三星客户锂电池论文

Coupled electrochemical thermal modelling of a novel Li-ion battery pack thermal management system Suman Basu a, Krishnan S. Hariharana, Subramanya Mayya Kolakea, Taewon Songb, Dong Kee Sohnb, Taejung Yeo b aNext Generation Research (SAIT-India), Samsung R maximum voltage of the cycler is 25 V. Thus, each cell of the pack is equilibrated at 4 V at the end of charging. Discharge is performed at 0.9 C (?15.6 A) and 0.6 C (?10.4 A) with a cutoff voltage of 16.5 V. Water is used as the coolant with a fl ow velocity of 0.2 m/s and inlet temperature of 296.45 K. Channel Conduc?on Element 18650 cells Coolant fl ow Coolant fl ow Fig. 1. Geometry of the pack and the thermal management system. S. Basu et al./Applied Energy 181 (2016) 1133 3. Mathematical model A three dimensional model is constructed to investigate the performance of the TMS in detail. The fl ow and conjugate heat transfer is modelled using commercial CFD package StarCCM + 10.06.010 49 while the electrochemical input is obtained from Battery Design Studio 10.06.010 50. It is possible to simulate the performance of a complete battery pack with cooling system using this combination 51. Although, full electrochemical model could be numerically expensive, it offers a comprehensive and complete picture of the thermal interaction as a result of operating conditions. To reduce the numerical cost, representative battery packs are constructed using symmetry of the complete battery pack. Electrochemical thermal model is used to compute the per- formance of the representative packs and the same are used to pre- dict the temperature of the pack at other parts. 3.1. Electrochemical model The electrochemical model is a three dimensional extension of the well-known Pseudo 2 Dimensional (P2D) model for 36 38,50. The fl ow and heat transfer is modelled using standard CFD schemes. The models are discussed briefl y here as the details are available widely in literature. Porous media formulation is implemented on the electrodes and separator domains of the Li-ion battery. Charge conservation in solid electrode phase (cathode and anode), as shown in Eq. (1), is modelled by discretizing the electrode domains in the through plane direction (while not resolving the individual particles). This is the fi rst dimension of the P2D model. The effect of porosity is incorporated through the effective electronic conductivity (reff s ). r? reff s r/s ? asin 01 Charge conservation in electrolyte phase, which encompasses both the electrode and separator phase, is modelled including the effect of electronic transference as per Eq. (2). r?jeff s r/e 2RgTjeff s F t0 ? 1 1 dlnf? dlnce ? rlnce ? asin 0 2 Lithium ion species transport equation is developed using the concentrated solution theory and is shown in Eq. (3). eece t ?r? Deff e rce ? 1 ? t0 F asin 03 The electrode and electrolyte phase potentials are connected by the reaction current. It is defi ned using the Butler-Volmer reaction in Eq. (4). in i0exp aaF RgT /s? /e? Eeq ? ? exp ? acF RgT /s? /e? Eeq ? 4 The quantity /s? /e? Eeq, also termed as over potential, denotes the voltage lost during cell operation at a fi nite charge/dis- charge rate. From Eq. (4) it can be inferred that electrode potential would the same as open-circuit potential (OCP) when the dis- charge rate is infi nitesimally small. The exchange current density is thus defi ned as, i0 Fkcackaaa ce cref e ?aa cmax s ? csaacac s 5 Lithium species conservation inside the electrode particle is achieved by unsteady diffusion equation in spherical coordinates. The electrode particles are assumed to spherical and the diffusion is isotropic. Therefore, the diffusion equation reduces to Eq. (6) where the spatial variation is only in the radial direction. The radial direction of the particle is the other direction of the P2D model described in Refs. 3638. cs t 1 r2 r Dsr2 cs r ? 6 The boundary condition for Eq. (6), at particle surface connects this Li-species conservation equation to the Li-ion conservation equation through the reaction current, as shown in Eq. (7). ?Ds cs r ? ? ? ? rRp in F 7 Energy equation takes the form of thermal conduction equation in the Li-ion cells where the conductivity is mass weighted average of all the constituents (Eq. (7). Heat is generated in the cell due to different mechanisms reversible, irreversible and ohmic. Qtot Qrev Qirr Qohm8 Reversible heat generation happens due to the variations in open circuit voltage with temperature and is calculated as the following. Qrev asinT Eeq T 9 The irreversible heat generation is due to the overpotential or the voltage loss due to fi nite current production rate as shown in Eq. (9). Qirr asin/s? /e? Eeq10 The Ohmic heat generation is due to the resistance to the elec- tronic transport in the solid phase and resistance to the ionic trans- port in the electrolyte phase as shown in Eq. (11). Qohm ?ie /el x ? ? is /s x ? 