Cylindrical lithium-ion batteries have the highest power density among all types of lithium-ion batteries. In the design, manufacturing, application, quality, and safety management, cylindrical lithium-ion batteries involve a variety of specifications. They are displayed in Figure 1-1.
Figure 1-1 Cylindrical lithium batteries with various specifications
Cylindrical lithium battery usually adopts spiral electrode assembly because there are a large number of axial interfaces between electrode and electrolyte layer in the radial conduction path, which makes the thermal conductivity of cylindrical lithium-ion battery exists nearly two orders of magnitude difference between radial and axial. As one of the important thermal physical performance parameters of lithium-ion batteries, the thermal conductivity of batteries of different specifications and directions need to be covered in the test, which makes the accurate test and evaluation of the thermal conductivity of cylindrical lithium-ion batteries face severe challenges in the following aspects:
(1) There are many testing methods for thermal conductivity, but given the special shape characteristics of the cylindrical lithium-ion battery, it is necessary to find a reasonable testing method first to ensure the accuracy of measurement results, which is particularly important for the design and thermal management of lithium-ion battery.
(2) Cylindrical lithium-ion battery is characterized by obvious anisotropy, which requires the testing method and instrument of thermal conductivity to possess anisotropy testing ability. At the same time, cylindrical lithium batteries are generally sealed structures, so it is not allowed to insert temperature sensors and other detectors in the battery, the test can only be used in a non-destructive form. It can be seen that anisotropy and nondestructive testing of cylindrical lithium batteries significantly increase the complexity and technical difficulty of testing technology, and even need to develop some new testing technology, such as radial thermal conductivity testing technology of cylindrical lithium-ion battery.
(3) It involves different thermal conductivity test methods and equipment because the thermal conductivity test of cylindrical lithium batteries involves different shapes and directions. However, in practical engineering applications, it is still hoped to optimize the testing methods and develop new testing technologies to achieve as few testing methods and instruments as possible to meet the thermal conductivity testing requirements of other specifications of lithium batteries as much as possible.
(4) Because lithium-ion battery also involves other thermal performance parameters and characterization parameters such as specific heat capacity and thermal runaway, it is required that the thermal conductivity test method and instrument can be integrated with other thermal performance parameters test instrument, which makes the test instrument has multi-function, and multiple parameters can be tested on one test instrument.
Given the problems and challenges mentioned above, this paper will review the thermal conductivity testing technologies of cylindrical lithium-ion batteries in recent years. And then put forward a more suitable practical method for measuring the thermal conductivity of cylindrical lithium-ion batteries based on the analysis and research of these technologies.
1. Summary of testing methods for thermal conductivity of cylindrical lithium batteries
Although there are some studies and reports on the thermal conductivity test of cylindrical lithium batteries, we only focus on those non-destructive thermal conductivity test methods for integral cylindrical lithium batteries for the consideration of applicability and practicability. A cylindrical lithium battery is a standard cylindrical structure. As for the radial and axial thermal conductivity, the quasi-steady state method of cylindrical structure is adopted by the current effective test methods, and the test model is shown in Figure 2-1.
Figure 2-1 Geometric model of radial heating(a) and axial heating (b)
In the above test model, the composition of cylindrical lithium batteries is assumed to be uniform to simplify operation and calculation. The radial test model is to load constant heat flow on the outer surface of the cylindrical battery or heat the battery so that the external surface temperature changes linearly, as shown in Figure 2-1 (a). The adiabatic state is shown on the axis of the cylindrical battery (z-direction).
Similarly, for the axial thermal conductivity test, as shown in Figure 2-1(b), only a constant heat flow is applied to the top of the cylindrical battery or the temperature of the top surface changes linearly, and the bottom of the battery is insulated, which can form the test model the same as Figure 2-1(a). And this test model is a typical one-dimensional quasi-steady-state test model.
To get the quasi-steady state test model shown in Figure 2-1, the basic structure of the radial thermal conductivity test device is designed as shown in Figure 2-2. And the whole device is placed in a vacuum vessel to reduce heat loss.
