Wall Turbulence Control

By Sedat Tardu

Wall turbulence control is a major subject, the investigation of which involves significant industrial, environmental and fundamental consequences. Wall Turbulence Control addresses recent advances achieved in active and passive wall turbulence control over the past two decades. This valuable reference for scientists, researchers and engineers provides an updated view of the research into this topic, including passive control, optimal and suboptimal control methodology, linear control and control using adaptive methods (neural networks), polymer and bubble injection, electromagnetic control and recent advances in control by plasma.

• Language: English
• Publisher: Wiley
• Release date: Feb 7, 2017
• ISBN: 9781119009054

Book preview

Table of Contents

Cover

Title

Copyright

Preface

Notations

1 General Points

1.1. Introduction

1.2. Tools to analyze and develop control strategies

2 Summary of the Main Characteristics of Wall Turbulence

2.1. Introduction

2.2. General equations

2.3. Notations

2.4. Reynolds equations

2.5. Exact relations and FIK identity

2.6. Equations for a turbulent boundary layer

2.7. Scales in a turbulent wall flow

2.8. Turbulent viscosity closures

2.9. Turbulent intensities of the velocity components

2.10. Vorticity and near wall coherent structures

3 Passive Control

3.1. Introduction

3.2. Large eddy (outer layer) breakup devices, LEBUs (OLDs)

3.3. Riblets

3.4. Superhydrophobic surfaces

4 Active Control

4.1. Introduction

4.2. Local blowing

4.3. Ad-hoc control

4.4. Transverse wall oscillations

4.5. Alternated spanwise Lorenz forcing and electromagnetic (EM) control

4.6. Extensions of spanwise forcing

4.7. Reynolds number dependence

4.8. Suboptimal active control

4.9. Optimal active control

4.10. Optimal linear control

4.11. Neural networks

4.12. Stochastic synchronization of the wall turbulence and dual control

Bibliography

Index

End User License Agreement

List of Tables

1 General Points

Table 1.1.Required characteristics of pressure sensors in wall bounded turbulent flows at a small-moderate Reynolds number

Table 1.2.Required characteristics of wall shear-stress sensors in wall bounded turbulent flows at a small-moderate Reynolds number

List of Illustrations

1 General Points

Figure 1.1.The sensor size effect on the measured pressure intensity

Figure 1.2.Capacitive pressure sensors. Adapted from [LOF 96]

Figure 1.3.Piezoresistive pressure sensors (adapted from [GUC 91]

Figure 1.4.Repartition of heat fluxes over a wall hot film

Figure 1.5.Equivalent longitudinal length of the wall hot film sensor as a function of the shear stress parameter for different fluid/substrate configurations

Figure 1.6.Frequency response of the wall hot films for different fluid/substrate configurations. The mean Péclet number is Pe = 30

Figure 1.7.Hot wall film designed by [KÄL 96]

Figure 1.8.Wall shear stress sensor according to [HUA 99]

Figure 1.9.Wall microsensor seen through a microscope. Dimensions: 50 μm long and 10 μm wide, Cavity: 50 × 30 μm², 0.5 μm deep

Figure 1.10.Microwire (adapted from [JIA 94])

Figure 1.11.Wall actuator (adapted from [JAC 98])

2 Summary of the Main Characteristics of Wall Turbulence

Figure 2.1.Reynolds shear and total stresses in wall units as a function of the distance to the wall. The solid line represents Reynolds shear stress. Direct numerical simulations in a turbulent channel flow a from [BAU 14]. For a color version of this figure, see www.iste.co.uk/tardu/turbulence.zip

Figure 2.2.Sublayers in a turbulent wall flow

Figure 2.3.Mean velocity profiles in a fully developed turbulent channel flow. The results were obtained by Bauer [BAU 14] using direct numerical simulations in the range Reτ = 180 to Reτ = 1100

Figure 2.4.Profiles of the Reynolds shear stress in wall units, in a fully developed turbulent channel flow according to [BAU 14]

Figure 2.5.Inverse of the diagnostic function versus wall distance in a fully developed turbulent channel flow, taken from [BAU 14]

Figure 2.6.Diagnostic function in inner scales, according to [OST 00]. The data are averaged over different profiles in the inner layer y/δ < 0.15 , where δ is the thickness of the boundary layer

Figure 2.7.The von Karman constant scaled by its value obtained by the renormalization group as a function of the Reynolds number. Experimental data harvested from [OST 00] and [NAG 95]. The figure is adapted from [TAR 11a]

Figure 2.8.Profiles of the turbulent intensity of the streamwise velocity fluctuations, according to [BAU 14]

Figure 2.9.Profiles of the turbulent intensity of the wall normal velocity fluctuations according to the DNSs performed by [BAU 14]

Figure 2.10.Profiles of the turbulent intensity of the spanwise velocity fluctuations according to [BAU 14]

Figure 2.11.Maximum of the streamwise velocity fluctuations turbulent intensity as a function of the Reynolds number. This figure is adapted from [HUT 07]

