Control of Synthetic Hairpin Vortices in Laminar Boundary Layer for Skin-Friction Reduction

Journal of Marine Science and Engineering

Article Control of Synthetic Hairpin Vortices in Laminar Boundary Layer for Skin-Friction Reduction

Bonguk Koo 1 and Yong-Duck Kang 2,*

1 Department of Naval Architecture and Marine Engineering, Changwon National University, 20 Changwondaehak-ro, Uichang-gu, Changwon-si, Gyeongsangnam-do 51140, Korea; [email protected] 2 Department of Naval Architecture and Ocean Engineering, Dong-Eui University, 176 Eomgwangro, Busanjin-gu, Busan 47430, Korea * Correspondence: [email protected]; Tel.: +82-(051)-890-2815

Received: 14 December 2019; Accepted: 9 January 2020; Published: 15 January 2020

Abstract: The results of flow visualization and hot-film measurement in a water channel are presented in this paper, in which the effectiveness of controlling synthetic hairpin vortices in the laminar boundary layer is examined to reduce skin friction. In this study, hairpin vortices were generated by periodically injecting vortex rings into a cross flow through a hole on a flat plate. To control the hairpin vortices, jets were issued from a nozzle directly onto the head of the hairpins. The results of the flow visualization demonstrated that the jets destroyed the hairpins by disconnecting the heads from their legs, after which the weakened hairpin vortices could not develop. Therefore, the circulation around the legs was reduced, which suggests that the direct intervention on the hairpin heads resulted in the reduction of streamwise stretching. Data obtained by a hot-film sensor showed that the high-speed regions outside the hairpin legs were reduced in speed by this control technique, leading to a decrease in the associated local skin friction.

Keywords: fuel efficiency; frictional resistance reduction; hull-fluid interaction; hairpin vortex; jet control

1. Introduction There is more attention to fuel efficiency of ships by national and international organizations due to increasing environmental pollution [1]. Therefore, various research topics have been proposed to reduce the frictional resistance that increases squarely with the ship speed. Reducing frictional resistance includes decreasing the wetted surface area, the ship speed, and the interaction between hull surface and fluid. However, the changes in the principal dimensions are risky and increase costs, therefore many researchers have tried to understand the mechanism of energy regeneration in the process of hull surface interaction with vortices generated in the boundary layer. Most authors have investigated the importance of streamwise vortical structures in the production of skin friction with a view to manipulating them to reduce drag [2–10]. It has been believed that coherent structures produce turbulent energy that is key to their ability to sustain themselves in boundary layers. Kline et al. [11] showed that the pumping motions within the viscous sublayer formed low-speed streaks by inducing a vortex pair, which interacted with the outer layer through burst events. Kim et al. [12] followed this work with flow visualization and hot-wire measurements, and observed the generation of highly intermittent turbulence near the wall, which became concentrated during burst events. Wallace et al. [13] showed that two main motions, the ejection-type motion with a negative streamwise velocity (u) and positive wall-normal velocity (v) and the sweep-type motion with positive streamwise velocity and negative wall-normal velocity,

