Direct numerical simulation of turbulent Taylor–Couette flow

Abstract

Direct numerical simulation (DNS) is used to investigate turbulent Taylor–Couette (TC) flow. A simulation was run for a Reynolds number of 3200 in an apparatus with a radius ratio of η = 0.617 and an aspect ratio of 4.58, which assumed a vortex pair wavelength of 2.29. Results reported include the mean velocity, velocity fluctuation intensities, Reynolds stress budgets, and visualizations of the instantaneous velocity fluctuation field. Secondary near-wall vortex pairs are observed near to the cylinder in addition to the Taylor vortex (TV) motion. Weaker evidence of secondary vortices is found at the outer cylinder where a banded structure has been identified. The azimuthal wall shear stress component shows large peaks and valleys at stagnation points on the surface of both cylinders where flow from neighbouring vortices impacts on the respective wall. These stagnation points correspond to locations where the secondary vortices have been identified. The effect of the mean TV motion is reflected in the Reynolds stress budgets which are similar to but more complex than those of two-dimensional boundary layers. Visualization of the turbulent velocity fluctuations reveals near-wall streaks at the inner cylinder.

Influence of global rotation and Reynolds number on the large-scale features of a turbulent Taylor–Couette flow

“…17 It is known that for the first transition the observed flow state can depend on the initial conditions. 8 When starting the inner cylinder from rest and accelerating it to 2 Hz in 20 s, the vortices grow very fast, reach a value with a velocity amplitude of 0.08 ms −1 , and then decay to become stabilized at a 16 In a subsequent measurement we start from Ro= Ro i and vary the rotation number in small increments, while maintaining a constant shear rate. We allow the system to spend 20 min in each state before acquiring PIV data.…”

“…15 and other torque scaling studies only deal with the case where only the inner cylinder rotates. 12,13 In that precise case, recent direct numerical simulations suggest that vortexlike structures still exist at high Reynolds number ͑Reտ 10 4 ͒, 16,17 whereas for counter-rotating cylinders, the flows at Reynolds numbers around 5000 are identified as "featureless states." 9 The structure of the flow is exemplified with a flow visualization in Fig.…”

Direct numerical simulations of local and global torque in Taylor–Couette flow up to Re = 30 000

“…These high Reynolds number experiments were complemented in narrow Reynolds number regimes with direct numerical simulations (DNS) of turbulent Taylor-Couette: Flow characteristics were analysed for the outer cylinder at rest (Bilson & Bremhorst 2007;Dong 2007;Pirrò & Quadrio 2008), for counter-rotating cylinders (Dong 2008b) and in the case of spiral turbulence (Meseguer et al 2009;Dong 2009;Dong & Zheng 2011). The highest Reynolds number (∼ 10 4 ) was achieved by Pirrò & Quadrio (2008), and it touches the Reynolds number range studied experimentally, but they do not analyse the turbulent transport and its contributions to the torque.…”

Experimental investigation of torque hysteresis behaviour of Taylor–Couette Flow

“…However, recent experimental and numerical studies (e.g. Bilson & Bremhorst 2007;Dong 2008;Ravelet, Delfos & Westerweel 2010;Tokgoz, Elsinga & Westerweel 2011;Huisman et al 2014;Ostilla-Mónico et al 2014a) showed the persistence of large-scale structures even at much higher Reynolds numbers.…”