# Induction Heating of a Fluidized Pebble Bed: Numerical and Experimental Analysis
###### Abstract  
The development of energy-efficient Power-to-Heat (PtH) technologies with high power density on a utility scale is a key element in the future of flexible energy systems. Although existing solutions for electric flow heaters (EFH) based on resistance heating have a high efficiency, the process outlet temperature and power output are limited by the lifetime of the contact heating elements. Inductively heated packed bed heaters can achieve higher gas outlet temperatures with a higher power density, which is essential for an efficient process. This paper focuses on the modeling, experimental validation and numerical analysis of inductively heated pebble bed gas heater. Foremost, a model that is based on a 3D finite volume method approach is introduced. After that, an experimental setup for different sphere arrangements is used to obtain results for concept verification and model validation. With the model validated, the design space for the PH concept is investigated by varying the heat transfer area and material properties of the pebble bed. Design solutions with high energy efficiency above 90% and power density over 5.5 MW/m3 are presented for magnetic as well as non-magnetic materials at laboratory and utility scale.  
power-to-heat; electric flow heater; induction gas heater; packed bed; numerical analysis +
Footnote †: journal: Applied  
EFH based on induction heating has the potential to achieve process temperatures above 700 \({}^{\circ}\)C for industrial scale applications due to the typically high induced power rating of more than 1 MW\({}_{\text{el}}\) per m\({}^{2}\)[8]. However, its equipment costs cannot compete with the costs of fossil gas fired heater systems. Therefore, for high process temperatures above 700 \({}^{\circ}\)C, natural gas heaters are preferred.  
Additionally, the induction fluid heater can be used for power plant applications in so called Carnot batteries (CB). In these batteries, electric power is converted to high-temperature (HT) heat that is first stored in a thermal energy storage (TES) system and then converted back to electricity in a thermal power cycle as needed. The EFH is mostly integrated into the charging cycle of the CB to raise the maximum temperature and hence the energy density of the system [9]. As a result, component size and thus the equipment cost are reduced [10].  
A promising application of EFHs is the Brayton battery [10; 11; 12], which is a subcategory of CBs. In a Brayton battery, the HT heat from the EFH is stored in a sensible TES while charging and converted back to electricity using the Brayton gas turbine cycle while discharging. The EFH is integrated into the charging heat pump cycle downstream of the air compressor to increase the inlet temperature of the sensible TES up to 1050 \({}^{\circ}\)C [10] and beyond [12]. [PERSON] [10] first showed that additional HT heat from EFHs increases the energy density of the system by 105% and reduces its costs by 35%. However, the author omitted details of PtH technology and of the EFH concept that enables such high process temperatures to be achieved. In addition to [PERSON]'s work, [PERSON] [12] presented an increase in energy density of 70% accompanied by a cost reduction of 23% applying a 17 MW EFH component. To fill the research gap of the missing EFH solution, the author proposed an induction air heater comprising an inductively heated pebble bed (PB) to generate HT process heat with a conversion efficiency of 85% and at temperatures above 1000 \({}^{\circ}\)C. The purpose of this work is to verify this PtH concept for the application in a Brayton battery and to provide a validated design tool along with suitable materials for energy-efficient HT operation.