Frohnapfel, B.

Hasegawa, Y.

Kasagi, N.

English

KITopen

XXII ICTAM, 25–29 August 2008, Adelaide, AustraliaFLOW CONTROL BY TURBULENCE STATE MODIFICATIONS IN THE NEAR-WALL REGIONBettina Frohnapfel∗, Peter Lammers∗∗, Yosuke Hasagawa∗ & Nobuhide Kasagi∗∗ Department of Mechanical Engineering, The University of Tokyo, Japan∗∗High Performance Computing Center, The University of Stuttgart, GermanySummary Significant drag reduction is obtained in numerical simulation of turbulent channel flow by forcing local turbulence in thenear-wall layer to approach a one-component state, where only the streamwise velocity fluctuation remains. The drag reduction rateobtained with the modified layer of a thicknessy+d≈ 5 is in the order of30%. This value is in agreement with the drag reductionrate estimated based on the FIK identity for a channel flow in which all turbulence has been suppressed in the near-wall layer. Thisfact suggests that the idealized damping of turbulence in the near-wall region, which has resulted in large drag reduction even at highReynolds numbers, is achievable by a mere reorganization of turbulent fluctuations.Since turbulent drag consumes large amounts of energy, its reduction is of great economical and ecological interest. Inorder to further advance the design of active and passive flow control techniques, it is important to investigate how muchand which part of a turbulent flow field needs to be controlled in order to achieve flow management with the least possibleeffort. Iwamoto et al. [1] show that significant drag reduction can be obtained by an idealized near-wall layer manipulationby which only turbulence near the wall is damped (resulting in a laminar flow field in this region). The drag reduction rateobtained is estimated employing the FIK identity introduced by Fukagata et al. [2], and it is revealed that even at highReynolds numbers large drag reduction can be attained without direct control of large scale turbulent structures. Sincecomplete damping of turbulence in a certain layer would be difficult in real applications, the effect of manipulation ofturbulence state in the near-wall region is investigated.Frohnapfel et al. [3] demonstrate that the mechanism of turbulent drag reduction is associated with increased anisotropy ofturbulence in the near-wall region. The highest possible value of turbulence anisotropy is related to the one-componentalstate of turbulence in the anisotropy invariant map (Lumley and Newman, [4]). It is shown by Jovanović d Hillerbrand[5] that for this special case the two-component motions close to the wall must additionally satisfy constraints of localaxisymmetry. Based on a statistical analysis of the velocity fluctuations, they conclude that small scale turbulence whosestatistical properties are invariant about the axis aligned with the mean flow direction will vanish in close proximity ofsolid boundaries (where the continuity equation dictates the limiting behavior of the velocity fluctuations). This analysissuggests that turbulence plotted in the anisotropy invariant map will approach the one-component state in the near-wallregion before completely disappearing for the case that reverse transition to a laminar flow occurs.Numerical experiments of a channel flow in which turbulence in the near-wall region is forced towards the one-componentlimit yield high drag reduction rates [3]. The forcing is applied by setting the spanwise velocity fluctuation equal to thewall-normal velocity fluctuation at grid points in a selected layer near the wall before the continuity equation is enforcedat each time step. According to [5] such forcing in the vicinity of the wall will result in a trend towards one-componentturbulence accompanied by significant suppression of small scale turbulence in this region.The resulting velocity fluctuations (rms values) for the case where forcing is applied to the regiony/δ ≤ 0.028 incomparison with the unforced channel flow case are presented in figure 1a. The spanwise (w) and wall-normal (v)velocity fluctuations are almost completely damped in the layer where the forcing is applied, whilst the streamwisevelocity fluctuation (u) is reduced but not completely damped. Thus, a one-component state of turbulence is established.Figure 1b shows the Reynolds shear stress distributions for the unforced and forced cases normalized withuτ of theuncontrolled case. For the controlled flow,−u+v+ is drastically decreased and practically no shear