Validation of Modeling Technique Using Discrete Components

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Chapter 3 Validation of Modeling Techniques Using Discrete Components

Current commercial software provides a very powerful method for carrying out thermal and flow simulations. However, it is very important that the users be aware of the mathematical foundation behind the software. Conservation of energy, conservation of mass and momentum, heat transfer coefficients, and calculation of pressure drop and flow resistance of flow field are the foundational concepts of heat transfer behind the software. In addition, it is also important to know how reliable the simulation results are. Therefore, verification by measurements is desired whenever possible. This chapter presents a modeling method for power electronics systems with the validation of results from experimental data. To validate the thermal modeling method for modeling a generic power electronics component, two discrete power electronics components were modeled using the Electronics System Cooling (ESC) program provided in I-DEAS release 8.
The validation approach is to perform a comparison of simulation results to experimental data such as thermocouple measurements and infrared images. Since the physical models in the computational simulations contain uncertainties due to a lack of complete understanding of the physical process, sensitivity and uncertainty analysis were performed to identify and quantify error and uncertainty in the models. The accuracy required in the validation is dependent on the application. Therefore, the validation should be flexible to allow various levels of accuracy.

General Modeling Characteristics

ESC is an available commercial thermal and computational fluid dynamics (CFD) program developed by the Maya Heat Transfer Technology Corporation. In ESC, the CFD solver technology uses an element-based method, allowing users to model turbulent flow as well as three-dimensional fluid velocity, temperature, and pressure distributions. The flow solver computes a solution to the nonlinear, coupled, partial differential equations for the conservation of mass, energy and momentum of the three-dimensional geometry. On the other hand, the thermal solver technology uses finite difference based methods and provides thermal coupling technology to create heat paths between discontinuous meshes .
Typical computational process includes modeling, meshing, defining boundary conditions and analysis options, solving, post processing and evaluation. Figure 3.1 presents an overview for ESC simulation.

Computational Modeling of MOSFETs

A discrete power electronics module such as a MOSFET consists of four elements: the gate, source, drain, and the substrate (Figure 3.2a). The basic functioning principle of the MOSFET is the control of a current flowing between two semiconductor electrodes. The drain and the source are placed on the same element, with a third electrode, the gate, between the drain and the source. Both the drain and the source are n-type semiconductor, and are isolated from the p-type substrate by reversed-biased p-n diodes. The voltage applied to the gate controls the flow of electrons from the source to the drain.
A commercial package of MOSFET is an assembly of parts bonded together by solder, adhesive, molding compound, and mechanical parts such as bolts and springs. In this study, two commercial packages TO247 mounted on a heat sink were used and modeled in simulation. Three major physical parts of MOSFET (a copper base plate, a silicon device and a plastic injected molded cover) were modeled to form a simple computational model of TO247 package. Because the heat transfer to the three terminals extending from the package was ignored, the terminals were not modeled. Figure 3.2b shows the physical parts of a commercial MOSFET.
The silicon device was assumed to have perfect contact with the compound molding cover. The soldered and thermal pad interfaces between various components were represented by equivalent thermal resistance values. These interfaces were the interface between the copper plate and the heat sink, and the soldered interface between the silicon device and the copper plate. Figure 3.3 illustrates the exploded view of the numerical model in I-DEAS.
A heat sink was used to increase the heat dissipation to the air. To provide airflow over the model, a flow channel was included in the simulation. Applying an inlet fan at one end of the channel, the other end of the channel was vented to an experimental measured ambient temperature of 23.5 C. The inlet fan provided a constant volumetric flow rate of 0.05 m3/s. With the fixed channel area, the outlet velocity was 2.22 m/s. Figure 3.4a shows the boundary conditions of the numerical model. The dimensions of the heat sink and the position of the MOSFETs on the heat sink are shown in Figure 3.4b (note that the dimensions are in the unit of millimeter).
The power loss from each MOSFET was determined from the experiment as discussed in Section 3.5.2. The power loss was assumed to be uniform across the top surface of silicon devices. In the modeling, finer grids were applied for the heat-dissipating surfaces. Within the MOSFET, there was a conduction path from the silicon device to the copper plate and the compound molding cover, from the copper plate to the heat sink, and convection from both the heat sink and the MOSFET to the ambient air. The thermal conductivities and thermal resistance values for all of the materials used in the models are listed in Table 3.1. These values were used to calculate relevant thermal coupling values in the simulations.

