DNS of Wall-Bounded Turbulent Flow: An Introduction

Abstract

This book covers the topic of direct numerical simulation (DNS) of wall-bounded turbulent flow by first principle approach. It is mandatory to track the flow from laminar state to fully developed turbulent state, and which has been solved very recently for specific cases. While one can attempt DNS of Navier-Stokes equation for fully developed turbulent flow, there would be ambiguity about specifying initial and boundary conditions. Moreover, such an exercise even if it is successful, then also it may not answer most of the fundamental questions related to the evolution of the flow field. First, by erroneous numerical methods and artificial excitations, one may achieve fully developed turbulence, but that approach should be avoided. Such simulations would not enlighten one in following the physical processes during transition. A detailed review and critique of some of the methods used for DNS and large eddy simulation (LES) of transitional and turbulent flows is given in Sengupta, T. K. (In the IUTAM Symposium Proceedings on Advances in Computation, Modeling and Control of Transitional and Turbulent Flows, 2015, [24]). This is of fundamental relevance for the contents of this book. Here, we present a more fundamental approach that studies the topic by considering the flow evolution from laminar to fully developed state by a thoroughly analyzed numerical method. The aim is to computationally reproduce the physical phenomena as recorded in classical transition experiments by Schubauer and Skramstad (J Aerosp Sci 14(2):69–78, 1947, [19]) for 2D transition and Klebanoff et al. (J Fluid Mech, 12:1–34, 1962, [10]) for the 3D routes. These experiments were designed after lots of soul searching in the fluid dynamic community, when experimentalists failed to detect some wave-solutions predicted by instability studies by Heisenberg, Tollmien and Schlichting. The reader is directed to the introductory discussion in Sengupta (Instabilities of flows and transition to turbulence. CRC Press, Taylor & Francis Group, Florida, 2012, [23]) about the historic development of the subject of instability studies and a brief account will be provided later.