Figure 2-2 Schematic diagram of the radial thermal conductivity measuring device with flexible heater, thin-film heat flow meter, and temperature measuring thermocouple
In order to reduce the influence of additional heat capacity, the heater, the heat flow meter, and the insulation layer are thin-film whenever possible. As a result, all measurements for temperature and heat flow are performed on the outer surface of the cell. For both radial and axial thermal conductivity measurements, the entire measurement device is wrapped with low thermal conductivity insulation to avoid heat dissipation in order to meet the assumption of no heat loss in the test model as much as possible.
The quasi-steady-state test model shown in Figure 2-1 is a traditional test method that is often used to measure the thermal conductivity of flexible and granular insulation materials at high temperatures. The temperature of an adiabatic surface (e.g., the axial temperature of a cylindrical sample) needs to be measured during standard quasi-steady-state testing. Under the condition of constant heat flow heating, after some time, the temperature of the heating surface and the adiabatic surface of the sample will reach the same heating rate, and the temperature difference between the sample and the sample in the direction of heat transfer will tend to be the same, which is called quasi-steady state. Thermal conductivity at different temperatures can be easily obtained by temperature measurement.
However, for cylindrical lithium batteries, temperature sensors are not allowed to be inserted in the center of the battery and can only be measured on the outer surface of the battery, which brings difficulties to measurement.
Research work of Jain's team
In order to solve the above problems, Drake in Jain's team at the University of Texas carried out specialty research  during his doctoral study, developed a novel testing technology, and reported it. The measuring device has the same structure as Figure 2-2, except that the thin-film heat flow meter is missing. During the test, the heating film temperature is linearly heated by electrification control after some time. The temperature change of the whole battery enters a quasi-steady-state process, and the temperature of the battery surface measured by the thermocouple gradually increases linearly. It is hoped that the temperature rise curve can be used to measure the relevant thermal performance parameters.
In addition, Drake and other people established the corresponding mathematical expression for the test model and conducted simulation by using the finite element method. They reported that the mathematical expression was in good agreement with the finite element simulation results(as shown in Figure 2-3) and calculated the axis line and radial of the battery and the temperature changes at different positions of the outer surface.
Figure 2-3 Comparison of Radial Mathematical Model and Finite Element Thermal Simulation
By analyzing the mathematical model, Drake and others came to the following conclusions: the thermal conductivity and specific heat capacity of the cell were obtained by measuring the intercept and slope of the linear segment of the temperature change on the outer surface of the cylindrical cell after entering the quasi-steady state, respectively. From this, they measured the radial and axial thermal conductivity and specific heat capacity of 26650 and 18650 cells, respectively. The test curves are shown in Figure 2-4 and Figure 2-5. The results of thermal conductivity and specific heat capacity of Li-ion battery are shown in Table 2-1.
Table 2-1 Measuring thermophysical properties of 26650 and 18650 batteries
Figure 2-4 Comparison of experimental data and analysis model of radial and axial thermal physical properties of 26650 lithium battery
Figure 2-5 Comparison of experimental data and analysis model for the measurement of radial and axial thermal physical properties of 18650 lithium batteries
According to the test method proposed by Drake, different thermal conductivity and specific heat capacity can be obtained by measuring the cylindrical lithium battery in different directions. Since the specific heat capacity has no directionality, the specific heat capacity measured in different directions should be the same, thus verifying the accuracy of the test method. Drake reported the test results of the 26650 lithium battery. The specific heat capacity measured by the axial test is 1605J/kgK, and that measured by the radial test is 1895J/kgK, a difference of nearly 15%.
Drake reported that this "small" difference was because the temperature in the radial experiment was tested at the center of the cell. However, it did not take into account the presence of metal lugs at the end of the cell. When metal spikes are considered in the axial test, the measured specific heat capacity is slightly lower due to the lower specific heat capacity of the metal compared to the organic solvents that make up the battery electrolyte. So it is reported that the axial measurement of specific heat capacity is considered more accurate because the fins are taken into account.
In addition, Drake reported a simple uncertainty analysis and concluded that the total measurement uncertainty of thermal conductivity and specific heat capacity was estimated at about 5%.
