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Extension to various thermal boundary conditions of the elliptic blending model for the turbulent heat flux and the temperature variance

Published online by Cambridge University Press:  20 October 2020

Gaëtan Mangeon Open the ORCID record for Gaëtan Mangeon [Opens in a new window] ,
Sofiane Benhamadouche ,
Jean-François Wald  and
Rémi Manceau
Gaëtan Mangeon
Affiliation:
MFEE Dept., EDF R&D, 06 quai Watier, 78400Chatou, France Laboratory of Mathematics and Applied Mathematics (LMAP), CNRS, Universite de Pau et des Pays de l'Adour, E2S UPPA, INRIA, project-team CAGIRE, 64013Pau, France
Sofiane Benhamadouche*
Affiliation:
MFEE Dept., EDF R&D, 06 quai Watier, 78400Chatou, France
Jean-François Wald
Affiliation:
MFEE Dept., EDF R&D, 06 quai Watier, 78400Chatou, France
Rémi Manceau
Affiliation:
Laboratory of Mathematics and Applied Mathematics (LMAP), CNRS, Universite de Pau et des Pays de l'Adour, E2S UPPA, INRIA, project-team CAGIRE, 64013Pau, France
*
†Email address for correspondence: sofiane.benhamadouche@edf.fr
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Abstract

A new formulation of the model used in the near-wall region for the turbulent heat flux is developed, in order to extend the elliptic blending differential flux model of Dehoux et al. (Intl J. Heat Fluid Flow, vol. 63, 2017, pp. 190–204) to various boundary conditions for the temperature: imposed wall temperature, imposed heat flux or conjugate heat transfer. The new model is developed on a theoretical basis in order to satisfy the near-wall budget of the turbulent heat flux and, consequently, its asymptotic behaviour in the vicinity of the wall, which is crucial for the correct prediction of heat transfer between the fluid and the wall. The models of the different terms are derived using Taylor series expansions and comparisons with recent direct numerical simulation data of channel flows with various boundary conditions. A priori tests show that this methodology makes it possible to drastically improve the physical representation of the wall–turbulence interaction. This new differential flux model relies on the thermal-to-mechanical time scale ratio which depends on the thermal boundary condition at the wall. The key element entering this ratio is $\varepsilon _\theta$, the dissipation rate of the temperature variance $\overline {{\theta '}^2}$. Thus, a new near-wall model for this dissipation rate is proposed, in the framework of the second-moment closure based on the elliptic blending strategy. The computations carried out in order to validate the new differential flux model demonstrate the very satisfactory prediction of heat transfer in the forced convection regime for all kinds of thermal boundary condition.

JFM classification

Turbulent Flows: Turbulence modelling
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 905 , 25 December 2020 , A1
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

