Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-14T04:55:03.160Z Has data issue: false hasContentIssue false
  • English
  • Français

Laminar vortex rings impinging onto porous walls with a constant porosity

Published online by Cambridge University Press:  05 January 2018

Yang Xu ,
Jin-Jun Wang Open the ORCID record for Jin-Jun Wang [Opens in a new window] ,
Li-Hao Feng Open the ORCID record for Li-Hao Feng [Opens in a new window] ,
Guo-Sheng He  and
Zhong-Yi Wang
Yang Xu
Affiliation:
Key Laboratory of Fluid Mechanics, Beijing University of Aeronautics and Astronautics, Ministry of Education, Beijing 100191, PR China
Jin-Jun Wang*
Affiliation:
Key Laboratory of Fluid Mechanics, Beijing University of Aeronautics and Astronautics, Ministry of Education, Beijing 100191, PR China
Li-Hao Feng
Affiliation:
Key Laboratory of Fluid Mechanics, Beijing University of Aeronautics and Astronautics, Ministry of Education, Beijing 100191, PR China
Guo-Sheng He
Affiliation:
Key Laboratory of Fluid Mechanics, Beijing University of Aeronautics and Astronautics, Ministry of Education, Beijing 100191, PR China
Zhong-Yi Wang
Affiliation:
Key Laboratory of Fluid Mechanics, Beijing University of Aeronautics and Astronautics, Ministry of Education, Beijing 100191, PR China
*
†Email address for correspondence: jjwang@buaa.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

JFM classification

Wakes/Jets: Jets Vortex Flows: Vortex dynamics Low-Reynolds-number flows: Porous media
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 837 , 25 February 2018 , pp. 729 - 764
Copyright
© 2018 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