J. Mar. Sci. Eng. 2020, 8, 45; doi:10.3390/jmse8010045 www.mdpi.com/journal/jmse J. Mar. Sci. Eng. 2020, 8, 45 2 of 14 contributed significantly to the Reynolds stress in the wall region. Kim [14] reported in his LES results that counter-rotating streamwise vortices were created as a result of “splatting” and also speculated that this pair of counter-rotating vortices could be the two legs of a hairpin vortex. The hairpin-vortex hypothesis first proposed by Theodorsen [15] was well documented by Head et al. [16] in their flow visualization studies over a range of Reynolds numbers. The vortices were elongated and developed into more hairpin-vortex shapes at a moderate Reynolds number and large-scale structures consisting of several vortices. Robinson [17] summarized this topic by reporting turbulent structures that consisted of hairpin legs in the buffer and log regions, whereas arches, necks, and the heads of hairpins occurred in the log and wake regions. More details of the development of hairpin vortexes were described by Smith et al. [18], both experimentally and computationally, who suggested that once formed, a vortex loop moved away from the wall by self-induction and downstream due to the background shear flow. The trailing legs of the loop remained in the wall region and were stretched to form a pair of streamwise vortices. Low-speed fluids accumulated between the legs and acted to pump those fluids away from the wall. Dhanak et al. [19] showed a highly simplified model that grew into a hairpin vortex in a two-dimensional simulation. As the head of the disturbed line vortex moved away from the surface, it developed into a horse-shoe shaped vortex and either side stretched toward the wall to form legs. Adrian [20] explained the development of a hairpin vortex as reaching around the edge of the boundary layer, with the head of the hairpin vortex moving faster at a higher mean velocity than the legs, which stayed near the wall. Thus, the legs underwent an intensification process resulting in the growth of the hairpin vortex toward the edge. The streamwise vortices forming at the near-wall region were parts of large-scale structures in the boundary layer. It is commonly believed that the downwash side of streamwise vortices induces high-speed fluid toward the wall, called a sweep event, whereas low-speed fluid moves away from the wall, which is called an ejection event. Kravchenko et al. [21] showed that high frictional drag was closely correlated with the sweep side of streamwise vortices. Furthermore, the authors considered that skin friction was increased when high-speed fluid was transported to the wall. Vortical structures, which are responsible for about half of the turbulence energy at the near-wall region, have been considered to be sustained by a cycle without the influence of outer flow [22,23]. Therefore, flow control methods have usually focused on the modification of near-wall structures. Although the outer flow did not stimulate the formation of near-wall structures, based on the analysis of Jimenez et al. [24], it did modulate their lengths with respect to the boundary layer. As the head of the hairpin vortex reached the edge of the boundary layer, the size of the vortex core of the legs was reduced and the vorticity was increased. This top-down process, wherein large-scale turbulence structures influence small-scale near-wall turbulence structures, could contribute to skin-friction drag. It was proposed that the superstructures not only superimposed a low wavenumber onto near-wall structures as a footprint, but they also interacted more progressively with small-scale motions as the Reynolds number increased [25–28]. Moreover, it was also suggested that the low wavenumber of the wall shear was due to the presence of the large-scale structures [29–33]. Based on the influence of streamwise vortices, many investigations regarding skin-friction reduction in turbulent boundary layers have directly targeted near-wall events [2,3]. As a passive control device without any energy input [4–6], riblets on the surface were used to manipulate near-wall structures. The researchers reported that drag reduction could be obtained when longitudinal vortices interacted to trigger the burst event, where closely spaced riblets reduced the amount of exposed area and restricted spanwise movement. Alternatively, active techniques that require energy input have been used to maximize the net drag reduction in terms of control efficiency. Du and Karniadakis [7] reported in their direct numerical simulation (DNS) by Lorentz force that a transverse traveling wave was more efficient than riblets for spanwise oscillation control. They showed that a traveling wave could remove alternating streamwise streaks and hairpin vortices. Choi et al. [8] carried out DNS to reduce skin friction by blowing and suction, depending on either sweep or ejection. They reported the mechanisms of drag reduction as occurring in two ways; first, active control hindered the sweep motions that J. Mar. Sci. Eng. 2020, 8, 45 3 of 14 bring high-speed velocity to the wall and, secondly, it deterred the regeneration of secondary vortices by preventing ejection motions. In references [9,10], they attempted real-time opposition control by wall-normal jets at the wall to cancel high-speed velocity toward the wall. They selectively counteracted sweep events at the near-wall region and obtained skin-friction reduction. Few methods have been proposed to reduce skin friction in the turbulent boundary layer by controlling the large-scale structures, although this approach would last longer and cover a wider area than wall-based controls with high Reynolds numbers [34,35]. Large-eddy break-up (LEBU) devices in the outer part of a boundary layer interrupt the energy production loop by directly interacting with the large-eddy structures, thereby weakening burst events near the wall and reducing skin-friction [36–40]. As the shedding wake behind the LEBU prevents large-scale structures from moving toward the wall, the events producing Reynolds stress at the wall could be reduced. Hutchins and Choi [41] used an array of thin vertical blade devices (VBDs) in the turbulent boundary layer to reduce local skin friction by up to 30% downstream of the blades. The authors explained that when large-eddy structures passed through the VBD array, their shoulders were sliced off and the link between the outer and inner structures was disconnected, thereby reducing skin-friction drag. Large-scale structures are recognized as the main features affecting turbulence production and dissipation through the boundary layer during its growth process. The aim of the present work was to investigate the effectiveness of an outer control strategy, whereby a direct intervention on the hairpin vortices is performed by control jets located outside the boundary layer to decrease the vorticity around the legs of the hairpin vortex and reduce the wall shear stress. The outer layer-based technique proposed in this study is not applicable in engineering purposes. However, as a part of a feasibility study for this ambitious attempt, the experiments have been carried out in a laminar boundary layer since the flow phenomenon is less complicated than that of a turbulent flow. It would have an additional advantage of manipulating energetic near-wall structures on top of the effect on large-scale structures. A detailed description of the initial stage of this study regarding the direct intervention on hairpin structures in the turbulent boundary layer can be found in Kang et al. [42]. This article presents how the flow with hairpin vortices was simulated in a laminar boundary layer. Then, a direct intervention of hairpin vortices was applied to reduce skin-friction drag. Both flow visualization and hot-film measurements were made to confirm this control methodology.

2. Experimental Set-Up

2.1. Water Channel with Dye System This study was conducted in an open water channel 7.3 m long with a cross section of 0.62 m 0.30 m (width height). We suspended a 4.0 m long flat plate with 20:1 elliptic leading edge × × made of Perspex 0.1 m from the bottom of the water channel, as shown in Figure1. A 0.25 m long flap was attached to the trailing edge of the test plate and set to 17◦ to get zero pressure gradient over a test plate. The flap angle was adjusted to separate fluid evenly into upper and lower at the leading edge. The streamwise direction was along the x-axis, the wall-normal direction was along the y-axis, and the spanwise direction was along the z-axis. Unlike a hot-wire probe, a hot-film sensor with an overheat ratio of 1.05 is very sensitive to temperature, so temperature control was very important during this experiment. The heat generated by the high-speed pump blades caused the water temperature to rise by 0.1 ◦C within 10 min. Thus, a heat exchanger made of copper pipe was installed in the upstream tank to maintain a constant water temperature by the passage of cold tap water. A 5 mm hole on the test plate was drilled 0.37 m from the leading edge, through which red dye was supplied to generate a vortex ring. To prevent disturbance inside the laminar boundary layer, a 0.25 mm jet nozzle was installed well outside the boundary layer at y/δ = 1.67, which was connected to a green dye tank. Each tube was connected to a 10.0 L plastic tank with a spigot, in which the same water level was maintained to maintain the same pressure. J. Mar. Sci. Eng. 2020, 8, 45 4 of 14 J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 4 of 13