11 ie ?jeff s r/e 2RgTjeff s F t0 ? 1 1 dlnf? dlnce ? rlnce ? 12 is ?reff s r/s13 3.2. Conjugate heat transfer model Heat transfer is through conduction in the conduction element and fl ow channel. Heat, generated in the cells, is transported from the cell to the conduction element and then to the fl ow channel. Heat is transported away by the coolant fl owing through the fl ow channel. The fl ow is modelled using mass conservation equation (Eq. (14) and momentum balance equation (Eq. (15) while energy Coolant fl ow Coolant fl ow T1 T2 Parallel connec?on Series connec?on Fig. 2. Locations of temperature measurements (T1 and T2) in the pack. 4S. Basu et al./Applied Energy 181 (2016) 113 equation is modelled using the advection-diffusion equation with a source (Eq. (16) 49. r?u 014 u t u ?ru ? 1 qr ? P lr2u15 qCpT t u ?rqCpT r? krT Qtot16 The fl ow is solved using segregated solver according to the SIMPLE algorithm 52 while the convection is solved with second order accuracy for both fl ow and energy 49. The solid-solid interfacesbetweencell-conductionelementandconduction element-channel, are modelled as imprinted interface. Contact resistance to heat transfer has been applied at these interfaces. The cell internal parameters are adopted from the previous publi- cation by the present group 53. Total heat generation (Qtot) due to cell operation is calculate through the electrochemical model as described in Eq. (8). This heat generation is an input to the energy equation (Eq. (16) of the conjugate heat transfer model. Temperature calculated from this model goes back as input to the electrochemical model. In the electrochemical model the equilibrium potential (Eeq) and other transport properties are strong functions of temperature 53. Thus the coupling between the electrochemical and thermal model is established. 4. Results and discussion As discussed in the previous sections, only the fi rst parallel connected branch consisting of fi ve cells are used for the fi rst com- putational model using the complete electrochemical thermal model as shown in Fig. 3. As the heat generation and transfer mechanisms remain same for all the branches, the temperature distribution in the fi rst parallel branch can be used to predict the temperature distribution in all other branches. The fi rst parallel branch is computed, as the fl ow inlet boundary condition is known for this branch. Similarly for the series branch, the fl ow channel along with fi rst set of series connected cells are computed. Evolu- tion of temperature in the streamwise direction can be resolved from this result. Temperature information from the series con- nected cells can be used along with the temperature distribution of the fi rst set of parallel connected branch to predict the temper- ature of the complete pack. This concept has been discussed in the subsequent sections. The mesh for the fi rst set of parallel connected cells, shown in Fig. 3, has 400,000 polyhedral cells and the time step size used for the computation is 1 s. The computation is performed on Intel i7 CPU using 5 cores. Simulation of about 3500 s of pack operation takes about 14 h of computation time. The open circuit potentials and entropies for both the electrodes are plotted in Fig. 4a and b respectively. The cathode information is based on in-house experiments and the anode information is adopted from literature 53. The magnitude of overpotentials at Channel Conduc?on Element 18650 cells Coolant inlet Coolant inlet T1 Fig. 3. Geometry and mesh of the fi rst row of parallel cells. Fig. 4. (a) Electrode OCP, (b) electrode entropy, (c) electrode overpotential and (d) total heat generation for 0.9 C discharge rate. S. Basu et al./Applied Energy 181 (2016) 1135 anode and cathode for 0.9 C discharge rate are also plotted in Fig. 4c. Cathode overpotential is greater than anode overpotential and it continues to increase as the discharge continues. As the cathode gets fi lled up by lithium during discharge, it is expected that near the end of discharge greater overpotential would be required for same lithium fl ow in the cathode. From this, it can be expected that the total heat generation would increase near the end of the discharge. As expected (Fig. 4d), total heat genera- tion in the battery is found to increases near the end of discharge. 