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Research Papers: Fundamental Issues and Canonical Flows

Drag Reduction Due to Streamwise Grooves in Turbulent Channel Flow

[+] Author and Article Information
C. T. DeGroot

Mem. ASME
Department of Mechanical
and Materials Engineering,
Western University,
London, ON N6A 5B9, Canada
e-mail: cdegroo5@uwo.ca

C. Wang

Department of Mechanical
and Materials Engineering,
Western University,
London, ON N6A 5B9, Canada;
The 41st Institute,
The Fourth Academy of CASC,
Xi'an 710025, China
e-mail: chencong0269@163.com

J. M. Floryan

Fellow ASME
Department of Mechanical
and Materials Engineering,
Western University,
London, ON N6A 5B9, Canada
e-mail: mfloryan@eng.uwo.ca

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received October 5, 2015; final manuscript received June 28, 2016; published online August 17, 2016. Assoc. Editor: Riccardo Mereu.

J. Fluids Eng 138(12), 121201 (Aug 17, 2016) (10 pages) Paper No: FE-15-1720; doi: 10.1115/1.4034098 History: Received October 05, 2015; Revised June 28, 2016

Drag reduction in turbulent channel flows has significant practical relevance for energy savings. Various methods have been proposed to reduce turbulent skin friction, including microscale surface modifications such as riblets or superhydrophobic surfaces. More recently, macroscale surface modifications in the form of longitudinal grooves have been shown to reduce drag in laminar channel flows. The purpose of this study is to show that these grooves also reduce drag in turbulent channel flows and to quantify the drag reduction as a function of the groove parameters. Results are obtained using computational fluid dynamics (CFD) simulations with turbulence modeled by the k–ω shear-stress transport (SST) model, which is first validated with direct numerical simulations (DNS). Based on the CFD results, a reduced geometry model is proposed which shows that the approximate drag reduction can be quantified by evaluating the drag reduction of the geometry given by the first Fourier mode of an arbitrary groove geometry. Results are presented to show the drag reducing potential of grooves as a function of Reynolds number as well as groove wave number, amplitude, and shape. The mechanism of drag reduction is discussed, which is found to be due to a rearrangement of the bulk fluid motion into high-velocity streamtubes in the widest portion of the channel opening, resulting in a change in the wall shear stress profile.

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References

Kim, J. , 2011, “ Physics and Control of Wall Turbulence for Drag Reduction,” Philos. Trans. R. Soc., A, 369(1940), pp. 1396–1411. [CrossRef]
Choi, H. , Moin, P. , and Kim, J. , 1994, “ Active Turbulence Control for Drag Reduction in Wall-Bounded Flows,” J. Fluid Mech., 262, pp. 75–110. [CrossRef]
Quadrio, M. , 2011, “ Drag Reduction in Turbulent Boundary Layers by In-Plane Wall Motion,” Philos. Trans. R. Soc., A, 369(1940), pp. 1428–1442. [CrossRef]
Choi, K. , Jukes, T. , and Whalley, R. , 2011, “ Turbulent Boundary-Layer Control With Plasma Actuators,” Philos. Trans. R. Soc., A, 369(1940), pp. 1443–1458. [CrossRef]
Walsh, M. J. , 1979, “ Riblets as a Viscous Drag Technique,” AIAA J., 17(7), pp. 770–771. [CrossRef]
Walsh, M. J. , 1980, “ Drag Characteristics of V-Groove and Transverse Curvature Riblets,” Proceedings of the Symposium on Viscous Flow Drag Reduction, Dallas, TX, Nov. 7–8, pp. 168–184.
Walsh, M. J. , 1983, “ Riblets as a Viscous Drag Technique,” AIAA J., 21(4), pp. 485–486. [CrossRef]
Mohammadi, A. , and Floryan, J. M. , 2013, “ Groove Optimization for Drag Reduction,” Phys. Fluids, 25(11), p. 113601. [CrossRef]
Mohammadi, A. , and Floryan, J. M. , 2013, “ Pressure Losses in Grooved Channels,” J. Fluid Mech., 725, pp. 23–54. [CrossRef]
Mohammadi, A. , and Floryan, J. M. , 2015, “ Numerical Analysis of Laminar-Drag-Reducing Grooves,” ASME J. Fluids Eng., 137(4), p. 041201. [CrossRef]
Moody, L. F. , 1944, “ Friction Factors for Pipe Flow,” Trans. ASME, 66(8), pp. 671–684.
García-Mayoral, R. , and Jiménez, J. , 2011, “ Drag Reduction by Riblets,” Philos. Trans. R. Soc. A, 369(1940), pp. 1412–1427. [CrossRef]
Szodruch, J. , 1991, “ Viscous Drag Reduction on Transport Aircraft,” AIAA Paper No. 91-0685.
Bechert, D. W. , Bruse, M. , Hage, W. , Hoeven, J. G. T. V. D. , and Hoppe, G. , 1997, “ Experiments on Drag-Reducing Surfaces and Their Optimization With an Adjustable Geometry,” J. Fluid Mech., 338(5), pp. 59–87. [CrossRef]
Itoh, M. , Tamano, S. , Iguchi, R. , Yokota, K. , Akino, N. , Hino, R. , and Kubo, S. , 2006, “ Turbulent Drag Reduction by the Seal Fur Surface,” Phys. Fluids, 18(6), p. 065102. [CrossRef]
Rothstein, J. P. , 2010, “ Slip on Superhydrophobic Surfaces,” Annu. Rev. Fluid Mech., 42(1), pp. 89–109. [CrossRef]
Mohammadi, A. , and Floryan, J. M. , 2012, “ Mechanism of Drag Reduction by Surface Corrugation,” Phys. Fluids, 24(1), p. 013602. [CrossRef]
Floryan, J. M. , 1997, “ Stability of Wall-Bounded Shear Layers in the Presence of Simulated Distributed Surface Roughness,” J. Fluid Mech., 335, pp. 29–55. [CrossRef]
Floryan, J. M. , 2007, “ Three-Dimensional Instabilities of Laminar Flow in a Rough Channel and the Concept of Hydraulically Smooth Wall,” Eur. J. Mech. (B/Fluids), 26(3), pp. 305–329. [CrossRef]
Mohammadi, A. , Moradi, H. V. , and Floryan, J. M. , 2015, “ New Instability Mode in a Grooved Channel,” J. Fluid Mech., 778, pp. 691–720. [CrossRef]
Wilcox, D. C. , 1998, Turbulence Modelling for CFD, 2nd ed., DCW Industries, La Cañada, CA.
ANSYS, 2010, “ ANSYS FLUENT 13.0 Theory Guide,” ANSYS, Inc., Canonsburg, PA.
Menter, F. R. , 1994, “ Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications,” AIAA J., 32(8), pp. 1598–1605. [CrossRef]
Menter, F. R. , 2011, “ Turbulence Modeling for Engineering Flows,” White paper, ANSYS Inc., Canonsburg, PA.
Celik, I. B. , Ghia, U. , Roache, P. J. , Frietas, C. J. , Coleman, H. , and Raad, P. E. , 2008, “ Procedure for Estimation and Reporting of Uncertainty Due to Discretization in CFD Applications,” ASME J. Fluids Eng., 130(7), p. 078001. [CrossRef]
Chen, Y. , Floryan, J. M. , Chew, Y. T. , and Khoo, B. C. , 2016, “ Groove-Induced Changes in Discharge in Channel Flow,” J. Fluid Mech., 799, pp. 297–333. [CrossRef]
Kim, J. , Moin, P. , and Moser, R. , 1987, “ Turbulence Statistics in Fully Developed Channel Flow at Low Reynolds Number,” J. Fluid Mech., 177, pp. 133–166. [CrossRef]
Orszag, S. A. , 1970, “ Analytical Theories of Turbulence,” J. Fluid Mech., 41(02), pp. 363–386. [CrossRef]
Gibbs, J. W. , 1898, “ Fourier's Series,” Nature, 59(1522), p. 200. [CrossRef]
Gibbs, J. W. , 1899, “ Fourier's Series,” Nature, 59(1539), p. 606. [CrossRef]
Hunter, J. D. , 2007, “ Matplotlib: A 2D Graphics Environment,” Comput. Sci. Eng., 9(3), pp. 90–95. [CrossRef]