Sensitivity and Uncertainty Analysis in Thermal Modeling of MOSFETs

A sensitivity analysis provides information on how the model depends upon the input parameters to the model. As a whole, sensitivity analyses are used to increase the confidence in the model and its prediction, by providing an understanding of how the model response variables respond to changes in the inputs. Therefore, it is related to uncertainty analyses. An uncertainty analysis aims to quantify the overall uncertainty associated with the results as a result of the individual uncertainties of the inputs to the model.
In the uncertainty analysis implemented here, a four-step analysis strategy was employed. First, we identified important sensitive parameters in the modeling. The second step involved the determination of the uncertainty for each of these parameters. The third step involved the determination of the sensitivity of each input parameter. Finally, the overall uncertainties on the critical output parameters were determined. The sensitivity coefficient is defined as the change in the nominal temperature with respect to the change in the input parameter values. For each parameter, the sensitivity coefficient was defined as a dimensionless term,  : where T∞ is the ambient temperature, and TN (β N ) and Ts (β S ) are the respective predicted temperatures for each parameter using β Ni and β Si . β Ni is the nominal value of sensitivity parameter.
In addition, TN (β Ni ) is also referred as the nominal temperature. Finally, the non- dimensional sensitivity difference, ∆ (β s )  , is defined by where ∆ (β s ) i is the one percent variation of the nominal value β Ni . Uncertainty of each parameter, σ i, is defined by where Xi+ is the sensitivity coefficient defined in Equation 3.1, and σ β i is the measurement uncertainties. The overall uncertainty for the jth output variable, σ j, was then defined as Np where Np is the number of critical parameters.

Experimental Setup

There is always a question of how accurate numerical simulations are when compared to experiments. Although there is a significant increase in the use of computational codes to predict the thermal behavior of electronic systems, numerical models should always be validated by experiments. To validate the thermal model discussed in Section 3.2, a well-designed experiment was conducted. This experiment consisted of two commercially-packaged MOSFETs, a heat sink, a fan, a flow channel, and two pieces of honey combs.
A wooden box as shown in Figure 3.5a was constructed as a flow channel. With two commercially-packaged MOSFETs (TO247) attached to a heat sink, the MOSFETs and the heat sink were placed at the center of the flow channel (Figure 3.5b). By painting the heat sink and the inner surface of the box with black paint of emissivity of 0.85, the emissivity of the surfaces could be maximized. To allow the infrared camera to be able to see through the wooden box, an infrared window was fitted into the top of the wooden box. One AC fan unit model 4600Z from PAPST-MOTOREN with volume flow rate capacity of 180 m3/hr was mounted at the outlet of the box. Also two sheets of honeycomb were placed at the two ends of the box to straighten the flow. Figure 3.6 shows the experiment set up.

Experimental Procedures

Calibration Step

The measurement procedure consisted of two distinct steps: a calibration step and a power step. In calibration step, a thermocouple was used to calibrate the infrared camera. An infrared camera PM290 with Thermogram, the data acquisition software, was used to record and capture thermal images. At the same time, three thermocouples were placed at the inlet of the flow (Figure 3.7a), on the heat sink as well as the bottom of TO247 (Figure 3.7b).
The thermocouple located at the inlet of the flow monitored the inlet airflow temperature throughout the experiment. At the same time, the thermocouple attached on the top surface of the heat sink (Thermocouple 2) was used to calibrate the infrared camera, before and during the experiment. Calibration was done such that the temperature displayed from the thermal image was as close as the temperature shown from Thermocouple 2. In this experiment, the infrared camera was calibrated to a difference of 0.1 C over a temperature rise of 5 C. To calibrate the infrared camera, emissivity and the background temperature in the infrared camera were adjusted to 0.91 and 22 C to achieve the desired calibration. Measurements from thermocouples were processed using a data acquisition system, Personal DAQ Model 55 and Personal DAQView. Full field thermal images and data from the infrared camera were saved in Thermogram.

