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Stable channel flow with spanwise heterogeneous surface temperature

Published online by Cambridge University Press:  06 January 2022

T. Bon Open the ORCID record for T. Bon [Opens in a new window]  and
J. Meyers Open the ORCID record for J. Meyers [Opens in a new window]
T. Bon*
Affiliation:
Department of Mechanical Engineering, KU Leuven, Celestijnenlaan 300, B3001 Leuven, Belgium
J. Meyers
Affiliation:
Department of Mechanical Engineering, KU Leuven, Celestijnenlaan 300, B3001 Leuven, Belgium
*
†Email address for correspondence: [email protected]
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Abstract

Recent studies have demonstrated that large secondary motions are excited by surface roughness with dominant spanwise length scales of the order of the flow's outer length scale. Inspired by this, we explore the effect of spanwise heterogeneous surface temperature in weakly to strongly stratified closed channel flow (at $Ri_\tau =120$, 960; $Re_\tau = 180$, 550) with direct numerical simulations. The configuration consists of equally sized strips of high and low temperature at the lower and upper boundaries, while an overall stable stratification is induced by imposing an average temperature difference between the top and bottom. We consider the influence of the width of the strips (${\rm \pi} /8 \leq \lambda /h \leq 4{\rm \pi} $), Reynolds number, stability and upper boundary condition on the mean flow structure, skin friction and heat transfer. Results indicate that secondary flows are excited, with alternating high- and low-momentum pathways and vortices, similar to the patterns induced by spanwise heterogeneous surface roughness. We find that the impact of the surface heterogeneity on the outer layer depends strongly on the spanwise heterogeneity length scale of the surface temperature. Comparison to stable channel flow with uniform temperature reveals that the heterogeneous surface temperature increases the global friction coefficient and reduces the global Nusselt number in most cases. However, for the high-Reynolds cases with $\lambda /h \geq {\rm \pi} /2$, we find a reduction of the friction coefficient. At stronger stability, the vertical extent of the vortices is reduced and the impact of the heterogeneous temperature on momentum and heat transfer is smaller.

JFM classification

Boundary Layers: Boundary layer stability Turbulent Flows: Stratified turbulence Flow Control: Drag reduction
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 933 , 25 February 2022 , A57
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