Figures

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Fig. 1

A schematic diagram showing a channel bounded by grooved upper and lower walls with average positions y=±1

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Fig. 2

Plot of the groove geometries and their relevant dimensions

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Fig. 3

Plot of the sinusoidal groove geometry with grooves on both the upper and lower walls. For the upper groove geometry, the solid line represents the in-phase or “wavy-walled channel,” while the dashed line represents the out-of-phase or “converging–diverging” channel.

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Fig. 4

Plot of DNS and RANS results for the change in discharge flow rate for a grooved channel with sinusoidal grooves on both walls (S = 0.5) in the out-of-phase position (β=π) in comparison to the smooth channel at Reτ=180

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Fig. 5

Plot of the friction factor modification as a function of Reynolds number for sinusoidal grooves on the lower wall with S = 1.0 and α=0.4 and for sinusoidal grooves on both walls with S = 0.75 and α=0.4

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Fig. 6

Contour plots of the streamwise velocity component in an yz-plane for Reynolds numbers of (a) 10,000, (b) 20,000, and (c) 30,000 with S = 0.75 and α=0.4 with grooves on both walls

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Fig. 7

Parity plot of the friction factor modification for reduced geometries, f′reduced, in comparison to the friction factor modification for actual geometries, f′actual, at Reynolds number Re = 2648 (Reτ=180). Dashed lines indicated the points where f′reduced=f′actual as well as the error bands where the friction factor modification is over- or under-estimated by 0.05 when considering the reduced geometry model.

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Fig. 8

Plot of the friction factor modification, f′, for sinusoidal grooves as a function of wave number, α, for various wave amplitudes, S, at Reynolds number Re = 2648 (Reτ=180)

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Fig. 9

Plot of the friction factor modification, f′, as a function of phase shift, β, for various wave amplitudes, S, at Reynolds number Re = 2648 (Reτ=180) and wave number α=0.5

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Fig. 10

Plot of the friction factor modification, f′, as a function of wave number, α, for various wave amplitudes, S, at Reynolds number Re = 2648 (Reτ=180) for (a) triangular, (b) trapezoidal, and (c) rectangular groove shapes

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Fig. 11

Contour plots of the streamwise velocity component in a yz-plane for (a) triangular, (b) trapezoidal, and (c) rectangular groove shapes with S = 0.75, α=0.6, and Re = 2648 (Reτ=180)

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Fig. 12

Contour plots of the streamwise velocity component in a yz-plane for (a) the smooth channel, (b) drag decreasing grooves on one wall with α=0.5, (c) drag decreasing grooves on both walls with α=0.5, and (d) drag increasing grooves on one wall with α=1.0. For all cases, S = 0.75 and Re = 2648 (Reτ=180).

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Fig. 13

Plot of the distribution of the streamwise component of the wall shear stress, τw, normalized by the wall shear stress for the smooth channel, τw,0 for the bottom wall (solid lines) and top wall (dashed lines). Grooves on one wall that decrease the friction factor (α=0.5) as well as grooves on one wall that increase the friction factor (α=1.0) are shown. Grooves on both walls that decrease the friction factor are also shown. For all cases, S = 0.75 and Re = 2648 (Reτ=180).

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