Delgado, A.

Frohnapfel, B.

Jovanovic, J.

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Viscous Drag Reduction withSurface-Embedded GroovesJovan Jovanović , Bettina Frohnapfel and Antonio DelgadoAbstract Turbulent drag reduction in wall-bounded flows is investigated ex-perimentally by considering the dynamic effects provoked by large variation ofanisotropy in the velocity fluctuations. It is shown that high drag reduction is ob-tained when the velocity fluctuations near the wall reach thestatistically axisym-metric state with invariance under rotation about the axis aligned with the meanflow. Deductions based on the analysis of near-wall turbulence leads to the designof the grooved surface topology, for which it is demonstrated experimentally thatcan produce a maximum drag reduction of DR≃ 25%. The drag reduction effectpersisted in a narrow range of flow velocities and for the repoted experimental con-ditions correspond to groove dimensions of about 0.8 viscoulength-scale.1 IntroductionA significant portion of the drag which counteracts the motion of a body through afluid is generated in the thin viscous region close to the solid boundary where theflow is nearly always turbulent. The viscous contribution tothe total drag amountsto about 50% on commercial aircraft, 90% on underwater vehicl s and almost 100%for pipe and channel flows [1]. If we consider current trends in the crude oil prices,worldwide expansion of public transport and initiatives for reduced pollution of theJovan JovanovićInstitute of Fluid Mechanics, Friedrich-Alexander University Erlangen-Nuremberg, Germany,e-mail: jovan.jovanovic@lstm.uni-erlangen.deBettina FrohnapfelCenter of Smart Interfaces, Darmstadt University of Technology, Petersenstraße 32,64287 Dratmstadt, Gremany, e-mail: frohnapfel@csi.tu-darmstadt.deAntonio DelgadoInstitute of Fluid Mechanics, Friedrich-Alexander University Erlangen-Nuremberg, Germany,e-mail: antonio.delgado@lstm.uni-erlangen.de12 Jovan Jovanović , Bettina Frohnapfel and Antonio Delgadoenvironment, the beneficial outcomes of reducing viscous drag and therefore energyconsumption are obvious. The fluid mechanics community is desperately searchingfor practical solutions in order to satisfy the expectations f society using all toolsand techniques available, but practically no success has been achieved so far.IIaIIIawallchannelcenterlineone-componentturbulenceaxisymmetricturbulencetwo-componentturbulencetwo-componentisotropic turbulenceisotropic turbulenceFig. 1 Anisotropy-invariant map according to Lumley [2] with the trajectory of a turbulent chan-nel flow (in red). The arrow ”wall” marks the position of the turb lence state at the wall. A move-ment of this point towards the upper right-hand corner (one-component turbulence) along the two-component line marks increasing anisotropy of turbulence as it is commonly found for a variety ofdifferent drag reduced flows.2 The Mechanism of Turbulent Drag ReductionThe origin of turbulence in wall-bounded flows can be analyzed by looking into theevolution of anisotropy in the turbulent stressesuiu j, which can be quantified us-ing the anisotropy tensor ([2]) defined asi j = uiu j/q2−1/3δi j (whereq2 = usus)and its scalar invariants IIa = ai ja ji and IIIa = ai ja jkaki. A plot of IIa versus IIIa foraxisymmetric turbulence, IIa = 3/2(4/3|III a|)2/3, and two-component turbulence,IIa = 2/9+2IIIa, defines the anisotropy-invariant map shown in figure 1 whichbounds all physically realizable turbulence ([2]). The twocurves in this figure rep-resent axisymmetric turbulence. The right-hand curve corresponds to turbulencewith the streamwise intensity component larger than in the other two directions,u21 > u23 = u22 (III a > 0), and the left-hand curve corresponds to axisymmetric turbu-Viscous Drag Reduction with Surface-Embedded Grooves 3lence withu21 < u23 = u22 (III a < 0). Along the straight line resides two-componentturbulence. The limiting states of turbulence are located athe corner points on theright- and left-hand sides of the anisotropy-invariant mapand correspond to one-component turbulence and isotropic two-component turbulence, respectively.In [3] and [4] it was shown that turbulent drag reduction is asociated with anincrease of the anisotropy of turbulence in the near-wall region for a number of dif-ferent flow control techniques. In this region, where the continuity equation and ano-slip boundary condition at the wall dictate turbulence to be two-componental,the turbulence anisotropy is directly proportional to the ratio between