Figure 1. Experimental configurations: (a) water channel with test plate; (b) hairpin vortex control by Figurejet with 1. hot-film Experimental measurement. configurations: (a) water channel with test plate; (b) hairpin vortex control by jet with hot-film measurement. 2.2. Sensor Calibration and Velocity Measurement 2.2. SensorThe data Calibration were obtained and Velocity using Measurement a Dantec 56C Constant Temperature Anemometry (CTA) system withThe a 55R15 data hot-filmwere obtained sensor using (Dantec a Dantec Dynamics, 56C Co Skovlunde,nstant Temperature Denmark). Anemometry This 3 mm long (CTA) probe system has witha sensor a 55R15 length hot-film of 1.25 sensor mm, which(Dantec was Dynamics, operated Skovlunde, at an overheat Denmark). ratio of This 1.05. 3 An mm automatic long probe traverse has a sensorsystem length was used of 1.25 to move mm, the which probe was around operated in the at YZ an plane, overheat which ratio was of controlled 1.05. An automatic by a stepper traverse motor. The traverse resolution was 6.25 µm per step in the wall-normal direction with an accuracy of 300 µm. system was used to move the probe around in the YZ plane, which was controlled by a stepper± motor. x = The traverse hot-film resolution sensor measured was 6.25 the μ streamwisem per step in velocity the wall-normal in the YZ plane direction at with41 cman accuracy from the leadingof ±300 edge. Velocity measurements were performed at 17 spanwise positions in the range of 8 mm z 8 μm. The hot-film sensor measured the streamwise velocity in the YZ plane at 𝑥=41 − cm from≤ the≤ leadingmm with edge. a 1.0 Velocity mm interval. measurements In addition, were a performed wall-normal at velocity17 spanwise scan positions was performed in the range at 36 of positions −8 mm ≤with z ≤ a8 0.1mm mm with interval a 1.0 mm from interval. the wall In to 1.5addition, mm, a a 0.5 wall-normal mm interval velocity to 7 mm, scan and was a 1.0 performed mm interval at 36 to positions17 mm. with a 0.1 mm interval from the wall to 1.5 mm, a 0.5 mm interval to 7 mm, and a 1.0 mm intervalTo calibrateto 17 mm. the hot-film sensor, it was placed in the free-stream region of the water channel. The outputTo calibrate voltage the ofhot-film the sensor sensor, was it sampled was placed at 100 in the Hz free-stream for 60 s and region was referenced of the water to thechannel. indicated The outputvelocity voltage of a Nixon of the 403 Streamflosensor was Velocity sampled Meter at 100 (Nixon Hz Flowmetersfor 60 s and Ltd, was Cheltenham, referenced UK).to the A vane-typeindicated anemometer measured the velocity range from 2.5 cm/s to 1.5 m/s with an accuracy of 2%. However, velocity of a Nixon 403 Streamflo Velocity Meter (Nixon Flowmeters Ltd, Cheltenham,± UK). A vane- typethe Nixon anemometer velocity measured meter had the diffi velocityculty operating range from below 2.5 the cm/s minimum to 1.5 m/s measured with an velocity. accuracy of ±2%. However,For this the reason, Nixon thevelocity hot-film meter sensor had was difficulty traversed operating through below the channel the minimum by the stepper measured motor velocity. in still water.For The this stepper reason, motor the hot-film was initially sensor accelerated was traversed and kept through at constant the channel speed beforeby the deceleratingstepper motor at thein stillend. water. Voltage The measurements stepper motor were was obtained initially accelerated during the constant-speedand kept at constant portion speed for comparison before decelerating with the atknown the end. velocity Voltage of the measurements motor. The sensor were onobtained the motor during was the moved constant-speed through the portion channel for several comparison times at with the known velocity of the motor. The sensor on the motor was moved through the channel several times at different speeds up to 5 cm/s. The calibration velocities at an ambient temperature

J.J. Mar. Mar. Sci. Sci. Eng. Eng.2020 2020, ,8 8,, 45 x FOR PEER REVIEW 5 5 of of14 13 J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 5 of 13 were averaged and plotted against the average voltage, as shown in Figure 2. Based on the sensor weredifferent averaged speeds and up toplotted 5 cm/ s.against The calibration the average velocities voltage, at as an shown ambient in temperature Figure 2. Based were on averaged the sensor and voltages against the referenced velocities, calibration curves were fitted with the fourth-order voltagesplotted againstagainst the the average referenced voltage, velocities, as shown calibr in Figureation 2curves. Based were on the fitted sensor with voltages the fourth-order against the polynomial. polynomial.referenced velocities, calibration curves were fitted with the fourth-order polynomial. The temperature was monitored using a platinum resistance thermometer (PRT) with an TheThe temperature waswas monitored monitored using using a platinum a platin resistanceum resistance thermometer thermometer (PRT) with(PRT) an with accuracy an accuracy of ±0.01 °C. The temperature drift in our experiment was ±0.2 °C. In practice, it was accuracyof 0.01 ofC. ±0.01 The temperature °C. The temperature drift in our drift experiment in our experiment was 0.2 C. was In practice,±0.2 °C. itIn was practice, impossible it was to impossible± ◦ to generate calibration curves for all temperatures,± so◦ to process the velocity data, linear impossiblegenerate calibration to generate curves calibration for all curves temperatures, for all temp so toeratures, process so the to velocity process data, the velocity linear interpolation data, linear interpolation was used to correct the temperature effect on the calibration curve. The free-stream interpolationwas used tocorrect was used the temperatureto correct the eff temperatureect on the calibration effect on curve. the calibration The free-stream curve. velocityThe free-stream drift was velocity drift was also corrected by constantly monitoring the Nixon velocity meter. velocityalso corrected drift was by constantlyalso corrected monitoring by consta thently Nixon monitoring velocity the meter. Nixon velocity meter.

