A system for determining Li-ion cell cooling coefficients

Graphical abstract


Hardware description
The CCC is calculated by comparing the sum of heat flow through all the fins, RQ fin , with the temperature gradient across the cell, DT cell . For accurate measurement of CCC it is critical that all other surfaces are well insulated such that heat loss through the fins is the dominant heat rejection pathway.
Apparatus assembly Fig. 1 shows the cell in it's insulated box. In the tab cooled case the fins are clamped to the positive and negative tabs and the upper surface of the cell is insulated. In the surface cooled case an aluminium plate covers the upper surface of the cell on top of which are the fins. In both cases clamping bars apply even pressure to the cell surface. During testing the box is filled with vermiculite (0:06 W m À1 K À1 [8]) to insulate the fins. Critical to this design is the ability to reuse the hardware for a large range of pouch cell sizes. To achieve this the clamping bar locations can be selected from any of 17 positions evenly spaced over the length of the box. The fins are designed to clamp onto any tab with a width and length smaller than 80 mm. Peltier elements at the distal end of the fins remove heat from the conductive system. The heat energy is carried away via the water cooled blocks.
The designs for two sets of fins are published alongside this paper (CCC-CAD.zip). 'Fin set 1' for measuring 2-4 W of heat, 'Fin set 2' for measuring 1-2 W heat. In most tests, two of these fin sets are used (i.e. one set on each tab or alternatively two sets sitting on the cell surface), giving a cell heat production range of 2-8 W with the equipment specified. Whilst difficult to specify an exact range, due to the unique composition and thus heat generation characteristics or a specific cell, our preliminary investigations have found that this range is practical for cells with a nominal capacity between 5Ah and 80Ah. This covers almost all pouch cells that are currently commercially available. It would however be simple to specify fins for higher or lower heat rates by following the methods described in Section 5.

CCC calculation
The heat passing through a single fin is described by Eq. 1 where Q fin (Fig. 1) is the heat passing through the fin, DT fin is the temperature gradient along a fin, DL is the distance between temperature measurements, A is the cross-sectional area of the fin and k is the thermal conductivity of the fin material.
The CCC is calculated from the total heat loss through all fins, RQ fin , and the temperature gradient across the cell, DT cell , once thermalisation has been achieved in a test. The test is repeated with multiple magnitudes of current using an alternating current drive cycle, such that a graph of RQ fin against DT cell can be plotted (Fig. 2). The CCC is then the gradient of a line of best fit through these points. In the case of tab cooling, DT cell is the difference between the temperature of the cell surface at the point furthest from the tabs and the average of the two tab temperatures. For surface cooling, DT cell is the difference in temperature between the top and bottom surfaces of the cell.  Additional lab equipment required A schematic of all elements is given in Fig. 3. To perform measurement of CCC the experimentalist must be equipped with: A galvanostatic-ready battery cycler with sufficient current magnitude capability to generate the required amount of heat during the alternating current drive cycle (approximately 2C for energy-dense cells and approximately 4C for powerdense cells). The alternating current drive cycle must have a frequency of at least 0.1 Hz (i.e. switching from charge to discharge or vice versa every five seconds) so that the cell's state of charge can be taken as a constant throughout the test.
A voltmeter capable of reading at the lV level for calculating the contact resistance between the wires and cell tabs.
A closed loop chiller with cooling power exceeding the maximum heating power of the two Peltier elements. A device for recording temperature measurements from thermocouples of thermistors (e.g. a Pico Technology TC-08 data logger). A Peltier controller. These systems are available commercially and control the current applied to a Peltier element in response to feedback from a temperature sensor in order to maintain constant temperature conditions. Measurement of CCC must occur under steady state thermal conditions, where cell heat generation is equal to cell heat rejection, and thus there is no heat gain or loss for the thermal masses of the insulation, cell or fins. The temperature sensor should be placed on the tabs for tab cooling or the top surface of the cell for surface cooling. The particular controller shown here uses additional feedback from under the Peltier elements to reduce temperature oscillations caused by changes in the external temperature [9]. Repeats of the validation were conducted without this feedback and produced comparable results when the lab temperature remained constant.

Summary
The Cell Cooling Coefficient (CCC) has been shown to provide information critical for the design of battery pack thermal management systems. The apparatus described in this paper provides a means to accurately measure CCC for the majority of sizes of pouch cell. The device can be used to measure the CCC of the cell through it's tabs or surface, providing a means to compare these two thermal management methods.   The Open Science Framweork (OSF) depository given above contains CAD and drawing files referred to in this document (CCC-CAD.zip) and the Bill of Materials (BOM) (CCC-BOM.xlsx).

Bill of materials
The complete BOM is provided as a separate file (see above). Where it applies, the part numbers in the BOM are the same as those of the corresponding CAD file.

