Direct numerical simulation of the turbulent flow in a pipe with annular cross section

Abstract

The turbulent flow in a pipe of annular cross section is studied for the first time through a direct numerical simulation (DNS) using the Navier–Stokes equations written in cylindrical coordinates. To this aim a novel numerical method is developed, which extends to the cylindrical coordinate system an existing, efficient method designed for cartesian coordinates, and allows us to eliminate the pressure and formulate the problem in two scalar unknowns. The unnecessary increase of resolution at smaller radius typically brought about by polar coordinates, with its consequent stability limitations, is avoided by changing the number of azimuthal Fourier modes with the radial coordinate itself. In addition, the azimuthal extension of the computational domain is reduced, for the cases with lowest curvature, by considering only a part of the annulus, without loss of physical significance of the results. A computer code based on this method is run on a desktop PC for the simulation (with up to 16 million degrees of freedom) of the turbulent flow in a pipe with annular cross section, in a range of relatively low curvatures. This investigation highlights that curvature effects are already evident, even on first order turbulence statistics like the mean axial velocity distribution, in a low-curvature range where it is commonly believed that the flow should be hardly distinguishable from the flow over a plane surface.