Flow over compliant rotating disks

Journal of Engineering Mathematics - Tập 57 - Trang 303-315 - 2006
Peter W. Carpenter1, Peter J. Thomas1
1Fluid Dynamics Research Centre, School of Engineering, University of Warwick, Coventry, UK

Tóm tắt

Flow over compliant materials and compliant coatings has been studied for decades because of the potential of using such materials for laminar-flow control. Since boundary layers in most flows of engineering interest are three-dimensional the classic rotating-disk flow geometry, the paradigm for studying three-dimensional boundary layers, has been adapted to investigate flow over compliant rotating disks. This paper reviews the literature on the existing experimental and theoretical research on flow over compliant rotating disks. The article concludes by evaluating the status of the available results and their implications as regards future research routes to investigate the capabilities of compliant materials for laminar-flow control.

Tài liệu tham khảo

Gray J (1936) Studies in animal locomotion, VI. The propulsion powers of the dolphin. J Exp Biol 13:192–199 Carpenter PW, Davies C, Lucey AD (2000) Hydrodynamics and compliant walls: Does the dolphin have a secret? Current Sci 79:758–765 Riley JJ, Gad-El-Hak M, Metcalfe M (1988) Compliant coatings. Ann Rev Fluid Mech 20:393–420 Carpenter PW (1997) Status of transition delay using compliant walls. Prog Astronaut Aeronaut 123:79–113 Carpenter PW, Lucey AD, Davies C (2001) Progress on the use of compliant walls for laminar-flow control. J Aircraft 38:504–512 Gad-El-Hak M (1996) Compliant coatings: a decade of progress. Appl Mech Rev 49:S1–S11 Gad-El-Hak M (2003) Drag reduction using compliant walls. In: Carpenter PW, Pedley TJ (eds) Flow past highly Boundaries and in collapsible tubes. Fluid Mechanics and its Applications, Kluwer Academic Publishers, vol 72. pp 191–229 Gregory N, Stuart JT, Walker WS (1955) On the stability of three-dimensional boundary layers with application to the flow due to a rotating disk. Phil Trans R Soc London Ser A 248:155–199 Cros A, Ali R, Le Gal P, Thomas PJ, Schouveiler L, Carpenter PW, Chauve MP (2003) Effects of wall compliance on the laminar–turbulent transition of torsional Couette flow. J Fluid Mech 481:177–186 Schouveiler L, Le Gal P, Chauve MP (1999) Spiral and circular waves in the flow between a rotating and a stationary disk. Exp Fluids 26:179–187 Fitzgerald ER, Fitzgerald JW (1998) Blubber and compliant coatings for drag reduction in water. V. Driving point shear impedance measurements on compliant surfaces. In: Meng JCS (ed) Proc Int Symp on Seawater Drag Reduction, 22–23 July, Newport, RI, USA, pp 211–214 Hansen RJ, Hunston DL (1974) An experimental study of turbulent flows over compliant surfaces. J Sound Vib 34(3):297–308 Hansen RJ, Hunston DL (1976) Further observations on flow-generated surface waves in compliant surfaces. J Sound Vib 46:593–595 Hansen RJ, Hunston DL (1983) Fluid-property effects on flow-generated waves on a flexible surface. J Fluid Mech 133:161–177 Hansen RJ, Hunston DL, NI CC, Reischman MM, Hoyt JW (1980) Hydrodynamic drag and surface deformations generated by liquid flows over flexible surfaces. Prog in Astronaut Aeronautics 72:439–452 Gad-El-Hak M, Blackwelder RF, Riley JJ (1984) On the interaction of compliant coatings with boundary layer flows. J Fluid Mech 140:257–280 Chung KH (1985) Composite compliant coatings for drag reduction utilising low modulus high damping silicone rubber. Ph. D. Thesis, MIT Gaster M (1987) Is the dolphin a red herring?. In: Liepmann HW, Narasimha R (eds) Proc IUTAM Symp on Turbulence Management and Relaminarisation. Springer, Bangalore India, pp 285–304 Dixon AE, Lucey AD, Carpenter PW (1994) Optimization of viscoelastic compliant walls for transition delay. AIAA J 32:256–267 Fitzgerald ER, Fitzgerald JW (1995) Blubber and compliant coatings for drag reduction in water. I. Viscoelastic properties of blubber and compliant coating materials. Mat Sci Eng C 2:209–214 Fitzgerald JW, Fitzgerald ER, Carey WM, von Winkle WA (1995) Blubber and compliant coatings for drag reduction in water. II. Matched shear impedance for compliant layer drag reduction. Mat Sci and Engng C 2:215–220 Fitzgerald JW, Fitzgerald ER, Martin JE (1998) Blubber and compliant coatings for drag reduction in water. III. Rotating disc drag measurements that mimic dolphin blubber. In: Tomlinson GR, Bullough WA (eds) Smart Materials and Structures. IOP Pub. Ltd., Bristol, UK, pp 543–550 Fitzgerald JW, Martin JE, Modert EF (1998) Blubber and compliant coatings for drag reduction in water. VI. Rotating disc apparatus for