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Groove-induced changes of discharge in channel flows

  • Yu Chen (a1) (a2), J. M. Floryan (a3), Y. T. Chew (a1) and B. C. Khoo (a1)

Abstract

The changes in discharge in pressure-driven flows through channels with longitudinal grooves have been investigated in the laminar flow regime and in the turbulent flow regime with moderate Reynolds numbers ( $Re_{2H}\approx 6000$ ) using both analytical and numerical methodologies. The results demonstrate that the long-wavelength grooves can increase discharge by 20 %–150 %, depending on the groove amplitude and the type of flow, while the short-wavelength grooves reduce the discharge. It has been shown that the reduced geometry model applies to the analysis of turbulent flows and the performance of grooves of arbitrary form is well approximated by the performance of grooves whose shape is represented by the dominant Fourier mode. The flow patterns, the turbulent kinetic energy as well as the Reynolds stresses were examined to identify the mechanisms leading to an increase in discharge. It is shown that the increase in discharge results from the rearrangement of the bulk fluid movement and not from the suppression of turbulence intensity. The turbulent kinetic energy and the Reynolds stresses are rearranged while their volume-averaged intensities remain the same as in the smooth channel. Analysis of the interaction of the groove patterns on both walls demonstrates that the converging–diverging configuration results in the greatest increase in discharge while the wavy channel configuration results in a reduction in discharge.

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Email address for correspondence: yuchen1986sg@gmail.com

References

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Abe, H., Kawamura, H. & Matsuo, Y. 2001 Direct numerical simulation of a fully developed turbulent channel flow with respect to the Reynolds number dependence. Trans. ASME J. Fluids Engng 123 (2), 382393.
Alekseev, V. V., Gachechiladze, I. A., Kiknadze, G. I. & Oleinikov, V. G. 1998 Tornado-like energy transfer on three-dimensional concavities of reliefs-structure of self-organizing flow, their visualisation, and surface streamlining mechanisms. In Transactions of the 2nd Russian Nat. Conf. of Heat Transfer, Heat Transfer Intensification Radiation and Complex Heat Transfer, vol. 6, pp. 3342. Publishing House of Moscow Energy Institute (MEI).
Balakumar, P. & Widnall, S. E. 1986 Application of unsteady aerodynamics to large-eddy breakup devices in a turbulent flow. Phys. Fluids 29 (6), 17791787.
Barthlott, W. & Neinhuis, C. 1997 Purity of the sacred lotus, or escape from contamination in biological surfaces. Planta 202 (1), 18.
Bechert, D. W. & Bartenwerfer, M. 1989 The viscous flow on surfaces with longitudinal ribs. J. Fluid Mech. 206, 105129.
Bechert, D. W., Bruse, M. & Hage, W. 2000 Experiments with three-dimensional riblets as an idealized model of shark skin. Exp. Fluids 28 (5), 403412.
Bechert, D. W., Bruse, M., Hage, W., Van Der Hoeven, J. G. T. & Hoppe, G. 1997 Experiments on drag-reducing surfaces and their optimization with an adjustable geometry. J. Fluid Mech. 338 (5), 5987.
Burgess, N. K., Oliveira, M. M. & Ligrani, P. M. 2003 Nusselt number behavior on deep dimpled surfaces within a channel. Trans. ASME J. Heat Transfer 125, 11.
Cabal, A., Szumbarski, J. & Floryan, J. M. 2001 Numerical simulation of flows over corrugated walls. Comput. Fluids 30 (6), 753776.
Chang, M. J., Chow, L. C. & Chang, W. S. 1991 Improved alternating-direction implicit method for solving transient three-dimensional heat diffusion problems. Numer. Heat Transfer B 19 (1), 6984.
Chen, Y., Chew, Y. T. & Khoo, B. C. 2010 Turbulent flow manipulation by passive devices. In Proceedings of the 13th Asian Congress of Fluid Mechanics, pp. 613616. The Asian Fluid Mechanics Committee (AFMC).
Choi, H., Moin, P. & Kim, J. 1993 Direct numerical simulation of turbulent flow over riblets. J. Fluid Mech. 255, 503539.
Choi, K.-S. 1989 Near-wall structure of a turbulent boundary layer with riblets. J. Fluid Mech. 208, 417458.
Choi, K.-S., Jukes, T. & Whalley, R. 2011 Turbulent boundary-layer control with plasma actuators. Phil. Trans. R. Soc. Lond. A 369 (1940), 14431458.
Daniello, R. J., Waterhouse, N. E. & Rothstein, J. P. 2009 Drag reduction in turbulent flows over superhydrophobic surfaces. Phys. Fluids 21 (8), 085103.
Darcy, H. 1857 Recherches Expérimentales Relatives au Mouvement de l’Eau dans les Tuyaux. Mallet-Bachelier.
Dean, B. & Bhushan, B. 2010 Shark-skin surfaces for fluid-drag reduction in turbulent flow: a review. Phil. Trans. R. Soc. Lond. A 368 (1929), 47754806.
Douglas, J. 1955 On the numerical integration of 2 u/∂x 2 + 2 u/∂y 2 = ∂u/∂t by implicit methods. J. Soc. Ind. Appl. Maths 3 (1), 4245.
Eckert, E. R. G. & Irvine, T. F. Jr. 1956 Flow in corners of passages with noncircular cross sections. Trans. ASME 78 (4), 709.
Gao, L. C. & McCarthy, T. J. 2006 A perfectly hydrophobic surface (𝜃a/𝜃r = 180/180). J. Am. Chem. Soc. 128 (28), 90529053.
García-Mayoral, R. & Jiménez, J. 2011 Drag reduction by riblets. Phil. Trans. R. Soc. Lond. A 369 (1940), 14121427.
Graham, J. M. R. 1998 The effect of a two-dimensional cascade of thin streamwise plates on homogeneous turbulence. J. Fluid Mech. 356, 125147.
Hagen, G. 1854 Uber den einfluss der temperatur auf die bewegung des wasser in röhren. Math. Abh. Akad. Wiss. 17.
Hoepffner, J. & Fukagata, K. 2009 Pumping or drag reduction? J. Fluid Mech. 635, 171187.
Incropera, F. P. & DeWitt, D. P. 2002 Fundamentals of Heat and Mass Transfer, 5th edn. Wiley.
Itoh, M., Tamano, S., Iguchi, R., Yokota, K., Akino, N., Hino, R. & Kubo, S. 2006 Turbulent drag reduction by the seal fur surface. Phys. Fluids 18, 065102.
Iuso, G., Onorato, M., Spazzini, P. G. & Di Cicca, G. M. 2002 Wall turbulence manipulation by large-scale streamwise vortices. J. Fluid Mech. 473, 2358.
Joseph, P., Cottin-Bizonne, C., Benoit, J.-M., Ybert, C., Journet, C., Tabeling, P. & Bocquet, L. 2006 Slippage of water past superhydrophobic carbon nanotube forests in microchannels. Phys. Rev. Lett. 97 (15), 156104.
Keating, A. & Piomelli, U. 2006 A dynamic stochastic forcing method as a wall-layer model for large-eddy simulation. J. Turbul. 7, N12.
Kim, J. 2011 Physics and control of wall turbulence for drag reduction. Phil. Trans. R. Soc. Lond. A 369 (1940), 13961411.
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133166.
Lienhart, H., Breuer, M. & Köksoy, C. 2008 Drag reduction by dimples?-a complementary experimental/numerical investigation. Intl J. Heat Fluid Flow 29 (3), 783791.
Martell, M., Perot, J. B. & Rothstein, J. P. 2009 Direct numerical simulations of turbulent flows over superhydrophobic surfaces. J. Fluid Mech. 620, 3141.
Min, T., Kang, S. M., Speyer, J. L. & Kim, J. 2006 Sustained sub-laminar drag in a fully developed channel flow. J. Fluid Mech. 558, 309318.
Mohammadi, A. & Floryan, J. M. 2015 Numerical analysis of laminar-drag-reducing grooves. Trans. ASME J. Fluids Engng 137 (4), 041201.
Mohammadi, M. & Floryan, J. M. 2013a Groove optimization for drag reduction. Phys. Fluids 25 (11), 113601.
