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Physical study of the non-equilibrium development of a turbulent thermal boundary layer

Published online by Cambridge University Press:  11 January 2022

M. Gelain Open the ORCID record for M. Gelain [Opens in a new window] ,
O. Gicquel Open the ORCID record for O. Gicquel [Opens in a new window] ,
A. Couilleaux  and
R. Vicquelin Open the ORCID record for R. Vicquelin [Opens in a new window]
M. Gelain*
Affiliation:
Laboratoire EM2C, CNRS, CentraleSupélec, Université Paris-Saclay, 8–10 rue Joliot Curie, 91190Gif-sur-Yvette, France Safran Aircraft Engines, Rond-point René Ravaud, 77550Moissy-Cramayel, France
O. Gicquel
Affiliation:
Laboratoire EM2C, CNRS, CentraleSupélec, Université Paris-Saclay, 8–10 rue Joliot Curie, 91190Gif-sur-Yvette, France
A. Couilleaux
Affiliation:
Safran Aircraft Engines, Rond-point René Ravaud, 77550Moissy-Cramayel, France
R. Vicquelin*
Affiliation:
Laboratoire EM2C, CNRS, CentraleSupélec, Université Paris-Saclay, 8–10 rue Joliot Curie, 91190Gif-sur-Yvette, France
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

The direct numerical simulation of a non-equilibrium turbulent heat transfer case is performed in a channel flow, where non-equilibrium is induced by a step change in surface temperature. The domain is thus made of two parts in the streamwise direction. Upstream, the flow is turbulent, homogeneous in temperature and the channel walls are adiabatic. The inflow conditions are extracted from a recycling plane located further downstream, so that a fully developed turbulent adiabatic flow reaches the second part. In the domain located downstream, isothermal boundary conditions are prescribed at the walls. The boundary layer, initially at equilibrium, is perturbed by the abrupt change of boundary conditions, and a non-equilibrium transient phase is observed until, further downstream, the flow reaches a new equilibrium state, presenting a fully developed thermal boundary layer. The work aims at identifying the non-equilibrium effects that are expected to be encountered in comparable flows, while providing the means to understand them. In particular, the study allows for the identification of an inner region of the developing boundary layer where several quantities are at equilibrium. Other quantities, instead, exhibit a behaviour of their own, especially in proximity to the leading edge. The analysis is supported by mean and root-mean-square profiles of temperature and velocity, as well as by budgets of first- and second-order moment balance equations for the enthalpy and momentum turbulent fields.

JFM classification

Boundary Layers: Boundary layer structure Turbulent Flows: Turbulent boundary layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 934 , 10 March 2022 , A6
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

