An investigation of viscoelastic turbulent channel flows using Karhunen-Loeve analysis

Direct numerical simulations of viscoelastic turbulent channel flows can provide invaluable data for polymer-induced drag reducing flows. However, such simulations can generate upto petabytes of data which requires enormous storage space and are difficult to handle. This thesis adresses issues concerning the applicability of Karhunen-Loeve (K-L) analysis to DNS of three-dimensional viscoelastic turbulent channel flows, in order to develop data reduction schemes. Further, flow visualizations of DNS data are able to show that viscoelastic turbulent channel flows have larger coherent structures in comparison to Newtonian turbulent channel flows. In turbulent flow literature, the importance of coherent structures is well established. It is believed that relevant information regarding the actual turbulence mechanism can be learned by studying the dynamics of coherent structures. In this thesis, we provide a time-dependent analysis of K-L modes and suggest new ways to fingerprint coherent structures using K-L modes.;Eduction of coherent structures from a three-dimensional (3-D) complex flow field is the first issue that we tackle in this thesis. For this purpose, we adopt the K-L method and develop our own code to implement K-L decomposition of a 3-D complex flow field in double Fourier space. The K-L modes by themselves do not directly represent the coherent structures existing in the flow. In order to establish a relationship between K-L modes and coherent structures, we develop strategies based on correlation analysis of time-series of K-L projection coefficients. We propose a new two-dimensional analysis of those correlations with respect to both the time and a moving frame velocity in order to detect coherent flow structures and their mean convective velocity.;In order to pass as a good data reduction procedure, it is important that the ability of K-L data reduction to approximate the DNS statistics be tested. Apart from good agreement with DNS results for velocity statistics, we find very poor agreement of average conformation trace obtained after K-L data reduction. The small-scales of turbulence discarded in a K-L data reduction plays an important role in the evolution of the polymer conformation. However, very little is known about the small scales of viscoelastic turbulence and how differently do they behave from their Newtonian counterparts.;Turbulent velocity fluctuations are representative of the large-scale motions of the flow, while their derivatives can be used to probe into small-scales of turbulence. As a case study, we calculate the PDFs of the velocity fluctuations and their derivatives of a viscoelastic turbulent channel flow and then compare against those for a Newtonian fluid at a friction Reynolds number 180. We also calculate the skewness and the flatness factors, present them as functions of the distance from the wall, further reveal and quantify the non-Gaussian characteristics of the turbulent structures and how they are distributed in the flow domain. The PDF analysis, clearly pointed out the significant modifications brought in by viscoelasticity in the small scales of channel turbulence, especially in the buffer layer.;K-L representation can be sensitive to its objective criterion as well as the parameters of the DNS used to generate the data for K-L decomposition. First, we investigate the dependence of K-L decomposition on three important numerical parameters: the size of the database (number of realizations), mesh resolution, and the computational channel size. Next, we suggest ways to modify the objective criterion to improve the representation of small scales in the top K-L modes. K-L data reduction obtained through K-L modes with enhanced representation of small scales of turbulence also fails to give a good approximation of average conformation trace obtained from DNS. Perhaps, large number of modes are required to properly account for the small scale contributions.;We, however, are able to find a compensation for the discarded small scales and loss of extensional nature of the flow by way of a rescaling of 0 Wer0 in the post-processing step where the conformation tensor is calculated based on the reconstructed K-L fields. We take this approach in a systematic way (the rescaling is based on quantities that are easily calculated from DNS). We also attach physical meaning to it by basing it on an estimate of the local extensional rate at the buffer layer. We therefore, hope that this approach can provide the starting point for future investigations into low-dimensional modeling of viscoelastic turbulence as well as other multiscale applications.