Direct numerical simulations (DNS) are performed to analyse the global transport properties of turbulent Taylor-Couette flow with inner rough wall up to Taylor number Ta = 1010. The dimensionless torque Nuω shows an effective scaling of Nuω ∝ Ta0.42±0.01, which is steeper than the ultimate regime effective scaling Nuω ∝ Ta0.38 seen for smooth inner and outer walls. It is found that at the inner rough wall, the dominant contribution to the torque comes from the pressure forces on the radial faces of the rough elements; while viscous shear stresses on the rough surfaces contribute little to Nuω. Thus, the log layer close to the rough wall depends on the roughness length scale, rather than on the viscous length scale. We then separate the torque contributed from the smooth inner wall and the rough outer wall. It is found that the smooth wall torque scaling follows Nus ∝ Ta0.38±0.01 s, in excellent agreement with the case where both walls are smooth. In contrast, the rough wall torque scaling follows Nur ∝ Ta0.47±0.03 r, very close to the pure ultimate regime scaling Nuω ∝ Ta1/2. The energy dissipation rate at the wall of an inner rough cylinder decreases significantly as a consequence of the wall shear stress reduction caused by the flow separation at the rough elements. On the other hand, the latter shed vortices in the bulk that are transported towards the outer cylinder and dissipated. Compared to the purely smooth case, the inner wall roughness renders the system more bulk dominated and thus increases the effective scaling exponent.
- Taylor-Couette flow
- Turbulent flows