Skip to main content

Laminar vortex rings impinging onto porous walls with a constant porosity

  • Yang Xu (a1), Jin-Jun Wang (a1), Li-Hao Feng (a1), Guo-Sheng He (a1) and Zhong-Yi Wang (a1)...

For the first time, an experiment has been conducted to investigate synthetic jet laminar vortex rings impinging onto porous walls with different geometries by time-resolved particle image velocimetry. The geometry of the porous wall is changed by varying the hole diameter on the wall (from 1.0 mm to 3.0 mm) when surface porosity is kept constant ( $\unicode[STIX]{x1D719}=75\,\%$ ). The finite-time Lyapunov exponent and phase-averaged vorticity field derived from particle image velocimetry data are presented to reveal the evolution of the vortical structures. A mechanism associated with vorticity cancellation is proposed to explain the formation of downstream transmitted vortex rings; and both the vortex ring trajectory and the time-mean flow feature are compared between different cases. It is found that the hole diameter significantly influences the evolution of the flow structures on both the upstream and downstream sides of the porous wall. In particular, for a porous wall with a small hole diameter ( $d_{h}^{\ast }=0.067$ , 0.10 and 0.133), the transmitted finger-type jets will reorganize into a well-formed transmitted vortex ring in the downstream flow. However, for the case of a large hole diameter of $d_{h}^{\ast }=0.20$ , the transmitted vortex ring is not well formed because of insufficient vorticity cancellation. Additionally, the residual vorticity gradually evolves into discrete jet-like structures downstream, which further weaken the intensity of the transmitted vortex ring. Consequently, the transmitted flow structures for the $d_{h}^{\ast }=0.20$ case would lose coherence more easily (or probably even transition to turbulence), resulting in a faster decay of the axial velocity and stronger entrainment of the transmitted jet. For all porous wall cases, the velocity profile of the transmitted jet exhibits self-similar behaviour in the far field ( $z/D_{0}\geqslant 6.03$ ), which agrees well with the velocity distribution of free synthetic jets. With the help of the control-volume approach, the time-mean drag of the porous wall is evaluated experimentally for the first time. It is shown that the porous wall drag increases with the decrease in the hole diameter. Moreover, for a porous wall with a small hole diameter ( $d_{h}^{\ast }=0.067$ , 0.10 and 0.133), it appears that the porous wall drag mainly derives from the viscous effect. However, as $d_{h}^{\ast }$ increases to 0.20, the form drag associated with the porous wall geometry becomes significant.

Corresponding author
Email address for correspondence:
Hide All
Adhikari, D. & Lim, T. T. 2009 The impact of a vortex ring on a porous screen. Fluid Dyn. Res. 41 (5), 051404.
Amitay, M., Smith, B. L. & Glezer, A.1998 Aerodynamic flow control using synthetic jet technology. AIAA Paper 98-0208.
Archer, P. J., Thomas, T. G. & Coleman, G. N. 2010 The instability of a vortex ring impinging on a free surface. J. Fluid Mech. 642, 7994.
Arik, M. 2008 Local heat transfer coefficients of a high-frequency synthetic jet during impingement cooling over flat surfaces. Heat Transfer Engng 29 (9), 763773.
Boomsma, K. & Poulikakos, D. 2002 The effects of compression and pore size variations on the liquid flow characteristics in metal foams. Trans. ASME J. Fluids Engng 124 (3), 263272.
Bradshaw, P. 1965 The effect of wind-tunnel screens on nominally two-dimensional boundary layers. J. Fluid Mech. 22 (4), 679687.
Cant, R., Castro, I. & Walklate, P. 2002 Plane jets impinging on porous walls. Exp. Fluids 32 (1), 1626.
Capp, S. P.1983 Experimental investigation of the turbulent axisymmetric jet. PhD dissertation, University at Buffalo, SUNY.
Cerretelli, C. & Williamson, C. H. K. 2003 The physical mechanism for vortex merging. J. Fluid Mech. 475, 4177.
