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A heat transfer model of fully developed turbulent channel flow

  • Alireza Ebadi (a1), Juan Carlos Cuevas Bautista (a1), Christopher M. White (a1), Gregory Chini (a1) and Joseph Klewicki (a2)...


Experimental and numerical studies over the past two decades indicate that as the Reynolds number becomes large the turbulent boundary layer is increasingly composed of zones of uniform streamwise momentum, segregated by narrow regions of high shear. Recent experimental evidence suggests that passive scalar fields (for example, temperature) in turbulent boundary layers at high Reynolds number show similar characteristics; namely, large uniform temperature zones (UTZs) separated by narrow regions of high gradient, which we term thermal fissures (TFs). Herein, a model informed by analysis of the mean scalar transport equation, and that leverages the dynamical model recently developed by the authors (Cuevas Bautista et al., J. Fluid Mech., vol. 858, 2019, pp. 609–633), is formulated to predict passive scalar transport using the UTZ/TF concept. First, a finite number of TFs are distributed across the boundary layer. In analogy with the aforementioned dynamical model, the wall-normal positions of the TFs and their characteristic temperatures are then perturbed to generate independent ensembles, from which statistical moments are computed. The model successfully reproduces the statistical profiles of the temperature field as well as the streamwise turbulent heat flux. Lastly, the Prandtl number dependency of the empirically chosen parameters is investigated. It is concluded that the higher-order statistics, especially the kurtosis, produced by the model are sensitive to the Prandtl number, while the mean temperature and turbulent heat flux do not show noticeable Prandtl number dependency.


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Cuevas Bautista, J. C., Ebadi, A., White, C. M., Chini, G. P. & Klewicki, J. C. 2019 A uniform momentum zone–vortical fissure model of the turbulent boundary layer. J. Fluid Mech. 858, 609633.
Eisma, H. E.2017 Pollutant dispersion in wall-bounded turbulent flows: an experimental assessment. PhD thesis, Delft University of Technology.
Finnigan, J. J., Shaw, R. H. & Patton, E. G. 2009 Turbulence structure above a vegetation canopy. J. Fluid Mech. 637, 387424.
Holt, J. & Proctor, R. 2008 The seasonal circulation and volume transport on the northwest European continental shelf: a fine-resolution model study. J. Geophys. Res. Oceans 113 (C6), 120.
Klewicki, J. C. 2013 Self-similar mean dynamics in turbulent wall flows. J. Fluid Mech. 718, 596621.
Klewicki, J., Philip, J., Marusic, I., Chauhan, K. & Morrill-Winter, C. 2014 Self-similarity in the inertial region of wall turbulence. Phys. Rev. E 90 (6), 063015.
Meinhart, C. D. & Adrian, R. J. 1995 On the existence of uniform momentum zones in a turbulent boundary layer. Phys. Fluids 7 (4), 694696.
Michioka, T. & Sato, A. 2012 Effect of incoming turbulent structure on pollutant removal from two-dimensional street canyon. Boundary-Layer Meteorol. 145 (3), 469484.
Perret, L. & Savory, E. 2013 Large-scale structures over a single street canyon immersed in an urban-type boundary layer. Boundary-Layer Meteorol. 148 (1), 111131.
Pirozzoli, S., Bernardini, M. & Orlandi, P. 2016 Passive scalars in turbulent channel flow at high Reynolds number. J. Fluid Mech. 788, 614639.
Priyadarshana, P. J. A., Klewicki, J. C., Treat, S. & Foss, J. F. 2007 Statistical structure of turbulent-boundary-layer velocity-vorticity products at high and low Reynolds numbers. J. Fluid Mech. 570, 307346.
Shraiman, B. I. & Siggia, E. D. 2006 Scalar turbulence. Nature 405, 639646.
Sreenivasan, K. R., Antonia, R. A. & Britz, D. 1979 Local isotropy and large structures in a heated turbulent jet. J. Fluid Mech. 94 (4), 745775.
Sreenivasan, K. R., Hunt, J. C. R., Phillips, O. M. & Williams, D. 1991 On local isotropy of passive scalars in turbulent shear flows. Proc. R. Soc. Lond. A 434 (1890), 165182.
Talluru, K. M., Philip, J. & Chauhan, K. A. 2018 Local transport of passive scalar released from a point source in a turbulent boundary layer. J. Fluid Mech. 846, 292317.
Vanderwel, C. & Tavoularis, S. 2016 Scalar dispersion by coherent structures in uniformly sheared flow generated in a water tunnel. J. Turbul. 17 (7), 633650.
Wei, T., Fife, P., Klewicki, J. & McMurtry, P. 2005a Properties of the mean momentum balance in turbulent boundary layer, pipe and channel flows. J. Fluid Mech. 522, 303327.
Wei, T., Fife, P., Klewicki, J. & McMurtry, P. 2005b Scaling heat transfer in fully developed turbulent channel flow. Intl J. Heat Mass Transfer 48 (25–26), 52845296.
Wroblewski, D. E., Coté, O. R., Hacker, J. M. & Dobosy, R. J. 2007 Cliff–ramp patterns and Kelvin–Helmholtz billows in stably stratified shear flow in the upper troposphere: analysis of aircraft measurements. J. Atmos. Sci. 64 (7), 25212539.
Zhou, A., Klewicki, J. & Pirozzoli, S. 2019 Properties of the scalar variance transport equation in turbulent channel flow. Phys. Rev. Fluids 4 (2), 024606.
Zhou, A., Pirozzoli, S. & Klewicki, J. 2017 Mean equation based scaling analysis of fully-developed turbulent channel flow with uniform heat generation. Intl J. Heat Mass Transfer 115, 5061.
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A heat transfer model of fully developed turbulent channel flow

  • Alireza Ebadi (a1), Juan Carlos Cuevas Bautista (a1), Christopher M. White (a1), Gregory Chini (a1) and Joseph Klewicki (a2)...


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