Optimization of An Air-Based Heat Management System for Dusty Particulate Matter-Covered Lithium-Ion Battery Packs

NOTE: The research technology roadmap is shown in Figure 1, where the modeling, simulation, and optimization software are used. The materials required are shown in the Table of Materials.

1. Creating the 3D model

NOTE: We used Solidworks to create the 3D model.

1. Draw a 252 mm x 175 mm rectangle, click Extrude Boss/Base, and enter 73. Create a new plane 4 mm from the outer surface.
2. Draw a rectangle 131 mm x 16 mm and click Linear Sketch Pattern. Enter 22 and 6 in spacing and number of instances, respectively. Select all four sides of the rectangle and click OK. Enter 180 in angle and run it again. This step is for symmetry in the center of the model.
3. Click Extrude Cut, enter 65, and click OK. Click Extrude Boss/Base and enter 65, uncheck Merge result, and click Reverse Direction and OK.
   NOTE: When the merge result is unchecked, the stretched entity becomes a separate entity. There are 23 parts in total, including 11 batteries, 11 dusty particulate matter, and 1 air domain.
4. Draw a rectangle 16 mm x 1 mm. Repeat steps 1.2 and 1.3.
5. Draw a rectangle 63 mm x 15 mm, click the rectangle's top edge and Linear Sketch Pattern. Enter 21, 3, and 270, and click OK. Click Split Line and the face of the cube, click OK.
6. Draw a rectangle 63 mm x 15 mm. Click Split Line and the face of the cube, click OK.
7. Click File and save it as an X_T file.
   NOTE: The specified size: L_box:73 mm; W_box:252 mm; H_box:175 mm; L_b, L_d:65 mm; W_b, W_d:10 mm; H_b:131 mm; H_d:1 mm; L_i:63 mm; W_i:15 mm; d₁, d₂:5 mm, d₃:6 mm is shown in Figure 2.
8. Drag the mesh component by clicking Toolbox > Component Systems > Mesh to the project schematic zone. Import the previously saved X_T file by clicking Geometry.
9. Enter the mesh-design modeler window, and the battery pack model, including 23 parts as independent bodies, is displayed again by clicking Generate.
10. Select all 23 parts of the battery to be a new part named as battery part, all dusty particulate matters of 23 parts as dust part, and air cavity as air part, in the tree outline for the convenience of subsequent hiding and naming objects.
11. First, right-click on BatteryPart and DustPart and select the Hide Part so that the pop-up will only show the air part.
12. Move the mouse to the selection toolbar to select Selection Filter: Bodies, right-click on the air cavity model on the graphics zone to select Named Selection, and rename the air cavity model on the details view zone as air domain.
13. Switch to Selection Filter: Faces, right-click and rename the surface that has been split into three pieces, from bottom to top, as inlet1, inlet2, and inlet3, the separate surface to the right of these three faces is named outlet, the remaining outer surface is named outerBorder, respectively.
14. Switch the Select Mode to the Box Select, click the Y axis to obtain the suitable view of the air cavity model for the convenience of box selecting, rename and number all inner surfaces as cavity surface1 to cavity surface11 using box selection.
15. In order to show only the batteryPart, right-click airPart and select Hide Part. Right-click batteryPart and select Show Part on the pop-up shortcut menu.
16. Move the mouse to the selection toolbar to select Selection Filter: Bodies, switch the Select Mode to Single Select, right-click on Each Battery Model on the Graphics zone to select the Named Selection, rename and number the 11 battery models on the details view zone as batteryDomain1 to batteryDomain11, respectively.
17. Furthermore, each battery model has six sides, then switch to Selection Filter: Faces, right-click on each Side of the Numbered batteryDomains to select Named Selection and rename them according to the orientation of the battery side. For example, rename six sides of the numbered batteryDomain1 as batteryDomain1_Upper, batteryDomain1_Lower, batteryDomain1_Left, batteryDomain1_Right, batteryDomain1_Front and batteryDomain1_Back.
18. In order to show only the dustPart, right-click batteryPart and select Hide Part. Right-click dustPart and select Show Part on the pop-up shortcut menu.
19. Move the mouse to the selection toolbar to select the Selection Filter: Bodies, right-click each dusty particulate matter model on the Graphics zone to select Named Selection, rename and number the 11 dusty particulate matter models on the details view zone as dpmDomain1 to dpmDomain11, respectively.
20. Furthermore, each dusty particulate matter model has six sides; then switch to the Selection Filter: Faces, right-click on Each Side of the Numbered dpmDomains to select Named Selection and rename them according to the orientation of the dusty particulate matter side. For example, rename six sides of numbered dpmDomain1 as dpmDomain1_Upper, dpmDomain1_Lower, dpmDomain1_Left, dpmDomain1_Right, dpmDomain1_Front, and dpmDomain1_Back.
21. Show all bodies and return to the initial window again.