REFERENCES

Allaerts, D. 2016 Large-eddy simulation of wind farms in conventionally neutral and stable atmospheric boundary layers. PhD thesis, KU Leuven.CrossRefGoogle Scholar
Anderson, W., Barros, J.M., Christensen, K.T. & Awasthi, A. 2015 Numerical and experimental study of mechanisms responsible for turbulent secondary flows in boundary layer flows over spanwise heterogeneous roughness. J. Fluid Mech. 768, 316–347.CrossRefGoogle Scholar
Armenio, V. & Sarkar, S. 2002 An investigation of stably stratified turbulent channel flow using large-eddy simulation. J. Fluid Mech. 459, 1–42.CrossRefGoogle Scholar
Atoufi, A., Scott, K.A. & Waite, M.L. 2019 Wall turbulence response to surface cooling and formation of strongly stable stratified boundary layers. Phys. Fluids 31 (8), 085114.CrossRefGoogle Scholar
Atoufi, A., Scott, K.A. & Waite, M.L. 2020 Characteristics of quasistationary near-wall turbulence subjected to strong stable stratification in open-channel flows. Phys. Rev. Fluids 5 (6), 064603.CrossRefGoogle Scholar
Barros, J.M. & Christensen, K.T. 2014 Observations of turbulent secondary flows in a rough-wall boundary layer. J. Fluid Mech. 748 (2), R1.CrossRefGoogle Scholar
Beyaztas, B.H., Firuzan, E. & Beyaztas, U. 2017 New block bootstrap methods: sufficient and/or ordered. Commun. Stat. Simul. Comput. 46 (5), 3942–3951.Google Scholar
Bou-Zeid, E., Anderson, W., Katul, G.G. & Mahrt, L. 2020 The persistent challenge of surface heterogeneity in boundary-layer meteorology: a review. Boundary-Layer Meteorol. 177 (2–3), 227–245.CrossRefGoogle Scholar
Bou-Zeid, E., Meneveau, C. & Parlange, M.B. 2004 Large-eddy simulation of neutral atmospheric boundary layer flow over heterogeneous surfaces: blending height and effective surface roughness. Water Resour. Res. 40 (2), W02505.CrossRefGoogle Scholar
Boufidi, E., Lavagnoli, S. & Fontaneto, F. 2020 A probabilistic uncertainty estimation method for turbulence parameters measured by hot-wire anemometry in short-duration wind tunnels. Trans. ASME: J. Engng Gas Turbines Power 142 (3), 031007.Google Scholar
Bradshaw, P. 1987 Turbulent secondary flows. Annu. Rev. Fluid Mech. 19, 53–74.CrossRefGoogle Scholar
Brethouwer, G., Duguet, Y. & Schlatter, P. 2012 Turbulent-laminar coexistence in wall flows with Coriolis, buoyancy or Lorentz forces. J. Fluid Mech. 704, 137–172.CrossRefGoogle Scholar
Brunsell, N.A., Mechem, D.B. & Anderson, M.C. 2011 Surface heterogeneity impacts on boundary layer dynamics via energy balance partitioning. Atmos. Chem. Phys. 11 (7), 3403–3416.CrossRefGoogle Scholar
Chung, D., Monty, J.P. & Hutchins, N. 2018 Similarity and structure of wall turbulence with lateral wall shear stress variations. J. Fluid Mech. 847, 591–613.CrossRefGoogle Scholar
Deusebio, E., Brethouwer, G., Schlatter, P. & Lindborg, E. 2014 A numerical study of the unstratified and stratified Ekman layer. J. Fluid Mech. 755, 672–704.CrossRefGoogle Scholar
Donda, J.M., van Hooijdonk, I.G., Moene, A.F., van Heijst, G.J., Clercx, H.J. & van de Wiel, B.J. 2016 The maximum sustainable heat flux in stably stratified channel flows. Q. J. R. Meteorol. Soc. 142 (695), 781–792.CrossRefGoogle Scholar
Donda, J.M., van Hooijdonk, I.G., Moene, A.F., Jonker, H.J., van Heijst, G.J., Clercx, H.J. & van de Wiel, B.J. 2015 Collapse of turbulence in stably stratified channel flow: A transient phenomenon. Q. J. R. Meteorol. Soc. 141 (691), 2137–2147.CrossRefGoogle Scholar
Druzhinin, O.A., Troitskaya, Y.I. & Zilitinkevich, S.S. 2016 Stably stratified air-flow over a waved water surface. Part 2: wave-induced pre-turbulent motions. Q. J. R. Meteorol. Soc. 142 (695), 773–780.CrossRefGoogle Scholar
Flores, O. & Riley, J.J. 2011 Analysis of turbulence collapse in the stably stratified surface layer using direct numerical simulation. Boundary-Layer Meteorol. 139 (2), 241–259.CrossRefGoogle Scholar
Forooghi, P., Yang, X.I.A. & Abkar, M. 2020 Roughness-induced secondary flows in stably stratified turbulent boundary layers. Phys. Fluids 32, 105118.CrossRefGoogle Scholar
Franz, V.H. 2007 Ratios: A short guide to confidence limits and proper use, arXiv:0710.2024.Google Scholar
Fukagata, K., Iwamoto, K. & Kasagi, N. 2005 Novel turbulence control strategy for simultaneously achieving friction drag reduction and heat transfer augmentation. In 4th International Symposium on Turbulence and Shear Flow Phenomena, vol. 1(3), pp. 307–312. Begel House Inc.Google Scholar
