Manipulating Flow Structures in Turbulent Pipe Flow

Two different tools, the non-empirical resolvent analysis and the data-based dynamic mode decomposition, are employed to assess the changes induced by transpiration in the dynamics of a turbulent pipe flow. The focus is on very large-scale motions. Both analyses permit the observation of streamwise waviness in the large flow structures and how the transpiration can inhibit fluctuation in localized axial positions. We discuss under which conditions an agreement between both methodologies can be achieved. INTRODUCTION A deep understanding of the physical mechanisms that act in wall-bounded turbulent flows is required for the design of efficient flow control strategies, as stated by Kim (2011). In this context, recent findings in high-Reynolds number wall-bounded turbulent flows highlight the energetic relevance of coherent structures other than the selfsustaining near-wall cycle (Kim et al., 1987; Jiménez & Pinelli, 1999). These flow structures, known as very largescale motions (VLSM), were recently reported by Guala et al. (2006) and Monty et al. (2007) and found to consist of long meandering slender streaks of high and low streamwise velocity that contain a significant fraction of the turbulent kinetic energy and shear stress production. Hence the contribution of these flow structures to the overall wall drag is of utmost importance at very high-Reynolds number. Hutchins & Marusic (2007) observed that these VLSM can reach locations near the wall, thus flow control strategies applied to the wall may have a strong influence on these motions. Consequently, control of these VLSM structures is highly desirable towards a drag increase or reduction in high-Reynolds pipe flow. Even though computational simulations are almost unaffordable at the Reynolds number in which these structures are energetically dominant, in the sense of producing a second peak in the streamwise turbulent intensity, which occurs for friction Reynolds number Reτ > 104 (Smits et al., 2011), the behavior of these structures can be observed in pipe flow experiments at moderate bulk-flow Reynolds numbers Re = 12500, as shown by the proper orthogonal decomposition of experimental data carried out by Hellström et al. (2011). As observed in the seminal work of Choi et al. (1994), one of the most potentially effective ways to achieve the manipulation of turbulent flow is the appliance of suction and blowing at the wall, also known as transpiration. The purpose of the present study is to observe how highand low-amplitude transpiration in pipe flow at a moderate bulk flow Reynolds number Re= 10000 can affect the very largescale motions of the flow. Particularly, we only focus on the effect on the flow of steady wall-normal blowing and suction, that varies sinusoidally in the streamwise direction. To address this, a direct numerical simulation (DNS) dataset for pipe flow at a moderate Reynolds number has been generated. This dataset consists of a wall transpiration parameter sweep in order to assess the effect of the transpiration parameters on the turbulent statistics and identify interesting drag increasing and reducing configurations. Here we employ the resolvent analysis to identify the flow structures that are amplified/damped by the effect of different transpiration configurations. The resolvent framework (McKeon & Sharma, 2010) consists of an amplification analysis of the Navier–Stokes equations in the wavenumber/frequency domain, which yields a linear relationship between the velocity fields and the non-linear terms sustaining the turbulence, and hence the mean profile though the Reynolds shear stress, via a resolvent operator. This framework has been already successfully employed by Sharma & McKeon (2013) to recreate complex coherent structures, VLSM among them, from a low-dimensional subset of modes. To complement this tool, a dynamic mode decomposition (Schmid, 2010; Rowley et al., 2009) (DMD) analysis on the turbulent DNS data is carried out to provide the most energetic flow structures. Gómez et al. (2014) 1 June 30 July 3, 2015 Melbourne, Australia 9 7A-1