REFERENCES

Abe, H., Kawamura, H. & Matsuo, Y. 2004 Surface heat-flux fluctuations in a turbulent channel flow up to $Re_\tau = 1020$ with $Pr = 0.025$ and $0.71$. Intl J. Heat Fluid Flow 25 (3), 404–419.CrossRefGoogle Scholar
Abe, K., Kondoh, T. & Nagano, Y. 1995 A new turbulence model for predicting fluid flow and heat transfer in separating and reattaching flows–II. Thermal field calculations. Intl J. Heat Mass Transfer 38, 1467–1481.CrossRefGoogle Scholar
Angelino, M., Goldstein, R. J. & Gori, F. 2019 Lateral edge effects on heat/mass transfer on a finite width surface within a turbulent boundary layer. Intl J. Heat Mass Transfer 138, 32–40.CrossRefGoogle Scholar
Archambeau, F., Méchitoua, N. & Sakiz, M. 2004 Code Saturne: a finite volume code for the computation of turbulent incompressible flows – industrial applications. Intl J. Finite Volume 1, 01115371.Google Scholar
Benhamadouche, S., Afgan, I. & Manceau, R. 2020 Numerical simulations of flow and heat transfer in a wall bounded pin matrix. Flow Turbul. Combust. 104 (1), 19–44.CrossRefGoogle Scholar
Billard, F. & Laurence, D. 2012 A robust $k-\varepsilon -v^2/k$ elliptic blending turbulence model applied to near-wall, separated and buoyant flows. Intl J. Heat Fluid Flow 33 (1), 45–58.CrossRefGoogle Scholar
Choi, S.-K., Han, J.-W. & Choi, H.-K. 2018 Performance of second-moment differential stress and flux models for natural convection in an enclosure. Intl Commun. Heat Mass Transfer 99, 54–61.CrossRefGoogle Scholar
Choi, S. K. & Kim, S. O. 2008 Treatment of turbulent heat fluxes with the elliptic-blending second-moment closure for turbulent natural convection flows. Intl J. Heat Mass Transfer 51 (9), 2377–2388.CrossRefGoogle Scholar
Craft, T., Iacovides, H. & Uapipatanakul, S. 2010 Towards the development of RANS models for conjugate heat transfer. J. Turbul. 11, N26.CrossRefGoogle Scholar
Craft, T. J., Ince, N. Z. & Launder, B. E. 1996 Recent developments in second-moment closure for buoyancy-affected flows. Dyn. Atmos. Oceans 23 (1), 99–114.CrossRefGoogle Scholar
Daly, B. J. & Harlow, F. H. 1970 Transport equations in turbulence. Phys. Fluids 13, 2634–2649.CrossRefGoogle Scholar
Dehoux, F. 2012 Modélisation statistique des écoulements turbulents en convection forcée, mixte et naturelle. PhD thesis, Université de Poitiers.Google Scholar
Dehoux, F., Benhamadouche, S. & Manceau, R. 2017 An elliptic blending differential flux model for natural, mixed and forced convection. Intl J. Heat Fluid Flow 63, 190–204.CrossRefGoogle Scholar
Dovizio, D., Shams, A. & Roelofs, F. 2019 Numerical prediction of flow and heat transfer in an infinite wire-wrapped fuel assembly. Nucl. Engng Des. 349, 193–205.CrossRefGoogle Scholar
Durbin, P. A. 1991 Near-wall turbulence closure modeling without ‘damping functions’. Theor. Comput. Fluid Dyn. 3 (1), 1–13.Google Scholar
Elghobashi, S. & Launder, B. E. 1983 Turbulent time scales and the dissipation rate of temperature variance in the thermal mixing layer. Phys. Fluids 26, 2415–2419.CrossRefGoogle Scholar
Flageul, C., Benhamadouche, S., Lamballais, E. & Laurence, D. 2015 DNS of turbulent channel flow with conjugate heat transfer: effect of thermal boundary conditions on the second moments and budgets. Intl J. Heat Fluid Flow 55, 34–44.CrossRefGoogle Scholar
Flageul, C., Benhamadouche, S., Lamballais, E. & Laurence, D. 2017 On the discontinuity of the dissipation rate associated with the temperature variance at the fluid-solid interface for cases with conjugate heat transfer. Intl J. Heat Mass Transfer 111, 321–328.CrossRefGoogle Scholar
Hanjalić, K. 2002 One-point closure models for buoyancy-driven turbulent flows. Annu. Rev. Fluid Mech. 34, 321–347.CrossRefGoogle Scholar