Building on Dr. Drake's research, Jain's team conducted additional research improvements . Dr. Drake's model for radial thermal conductivity testing of cylindrical lithium batteries is that what enters the cell is a constant heat flow that does not change over time. However, the absorption of heat by wrapped insulation and heaters in the form of thin films, for example, makes it possible that the true heat flow into the cell may change over time. The new study, therefore, modifies the analytical model to address these heat losses, deriving a more generalized expression for the cell surface temperature rise under variable heating heat flow conditions. Moreover, they redefined the radial thermal conductivity test method to improve the accuracy of radial thermal conductivity measurements.
In this study, the team tested two homogeneous materials(Delrin and acrylic resin) and the 26650 lithium-ion battery. The redefined thermal conductivity test method did not follow the test method reported by Dr. Drake in the previous period but used the sample surface temperature obtained from the test. Ascending curve, combined with sensitivity analysis and parameter estimation methods to calculate the thermal conductivity.
This study used the measurement device shown in Figure 2-2, that is, a thin-film heat flow meter was added to Drake's test device to detect the amount of heat flow that actually enters the cylindrical lithium battery after a constant heat flow. The test results are as follows as shown in Figure 2-6, it can be seen from the test results that there is significant heat loss that changes over time.
Figure 2-6(a) Input battery heat flow over time; (b) Enter the battery heat flow, heat loss, and the total change over time, the dotted line represents the constant heat flow loaded to the thin film heater
To effectively evaluate the improved test method, the transient planar heat source method was used to separately measure the thermal conductivity of Delrin and acrylic samples and conduct a comparative test. The test results are shown in Table 2-2.
Table 2-2 Comparison of the results of the two measurement methods
In this improved study by Jain's team, only the thermal conductivity parameter was estimated in the parameter estimation calculation, and the specific heat capacity was not estimated. The reason is that the specific heat capacity must be calculated in the parameter estimation process, and then the specific heat capacity is calculated based on the specific heat capacity. Estimating the thermal conductivity, and the error of the specific heat capacity will have a greater impact on the thermal conductivity. Therefore, in this study, the specific heat capacity of the battery was measured independently by a calorimeter, and the specific heat capacity of Delrin and acrylic resin was measured by the transient planar heat source method.
This improved study by Jain's team reported uncertainty of 7% for the measurement of radial thermal conductivity. As shown in Table 2-2, the difference between the two methods was 9-15%. The smaller the thermal conductivity, the greater the measurement error.
Research by Spinner et al.
To do more in-depth research on cylindrical lithium batteries, Spinner and others of the US Naval Research Laboratory used four methods: analysis, calorimetry, numerical and experimental methods to test and study the thermophysical properties of commercial 18650 lithium-ion batteries:
(1) The first method is based on the analytical expression of the radial thermal conductivity obtained from the time-varying thermal conductivity equation, and then based on the experimental measurement values of natural convection heating and cooling of the lithium battery, the parameter estimation method is used to obtain the radial thermal conductivity of the lithium battery and Specific heat capacity.
(2) The second method is to use a self-made simple calorimeter to test the specific heat capacity of the lithium battery.
(3) The third method is to use the analytical expression of the radial heat conduction equation, combined with the constant heat flow test measurement results shown in Figure 2-2, and use the numerical difference and reference estimation methods to obtain the radial thermal conductivity and specific heat capacity.
(4) The fourth method completely adopts the axial thermal conductivity test method of Drake et al. . According to the quasi-steady-state change curve of battery surface temperature, the axial thermal conductivity and specific heat capacity are calculated by intercept and slope.
In the first radial thermal conductivity test, a lithium battery with a thermocouple attached to its surface is placed in a closed chamber with an initial temperature. After the initial temperature of the lithium battery and the chamber are both stable, the temperature of the chamber is stepped up. The higher or lower it is to a new temperature, the lithium battery is heated or cooled by surface convection heat transfer, and the temperature measuring thermocouple detects the change of battery surface temperature with time during the whole process. This is a typical lateral convective heat exchange model of a cylindrical sample. Spinner et al. established an analytical expression of the battery surface temperature change based on this heat transfer model, and then used parameter estimation techniques and combined with the surface temperature change data obtained from the test to calculate The radial thermal conductivity and specific heat capacity of lithium batteries are 0.55±0.23W/mK and 972±92J/kgK, respectively.