Mohammadi, M. & Floryan, J. M. 2013b Pressure losses in grooved channels. J. Fluid Mech. 725, 2354.
Moin, P. & Kim, J. 1982 Numerical investigation of turbulent channel flow. J. Fluid Mech. 118, 341377.
Moody, L. F. 1944 Friction factors for pipe flow. Trans. ASME 66 (8), 671684.
Moradi, H. V. & Floryan, J. M. 2013 Flows in annuli with longitudinal grooves. J. Fluid Mech. 716, 280315.
Moser, R. D., Kim, J. & Mansour, N. N. 1999 Direct numerical simulation of turbulent channel flow up to Re 𝜏 = 590. Phys. Fluids 11, 943.
Nikuradse, J.1933 Strömungsgesetze in rauhen rohren. VDI-Forschungscheft 361; also NACA TM 1292 (1950).
Ou, J., Perot, B. & Rothstein, J. P. 2004 Laminar drag reduction in microchannels using ultrahydrophobic surfaces. Phys. Fluids 16 (12), 46354643.
Ou, J. & Rothstein, J. P. 2005 Direct velocity measurements of the flow past drag-reducing ultrahydrophobic surfaces. Phys. Fluids 17 (10), 103606.
Park, H. W., Park, H. M. & Kim, J. 2013 A numerical study of the effects of superhydrophobic surface on skin-friction drag in turbulent channel flow. Phys. Fluids 25 (11), 110815.
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.
Quadrio, M. 2011 Drag reduction in turbulent boundary layers by in-plane wall motion. Phil. Trans. R. Soc. Lond. A 369 (1940), 14281442.
Quadrio, M., Floryan, J. M. & Luchini, P. 2007 Effect of streamwise-periodic wall transpiration on turbulent friction drag. J. Fluid Mech. 576, 425444.
Quéré, D. 2008 Wetting and roughness. Annu. Rev. Mater. Res. 38, 7199.
Reyssat, M., Yeomans, J. M. & Quéré, D. 2008 Impalement of fakir drops. Europhys. Lett. 81, 26006.
Rothstein, J. P. 2010 Slip on superhydrophobic surfaces. Annu. Rev. Fluid Mech. 42, 89109.
Sagong, W., Kim, C., Choi, S., Jeon, W. P. & Choi, H. 2008 Does the sailfish skin reduce the skin friction like the shark skin? Phys. Fluids 20, 101510.
Sahlin, A., Alfredsson, P. H. & Johansson, A. V. 1986 Direct drag measurements for a flat plate with passive boundary layer manipulators. Phys. Fluids 29 (3), 696700.
Sahlin, A., Johansson, A. V. & Alfredsson, P. H. 1988 The possibility of drag reduction by outer layer manipulators in turbulent boundary layers. Phys. Fluids 31 (10), 28142820.
Samaha, M. A., Tafreshi, H. V. & Gad-el Hak, M. 2011 Modeling drag reduction and meniscus stability of superhydrophobic surfaces comprised of random roughness. Phys. Fluids 23 (1), 012001.
Savill, A. M. & Mumford, J. C. 1988 Manipulation of turbulent boundary layers by outer-layer devices: skin-friction and flow-visualization results. J. Fluid Mech. 191, 389418.
Schoppa, W. & Hussain, F. 1998 A large-scale control strategy for drag reduction in turbulent boundary layers. Phys. Fluids 10, 1049.
Shur, M., Spalart, P. R., Strelets, M. & Travin, A. 1999 Detached-eddy simulation of an airfoil at high angle of attack. In Fourth International Symposium on Engineering Turbulence Modelling and Experiments, pp. 669678. Elsevier.
Sirovich, L. & Karlsson, S. 1997 Turbulent drag reduction by passive mechanisms. Nature 388, 753755.
Spalart, P. R. & Allmaras, S. R. 1992 A one-equation turbulence model for aerodynamic flows. AIAA Paper 1992-04-39 1 (2), 521.
Spalart, P. R., Jou, W. H. & Allmaras, M. S. S. R. 1997 Comments on the feasibility of les for wings and on hybrid RANS/LES approach. In Proceedings of the First AFOSR International Conference on DNS/LES, p. 137. Greyden Press.
Sudo, S., Tsuyuki, K., Ito, Y. & Ikohagi, T. 2002 A study on the surface shape of fish scales. JSME Intl J. C 45 (4), 11001105.
Tay, C. M. J., Khoo, B. C. & Chew, Y. T. 2015 Mechanics of drag reduction by shallow dimples in channel flow. Phys. Fluids 27 (3), 035109.
Truesdell, R., Mammoli, A., Vorobieff, P., van Swol, F. & Brinker, C. J. 2006 Drag reduction on a patterned superhydrophobic surface. Phys. Rev. Lett. 97 (4), 044504.
Tu, S., Aliabadi, S., Patel, R. & Watts, M. 2009 An implementation of the Spalart–Allmaras DES model in an implicit unstructured hybrid finite volume/element solver for incompressible turbulent flow. Intl J. Numer. Meth. Fluids 59 (9), 10511062.
Veldhuis, L. L. M. & Vervoort, E.2009 Drag effect of a dented surface in a turbulent flow. AIAA Paper 2009-3950; San Antonio, Texas.
Walsh, M. J. 1980 Drag characteristics of V-groove and transverse curvature riblets. In Viscous Flow Drag Reduction, pp. 168184. AIAA.
Walsh, M. J. 1983 Riblets as a viscous drag reduction technique. AIAA J. 21, 485486.
Walsh, M. J. & Lindeman, A. M.1984 Optimization and application of riblets for turbulent drag reduction. AIAA Paper 84-0347.
Walsh, M. J. & Weinstein, L. M.1978 Drag and heat transfer on surfaces with small longitudinal fins. AIAA Paper 78-1161.
Wang, Z., Yeo, K. S. & Khoo, B. C. 2006 DNS of low Reynolds number turbulent flows in dimpled channels. J. Turbul. 7, 37.
Wesseling, P. & Oosterlee, C. W. 2001 Geometric multigrid with applications to computational fluid dynamics. J. Comput. Appl. Maths 128 (1–2), 311334.
Zhang, X., Shi, F., Niu, J., Jiang, Y. G. & Wang, Z. Q. 2008 Superhydrophobic surfaces: from structural control to functional application. J. Mater. Chem. 18 (6), 621633.
Zhou, M., Li, J., Wu, C. X., Zhou, X. K. & Cai, L. 2011 Fluid drag reduction on superhydrophobic surfaces coated with carbon nanotube forests (cnts). Soft Matt. 7 (9), 43914396.
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Groove-induced changes of discharge in channel flows

  • Yu Chen (a1) (a2), J. M. Floryan (a3), Y. T. Chew (a1) and B. C. Khoo (a1)

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