Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-22T12:26:04.087Z Has data issue: false hasContentIssue false
  • English
  • Français

Periodically arranged co-flowing jets

Published online by Cambridge University Press:  26 April 2006

E. Villermaux  and
E. J. Hopfinger
E. Villermaux
Affiliation:
Institut de Mécanique de Grenoble/LEGI-CNRS, BP 53X, 38041 Grenoble Cedex, France
E. J. Hopfinger
Affiliation:
Institut de Mécanique de Grenoble/LEGI-CNRS, BP 53X, 38041 Grenoble Cedex, France
Get access Rights & Permissions [Opens in a new window]

Abstract

The problem of a periodic planar arrangement of a large number of co-flowing, interacting jets is investigated. It is shown that this interaction gives rise to strong nearfield oscillations of large-scale spatial coherence and to far-field inhomogeneities. In the experiments performed, the jets were produced behind a flat plate perforated by holes arranged in a square or triangular periodic pattern and placed perpendicular to a uniform flow. At moderate Reynolds numbers, the interaction results in a remarkable low-frequency oscillation of the merging distance of the jets downstream of the plate. A detailed description of the recirculating flow in the cavities between the jets emphasizes the role of the backflow in the cavities on the oscillatory behaviour. This description is supported by measurements of the local fluctuating velocity and pressure, two-point correlation measurements and quantitative flow visualizations. These experimental observations suggest a new formulation for the instability dynamics of such unstable recirculating flows. This formulation, based on the nonlinear delayed saturation of the jet's shear layer instability (NLDS model) predicts successfully the dependence of the oscillation of the merging distance on the jet Reynolds number and on the local geometrical features of the confinement of the jets. Furthermore, it is shown that the diffusion of mass coming from one jet, seeded with an inert dye, gives rise to an exponential diffusion front over a distance corresponding to a few mesh sizes indicating a strong local coupling of the jets. At the scale of the whole jet assembly, the oscillations are organized as large-scale travelling waves, propagating from the boundaries of the domain to its centre. This symmetry-breaking property is discussed and supplemented by a spatio-temporal simulation of an array of coupled oscillators.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 263 , 25 March 1994 , pp. 63 - 92
Copyright
© 1994 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