4.1. Validation Validation is performed for 0.9 C and 0.6 C discharge starting at a temperature of 296.45 K. Water is used as the coolant and it fl ows atatemperatureof296.45 Kand0.2 m/s.This fl owrate corresponds to a Reynolds number of 1800 which is lower than the transition Reynolds number for fl ow in pipe. Therefore, laminar fl ow model is used in the computation. Contact resistance of 0.0025 m2K W?1is used in the case of solid-solid interfaces. The pack is discharged then at 0.9 C rate. As the operating Reynolds and Prandtl numbers are 1800 and 7 respectively, the heat transfer Peclet number is greater than 10,000. Hence, it can be concluded that advection is much stronger than conduction in the fl ow. Therefore, the temperature of any conduction element is not affected by the downstream conduction elements. Thus, an electrochemical-thermal model of the fi rst conduction element along with the TMS is considered for validation, as it has no ther- mal effect from the downstream cells. Voltage and temperature of the cell marked T1 in Fig. 3 is com- pared with the measurement taken at the cell marked T1 in Fig. 2. Accuracy of prediction is calculated as per the Eq. (17), where N denotes the number of observations. Accuracyavg 1 ? 1 N X N jVexp? Vmodj Vexp 17 Experimental and computed discharge voltages at 0.9 C rate for cell T1 are compared in Fig. 5. Average accuracy is more than 95% while the maximum absolute deviation is less than 0.1 V. Temper- ature comparison for cell T1 at 0.6 C and 0.9 C discharge rates are shown in Fig. 6. The total temperature rise has been predicted cor- rectly in both the cases. For 0.6 C discharge rate, the computed temperature profi le closely follows the experimental temperature profi le. For 0.9 C discharge rate, there is a mismatch at around 1000 s, which reduces later and from 2000 s onwards, excellent agreement is achieved. The maximum absolute error in tempera- ture prediction is 1 K and average accuracy is 90%. Therefore, it is concluded that this model has excellent electrochemical and ther- mal prediction capabilities. Furthermore, the temperature rise in the battery pack using the present TMS (4 K 0.9 C discharge rate) is of the same order as advanced graphene augmented PCM based TMS reported in literature 17,18. Although such PCM based TMS are more compact, the present TMS does not need any novel mate- rial and hence, can be produced economically. 4.2. Analysis of thermal performance 4.2.1. Parallel connection The temperature contour of the fi rst parallel branch, at the end of 0.9 C discharge, is shown in Fig. 7. Other parameters remain the Fig. 5. Discharge voltage comparison at 0.9 C discharge rate for cell T1. Fig. 6. Temperature comparison for cell T1. 5 1 4 3 2 Fig. 7. Temperature of the fi rst parallel branch of the pack and the cells. 6S. Basu et al./Applied Energy 181 (2016) 113 same as in the previous subsection. It is clear from the contour that there is a jump in temperature, from the cells to the conduction element and from the conduction element to the channel. This is due to the contact resistance at the metal to metal interfaces. The cell marked 5 is slightly hotter than the cell marked 1 due to the longer distance between the cell marked 1 and the cooling channel. The temperature variation in a single cell is found to be on the order of 0.2 K. The difference in average temperatures, between the cells, is found to be on the order of 0.5 K. Therefore, it can be concluded that the fi rst parallel branch experiences a quite uni- form temperature distribution. Three dimensional contour of the current density, heat genera- tion and temperature of the cell marked as 5 in Fig. 7, is plotted in Fig. 8. The negative current density increases from the center to the surface (Fig. 4a) as the negative current collector is placed close to the outer surface. On the other hand, the positive current density is high near the center as the positive current collector is places at the center. As the NCA (cathode active material) electronic conduc- tivity is less than that of graphite (anode active material) 53, cathode transport resistance is more than anode. The cathode cur- rent collector made of aluminum offer more resistance than the anode current collector made of copper. Therefore, to minimize the resistance, more reaction takes place near the top where the cathode end of the cell is located. As a result, the heat generation (Fig. 4c) and the temperature (Fig. 4d) is found to be greater near the top. The temperature variation in the axial direction is of the order of 0.1 K as the conduction element outside the cell helps in spreading the heat thereby alleviating a possible hotspot. 