature. The Mikron M7815 requires an emissivity value for the surface to be measured. In the case of these images the epoxy covering the nodes and surface of the aluminum block has different emissivity values. The emissivity value entered into the camera was adjusted to correctly capture the temperature of the epoxy at the nodes Figure 10: Thermal image of experiment 1 where the fixed temperature 50 C

7 Figure 11: Thermal image of experiment 1 where the fixed temperature 75 C Experiment 2 Figure 12: Thermal image of experiment 1 where the fixed temperature 100 C The experimental setup of experiment 1 was modified to create Experiment 2. The free convection boundary condition at the top face of the aluminum block was replaced by a fixed temperature boundary condition. The fixed temperature boundary condition was achieved by placing an adjustable thermoelectric cooler in contact with the top surface. Figure 13 illustrates the nodal locations with red dots and the location of the fixed temperature boundary conditions with yellow lines. Figure 14 illustrates the experimental set up used in Experiment 1.

8 Figure 13: Nodal locations and boundary conditions Experiment 2 Results Figure 14: Experimental set up used in Experiment 2 Figure 15 shows the data for Experiment 2 for two separate cases. The cells of each grid highlighted in red correspond to the red dots on the aluminum block shown in Figure 13. The cells highlighted in yellow correspond to the fixed temperature boundary conditions. The temperature of the fixed temperature boundary condition was fixed using the hot plate and cold plate thermoelectric cooler.

9 Case 1 Case Figure 15: Nodal temperatures for Experiment 2 for Case 1 and Case 2 Simulating Experiment 2 A more in-depth (than simple2d) script was written using the finite difference methodology in Matlab to predict the nodal temperatures in Experiment 2 as accurately as possible. The simulation script for experiment 1 was modified by replacing the code that accounted for the free convection boundary condition at the top of the block with code that models a fixed temperature boundary condition. Figures 16 and 17 show the experimental and simulated nodal temperatures for comparison. Experiment Simulated Free Convection Coefficients (W/m 2 C) Figure 16: Experiment, simulated nodal temperatures and convection coefficients for Case 1

10 Experiment Simulated Free Convection Coefficients (W/m 2 C) Figure 17: Experiment, simulated nodal temperatures and convection coefficients for Case 2 The average absolute difference between experimental and simulated nodal temperatures was found to be 1.29 C with a minimum and maximum difference found to be 0.84 C and 1.78 C. Simulation vs. Experimentation: Sources of Error The differences in the simulated nodal temperatures and experimental data may have resulted in uncertainty of the convection coefficient on the left, top and right face of the aluminum block. Convection boundary conditions are particularly notorious for their non-constant behavior and the correlations developed to model convection boundary conditions may have uncertainty up to ±25%. The uncertainties of the boundary conditions must be understood as well. In the case of experiment 1, established well tested correlations were used to calculate the convection coefficient when necessary. More information about these correlations can be found in the How to Calculate the Free Convection Coefficient document. Other sources of error between simulated and experimental data may have resulted from heat loss through the high temperature insulation and/or air flow over the exposed faces of the aluminum block. The experiment was designed to have free convection on the exposed surfaces of the aluminum block. The exposed surfaces may have been subjected to forced convection by air flow around the experimental apparatus due to building ventilation system.