Fukagata, K., Kaoru, I. & Nobuhide, K. 2004 Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows. Phys. Fluids 76, 199–202.Google Scholar
Gage, K.S. & Reid, W. 1968 The stability of plane poiseuille flow. J. Fluid Mech. 33 (1), 21–32.CrossRefGoogle Scholar
García-Villalba, M. & del Álamo, J.C. 2011 Turbulence modification by stable stratification in channel flow. Phys. Fluids. 23 (4), 045104.CrossRefGoogle Scholar
García-Villalba, M., Azagra, E. & Uhlmann, M. 2011 A numerical study of turbulent stably-stratified plane Couette flow. In High Performance Computing in Science and Engineering'10. pp. 251-261. Springer.CrossRefGoogle Scholar
Garg, R.P., Ferziger, J.H., Monismith, S.G. & Koseff, J.R. 2000 Stably stratified turbulent channel flows. I. Stratification regimes and turbulence suppression mechanism. Phys. Fluids 12 (10), 2569–2594.CrossRefGoogle Scholar
He, P. 2016 A high order finite difference solver for massively parallel simulations of stably stratified turbulent channel flows. Comput. Fluids 127, 161–173.CrossRefGoogle Scholar
He, P. & Basu, S. 2015 Direct numerical simulation of intermittent turbulence under stably stratified conditions. Nonlinear Process. Geophys. 22 (4), 447–471.CrossRefGoogle Scholar
He, P. & Basu, S. 2016 Development of similarity relationships for energy dissipation rate and temperature structure parameter in stably stratified flows: a direct numerical simulation approach. Environ. Fluid Mech. 16 (2), 373–399.CrossRefGoogle Scholar
van Hooijdonk, I.G., Clercx, H.J., Ansorge, C., Moene, A.F. & van de Wiel, B.J. 2018 Parameters for the collapse of turbulence in the stratified plane Couette flow. J. Atmos. Sci. 75 (9), 3211–3231.CrossRefGoogle Scholar
Hwang, H.G. & Lee, J.H. 2018 Secondary flows in turbulent boundary layers over longitudinal surface roughness. Phys. Rev. Fluids 3 (1), 014608.CrossRefGoogle Scholar
Iida, O., Kasagi, N. & Nagano, Y. 2002 Direct numerical simulation of turbulent channel flow under stable density stratification. Intl J. Heat Mass Transfer 45 (8), 1693–1703.CrossRefGoogle Scholar
Kevin, K., Monty, J.P., Bai, H.L., Pathikonda, G., Nugroho, B., Barros, J.M., Christensen, K.T. & Hutchins, N. 2017 Cross-stream stereoscopic particle image velocimetry of a modified turbulent boundary layer over directional surface pattern. J. Fluid Mech. 813, 412–435.CrossRefGoogle Scholar
Leonardi, S., Orlandi, P., Djenidi, L. & Antonia, R.A. 2015 Heat transfer in a turbulent channel flow with square bars or circular rods on one wall. J. Fluid Mech. 776, 512–530.CrossRefGoogle Scholar
Mahrt, L. 2014 Stably stratified atmospheric boundary layers. Annu. Rev. Fluid Mech. 46, 23–45.CrossRefGoogle Scholar
Margairaz, F., Pardyjak, E.R. & Calaf, M. 2020 Surface thermal heterogeneities and the atmospheric boundary layer: the relevance of dispersive fluxes. Boundary-Layer Meteorol. 175 (3), 369–395.CrossRefGoogle Scholar
Medjnoun, T., Rodriguez-Lopez, E., Ferreira, M.A., Griffiths, T., Meyers, J. & Ganapathisubramani, B. 2021 Turbulent boundary-layer flow over regular multiscale roughness. J. Fluid Mech. 917, A1.CrossRefGoogle Scholar
Medjnoun, T., Vanderwel, C. & Ganapathisubramani, B. 2018 Characteristics of turbulent boundary layers over smooth surfaces with spanwise heterogeneities. J. Fluid Mech. 838, 516–543.CrossRefGoogle Scholar
Medjnoun, T., Vanderwel, C. & Ganapathisubramani, B. 2020 Effects of heterogeneous surface geometry on secondary flows in turbulent boundary layers. J. Fluid Mech. 886, A31.CrossRefGoogle Scholar
Mills, A. & Coimbra, C. 1999 Basic Heat and Mass Transfer, 3rd edn. Prentice Hall.Google Scholar
Mironov, D.V. & Sullivan, P.P. 2016 Second-moment budgets and mixing intensity in the stably stratified atmospheric boundary layer over thermally heterogeneous surfaces. J. Atmos. Sci. 73 (1), 449–464.CrossRefGoogle Scholar
Nieuwstadt, F.T. 2005 Direct numerical simulation of stable channel flow at large stability. Boundary-Layer Meteorol. 116 (2), 277–299.CrossRefGoogle Scholar
Nikora, V.I., Stoesser, T., Cameron, S.M., Stewart, M., Papadopoulos, K., Ouro, P., McSherry, R., Zampiron, A., Marusic, I. & Falconer, R.A. 2019 Friction factor decomposition for rough-wall flows: theoretical background and application to open-channel flows. J. Fluid Mech. 872, 626–664.CrossRefGoogle Scholar