Fins
In the design, the selection of fin length and diameter has been chosen with the following factors taken into account: The temperature gradient along the fins should be 8 K < DT < 16 K for a reasonable range of heat flow. This is a compromise between error induced by limitations in accuracy of temperature measurement requiring a large gradient and physical limitations from formation of condensation requiring that the cold end be > 5 C. N.B. heat gain through the insulation at the fin cold produces a fixed percentage error in the CCC which does not increase with decreasing cold end temperature. The location of the temperature measurement (estimated at AE0:5 mm) requires that the thermistors be far enough apart to limit this error to 1%.
Eq. 1 can be used to determine the appropriate length and diameter dimensions. For large cells, which use two of the double sets (Fig. 4), the maximum heat generation was taken as _ q ¼ 8 W. By fixing L ¼ 100 mm; DT < 16 K and k ¼ 127 W m À1 K À1 gives A > 406:5 mm 2 . This gives a diameter for each of the four fins of D > 11:4 mm. 12 mm was chosen for this design but the same approach could be used to design different fins with other dimensions. The heat flow is likely to be inhomogeneous at the point at which it enters the fins. Our models show that a space of 5 mm from the aluminium plate to the thermistor is sufficient to ensure accurate heat flow measurement. To accommodate this and the 8 mm plate thickness the brass bars must be cut to a length of 126 mm.

Insulating box
For this design a 600 mm Â 400 mm Euro container (INS1-BOX) encloses the cell and insulation. Other similarly sized boxes could be used instead.  3. Screw the Peltier and water cooling block to the aluminium plate with thermal interface material in between. Nylon screws (PELT8-SCREW) should be used here since their low thermal conductivity is critical for avoiding unwanted thermal short circuits across the Peltier element.

Fin separator
The fin separator (SETUP4-SEPARATOR) is necessary where cell tabs are close enough together that there is a risk that touching fins will cause a short circuit of the cell. For smaller cells this part may also make system assembly easier by combining both fin sets into a single rigid body. The part, which should be 3D printed, clips around the (PELT3-PLATE) under the water cooling blocks and is secured with a cable tie on each side (Fig. 8). Within the CAD file is a parameter ''SEPARATION DISTANCE" that should be set to the desired separation of the Peltier plates. For fin set 2 and one orientation of fin set 1 the separation at the Peltier plates is the same as at the fin base.

Operation instructions
Below are instructions for setup of the cell in the system and the procedure to begin testing. Low internal resistance Li-Ion cells can be dangerous if not handled correctly. Particular care should be taken to avoid short circuiting the tabs through the fins. In these instructions safety critical steps have been underlined however at all stages good judgement from users is required.