streamwise(u21) and spanwise (u23) stress components: with the streamwise component gen-erally larger than the spanwise one. The increase of turbulence anisotropy, whichcan be captured in the anisotropy-invariant map as shown in figure 1, is most nat-urally achieved with a suppression of the spanwise stress components which cor-responds to forcing turbulence to satisfy axisymmetry simultaneously at large andsmall scales very close to the wall with invariance under rotati n about the axisaligned with the mean flow [3].Fig. 2 Turbulent dissipation rate at the wall(ε)wall normalized with the wall shear velocity and thekinematic viscosity of the flow medium versus the anisotropyf turbulence at the wall(IIa)wall.A best-fit line through the numerical data extrapolates fairly well the expected trend as the one-component limit (II=2/3) is approached [3].4 Jovan Jovanović , Bettina Frohnapfel and Antonio DelgadoFor this special situation theoretical considerations andnumerical simulationsshow that the dissipation rate must vanish at the wall,εwall → 0 ([3]). This funda-mental deduction, which is displayed figure 2, implies that as long as turbulenceassume the one-component state at the wall the energy of turbulence (k = 1/2q2)cannot be amplified sincek grows ask → (εwall/ν)x22/2 as the wall is approached,x2 → 0. Under such circumstances, the averaged total energy dissipation rateΦ:1V∫VI︷ ︸︸ ︷ν(∂U i∂x j+∂U j∂xi)∂U i∂x j+II︷ ︸︸ ︷ν(∂ui∂x j+∂u j∂xi)∂ui∂x j︸ ︷︷ ︸ΦdV =AwτwUBρV, (1)which is composed of the direct dissipation (I) and the turbulent dissipationε (II)and which can be evaluated from the work done against the wallshears stressτw perunit mass of the working fluidρV , whereAw is the wetted surface area andUB isthe bulk velocity, assumes a minimum at sufficiently high Reynolds numbers and alarge drag reduction must occur as a logical consequence. This expectation resultsfrom an order of magnitude analysis, which shows that the largest contribution toΦis due to the turbulent dissipation, which reaches a maximumvalue at the wall.3 Experimental Investigations3.1 Grooved Surface TopologyA surface topology with grooves embedded in the wall and aligned in the streamwisedirection as shown in figure 3 was designed. Inside a groove, the velocity fluctua-tions are suppressed not only in the normal but also in the spanwise direction dueto the side walls and therefore it is expected that turbulence i the groove will tendtoward the one-component limit at the wall. Direct numerical simulations confirmthat such turbulence is almost axisymmetric with invariance to rotation about theaxis aligned with the mean flow direction [5].A grooved surface pattern was produced by milling grooves into flat metal platesand subsequent polishing of the plates. Groove dimensions of h ≈ 150µm with aseparation of 2h ≈ 300µm were produced in metal plates of the dimensions 1.5m×0.3m which served as replacement for the smooth top and bottom walls of a two-dimensional channel flow facility shown in figure 4.Viscous Drag Reduction with Surface-Embedded Grooves 52hgroovesx1x3x2x = 02x = 02hhFig. 3 Inside the grooves the flow is forced towards the one-component limit. Sketched are trajec-tories across the anisotropy-invariant maps for each portion of the surface.3.2 Channel Test RigThe channel flow facility is driven by a centrifugal blower. The air stream is guidedthrough a well-designed settling chamber to ensure uniformflow condition at thechannel inlet. On the suction side of the blower, a Venturi nozzle was located, whichallowed the determination of the volume flow rate. The channel its lf is L = 3.5mlong andB = 300mm wide and can be adjusted to heights ofH = 25, 35and41mm.At the channel inlet a trip is installed to ensure turbulent flow conditions and re-producible results at low Reynolds number. After the trip, alength of 0.7m is pro-vided for the flow development, which corresponds tox1/H = 28.0, 20.0and17.0,respectively. The following 2.8m of the channel comprise the test section which isequipped with 14 pressure taps of 300µm diameter at intervals of 200mm locatedon both of the channel side walls. For the determination of the pressure drop over thechannel length, the static pressure at the first measuring station (i.e. the one closestto the inlet of the channel) is compared with readings from subsequent measuringstations.The test section is divided into two parts of equal length. Ineach part of the testsection, the top and bottom walls are interchangeable so that smooth and groovedchannel walls can be installed. To evaluate the drag