Hostname: page-component-848d4c4894-pjpqr Total loading time: 0 Render date: 2024-06-20T10:49:39.940Z Has data issue: false hasContentIssue false
  • English
  • Français

Reducing flow separation of an inclined plate via travelling waves

Published online by Cambridge University Press:  18 October 2019

A. M. Akbarzadeh Open the ORCID record for A. M. Akbarzadeh [Opens in a new window]  and
I. Borazjani Open the ORCID record for I. Borazjani [Opens in a new window]
A. M. Akbarzadeh
Affiliation:
J. Mike Walker ’66 Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843, USA
I. Borazjani*
Affiliation:
J. Mike Walker ’66 Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843, USA
*
†Email address for correspondence: iman@tamu.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Many aquatic animals propel themselves by generating backward traveling waves over their body, which is thought to reattach the flow when the wave speed ($C=\unicode[STIX]{x1D706}f$, where $\unicode[STIX]{x1D706}$ is wavelength and $f$ is frequency) is larger than the swimming speed ($U$). This has inspired the use of travelling waves, which have recently been generated at low amplitudes using smart materials, to reduce flow separation on an inclined plate. To see if low-amplitude travelling waves (amplitude approximately 0.01 of chord length $L$) can reduce the separation on an inclined plate, large-eddy simulations are performed. The simulations are carried out for Reynolds number ($Re$) 20 000 and an angle of attack of $10^{\circ }$ with different wavelengths and frequencies. The travelling waves at a low reduced frequency ($f^{\ast }=fL/U=6$ and $\unicode[STIX]{x1D706}^{\ast }=\unicode[STIX]{x1D706}/L=0.2$, where $U$ is free-stream velocity) do not affect the flow separation and aerodynamic performance compared to the flat inclined plate. Nevertheless, increasing the wave speed by increasing the reduced frequency to 20 and 30 reduces flow separation. However, increasing the wave speed by increasing the wavelength, in contrast to the common belief, does not monotonically reduce the flow separation. In fact, increasing the wave speed by increasing the wavelength from 0.15 to 0.5 at constant frequency $f^{\ast }=20$ increases the separation, but increasing from 0.5 to 1.0 and 2.0, interestingly, reduces flow separation. These observations indicate that the wave speed is not the only parameter for flow reattachment, but both wavelength and frequency individually impact flow separation by affecting two competing but interconnected mechanisms: the axial momentum, imparted onto the fluid by the undulations, tends to reattach the flow but the lateral velocity tends to detach it. In fact, increasing $f^{\ast }$ and $\unicode[STIX]{x1D706}^{\ast }$ increases both the axial momentum and the lateral velocity, which are competing to attach and detach the flow, respectively.

JFM classification

Biological Fluid Dynamics: Swimming/flying Biological Fluid Dynamics: Propulsion Wakes/Jets: Separated flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 880 , 10 December 2019 , pp. 831 - 863
Copyright
© 2019 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Akbarzadeh, A. & Borazjani, I. 2019 A numerical study on controlling flow separation via surface morphing in the form of backward traveling waves. In AIAA Aviation 2019 Forum. American Institute of Aeronautics and Astronautics.Google Scholar
Al-Marouf, M. & Samtaney, R. 2017 A versatile embedded boundary adaptive mesh method for compressible flow in complex geometry. J. Comput. Phys. 337, 339–378.Google Scholar
