Disentangling the origins of torque enhancement through wall roughness in Taylor-Couette turbulence

Abstract

Direct numerical simulations (DNSs) are performed to analyze the global transport properties of turbulent Taylor-Couette flow with inner rough wall up to Taylor number $Ta=10^{10}$. The dimensionless torque $N{u}_{\omega }$ shows an effective scaling of $N{u}_{\omega }\propto T{a}^{0.42\pm 0.01}$, which is steeper than the ultimate regime effective scaling $N{u}_{\omega }\propto T{a}^{0.38}$ 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 $N{u}_{\omega }$. 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 $N{u}_s\propto T{a}_s^{0.38\pm 0.01}$, in excellent agreement with the case where both walls are smooth. In contrast, the rough wall torque scaling follows $N{u}_r\propto T{a}_r^{0.47\pm 0.03}$, very close to the pure ultimate regime scaling $N{u}_{\omega }\propto T{a}^{1/2}$. The energy dissipation rate at the wall of 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.

To be published on JFM

References in corpus (3)

• High Reynolds number Taylor-Couette turbulence
• Exploring the phase diagram of fully turbulent Taylor-Couette flow
• The near-wall region of highly turbulent Taylor-Couette flow

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