Hanjalić, K. & Launder, B. E. 2011 Modelling Turbulence in Engineering and the Environment. Second-Moment Routes to Closure. Cambridge University Press.CrossRefGoogle Scholar
Howard, R. & Serre, E. 2015 Large-eddy simulation in a mixing tee junction: high-order turbulent statistics analysis. Intl J. Heat Fluid Flow 51, 65–77.CrossRefGoogle Scholar
Howard, R. & Serre, E. 2017 Large eddy simulation in $code\_saturne$ of thermal mixing in a T-junction with brass walls. Intl J. Heat Fluid Flow 63, 119–127.CrossRefGoogle Scholar
Jones, W. P. & Musonge, P. 1988 Closure of the Reynolds stress and scalar flux equations. Phys. Fluids 31, 3589–3604.CrossRefGoogle Scholar
Kasagi, N., Kasagi, N. & Kuroda, A. 1992 Direct numerical simulation of passive scalar field in a turbulent channel flow. Trans. ASME: J. Heat Transfer 114, 598–606.CrossRefGoogle Scholar
Kasagi, N., Kuroda, A. & Hirata, M. 1989 Numerical investigation of near-wall turbulent heat transfer taking into account the unsteady heat conduction in the solid wall. Trans. ASME: J. Heat Transfer 111, 385–392.CrossRefGoogle Scholar
Launder, B. E. 1988 On the computation of convective heat transfer in complex turbulent flows. Trans. ASME: J. Heat Transfer 110, 1112–1128.CrossRefGoogle Scholar
Manceau, R. 2015 Recent progress in the development of the elliptic blending Reynolds-stress model. Intl J. Heat Fluid Flow 51, 195–220.CrossRefGoogle Scholar
Manceau, R. & Hanjalić, K. 2002 Elliptic blending model: a new near-wall Reynolds-stress turbulence closure. Phys. Fluids 14 (2), 744–754.CrossRefGoogle Scholar
Manceau, R., Parneix, S. & Laurence, D. 2000 Turbulent heat transfer predictions using the $v^2-f$ model on unstructured meshes. Intl J. Heat Fluid Flow 21 (3), 320–328.CrossRefGoogle Scholar
Nagano, Y. 2002 Modelling heat transfer in near-wall flows. In Closure Strategies for Turbulent and Transitional Flows, pp. 188–247. Cambridge University Press.Google Scholar
Newman, G. R., Launder, B. E. & Lumley, J. L. 1981 Modelling the behaviour of homogeneous scalar turbulence. J. Fluid Mech. 111, 217–232.CrossRefGoogle Scholar
Parneix, S., Behnia, M. & Durbin, P. A. 1998 Predictions of turbulent heat transfer in an axisymmetric jet impinging on a heated pedestal. Trans. ASME: J. Heat Transfer 120, 1–7.Google Scholar
Pope, S. B. 1983 Consistent modeling of scalars in turbulent flows. Phys. Fluids 26 (2), 404–408.CrossRefGoogle Scholar
Shikazono, N. & Kasagi, N. 1996 Second-moment closure for turbulent scalar transport at various Prandtl numbers. Intl J. Heat Mass Transfer 39 (14), 2977–2987.CrossRefGoogle Scholar
Shin, J. K., An, J. S., Choi, Y. D., Kim, Y. C. & Kim, M. S. 2008 Elliptic relaxation second moment closure for the turbulent heat fluxes. J. Turbul. 9, 1–29.CrossRefGoogle Scholar
Sommer, T. P., So, R. M. C. & Zhang, H. S. 1994 Heat transfer modeling and the assumption of zero wall temperature fluctuations. Trans. ASME: J. Heat Transfer 116 (4), 855–863.CrossRefGoogle Scholar
Spalding, D. B. 1971 Concentration fluctuations in a round turbulent free jet. Chem. Engng Sci. 26 (1), 95–107.CrossRefGoogle Scholar
Tiselj, I., Bergant, R., Mavko, B., Bajsić, I. & Hetsroni, G. 2001 DNS of turbulent heat transfer in channel flow with heat conduction in the solid wall. Trans. ASME: J. Heat Transfer 123, 849–857.CrossRefGoogle Scholar
Yang, G., Iacovides, H., Craft, T. & Apsley, D. 2019 RANS modelling for temperature variance in conjugate heat transfer. In Proceedings of 5th World Congress on Mechanical, Chemical, and Material Engineering, Lisbon, Portugal. Avestia.CrossRefGoogle Scholar
Zeman, O. & Lumley, J. L. 1976 Modeling buoyancy driven mixed layers. J. Atmos. Sci. 33, 1974–1988.2.0.CO;2>CrossRefGoogle Scholar