2. Generate the mesh model

NOTE: Finite element meshing is a very important step in finite element numerical simulation analysis, which directly affects the accuracy of subsequent numerical analysis results. The renamed entities are then meshed.

1. In order to mesh the air domain, battery domain, and dpm domain independently, drag two Mesh components again from Toolbox > Component Systems > Mesh to the project schematic zone and rename them as airFEM, batteryFEM, and dpmFEM, respectively. Hold the airFEM > Geometry with the left mouse button and drag it to the batteryFEM > Geometry.
2. Next, hold the batteryFEM > Geometry with the left mouse button and drag it to the dpmFEM > Geometry. Right-click the Lines among the three mesh components and select Delete to disassociate them from each other.
3. Double-click airFEM's Mesh, enter the meshing window, right-click batteryPart and dustPart to select the Suppress Body, and change the physical preference from mechanical to CFD. Generate the FEM air domain model through the face sizing of 2 mm and the body sizing of 4 mm by clicking Update and return to the initial window.
4. Double-click batteryFEM's Mesh, enter the meshing window, right-click airPart and dustPart to select the Suppress Body, and change the physical preference from Mechanical to CFD. Generate the FEM battery domain model through the body sizing 2 mm by clicking Update and return to the initial window.
5. Double-click dpmFEM's Mesh, enter the meshing window, right-click airPart and batteryPart to select Suppress Body, and change the physical preference from Mechanical to CFD. Generate the FEM dpm domain model through body sizing 2 mm by clicking Update, return to the initial window.
   NOTE: Figure 3A shows the grid of the air domain, Figure 3B shows the grid of the battery domain, and Figure 3C shows the grid of the dpm domain.
6. Set the minimum size of the air grid to 4 mm and the minimum size of the battery and dusty particulate matter grid to 2 mm. Ensure that the grid is solution independent, change the minimum cell size of the grid, and perform a grid sensitivity study.
   NOTE: As shown in Figure 4, with the number of grids increasing from 519343 to 1053849, the maximum battery temperature changes are less than 0.6 K. Considering the computation ability and accuracy, the following analysis is based on the grid model with 931189 grids.

