Direct numerical simulations of Taylor–Couette turbulence: the effects of sand grain roughness

Abstract

Progress in roughness research, mapping any given roughness geometry to its fluid dynamic behaviour, has been hampered by the lack of accurate and direct measurements of skin-friction drag, especially in open systems. The Taylor-Couette (TC) system has the benefit of being a closed system, but its potential for characterizing irregular, realistic, 3-D roughness has not been previously considered in depth.Here, we present direct numerical simulations (DNSs) of TC turbulence with sand grain roughness mounted on the inner cylinder. The model proposed by Scotti (Phys. Fluids, vol. 18, 031701, 2006) has been improved to simulate a random rough surface of monodisperse sand grains, which is characterized by the equivalent sand grain height k s . Taylor numbers range from T a = 1.0 × 10 7 (corresponding to Re τ = 82) to T a = 1.0 × 10 9 (Re τ = 635). We focus on the influence of the roughness height k + s in the transitionally rough regime, through simulations of TC with rough surfaces, ranging from k + s = 5 up to k + s = 92, where the superscript '+' indicates non-dimensionalization in viscous units.We analyse the global response of the system, expressed both by the dimensionless angular velocity transport N u ω and by the friction factor C f . An increase in friction with increasing roughness height is accompanied with enhanced plume ejection from the inner cylinder. Subsequently, we investigate the local response of the fluid flow over the rough surface. The equivalent sand grain roughness k + s is calculated to be 1.33k, where k is the size of the sand grains. We find that the downwards shift of the logarithmic layer, due to transitionally rough sand grains exhibits remarkably similar behavior to that of the Nikuradse (VDI-Forschungsheft 361, 1933) data of sand grain roughness in pipe flow, regardless of the Taylor number dependent constants of the logarithmic layer.

Controlling secondary flow in Taylor–Couette turbulence through spanwise-varying roughness

“…The findings presented in figure 3 show that the presence of the roughness affects the relative turbulence statistics in the bulk of the flow, far away from the roughness sublayer region (in contrast to homogeneous roughness in TC flow (Berghout et al 2018)), reminiscent to what is found in studies of pipe and channel flow (Koeltzsch et al 2002;Chung et al 2018). Figure 3(b) shows the axial variations of the friction factor c f (z) (see section 1) on both the inner cylinder and the outer cylinder.…”

Towards boiling Taylor-Couette turbulence

“…The results from Fig. 3.3 hints that the presence of the roughness might have an effect on the morphology of the flow, far away from the roughness sublayer region [133], on the order of the gap width d, and reminiscent to what is found in studies of pipe and channel flow [115,117]. To gain more insight into how the roughness alters the flow, we set out to measure the velocity field in the meridional plane using PIV at multiple heights.…”

“…They attribute this to a dominance of the pressure drag over the viscous drag on the cylinders. Structure in the form of grooves in the streamwise direction were studied by Very recently, [133] studied the influence of sandgrain roughness in TC flow, and found similarity of the roughness function with the same type of roughness in pipe flow [134]. We highlight that none of the works described above, reported an influence of the roughness over the axial wavelength of the rolls.…”

“…Having discussed the dynamics of the TTVs and the corresponding global response, in terms of the dimensionless torque, we now set out to study the streamwise, angular, velocity profiles (rather than the azimuthal profiles, as discussed in [140] and [133]). To allow for straightforward comparison between the respective velocity profiles, we run the DNS at constant friction Reynolds number Re τ = 690 ± 10.…”

Multi-phase wall-bounded turbulence

“…They attribute this to a dominance of the pressure drag over the viscous drag on the cylinders. Structure in the form of grooves in the streamwise direction were studied by Very recently, [203] studied the influence of sandgrain roughness in TC flow, and found similarity of the roughness function with the same type of roughness in pipe flow [204]. We highlight that none of the works described above, reported an influence of the roughness over the axial wavelength of the rolls.…”