Power Step

To determine the power loss from the MOSFETs, a power supply with two amperes was supplied to the discrete modules. Two voltage/current multi-meters were used to measure the voltage and current across the MOSFETs. The circuit diagram is shown in Figure 3.8. Then, the power loss, Qloss, could be calculated using Equation 3.7: Qloss=V*I, (3.7) where V is the measured voltage and I is the measured current. The voltage and current associated with the power loss that established across the silicon chips was then measured and the power loss was calculated to be 8.62 W using Equation 3.7. In this experiment, the modules were allowed to achieve steady state.
It was also critical to know how accurate the measured power loss was because any uncertainty in the measured power loss could result in the difference between simulation result and experiment result. The most important feature in the MOSFET was the resistance across the MOSFET when the device was operating. Power consumption and incidental heat generation increased with this resistance. By using reverse bias to deplete the current carriers in the channel with direct current, the power loss could be measured accurately within 0.5%.

Results and Discussions

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Calibration of the Infrared Camera

Measurements from the thermocouples were processed using a data acquisition system—Personal DAQ Model 55 and Personal DAQView. The measured surface temperature contours from the infrared camera were compared with the predicted temperature distributions from simulations. Figure 3.9 shows calibration curve for the infrared camera using thermocouple with 8.616 W of power loss from both MOSFETs. In this experiment, the step resolution for the infrared camera was 0.1 C while the step resolution for data acquisition system was 0.01 C. At the calibration point (Thermocouple 3 in Figure 3.7b), both the temperature from the infrared camera and the thermocouple showed about 31.6 C during steady-state condition. With the most deviation of 0.43 C between the infrared camera and the thermocouple over the temperature rise of 13.3 C, the infrared camera was considered well calibrated. Therefore, the temperature image from the infrared camera could represent an actual temperature field within the same percent of errors as the thermocouples.
Located at the bottom of the MOSFET, the thermocouple (Thermocouple 2 in Figure 3.7b) showed a maximum of 37.3 C at steady-state condition. The airflow temperature was at an average of 23.5 C throughout the experiment. In addition, the infrared camera showed that the highest temperature on the top surface of the molded plastic cover was 36 C.

Sensitivity and Uncertainties in Numerical Model

As mentioned in Section 3.3, uncertainty analyses involve identifying critical input parameters and critical output variables. The critical input parameters are the inputs to the numerical models such as the power losses, the interface conditions, and the boundary conditions. On the other hand, the critical output variables are the output results that we are interested at. These critical output variables can be the temperature at certain locations in the numerical model. In this case, we were able to identify five critical input parameters in the model. Table 3.2 lists these five input parameters with the nominal values used in the modeling as well as the uncertainty for each of these parameters. Solder resistance and thermal pad resistance are illustrated in Figure 3.3. Besides the power loss, the uncertainties for the other four parameters were rough estimates due to the lack of physical knowledge. The uncertainties for the solder resistance and the thermal pad resistance were estimated as 80% of the nominal values. The contact resistance was estimated as 200% error while the air flow rate was estimated as 50% error. On the other hand, direct current (DC) was supplied to power up the MOSFETs so that power loss was able to be determined within 0.5% of error.
Three critical output variables were selected to study the uncertainty in the numerical model. One is the temperature at the top surface of the MOSFET. The second critical output variable is the temperature at the top surface of the silicon and the third critical output variable is the temperature on the heat sink located between the two MOSFETs as shown in Figure 3.10. The overall uncertainties for these three output variables were calculated using Equation 3.6 described in Section 3.3 and results were listed in Table 3.3.

Abstract
Acknowledgments
Nomenclature
Acronyms
List of Figures
Lists of Tables
1 Introduction
1.1 Background and Motivation
1.2 Overview of Power Electronics
1.3 Research Goals and Approach
1.4 Thesis Outline
2 Literature Review
2.1 Active Cooling Technologies
2.2 Passive Cooling Technologies
2.3 Overview of Thermal Modeling in Electronic Systems
2.4 Uncertainty Analysis
2.5 Summary
3 Validation of Modeling Technique Using Discrete Components
3.1 General Modeling Characteristics
3.2 Computational Modeling of MOSFETs
3.3 Sensitivity and Uncertainty Analysis in Thermal Modeling of MOSFETs
3.4 Experimental Setup
3.5 Experimental Procedures
3.6 Results and Discussions
4 Thermal Design of Active Integrated Power Electronics Modules (IPEMs)
4.1 Electrical and Packaging Constraints
4.2 Design Strategy
4.3 Thermal Modeling of Active IPEM
4.4 Parametric Analysis
4.5 Sensitivity and Uncertainty Analysis
5 Results and Discussions
5.1 Parametric Study
5.2 Sensitivity and Uncertainty Analysis
5.3 Solution and Results Convergence
6 Conclusions and Recommendations
References
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