Physics-based Thermal Model Research Articles

(Digital Presentation) Thermal Behaviour Prediction of Commercial Lithium-Ion Cells Under Different C-Rate and Ambient Conditions Using Surrogate Modelling

Lithium-ion batteries (LIBs) have found widespread application in energy storage due to their high energy density, low self-discharge and low maintenance characteristics. However, the stability and longevity of the batteries under extreme operating conditions is yet to be fully understood. Numerous experimental and simulation studies have been performed to elucidate the effect of temperature, current, depth of discharge, and the number of cycles [1,2,3] on the performance of LIBs. These studies show that the solid-electrolyte interface (SEI) layer and gas formation accelerate at high C-rates due to increased electrolyte decomposition [4,5]. Consequently, the cell's internal resistance increases, resulting in ever-increasing irreversible heat generation inside the cell [6]. This heat generation leads to high internal temperature and a corresponding reduction in cell capacity. The data of cell temperature for a wide range of ambient temperatures and cycling rates is limited because cell performance is typically reported at room temperature. The design of battery packs for electric vehicles(EVs) is also based on test data taken at room conditions. Given that the cell's capacity, specific energy, maximum power output is bound to depend on C-rate and ambient temperature, it is necessary to test and design battery packs based on these parameters.The thermal characteristics of a lithium-ion cell can be predicted using a physics-based thermal model or data-driven methods (DDM) relying on empirical data. Experimental determination of internal cell parameters required in physics-based thermal models is challenging and time-consuming for commercial cells. On the other hand, DDM requires only cell cycling data at specific operating conditions, thereby eliminating the need for internal parameter estimation. This model predicts the experimental input and output data pattern and fits the response surface to estimate the unknown output. In this study, surrogate modelling has been employed to estimate the surface temperature, capacity, energy, and average power of commercial lithium-ion cells for different discharge currents and ambient temperatures. Surrogate modelling, a popular data analysis and reduced-order modelling technique, aims to find a global minimum of a particular objective function using a few objective function evaluations [7]. The surrogate-based model divides experimental data into training and test data sets. The training data set is employed to train the algorithm. After that, the testing data set is used to validate the model's accuracy. Experiments were performed to develop a surrogate model, with the number of experiments decided using the design of experiments[8] for a current range of 0.5C to 3C-rate and ambient temperature range of 0°C to 45°C . The cycling of cells was performed using a high current battery cycler (Arbin), and the ambient temperature was maintained using a thermal chamber (Cincinnati). The surface temperature of commercial 18650 (NMC811) lithium-ion cells was recorded using T-type thermocouples and a National Instruments DAQ module. A polynomial response surface was fitted using surrogate modelling on experimentally obtained data. The response surface shown in figure 1. contains nine data points for the preliminary study, sub-divided into a set of seven training and two testing data. The prediction error sum of squares (PRESS) is currently bounded within 10% due to the limited training data set availability and is expected to be within a band of 1% after adding data from ongoing experiments. The estimation of temperature, capacity, and specific energy can be used to optimize and develop an improved thermal management system for electric vehicles that works under various operating conditions. References Waldmann, T., Wilka, M., Kasper, M., Fleischhammer, M., & Wohlfahrt-Mehrens, M. (2014). Journal of Power Sources, 262, 129-135.Guan, T., Sun, S., Yu, F., Gao, Y., Fan, P., Zuo, P., Du,C., & Yin, G. (2018). Electrochimica Acta, 279, 204-212.Simolka, M., Heger, J. F., Traub, N., Kaess, H., & Friedrich, K. A. (2020). Journal of The Electrochemical Society, 167(11), 110502.Xu, B., Diao, W., Wen, G., Choe, S. Y., Kim, J., & Pecht, M. (2021). Journal of Power Sources, 510, 230390.Rashid, M., & Gupta, A. (2017). Electrochimica Acta, 231, 171-184.Leng, F., Tan, C. M., & Pecht, M. (2015). Scientific reports, 5(1), 1-12.Queipo, N. V., Haftka, R. T., Shyy, W., Goel, T., Vaidyanathan, R., & Tucker, P. K. (2005). Progress in aerospace sciences, 41(1), 1-28.Li, W., Xiao, M., Peng, X., Garg, A., & Gao, L. (2019). Applied Thermal Engineering, 147, 90-100. Figure 1

Physics-Based Predictive Model of Lack-of-Fusion Porosity in Laser Powder Bed Fusion Considering Cap Area

This work proposed a computationally efficient analytical modeling strategy to calculate the product porosity in laser powder bed fusion (LPBF) induced by a lack-of-fusion defect, with the consideration of cap area in solidified molten pools, influence of powder bed characteristics on material properties, and un-melted powders in the lack-of-fusion portion. The powder packing pattern and powder bed void fraction were estimated by an advancing front method and the technique of image analysis. The effects of powder bed characteristics on the material properties were considered by analytical models with solid properties and powder bed void fraction as inputs. A physics-based thermal model was utilized to calculate the temperature distribution and molten pool size. The molten pool cross section in transvers direction was assumed to be dual half-elliptical. Based on this assumption and molten pool size, the geometry of the molten pool cross section with cap area was determined. The overlapping pattern of molten pools in adjacent scan tracks and layers was then obtained with given hatch space and layer thickness. The lack-of-fusion area fraction was obtained through image analysis of the overlapping pattern. The lack-of-fusion porosity was the multiplication of the lack-of-fusion area fraction and powder bed void fraction. The predictions of porosity under different process conditions were compared with experimental results of 316L stainless steel and showed a better predictive accuracy than the predictions that did not consider cap area. The proposed analytical modeling method has no numerical calculations, which ensures its low computational cost. Thus, the proposed model can be a convenient tool for the fast computation of lack-of-fusion-induced porosity and can help the quality control in LPBF.

ShelTherm: An aid-centric thermal model for shelter design

The growing displacement crisis leaves many housed in simple shelters, which are bespoke to each setting, often sited in harsh climates and normally unconditioned. Measurements have shown that the thermal environment within the shelters can be life-threatening. Hence aid agencies are interested in improving these conditions. Unfortunately, given the skill set within agencies, there is little possibility to use complex thermal modelling to predict the impact of different materials or constructions. Hence the need to provide simple methods. In this work, we introduce a new physics-based thermal model (ShelTherm) for simple structures and encapsulate it within a tool designed to be used by humanitarian staff. Unlike other reduced models, the method is capable of dealing with high ventilation/infiltration rates, thin materials (such as tarpaulin) and high U-values. The model was validated over a wide variety of architectures, materials and climates. Mean error against observed data from a variety of real shelters was +0.94 °C (s.d. 0.79 °C), comparing favourably against the well-known reduced model CIBSE Admittance method (+4.95 °C, s.d. 0.89 °C) and the industry standard Energy+ (+0.60 °C, s.d. 0.32 °C). ISO 13792:2012(E) classified it as a Class 1 model, the highest possible. The differences between the new method and Energy+ across block, tarpaulin and stone shelters in Ethiopia, Bangladesh and Nepal were always less than 1.3 °C, and +0.24 °C for shelters in a mild climate. Humanitarian workers classed the tool as “easy” or “very easy” to use. The typical time to model a shelter by a first-time user was 34 minutes. ShelTherm can hence be seen as highly fit-for-purpose due to its overall accuracy and ease of use.