stress exists in theregion where the forcing is applied; this is associated with the notable suppression ofv in this region. This change in theReynolds shear stress suggests significant drag reduction.In [1] and [2], it is demonstrated that the amount of drag reduction directly corresponds to the difference in the integralsof a weighted Reynolds shear stress distribution(−u+v+)weightedgiven by:(−u+v+)weighted= 3(1 −yδ) (−u+v+). (1)This distribution is also included in figure 1b. The difference in the areas underneath these two curves, which interpretedas the resulting drag reduction, reaches31%. It is equivalent to the value obtained when drag reduction is based on thechange in the wall shear stress:DR = 1 −τw(τw)0, (2)where(τw)0 corresponds to the wall shear stress in the uncontrolled flow. Since the region where the forcing is appliedis much thinner compared to the channel half width,y/δ ≤ 0.028, the difference in the area underneath the weightedReynolds shear stress distribution is almost negligible for this region. This suggests that the drag reduction is mainlyattributed to the reduction of Reynolds shear stress further away from the wall.1y/durms, vrms, wrms00.20.40.60.810 0.05 0.1 0.2uvwu w/ forcingv w/ forcingw w/ forcingy/d- uv,   3(1-y/)(d++- uv)0.00.51.01.52.00.0 0.2 0.4 0.6 1.0Reynolds shear stress w/o forcingReynolds shear stress w/ forcingweighted Reynolds shear stress w/o forcingweighted Reynolds shear stress w/ forcingb)a)Figure 1. a) RMS velocity fluctuations in the near-wall region without and with forcing in the regiony/δ ≤ yd/δ = 0.028. b) Originaland weighted Reynolds shear stress distribution with and without forcing, normalized with the friction velocityuτ of the uncontrolledflow. The red point marks the position ofyd/δ in both figures.For the idealized near-wall modifications of [1], the FIK identity allows to calculate the drag reductionDR i terms ofthe Reynolds numberReτ of the uncontrolled flow and the relative thickness of the damping layeryd/δ:1κlnReτ + F =ydδ(1 −ydδ+13y2dδ2)(1 − DR)Reτ +(1 −ydδ)3/2(1 − DR)1/2×[1κln{(1 −ydδ)3/2(1 − DR)1/2Reτ}+ F](3)with κ = 0.41 andF = 3.2. In [1] this identity was verified for a Reynolds number range of103 < Reτ < 5×105, whilethe damping layer thicknesses of10 < y+d < 60 were analyzed. In the present simulations, not all turbulence in the near-wall region is damped, but one-component turbulence state is approached. The spanwise and wall-normal fluctuations aresignificantly damped while the streamwise component remains. The Reynolds number for the corresponding uncontrolledchannel flow isReτ = 180 and the thickness of the modified layery+d = 5.1. In spite of these differences, the aboveidentity equation is employed to check whether it can be used to estimate the drag reduction rate. ForR τ = 180 andy/δ = 0.028, the drag reduction rate is calculated asDR = 29%. This result is in good agreement with the actual valueof DR = 31%.The numerical experiment is also carried out for even thinner modified layers ofy+d = 3.2 and2.2. For all cases, equation3 yields reasonable predictions of the drag reduction rate. Future work will concentrate on extending the numericalexperiment to a thickness ofy+d that correspond to the ones reported in [1] to investigate whether enforcing of one-component turbulence in a certain damping layer will yield the same drag reduction rate as the total suppression ofturbulence in this region.References[1] Iwamoto K., Fukagata K., Kasagi N., Suzuki Y.: Friction drag reduction achievable by near-wall turbulence manipulation at high Reynoldsnumbers.Phys. Fluids 17:011702, 2005.[2] Fukagata K., Iwamoto K., Kasagi N.: Contribution of Reynolds stress distribution to the skin friction in wall bounded flows.Phys. Fluids 14:L73, 2002.[3] Frohnapfel B., Lammers P., Jovanović J., Durst F.: Interpretation of the mechanism associated with turbulent drag reduction in terms of anisotropyinvariants.J. Fluid Mech 577:457–466, 2007.[4] Lumley J.L., Newman G.R.: The return to isotropy of homogeneous turbulence.J. Fluid Mech 82:161–178, 1977.[5] Jovanovíc J., Hillerbrand R.: On the peculiar property of the velocity fluctuations in wall-bounded flows.J. Thermal Sci. 9:3–12, 2005.2

Flow control by turbulence state modifications in the near-wall region

https://publikationen.bibliothek.kit.edu/1000029324/2233607

Flow control by turbulence state modifications in the near-wall region

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