Adhikari, D. & Lim, T. T. 2009 The impact of a vortex ring on a porous screen. Fluid Dyn. Res. 41 (5), 051404.Google Scholar
Amitay, M., Smith, B. L. & Glezer, A.1998 Aerodynamic flow control using synthetic jet technology. AIAA Paper 98-0208.10.2514/6.1998-208Google Scholar
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, 79–94.Google Scholar
Arik, M. 2008 Local heat transfer coefficients of a high-frequency synthetic jet during impingement cooling over flat surfaces. Heat Transfer Engng 29 (9), 763–773.10.1080/01457630802053769Google Scholar
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), 263–272.Google Scholar
Bradshaw, P. 1965 The effect of wind-tunnel screens on nominally two-dimensional boundary layers. J. Fluid Mech. 22 (4), 679–687.Google Scholar
Cant, R., Castro, I. & Walklate, P. 2002 Plane jets impinging on porous walls. Exp. Fluids 32 (1), 16–26.10.1007/s003480200002Google Scholar
Capp, S. P.1983 Experimental investigation of the turbulent axisymmetric jet. PhD dissertation, University at Buffalo, SUNY.Google Scholar
Cerretelli, C. & Williamson, C. H. K. 2003 The physical mechanism for vortex merging. J. Fluid Mech. 475, 41–77.10.1017/S0022112002002847Google Scholar
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), 2578–2584.10.1007/s11431-012-4970-yGoogle Scholar
Cheng, M., Lou, J. & Lim, T. T. 2014 A numerical study of a vortex ring impacting a permeable wall. Phys. Fluids 26 (10), 103602.10.1063/1.4897519Google Scholar
Cheng, M., Lou, J. & Lim, T. T. 2015 Leapfrogging of multiple coaxial viscous vortex rings. Phys. Fluids 27 (3), 031702.10.1063/1.4915890Google Scholar
Cheng, M., Lou, J. & Luo, L. S. 2010 Numerical study of a vortex ring impacting a flat wall. J. Fluid Mech. 660, 430–455.Google Scholar
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), 1391–1401.10.1063/1.868527Google Scholar
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, 331–336.Google Scholar
Dabiri, J. O. & Gharib, M. 2004 Fluid entrainment by isolated vortex rings. J. Fluid Mech. 511, 311–331.10.1017/S0022112004009784Google Scholar
Dazin, A., Dupont, P. & Stanislas, M. 2006 Experimental characterization of the instability of the vortex ring. Part I: linear phase. Exp. Fluids 40 (3), 383–399.Google Scholar
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), 5058–5071.Google Scholar
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.Google Scholar
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, 232–259.Google Scholar
Gan, L., Dawson, J. R. & Nickels, T. B. 2012 On the drag of turbulent vortex rings. J. Fluid Mech. 709, 85–105.Google Scholar
Gao, L. & Yu, S. C. M. 2012 Development of the trailing shear layer in a starting jet during pinch-off. J. Fluid Mech. 700, 382–405.Google Scholar
Gharib, M., Rambod, E. & Shariff, K. 1998 A universal time scale for vortex ring formation. J. Fluid Mech. 360, 121–140.10.1017/S0022112097008410Google Scholar
Ghosh, D. & Baeder, J. D. 2012 High-order accurate incompressible Navier–Stokes algorithm for vortex–ring interactions with solid wall. AIAA J. 50 (11), 2408–2422.Google Scholar
Glezer, A. 1988 The formation of vortex rings. Phys. Fluids 31 (12), 3532–3542.Google Scholar
Greco, C. S., Cardone, G. & Soria, J. 2017 On the behaviour of impinging zero-net-mass-flux jets. J. Fluid Mech. 810, 25–59.Google Scholar
Gresho, P. M. & Sani, R. L. 1987 On pressure boundary conditions for the incompressible Navier–Stokes equations. Intl J. Numer. Meth. Fluids 7 (10), 1111–1145.Google Scholar
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. 671–676.Google Scholar
Haller, G. & Yuan, G. 2000 Lagrangian coherent structures and mixing in two-dimensional turbulence. Physica D 147 (3), 352–370.Google Scholar
Hrynuk, J. T., van Luipen, J. & Bohl, D. 2012 Flow visualization of a vortex ring interaction with porous surfaces. Phys. Fluids 24 (3), 037103.10.1063/1.3695377Google Scholar
James, R. D., Jacobs, J. W. & Glezer, A. 1996 A round turbulent jet produced by an oscillating diaphragm. Phys. Fluids 8 (9), 2484–2495.Google Scholar
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), 269–277.Google Scholar
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), 1271–1281.10.1063/1.1564600Google Scholar
Kurtulus, D. F., Scarano, F. & David, L. 2007 Unsteady aerodynamic forces estimation on a square cylinder by TR-PIV. Exp. Fluids 42 (2), 185–196.Google Scholar
Lage, J. L., Krueger, P. S. & Narasimhan, A. 2005 Protocol for measuring permeability and form coefficient of porous media. Phys. Fluids 17 (8), 088101.10.1063/1.1979307Google Scholar
Lim, T. T. & Nickels, T. B. 1995 Vortex rings. In Fluid Vortices (ed. Green, S. I.), pp. 95–153. Springer.Google Scholar
