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Turbulent flow through a high aspect ratio cooling duct with asymmetric wall heating

  • Thomas Kaller (a1), Vito Pasquariello (a1), Stefan Hickel (a2) and Nikolaus A. Adams (a1)
Abstract

We present well-resolved large-eddy simulations of turbulent flow through a straight, high aspect ratio cooling duct operated with water at a bulk Reynolds number of $Re_{b}=110\times 10^{3}$ and an average Nusselt number of $Nu_{xz}=371$ . The geometry and boundary conditions follow an experimental reference case and good agreement with the experimental results is achieved. The current investigation focuses on the influence of asymmetric wall heating on the duct flow field, specifically on the interaction of turbulence-induced secondary flow and turbulent heat transfer, and the associated spatial development of the thermal boundary layer and the inferred viscosity variation. The viscosity reduction towards the heated wall causes a decrease in turbulent mixing, turbulent length scales and turbulence anisotropy as well as a weakening of turbulent ejections. Overall, the secondary flow strength becomes increasingly less intense along the length of the spatially resolved heated duct as compared to an adiabatic duct. Furthermore, we show that the assumption of a constant turbulent Prandtl number is invalid for turbulent heat transfer in an asymmetrically heated duct.

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Corresponding author
Email address for correspondence: thomas.kaller@tum.de
References
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Baines, W. D. & Brundrett, E. 1964 The production and diffusion of vorticity in duct flow. J. Fluid Mech. 19, 375394.
Banerjee, S., Krahl, R., Durst, F. & Zenger, C. 2007 Presentation of anisotropy properties of turbulence, invariants versus eigenvalue approaches. J. Turbul. 8 (32), 127.
Choi, H. S. & Park, T. S. 2013 The influence of streamwise vortices on turbulent heat transfer in rectangular ducts with various aspect ratios. Intl J. Heat Fluid Flow 40, 114.
Choi, K.-S. & Lumley, J. L. 2001 The return to isotropy of homogeneous turbulence. J. Fluid Mech. 436, 5984.
Demuren, A. O. & Rodi, W. 1984 Calculation of turbulence-driven secondary motion in non-circular ducts. J. Fluid Mech. 140, 189222.
Emory, M. & Iaccarino, G. 2014 Visualizing turbulence anisotropy in the spatial domain with componentality contours. In Annual Research Briefs, Center for Turbulence Research, Stanford University, pp. 123138.
Gavrilakis, S. 1992 Numerical simulation of low-Reynolds-number turbulent flow through a straight square duct. J. Fluid Mech. 244, 101129.
Gessner, F. B. & Jones, J. B. 1965 On some aspects of fully-developed turbulent flow in rectangular channels. J. Fluid Mech. 23 (4), 689713.
Gottlieb, S. & Shu, C. 1998 Total variation diminishing Runge–Kutta schemes. Maths Comput. 67 (221), 7385.
Grilli, M., Schmid, P. J., Hickel, S. & Adams, N. A. 2012 Analysis of unsteady behaviour in shockwave turbulent boundary layer interaction. J. Fluid Mech. 700, 1628.
Hébrard, J., Métais, O. & Salinas-Vásquez, M. 2004 Large-eddy simulation of turbulent duct flow: heating and curvature effects. Intl J. Heat Fluid Flow 25 (4), 569580.
Hébrard, J., Salinas-Vásquez, M. & Métais, O. 2005 Spatial development of turbulent flow within a heated duct. J. Turbul. 6, N8.
Hickel, S. & Adams, N. A. 2007 On implicit subgrid-scale modeling in wall-bounded flows. Phys. Fluids 19, 105106.
Hickel, S. & Adams, N. A. 2008 Implicit LES applied to zero-pressure-gradient and adverse-pressure-gradient boundary-layer turbulence. Intl J. Heat Fluid Flow 29, 626639.
Hickel, S., Adams, N. A. & Domaradzki, J. A. 2006 An adaptive local deconvolution method for implicit LES. J. Comput. Phys. 213 (1), 413436.
Hickel, S., Adams, N. A. & Mansour, N. N. 2007 Implicit subgrid-scale modeling for large-eddy simulation of passive-scalar mixing. Phys. Fluids 19 (9), 095102.