Alam, M. & Sandham, N. D. 2000 Direct numerical simulation of short laminar separation bubbles with turbulent reattachment. J. Fluid Mech. 410, 1–28.Google Scholar
Anderson, E. J., McGillis, W. R. & Grosenbaugh, M. A. 2001 The boundary layer of swimming fish. J. Expl Biol. 204 (1), 81–102.Google Scholar
Anderson, J. D. Jr 1985 Fundamentals of Aerodynamics. Tata McGraw-Hill Education.Google Scholar
Asadi, H., Asgharzadeh, H. & Borazjani, I. 2018 On the scaling of propagation of periodically generated vortex rings. J. Fluid Mech. 853, 150–170.Google Scholar
Asgharzadeh, H., Asadi, H., Meng, H. & Borazjani, I. 2019 A non-dimensional parameter for classification of the flow in intracranial aneurysms. II. Patient-specific geometries. Phys. Fluids 31 (3), 031905.Google Scholar
Asgharzadeh, H. & Borazjani, I. 2017 A Newton–Krylov method with an approximate analytical Jacobian for implicit solution of Navier–Stokes equations on staggered overset-curvilinear grids with immersed boundaries. J. Comput. Phys. 331, 227–256.Google Scholar
Bani-Hani, M. A. & Karami, M. A. 2015 Analytical structural optimization and experimental verifications for traveling wave generation in self-assembling swimming smart boxes. Smart Mater. Struct. 24 (9), 094005.Google Scholar
Beem, H. R., Rival, D. E. & Triantafyllou, M. S. 2012 On the stabilization of leading-edge vortices with spanwise flow. Exp. Fluids 52 (2), 511–517.Google Scholar
Bohl, D. G. & Koochesfahani, M. M. 2009 Mtv measurements of the vortical field in the wake of an airfoil oscillating at high reduced frequency. J. Fluid Mech. 620, 63–88.Google Scholar
Borazjani, I. & Daghooghi, M. 2013 The fish tail motion forms an attached leading edge vortex. Proc. R. Soc. Lond. B 280 (1756), 2012–2071.Google Scholar
Borazjani, I., Ge, L. & Sotiropoulos, F. 2008 Curvilinear immersed boundary method for simulating fluid structure interaction with complex 3D rigid bodies. J. Comput. Phys. 227 (16), 7587–7620.Google Scholar
Borazjani, I. & Sotiropoulos, F. 2008 Numerical investigation of the hydrodynamics of carangiform swimming in the transitional and inertial flow regimes. J. Expl Biol. 211 (10), 1541–1558.Google Scholar
Borazjani, I. & Sotiropoulos, F. 2009 Numerical investigation of the hydrodynamics of anguilliform swimming in the transitional and inertial flow regimes. J. Expl Biol. 212 (4), 576–592.Google Scholar
Borazjani, I. & Sotiropoulos, F. 2010 On the role of form and kinematics on the hydrodynamics of self-propelled body/caudal fin swimming. J. Expl Biol. 213 (1), 89–107.Google Scholar
Borazjani, I., Sotiropoulos, F., Tytell, E. D. & Lauder, G. V. 2012 Hydrodynamics of the bluegill sunfish c-start escape response: three-dimensional simulations and comparison with experimental data. J. Expl Biol. 215 (4), 671–684.Google Scholar
Bottom, R. G. II, Borazjani, I., Blevins, E. L. & Lauder, G. V. 2016 Hydrodynamics of swimming in stingrays: numerical simulations and the role of the leading-edge vortex. J. Fluid Mech. 788, 407–443.Google Scholar
Braslow, A. L., Hicks, R. M. & Harris, R. V1966 Use of grit-type boundary-layer-transition trips on wind-tunnel models. NASA TN-D-3579.Google Scholar
Daghooghi, M. & Borazjani, I. 2015 The hydrodynamic advantages of synchronized swimming in a rectangular pattern. Bioinspir. Biomim. 10 (5), 056018.Google Scholar
DeMauro, E. P., DellOrso, H., Zaremski, S., Leong, C. M. & Amitay, M. 2015 Control of laminar separation bubble on NACA 0009 airfoil using electroactive polymers. AIAA J. 53 (8), 2270–2279.Google Scholar
