Data-based model reduction for phase change problems with convective heat transfer. (5th February 2021)

• Record Type: Journal Article
• Authors: Pernsteiner, Dominik; Schirrer, Alexander; Kasper, Lukas; Hofmann, René; Jakubek, Stefan
• Is Part Of: Applied thermal engineering. Volume 184(2021)
• Publication Date: 2021-02-05
• Subjects: Phase change material -- Model reduction -- Convective and conductive heat transfer -- Singular value decomposition -- Stream function; Heat engineering -- Periodicals; Heating -- Equipment and supplies -- Periodicals; Periodicals; 621.40205
• DOI: 10.1016/j.applthermaleng.2020.116228
• Languages: English
• ISSNs: 1359-4311

Abstract

Highlights: Model reduction for convective heat transfer problems in varying domains is proposed. The method greatly reduces computational effort while maintaining accuracy. The novel data-based method uses a stream function and singular value decomposition. Significant reduction of model complexity enables simulation in real time. The reduced model is robust with respect to mesh and time step enlargement. Abstract: 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.