Numerical Simulation of Turbulent Flow in Concentric Annuli

In this paper we consider a fully developed turbulent flow in a round pipe with a small inner annulus. The diameter of the inner annulus is less than 10% of the diameter of the outer pipe. As a consequence, the surface area of the inner pipe compared to the outer pipe is small. The friction exerted by the wall on the flow is proportional to the surface area and the wall shear stress. Due to the small surface area of the inner annulus the additional stress on the flow due to the presence of the annulus may expected to be negligible. However, it will be shown that the inner annulus drastically changes the flow patterns and gives rise to unexpected scaling properties. In previous studies (Chung et al., Int J Heat Fluid Flow 23:426–440, 2002; Churchill and Chan, AIChE J 41:2513–2521, 1995) it was argued that radial position of the point of zero shear stress does not coincide with the radial location of the point of maximum axial velocity. In our direct numerical simulations we observe a coincidence of these points within the numerical accuracy of our model. It is shown that the velocity profile close to the inner annulus is logarithmic.