3. Simulation analysis

1. Drag Fluid Flow from Toolbox > Analysis Systems > Fluid Flow into the project schematic zone. Hold airFEM > Mesh, then batteryFEM > Mesh and dpmFEM > Mesh with the left mouse button and drag them to Fluid Flow > Setup. Right-click Fluid Flow > Setup and select Update to enter the set window.
2. Verify the validity of the FEM model and check whether the mesh has a negative volume. The software automatically suggests the volume of the model, and a reasonable model value is positive. If there is any problem with the divided grid or model settings, an error message will pop up to tell.
3. Activate the energy equation in heat transfer models. Enter the setting interface of the viscous model and the radiation model and select the K-epsilon Model and the Discrete Ordinates Model.
   NOTE: As shown in Figure 5, comparing four viscous models, the calculation results of the Spalart-Allmaras model are quite different from those of other models. The results of the Standard K-epsilon model are like those of other K-epsilon models. The Standard K-epsilon model with higher stability and economy is widely used; the following analysis is based on the Standard K-epsilon model.
4. Set the new materials with different attributes for air material, battery material, dpm material, and battery box material based on Table 1.
   NOTE: Inside the battery pack, there are three different physical materials: air as a fluid and the rest as a solid. Next, set up the material.
   1. Change the fluid type of the numbered battery domains to the Solid type and change the dpm material to the battery material on the Solid window by double-clicking each Battery Domain. Subsequently, choose the Source Terms item and click the highlighted Source Terms to add an energy source by assigning the number in the number of energy sources and selecting Constant type to input the value of 209993 w/m³.
   2. Change the fluid type of the numbered dpm domains to Solid type.
5. Next, set the interface for simulation calculation of several different domains according to the actual setting flow rate and heat transfer coefficient as described below.
   1. Convert the type of all renamed surfaces, including the inner surfaces of the air domain and all sides of the battery domains, as well as dpm domains from the default wall to the interface. Once the above steps are finished successfully, the mesh interfaces will be generated immediately.
   2. Click the Mesh Interfaces and enter the Create/Edit Mesh Interfaces window. Match the cavity surfaces to all sides except the battery domains' upper sides and the dpm domian's lower sides. Next, name and number them as interface1 to interface11, respectively. So, the 11 mesh interfaces can be created among the air domain and battery domians as well as dpm domains.
   3. Match the battery domains' upper sides and the dpm domains' lower sides. Next, name and number them as interface12 to interface22, respectively. Then, the 11 mesh interfaces are created between the battery domains and dpm domains.
   4. Assign the surface of the outer border as the wall thermal boundary condition by setting the heat transfer coefficient as 5 in the mixed thermal condition and changing its material from default aluminum to the previously self-defined battery box material.
   5. Set airflow velocities of all inlets as 5 m/s in the velocity inlet window and the gauge pressure of the outlet as zero in the pressure outlet window.
6. Next, set the state of the computing domain at the initial moment, such as the initial temperature of 300 K, which will affect the process of computing convergence.
   1. Set the type of solution initialization as the standard initialization before initializing.
   2. Set the Number of Iterations as 2000.
   3. Click Calculate to simulate. Return to the initial window until the simulation is finished.
7. The above part completes the simulation calculation of the temperature and air velocity inside the battery pack and then displays the simulation result in Result. Perform the following steps in the results displayed.
   1. Double-click Fluid Flow > Results to enter the CFD post window, then click the icon of Contour in the toolbox.
   2. Select All Sides of the Batteries in the location selector and change pressure to temperature. Then click Apply to generate the temperature contour of the batteries.
   3. Click File > Export to select the temperature of the selected variable(s). Click the Dropdown button of the locations to pop up the location selector window where all battery domains should be selected. Click OK and Save button to quit.
      NOTE: A spreadsheet whose data corresponds to the temperatures of all batteries' mesh nodes will be saved automatically when the save button is clicked.
   4. Open the spreadsheet to find the maximum value, which indicates the maximum temperature of the batteries in a dusty environment at 5 m/s of all airflow inlets.
   5. Acquire the maximum temperature of the batteries under the free-dust state as the expected temperature and compare it with the maximum temperature under the dusty state; the result shows the entire temperature increasing.
      NOTE: To acquire the maximum temperature of batteries in a dust-free environment, the new battery pack model shown in Figure 6 should be re-established, and all the steps 1.1-3.4.3 should be repeated.
   6. In order to lower the maximum temperature inside the battery pack, set the airflow velocities at the inlets from 5 m/s to 6 m/s, increase by 5%, and calculate the corresponding maximum temperatures of the dusty-covered batteries.
      NOTE: The sensitivity analysis of airflow velocity parameters should be done well in advance before changing the parameter values. As shown in Figure 7 and Table 2, we have kept the same total flow for each of the seven groups of different inlet airflow velocity combinations. There still be an obvious variation in the maximum temperature owing to the difference in airflow velocity allocation. In other words, there is somehow a strong correlation between the airflow velocity combination and the maximum temperature. Therefore, those velocity parameters can be used as design variables.
   7. Plot the temperature-velocity curve as shown in Figure 8, where the red line indicates the temperature characteristic curve decreases with the increase of airflow velocity, and the blue line represents the expected temperature.
   8. Maintain an increase in airflow velocity of 10%. When the velocity increment is more than 10%, the maximum temperature is already lower than the expected temperature, but this does not meet the purpose of low energy consumption. For the remaining air flow rate, reduce the maximum temperature of the battery pack to the expected temperature through optimization, thus achieving the goal of low energy consumption.

