Ansys Maxwell: Deriving Thermal Modifier Coefficients from Experimental Data
Hello everyone, thank you for joining. In my previous video, I discussed a thermal simulation of a bus bar, which involved a two-way co-simulation between Ansys Maxwell and Icepack. In that video, we explored the thermal modifier and set constants for the quadratic. In this video, I will explain how I derived those values.
Process Overview
The process involves taking raw experimental data and extracting the coefficients needed for Ansys Maxwell's thermal modifier feature. To begin, reliable experimental data is essential. For this video, I am using data from a text titled "Electrical Resistivity of Copper, Gold, Palladium, and Silver" by R. A. Matula, published by the Center for Information and Numerical Data Analysis and Synthesis at Purdue University. This publication is part of a series of critically evaluated reference data compilations, ensuring the data's trustworthiness.
Data Conversion and Plotting
- We will use Table 2, which provides recommended values for the electrical resistivity of copper as a function of temperature.
- The data is initially in degrees Kelvin and resistivity, but we will convert it to degrees Celsius and conductivity for Ansys Maxwell.
- After plotting the data, we perform conversions to Celsius and conductivity.
The temperature range is very large, so we filter the data to a smaller window and interpolate between those points. This results in a smooth curve that accurately represents the material's behavior within our specified temperature range.
Conductivity and Normalization
After interpolation, I checked the conductivity value at 22 degrees Celsius, which was slightly higher than Ansys Maxwell's built-in value. We use this custom value for a more accurate model. You can save this curve to a file with all data points. A more useful approach is normalizing the curve to the found conductivity value:
- Divide all rows by the conductivity value.
- This dataset can be used for the temperature-dependent thermal modifier.
Quadratic Coefficients Extraction
Returning to Ansys Maxwell, we examine the equation for conductivity:
- Define a reference temperature, in this case, 22 degrees Celsius.
- Use the interpolated conductivity for reference temperature and conductivity.
- Calculate delta T for all data points.
- Represent the left side of the rearranged equation by variable Y.
Perform a least squares regression to calculate the coefficients that best fit the data. The first value in the coefficients array is C1, and the second is C2. After running this, the quadratic fit is plotted, showing a good fit within the operating data range, providing confidence in our coefficients.
Implementation in Ansys Maxwell
Enter the derived coefficients directly into Ansys Maxwell's properties window, using 22 for the reference temperature. To use the temperature-dependent dataset, click "Edit Dataset" and import your datasets as a tab file.
That's it for this video. I hope this was helpful. If you have any questions, please contact us at Ozen Engineering, Inc. for more information.
Hello everyone, thank you for joining. In my previous video, I discussed this thermal simulation of a bus bar. It's a two-way co-simulation between Ansys Maxwell and Icepack. And in that video, we discussed the thermal modifier, and I set these constants for the quadratic.
In this video, I wanted to go over how I got those values. The process that I'll be walking through is how to take raw experimental data and extract the coefficients needed for Ansys Maxwell's thermal modifier feature. To get started, we'll need some reliable experimental data.
For this video, I'm using data from a text titled "Electrical Resistivity of Copper, Gold, Palladium, and Silver" by R. A. Matula. This is a publication from the Center for Information and Numerical Data Analysis and Synthesis at Purdue University.
This text is part of a series of critically evaluated reference data compilations, so all of the values here are going to be highly trustworthy and based on a thorough analysis of existing literature.
Specifically, we will be using Table 2, which provides the recommended values for the electrical resistivity of copper as a function of temperature.
This data is in degrees Kelvin and as a function of resistivity, but the way that I am going to be entering it into Ansys Maxwell is in degrees Celsius and as conductivity. So, I am going to perform just some quick conversions, but first, let's go ahead and plot this data here in this table.
Very large temperature range, so we'll go ahead and perform those conversions. Here we can see it is now Celsius and conductivity.
This is, like I was saying, a very, very wide temperature range, and I don't need to worry about what's happening to copper at cryonic temperatures or at really, really high temperatures. So, I'm just going to filter this data to a smaller window and interpolate between those points.
So, here we can see that. This is a nice, smooth curve that accurately represents the material's behavior within our specified temperature range.
So, after interpolating, I checked the value for the conductivity at 22 degrees Celsius, and I found this value for the conductivity, which is slightly higher than Ansys Maxwell's built-in value. But we're going to go ahead and use this custom value to build just a slightly more accurate model.
Now, if I want, I can go ahead and just save this curve to a file with all of its data points, which we can see here. Something that I find a little bit more useful is taking that value for the conductivity that we found and normalizing this curve to it.
So, divide all those rows by that, and we can see this dataset here. This is a set that we can use for our temperature-dependent thermal modifier, which I show how to include in just a minute. But first, let's go back to the quadratic and extracting those coefficients.
Going back to Ansys Maxwell, we can see the equation that it's going to use for the conductivity. Here, this is the conductivity at a given temperature, and this is the conductivity at a reference temperature. C1 and C2 are the thermal modifier coefficients that we need to find.
This is a temperature difference, and we can just really easily rearrange this equation into linear form, making it suitable for a least squares fit.
We start by defining some reference temperature, which in this case is that 22 degrees C that I was targeting earlier for the interpolation, as well as that same interpolated conductivity.
For the temperature reference and the conductivity reference, the temperature and the conductivity are taken from this curve, and we calculate delta t for all the data points. And the left side of our rearranged equation is then represented by this variable y.
The last thing to do is perform a least squares regression. This is going to take our delta t and our delta t square value, and it is going to calculate the coefficients that provide the best fit for our data.
So, the first value in those coefficients array is C1, and the second is C 2. So, we can run this, and here I've plotted the quadratic fit that I calculated, and we can also see what these coefficients are.
So, that's a pretty good fit, especially within the data range that I know we're going to be operating in. The two lines almost overlap perfectly, so this gives us good confidence in our coefficients.
We can now take these precise, experimentally derived coefficients and enter them directly into Ansys Maxwell's properties window. 22 for the reference, and of course, those values that we derived.
Last thing, if you want to use the temperature-dependent dataset from earlier, you can click this button and click Edit Dataset. You can import your datasets if you'd like; in my case, I'm going to import this as a tab file. And you can see there's my thermal modifier.
That's it for this one; I hope that this was helpful. If you have any questions at all, please contact us at https://ozeninc.com/contact for more information.
