In this section, our simulation results are presented and discussed. To this end, it is important to remember the definitions of the operational and optimal operating temperature ranges, which are discussed in
Section 1.1. The cell temperature must be kept within the operational temperature range for it to operate in the way it is designed to behave and to avoid any failures. This range is from 253.15 K to 333 K. On the other hand, the optimal operating range refers to the range within which the cell temperature should ideally be maintained in order to achieve its best performance and minimise the rate of degradation, which is between 288.15 K and 308.15 K.
3.1. Benchmark Cases
Before our feasibility and parametric study results are presented, three benchmark cases are discussed. This is to investigate whether PCM-based BTMS can be used to improve battery operating conditions. The cases are: (1) real flight conditions; (2) no heat generation assumed, and (3) perfect adiabatic conditions. Although the last two cases are not representative of realistic flight conditions, they help to provide insight into the previously mentioned objective.
It is important to discuss the effects of heat loss and generation (cases (2) and (3), respectively) separately, as the power and ambient temperature profiles used in this work are for the general case (as described in
Section 2.5), and the effect of one can outweigh that of the other depending on the type of flight. As can be seen in
Figure 8, case (2) shows that when only the heat loss is considered the averaged battery temperature drops to nearly 273.15 K, which is below the lower limit of the optimal battery operating temperature range. This highlights the concerns raised regarding the cruise phase of any flight profile. When the power demand from the powertrain is low, there is little heat generation and the overall temperature is expected to drop due to the low ambient temperatures and high convection cooling coefficients. On the other hand, when only heat generation is taken into account (case 3), the temperature crosses the upper limit. These two cases highlight the fact that thermal control of the battery pack is necessary; it cannot be entirely insulated to create an adiabatic system. This justifies the purpose of the presented investigation of PCM-based BTMS usage cases, as a correctly designed BTMS using a PCM is able to provide insulation as well as offering a heat sink from the system to maintain an ideal operating window.
Case (1) aims to be representative of real flight conditions, considering both heat loss and generation. The temperature profile shows that the effects of heat loss and generation balance each other out to keep the battery temperature within the optimal range. Nonetheless, it is important to note that flight conditions may vary depending on the date and route of flights, as previously discussed. For instance, unlike the regional flight modeled here, international flights with a longer cruising period experience cell temperatures dropping further, causing the curve to be closer to case (2). Therefore, use of a BTMS would allow flexibility in the operation of flights and provide an extra layer of safety in case of emergency or if unexpected actions need to be taken. In addition, the BTMS helps to achieve a uniform temperature distribution throughout the battery pack during those flight stages in which a sudden peak in power use is required, such as take-off. In this respect, a PCM-based BTMS can act as a passive thermal control mechanism, absorbing heat energy during moments of high discharge and releasing heat back into the battery during periods of low power demand.
3.2. Parametric Study of PCM Properties
In this subsection and the following one, parametric studies are conducted. As a performance indicator of the BTMS, the root mean squared difference (RMSD) is defined as
where
is the number of time steps,
n represents each time step, and
is the volume averaged battery temperature in Kelvin. RMSD is simply a measure of how much
is off the optimal battery temperature range (between 288.15 K and 308.15 K). Consequently, the lower RMSD is, the better performance the PCM-based BTMS is observed to deliver. It is noteworthy to emphasise that performance is inversely proportional to RMSD; thus, in this paper the level of BTMS performance is defined as follows:
Using the variable defined above, a parametric study on PCM properties is carried out in this subsection. More specifically, this study examines the latent heat of fusion and thermal conductivity of the PCM at fixed values of the initial and melting temperatures of the battery pack and PCM, respectively. For both temperatures, 298.15 K was used, which is the mid-point of the optimal temperature range. To allow the PCM to be in its complete solid form (i.e., remaining latent heat capacity is 100%) at the beginning of flight in a case where initial and melting temperatures are meant to be the same, the initial temperature was purposely lowered by 0.01 K. The effect of both temperatures is examined in the following subsection.
It can be observed from
Figure 9a,b that increasing the thermal conductivity corresponds to improved performance of the BTMS. This is because heat is transformed across the battery pack, thereby removing the issue of the PCM partially melting near the cell surfaces. However, it is clear from
Figure 9a that BTMS performance is far more sensitive to changes in the latent heat of fusion. Hence, it is logical to focus on the relationship between performance and latent heat of fusion.
Figure 9c suggests that the performance improves with increasing latent heat of fusion in a close to exponential manner. It should be remembered that in this study the mass of BTMS is set to be 5% of that of battery, which makes the thickness of the PCM layer quite small. With this in mind, the heat conduction rate across the thickness of the PCM layer is excellent, meaning even a very low thermal conductivity does not create a significant insulating layer of PCM from the perspective of the cell generating heat. On the other hand, because the volume of PCM used is consequently low, the PCM should be intrinsically able to capacitate a large amount of energy in the form of latent heat in order to effectively control the temperature of the pack. Hence, it is concluded that for the application of PCM-based BTMS to flights, increasing latent heat of fusion should be prioritised over increasing thermal conductivity. Thus, the data suggest that composite PCM (CPCM) is not suitable for battery flight applications; the mass of PCM that can be used to maintain a high battery pack specific energy means that adding conductive materials is unnecessary and wasteful with respect to the property that ultimately needs to be maximised, that is, thermal storage capacity.