4. Optimal Latin hypercube sampling and response surface modeling

NOTE: For the retained flow rates of 5 m/s-5.5 m/s, samples are selected to construct different flow rate combinations within this flow rate range. The velocity combinations are simulated to obtain the maximum temperature. Construct the function of velocity and maximum temperature.

1. Open a new empty spreadsheet to create a table whose rows in the first column are named inlet1, inlet2, and inlet3, and save the file as sampling.xlsx.
2. Run the optimization software and drag the Spreadsheet icon onto the single arrow of Task 1. Next, double-click the Spreadsheet icon to pop up the Component Editor-Excel window.
3. Import the sampling.xlsx by clicking the Browse button and map the inlet1, inlet2, and inlet3 to the A1, A2, and A3 as parameters by clicking the Add this mapping. Click the OK button to return to the initial window.
4. Drag the DOE icon into Task1 and double-click it to pop up the Component Editor-DOE window. Select the OptimOKal Latin Hypercube and set the Number of Points as 15 in the General window.
5. Switch to the Factors window and set 5.5 as the upper limit and 5 as the lower limit for A1, A2, and A3.
6. Switch to the Design Matrix window and click Generate to generate the random sampling points corresponding to the different inlet velocities. Shut down optimization software.
7. Take the velocity combinations arrays of the random sampling points back to calculate and repeat steps 3.5.5-3.7.5 to obtain the corresponding temperature array composed of the maximum temperatures of batteries.
8. Combine the predictor variables x1, x2, and x3 of the velocity combinations arrays and y of the temperature arrays to form a new table of variables, as shown in Table 3, and save it as a sample.txt file. Import the file to fit a response surface model.
9. Rerun the optimization software and drag the Approximation icon onto the single arrow of Task1. Double-click the Task1 icon to pop up the component editor-approximation window to select the Response Surface Model.
10. Switch to the Data File window and import the sample.txt file containing the prediction variables.
11. Switch to the Parameters window and click the Scan to open the parameters in the data file window where the predictor variables of x1, x2, and x3 are defined as input and y as output.
12. Switch to the Technique Options window and select the Quadratic in polynomial order. Switch to the Error Analysis Options window and select the Cross-Validation in the error analysis method.
13. Switch to the View Data window and click Initialize Now to obtain the coefficients of the quadratic linear regression equation.
14. Click the Error Analysis button to pop up the approximation error analysis window to check whether the errors can satisfy with the acceptable standards for each error type. Close the approximation component window. If the arbitrary error cannot satisfy the corresponding acceptable standards, then add more sample points to participate in the model fitting.

5. Adaptive simulated annealing algorithm-based approximate fitting model

NOTE: Next, software and algorithm are used to find the optimal value of the approximate model

1. Drag the Optimization icon into Task1 and double-click it to pop up the component editor-optimization window. Select the Adaptive Simulated Annealing (ASA) in the optimization technique.
2. Switch to the Variables window to set 5.5 as the upper limit and 5 as the lower limit.
3. Switch to the Objectives window and select the Y parameter before closing the component editor-optimization window.
4. Click the Run Optimization button and wait for the optimization result.