REFERENCES

Abe, H., Kawamura, H. & Matsuo, Y. 2001 Direct numerical simulation of a fully developed turbulent channel flow with respect to the Reynolds number dependence. Trans. ASME J. Fluids Engng 123 (2), 382–393.CrossRefGoogle Scholar
Antonia, R.A., Danh, H.Q. & Prabhu, A. 1977 Response of a turbulent boundary layer to a step change in surface heat flux. J. Fluid Mech. 80 (1), 153–177.CrossRefGoogle Scholar
Bellec, M., Toutant, A. & Olalde, G. 2017 Large eddy simulations of thermal boundary layer developments in a turbulent channel flow under asymmetrical heating. Comput. Fluids 151, 159–176.CrossRefGoogle Scholar
Biles, D., Ebadi, A., Allard, M.P. & White, C.M. 2019 The design and validation of a thermal boundary layer wall plate. J. Fluids Engng 141 (12).CrossRefGoogle Scholar
Blom, J. 1970 An experimental determination of the turbulent Prandtl number in a developing temperature boundary layer. PhD thesis, Technische Hogeschool Eindhoven.CrossRefGoogle Scholar
Coleman, G.N., Kim, J. & Moser, R.D. 1995 A numerical study of turbulent supersonic isothermal-wall channel flow. J. Fluid Mech. 305, 159–183.CrossRefGoogle Scholar
Colin, O. & Rudgyard, M. 2000 Development of high-order Taylor–Galerkin schemes for LES. J. Comput. Phys. 162 (2), 338–371.CrossRefGoogle Scholar
Fulachier, L. 1972 Contribution à l’étude des analogies des champs dynamique et thermique dans une couche limite turbulente: effet de l'aspiration. PhD thesis, Université de Provence.Google Scholar
Hattori, H., Houra, T. & Nagano, Y. 2007 Direct numerical simulation of stable and unstable turbulent thermal boundary layers. Intl J. Heat Fluid Flow 28 (6), 1262–1271.CrossRefGoogle Scholar
Hattori, H., Yamada, S. & Houra, T. 2012 DNS study of effects of suddenly-vanishing wall heating in turbulent boundary layer. J. Therm. Sci. Technol. 7 (1), 313–321.CrossRefGoogle Scholar
Hattori, H., Yamada, S., Tanaka, M., Houra, T. & Nagano, Y. 2013 DNS, LES and RANS of turbulent heat transfer in boundary layer with suddenly changing wall thermal conditions. Intl J. Heat Fluid Flow 41, 34–44.CrossRefGoogle Scholar
Hoffmann, P.H. & Perry, A.E. 1979 The development of turbulent thermal layers on flat plates. Intl J. Heat Mass Transfer 22 (1), 39–46.CrossRefGoogle Scholar
Huang, P.G. & Coleman, G.N. 1994 Van Driest transformation and compressible wall-bounded flows. AIAA J. 32 (10), 2110–2113.CrossRefGoogle Scholar
Huang, P.G., Coleman, G.N. & Bradshaw, P. 1995 Compressible turbulent channel flows: DNS results and modelling. J. Fluid Mech. 305, 185–218.CrossRefGoogle Scholar
Johnson, D.S. 1959 Velocity and temperature fluctuation measurements in a turbulent boundary layer downstream of a stepwise discontinuity in wall temperature. J. Appl. Mech. 26, 325–336.CrossRefGoogle Scholar
Johnson, D.S. & Whippany, N.J. 1957 Velocity, temperature and heat transfer measurements in a turbulent boundary layer downstream of a stepwise discontinuity in wall temperature. Trans. ASME J. Appl. Mech. 24, 2–8.CrossRefGoogle Scholar
Kasagi, N., Tomita, Y. & Kuroda, A. 1992 Direct numerical simulation of passive scalar field in a turbulent channel flow. J. Heat Transfer, 114, 598–606.CrossRefGoogle Scholar
Kawai, S. & Larsson, J. 2012 Wall-modeling in large eddy simulation: length scales, grid resolution, and accuracy. Phys. Fluids 24 (1), 015105.CrossRefGoogle Scholar
Kawamura, H., Abe, H. & Matsuo, Y. 1999 DNS of turbulent heat transfer in channel flow with respect to Reynolds and Prandtl number effects. Intl J. Heat Fluid Flow 20 (3), 196–207.CrossRefGoogle Scholar
Kawamura, H., Abe, H. & Shingai, K. 2000 DNS of turbulence and heat transport in a channel flow with different Reynolds and Prandtl numbers and boundary conditions. Turbul. Heat Mass Transfer 3, 15–32.Google Scholar