Chen, Z. J. & Wang, J. J. 2012 Numerical investigation on synthetic jet flow control inside an S-inlet duct. Sci. China–Technol. Sci. 55 (9), 25782584.
Cheng, M., Lou, J. & Lim, T. T. 2014 A numerical study of a vortex ring impacting a permeable wall. Phys. Fluids 26 (10), 103602.
Cheng, M., Lou, J. & Lim, T. T. 2015 Leapfrogging of multiple coaxial viscous vortex rings. Phys. Fluids 27 (3), 031702.
Cheng, M., Lou, J. & Luo, L. S. 2010 Numerical study of a vortex ring impacting a flat wall. J. Fluid Mech. 660, 430455.
Chu, C. C., Wang, C. T. & Chang, C. C. 1995 A vortex ring impinging on a solid plane surface – vortex structure and surface force. Phys. Fluids 7 (6), 13911401.
Dabiri, J. O., Bose, S., Gemmell, B. J., Colin, S. P. & Costello, J. H. 2014 An algorithm to estimate unsteady and quasi-steady pressure fields from velocity field measurements. J. Exp. Biol. 217, 331336.
Dabiri, J. O. & Gharib, M. 2004 Fluid entrainment by isolated vortex rings. J. Fluid Mech. 511, 311331.
Dazin, A., Dupont, P. & Stanislas, M. 2006 Experimental characterization of the instability of the vortex ring. Part I: linear phase. Exp. Fluids 40 (3), 383399.
Dogruoz, M. B., Urdaneta, M. & Ortega, A. 2005 Experiments and modeling of the hydraulic resistance and heat transfer of in-line square pin fin heat sinks with top by-pass flow. Intl J. Heat Mass Transfer 48 (23), 50585071.
El Hassan, M., Assoum, H. H., Martinuzzi, R., Sobolik, V., Abed-Meraim, K. & Sakout, A. 2013 Experimental investigation of the wall shear stress in a circular impinging jet. Phys. Fluids 25 (7), 077101.
Feng, L. H. & Wang, J. J. 2010 Circular cylinder vortex-synchronization control with a synthetic jet positioned at the rear stagnation point. J. Fluid Mech. 662, 232259.
Gan, L., Dawson, J. R. & Nickels, T. B. 2012 On the drag of turbulent vortex rings. J. Fluid Mech. 709, 85105.
Gao, L. & Yu, S. C. M. 2012 Development of the trailing shear layer in a starting jet during pinch-off. J. Fluid Mech. 700, 382405.
Gharib, M., Rambod, E. & Shariff, K. 1998 A universal time scale for vortex ring formation. J. Fluid Mech. 360, 121140.
Ghosh, D. & Baeder, J. D. 2012 High-order accurate incompressible Navier–Stokes algorithm for vortex–ring interactions with solid wall. AIAA J. 50 (11), 24082422.
Glezer, A. 1988 The formation of vortex rings. Phys. Fluids 31 (12), 35323542.
Greco, C. S., Cardone, G. & Soria, J. 2017 On the behaviour of impinging zero-net-mass-flux jets. J. Fluid Mech. 810, 2559.
Gresho, P. M. & Sani, R. L. 1987 On pressure boundary conditions for the incompressible Navier–Stokes equations. Intl J. Numer. Meth. Fluids 7 (10), 11111145.
Gurka, R., Liberzon, A., Hefetz, D., Rubinstein, D. & Shavit, U. 1999 Computation of pressure distribution using PIV velocity data. In 3rd International Workshop on Particle Image Velocimetry, Santa Barbara, pp. 671676.
Haller, G. & Yuan, G. 2000 Lagrangian coherent structures and mixing in two-dimensional turbulence. Physica D 147 (3), 352370.
Hrynuk, J. T., van Luipen, J. & Bohl, D. 2012 Flow visualization of a vortex ring interaction with porous surfaces. Phys. Fluids 24 (3), 037103.
James, R. D., Jacobs, J. W. & Glezer, A. 1996 A round turbulent jet produced by an oscillating diaphragm. Phys. Fluids 8 (9), 24842495.