Setup
The following describes the test setup procedure. It is recommended that as much of this setup at possible is performed outside the insulating box to facilitate good access to the cell surfaces.
1. Attach positive and negative battery cycler cables to the top surface of the tab bottom plates (FIN3-TABBTTM) making sure to clean the contacts with solvent (e.g. isopropanol). 2. Choose a pair of fin sets with size appropriate for the cell being tested. The large fin sets will be required where tabs are wider than 30 mm or if the heat produced is likely to be greater than 4 W for a > 0:5 K temperature gradient. This is often true for cells with capacity over 15 Ah. 3. Bolt a Peltier assembly to each fin set using the 6 mm clearance holes in the fin assembly top plate (FIN7-MEDTOP or FIN8-SMLTOP) and the M6 screw holes in the Peltier Plate (PELT3-PLATE). Thermal interface material should be included at each interface (CONS1-INTERFACE) (Fig. 7). 4. Carefully remove the cell from it's packaging. 5. Cut a pieces of XPS foam (CONS2-FOAM) to raise the cell and support the tabs so that they can lie flat without stress or strain being imparted on the cell tabs and tab welds. Take into account the thickness of FIN3-TABBTTM under each tab. This sort of foam easily cuts with a hand saw or coping saw. The foam thicknesses and sizes required will depend on the cell being tested. 6. Clean the top surface of the bottom tab clamps (FIN3-TABBTTM) with solvent. 7. If using the fin separator (SETUP4-SEPARATOR and Section 5.4) ensure this is now attached to the fin-Peltier assemblies.
If CCC tab is under investigation (Fig. 9a): 1. Place one GEN1-THERMO on the top and bottom surfaces of the cell at locations the furthest from each tab but at least 5 mm in from the outer edges of the electrode-stack. Secure with Kapton tape.
2. While ensuring negative tab remains insulated, remove the cover from the positive tab and clean the tab. 3. Using Kapton tap place 1Â GEN1-THERMO at the tab centre. If separate temperature sensors are required for feedback to the Peltier controller place them either next to GEN1-THERMO or, if the tabs are small, elsewhere on the tab clamp surface. 4. Cut a piece of 1 mm thick thermal interface material to the same size as the tab. To reduce pressure on the thermistor, remove the part of the interface under which the thermistor lies.  6. Any areas of the fin set that could contact the other fin set during assembly should now be covered with insulating tape (Kapton or PVC) before the other tab is uncovered. 7. Repeat steps [2][3][4][5] with the other tab. 8. Place the cell assembly in the box on supporting pieces of insulation. 9. Cut a piece of expanded polystyrene with thickness greater than 50 mm, enough to cover the whole top surface of the cell. Place on top of the cell. 10. Depending on the size of the cell, one, two or three clamping bars will be required. Place the studding clamping rods through holes in the box such that bars are evenly spread across the insulation on top of the cell. Fit the clamping bars and springs to the rods as per Fig. 1. Use Eq. 2 to find the correct length to tighten the springs to exert the pressure suggested by the cell manufacturer. N.B. the springs given in this design can produce a maximum force of 169 N in their linear range, i.e. 338 N per bar.  If CCC surface is under investigation (Fig. 9b): 1. Place one GEN1-THERMO on the top and bottom surfaces of the cell, in the centre of the electrode-stack. Secure with Kapton tape.
2. While ensuring negative tab remains insulated, remove the cover from the positive tab and clean the tab.
3. Clamp the tab between the empty tab top plate (FIN4-TABTOP) and corresponding (positive or negative) tab bottom plate.
4. Any areas of the positive tab clamps that could contact the negative one should be covered in insulating tape (Kapton or PVC) before the other tab is uncovered. 5. Repeat steps [2][3][4] with the other tab. 6. Place the cell assembly in the box on supporting pieces of insulation. 7. Place an aluminium plate of thickness > 8 mm and just larger in width and length than the electrode-stack on top of the cell. Apply Kapton tape on any edges that might come into contact with tab clamps. 8. Place one or two fin/Peltier assemblies onto the aluminium plate with thermal interface material (CONS1-INTERFACE) or thermal paste across the whole contact. 9. Depending on the size of the cell and number of fin sets, one, two or three clamping bars will be required. Place the studding clamping rods through holes in the box such that bars are evenly spread across the insulation on top of the cell. Fit the clamping bars and springs to the rods as per Fig. 1. Use Eq. 2 to find the correct length to tighten the springs to exert the pressure suggested by the cell manufacturer. N.B. the springs given in this design can produce a maximum force of 169 N in their linear range, i.e. 338 N per bar.
For all experiments: 1. Cover any unused clamping rod holes in the box with tape. 2. Plug the water cooling blocks into the cooling system using PELT6-HOSE. 3. Plug the Peltier elements into the output on the Peltier control box that correspond to the thermistor directly under that Peltier. 4. Measure the contact resistance between the cables and the cell tabs, R contactPos and R contactNeg . This can be done by using the battery cycler to pass a 10A current through the cell and measuring the voltage drop with a precision voltmeter. Contact between the probe and the tab can be made through the slots in the cell tab clamps. 5. Fill the box with vermiculite and gently agitate the box to allow it to settle (Fig. 10).
Testing procedure For measuring the CCC tab , the tab temperature, T set should be kept close to ambient temperature. This reduces heat losses through the cables, an area we have identified as a source of error for this measurement.
For measuring the CCC surface , the cell top temperature, T set , should be kept 1 C below ambient temperature. This reduces heat losses through the bottom of the cell, an area we have identified as a source of error for this measurement.
To run the experiment: 1. On the battery cycler prepare the test protocol given in Fig. 11 For the test measurements to be accurate the cell must be tested at pulsing currents such that the range of heat generation in the cell spans the full range of measurable heat rates in the chosen fin sets. In order to minimise error it is also recommended that temperature gradient across the cell be greater than 0:5 C. Precise prediction of heat generation using cell datasheets is not always possible so an iterative approach may need to be taken. One method is to perform the test as normal but using only a 1C pulsing current. Record the heat generation, Q 1C , and temperature gradient, DT 1C , at 1C. Then use Eq. 3 to find the minimum and maximum C rates, N, that should be used. In cases where small cell temperature gradients are the limiting factor the same analysis can be performed but replacing Q 1C with DT 1C and Q min with DT min to find N min .
It is recommended that a square root progression in current magnitude is used so that there is a linear progression in heat generation, since heat generation is expected to increase with the square of current magnitude. An example to give 6 C-rates in the range is given in Eq. 4.
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 6. Undo tab clamps one at a time taking care to cover tabs with insulating tape as soon as they are exposed. 7. Remove cell.

Data processing
1. Take the time average temperature readings for the last 10 min (600 s) at each pulsing current (example for surface cooling CCC temperature data shown in Fig. 12). 2. For each fin, DT fin should be found. Each Q fin can then be calculated by Eq. 1. This must be done for each test conducted, i.e.
for each current magnitude. See example in Fig. 12, where each region for data extraction is annotated.
For a surface cooled test: 1. Calculate the DT cell by comparing the time averaged temperatures. Where multiple locations have been measured take the average DT cell . 2. Sum every Q fin in the system to give Q tot .
For a tab cooled test: 1. Take the average of the cell top and bottom temperature at the point furthest from the tabs to give T cell 2. Find the temperature difference between each tab and T cell to give DT pos and DT neg .
3. Calculate DT cell as the average of DT pos and DT neg . 4. Take the total heat output from each tab (calculated in step 2), Q pos and Q neg . Deduct from each the resistive heat, Q ohmic , generated at each tab under each pulsing current using the tab contact resistance found during setup and the formula Q ohmic ¼ I 2 R. This gives a new Q posNet and Q negNet to be used in the next step that only includes heat generated in the cell (Eq. 5). 5. Sum Q posNet and Q negNet to give Q tot In either case plot DT cell against Q tot . The gradient of the line of best fit through the points gives the CCC. An example of this is shown in Fig. 13, which is discussed in the following section.   Validation and characterisation Validation of results was performed by comparison with values collected using the systems described in [5] and [6]. The cells tested are given Table 1, and their assigned references will be used to refer to them in this analysis (Table 2). Fig. 13a shows all results from CCC surface tests conducted using the presented apparatus. Fig. 13b shows all results from the CCC tab tests. Table 1 provides results. As previously introduced, the CCC values are simply the gradient of each line shown in Fig. 13a and b respectively.
It is important to note that it is not the intention of this analysis to evaluate the presented apparatus's performance against the system for measuring the CCC surface that was used in [6]. The former system had known errors which are discussed extensively in the original paper and may be summarised as: 1. Heat loss through the 'hot' surface of the cell is unavoidable because the insulation is not perfect. Whilst measures to account for this heat loss are implemented, they do not entirely eliminate the source of error. Proposals were made to improve the thermal control system in order to ensure the cell 'hot' surface may be held at ambient temperature, thus eliminating the temperature gradient to the ambient, and thus any losses from the 'hot' surface to the ambient. 2. Temperature difference across the cell under test is small and therefore oscillations in temperature at steady state, due to the substandard performance of the Peltier control system, lead to significant imprecision in extracting the true temperature difference. 3. Imprecise methods of compressing the cooling fins onto the cell leads to deviating thermal interface performance (from cell 'cooled' surface to fins), and thus deviating thermal performance of the entire apparatus from one test to the next.
The presented apparatus has addressed the previous limitations through improved design and procedural methods: 1. Better insulation (vermiculite fills the complex topology of the apparatus) to reduce heat loss.
2. Improved choice of thermal control locations to ensure there is not a significant temperature gradient from the 'hot' surface of the cell to the ambient. 3. Compression bars with controllable force to ensure the desired pressure is always exerted on the cell, from the cooling plate and fins.
As a result, the measured values of CCC surface were expected to deviate significantly from the past measurements, and the new values are now viewed as a more reliable measure of each cell's thermal performance.
Strength to this argument may be found by considering the CCC surface measurements from K50, which do not see significant deviation from the previous setup (1.00 W/K) to the current (1.00 W/K). This cell is significantly smaller than the other three cells tested, and subsequently error due to losses through the 'hot' surface of the cell was expected have a less dominant effect. Following this trend, the largest cell (A123) sees the greatest change, the previous measured value (4.70 W/K) is 36% smaller than the new value (7.33 W/K) The methods presented in [5] are significantly more robust, and as a result the apparatus set out in this paper to measure the CCC tab is conceptually very similar that used previously. There is very good agreement with the previous and current sets of results for the AMTE cell and the K50 cell, with deviation from previous to current at 6% and 3% respectively. These cells have large tabs (with respect to their electrode-stack size) located at either end of the cell, and therefore are ideally designed to limit the temperature gradient along the electrode-stack length. This means that it is easy to maintain a small temperature difference from the cell surface to the ambient, and thus losses to the ambient are small. All this creates a good scenario for a robust CCC experiment to be conducted.   The larger deviation observed for the A123 cell (30%) represents the inadequacy of this cell to be tab cooled, and thus the difficulty in measuring a consist and sensible value for the tab CCC. The poor cell design is discussed at length in [2]. The A123 has small tabs, located very close to one another, at one end of a large electrode-stack. This leads to a large temperature gradient along the length of the cell. As a result, it is impossible to maintain a negligible temperature difference from all external surfaces of the cell to the ambient, since the temperature of the external surfaces varies so much across the cell's geometry. Therefore, losses to the ambient are inevitable, and add an unknown error to the CCC measurement process. Finally, it must be mentioned that the tabs on K75 were so small that an experiment could not be conducted within the scope of this project. K75 is not designed to be tab cooled, and as such this is not seen as a limitation to the presented apparatus.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.