Figure 2.12.Distributions of the maximum value of the Reynolds shear stress in turbulent boundary layers. This figure is adapted from [FER 96]. The estimation is based on relation [2.44]. See [TAR 11a] for further details

Figure 2.13.Streamwise vorticity production in a canonic wall flow; a) Production by stretching; b) Production by tilting of the wall normal vorticity by the local shear; c) Production by twisting of the spanwise component under the spanwise gradient of the local longitudinal velocity component

Figure 2.14.Transfer of the spanwise vorticity component into normal and streamwise vorticity in the inner layer. The local zones of streamwise vorticity may roll up into coherent quasi-longitudinal vortices

Figure 2.15.Quasi-longitudinal vortices (QLVs) and the associated wall stress field (turbulent channel with Reτ = 180 ). For a color version of this figure, see www.iste.co.uk/tardu/turbulence.zip

Figure 2.16.Structural elements associated with quasi-streamwise vortices in the inner sublayer

Figure 2.17.Effect on drag caused by elimination of the walls of vorticity ωy± shown in Figure 2.16, according to [JIM 99] at Reτ = 200 . The filtered zone is indicated by The filtration at , shown by A in the figure, has little effect on the drag. A sudden elimination of the near-wall turbulent activity takes place when the filtered zone includes the thin layer 50 < y+ < 70 B

Figure 2.18.Bypass of the streak instability part of the regeneration cycle in the mechanism proposed by Tardu [TAR 08b]

Figure 2.19.View of a section of two counter rotating vortices in the plane y-z. The pair A regenerates the wall-normal vorticity layers ωy±A which are positive and negative, respectively, on the left and on the right. Two similar vorticity layers ωy±B are regenerated by the pair B. The pair B is shifted in relation to the center of symmetry of A

Figure 2.20.Turbulent intensities of the spanwise, wall normal and streamwise vorticity components in a fully developed channel turbulent flow for 180 < Reτ < 1100 , according to [TAR 16]

3 Passive Control

Figure 3.1.Outer layer devices

Figure 3.2.A simple conceptual model of the formation of groups of coherent structures (LSM). The figure is adapted from [TAR 91]

Figure 3.3.A plausible scenario of interaction of the contrarotating wake vortices with the arch vortical structures relatively away from the wall. The figure is adapted from [TAR 91]

Figure 3.4.Plausible effect of the OLDs on the near wall structures stability. The figure is adapted from [TAR 91]

Figure 3.5.Riblets geometry

Figure 3.6.Skin patterns of fast sharks [REI 85]. The figure is adapted from [BEC 00]

Figure 3.7.Drag reduction obtained by scalloped riblets; a) and by blade riblets; b). The figure is adapted from [BEC 97]

Figure 3.8.Virtual origins of the longitudinal and spanwise velocity components within the grooves and the definition of the protrusion height. The figure is adapted from [BEC 97]

Figure 3.9.a) Distribution of the bursting frequency [TAR 93] and turbulent intensity of the streamwise and spanwise vorticity fluctuations [CHO 93]. BME and BSE refer, respectively, to the bursts with multiple and single ejections. They have to be interpreted as the regeneration frequency of the clusters of the quasi-streamwise vortices and solitary coherent structures [TAR 14]. The subindices Riblets and CBL designate the manipulated (by the riblets) and canonical boundary layers. The origin in y+ is the tip of the riblets and the friction velocity on the smooth wall is used in the non-dimensionalization. The figure is adapted from [TAR 95]; b) Flatness of du'/dt according to [TAR 93]

Figure 3.10.Riblets drag reduction mechanism suggested by Choi et al. [CHO 93]

Figure 3.11.Possible effect of a quasi-streamwise vortex on the flow near the riblets. The figure is adapted from [TAR 95]

Figure 3.12.Intermittent decrease in the enhancement of secondary wall normal vorticity by interaction with protrusion height. The figure is adapted from [TAR 95]

Figure 3.13.Water drop on a superhydrophobic surface. The surface is patterned with 15 /m wide ridges spaced 45 /m apart. The figure is adapted from [ROT 10]

Figure 3.14.Micronano scale rougness texture of the wall combined with its chemical hydrophobic treatment leads to the gas-liquid menisci over which the liquid can slip. The figure is adapted from [OU 04]

Figure 3.15.Examples of superhydrophic textures. Plasma-etched polypropylene surface a), a lithographically etched silicon surface patterned with cubic microposts b). The figure is adapted from [OU 04]

Figure 3.16.Mean velocity profiles expressed in the form in drag-reducing streamwise and combined slip configurations. Direct numerical simulations at Reτ = 180. The figure is adapted from [MIN 04]

Figure 3.17.Drag decrease (DR>0) and increase (DR<0) in turbulent superhydrophobic channel flows according to [FUK 06]. Crosses: data from [MIN 04], circles: DNS at Reτ = 180 from [FUK 06], squares: DNS at Re τ = 400 from [FUK 06]. The dotted lines correspond to the [FUK 06] prediction at Reτ = 10⁶

