Numerical Simulation of Turbulent Flow in Concentric Annuli

Abstract

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.

Predicting turbulence-induced vibration in axial annular flow by means of large-eddy simulations

“…There is also reasonable agreement with experimental values of Nouri et al (1993), who located the maximal velocity of 1.22 times the bulk velocity at 0.43 times the channel width. The exact location of the maximum velocity in comparison to the point of zero Reynolds shear stresses has been a point of debate in the literature, with some authors stating that they coincide (Boersma and Breugem (2011)), while others state they do not (Chung et al (2002)). As the current simulations model a (very small) fraction of these shear stresses, this is not analyzed in the present simulations.…”

“…In the viscous sublayer, the mean axial velocity profile can be approximated by the following expression (Boersma and Breugem (2011))…”

“…), while Boersma and Breugem (2011) use f = y + r + i +y + . The former expression has the advantage that it reduces to the well-known logarithmic expression for flow over a flat plate if r i is sufficiently large.…”

“…The former expression has the advantage that it reduces to the well-known logarithmic expression for flow over a flat plate if r i is sufficiently large. Note that in the expression of Boersma and Breugem (2011), the numbers C 1 , C 2 are not constants. Instead, they depend on the ratio of the inner wall over external wall radius.…”

“…In this annular configuration most numerical research is limited to the computation and analysis of the velocity field (Boersma and Breugem, 2011;Chung et al, 2002). However, Moreno (2000) computed the wall pressure spectrum in an annular flow domain using LES, but the results still suffered from a limited spatial resolution.…”