reduction performance of thesurface grooves, the pressure drop in a channel with and without grooves needs tobe compared. To ensure identical operating conditions for both cases, an in line set-up is chosen in which one part of the test section has smooth walls hile the secondpart is equipped with grooved walls. Based on pressure drop measurements in thesubsequent parts of the test section, drag reduction is evaluated according to:DR = 1−(∆ p/∆ l)grooved(∆ p/∆ l)smooth. (2)6 Jovan Jovanović , Bettina Frohnapfel and Antonio Delgado123413dT2T10.23500H = 0.0251H = 0.0352H0.3temperaturegrooved surfacechannel cross sectionsmooth surfacehot wiretripout- +pressure scannerintegrating DVHöntzschpressure transducerDISA55D31outE~ pDout:,eECTAamplifierintegrating DVFig. 4 Experimental set up and instrumentation used for drag reduction and turbulence measure-ments.The grooved walls can either be inserted at the beginning or the end of the channeltest section. In preliminary measurements it was established t at the arrangement ofgrooved top and bottom walls followed by smooth ones yields the more conservativeestimate of drag reduction. Therefore, measurements are carri d out in this set-up.Further details on the measurement facility and measurement accuracy can be foundin [6].3.3 Experimental ResultsThe set of drag reduction measurements was carried out for the channel heights ofH = 25, 35and41mm with groove dimension ofh ≈ 150µm. Figure 5 shows alldrag reduction data obtained. These measurements were carri d out in a Reynoldsnumber range ofReb ≈ 1000-45000. Over a wide range of Reynolds number themeasured drag reduction deduced from pressure drop measurements is within thelimit of the measurement accuracy. However, in very narrow range of flow velocitiesfor three channel heights significant drag reduction of up to25% are detected. Thedrag reduction data collapse if plotted versus the dimensionless groove sizeh+ =huτ/ν and show a common peak for a dimensionless groove size ofh+ ≈ 0.8. Forgrooves withh≈ 150µm the corresponding Reynolds number where drag reductionoccurs is in the range ofReb = 2300−3200.Ongoing experimental investigations of drag reduction by flow control of ve-locity fluctuations in the near-wall region of naturally developing boundary layersusing surface embedded groves show that the drag reduction effect can be evenincreased at high Reynolds numbers [7]. These results support indirectly the mech-Viscous Drag Reduction with Surface-Embedded Grooves 7-50510152025h+DR [%]350.5 1 10H=25mmH=35mmH=41mmSSFig. 5 Drag reduction versus dimensionless groove dimension for different heights of the channeltest section(right).anism responsible for laminar to turbulence transition andbreakdown to turbulenceelaborated by the authors [8], [9].This work was sponsored by grant Jo 240/5-1 from the DeutscheForschungsge-meinschaft. The authors gratefully acknowledge this support.References1. Lee, K.H., Cortelezzi, L., Kim, J., Speyer J.: Application f reduced-order controller to tur-bulent flows for drag reduction.Phys. Fluids 13, 1321, 2001.2. Lumley, J.L.: Computational modelling of turbulent flows. Adv. Appl. Mech. 18, pp. 123-176,1978.3. Jovanović, J., Hillerbrand, R.: On the peculiar property of the velocity fluctuations in wall-bounded flows.Thermal Science 9, pp. 3-12, 2005.4. Frohnapfel, B., Lammers, P., Jovanović, J., Durst, F.: Interpretation of the mechanism asso-ciated with turbulent drag reduction in terms of anisotropyinvariants.J. Fluid Mech. 577:457-466, 2007.5. Frohnapfel, B.: Flow control of near-wall turbulence. PhD thesis, University Erlangen-Nuremberg, Shaker Verlag, Aachen, 2007.6. Frohnapfel, B., Jovanović, J., Delgado, A.: Experimental investigation of turbulent drag re-duction by surface embedded grooves.J. Fluid Mech. 590: 107-116, 2007.7. Jovanović, J., Frohnapfel, B. and Lienhart, H.: Furtherm asurments of viscous drag reductionin a groove-modified channel flow. To be submitted toJ. Fluid Mech., 2009.8. Jovanović, J. and Pashtrapanska, M.: On the criterion for the determination transition onsetand breakdown to turbulence in wall-bounded flows.J. Fluids Eng., 126, 626–633, 2004.9. Jovanović, J., Frohnapfel, B.,Škaljić, E. and Jovanović, M.: Persistence of the laminarregimein a flat plate boundary layer at very high Reynolds number. Thermal Science,10, 63–96,2006.

Viscous drag reduction with surface-embedded grooves

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Viscous drag reduction with surface-embedded grooves

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