To evaluate the accuracy of the measurement, the calorimetry method was used to measure the specific heat capacity of the 18650 lithium battery, aluminum, and Teflon as a comparison. For each measurement, four samples were selected and bundled together to measure. In this way, the total heat capacity will increase, and the measurement will be more exact. The measurement results are shown in Table 2-3.
Table 2-3 The specific heat capacity obtained by calorimetry is compared with the specific heat capacity values reported in the literature for aluminum (type 6061), Teflon, and 18650 LiCoO2 batteries.
In the third radial thermal conductivity test, a Teflon cylinder with similar geometry to the 18650 battery was first compared, with thermal conductivity of 0.232±0.003W/mK and specific heat capacity of 1203±8J/kgK, respectively. Then, nine different constant heat flux tests were carried out on the 18650 battery. The results of the nine measurements were in good agreement, with the mean thermal conductivity and specific heat capacity of 0.300±0.015W/mK and 814±19J/kgK, respectively.
It can be seen from the results obtained by the third technique that the specific heat capacity data of 814±19J/kgK is nearly 9% lower than the calorimeter measurement result of 896±31J/kgK. Therefore, Spinner et al. gave up the measurement of specific heat capacity and directly used the measurement result of specific heat capacity of calorimeter, while the direct parameter was used to estimate the radial thermal conductivity. Thus, the thermal conductivity obtained was 0.219±0.020W/mK, and this result was considered to be the best estimate. But there was no further examination of whether this conclusion was correct, such as using other methods to accurately measure the thermal conductivity of Teflon and then comparing it.
In the fourth axial thermal conductivity test, an axial thermal conductivity of 21.9±1.7W/mK was measured. But there are no specific heat capacity measurements were given.
Comparing the results of Spinner et al. with those of Drake et al., it can be seen that the measured results of axial thermal conductivity and specific heat capacity differ greatly except that the measured results of radial thermal conductivity are similar.
Research of Murashko team
To enable online measurement of thermal performance (thermal diffusivity and calorific value) of cylindrical lithium batteries during operation, Murashko's team developed and investigated an alternative test method .
The test model is shown in Figure 2-7(b), the cylindrical battery should be regarded as an infinite cylinder. For this purpose, as shown in Figure 2-7(a), fiber wool is used for heat insulation at both ends of the cylindrical battery. The temperature and heat flow on the battery surface is measured by using a PT100 temperature sensor and a heat flow sensor (GHFS) respectively.
Figure 2-7 (a) Cylindrical battery with heat insulation, GHFS, and PT100 sensor;(b) Infinite cylinder
For the measurement of the thermal performance of cylindrical lithium batteries, the cylindrical battery is treated as a cylindrical sample with an internal heat source. For the internal heat source cylindrical heat transfer model, analytical expressions for surface temperature and surface heat flow are established. The surface temperature and heat flow of the battery obtained by the test are used to calculate the radial thermal conductivity, radial thermal diffusivity, specific heat capacity, and battery calorific value using parameter estimation methods. Two different tests were carried out, and the test results are shown in Table 2-4 and Table 2-5:
Table 2-4 Thermal parameter calculation results after the first test
Table 2-5 Thermal parameter calculation results after the second test
It can be seen from the above two test results that the method adopted is difficult to measure the specific heat capacity and radial thermal conductivity at the same time, and the errors of radial thermal conductivity and thermal diffusivity are huge. But this method can be used to measure the specific heat capacity of cylindrical batteries.