Krishnan, G. & Mohseni, K. 2010 An experimental study of a radial wall jet formed by the normal impingement of a round synthetic jet. Eur. J. Mech. (B/Fluids) 29 (4), 269277.
Krueger, P. S. & Gharib, M. 2003 The significance of vortex ring formation to the impulse and thrust of a starting jet. Phys. Fluids 15 (5), 12711281.
Kurtulus, D. F., Scarano, F. & David, L. 2007 Unsteady aerodynamic forces estimation on a square cylinder by TR-PIV. Exp. Fluids 42 (2), 185196.
Lage, J. L., Krueger, P. S. & Narasimhan, A. 2005 Protocol for measuring permeability and form coefficient of porous media. Phys. Fluids 17 (8), 088101.
Lim, T. T. & Nickels, T. B. 1995 Vortex rings. In Fluid Vortices (ed. Green, S. I.), pp. 95153. Springer.
Liu, X. & Katz, J. 2013 Vortex–corner interactions in a cavity shear layer elucidated by time-resolved measurements of the pressure field. J. Fluid Mech. 728, 417457.
Maxworthy, T. 1977 Some experimental studies of vortex rings. J. Fluid Mech. 81, 465495.
Mittal, R. & Rampunggoon, P. 2002 On the virtual aeroshaping effect of synthetic jets. Phys. Fluids 14 (4), 15331536.
Moreira, R. G. 2001 Impingement drying of foods using hot air and superheated steam. J. Food Engng 49 (4), 291295.
Muskat, M. & Botset, H. G. 1931 Flow of gas through porous materials. Physics 1 (1), 2747.
Musta, M. N. & Krueger, P. S. 2014 Interaction of vortex rings with multiple permeable screens. Phys. Fluids 26 (11), 113101.
Musta, M. N. & Krueger, P. S. 2015 Interaction of steady jets with an array of permeable screens. Exp. Fluids 56 (3), 122.
Naaktgeboren, C., Krueger, P. S. & Lage, J. L. 2012a Interaction of a laminar vortex ring with a thin permeable screen. J. Fluid Mech. 707, 260286.
Naaktgeboren, C., Krueger, P. S. & Lage, J. L. 2012b Inlet and outlet pressure-drop effects on the determination of permeability and form coefficient of a porous medium. Trans. ASME J. Fluids Engng 134 (5), 051209.
New, T. H., Shi, S. & Zang, B. 2016 Some observations on vortex-ring collisions upon inclined surface. Exp. Fluids 57 (6), 118.
Onu, K., Huhn, F. & Haller, G. 2015 LCS tool: a computational platform for Lagrangian coherent structures. J. Comput. Sci. 7, 2636.
Orlandi, P. & Verzicco, R. 1993 Vortex rings impinging on walls: axisymmetric and three-dimensional simulations. J. Fluid Mech. 256, 615646.
van Oudheusden, B. W. 2013 PIV-based pressure measurement. Meas. Sci. Technol. 24 (3), 032001.
Pan, C., Wang, J. J. & Zhang, C. 2009 Identification of Lagrangian coherent structures in the turbulent boundary layer. Sci. China Ser. G–Phys. Mech. 52 (2), 248257.
Panchapakesan, N. R. & Lumley, J. L. 1993 Turbulence measurements in axisymmetric jets of air and helium. Part 1. Air jet. J. Fluid Mech. 246, 197223.
Persoons, T., McGuinn, A. & Murray, D. B. 2011 A general correlation for the stagnation point Nusselt number of an axisymmetric impinging synthetic jet. Intl J. Heat Mass Transfer 54 (17), 39003908.
Qu, Y., Wang, J. J., Sun, M., Feng, L. H., Pan, C., Gao, Q. & He, G. S. 2017 Wake vortex evolution of square cylinder with a slot synthetic jet positioned at the rear surface. J. Fluid Mech. 812, 940965.
Shadden, S. C., Dabiri, J. O. & Marsden, J. E. 2006 Lagrangian analysis of fluid transport in empirical vortex ring flows. Phys. Fluids 18 (4), 047105.