ο 20.81ο C 3.6 20.81 Cο 21.12ο C 3.6 21.12 Cο 21.45ο C 21.45 C

3.2 3.2

2.8 2.8 Hot-film voltage (V) Hot-film voltage (V) 2.4 2.4

2 2 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0 0.02 0.04 0.06Velocity0.08 (m/s) 0.1 0.12 0.14 Velocity (m/s) Figure 2. Hot-film calibration at three temperatures. FigureFigure 2. 2. Hot-filmHot-film calibration calibration at at three three temperatures. temperatures. The boundary layer over the test plate remained laminar up to at least the measurement location, TheThe boundary boundary layer layer over over the the test test plate plate remained remained laminar laminar up up to to at at least least the the measurement measurement location, location, where the boundary layer thickness δ was about 9 mm. The Reynolds number based on the distance wherewhere the the boundary boundary layer layer thickness thickness δδ waswas about about 9 9 mm. mm. The The Reynolds Reynolds number number based based on on the the distance distance 4 fromfrom thethe leadingleading edgeedge waswasRe 𝑅𝑒x ==𝑈U ∙𝑥/𝜈=4.1×10x/ν = 4.1 10 ,, wherewhere x𝑥is is the the distance distancefrom from the the leading leading from the leading edge was 𝑅𝑒 =𝑈∞∙𝑥/𝜈=4.1×10· × , where 𝑥 is the distance from the leading edgeedge (0.41 (0.41 m), m),U 𝑈is is the the free-stream free-stream velocityvelocity (0.10(0.10 mm/s),/s), andandν νis is the the kinematic kinematic viscosity viscosity of of the the water water edge (0.41 m), 𝑈 is the free-stream velocity (0.10 m/s), and ν is the kinematic viscosity of the water (1.005 × 106 m2 ∞2/s). The nondimensional velocity profile of the laminar boundary layer showed good ((1.0051.005 ×10 − mm2//s).s). The nondimensional velocity profile profile of of the the laminar laminar boundary boundary layer layer showed showed good good agreement× with the Blasius profile [43], as illustrated in Figure 3. agreementagreement with with the the Blasius Blasius profile profile [43], [43], as as illustrated illustrated in in Figure Figure 33..

3.5 3.5

3 3

2.5 2.5

* 2 δ * δ y/

y/ 1.5 1.5

1 1

0.5 0.5

0 0 0 0.2 0.4 0.6 0.8 1 1.2 0 0.2 0.4 0.6u/U 0.8 1 1.2 u/U ∞ ∞ FigureFigure 3. 3.Comparison Comparison ofof thethe experimentalexperimental datadata (closed(closed circles)circles) withwith thethe BlasiusBlasius proﬁleprofile (black(black line).line). Figure 3. Comparison of the experimental data (closed circles) with the Blasius profile (black line). ErrorError bar bar is is indicated indicated at at data data points. points. Error bar is indicated at data points.

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2.3. Hairpin Vortex Generation and Jet Control Figure4 4 shows shows thethe velocityvelocity changechange ofof thethe controlcontrol jetsjets at at thethe nozzlenozzle exitexit andand thatthat aboveabove thethe vortexvortex ring inin thethe still still water. water. The The locations locations of theof the hot-film hot-fi sensorlm sensor for measuringfor measuring the velocity the velocity were inwere the centerin the ofcenter the holeof the and hole at theand jet at nozzle the jet exit.nozzle In creatingexit. In cr vortexeating rings vortex from rings the from test plate the test through plate thethrough 5 mm the hole, 5 amm Sirai hole, S105-06 a Sirai solenoid S105-06 pinch solenoid valve pinch was valve actuated was byactu a Waveated by Factory a Wave 1976 Factory signal 1976 generator. signal generator. The valve was a two-way, normal-closure-typenormal-closure-type valvevalve withwith aa 650650 gg pinchingpinching strength.strength. The pinch valve openedopened a 5a mm5 mm clear clear C-FLEX C-FLEX® tube® tube (SAINT-GOBAIN, (SAINT-GOBAIN, Charny, Charny, France) France) when the when signal the generator signal generatedgenerator generated a square wave a square with wave a 90 mswith duration a 90 ms at duration a frequency at a frequency of 1 Hz. The of 1 red Hz. dye The initially red dye formed initially a vortexformed ring a vortex at the ring exit at of the the exit hole, of andthe thenhole, grewand th intoen grew a hairpin into vortexa hairpin with vortex cross with flow, cross as shown flow, inas Figureshown5 in. This Figure produced 5. This theproduced same vorticity the same distribution vorticity distribution around the around hairpin the structure hairpin in structure the turbulent in the boundaryturbulent boundary layer. An identicallayer. An solenoid identical pinch-valve solenoid pinch-valve system was system used to was issue used control to issue jets towardcontrol thejets hairpintoward vortices.the hairpin The vortices. valve was The opened valve was for 150 opened ms to for issue 150 jets ms through to issue a jets nozzle through to counteract a nozzle the to velocitycounteract field the at velocity the head field of the at hairpinthe head vortices. of the hairpin The jet vortices. velocity wasThe jetuJET velocity= 0.017 was m/ s𝑢 and = the 0.017 pulsing m/s wall-normaland the pulsing velocity wall-normal for creating velocity vortex for rings creating was vortexuHV = rings0.22 mwas/s in 𝑢 still = water. 0.22 m/s in still water.

Figure 4.4. Velocity changes of (a) jetjet ((u𝑢Jet)) andand ((bb)) hairpinhairpin vortexvortex ((u𝑢HV)) inin stillstill water.water. TheThe solidsolid lineline shows the velocity changechange andand thethe dotteddotted lineline showsshows thethe timingtiming ofof thethe pinchpinch valve.valve.

Figure5 5 shows shows aa sequencesequence ofof thethe developmentdevelopment of of a a hairpin hairpin vortex vortex from from a a vortex vortex ring. ring. WhenWhen thethe vortex ringring is is pumped pumped into into the the cross cross flow, flow, outbound outbound vorticity vorticity is generated is generated around around the ring. the The ring. arrows The inarrows the figure in the indicate figure the indicate vorticity the distributions vorticity dist aroundributions the hairpinaround vortex.the hairpin However, vortex. the However, upstream partthe ofupstream the vortex part ring of isthe canceled vortex byring the is incomingcanceled flowby the [44 incoming], which results flow [44], in a reductionwhich results of the in self-induceda reduction velocity.of the self-induced In contrast, velocity. the downstream In contrast, part ofthe the downst vortexream ring part develops of the into vortex the head ring ofdevelops a hairpin into vortex the ashead it is of convected a hairpin byvortex the cross as it flow.is convected This figure by th alsoe cross shows flow. the streamwiseThis figure stretchingalso shows of the the streamwise side of the vortexstretching ring of becoming the side of hairpin the vortex legs. ring Once becoming the downstream hairpin legs. part Once of the the ring downstream has moved part away of from the ring the wall,has moved it convects away faster from thanthe wall, the upstream it convects part. faster than the upstream part. Chang and Vakili [[45]45] andand SauSau andand MaheshMahesh [[46]46] studiedstudied the dynamics and trajectories of vortex rings in aa uniformuniform crosscross flowflow toto increaseincrease mixing.mixing. TheyThey concludedconcluded thatthat nono considerableconsiderable interactioninteraction occurred between neighboring vortex rings below a pinchingpinching frequency of 4 Hz for a jet-to-crossflow jet-to-crossflow velocity ratioratio ofof 3.3. InIn this this study, study, vortex vortex rings rings were were introduced introduced at aat wall-normal a wall-normal velocity velocity of 0.22 of 0.22 m/s intom/s ainto boundary a boundary layer withlayer a with free-stream a free-stream velocity velocity of 0.10m of/s. 0.10 Tominimize m/s. To minimize interference interference between successive between rings,successive the jet-to-crossflow rings, the jet-to-crossflow velocity ratio velocity was 2.2 ra andtio the was frequency 2.2 and the of producing frequency vortex of producing rings was vortex 1 Hz. rings was 1 Hz.

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Figure 5. Development of hairpin vortex from vortex ring issued through test plate in cross flow. Figure 5. Development of hairpin vortex from vortex ring issued through test plate in cross flow. FigureArrows 5. indicate Development vorticity of distribu hairpintions vortex around from the vortex hairpin ring vortex. issued through test plate in cross flow. Arrows indicate vorticity distributions around the hairpin vortex. Arrows indicate vorticity distributions around the hairpin vortex. 2.4. Vortex Vortex Control Control Methodology Methodology 2.4. Vortex Control Methodology Figure 66 illustratesillustrates thethe conceptconcept ofof directdirect interventionintervention onon hairpinhairpin vortices.vortices. TheThe blackblack squaresquare atat thethe toptop of ofFigure the the figure figure 6 illustrates is is the the jet jetthe nozzle, nozzle, concept and and of the direct the gray gray interven arro arroww indicatestion indicates on hairpin the the direction vortices. direction of The the of thecontrolblack control square jet onto jet at onto the topheadthe of head ofthe the offigure thehairpin is hairpin the vortex.jet vortex.nozzle, The and The black the black grayarrows arrows arro arw aroundound indicates the the thehairpin hairpin direction vortex vortex of theindicate indicate control the the jet vorticity onto the headdistribution. of the The Thehairpin hot-film hot-film vortex. sensor sensor The is blacklocated located arrows at at the the right rightaround top top corner.the corner. hairpin When When vortex the the vortex vortex indicate ring ring is isthe introduced introduced vorticity distribution.intointo the boundary The hot-film layer, sensor an outboundoutbound is located vorticityvorticity at the right formsforms top aroundaround corner. thethe When ring.ring. the This vortex vorticity ring is distribution introduced intocauses the a a boundaryKutta–Joukowski layer, an lift lift outbound (Magnus (Magnus effect),vorticity effect), such forms that around the downstream the ring. partThis of vorticity the vortex distribution ring tilts causesupwards a Kutta–Joukowski [44,45]. [44,45]. First, First, the the liftupwash upwash (Magnus of of low-speed effect), low-speed such velocity velocity that the in inthedownstream the center center of ofthepart the hairpin of hairpin the vortexvortex vortex ringis hit is tilts hitby upwardstheby thecontrol control [44,45]. jet. jet.Here, First, Here, we the set we upwash the set jet the velocityof jet low-speed velocity to be to velocityequal be equal in in magnitude the in magnitudecenter butof the opposite but hairpin opposite in vortex direction. in direction. is hit The by theimpingementThe control impingement jet. of Here, the of control thewe controlset jetthe on jet jet the velocity on hairpin the hairpin to vortex be equal vortex disconnects in disconnects magnitude the heads thebutheads opposite from from their in their structuresdirection. structures Theand impingementdetachesand detaches them of them from the fromcontrol the therest jet rest ofon ofthe the hairpinvortical vortical vortex stru structures.ctures. disconnects By By detaching detaching the heads the the from heads, heads, their thethe structures streamwise and detachesstretching them of of the from hairpin the legs rest is of reduced, the vortical leading stru to ctures. a reduction By detaching in vortex the circulation. heads, the This, This, streamwise in in turn, turn, stretchingreducesreduces the of downwash the hairpin of legs high-momentum is reduced, leading fluidfluid fromto a reduction the velocity in inducedinduced vortex circulation. outsideoutside thethe This, hairpinhairpin in legs.turn,legs. reduces the downwash of high-momentum fluid from the velocity induced outside the hairpin legs.

FigureFigure 6. 6. ConceptualConceptual illustration illustration of of the the control control strategy. strategy. Figure 6. Conceptual illustration of the control strategy. 3. Results Results and and Discussion Discussion 3. Results and Discussion As a part of a feasibility study for an ambitious attempt, flow ﬂow visualization and hot-film hot-ﬁlm measurementAs a part were wereof a performed performedfeasibility at study theat the laminar for laminar an boundary ambitious boun todary verifyattempt, to thatverify flow controlling thatvisualization controlling large-scale and large-scale structures hot-film measurementstructurescould cause could a cascadewere cause performed of a changes cascade in atof small-scale changesthe laminar in structures smal bounl-scaledary at thestructures to near-wall verify at thatregion.the near-wallcontrolling In thecontrol region. large-scale of In large the structurescontrolstructures, of largecould a periodic structures, cause series a cascade a of periodic hairpin of changes series vortices ofin is hairpinsmal neededl-scale vortices to achievestructures is needed precisely at the to near-wall timedachieve control. precisely region. However, Intimed the control of large structures, a periodic series of hairpin vortices is needed to achieve precisely timed