Nikuradse, J. 1933 Strömungsgesetze in rauhen Rohren (English translation: Laws of flow in rough pipes). VDI Forschungsheft 361, 0.Google Scholar
Patton, E.G., Sullivan, P.P. & Moeng, C.H. 2005 The influence of idealized heterogeneity on wet and dry planetary boundary layers coupled to the land surface. J. Atmos. Sci. 62 (7 I), 2078–2097.CrossRefGoogle Scholar
Pope, S. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Poulos, G.S., et al. 2002 CASES-99: A comprehensive investigation of the stable nocturnal boundary layer. Bull. Am. Meteorol. Soc. 83 (4), 555–581.2.3.CO;2>CrossRefGoogle Scholar
Raupach, M.R. & Shaw, R.H. 1982 Averaging procedures for flow within vegetation canopies. Boundary-Layer Meteorol. 22 (1), 79–90.CrossRefGoogle Scholar
Reynolds, W. & Hussain, A. 1972 The mechanics of an organized wave in turbulent shear flow. Part 3. Theoretical models and comparisons with experiments. J. Fluid Mech. 54, 263–288.CrossRefGoogle Scholar
Roo, F.D. & Mauder, M. 2018 The influence of idealized surface heterogeneity on turbulent flux measurements: a parameter study with large-eddy simulation. Atmos. Chem. Phys. 18, 5059–5074.Google Scholar
Sorbjan, Z. 2010 Gradient-based scales and similarity laws in the stable boundary layer. Q. J. R. Meteorol. Soc. 136 (650), 1243–1254.CrossRefGoogle Scholar
Stoll, R. & Porté-Agel, F. 2008 Large-eddy simulation of the stable atmospheric boundary layer using dynamic models with different averaging schemes. Boundary-Layer Meteorol. 126 (1), 1–28.CrossRefGoogle Scholar
Stoll, R. & Porté-Agel, F. 2009 Surface heterogeneity effects on regional-scale fluxes in stable boundary layers: surface temperature transitions. J. Atmos. Sci. 66 (2), 412–431.CrossRefGoogle Scholar
Stroh, A., Schäfer, K., Forooghi, P. & Frohnapfel, B. 2020 Secondary flow and heat transfer in turbulent flow over streamwise ridges. Intl J. Heat Fluid Flow 81, 108518.CrossRefGoogle Scholar
Stull, R.B. 1988 An Introduction to Boundary Layer Meteorology. Kluwer.CrossRefGoogle Scholar
Van Heerwaarden, C.C., Mellado, J.P. & de Lozar, A. 2014 Scaling laws for the heterogeneously heated free convective boundary layer. J. Atmos. Sci. 71 (11), 3975–4000.CrossRefGoogle Scholar
Vanderwel, C. & Ganapathisubramani, B. 2015 Effects of spanwise spacing on large-scale secondary flows in rough-wall turbulent boundary layers. J. Fluid Mech. 774, R2.CrossRefGoogle Scholar
Vanderwel, C., Stroh, A., Kriegseis, J., Frohnapfel, B. & Ganapathisubramani, B. 2019 The instantaneous structure of secondary flows in turbulent boundary layers. J. Fluid Mech. 862, 845–870.CrossRefGoogle Scholar
Vermaas, D.A., Uijttewaal, W.S. & Hoitink, A.J. 2011 Lateral transfer of streamwise momentum caused by a roughness transition across a shallow channel. Water Resour. Res. 47 (2), W02530.CrossRefGoogle Scholar
Verstappen, R.W. & Veldman, A.E. 2003 Symmetry-preserving discretization of turbulent flow. J. Comput. Phys. 187 (1), 343–368.CrossRefGoogle Scholar
Wang, Z.Q. & Cheng, N.S. 2005 Secondary flows over artificial bed strips. Adv. Water Resour. 28 (5), 441–450.CrossRefGoogle Scholar
Williams, O., Hohman, T., Van Buren, T., Bou-Zeid, E. & Smits, A.J. 2017 The effect of stable thermal stratification on turbulent boundary layer statistics. J. Fluid Mech. 812, 1039–1075.CrossRefGoogle Scholar
Wunsch, C. & Ferrari, R. 2004 Vertical mixing, energy, and the general circulation of the oceans. Annu. Rev. Fluid Mech. 36 (1), 281–314.CrossRefGoogle Scholar
Wyngaard, J.C. 2010 Turbulence in the Atmosphere. Cambridge University Press.CrossRefGoogle Scholar
Yang, J. & Anderson, W. 2018 Numerical study of turbulent channel flow over surfaces with variable spanwise heterogeneities: topographically-driven secondary flows affect outer-layer similarity of turbulent length scales. Flow Turbul. Combust. 100 (1), 1–17.CrossRefGoogle Scholar
Zhou, Q., Taylor, J.R. & Caulfield, C.P. 2017 Self-similar mixing in stratified plane Couette flow for varying Prandtl number. J. Fluid Mech. 820, 86–120.CrossRefGoogle Scholar
Zonta, F. 2013 Nusselt number and friction factor in thermally stratified turbulent channel flow under non-Oberbeck-Boussinesq conditions. Intl J. Heat Fluid Flow 44, 489–494.CrossRefGoogle Scholar
Zonta, F. & Soldati, A. 2018 Stably stratified wall-bounded turbulence. Appl. Mech. Rev. 70 (4), 040801.CrossRefGoogle Scholar