Hirota, M., Fujita, H., Yokosawa, H., Nakai, H. & Itoh, H. 1997 Turbulent heat transfer in a square duct. Intl J. Heat Fluid Flow 18 (1), 170180.
Huser, A. & Biringen, S. 1993 Direct numerical simulation of turbulent flow in a square duct. J. Fluid Mech. 257, 6595.
IAPWS 2008 Release on the IAPWS formulation 2008 for the viscosity of ordinary water substance. The International Association for the Properties of Water and Steam (IAPWS). Available from http://www.iapws.org.
IAPWS 2011 Release on the IAPWS formulation 2011 for the thermal conductivity of ordinary water substance. The International Association for the Properties of Water and Steam (IAPWS). Available from http://www.iapws.org.
Kaller, T., Pasquariello, V., Hickel, S. & Adams, N. A. 2017 Large-eddy simulation of the high-Reynolds-number flow through a high-aspect-ratio cooling duct. In Proceedings of the 10th International Symposium on Turbulence and Shear Flow Phenomena (TSFP-10), Chicago, USA.
Kang, S. & Iaccarino, G. 2010 Computation of turbulent Prandtl number for mixed convection around a heated cylinder. In Annual Research Briefs, Center for Turbulence Research, Stanford University, pp. 295304.
Kays, W. M. 1994 Turbulent Prandtl number – where are we? Trans. ASME J. Heat Transfer 116 (2), 284295.
Launder, B. E. & Ying, W. M. 1972 Secondary flows in ducts of square cross-section. J. Fluid Mech. 54 (2), 289295.
Lee, J., Jung, S. Y., Sung, H. J. & Zaki, T. A. 2013 Effect of wall heating on turbulent boundary layers with temperature-dependent viscosity. J. Fluid Mech. 726, 196225.
Lumley, J. L. 1978 Computational modeling of turbulent flows. Adv. Appl. Mech. 18, 123176.
Madabhushi, R. K. & Vanka, S. P. 1991 Large eddy simulation of turbulence-driven secondary flow in a square duct. Phys. Fluids A 3 (11), 27342745.
Melling, A. & Whitelaw, J. H. 1976 Turbulent flow in a rectangular duct. J. Fluid Mech. 78 (2), 289315.
Monin, A. S., Yaglom, A. M. & Lumley, J. L. 2007 Statistical Fluid Mechanics, Volume II: Mechanics of Turbulence. Dover.
Monty, J. P.2005 Developments in smooth wall turbulent duct flows. PhD thesis, The University of Melbourne.
Monty, J. P., Stewart, J. A., Williams, R. C. & Chong, M. S. 2007 Large-scale features in turbulent pipe and channel flows. J. Fluid Mech. 589, 147156.
O’Neill, P. L., Nicolaides, D., Honnery, D. & Soria, J. 2004 Autocorrelation functions and the determination of integral length with reference to experimental and numerical data. In Proceedings of the Fifteenth Australasian Fluid Mechanics Conference (ed. Behnia, M., Lin, W. & McBain, G. D.). The University of Sydney.
Pallares, J. & Davidson, L. 2002 Large-eddy simulations of turbulent heat transfer in stationary and rotating square ducts. Phys. Fluids 14 (8), 28042816.
Pasquariello, V., Grilli, M., Hickel, S. & Adams, N. A. 2014 Large-eddy simulation of passive shock-wave/boundary-layer interaction control. Intl J. Heat Fluid Flow 49, 116127.
Pasquariello, V., Hickel, S. & Adams, N. A. 2017 Unsteady effects of strong shock-wave/boundary-layer interaction at high Reynolds number. J. Fluid Mech. 823, 617657.
Patel, A., Boersma, B. J. & Pecnik, R. 2016 The influence of near-wall density and viscosity gradients on turbulence in channel flows. J. Fluid Mech. 809, 793820.
Pinelli, A., Uhlmann, M., Sekimoto, A. & Kawahara, G. 2010 Reynolds number dependence of mean flow structure in square duct turbulence. J. Fluid Mech. 644, 107122.
Pirozzoli, S., Grasso, F. & Gatski, T. B. 2004 Direct numerical simulation and analysis of a spatially evolving supersonic turbulent boundary layer at M = 2. 25. Phys. Fluids 16 (3), 530545.
