Hostname: page-component-8448b6f56d-c47g7 Total loading time: 0 Render date: 2024-04-24T08:47:41.200Z Has data issue: false hasContentIssue false
  • English
  • Français

Statistics of fully turbulent impinging jets

Published online by Cambridge University Press:  24 July 2017

Robert Wilke Open the ORCID record for Robert Wilke [Opens in a new window]  and
Jörn Sesterhenn
Robert Wilke
Affiliation:
Institute of Fluid Dynamics and Technical Acoustics, TU Berlin, Müller-Breslau-Str. 15, 10623 Berlin, Germany
Jörn Sesterhenn*
Affiliation:
Institute of Fluid Dynamics and Technical Acoustics, TU Berlin, Müller-Breslau-Str. 15, 10623 Berlin, Germany
*
†Email address for correspondence: joern.sesterhenn@tu-berlin.de
Get access Rights & Permissions [Opens in a new window]

Abstract

Direct numerical simulations (DNS) of subsonic and supersonic impinging jets with Reynolds numbers of 3300 and 8000 are carried out to analyse their statistical properties with respect to heat transfer. The Reynolds number range is at low or moderate values in terms of practical applications, but very high regarding the technical possibilities of DNS. A Reynolds number of 8000 is technically relevant for the cooling of turbine blades. In this case, the flow is dominated by primary and secondary vortex rings. Statistics of turbulent heat fluxes and Reynolds stresses as well as the Nusselt number are provided and brought into accordance with these vortices. Velocity and temperature fluctuations were found to have a positive influence on cooling of the impinging plate. Beside the description of the flow, a second aim of this article is the provision of data for improvement of turbulence models. Modern large eddy simulations are still not able to precisely predict impingement heat transfer (Dairay et al., Intl J. Heat Fluid Flow, vol. 50 (0), 2014, pp. 177–187). Common relations between heat and mass transfer respectively temperature and velocity fields are applied to the impinging jet. These relations include the Reynolds and Chilton Colburn analogy, the Crocco–Busemann relation and the generalised Reynolds analogy (GRA). It was found that the first two deliver useful values if the distance to the jet axis is larger than one diameter, away from the strong pressure gradient around the stagnation point. The GRA, in contrast, precisely predicts the mean temperature field if no axial velocity gradient is present. The estimation of temperature fluctuations according to the GRA fails. As third main topic of this article, the influence of the Mach number on heat transfer and the flow field, is studied. Against the common practise of neglecting compressibility effects in experimental Nusselt correlations, we observed that higher Mach numbers (up to 1.1) have a positive influence on heat transfer in the deflection zone due to higher flow fluctuations.

JFM classification

Wakes/Jets: Jets Turbulent Flows: Turbulent Flows Vortex Flows: Vortex dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 825 , 25 August 2017 , pp. 795 - 824
Check for updates
Copyright
© 2017 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

