A Robust Scheme for Control of Skin Friction and Heat

Using direct numerical simulations of turbulent channel flow, we present a new method for skin friction reduction by prevention of streamwise vortex formation near the wall. Based on recent evidence of streak instability-induced vortex generation, we develop a new technique for drag reduction, enabling large-scale flow forcing without requiring instantaneous flow information. As proof-of-principle, x-independent forcing, with a wavelength of 400 wall units and an amplitude of only 6% of the centerline velocity, produces a significant sustained drag reduction: 20% for imposed counterrotating streamwise vortices and 50% for colliding, z-directed wall jets. The drag reduction results from weakened longitudinal vortices near the wall, due to forcing-induced suppression of the underlying streak instability. In particular, the forcing significantly weakens the wall-normal vorticity flanking lifted low-speed streaks, thereby arresting the streaks' instability responsible for vortex generation. These results suggest promising new drag reduction strategies, e.g. passive vortex generators or colliding spanwise jets from x-aligned slots, involving large-scale (hence more durable) actuation and requiring no wall sensors or control logic. Objectives Streamwise vortices are now known to dominate near-wall turbulence production and transport, but their physical nature poses some formidable obstacles: (i) small dominant lengthscales (0(0.1 mm) for aircraft), (ii) random (x,z) locations, and (iii) apparently complex spatiotemporal dynamics. The most logical approach to CS-based reduction of drag and heat transfer is to simply prevent vortex formation in the first place (in contrast to many approaches which counteract the wall interaction of fully developed CS). It has long been hypothesized that a major source of turbulence production near the wall is the instability of inflectional low-speed streaks (e.g. [1-2]), although most details still remain unresolved. In particular, the following key issues have yet to be addressed in detail: (i) the relationship between streak instability and the formation mechanism of longitudinal vortices, (ii) physical space (3D) vortex dynamics arising from streak instability, and (iii) streak instability control strategies aimed at drag reduction. As an alternative to popular microscale control approaches, our objective nere is to investigate a new large-scale control approach explicitly designed to disrupt the naturally occurring vortex regeneration mechanism. We investigate CS suppression through largescale manipulation of streak instability, and explain the observed control effect using DHC QUATrnw ^PPreved for public release J HVAbiTYINSPECTED 4 165 distribution unlimited. instability and vortex dynamics concepts. For additional details of our drag reduction approach, the reader is referrred to Schoppa & Hussain. Computational Approach In the following, we address vortex regeneration and its control using direct numerical simulations of the Navier-Stokes equations. Periodic boundary conditions are used in x and z, and the no-slip condition is applied on the two walls normal to y; see Kim et a/. for the simulation algorithm details. The control simulations are initialized with fulldomain channel flow turbulence at Re=\S00 and 3200, with 48x65x48 and 192x129x192 dealiased Fourier modes respectively. Actuation is represented by an applied control flow, either maintained at a constant amplitude or allowed to freely evolve, superimposed onto the turbulence. Results & Discussion In the following, we investigate drag reduction by: (i) a spanwise row of counter-rotating, x-independent streamwise vortices, centered in the outer region (at the channel centerline) and (ii) ^-independent, z-directed colliding wall jets. As a simple model of streamwise vortex generators or spanwise slot jets, we consider a control flow of the form t/con=0 VCo„(y,z)=-Aßcos(ßz)( 1 +cosK(y/h-1)) Wcon(y,z)=-AKsm$z)smn(y/h-1), (1) which satisfies the continuity equation and the no-slip condition on the channel walls (at y=0,2/z), where A is the control amplitude and 2jt/ß=400. To demonstrate proof-ofprinciple for large-scale forcing, the z wavelength of the control flow is four times the characteristic streak spacing of approximately 100 wall units; even much larger-scale control (although computationally prohibitive) may be possible in practice. As illustrated in Fig. 1(a), the control flow (1) has a much larger scale than local minima of w(y,z) near the wall, representing lifted low-speed streaks. For simplicity, we focus on the lower half of the channel (i.e. ye [0,h]) in this and other figures; the upper half yields similar results. For a full period in z, (1) represents an array of counter-rotating 2D streamwise vortices (Fig. la), termed vortex control. Over the half period ßze[7C/2,37t/2], (1) resembles colliding, spanwise-directed 2D wall jets (region WJ in Fig. la), referred to as wall jet control. Thus, we actually simulate a single control flow, distinguishing vortex and wall jet control by the region of z considered. In practice, the relative extents of diverging (outside WJ) and converging (inside WJ) wall jets can be adjusted to reduce the former. To assess potential drag reduction, the time evolution of wall-integrated shear is shown in Fig. 2 for several control cases. For both, we consider two methods of forcing: (i) free forcing in which the control flow (1) is superimposed onto a turbulent flowfield at t0=0 and allowed to freely evolve, and (ii) frozen forcing with the x-mean Fourier coefficients of the control flow maintained constant in time. For frozen forcing, VCon and Wcon are specified as the flowfield resulting after one turnover time of viscous, 2D evolution of the initial condition (1). Significantly, Fig. 2 reveals that substantial drag reduction, sustained in time for frozen forcing, is attainable 20% for vortex control and 50% for wall jet control. In both