Parametric Reduced-Order Modeling of Battery Thermal Management Systems for Varying Rates of Cooling Liquid Flow

The thermal management system in battery packs for electrical/hybrid electric vehicles plays an important role in maintaining good performance and health of battery cells. In order to optimize the thermal management system design, computational fluid dynamics (CFD) simulations are often used. The CFD is a powerful tool that can accurately simulate the thermal behavior of the system using numerical computation techniques such as finite volume method. However, the days-long computational expense means that the CFD-based simulations are still unsuitable for situations when rapid results are required, for example for online predictive control or fast-pace optimization design. A new method of reduced-order modeling of battery thermal management systems (BTMS) was presented in [1]. Given a CFD model, the algorithm based on projection on Krylov-subspace yields a reduced-order model (ROM). The ROM accurately predicts the system’s transient response to arbitrary internal heating of individual batteries and temperature of cooling liquid at inlet. Unlike conventional Krylov-subspace approaches, the algorithm does not require the system matrix of the CFD model. Therefore, the method is more suitable for use with commercial CFD software which does not allow access to such internal information. The ROM uses a drastically reduced number of degrees of freedom requiring drastically reduced simulation time. This paper extends our ROM by including the mass flow rate of cooling liquid as a model parameter. The task is accomplished by interpolating the system matrices after several local reduced-order models are constructed at discrete mass flow rates (MFR). In order to interpolate the local ROMs, we first need to transform the local ROMs onto a common subspace. The transformation matrix is obtained by applying the singular value decomposition (SVD) to the local projection matrices. In this paper, three local ROMs are built at 3 different MFRs. After these local ROMs are transformed according to the above procedure, a parametric reduced-order model (pROM) is constructed via quadratic interpolation. The constructed pROM is tested against the new MFRs different from those used for building the local ROMs. For each new MFR, the pROM produced a transient response that is almost indistinguishable from that of the CFD model (e.g., see Figure 1). The several thousand core-hour computational time needed for CFD simulations is replaced by a few tens of seconds using the pROM on a personal computer. The low computing load of the pROM is deemed adequate for on-board applications. Reference [1] Xiang L, Lee CW, Zikanov O, Hsu C-C. Efficient reduced order model for heat transfer in a battery pack of an electric vehicle. Applied Thermal Engineering. 2022; 201:117641. Figure 1 Figure 1