J. Mar. Sci. Eng. 2020, 8, 45 8 of 14 J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 8 of 13 control.an experimental However, configuration an experimental with configuration a hemisphere wi [47th,48 a ]hemisphere or fluid injection [47,48] through or fluid ainjection flat plate through [49–51] ahas flat produced plate [49–51] hairpin has vortexproduced structures hairpin with vortex jitters. structures with jitters. Thus,Thus, we we introduced introduced a a new new system system wherein wherein a a vortex vortex ring ring was was generated generated through through a a hole hole on on a a flat flat plate,plate, which which developed developed into into a a hairpin hairpin vortex vortex with with a a cross cross flow, flow, as as shown shown in in Figure Figure 77,, wherewhere thethe leftleft columncolumn shows shows the the no-control no-control case case and and the the right the control case. TheThe solid solid line line at at the the top top of of each each photograph photograph in in the the figure figure indicates indicates the the jet jet nozzle nozzle and and the the dotted dotted lineline in in Figure Figure 7h7h shows shows the the measurement measurement position position at at𝑥x = 4.4δ4.4, whereδ, where the thehot-film hot-film sensor sensor scanned scanned the streamwisethe streamwise velocities velocities in the in YZ the plane. YZ plane. The time The timeinterval interval between between successive successive photos photos was 0.12 was s. 0.12 The s. downstreamThe downstream part partof the of thevortex vortex ring ring developed developed into into the the head head of ofa hairpin a hairpin vortex vortex toward toward the the boundary boundary edgeedge as as it it was was being being convected convected by by the the cross cross flow flow at at the the initial initial wall-normal wall-normal velocity. velocity. In In contrast contrast to to this, this, thethe upstream upstream part part of of the the ring ring vortex vortex was was weakened weakened by bythe the interaction interaction with with the theincoming incoming flow flow in the in oppositethe opposite direction direction and remained and remained near the near wall the region. wall region. Once the Once downstream the downstream part of the part ring of themoved ring awaymoved from away the from wall, the it convected wall, it convected faster than faster the than upstream the upstream part due part to duethe higher to the highermean velocity. mean velocity. As a result,As a result, the upstreamthe upstream part partexperienced experienced a stretching a stretching and and intensification intensification process. process. Then, Then, the the control control jet jet hithit the the head head of of the the hairpin hairpin vortex, vortex, as as shown shown on on the the right right side side of of Figure Figure 7d,7d, and the interaction between thethe control control jet jet and hairpin vortex continuedcontinued afterwards.afterwards. ThisThis flowflow visualizationvisualization shownshown inin Figure Figure7 f–h7f– hdemonstrates demonstrates that that the the head head of of the the hairpin hairpin vortex vortex was was being being disconnected disconnected from from the the rest rest of of structure. structure.

FigureFigure 7. 7. TimeTime series series of of the the flow ﬂow visualization visualization of of the the no-c no-controlontrol case case (left (left column) column) and and that that with with control control (right(right column) column) at at 𝑥x = =4.4 4.4𝛿δ indicated indicated inin ((hh),), withwith thethe dotteddotted line indicating the position position of of the the hot-film hot-ﬁlm sensorsensor for for scanning scanning the the YZ YZ plane. plane. (a (a) )vortex vortex ring ring created created on on the the left left corner; corner; ( (bb––dd)) hairpin hairpin vortex vortex developmentdevelopment reaching reaching to to boundary boundary edge; edge; ( e––h)) streamwise streamwise stretching process of legs.

FigureFigure 8 shows the phase-locked averaged velocity fluctuations ﬂuctuations in the the YZ YZ plane plane at at 𝑥x = =4.4 4.4𝛿δ,, with with thethe left left column column showing showing the the no-control no-control case case and and th thee right right column column the the control control case. The The time time interval interval betweenbetween successive successive photos photos was was 0.05 0.05 s. s.

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Figure 8. Phase-locked averaged velocity ﬂuctuationsfluctuations of the YZ plane at xx == 4.4δ, as indicated by the dotted line in the last ﬁgurefigure ofof FigureFigure7 7.. InducedInduced highhigh (white)(white) andand lowlow (black) (black) momentummomentum towardstowards near-wall: ( a,b) by vorticity of neck part; (c,d) by vorticity of leg part.