4 Active Control

Figure 4.1.Dimensions of the spanwise blowing slot in mm used in [TAR 01] (top) and the phase average of the blowing velocity over the period T (bottom). The experiments were realized in a wind tunnel with at a Reynolds number based on the boundary layer thickness The thickness of the spanwise slot is 7 wall units. The amplitude of the local blowing is 5 viscous units. The imposed frequency is f+ = 0.017

Figure 4.2.Phase averages of the wall shear stress (left) and wall shear stress intensity (right) scaled with their respective standard uncontrolled values (SBL) at different streamwise distances from the slot. Arrows show the arrival of the secondary spanwise vorticity layer that locally increases the shear stress. The figure is adapted from [TAR 01]

Figure 4.3.Physical mechanism governing the sinusoidal time periodical blowing in the high-frequency regime according to [TAR 01]

Figure 4.4.Time mean wall shear stress versus the streamwise distance from the slot in wall units in the steady, dissymmetrical (DB) and sinusoidal blowing (SB) cases (see [TAR 09a]). Experimental results obtained in a turbulent boundary layer at Reτ = 500

Figure 4.5.Principle of dual control with unsteady localized blowing used as probing control. The system anticipates on future decision by using a Kalman filter as a predictor. The nominal control u0 is the optimum deterministic strategy on the estimated state without turbulence. The cautious control is imposed by turbulence. The probing aims to reduce uncertainty. The figure is adapted from [TAR 01]

Figure 4.6.Ad-hoc v (top) and w control according to [CHO 94]

Figure 4.7.Drag history under ad-hoc v (top) and w control (bottom) in a turbulent channel flow at Reτ = 180 according to [DOC 06]. The detection plane is at y+ = 10. The ad-hoc control under the localized unsteady blowing will be discussed later in this chapter

Figure 4.8.Snapshots of the wall normal velocity and the λ2, structures [JEO 95] under the ad-hoc control with the detection plane at a) y+ = 10 and at b) y+ = 5. The quantities are normalized by the inner variables of the standard channel flow. It is clearly seen that the wall intervention is particularly strong in the immediate neighborhood of the coherent structures. For details, see [TAR 09a]. For a color version of this figure, see www.iste.co.uk/tardu/turbulence.zip

Figure 4.9.Drag reduction history under the ad-hoc external force effect according to equation [4.9] according to [BOU 04]

Figure 4.10.Control by spanwise oscillating wall

Figure 4.11.Amount of drag reduction in a wall flow manipulated by a spanwise oscillating wall versus the similarity parameter defined in equation [4.15] according to [QUA 04] from whom this figure is adapted. The parameters chosen by these authors are and

Figure 4.12.Experimental flow visualization of the near wall streaky structures over a spanwise oscillating wall after [CHO 98] at y+ = 8, during the upward (top) and downward phases. The figure is adapted from [KAR 03]. For a color version of this figure, see www.iste.co.uk/tardu/turbulence.zip

Figure 4.13.Low (bright regions) and high-speed streaks at y+ = 6 and Reτ = 500, in a turbulent channel subject to spanwise wall oscillations according to [TOU 12]: a) canonical unmanipulated flow, the wall streaks are elongated and meandering in the streamwise direction; b) manipulated flow with the streaks are now clearly shifted in the spanwise direction; c) manipulated flow with the low- and highspeed streaks loose their coherence, the small-scale streaks disappear. For a color version of this figure, see www.iste.co.uk/tardu/turbulence.zip

Figure 4.14.Oscillating spanwise Lorenz force can be generated by alternating the polarity of the electrodes in time. The figure is adapted from [BER 00]

Figure 4.15.Drag reduction history in a turbulent channel at Reτ = 180 according to [MON 09] with spanwise oscillating electromagnetic force field for different oscillating periods T in wall units. The Stuart number is 200 in a) and 400 in b). The magnet pitch P and the distance d (see Figure 4.16) are 35 and 4.4 wall units, respectively

Figure 4.16.EM actuator geometry [MON 09]

Figure 4.17.Spanwise oscillations of the wall normal vorticity layers separating the low- and high-speed streaks in a turbulent channel flow submitted to transverse oscillating electromagnetic force at y+ = 20. The Stuart number is 200 and the imposed period is T+ = 120. Top at t+ = 90, below at t+ = 150. The figure is adapted from [MON 09]

Figure 4.18Temporal evolution of a wall normal vorticity layer during the forced-spanwise oscillations clearly showing the strong bent over of the ωy layers. See [MON 09] for a colored and more clear version of this figure

Figure 4.19.Drag reduction under a transverse traveling wave as reported by Montesino [MON 09]. Different parameters related to the simulations (turbulent channel flow at a Karman number of 180) are provided in the figure. The intensity I appearing in equation [4.26] is the Stuart number which is equal to 100 in this case

Figure 4.20.Drag reduction a) and net save of power b) obtained by spanwise velocity waves traveling in the streamwise direction (see equation [4.27]). The parameters in wall units are Note that the imposed time period is roughly three times larger than the optimum period of purely oscillating wall spanwise velocity and that the streamwise wavelength is comparable to the longitudinal extend of the near wall streaks. The amplitude and Reτ