# Induction Heating of a Fluidized Pebble Bed: Numerical and Experimental Analysis
### Conceptual Arrangement of the Induction Gas Hater  
The concept of such an inductively heated pebble bed (PB) gas heater is illustrated in Figure 1. It comprises a PB located inside of an insulated induction heating coil. On the one hand, the insulation and the ceramic tube prevent a direct short circuit between the induction coil and the PB. On the other hand, they minimize the heat loss from the hot packed bed to the ambient. In addition to this loss, Figure 1 shows ohmic losses of the induction coil, which are removed as waste heat by the water-cooling system. Furthermore, the illustrated heat balance indicates the volumetric heat \(\dot{q}_{ind}\) induced inside the PB which is further transferred as HT heat \(\dot{Q}_{th}\) to the upflowing air stream. This PtH concept enables a high and uniformly distributed power density within the granular bed, as eddy currents are induced in each sphere and heat them up according to the Joule effect. In addition, the packed bed provides a high specific heat transfer area that is often accompanied with a turbulent fluid flow which leads to an efficient heat transfer to the air flow. Both these conceptual advantages allow the efficient generation and transport of HT heat to achieve gas outlet temperatures up to 1050 \({}^{\circ}\)C [10] required for an application of the induction gas heater concept in a Brayton battery. Few authors have studied induction heating concepts for heating applications with different HTFs. [PERSON] et al. [8] were the first to present a tubular PtH concept of an induction heater to heat an oil flow. The laboratory setup uses a mild steel tube that is shrunk on to a stainless liner to heat the oil stream by 30 \({}^{\circ}\)C to temperatures far below 70 \({}^{\circ}\)C. The tubular concept achieves a process efficiency above 80% with an input power of 888 W. Another tubular concept in a similar power range was proposed by [PERSON] et al. [13] to heat up an air flow to 50-60 \({}^{\circ}\)C for the purpose of drying fruits and vegetables. The authors studied two induction air heater prototypes These prototypes respectively achieved efficiencies of 77% and 87%, using insulataddition, the authors observed the significant influence of the flow rate on efficiency, which increases by approximately 17% for a doubling in the flow rate. In another work, [PERSON] [14] modified the tubular concept using five additional carbon steel disks, which are arranged perpendicular to the air flow. This measure resulted in a decline in efficiency from 29% to 16% due to the presence of the disks. [PERSON]'s tubular heater concepts aim to generate heat far below the Curie point of steel (768 \({}^{\circ}\)C) where carbon steel tubes with a small specific heat transfer area are sufficient to ensure high efficiency. The application in a Brayton battery, however, requires outlet temperatures far above the Curie point of steel, where a large specific heat transfer area is required to ensure a small temperature difference between solid and fluid. In contrast to the tubular concepts, the inductively heated PB concept from Figure 1 offers a significantly higher specific heat transfer area. Therefore, various scientific studies used the inductively heated PB as a volumetric heat source to predict heat transfer rates for various HTFs [15; 16; 17; 18]. [PERSON] et al. [15] and [PERSON] et al. [16] reported linear temperature distribution for packed beds with induction heating. [PERSON] et al. [17] used induction heating to study flow boiling heat transfer effects of inductively heated packed bed. [PERSON] et al. [18] used an induction heating coil to generate heat inside the spheres in an effort to simulate conditions which are present in a fluidized nuclear reactor. However, these studies determined the electrically generated heat inside the randomly-packed bed exclusively through experiments either by means of an oscilloscope measurement at coil terminals or by the measurement from the power converter. In contrast, [PERSON] et al.