In Figure8a, the white patches indicate the increased velocity fluctuations caused by the wallward In Figure 8a, the white patches indicate the increased velocity fluctuations caused by the (sweep) motion outside the hairpin vortex, and the black patches indicate the decreased velocity wallward (sweep) motion outside the hairpin vortex, and the black patches indicate the decreased fluctuations by the upwash (ejection) motion inside the hairpin vortex. As time elapsed, the vortex velocity fluctuations by the upwash (ejection) motion inside the hairpin vortex. As time elapsed, the legs passed through the measurement position so that their high velocities were approaching the vortex legs passed through the measurement position so that their high velocities were approaching wall, thereby increasing the skin friction. The measured velocity fluctuations correspond to those the wall, thereby increasing the skin friction. The measured velocity fluctuations correspond to those in Figure7e, although the visualization results indicate the hairpin vortex structure itself with dye. in Figure 7e, although the visualization results indicate the hairpin vortex structure itself with dye. Therefore, thethe hairpinhairpin vortexvortex structure structure would would exist exis betweent between the the low low and and high high velocity velocity fluctuations. fluctuations. In FigureIn Figure8d, it8d, can it becan clearly be clearly seen thatseen as that soon as assoon the controlas the control jet hit the jet headhit the of thehead hairpin of the vortex,hairpin both vortex, the low-both andthe low- high-velocity and high-velocity fluctuations fluctuations were reduced were and reduced this also and aff ectedthis also the affected legs as shown. the legs We as consider shown. thatWe consider the jet stopped that the the jet stretching stopped andthe stretching intensification and ofintensification the legs by breaking of the legs the linkby breaking between the legslink andbetween the head, the legs thereby and the reducing head, thereby the velocity reducing fluctuations. the velocity fluctuations. Ensemble-averaged velocity fluctuations fluctuations were usedused to reconstruct a three-dimensionalthree-dimensional hairpin vortex. Figure 99 showsshows thethe isosurfacesisosurfaces ofof streamwisestreamwise velocityvelocity fluctuations,fluctuations, whereinwherein velocitiesvelocities higherhigher than thethe meanmean velocityvelocity areare in in red red and and lower lower velocities velocities are are in in blue. blue. Red Red color color indicates indicates the the isosurface isosurface of u/U = 2.7% and blue color indicates that of u/U = 8.2%. of u∞/U∞ = 2.7% and blue color indicates that of u/∞U∞ =− −8.2%. In FigureFigure9 a,9a, the the hairpin hairpin vortex vortex colored colored dark dark gray gray is located is located between between the low-speed the low-speed and high-speed and high- velocities.speed velocities. The hairpin The hairpin vortex vortex drew the drew low-speed the low-speed fluids fromfluids the from wall the by wall pumping by pumping between between its legs, whileits legs, inducing while high-speedinducing high-speed fluids around fluids the hairpinaround vortex.the hairpin Here, thevortex. hairpin Here, vortex the structurehairpin vortex can be detectedstructure bycan a be marker detected function by a marker defined function by Equation defined (1) as by follows: Equation (1) as follows: s !2 !2 𝜕∂〈𝑢u〉 ∂𝜕〈u𝑢〉 ΨΨ == h i ++ h i (1)(1) hp 𝜕𝑧∂z ∂𝜕𝑦y where 〈u𝑢〉denotes denotes the the ensemble-averaged ensemble-averaged streamwise streamwise velocity velocity fluctuation. fluctuation. h i Thus, the detected vortical structure waswas revealedrevealed withwith thethe markermarker functionfunction ΨΨhphp = 420. Hutchins [52] [52] devised the marker marker function function Ψhp by by squaringsquaring thethe vorticityvorticity componentscomponents in terms of the spatial gradient of the streamwise velocity. However, this marker function only works in and around near-wallnear-wall turbulentturbulent structures, structures, where where the the streamwise streamwise velocity velocityu is u stronglyis strongly correlated correlated with with the ∂w ∂v negativethe negative wall-normal wall-normal velocity velocity–v. The–𝑣. The streamwise streamwise vorticity vorticity is defined is defined as ω asx =ωx( = ( −), where), wherew isw ∂y − ∂z spanwise velocity. This does not involve the streamwise velocity. However, ejection ( u and +v) and is spanwise velocity. This does not involve the streamwise velocity. However, ejection− (−u and +v) sweep (+u and v) events are highly correlated in the near-wall region, so that wall-normal velocity is and sweep (+u− and −v) events are highly correlated in the near-wall region, so that wall-normal velocity is replaced by streamwise velocity, where streamwise vortices are predominant. Thus, the

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J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 10 of 13 replaced by streamwise velocity, where streamwise vortices are predominant. Thus, the streamwise ∂w ∂( u) ∂u ) streamwisevorticity can vorticity be simpliﬁed can be as simplifiedωx = ( as −ωx )= ( .− In the) same. process, In the same wall-normal process, vorticity wall-normal can be ∂y − ∂z ≈ ∂z ∂u ∂w ∂u ∂v ∂u ∂u vorticitygiven as canωy =be( given as) ωy = (as well− ) as spanwise as well vorticity as spanwiseωz= (vorticity) ωz= ( . − )− . ∂z − ∂x ≈ ∂z ∂x − ∂y ≈ − ∂y

FigureFigure 9. 9. IsosurfacesIsosurfaces of of ensemble ensemble averaged averaged streamwise streamwise velocity velocity fluctuations. ﬂuctuations. (a) No (a) control No control and and(b) control.(b) control.

WeWe obtainedobtained the the streamwise streamwise length length from from the time-series the time-series data using data Taylor’s using frozen-ﬂowTaylor’s frozen-flow hypothesis hypothesisby taking theby free-streamtaking the free-stream velocity as velocity the convection as the velocity.convection The velocity. length The scales length were scales normalized were + = + normalizedby the viscous by the wall viscous unit, lwall unit,l uτ/ ν𝑙 , with=𝑙∙𝑢uτ/𝜈=, 0.0045with 𝑢 m / =s. 0.0045 The hairpinm/s. The vortex hairpin was vortexx was200 𝑥 long, + + · ≈ y 60 high,𝑦 and z 25 wide,𝑧 which is similar to the vortex size shown in Figure7. With the control 200 ≈long, 60 high,≈ and 25 wide, which is similar to the vortex size shown in Figure 7. Within Figure the control9, the control in Figure jet counteracted 9, the control and jet weakenedcounteracted the and upwash weakened motion the within upwash the hairpinmotion within vortex. theThe hairpin area of vortex. low-speed The velocityarea of low-speed was reduced velocity up to was 40% reduced compared up with to 40% the compared no-control with case the and no- the controlhigh-speed case areaand the was high-speed also decreased. area Thewas redalso patch decre pointedased. The by red a black patch arrow pointed in Figure by a black9b was arrow caused in Figureby the 9b penetration was caused of theby jetthe towardpenetration the wall, of the because jet toward the jet the velocity wall, because was slightly the jet higher velocity than was the slightlyupwash higher velocity. than the upwash velocity. TheThe main main cause cause of of the the skin skin friction friction with with emb embeddededded hairpin hairpin vortices vortices is is the the vorticity vorticity increase increase associatedassociated with with the the stretching stretching legs, legs, which which bring bring cont continuouslyinuously high high velocity velocity to to the the wall. Figure Figure 1010 comparescompares the the circulation circulation around around the the hairpin hairpin structure structure with with and and without without control. control. To To determine determine the the effecteﬀect of thethe control control jet jet in reducingin reducing the skinthe skin friction friction of the of hairpin the hairpin vortex, thevortex, circulation the circulation was computed was ω = ( ∂ω ∂v ) computedby integrating by integrating the streamwise the streamwise vorticity, vorticity,x ∂y ω ∂z=. Due− to) the. Due fact to that the thefact streamwisethat the streamwise vorticity − vorticity ω is proportional to 𝜕𝑢/𝜕𝑧, the total circulation Γ around the hairpin vortex structure was calculated by integrating the streamwise vorticity ω over the cross-sectional area. The control