Albaréde, P. & Monkewitz, P. A. 1992 A model for the formation of oblique shedding and ‘chevron’ patterns in cylinder wakes. Phys. Fluids A 4, 744–756.Google Scholar
Albaréde, P., Provansal, M. & Boyer, L. 1990 The Ginzburg-Landau equation as a model for the three-dimensional wake of an elongated bluff body. C. R. Acad. Sci. Paris 310 (II), 459–464.Google Scholar
Back, L. H. & Roschke, E. J. 1972 Shear-layer flow regimes and wave instabilities and reattachment lengths downstream of an abrupt circular expansion. Trans. ASME E: J. Appl. Mech. 677–681.Google Scholar
Baines, W. D. & Peterson, E. G. 1951 An investigation of flows through screens. Trans. ASME 73, 467–480.Google Scholar
Becker, H. A. & Massaro, T. A. 1968 Vortex evolution in a round jet. J. Fluid Mech. 31, 435–448.Google Scholar
Bergé, P. & Dubois, M. 1988 Etude expérimentale des transitions vers le chaos en convection de Rayleigh-Bénard. In Le Chaos. Collection CEA, Eyrolles, Paris.
Bearman, P. W. 1965 Investigation of the flow behind a two dimensional model with a blunt trailing edge and fitted with splitter plates. J. Fluid Mech. 21, 241–255.Google Scholar
Bouchaud, J. P. & Georges, A. 1990 Anomalous diffusion in disordered media: statistical mechanisms, models and physical applications. Phys. Rep. 4, 5, 127–293.Google Scholar
Cardoso, O. & Tabeling, P. 1991 Anomalous diffusion in a linear system of vortices. Eur. J. Mech. B/Fluids 8, 459–470.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Clarendon Press, Oxford.
Chomaz, J. M., Huerre, P. & Redekopp, L. G. 1988 Bifurcation to local and global modes in spatially developing flows. Phys. Rev. Lett. 60, 25–28.Google Scholar
Comte-Bellot, G. & Corrsin, S. 1966 The use of a contraction to improve the isotropy of a gridgenerated turbulence. J. Fluid Mech. 25, 657–682.Google Scholar
Corcos, G. M. 1979 The mixing layer: deterministic models of a turbulent flow. Rep. FM-79-2. Mech. Engng Dept., University of California, Berkeley.Google Scholar
Corrsin, S. 1944 Investigation of the behavior of parallel two-dimensional air jets. NACA ACR 4H24.Google Scholar
Crighton, D. G. 1992 The edge-tone feedback cycle; linear theory for the operating stages. J. Fluid Mech. 234, 361–391.Google Scholar
Daviaud, F., Burnol, A. & Ronsin, O. 1991 Travelling and standing waves in a spatially forced 2D convection experiment. Europhys. Lett. 16, 667–672.Google Scholar
Douady, S. 1990 Experimental study of the Faraday instability. J. Fluid Mech. 221, 383–409.Google Scholar
Eaton, J. K. & Johnston, J. P. 1980 A review of research on subsonic turbulent flow reattachment. AIAA paper 80-1438, pp. 1–11.Google Scholar
Eaton, J. K. & Johnston, J. P. 1982 Low frequency unsteadiness of a reattaching turbulent shear layer. In Turbulent Shear Flows 3 (ed. L. J. S. Bradbury, F. Durst, B. E. Launder et al.), pp. 162–170. Springer.
Fauve, S. 1991 Pattern in Fluid Flow. Woods Hole Oceanogr. Inst. Tech. Rep. WHOI-92-16. Woods Hole Oceanographic Institution.Google Scholar
Groth, J. & Johansson, A. V. 1988 Turbulence reduction by screens. J. Fluid Mech. 197, 139–155.Google Scholar
Ho, C. M. & Nosseir, N. S. 1981 Dynamics of an impinging jet. Part 1. The feedback phenomenon. J. Fluid Mech. 105, 119–142.Google Scholar
Huerre, P. & Monkewitz, P. A. 1990 Local and global instability in spatially developing flows. Ann. Rev. Fluid Mech. 22, 473–537.Google Scholar
Keller, J. J. 1982 Nonlinear self-excited acoustic oscillations within fixed boundaries. J. Fluid Mech. 123, 267–281.Google Scholar
Landau, L. D. 1944 On the problem of turbulence. C. R. Acad. Sci. URSS 44, 311–314.Google Scholar
Landau, L. D. & Lifchitz, E. M. 1989 Mécanique des Fluides. Moscow: Mir.
Manneville, P. 1991 Dissipative Structures and Weak Turbulence. Academic.
Mitchell, C. E., Crocco, L. & Sirignano, W. A. 1969 Nonlinear longitudinal instability in rocket motors with concentrated combustion. Combust. Sci. Tech. 1, 35–64.Google Scholar
Monkewitz, P. A. & Bechert, D. W., Barsikow, B. & Lehmann, B. 1990 Self-excited oscillations and mixing in a heated round jet. J. Fluid Mech. 213, 611–639.Google Scholar
Pomeau, Y., Pumir, A. & Young, W. 1989 Anomalous diffusion of tracer in convection rolls. Phys. Fluids A 1, 462–469.Google Scholar
Powell, A. 1961 On the edgetone. J. Acoust. Soc. Am. 33, 395–409.Google Scholar
Rockwell, D. & Naudascher, E. 1979 Self-sustained oscillations of impinging free shear layers. Ann. Rev. Fluid Mech. 11, 67–94.Google Scholar
Saarloos, W. van & Hohenberg, P. C. 1992 Fronts, pulses, sources and sinks in generalized complex Ginzburg—Landau equations. Physica D 56, 303–367.Google Scholar
Somméria, J. 1986 Experimental study of the two dimensional inverse energy cascade in a square box. J. Fluid Mech. 170, 139–168.Google Scholar
Stewartson, K. & Stuart, J. T. 1971 A non-linear instability theory for a wave system in plane Poiseuille flow. J. Fluid Mech. 48, 529–545.Google Scholar
Tabeling, P., Cardoso, O. & Perrin, B. 1990 Chaos in a linear array of vortices. J. Fluid Mech. 213, 511–530.Google Scholar
Villermaux, E. & Hopfinger, E. J. 1994 Self-sustained oscillations of a confined jet: a case study for the non-linear delayed saturation model. Phrsica D (to appear).Google Scholar
Villermaux, E., Somméria, J., Gagne, Y. & Hopfinger, E. J. 1991 Oscillatory instability and genesis of turbulence behind a high solidity grid. Eur. J. Mech. B/Fluids 10, 427–439.Google Scholar
Williamson, C. H. K. 1989 Oblique and parallel modes of vortex shedding in the wake of a circular cylinder at low Reynolds numbers. J. Fluid Mech. 206, 579–627.Google Scholar
Yu, K. H., Trouvé, A. & Daily, J. W. 1991 Low-frequency pressure oscillations in a model ramjet combustor. J. Fluid Mech. 232, 47–72.Google Scholar