drag measurement on compliant layers. In: Meng JCS (ed) Proc Int Symp on Seawater Drag Reduction, 22–23 July, Newport, RI, USA, pp 215-218 von Kármán Th (1921) Über laminare und turbulente Reibung. Zeitschrift für angewandte Mathematik und Mechanik 1:233–252 Lilly DK (1966) On the instability of Ekman boundary flow. J Atmos Sci 23:481–494 Malik MR, Wilkinson SP, Orszag SA (1981) Instability and transition in rotating disk flow. AIAA J 19:1131–1138 Cooper AJ, Carpenter PW (1997) The stability of rotating-disc boundary-layer flow over a compliant wall. Part 1. Type I and II instabilities. J Fluid Mech 350:231–259 Wilkinson SP, Malik MR (1985) Stability experiments in the flow over a rotating disk. AIAA J 23:588–595 Mack LM The wave pattern produced by point source on a rotating disk. AIAA Paper 85-0490 Balakumar P, Malik MR (1990) Travelling disturbances in rotating-disk flow. Theor and Comp Fluid Dyn 2:125–137 Smith NH (1946) Exploratory investigation of laminar-boundary-layer oscillations on a rotating disk. N.A.C.A. TN 1227 Jarre S, Le Gal P, Chauve MP (1996) Experimental study of rotating disk instability. I. Natural flow. Phys Fluids 8:496–508 Jarre S, Le Gal P, Chauve MP (1996) Experimental study of rotating disk instability. II. Forced flow. Phys Fluids 8:2985–2994 Jarre S, Le Gal P, Chauve MP (1991) Experimental analysis of the instability of the boundary layer over a rotating disk. Europhys Lett 14:649–654 Le Gal P (1992) Complex demodulation applied to the transition to turbulence of the flow over a rotating disk. Phys Fluids A 4:2523–2528 Lingwood RJ (1995) Absolute instability of the boundary layer on a rotating disk. J Fluid Mech 299:17–33 Lingwood RJ (1996) An experimental-study of absolute instability of the rotating-disk boundary-layer flow. J Fluid Mech 314:373–405 Faller AJ (1963) An experimental study of the instability of the laminar Ekman boundary layer. J Fluid Mech 15:560–576 Koch W (1986) Direct resonance in Orr-Sommerfeld problems. Acta Mech 58:11–29 Davies C, Carpenter PW (2001) A novel velocity-vorticity formulation of the Navier-Stokes equations with applications to boundary-layer disturbance evolution. J Comp Phys 172:119–165 Carpenter PW, Garrad AD (1985) The hydrodynamic stability of flows over Kramer-type compliant walls. Pt 1. Schlichting Instabilities. J Fluid Mech 155:456–510 Lingwood RJ (1997) Absolute instability of the Ekman layer and related rotating flows. J Fluid Mech 331:405–428 Cooper AJ, Carpenter PW (1997) The stability of rotating-disc boundary-layer flow over a compliant wall. Part 2. Absolute instability. J Fluid Mech 350:261–270 Davies C, Carpenter PW (2003) Global behaviour corresponding to the absolute instability of the rotating-disc boundary layer. J Fluid Mech 486:287–329 Pier B (2003) Finite-amplitude crossflow vortices, secondary instability and transition in the rotating-disk boundary layer. J Fluid Mech 487:315–343 Othman H (2005) Experimental study of absolute instability of a rotating-disk boundary layer. PhD dissertation, University of Notre Dame, USA Othman H, Corke TC (2006) Experimental investigation of absolute instability of a rotating-disk boundary layer. J Fluid Mech 565:63–94 Carpenter PW, Thomas PJ, Nagata M (2003) Rotating flows over compliant walls. In: Carpenter PW, Pedley TJ (ed) Flow past highly Compliant Boundaries and in collapsible tubes. Fluid Mechanics and its Applications, Kluwer Academic Publishers, vol 72. pp 167–187 Allen L, Bridges TJ (2003) Hydrodynamic stability of the Ekman boundary layer including interaction with a compliant surface: a numerical framework. Euro J Mech B/Fluids 22:239-258 Colley AJ, Thomas PJ, Carpenter PW, Cooper AJ (1999) An experimental study of boundary-layer transition over a rotating, compliant disc. Phys Fluids 11:3340–3352 Colley AJ, Carpenter PW (2000) Experiments on boundary-layer transition over a rotating compliant disc – New experimental method. In abstracts of: 4th EUROMECH Fluid Mech. Conf., Eindhoven, The Netherlands, 19–23 November Colley AJ, Carpenter PW, Thomas PJ, Ali R, Zoueshtiagh F (2006) Experimental verification of Type-II-eigenmode destabilization in the boundary layer over a compliant rotating disk. Phys Fluids 18:054107 Owen JM, Rogers RH (1989) Flow and heat transfer in rotating-disc Systems, vol. 1 - Rotor-Stator Systems. Research Studies Press Ltd., Taunton, Somerset, UK Schouveiler L, Le Gal P, Chauve MP (1998) Stability of a travelling roll system in a rotating disk flow. Phys Fluids 10:2695–2697 Schouveiler L, Le Gal P, Chauve MP (2001) Instabilities of the flow between a rotating and a stationary disk. J Fluid Mech 443:329–350