Data-based model reduction for phase change problems with convective heat transfer

Latent heat thermal energy storages (LHTES) exploit the high energy density of phase change material (PCM). The typically low thermal conductivity of PCM limits the charging and discharging rates and poses considerable challenges for dynamic storage operation. To operate LHTES efficiently and to exploit their full potential, new methods are required to obtain accurate and fast models for state of charge estimation and control tasks. In LHTES the heat transfer in low viscosity PCM is driven by conduction and also significantly by convective transport. In previous works, various high-precision models have been developed which employ finite element, difference and volume methods to solve the coupled Navier–Stokes and energy equations, but they incur large computational effort. In the present work, a novel, high-fidelity model reduction technique is proposed to achieve real-time capability while preserving high model accuracy. The idea is to short-cut the laborious solution of the Navier–Stokes equations by an efficiently parametrized, data-based model which approximates the stream function of the typical convection flow pattern by singular value decomposition. To account for the complexity of the solution-dependent flow domain, a suitable transformation method is proposed. The efficiency and accuracy of the proposed reduction method is demonstrated in typical operating modes.