3.3. Initial and Melting Temperatures
In this subsection, the temperature of the battery pack at the beginning of a flight and melting temperature of PCM are tested. These tests were conducted by considering the best PCM properties found in the previous subsection; the latent heat of fusion is set to be 260 kJ kg−1, which is the maximum value used in the previous parametric study. Three different melting temperatures of PCM are examined, selected to perform across the optimal temperature range at intervals of 10 K. Considering that at a given melting temperature the PCM maintains a constant temperature under a continuous heat supply, it is sensible to use a PCM with a melting temperature within the desired temperature range. For the initial temperatures, the cases of 288.15 K and 298.15 K are considered. An initial temperature equal to the upper limit of the optimal range is not considered in light of the fact that the average temperature increases during take-off, which would make the average temperature higher than the upper limit from the start.
In
Figure 10a, for the case with a melting temperature of 288.15 K and initial temperature of 298.15 K, the temperature at the last phase of a flight passes beyond the upper limit. This is because at the start of a flight, the solid fraction of PCM is 0 (i.e., the PCM is fully melted because the temperature of the PCM is greater than the melting temperature), as shown in
Figure 11a. This can be determined from the fact that the temperature does not maintain a constant temperature at any point of flight, which means that the PCM remains fully melted from the beginning of the flight. Hence, it can be said that this case is the one with the worst BTMS performance. This suggests that for PCM-based BTMS to effectively manage temperature of batteries on regional passenger airplanes, two conditions are necessary: (1) the melting temperature of the PCM is within the ideal temperature operating window of the battery and (2) the initial temperature of the battery pack is below the melting temperature of the PCM. The best case would be for the PCM to start a flight in its completely solid form.
For all the other cases, the temperature over the entire flight duration predominantly falls within the optimal range. However, the cases with melting temperature of 298.15 K in
Figure 10b specifically provide performance superior to that of all other scenarios. This is because the full temperature window that these two cases span is small relative to those of cases with melting temperatures other than 298.15 K, as can be observed in
Table 8. Moreover, this scenario spends a greater amount of time in the center of the ideal temperature operating window relative to all other scenarios. Taking the case with a melting temperature of 308.15 K as an example,
Figure 11c shows that the PCM starts to melt at around the onset of the last quarter of the flight, and the cell temperature increases to reach the melting temperature before then, as can be seen in
Figure 10c. This means that the case with a melting temperature of 298.15 K has relatively high tolerance to sudden variations of temperature due to unplanned events. Such events may include sharp changes in ambient temperature, expected adjustment of air routes owing to severe weather conditions, and emergency landings. Further, it can be noted that the temperature profile is maintained at the melting temperature for a longer period. Here, it is important to highlight that this melting procedure does not terminate before the end of take-off (as shown in
Figure 11b), after which power usage and the resulting battery heat generation rate is relatively low. Thus, the BTMS is capable of absorbing all heat generated over the entire take-off phase. It then uses this stored heat to prevent the battery temperature from decreasing due to low ambient temperature during the cruise phase. The significance of this benefit is inherently enhanced as the flight duration increases (e.g., international flights), where the battery discharge rate is lower (i.e., lower heat generation rate) with the longer cruise phase and keeping the cells warm is the primary role of the thermal system.
Thus, having analysed all the cases with different PCM melting and initial temperatures, it is concluded that a PCM with a melting temperature of 298.15 K has the most promising characteristics for further investigation, for the reasons discussed above.
For the case without BTMS under real flight conditions, presented in
Figure 8 in
Section 3.1, the temperature falls and rises over the duration of the flight such that most of time the temperature remains in the centre of the optimal temperature operating window, which is ideal. On the other hand, with BTMS it can be seen that the temperature only increases, eventually reaching the upper limit of the range at the end of the flight. This stems from two factors. First, a thin layer of insulation was added to the outskirt of the BTMS. Second, the PCM has thermal conductivity, which can be as low as that of the insulation. These two factors mean that the effect of heat convection to the ambient temperature at a high cruising altitude is minimised by limiting the rate of heat transfer through conduction across the BTMS; this becomes significantly important for the application of prolonged flights as compared to the regional one-hour flight studied here, such as international flights, where the cruising phase (low ambient temperature and heat generation rate) accounts for the most of flight duration. This implies that the main role of the BTMS in such cases is to absorb and store the heat generated from the battery; it can be seen in
Figure 11b,c that the BTMS is capable of doing this, reemphasising that the latent heat of fusion should take the highest priority among all of the PCM properties that need to be optimised.