Shariff, K. & Leonard, A. 1992 Vortex rings. Annu. Rev. Fluid Mech. 24 (1), 235279.
Shuster, J. M. & Smith, D. R. 2007 Experimental study of the formation and scaling of a round synthetic jet. Phys. Fluids 19 (4), 045109.
Silva, L. & Ortega, A. 2013 Convective heat transfer in an impinging synthetic jet: a numerical investigation of a canonical geometry. Trans. ASME J. Heat Transfer 135 (8), 082201.
Silva, L. & Ortega, A. 2017 Vortex dynamics and mechanisms of heat transfer enhancement in synthetic jet impingement. Intl J. Therm. Sci. 112, 153164.
Silva, L., Ortega, A. & Rose, I. 2015 Experimental convective heat transfer in a geometrically large two-dimensional impinging synthetic jet. Intl J. Therm. Sci. 90, 339350.
Smith, B. L. & Glezer, A. 1998 The formation and evolution of synthetic jets. Phys. Fluids 10 (9), 22812297.
Stanaway, S., Shariff, K. & Hussain, F. 1988 Head-on collision of viscous vortex rings. In Studying Turbulence Using Numerical Simulation Databases 2: Proceedings of the 1988 CTR Summer Program, pp. 287309. Stanford University.
Sutera, S. P. & Skalak, R. 1993 The history of Poiseuille’s law. Annu. Rev. Fluid Mech. 25 (1), 120.
Vanierschot, M. & van den Bulck, E. 2008 Planar pressure field determination in the initial merging zone of an annular swirling jet based on stereo-PIV measurements. Sensors 8 (12), 75967608.
Verzicco, R. & Orlandi, P. 1996 Wall/vortex-ring interactions. Appl. Mech. Rev. 49 (10), 447461.
Walker, J. D. A., Smith, C. R., Cerra, A. W. & Doligalski, T. L. 1987 The impact of a vortex ring on a wall. J. Fluid Mech. 181, 99140.
Wang, Z. Y., Gao, Q., Wang, C. Y., Wei, R. J. & Wang, J. J. 2016 An irrotation correction on pressure gradient and orthogonal-path integration for PIV-based pressure reconstruction. Exp. Fluids 57 (6), 116.
Webb, S. & Castro, I. P. 2006 Axisymmetric jets impinging on porous walls. Exp. Fluids 40 (6), 951961.
Weigand, A. & Gharib, M. 1995 Turbulent vortex ring/free surface interaction. Trans. ASME J. Fluids Engng 117, 374381.
Widnall, S. E., Bliss, D. B. & Tsai, C. Y. 1974 The instability of short waves on a vortex ring. J. Fluid Mech. 66, 3547.
Wilson, L., Narasimhan, A. & Venkateshan, S. P. 2006 Permeability and form coefficient measurement of porous inserts with non-Darcy model using non-plug flow experiments. Trans. ASME J. Fluids Engng 128 (3), 638642.
Xu, Y., Feng, L. H. & Wang, J. J. 2013 Experimental investigation of a synthetic jet impinging on a fixed wall. Exp. Fluids 54 (5), 113.
Xu, Y., He, G. S., Kulkarni, V. & Wang, J. J. 2017 Experimental investigation of influence of Reynolds number on synthetic jet vortex rings impinging onto a solid wall. Exp. Fluids 58 (1), 6.
Xu, Y. & Wang, J. J. 2016 Flow structure evolution for laminar vortex rings impinging onto a fixed solid wall. J. Expl Therm. Fluid Sci. 75, 211219.
Zhang, P. F. & Wang, J. J. 2007 Novel signal wave pattern to generate more efficient synthetic jet. AIAA J. 45 (5), 10581065.
Zhong, S., Jabbal, M., Tang, H., Garcillan, L., Guo, F., Wood, N. & Warsop, C. 2007 Towards the design of synthetic-jet actuators for full-scale flight conditions. Part 2: low-dimensional performance prediction models and actuator design method. Flow Turbul. Combust. 78 (4), 309329.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *

JFM classification


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed