Turbulent flow in smooth concentric annuli with small radius ratios

Abstract

Fully developed turbulent flow through three concentric annuli was investigated experimentally for a Reynolds-number rangeRe= 2 × 104−2 × 105. Measurements were made of the pressure drop, the positions of zero shear stress and maximum velocity, and the velocity distribution in annuli of radius ratios α = 0.02, 0.04 and 0.1, respectively. The results for the key problem in the flow through annuli, the position of zero shear stress, showed that this position is not coincident with the position of maximum velocity. Furthermore, the investigation showed the strong influence of spacers on the velocity and shear-stress distributions. The numerous theoretical and experimental results in the literature which are based on the coincidence of the positions of zero shear stress and maximum velocity are not in agreement with reality.

Numerical Simulation of Turbulent Flow in Concentric Annuli

“…Very close to the annulus, in the first 10-25 viscous units (r + = (r − r a ) √ τ a /ρ/ν) the profile is logarithmic, which agrees with the result given by equation (9). For comparison we have also included some of the experimental data reported by [3]. The agreement between the experimental data and simulation is reasonably good.…”

“…6, equation (9) agrees nicely with the result of the DNS in the region r ≈ r a . From the literature, see for instance [3], it is known that the r value (r m ) for which the mean velocity reaches a maximum, is given by the following empirical relation…”

“…Most of this work focuses on the determination of the friction factor and on the radial location of the maximum streamwize velocity. In the paper of Rehme [3] it is argued that the radial position for which the maximum axial velocity is obtained does not coincide with the position for which the Reynolds shear stress becomes zero. Churchill and co-workers [4,7] use this observation to argue that eddy viscosity models can not be used to predict this flow and that this observation has implications for other turbulent flows.…”

“…In the past annular turbulent pipe flow with an inner annulus has been studied quite extensively by Brighton and Jones [5], Quarmby [6] and Rehme [3]. Most of this work focuses on the determination of the friction factor and on the radial location of the maximum streamwize velocity.…”

“…In our simulations we do not observe a non-coincidence between the point where the Reynolds shear stress is zero and the location of the maximum mean velocity. It is argued that the experimental observations of Rehme [3] are biased by measurement errors or end effects in the experimental setup. The work of Churchill and co-workers is based on these observations.…”