DNS of rotating buoyancy– and surface tension–driven flow

The combination of turbulent buoyant flow with a free surface (Rayleigh–Bénard–Marangoni convection) and rotation is hardly investigated in detail, especially for low Prandtl number fluids, although it can be found in several applications such as Czochralski (Cz) crystal growth. Therefore, a Direct Numerical Simulation (DNS) of such a Cz case with an idealized cylindrical crucible geometry of 170 mm radius and a rotating crystal of 50 mm radius was conducted applying realistic boundary conditions, which lead to the dimensionless numbers of Re=4.7×104,Gr=2.2×109,Ma=2.8×104Re=4.7×104,Gr=2.2×109,Ma=2.8×104, and Ra=2.8×107Ra=2.8×107. The computational grid contained ca. 8.4 million control volumes to resolve all turbulent scales based on a finite-volume scheme for curvilinear block-structured grids and an explicit time discretization. The resulting velocity and temperature fields show fully developed three-dimensional turbulence and are characterized by thermal buoyant plumes rising from the bottom of the crucible to the free surface, surface tension effects, and the strong impact of the counterrotating crystal. The analysis of the instantaneous flow revealed that in the rotating melt a large, slowly moving spiral vortex evolves. The averaged data show the formation of Bénard cell-like structures. Below the crystal, along the free surface, and especially at the corner of the crystal, the turbulence intensity is strongest. The DNS results were generated and analyzed in detail in order to serve as a reference and will also be made available to the public for further investigations. Within an ongoing study these data will be used to validate computations for practical applications employing the Large-Eddy Simulation (LES) technique, which is used to model the turbulent flow and temperature field in order to save computational time compared to DNS.