Donovan, J., Kral, L. & Cary, A. 1998 Active flow control applied to an airfoil. In 36th AIAA Aerospace Sciences Meeting and Exhibit. American Institute of Aeronautics and Astronautics.Google Scholar
Ehrenstein, U. & Eloy, C. 2013 Skin friction on a moving wall and its implications for swimming animals. J. Fluid Mech. 718, 321–346.Google Scholar
Ellington, C. P., den berg, C. V., Wilmott, A. P. & Thomas, A. L. R. 1996 Leading-edge vortices in insect flight. Nature 384, 626–630.Google Scholar
Fish, F. E. & Lauder, G. V. 2006 Passive and active flow control by swimming fishes and mammals. Annu. Rev. Fluid Mech. 38, 193–224.Google Scholar
Franck, J. A. & Breuer, K. S. 2017 Unsteady high-lift mechanisms from heaving flat plate simulations. Intl J. Heat Fluid Flow 67, 230–239.Google Scholar
Ge, L. & Sotiropoulos, F. 2007 A numerical method for solving the 3D unsteady incompressible Navier–Stokes equations in curvilinear domains with complex immersed boundaries. J. Comput. Phys. 225 (2), 1782–1809.Google Scholar
Gilmanov, A. & Sotiropoulos, F. 2005 A hybrid Cartesian/immersed boundary method for simulating flows with 3D, geometrically complex, moving bodies. J. Comput. Phys. 207 (2), 457–492.Google Scholar
Godoy-Diana, R. & Thiria, B. 2018 On the diverse roles of fluid dynamic drag in animal swimming and flying. J. R. Soc. Interface 15 (139), 20170715.Google Scholar
Greenblatt, D. & Wygnanski, I. J. 2000 The control of flow separation by periodic excitation. Prog. Aerosp. Sci. 36 (7), 487–545.Google Scholar
Hammer, P. R.2016 Computational study of the effect of Reynolds number and motion trajectory asymmetry on the aerodynamics of a pitching airfoil at low Reynolds number. PhD thesis, Michigan State University.Google Scholar
Hedayat, M., Asgharzadeh, H. & Borazjani, I. 2017 Platelet activation of mechanical versus bioprosthetic heart valves during systole. J. Biomech. 56, 111–116.Google Scholar
Hedayat, M. & Borazjani, I. 2019 Comparison of platelet activation through hinge versus bulk flow in bileaflet mechanical heart valves. J. Biomech. 83, 280–290.Google Scholar
Jones, G., Santer, M., Debiasi, M. & Papadakis, G. 2018 Control of flow separation around an airfoil at low Reynolds numbers using periodic surface morphing. J. Fluids Struct. 76, 536–557.Google Scholar
Kang, S., Borazjani, I., Colby, J. A. & Sotiropoulos, F. 2012 Numerical simulation of 3D flow past a real-life marine hydrokinetic turbine. Adv. Water Resour. 39, 33–43.Google Scholar
Kim, D. & Gharib, M. 2010 Experimental study of three-dimensional vortex structures in translating and rotating plates. Exp. Fluids 49 (1), 329–339.Google Scholar
Lachmann, G. V. 2014 Boundary Layer and Flow Control: Its Principles and Application. Elsevier.Google Scholar
Lai, J. C. S. & Platzer, M. F. 1999 Jet characteristics of a plunging airfoil. AIAA J. 37 (12), 1529–1537.Google Scholar
Lentink, D., Dickson, W. B., van Leeuwen, J. L. & Dickinson, M. H. 2009 Leading-edge vortices elevate lift of autorotating plant seeds. Science 324, 1438–1440.Google Scholar
Lighthill, M. J. 1960 Note on the swimming of slender fish. J. Fluid Mech. 9 (2), 305–317.Google Scholar
Lilly, D. K. 1992 A proposed modification of the germano subgrid-scale closure method. Phys. Fluids A 4 (3), 633–635.Google Scholar
Lin, J. C. 2002 Review of research on low-profile vortex generators to control boundary-layer separation. Prog. Aerosp. Sci. 38 (4–5), 389–420.Google Scholar