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, 417–457.Google Scholar
Maxworthy, T. 1977 Some experimental studies of vortex rings. J. Fluid Mech. 81, 465–495.10.1017/S0022112077002171Google Scholar
Mittal, R. & Rampunggoon, P. 2002 On the virtual aeroshaping effect of synthetic jets. Phys. Fluids 14 (4), 1533–1536.10.1063/1.1453470Google Scholar
Moreira, R. G. 2001 Impingement drying of foods using hot air and superheated steam. J. Food Engng 49 (4), 291–295.Google Scholar
Muskat, M. & Botset, H. G. 1931 Flow of gas through porous materials. Physics 1 (1), 27–47.Google Scholar
Musta, M. N. & Krueger, P. S. 2014 Interaction of vortex rings with multiple permeable screens. Phys. Fluids 26 (11), 113101.10.1063/1.4900769Google Scholar
Musta, M. N. & Krueger, P. S. 2015 Interaction of steady jets with an array of permeable screens. Exp. Fluids 56 (3), 1–22.10.1007/s00348-015-1925-7Google Scholar
Naaktgeboren, C., Krueger, P. S. & Lage, J. L. 2012a Interaction of a laminar vortex ring with a thin permeable screen. J. Fluid Mech. 707, 260–286.10.1017/jfm.2012.277Google Scholar
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), 051209.10.1115/1.4006614Google Scholar
New, T. H., Shi, S. & Zang, B. 2016 Some observations on vortex-ring collisions upon inclined surface. Exp. Fluids 57 (6), 1–18.Google Scholar
Onu, K., Huhn, F. & Haller, G. 2015 LCS tool: a computational platform for Lagrangian coherent structures. J. Comput. Sci. 7, 26–36.10.1016/j.jocs.2014.12.002Google Scholar
Orlandi, P. & Verzicco, R. 1993 Vortex rings impinging on walls: axisymmetric and three-dimensional simulations. J. Fluid Mech. 256, 615–646.Google Scholar
van Oudheusden, B. W. 2013 PIV-based pressure measurement. Meas. Sci. Technol. 24 (3), 032001.Google Scholar
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), 248–257.10.1007/s11433-009-0033-1Google Scholar
Panchapakesan, N. R. & Lumley, J. L. 1993 Turbulence measurements in axisymmetric jets of air and helium. Part 1. Air jet. J. Fluid Mech. 246, 197–223.Google Scholar
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), 3900–3908.Google Scholar
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, 940–965.10.1017/jfm.2016.833Google Scholar
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.Google Scholar
Shariff, K. & Leonard, A. 1992 Vortex rings. Annu. Rev. Fluid Mech. 24 (1), 235–279.Google Scholar
Shuster, J. M. & Smith, D. R. 2007 Experimental study of the formation and scaling of a round synthetic jet. Phys. Fluids 19 (4), 045109.10.1063/1.2711481Google Scholar
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.Google Scholar
Silva, L. & Ortega, A. 2017 Vortex dynamics and mechanisms of heat transfer enhancement in synthetic jet impingement. Intl J. Therm. Sci. 112, 153–164.Google Scholar
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, 339–350.Google Scholar
Smith, B. L. & Glezer, A. 1998 The formation and evolution of synthetic jets. Phys. Fluids 10 (9), 2281–2297.Google Scholar
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. 287–309. Stanford University.Google Scholar
Sutera, S. P. & Skalak, R. 1993 The history of Poiseuille’s law. Annu. Rev. Fluid Mech. 25 (1), 1–20.10.1146/annurev.fl.25.010193.000245Google Scholar
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), 7596–7608.Google Scholar
Verzicco, R. & Orlandi, P. 1996 Wall/vortex-ring interactions. Appl. Mech. Rev. 49 (10), 447–461.Google Scholar
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, 99–140.10.1017/S0022112087002027Google Scholar
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), 1–16.Google Scholar
Webb, S. & Castro, I. P. 2006 Axisymmetric jets impinging on porous walls. Exp. Fluids 40 (6), 951–961.10.1007/s00348-006-0131-zGoogle Scholar
Weigand, A. & Gharib, M. 1995 Turbulent vortex ring/free surface interaction. Trans. ASME J. Fluids Engng 117, 374–381.Google Scholar
Widnall, S. E., Bliss, D. B. & Tsai, C. Y. 1974 The instability of short waves on a vortex ring. J. Fluid Mech. 66, 35–47.Google Scholar
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), 638–642.Google Scholar
Xu, Y., Feng, L. H. & Wang, J. J. 2013 Experimental investigation of a synthetic jet impinging on a fixed wall. Exp. Fluids 54 (5), 1–13.10.1007/s00348-013-1512-8Google Scholar
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.Google Scholar
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, 211–219.10.1016/j.expthermflusci.2016.02.010Google Scholar
Zhang, P. F. & Wang, J. J. 2007 Novel signal wave pattern to generate more efficient synthetic jet. AIAA J. 45 (5), 1058–1065.10.2514/1.25445Google Scholar
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), 309–329.Google Scholar