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Groove-induced changes of discharge in channel flows

Published online by Cambridge University Press:  23 June 2016

Yu Chen ,
J. M. Floryan ,
Y. T. Chew  and
B. C. Khoo
Yu Chen*
Affiliation:
Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore 117575, Singapore Institute of High Performance Computing, Agency for Science, Technology and Research, 1 Fusionopolis Way, #16-16 Connexis, Singapore 138632, Singapore
J. M. Floryan
Affiliation:
Department of Mechanical and Materials Engineering, The University of Western Ontario, London, Ontario, N6A5B9, Canada
Y. T. Chew
Affiliation:
Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore 117575, Singapore
B. C. Khoo
Affiliation:
Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore 117575, Singapore
*
†Email address for correspondence: [email protected]
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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.

JFM classification

Flow Control: Drag reduction Flow Control: Flow Control Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 799 , 25 July 2016 , pp. 297 - 333
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Copyright
© 2016 Cambridge University Press 

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References

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), 382–393.CrossRefGoogle Scholar
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. 33–42. Publishing House of Moscow Energy Institute (MEI).Google Scholar
Balakumar, P. & Widnall, S. E. 1986 Application of unsteady aerodynamics to large-eddy breakup devices in a turbulent flow. Phys. Fluids 29 (6), 1779–1787.CrossRefGoogle Scholar
Barthlott, W. & Neinhuis, C. 1997 Purity of the sacred lotus, or escape from contamination in biological surfaces. Planta 202 (1), 1–8.CrossRefGoogle Scholar
Bechert, D. W. & Bartenwerfer, M. 1989 The viscous flow on surfaces with longitudinal ribs. J. Fluid Mech. 206, 105–129.CrossRefGoogle Scholar
Bechert, D. W., Bruse, M. & Hage, W. 2000 Experiments with three-dimensional riblets as an idealized model of shark skin. Exp. Fluids 28 (5), 403–412.CrossRefGoogle Scholar
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), 59–87.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Cabal, A., Szumbarski, J. & Floryan, J. M. 2001 Numerical simulation of flows over corrugated walls. Comput. Fluids 30 (6), 753–776.CrossRefGoogle Scholar
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), 69–84.CrossRefGoogle Scholar
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. 613–616. The Asian Fluid Mechanics Committee (AFMC).Google Scholar
Choi, H., Moin, P. & Kim, J. 1993 Direct numerical simulation of turbulent flow over riblets. J. Fluid Mech. 255, 503–539.CrossRefGoogle Scholar
Choi, K.-S. 1989 Near-wall structure of a turbulent boundary layer with riblets. J. Fluid Mech. 208, 417–458.CrossRefGoogle Scholar
Choi, K.-S., Jukes, T. & Whalley, R. 2011 Turbulent boundary-layer control with plasma actuators. Phil. Trans. R. Soc. Lond. A 369 (1940), 1443–1458.Google ScholarPubMed
Daniello, R. J., Waterhouse, N. E. & Rothstein, J. P. 2009 Drag reduction in turbulent flows over superhydrophobic surfaces. Phys. Fluids 21 (8), 085103.CrossRefGoogle Scholar
Darcy, H. 1857 Recherches Expérimentales Relatives au Mouvement de l’Eau dans les Tuyaux. Mallet-Bachelier.Google Scholar
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), 4775–4806.Google ScholarPubMed
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), 42–45.Google Scholar
Eckert, E. R. G. & Irvine, T. F. Jr. 1956 Flow in corners of passages with noncircular cross sections. Trans. ASME 78 (4), 709.Google Scholar
Gao, L. C. & McCarthy, T. J. 2006 A perfectly hydrophobic surface (𝜃a/𝜃r = 180/180). J. Am. Chem. Soc. 128 (28), 9052–9053.CrossRefGoogle Scholar
García-Mayoral, R. & Jiménez, J. 2011 Drag reduction by riblets. Phil. Trans. R. Soc. Lond. A 369 (1940), 1412–1427.Google ScholarPubMed
Graham, J. M. R. 1998 The effect of a two-dimensional cascade of thin streamwise plates on homogeneous turbulence. J. Fluid Mech. 356, 125–147.CrossRefGoogle Scholar
Hagen, G. 1854 Uber den einfluss der temperatur auf die bewegung des wasser in röhren. Math. Abh. Akad. Wiss. 17.Google Scholar
Hoepffner, J. & Fukagata, K. 2009 Pumping or drag reduction? J. Fluid Mech. 635, 171–187.CrossRefGoogle Scholar
Incropera, F. P. & DeWitt, D. P. 2002 Fundamentals of Heat and Mass Transfer, 5th edn. Wiley.Google Scholar
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.CrossRefGoogle Scholar
Iuso, G., Onorato, M., Spazzini, P. G. & Di Cicca, G. M. 2002 Wall turbulence manipulation by large-scale streamwise vortices. J. Fluid Mech. 473, 23–58.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
Keating, A. & Piomelli, U. 2006 A dynamic stochastic forcing method as a wall-layer model for large-eddy simulation. J. Turbul. 7, N12.CrossRefGoogle Scholar
