Analysis of wall mass transfer in turbulent pipe flow combining extended proper orthogonal decomposition and Fukugata-Iwamoto-Kasagi identity

We combine extended proper orthogonal decomposition (EPOD) together with the Fukagata-Iwamoto-Kasagi (FIK) identity to quantify the role of individual coherent structures on the wall mass transfer in a turbulent pipe flow. Direct numerical simulation at a Reynolds number of 5300 (based on bulk velocity) is performed with the passive scalar released at the pipe inlet. The proper orthogonal decomposition (POD) eigenvalues show that the scalar field can be described by a more compact set of modes compared to the velocity field, and that these modes are skewed towards higher azimuthal wave numbers. POD modes for the scalar and EPOD modes for the velocity are visualized in the cross-stream plane to infer the capacity of each mode to transport scalar to and from the wall. A form of the FIK identity is derived for the wall mass transfer coefficient (Sherwood number, Sh) and employed to separate the contributions of the mean and fluctuating velocity and scalar fields. The FIK decomposition shows that the turbulent velocity/scalar correlations account for up to 65.8% of the total Sh. The contribution of each POD and EPOD mode to the Sh number is also computed; it is found that, using azimuthal wave numbers m = 1-15 and POD modes n = 1-10, it is possible to reconstruct 49% of the turbulent component of Sh, with the velocity modes containing only 31% of the turbulent kinetic energy. Quadrant analysis shows that these modes are related to ejection and sweep events near the wall, with the ejection events dominating.