4.2.2. Series connection The fi rst row of series connected cells of the side marked 1 in Fig. 6, along with the fl ow channel is simulated using the same parameters mentioned in the previous subsection. The mesh for this model consists of about 570,000 cells and the computation time for complete discharge at 0.9 C rate takes about 18 h in 6 CPU parallel computation. The temperature contours of the cells and the TMS at the end of discharge is shown in Fig. 9. Temperature contour of the cross-section at the mid-height of the cell is also plotted in the same fi gure. The cells are fl ipped alternatively to connect in series. Thus the hot spots on the cells are found to be alternating. Temperature variation across a single cell is of the order of 0.2 K, which is the same as the cells in parallel confi gura- tion. The difference in average temperatures between the six cells is of the order of 0.1 K which is smaller than that for the parallel cells. The reason for that is that, each of this cell is connected directly to the coolant channel and therefore can get cooled more effi ciently. Due to the contact resistance a step change in temper- ature could be observed between cell-conduction element and conduction element fl ow channel. In the temperature contour of the cross section, the temperature rise in the cells and also the fl ow channel is observed. The increase in the temperature the coolant is less than 0.01 K and thus it could not be resolved in this contour Fig. 8. Current densities, volumetric heat generation and temperature of the jelly roll and the can of cell 5 in Fig. 7. S. Basu et al./Applied Energy 181 (2016) 1137 scale. From this result, it can be concluded that the fl ow rate is much greater compared to the thermal load. Effect of fl ow rate on the thermal performance has been discussed in subsequent chapters. Average temperatures of cells shown in Figs. 7 and 9 are plotted in Fig. 10a and b. The cells are marked in the same way as Fig. 7 in Fig. 10a. The temperature of cell 3, the middle cell, is the hottest while the cells 1 is coolest. Temperature of cell 5 is slightly greater than that of cell 1 for the complete discharge. The difference in average temperature between hottest and coldest cells is 0.5 K. Temperature rise of all the cells exhibit the same pattern. There- fore, it might be possible to predict the temperature of the other cells, given the temperature of one cell. As there is clearly a pattern to the temperature rise, a suitably defi ned temperature coeffi cient can be useful in predicting the temperature of other cells given the temperature of one cell. It would reduce the need for multiple sen- sors and simplify the temperature control system greatly. On extension of this idea, battery modules with single temperature sensor can effectively predict the temperature of all the individual cells and offer a more robust and safe TMS. The average temperature of the cells connected in series are plotted in Fig. 10b, where the cells are marked in the same way as Fig. 9. The temperatures of the cells increase from 1 to 6 as these are placed along the fl ow direction. As the fl ow is large enough in this case, the temperature of the coolant increases only slightly (Fig. 9). Therefore, the cells in the series behave almost identically. 4.2.3. Temperature coeffi cients Temperature coeffi cients are defi ned as the following for the ith series cells (Eq. (18) and the jth parallel cells (Eq. (19). CS i Ti? TC inlet T1? TC inlet 18 CP j Tj? TC inlet T1? TC inlet 19 The inlet temperature is denoted by TC inlet and the temperature of cell 1 (shown in Figs. 7 and 9) is denoted by T1. The parallel con- nected cells are also connected thermally through the conduction elements, while the series connected cells adj