Huang Jian from Xiamen University and others reported in 2020 their research work on the thermal conductivity anisotropy test of 18650 cylindrical lithium-ion batteries . The test method is a combination of the ASTM D5470 steady-state constant heat flow method and CFD simulation. The upper and lower heat flow meters of different sizes and shapes are used to test different types of cylindrical lithium batteries clamped between the upper and lower heat flow meters. For the axial thermal conductivity test of cylindrical lithium batteries, as Figure 2-8, a small diameter copper rod heat flow meter is used. The copper rod heat flow meter of the upper and lower structure clamps the vertical cylindrical lithium battery in the middle. The upper and lower surfaces of the battery are respectively controlled at different temperatures to form a stable temperature gradient in the axial direction of the battery, thereby measuring the axial thermal conductivity.
Figure 2-8 Axial thermal conductivity test;(a)Measuring device,(b) Schematic diagram of the device structure
As shown in Figure 2-9, the steady-state method still is used to measure the radial thermal conductivity of the battery. But the size of the upper and lower copper rod heat flow meters is enlarged, and the end faces of the upper and lower heat flow meters are attached to the outer surface of the arc-shaped battery to ensure a stable temperature gradient in the diameter direction of the battery. It can be seen from Figure 2-9 that the structure of this instrument does not test the true radial thermal conductivity.
Figure 2-9 Radial thermal conductivity test; (a) Measuring device, (b) Device structure front view, (c) Side view
The researchers measured the thermal conductivity of 316 stainless steel (14.494 W/mK) using the transient planar heat source method, and then shaped the 316 stainless steel into a 18650 cylindrical lithium-ion battery. Next, the experimental object was placed into the two above-mentioned test instruments for testing to assess the measurement accuracy. The deviation of axial test results is -0.649%, and the deviation of radial test results is 2.394%.
In the subsequent test of the axial thermal conductivity of the 18650 cylindrical lithium-ion battery, the temperature at the top of the battery was controlled at 125.7°C, and the temperature at the bottom was controlled at 31.3°C. The measured axial thermal conductivity at a temperature difference of nearly 94.4°C was 11.5W/mK. . In the radial thermal conductivity test, the measured result is 4.324W/mK.
Whether this test method can accurately measure the anisotropic thermal conductivity of cylindrical lithium batteries is very arguable. The main problem is that in the process of testing the radial thermal conductivity, the arrangement of the upper and lower copper heat flow meters and the cylindrical battery is very easy to find heat. The shortest path for transfer, such as heat transfer from the battery casing, will inevitably increase the heat transfer on the one hand, and shorten the heat transfer path on the other. Both effects will increase the thermal conductivity test. Moreover, this up-and-down heat transfer structure is not the true radial heat transfer of the battery, and the thermal conductivity obtained is not the true point size radial thermal conductivity.
Bhundiya and others of the California Institute of Technology also carried out test research on 18650 and 26650 cylindrical lithium-ion batteries . Before testing, the battery under test is disassembled and the radial thermal conductivity of the lithium battery is measured by heating the center axis of the column cell with a nickel-chromium alloy wire energized. The thermal conductivity of the 18650 lithium battery was 0.43±0.07WmK, and the thermal conductivity of the 22650 lithium battery was 0.20±0.04W/mK. It is clear that both measurements are much larger than the values reported by Drake et al. (0.20 ± 0.01 W/mK and 0.15 ± 0.01 W/mK) , and the entire test setup is very rudimentary. There is no thermal protection around the tested battery and there is convection heat loss, and the repeatability of the measurement results is over 10%. The most important one is that the measured contact pressure is inconsistent with the actual and brings large thermal resistance, and the other is that the material with known thermal conductivity is not used for examination and verification. Despite the large difference in the test results, it is at least another proof that the effect of interlayer contact thermal resistance in cylindrical Li-ion batteries is very obvious. The test may also demonstrate that the radial thermal conductivity of lithium batteries from different manufacturers varies considerably, mainly due to different manufacturing processes.
3. Analysis and comment
As shown above, the domestic and abroad research is very ambiguous and chaotic. For the testing of the anisotropic thermal conductivity of cylindrical lithium-ion batteries, the related research is not clear or effective. Many problems are mainly manifested as follows:
(1) The most intuitive performance is that the measurement results of anisotropy of thermal conductivity are very poor, and the measurement of specific heat capacity has a slight effect, which shows that the measurement of specific heat capacity is not sensitive to various error factors.
