Context
Circulating fluidized beds have exceptional characteristics in terms of transport and mixing, contact between the dispersed phase and the gaseous medium, thermal inertia and wall heat transfer. These characteristics make them very present in the field of energy, particularly for the development of innovative processes that meet the challenges of energy transition. Gas-solid circulating fluidized beds are studied by PROMES as an alternative to heat transfer fluids which are used to transport the heat obtained from solar radiation in concentrated solar power plants, in particular within the framework of the European projects CSP2 and Next-CSP [1 - 4]. In this process, solar radiation is concentrated on vertical tubes within which a gas-particle mixture circulates. Understanding and mastering the flow regimes and the associated heat transfers, currently remain scientific obstacles for the development of this technology. The couplings between the dynamics, the thermal, the two-phase nature of the flow, the wall effects and the radiative transfers make the physics particularly complex. To better understand these couplings, the PROMES laboratory is developing fine numerical methods where fluid-particle interactions are explicitly simulated. The high-performance computing (HPC) code TrioCFD based on a Front-Tracking method has been modified to allow the simulation of solid particles [5]. It has been successfully used to simulate fluidized bed flows with several thousand particles (see Figure 1). However, the current method does not take radiative transfers into account.
The analysis of the technological locks related to the solar application identifies as a priority the development of the coupled simulation of the transport and the transfers of heat by conduction and by radiation in the gas-solid fluidized beds at high temperature. The major scientific challenge concerns the identification of the role of particle-particle and particle-wall radiative transfers through the study of its coupling with hydrodynamics. This development, essential for the application to concentrated solar power plants, has never before been carried out in the context of fine simulations of fluid-particle flow and constitutes a major opening towards multi-physics coupling.

Work to be done
Three stages of work to be carried out have been identified.
The first step consists in implementing the radiative transfers between the walls and the particles or between the particles within TrioCFD using the Front-Tracking method. This method has the advantage of using a mobile surface mesh to follow the fluid/solid interface. This mobile grid will be used for the calculation of the radiative transfers (see figure 2). The gaseous medium being considered as transparent, the particles as weakly reflective and the diffraction being able to be neglected, the radiosity method and the Monte-Carlo method will be evaluated to calculate the net radiative fluxes exchanged by each elementary surface of a particle and at each time step by following their displacement [6]. Two possibilities are considered: implementing a method for solving radiative transfers (radiosities or Monte-Carlo) within TrioCFD (online coupling) or coupling TrioCFD with another existing software for radiative transfer calculations (offline coupling). For this second possibility, the surface mesh of the particles and the temperature at the interfaces must be communicated to the external software. On this part of the work, the supervision will be reinforced by Cyril Caliot (CNRS, LMAP, UPPA) who has expertise in models and methods for solving radiative transfers.
The second step of the project will consist in validating the developments carried out on simple configurations. For example, by considering only the radiative transfers in geometries where the form factors are known.
The third step of the project consists in the implementation of fine simulation tools on simplified but representative configurations of the application to concentrated solar power plants to analyze and quantify the physical phenomena involved. The planned anisothermal flow configurations are: (i) The flow of a gas through a fixed network of particles; (ii) A small-scale gas-solid fluidized-bed type flow. Fine simulations will be carried out taking into account the coupling between transport and heat transfer by conduction and radiation between the particles and the walls.