Polygonal cell structures in particle-laden turbulent Rayleigh–Bénard convection

We report our finding from direct numerical simulations that polygonal cell structures are formed by inertial particles in turbulent Rayleigh–Bénard convection in a large aspect ratio channel at Rayleigh numbers of $10^6, 10^7$ and $10^8$ , and Prandtl number of 0.7. The settling of small particles modified the flow structures only through momentum interactions. From the simulations performed for various sizes and mass loadings of particles, we discovered that for small- and intermediate-sized particles, cell structures such as square, pentagonal or hexagonal cells were observed, whereas a roll structure was formed by large particles. As the mass loading increased, the sizes of the cells or rolls decreased for all particle sizes. The Nusselt number increased with the mass loading of intermediate and large particles, whereas it decreased with the mass loading of small particles compared with the value for particle-free convection. A detailed investigation of the effective feedback forces of the settling particles inside the hot and cold plumes near the walls revealed that the feedback forces break the up–down symmetry between the hot and cold plumes near the surfaces. This enhances the hot plume ascent while not affecting the cold plume, which leads to the preferred formation of cellular structures. The energy budget analysis provides a detailed interaction between particles and fluid, revealing that the net energy is transferred from the fluid to particles when the particles are small, while settling intermediate and large particles drag the fluid so strongly that energy is transferred from particles to fluid.