Pirozzoli, S., Modesti, D., Orlandi, P. & Grasso, F. 2018 Turbulence and secondary motions in square duct flow. J. Fluid Mech. 840, 631655.
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.
Qin, Z. & Pletcher, R. H. 2006 Large eddy simulation of turbulent heat transfer in a rotating square duct. Intl J. Heat Fluid Flow 27, 371390.
Quaatz, J. F., Giglmaier, M., Hickel, S. & Adams, N. A. 2014 Large-eddy simulation of a pseudo-shock system in a Laval nozzle. Intl J. Heat Fluid Flow 49, 108115.
Remmler, S. & Hickel, S. 2012 Direct and large eddy simulation of stratified turbulence. Intl J. Heat Fluid Flow 35, 1324.
Rochlitz, H., Scholz, P. & Fuchs, T. 2015 The flow field in a high aspect ratio cooling duct with and without one heated wall. Exp. Fluids 56 (12), 113.
Salinas-Vásquez, M. & Métais, O. 2002 Large-eddy simulation of the turbulent flow through a heated square duct. J. Fluid Mech. 453, 201238.
Salinas-Vásquez, M., Vicente Rodríguez, W. & Issa, R. 2005 Effects of ridged walls on the heat transfer in a heated square duct. Intl J. Heat Mass Transfer 48 (10), 20502063.
Sameen, A. & Govindarajan, R. 2007 The effect of wall heating on instability of channel flow. J. Fluid Mech. 577, 417442.
Sekimoto, A., Kawahara, G., Sekiyama, K., Uhlmann, M. & Pinelli, A. 2011 Turbulence- and buoyancy-driven secondary flows in a horizontal square duct heated from below. Phys. Fluids 23 (7), 075103.
Shah, R. K. & London, A. L. 1978 Laminar Flow Forced Convection in Ducts. Academic Press.
Simonsen, A. J. & Krogstad, P. Å. 2005 Turbulent stress invariant analysis: clarification of existing terminology. Phys. Fluids 17 (8), 14.
Vidal, A., Vinuesa, R., Schlatter, P. & Nagib, H. M. 2017a Impact of corner geometry on the secondary flow in turbulent ducts. In Proceedings of the 10th International Symposium on Turbulence and Shear Flow Phenomena (TSFP-10), Chicago, USA.
Vidal, A., Vinuesa, R., Schlatter, P. & Nagib, H. M. 2017b Influence of corner geometry on the secondary flow in turbulent square ducts. Intl J. Heat Fluid Flow 67, 6978.
Vinuesa, R., Noorani, A., Lozano-Duran, A., El Khoury, G., Schlatter, P., Fischer, P. F. & Nagib, N. M. 2014 Aspect ratio effects in turbulent duct flows studied through direct numerical simulation. J. Turbul. 15 (10), 677706.
Wallace, J. M. 2016 Quadrant analysis in turbulence research: history and evolution. Annu. Rev. Fluid Mech. 48 (1), 131158.
Wallace, J. M., Eckelmann, H. & Brodkey, R. S. 1972 The wall region in turbulent shear flow. J. Fluid Mech. 54 (1), 3948.
Wardana, I. N. G., Ueda, T. & Mizomoto, M. 1994 Effect of strong wall heating on turbulence statistics of a channel flow. Exp. Fluids 18 (1), 8794.
Willmarth, W. W. & Lu, S. S. 1972 Structure of the Reynolds stress near the wall. J. Fluid Mech. 55 (1), 6592.
Yang, H., Chen, T. & Zhu, Z. 2009 Numerical study of forced turbulent heat convection in a straight square duct. Intl J. Heat Mass Transfer 52 (13–14), 31283136.
Zhang, H., Xavier Trias, F., Gorobets, A., Tan, Y. & Oliva, A. 2015 Direct numerical simulation of a fully developed turbulent square duct flow up to Re 𝜏 = 1200. Intl J. Heat Fluid Flow 54, 258267.
Zhu, Z., Yang, H. & Chen, T. 2010 Numerical study of turbulent heat and fluid flow in a straight square duct at higher Reynolds numbers. Intl J. Heat Mass Transfer 53 (1–3), 356364.
Zonta, F., Marchioli, C. & Soldati, A. 2012 Modulation of turbulence in forced convection by temperature-dependent viscosity. J. Fluid Mech. 697, 150174.
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