Liu, G., Ren, Y., Dong, H., Akanyeti, O., Liao, J. C. & Lauder, G. V. 2017 Computational analysis of vortex dynamics and performance enhancement due to body–fin and fin–fin interactions in fish-like locomotion. J. Fluid Mech. 829, 65–88.Google Scholar
Mamori, H., Iwamoto, K. & Murata, A. 2014 Effect of the parameters of traveling waves created by blowing and suction on the relaminarization phenomena in fully developed turbulent channel flow. Phys. Fluids 26 (1), 015101.Google Scholar
Mancini, P., Manar, F., Granlund, K., Ol, M. V. & Jones, A. R. 2015 Unsteady aerodynamic characteristics of a translating rigid wing at low Reynolds number. Phys. Fluids 27 (12), 123102.Google Scholar
Mueller, T. J. & Batil, S. M. 1982 Experimental studies of separation on a two-dimensional airfoil at low Reynolds numbers. AIAA J. 20 (4), 457–463.Google Scholar
Muijres, F. T., Johansson, L. C., Barfield, R., Wolf, M., Spedding., G. R. & Hedenström, A. 2008 Leading-edge vortex improves lift in slow-flying bats. Science 319, 1250–1253.Google Scholar
Nakanishi, R., Mamori, H. & Fukagata, K. 2012 Relaminarization of turbulent channel flow using traveling wave-like wall deformation. Intl J. Heat Fluid Flow 35, 152–159.Google Scholar
Payne, P. R. 1981 The virtual mass of a rectangular flat plate of finite aspect ratio. Ocean Engng 8 (5), 541–545.Google Scholar
Pelletier, A. & Mueller, T. J. 2000 Low Reynolds number aerodynamics of low-aspect-ratio, thin/flat/cambered-plate wings. J. Aircraft 37 (5), 825–832.Google Scholar
Piñeirua, M., Godoy-Diana, R. & Thiria, B. 2015 Resistive thrust production can be as crucial as added mass mechanisms for inertial undulatory swimmers. Phys. Rev. E 92 (2), 021001.Google Scholar
Pope, S. B. & Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.Google Scholar
Quinn, D. B., Lauder, G. V. & Smits, A. J. 2014 Scaling the propulsive performance of heaving flexible panels. J. Fluid Mech. 738, 250–267.Google Scholar
Ramamurti, R. & Sandberg, W. 2001 Simulation of flow about flapping airfoils using finite element incompressible flow solver. AIAA J. 39 (2), 253–260.Google Scholar
Sarpkaya, T. 1975 An inviscid model of two-dimensional vortex shedding for transient and asymptotically steady separated flow over an inclined plate. J. Fluid Mech. 68 (1), 109–128.Google Scholar
Schlichting, H. & Gersten, K. 2016 Boundary-Layer Theory. Springer.Google Scholar
Shen, L., Zhang, X., Yue, D. K. P. & Triantafyllou, M. S. 2003 Turbulent flow over a flexible wall undergoing a streamwise travelling wave motion. J. Fluid Mech. 484, 197–221.Google Scholar
Shyy, W. & Liu, H. 2007 Flapping wings and aerodynamic lift: the role of leading-edge vortices. AIAA 45, 2817–2819.Google Scholar
Taneda, S. 1976 Visual study of unsteady separated flows around bodies. Prog. Aerosp. Sci. 17, 287–348.Google Scholar
Tangler, J. L. 2004 Insight into wind turbine stall and post-stall aerodynamics. Wind Energy 7, 247–260.Google Scholar
Triantafyllou, M. S., Triantafyllou, G. S. & Yue, D. K. P. 2000 Hydrodynamics of fishlike swimming. Annu. Rev. Fluid Mech. 32 (1), 33–53.Google Scholar
Visbal, M. 2011 Three-dimensional flow structure on a heaving low-aspect-ratio wing. In 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, p. 219.Google Scholar
Wu, C.-J., Wang, L. & Wu, J.-Z. 2007 Suppression of the von kármán vortex street behind a circular cylinder by a travelling wave generated by a flexible surface. J. Fluid Mech. 574, 365–391.Google Scholar
Wu, T. Y.-T. 1961 Swimming of a waving plate. J. Fluid Mech. 10 (3), 321–344.Google Scholar