Velocity and conformation statistics based on reduced Karhunen–Loeve projection data from DNS of viscoelastic turbulent channel flow

Abstract

To investigate the effectiveness of the Karhunen–Loeve (K–L) method as a data reduction approach, we study here its effect on the velocity and conformation statistics in a drag reducing turbulent polymer flow. The K–L method has been used to construct a set of basis velocity eigenfunctions from a large number of independent realizations of the velocity. Those were obtained from direct numerical simulation (DNS) of a viscoelastic turbulent channel flow using the Giesekus model. A subset of the K–L eigenfunctions, large enough to contain more than 90% of the fluctuating kinetic energy of the flow on the average, has then been subsequently used to obtain time series of projection coefficients of the velocity fields generated further from DNS. In a post-processing step, velocity fields were reconstructed using selected subsets of the projection coefficients. Those reconstructed velocity fields were then used to evaluate turbulent statistics as well as to integrate the constitutive equation. The turbulent statistics (r.m.s. velocities, Reynolds stress etc.) thus constructed showed good agreement with the full results from DNS. The Reynolds stress anisotropy was also calculated in this work for the first time. It was found to increase with viscoelasticity that was well reproduced in the reduced K–L data except near the channel centerline where the K–L data showed some loss of anisotropy. The biggest differences however between the K–L reduced data and the full DNS results were seen in the conformation statistics. The average polymer conformation extracted from the K–L reduced data was significantly less than that corresponding to the full DNS results anywhere except in the shear-dominated wall region. A further comparison of the energy and dissipation spectra between the full DNS and the K–L reconstructed data illustrated the impact of the K–L process in resulting to a significant damping of small turbulent scales even those contributing to the maximum in turbulent dissipation. This may also be the principal reason behind the poor quality of the K–L reconstructed conformation data.