Extended proper orthogonal decomposition of non-homogeneous thermal fields in a turbulent pipe flow

This manuscript analyzes the role of coherent structures in turbulent thermal transport in pipe flows. A Proper Orthogonal Decomposition (POD) analysis is performed on a direct numerical simulation dataset with non-homogeneous boundary conditions, heated on the upper side, representative of solar receivers (Antoranz et al., 2015, Int. J. Heat Fluid Flow, 55). Three flow conditions are analyzed: with friction Reynolds number equal to 180 and Prandtl number equal to 0.7 and 4 and with friction Reynolds number equal to 360 and Prandtl number equal to 0.7. Both POD and extended POD modes are presented and compared. This allows to visualize the main flow modes in terms of both turbulent kinetic energy and temperature fluctuations, analyzing their contribution to the turbulent transport of heat. The POD analysis shows that the temperature fluctuations are described by a more compact modal subspace than the turbulent kinetic energy. The effect of increasing the Reynolds number is to produce a thinner boundary layer, with a slightly less compact representation of both kinetic energy and temperature fluctuations. The increase of the Prandtl number, instead, results in a thinner thermal boundary layer with a greater scale separation between thermal fluctuations and kinetic energy. Temperature POD modes together with velocity extended POD modes are used to analyze and quantify the mode contribution to turbulent thermal transport. Results show that the correlation between velocity and temperature is such that it is possible to describe roughly 100% of the turbulent heat transport and temperature fluctuations with only 40% of the kinetic energy. For the cases with Pr = 0.7, the first extended POD mode is a large vertical jet flanked by a pair of counter-rotating vortices near the heated part of the pipe. This single structure accounts for up to 10% of the turbulent heat transport. (C) 2017 Elsevier Ltd. All rights reserved.