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J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 11 of 13 ωx is proportional to ∂u/∂z, the total circulation Γx around the hairpin vortex structure was calculated byjet integrating targeted the the neck streamwise and head vorticity part of ωhairpinx over vortex the cross-sectional at 225 ≤ x+ ≤ area.300 and The suppressed control jet the targeted circulation the neckaround and headthem. part As ofthe hairpin head vortexdetaches at 225 fromx +the 300rest andof the suppressed vortical thestructure, circulation the aroundstretching them. and ≤ ≤ Asintensifying the head detaches process from of the the legs rest ofis thereduced vortical at structure,45 ≤ x+ ≤ the200. stretching In other andwords, intensifying the reduction process inof the thecirculation legs is reduced leads at to 45 a decreasex+ 200. in In the other downwash words, the of reduction high-momentum in the circulation fluid outside leads to the a decrease legs. The ≤ ≤ incirculation the downwash relating of high-momentum to the wallward ﬂuidmomentum outside of the induced legs. The flow circulation by the legs relating was toreduced the wallward by up to momentum60%. of induced ﬂow by the legs was reduced by up to 60%.

FigureFigure 10. 10.Comparison Comparison of of the the circulation circulation along along the the streamwise streamwise direction. direction. No No control control (open (open circle) circle) and and controlcontrol (closed (closed triangle) triangle) cases. cases.

4. Conclusions 4. Conclusions The first objective of this study was to create a single hairpin vortex in a laminar boundary layer. The first objective of this study was to create a single hairpin vortex in a laminar boundary layer. To do so, a vortex ring issuing through a hole on a flat plate was used to generate a hairpin vortex. To do so, a vortex ring issuing through a hole on a flat plate was used to generate a hairpin vortex. In the flow visualization results, once a vortex ring pulsed into the cross flow, it developed a hairpin In the flow visualization results, once a vortex ring pulsed into the cross flow, it developed a hairpin vortex structure. Next, a direct control strategy was applied to target the hairpin vortex with a view to vortex structure. Next, a direct control strategy was applied to target the hairpin vortex with a view reducing the skin friction. It was observed in both the flow visualization and hot-film measurement to reducing the skin friction. It was observed in both the flow visualization and hot-film measurement that the control jet from a nozzle disconnected the link between the vortex head and its legs, which that the control jet from a nozzle disconnected the link between the vortex head and its legs, which diminished the velocity fluctuations. This meant that the control jet disconnected the head from the diminished the velocity fluctuations. This meant that the control jet disconnected the head from the vortex shoulders and detached it from the rest of the vortical structure. As a result, the circulation vortex shoulders and detached it from the rest of the vortical structure. As a result, the circulation around the legs was reduced. This, in turn, decreased the downwash of high-momentum fluid outside around the legs was reduced. This, in turn, decreased the downwash of high-momentum fluid the legs. outside the legs. Based on Taylor’s frozen-flow hypothesis and the marker function, the ensemble averaged velocity Based on Taylor’s frozen-flow hypothesis and the marker function, the ensemble averaged fluctuationsvelocity fluctuations revealed a revealed three-dimensional a three-dimensional hairpin vortex hairpin structure vortex between structure the between positive the and positive negative and velocitynegative fluctuations. velocity fluctuations. This enabled This a demonstration enabled a demonstration of how the control of how jet etheffectively control destroyed jet effectively the hairpindestroyed vortex the structure. hairpin Avortex comparison structure. of theA comparis circulationson wasof the made, circulations based on was the streamwisemade, based vortex on the ωx, which showed that the circulation by the legs was reduced by up to 60%. We speculate that the streamwise vortex ω, which showed that the circulation by the legs was reduced by up to 60%. We weakenedspeculate vorticity that the caused weakened the reduction vorticity in caused skin friction the reduction by decreasing in skin the friction high momentum by decreasing toward the thehigh wall.momentum The total toward skin-friction the wall. reduction The total could skin-friction be adjusted reduction depending could on the be frequencyadjusted depending with which on the the hairpinfrequency vortices with were which targeted. the hairpin If the vortices hairpin vorticeswere targ wereeted. generated If the hairpin and controlledvortices were more generated frequently, and it wouldcontrolled be expected more frequently, that the reduction it would in thebe expected friction drag that could the reduction be increased. in the In addition, friction ifdrag the controlcould be jetincreased. was exactly In matched addition, with if thethe upwashcontrol velocity,jet was greaterexactly reduction matched wouldwith the be expected. upwash Thisvelocity, study greater was conductedreduction as would a preliminary be expected. work This for an study investigation was conducted of large-scale as a preliminary turbulent-boundary-layer work for an investigation control. of large-scale turbulent-boundary-layer control.

Author Contributions: Conceptualization, Y.-D.K.; methodology, B.K. and Y.-D.K.; software, B.K. and Y.-D.K.; validation, Y.-D.K.; data curation, B.K. and Y.-D.K.; writing—original draft preparation, B.K.; writing—review and editing, Y.-D.K.; visualization, Y.-D.K. All authors have read and agreed to the published version of the manuscript.

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