Effects of the computational domain size on direct numerical simulations of Taylor-Couette turbulence with stationary outer cylinder

Abstract

In search for the cheapest but still reliable numerical simulation, a systematic study on the effect of the computational domain (“box”) size on direct numerical simulations of Taylor-Couette flow was performed. Four boxes with varying azimuthal and axial extents were used. The radius ratio between the inner cylinder and the outer cylinder was fixed to η = ri/ro = 0.909. The outer cylinder was kept stationary, while the inner rotated at a Reynolds number Rei = 105. Profiles of mean and fluctuation velocities are compared, as well as autocorrelations and velocity spectra. The smallest box is found to accurately reproduce the torque and mean azimuthal velocity profiles of larger boxes, while having smaller values of the fluctuations than the larger boxes. The axial extent of the box directly reflects on the Taylor-rolls and plays a crucial role on the correlations and spectra. The azimuthal extent is found to play a minor role in the simulations, as the boxes are large enough. For all boxes studied, the spectra do not reach a box independent maximum.