Kim, J. & Moin, P. 1989 Transport of passive scalars in a turbulent channel flow. In Turbulent Shear Flows 6, pp. 85–96. Springer.CrossRefGoogle Scholar
Larsson, J., Kawai, S., Bodart, J. & Bermejo-Moreno, I. 2016 Large eddy simulation with modeled wall-stress: recent progress and future directions. Mech. Engng Rev. 3 (1), 15–00418.Google Scholar
Manhart, M., Peller, N. & Brun, C. 2008 Near-wall scaling for turbulent boundary layers with adverse pressure gradient. Theor. Comput. Fluid Dyn. 22 (3–4), 243–260.CrossRefGoogle Scholar
Morinishi, Y., Tamano, S. & Nakabayashi, K. 2004 Direct numerical simulation of compressible turbulent channel flow between adiabatic and isothermal walls. J. Fluid Mech. 502, 273–308.CrossRefGoogle Scholar
Morkovin, M.V. 1962 Effects of compressibility on turbulent flows. In The Mechanics of Turbulence (ed. A. Favre), pp. 367–380. Gordon and Breach.Google Scholar
Moureau, V., Lartigue, G., Sommerer, Y., Angelberger, C., Colin, O. & Poinsot, T. 2005 Numerical methods for unsteady compressible multi-component reacting flows on fixed and moving grids. J. Comput. Phys. 202 (2), 710–736.CrossRefGoogle Scholar
Ng, T.T., Talbot, L., Cheng, R.K. & Robben, F. 1983 The turbulent boundary layer over a flat plate with strong stepwise heating. In Laser Doppler Anemometry in Fluid Mechanics (ed. R.J. Adrian et al. ), vol. 1, pp. 229–237. Ladoan-Instituto Superior Technico.Google Scholar
Nicoud, F.C. 1999 Numerical study of a channel flow with variable properties. In CTR Annu. Res. Briefs 1998, pp. 289–310. Center for Turbulence Research.Google Scholar
Papavassiliou, D.V. & Hanratty, T.J. 1997 Transport of a passive scalar in a turbulent channel flow. Intl J. Heat Mass Transfer 40 (6), 1303–1311.CrossRefGoogle Scholar
Patel, A., Peeters, J.W.R., Boersma, B.J. & Pecnik, R. 2015 Semi-local scaling and turbulence modulation in variable property turbulent channel flows. Phys. Fluids 27 (9), 095101.Google Scholar
Poinsot, T. & Veynante, D. 2005 Theoretical and Numerical Combustion. RT Edwards.Google Scholar
Sanchez, M., Aulery, F., Toutant, A. and Françoise, B. 2014 Large eddy simulations of thermal boundary layer spatial development in a turbulent channel flow. J. Fluids Engng 136 (6).Google Scholar
Schonfeld, T. & Rudgyard, M. 1999 Steady and unsteady flow simulations using the hybrid flow solver AVBP. AIAA J. 37 (11), 1378–1385.CrossRefGoogle Scholar
Seki, Y. & Kawamura, H. 2005 DNS of turbulent heat transfer in a channel flow with streamwisely varying thermal boundary condition. In TSFP Digital Library Online. Begel House.CrossRefGoogle Scholar
Simpson, R.L. 1983 A model for the backflow mean velocity profile. AIAA J. 21 (1), 142–143.CrossRefGoogle Scholar
Spalding, D.B. 1961 Heat transfer to a turbulent stream from a surface with a step-wise discontinuity in wall temperature. Intl Dev. Heat Transfer, 439–446.Google Scholar
Tamano, S. & Morinishi, Y. 2006 Effect of different thermal wall boundary conditions on compressible turbulent channel flow at $m= 1.5$. J. Fluid Mech. 548, 361–373.CrossRefGoogle Scholar
Taylor, R.P., Love, P.H., Coleman, H.W. & Hosni, M.H. 1990 Heat transfer measurements in incompressible turbulent flat plate boundary layers with step wall temperature boundary conditions. ASME Trans. J. Heat Transfer 112, 245–247.Google Scholar
Teitel, M. & Antonia, R.A. 1993 A step change in wall heat flux in a turbulent channel flow. Intl J. Heat Mass Transfer 36 (6), 1707–1709.CrossRefGoogle Scholar
Toutant, A. & Bataille, F. 2013 Turbulence statistics in a fully developed channel flow submitted to a high temperature gradient. Intl J. Therm. Sci. 74, 104–118.Google Scholar
Vicquelin, R., Zhang, Y.F., Gicquel, O. & Taine, J. 2014 Effects of radiation in turbulent channel flow: analysis of coupled direct numerical simulations. J. Fluid Mech. 753, 360–401.Google Scholar
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