Kim, J. 2011 Physics and control of wall turbulence for drag reduction. Phil. Trans. R. Soc. Lond. A 369 (1940), 1396–1411.Google ScholarPubMed
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.CrossRefGoogle Scholar
Lienhart, H., Breuer, M. & Köksoy, C. 2008 Drag reduction by dimples?-a complementary experimental/numerical investigation. Intl J. Heat Fluid Flow 29 (3), 783–791.CrossRefGoogle Scholar
Martell, M., Perot, J. B. & Rothstein, J. P. 2009 Direct numerical simulations of turbulent flows over superhydrophobic surfaces. J. Fluid Mech. 620, 31–41.CrossRefGoogle Scholar
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, 309–318.CrossRefGoogle Scholar
Mohammadi, A. & Floryan, J. M. 2015 Numerical analysis of laminar-drag-reducing grooves. Trans. ASME J. Fluids Engng 137 (4), 041201.CrossRefGoogle Scholar
Mohammadi, M. & Floryan, J. M. 2013a Groove optimization for drag reduction. Phys. Fluids 25 (11), 113601.CrossRefGoogle Scholar
Mohammadi, M. & Floryan, J. M. 2013b Pressure losses in grooved channels. J. Fluid Mech. 725, 23–54.CrossRefGoogle Scholar
Moin, P. & Kim, J. 1982 Numerical investigation of turbulent channel flow. J. Fluid Mech. 118, 341–377.CrossRefGoogle Scholar
Moody, L. F. 1944 Friction factors for pipe flow. Trans. ASME 66 (8), 671–684.Google Scholar
Moradi, H. V. & Floryan, J. M. 2013 Flows in annuli with longitudinal grooves. J. Fluid Mech. 716, 280–315.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Nikuradse, J.1933 Strömungsgesetze in rauhen rohren. VDI-Forschungscheft 361; also NACA TM 1292 (1950).Google Scholar
Ou, J., Perot, B. & Rothstein, J. P. 2004 Laminar drag reduction in microchannels using ultrahydrophobic surfaces. Phys. Fluids 16 (12), 4635–4643.CrossRefGoogle Scholar
Ou, J. & Rothstein, J. P. 2005 Direct velocity measurements of the flow past drag-reducing ultrahydrophobic surfaces. Phys. Fluids 17 (10), 103606.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Quadrio, M. 2011 Drag reduction in turbulent boundary layers by in-plane wall motion. Phil. Trans. R. Soc. Lond. A 369 (1940), 1428–1442.Google ScholarPubMed
Quadrio, M., Floryan, J. M. & Luchini, P. 2007 Effect of streamwise-periodic wall transpiration on turbulent friction drag. J. Fluid Mech. 576, 425–444.CrossRefGoogle Scholar
Quéré, D. 2008 Wetting and roughness. Annu. Rev. Mater. Res. 38, 71–99.CrossRefGoogle Scholar
Reyssat, M., Yeomans, J. M. & Quéré, D. 2008 Impalement of fakir drops. Europhys. Lett. 81, 26006.CrossRefGoogle Scholar
Rothstein, J. P. 2010 Slip on superhydrophobic surfaces. Annu. Rev. Fluid Mech. 42, 89–109.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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), 696–700.CrossRefGoogle Scholar
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), 2814–2820.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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, 389–418.CrossRefGoogle Scholar
Schoppa, W. & Hussain, F. 1998 A large-scale control strategy for drag reduction in turbulent boundary layers. Phys. Fluids 10, 1049.CrossRefGoogle Scholar
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. 669–678. Elsevier.CrossRefGoogle Scholar
Sirovich, L. & Karlsson, S. 1997 Turbulent drag reduction by passive mechanisms. Nature 388, 753–755.CrossRefGoogle Scholar
Spalart, P. R. & Allmaras, S. R. 1992 A one-equation turbulence model for aerodynamic flows. AIAA Paper 1992-04-39 1 (2), 5–21.Google Scholar
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.Google Scholar
Sudo, S., Tsuyuki, K., Ito, Y. & Ikohagi, T. 2002 A study on the surface shape of fish scales. JSME Intl J. C 45 (4), 1100–1105.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
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), 1051–1062.CrossRefGoogle Scholar
Veldhuis, L. L. M. & Vervoort, E.2009 Drag effect of a dented surface in a turbulent flow. AIAA Paper 2009-3950; San Antonio, Texas.CrossRefGoogle Scholar
Walsh, M. J. 1980 Drag characteristics of V-groove and transverse curvature riblets. In Viscous Flow Drag Reduction, pp. 168–184. AIAA.Google Scholar
Walsh, M. J. 1983 Riblets as a viscous drag reduction technique. AIAA J. 21, 485–486.CrossRefGoogle Scholar
Walsh, M. J. & Lindeman, A. M.1984 Optimization and application of riblets for turbulent drag reduction. AIAA Paper 84-0347.CrossRefGoogle Scholar
Walsh, M. J. & Weinstein, L. M.1978 Drag and heat transfer on surfaces with small longitudinal fins. AIAA Paper 78-1161.CrossRefGoogle Scholar
Wang, Z., Yeo, K. S. & Khoo, B. C. 2006 DNS of low Reynolds number turbulent flows in dimpled channels. J. Turbul. 7, 37.CrossRefGoogle Scholar
Wesseling, P. & Oosterlee, C. W. 2001 Geometric multigrid with applications to computational fluid dynamics. J. Comput. Appl. Maths 128 (1–2), 311–334.CrossRefGoogle Scholar
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), 621–633.CrossRefGoogle Scholar
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), 4391–4396.Google Scholar