(2) A constant heat flux model has been established for measuring the radial thermal conductivity of cylindrical lithium-ion batteries, and a very beautiful mathematical expression has been derived, but it is not well used in practical tests. It may be that the influence of various boundary conditions is too great to directly use the corresponding mathematical expressions to obtain accurate measurement results, and the various parameter estimation methods adopted do not improve the measurement accuracy.
(3) In the process of thermal performance testing, the mathematical model does not accurately describe the various changes and boundary conditions of the actual measurement device. Therefore, in thermal performance testing, the most important thing is to simulate and calculate the test method, verify the accuracy of the test model and quantify the influence of various boundary conditions, and establish the corresponding calibration method. This is the key to ensuring the accuracy of measurement, which is not covered by the above-mentioned domestic and international studies, and there is no way to improve the measurement accuracy. Many research teams thus blindly adopted more other methods to do the effort, but basically ineffective.
(4) There are a lot of common sense mistakes in the above foreign test studies. The most typical error is that thermal performance measurements should never be made in a vacuum. Attempts to reduce the effects of convection and radiant heat loss under vacuum conditions are often overwritten by the negative effects of the simultaneous increase of void contact thermal resistance under vacuum. Vacuum testing is bound to increase the contact thermal resistance between the heating film, the film heat flow meter, and the thermocouple, which is also one of the main reasons for the huge measurement error in the above foreign research. In addition, if the control of vacuum degree is unstable or not, the change of pore type contact thermal resistance can also bring large fluctuations to the measurement.
To sum up, although there are still many problems in domestic and foreign studies, there are the following two gains:
(1) An effective attempt was made to test the anisotropic thermal performance of a cylindrical lithium-ion battery. Especially for non-destructive testing methods, it is proved that it is possible to determine anisotropic thermal conductivity and specific heat capacity only by measuring the change of battery surface temperature. This proof is of great significance for the follow-up research and solving the problem of thermal performance testing of lithium-ion batteries.
(2) Through the efforts made in recent years, a consensus has been formed for the testing of battery thermal performance. And that means no matter what test methods and technical means are used, it is necessary to conduct non-destructive testing following the engineering requirements. Secondly, the accuracy of the final measurement needs to use comparable testing methods and means for comparative assessment.
4. Proposal and research of new methods
Through the above review and analysis of various testing methods for radial thermal conductivity of cylindrical lithium-ion batteries, it can be seen that the testing methods with real engineering significance have the following characteristics:
(1) Non-destructive measurement: the lithium battery cannot be disassembled for measurement, or the various performances and boundary conditions of the battery will be changed.
(2) The surface measurement approach, where all test loading takes place on the outer surface of the cylindrical cell, has been relatively successful in reporting constant heat flux loading on the cell surface.
The boundary conditions can be divided into three types in the thermophysical properties of materials, namely, the first type is constant temperature, the second type is constant heat flow, and the third type is alternating temperature or heat flow. It can be seen that the three boundary condition testing models can be used to measure the radial thermal conductivity of cylindrical lithium-ion batteries that cannot be disassembled. The commonly used method in the above review is the second type of boundary conditions, which means that the first and third types of boundary conditions can also be used to measure the radial thermal conductivity of lithium batteries.
As a result, Shanghai Yiyang Industrial Co., Ltd. used the first type of boundary condition test method to research the radial thermal conductivity test technology, established a constant temperature test model, deduced the corresponding surface temperature analytical expression, and verified it with finite element simulation. The accuracy of the test model is verified, and the accuracy of the constant heat flow test model is also verified.
Through research, it is found that the constant temperature test method using the first type of boundary conditions can more accurately measure the radial thermal conductivity of the lithium battery, and at the same time can measure the specific heat capacity and the radial thermal diffusivity. More importantly, the constant temperature measurement method can be easily promoted and applied to the thermal performance and thermal runaway testing of prismatic and bagged lithium-ion batteries, and can be used as an important supplement to the current commonly used accelerated calorimeter testing technology.
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