Bogey, C., de Cacqueray, N. & Bailly, C. 2009 A shock-capturing methodology based on adaptative spatial filtering for high-order non-linear computations. J. Comput. Phys. 228 (5), 1447–1465.Google Scholar
Busemann, A. 1931 Handbuch der Experimentalphysik, vol. 4. Geest und Portig.Google Scholar
Chilton, T. H. & Colburn, A. P. 1934 Mass transfer (absorption) coefficients prediction from data on heat transfer and fluid friction. Ind. Engng Chem. 26 (11), 1183–1187.Google Scholar
Chung, Y. M. & Luo, K. H. 2002 Unsteady heat transfer analysis of an impinging jet. J. Heat Transfer 124 (6), 1039–1048.CrossRefGoogle Scholar
Crocco, L. 1932 Sulla trasmissione del calore da una lamina piana a un fluido scorrente ad alta velocita. L’Aerotecnica 12, 181–197.Google Scholar
Cziesla, T., Biswas, G., Chattopadhyay, H. & Mitra, N. K. 2001 Large-eddy simulation of flow and heat transfer in an impinging slot jet. Intl J. Heat Fluid Flow 22 (5), 500–508.Google Scholar
Dairay, T., Fortuné, V., Lamballais, E. & Brizzi, L. E. 2014 LES of a turbulent jet impinging on a heated wall using high-order numerical schemes. Intl J. Heat Fluid Flow 50 (0), 177–187.Google Scholar
Dairay, T., Fortuné, V., Lamballais, E. & Brizzi, L.-E. 2015 Direct numerical simulation of a turbulent jet impinging on a heated wall. J. Fluid Mech. 764, 362–394.CrossRefGoogle Scholar
Davidson, L. 2007 Inlet boundary conditions for embedded les. In First CEAS European Air and Space Conference, pp. 10–13. Chalmers University of Technology.Google Scholar
Eggels, J. G. M., Unger, F., Weiss, M. H., Westerweel, J., Adrian, R. J., Friedrich, R. & Nieuwstadt, F. T. M. 1994 Fully developed turbulent pipe flow: a comparison between direct numerical simulation and experiment. J. Fluid Mech. 268, 175–210.Google Scholar
Eidson, T. M. & Erlebacher, G. 1995 Implementation of a fully balanced periodic tridiagonal solver on a parallel distributed memory architecture. Concurrency: Practice and Experience 7 (4), 273–302.Google Scholar
Freund, J. B. 2001 Noise sources in a low-Reynolds-number turbulent jet at Mach 0.9. J. Fluid Mech. 438, 277–305.Google Scholar
Hattori, H. & Nagano, Y. 2004 Direct numerical simulation of turbulent heat transfer in plane impinging jet. Intl J. Heat Fluid Flow 25 (5), 749–758.Google Scholar
Hrycak, P.1981 Heat transfer from impinging jets. A literature review. Tech. Rep. New Jersey Institute of Technology.Google Scholar
Jambunathan, K., Lai, E., Moss, M. A. & Button, B. L. 1992 A review of heat transfer data for single circular jet impingement. Intl J. Heat Fluid Flow 13 (2), 106–115.Google Scholar
Janetzke, T.2010 Experimentelle untersuchungen zur effizienzsteigerung von prallkühlkonfigurationen durch dynamische ringwirbel hoher amplitude. PhD thesis, TU Berlin.Google Scholar
Kakag, S. & Yenner, Y. 1995 Convective Heat Transfer, 2nd edn. Crc Pr Inc.Google Scholar
Lechner, R., Sesterhenn, J. & Friedrich, R. 2001 Turbulent supersonic channel flow. J. Turbul. 2 (1), 001–001.Google Scholar
Lee, J. & Lee, S.-J. 1999 Stagnation region heat transfer of a turbulent axisymmetric jet impingement. Expl Heat Transfer 12 (2), 137–156.Google Scholar
Livingood, J. N. B. & Hrycak, P.1973 Impingement heat transfer from turbulent air jets to flat plates: a literature survey NASA, Lewis Research Center.Google Scholar
Moser, R. D. & Moin, P.1984 Direct numerical simulation of curved turbulent channel flow. NASA, Ames Research Center.Google Scholar
Rubesin, M. W.1990 Extra compressibility terms for favre-averaged two-equation models of inhomogeneous turbulent flows. NASA STI/Recom Tech. Rep. No. 90, 23701.Google Scholar
Satake, S.-I. & Kunugi, T. 1998 Direct numerical simulation of an impinging jet into parallel disks. Intl J. Numer. Meth. Heat Fluid Flow 8 (7), 768–780.Google Scholar
Schulze, J.2013 Adjoint based jet-noise minimization. PhD thesis, TU Berlin.Google Scholar
Sesterhenn, J. 2001 A characteristic–type formulation of the Navier–Stokes equations for high order upwind schemes. Comput. Fluids 30 (1), 37–67.Google Scholar
Viskanta, R. 1993 Heat transfer to impinging isothermal gas and flame jets. Exp. Therm. Fluid Sci. 6 (2), 111–134.Google Scholar
Walz, A.1962 Compressible turbulent boundary layers. Ed. du Centre National de la Recherche scientifique.Google Scholar
Weigand, B. & Spring, S. 2011 Multiple jet impingement – a review. Heat Transfer Res. 42 (2), 101–142.Google Scholar
Wilke, R.2017 The impinging jet. PhD thesis, Technische Universität Berlin.Google Scholar
Wilke, R. & Sesterhenn, J. 2015a Direct numerical simulation of heat transfer of a round subsonic impinging jet. In Active Flow and Combustion Control 2014, pp. 147–159. Springer.Google Scholar
Wilke, R. & Sesterhenn, J. 2015b Numerical simulation of impinging jets. In High Performance Computing in Science and Engineering ’14, pp. 275–287. Springer.Google Scholar
Wilke, R. & Sesterhenn, J. 2016a Numerical simulation of subsonic and supersonic impinging jets. In High Performance Computing in Science and Engineering ’15, pp. 349–369. Springer.Google Scholar
Wilke, R. & Sesterhenn, J.2016b On the origin of impinging tones at low supersonic flow. Preprint, arXiv:1604.05624.Google Scholar
Zhang, Y.-S., Bi, W.-T., Hussain, F. & She, Z.-S. 2014 A generalized Reynolds analogy for compressible wall-bounded turbulent flows. J. Fluid Mech. 739, 392–420.Google Scholar
Zuckerman, N. & Lior, N. 2005 Impingement heat transfer: correlations and numerical modeling. J. Heat Transfer 127 (5), 544–552.Google Scholar