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Temporal modulation on mixed convection in turbulent channels
Published online by Cambridge University Press: 06 March 2025
Abstract
We studied flow organization and heat transfer properties in mixed turbulent convection within Poiseuille–Rayleigh–Bénard channels subjected to temporally modulated sinusoidal wall temperatures. Three-dimensional direct numerical simulations were performed for Rayleigh numbers in the range 
$10^6 \leqslant Ra \leqslant 10^8$, a Prandtl number 
$Pr = 0.71$ and a bulk Reynolds number 
$Re_b \approx 5623$. We found that high-frequency wall temperature oscillations had minimal impact on flow structures, while low-frequency oscillations induced adaptive changes, forming stable stratified layers during cooling. Proper orthogonal decomposition (POD) analysis revealed a dominant streamwise unidirectional shear flow mode. Large-scale rolls oriented in the streamwise direction appeared as higher POD modes and were significantly influenced by lower-frequency wall temperature variations. Long-time-averaged statistics showed that the Nusselt number increased with decreasing frequency by up to 96 %, while the friction coefficient varied by less than 15 %. High-frequency modulation predominantly influenced near-wall regions, enhancing convective effects, whereas low frequencies reduced these effects via stable stratified layer formation. Phase-averaged statistics showed that high-frequency modulation resulted in phase-stable streamwise velocity and temperature profiles, while low-frequency modulation caused significant variations due to weakened turbulence. Turbulent kinetic energy (TKE) profiles remained high near the wall during both heating and cooling at high frequency, but decreased during cooling at low frequencies. A TKE budget analysis revealed that during heating, TKE production was dominated by shear near the wall and by buoyancy in the bulk region; while during cooling, the production, distribution and dissipation of TKE were all nearly zero.
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References
Ahlers, G., Grossmann, S. & Lohse, D. 2009 Heat transfer and large scale dynamics in turbulent Rayleigh–Bénard convection. Rev. Mod. Phys. 81 (2), 503–537.CrossRefGoogle Scholar
Andreotti, B., Fourriere, A., Ould-Kaddour, F., Murray, B. & Claudin, P. 2009 Giant aeolian dune size determined by the average depth of the atmospheric boundary layer. Nature 457 (7233), 1120–1123.CrossRefGoogle ScholarPubMed
Berkooz, G., Holmes, P. & Lumley, J.L. 1993 The proper orthogonal decomposition in the analysis of turbulent flows. Annu. Rev. Fluid Mech. 25 (1), 539–575.CrossRefGoogle Scholar
Bernardini, M., Pirozzoli, S. & Orlandi, P. 2014 Velocity statistics in turbulent channel flow up to
$Re_{\tau }=4000$
. J. Fluid Mech. 742, 171–191.CrossRefGoogle Scholar
$Re_{\tau }=4000$
. J. Fluid Mech. 742, 171–191.CrossRefGoogle ScholarBlass, A., Tabak, P., Verzicco, R., Stevens, R.J.A.M. & Lohse, D. 2021 The effect of Prandtl number on turbulent sheared thermal convection. J. Fluid Mech. 910, A37.CrossRefGoogle Scholar
Blass, A., Zhu, X., Verzicco, R., Lohse, D. & Stevens, R.J.A.M. 2020 Flow organization and heat transfer in turbulent wall sheared thermal convection. J. Fluid Mech. 897, A22.CrossRefGoogle ScholarPubMed
Brown, R.A. 1980 Longitudinal instabilities and secondary flows in the planetary boundary layer: a review. Rev. Geophys. 18 (3), 683–697.CrossRefGoogle Scholar
Castillo-Castellanos, A., Sergent, A., Podvin, B. & Rossi, M. 2019 Cessation and reversals of large-scale structures in square Rayleigh–Bénard cells. J. Fluid Mech. 877, 922–954.CrossRefGoogle Scholar
Caulfield, C.P. 2021 Layering, instabilities, and mixing in turbulent stratified flows. Annu. Rev. Fluid Mech. 53 (1), 113–145.CrossRefGoogle Scholar
Chen, X. & Sreenivasan, K.R. 2023 Reynolds number asymptotics of wall-turbulence fluctuations. J. Fluid Mech. 976, A21.CrossRefGoogle Scholar
Chilla, T., Evrard, E. & Schulz, C. 2012 On the territoriality of cross-border cooperation: “Institutional Mapping” in a multi-level context. Eur. Plan. Stud. 20 (6), 961–980.CrossRefGoogle Scholar
Choi, K.-S. 2002 Near-wall structure of turbulent boundary layer with spanwise-wall oscillation. Phys. Fluids 14 (7), 2530–2542.CrossRefGoogle Scholar
Cossu, C. 2022 Onset of large-scale convection in wall-bounded turbulent shear flows. J. Fluid Mech. 945, A33.CrossRefGoogle Scholar
Dror, T., Koren, I., Liu, H. & Altaratz, O. 2023 Convective steady state in shallow cloud fields. Phys. Rev. Lett. 131 (13), 134201.CrossRefGoogle Scholar
Dupont, S. & Patton, E.G. 2022 On the influence of large-scale atmospheric motions on near-surface turbulence: comparison between flows over low-roughness and tall vegetation canopies. Boundary-Layer Meteorol. 184 (2), 195–230.CrossRefGoogle Scholar
Ebadi, A., White, C.M., Pond, I. & Dubief, Y. 2019 Mean dynamics and transition to turbulence in oscillatory channel flow. J. Fluid Mech. 880, 864–889.CrossRefGoogle Scholar
Garai, A., Kleissl, J. & Sarkar, S. 2014 Flow and heat transfer in convectively unstable turbulent channel flow with solid-wall heat conduction. J. Fluid Mech. 757, 57–81.CrossRefGoogle Scholar
Gasteuil, Y., Shew, W.L., Gibert, M., Chillà, F., Castaing, B. & Pinton, J.-F. 2007 Lagrangian temperature, velocity, and local heat flux measurement in Rayleigh–Bénard convection. Phys. Rev. Lett. 99 (23), 234302.CrossRefGoogle ScholarPubMed
Graham, M.D. & Floryan, D. 2021 Exact coherent states and the nonlinear dynamics of wall-bounded turbulent flows. Annu. Rev. Fluid Mech. 53 (1), 227–253.CrossRefGoogle Scholar
Hanna, S.R. 1969 The formation of longitudinal sand dunes by large helical eddies in the atmosphere. J. Appl. Meteorol. 8 (6), 874–883.2.0.CO;2>CrossRefGoogle Scholar
Howland, C.J., Yerragolam, G.S., Verzicco, R. & Lohse, D. 2024 Turbulent mixed convection in vertical and horizontal channels. J. Fluid Mech. 998, A48.CrossRefGoogle Scholar
Huang, Y.-X. & Zhou, Q. 2013 Counter-gradient heat transport in two-dimensional turbulent Rayleigh–Bénard convection. J. Fluid Mech. 737, R3.CrossRefGoogle Scholar
Hunt, J.C.R., Wray, A.A. & Moin, P. 1988 Eddies, streams, and convergence zones in turbulent flows. In Studying Turbulence Using Numerical Simulation Databases, 2. Proceedings of the 1988 Summer Program. pp. 193–208.Google Scholar
Iida, O. & Kasagi, N. 1997 Direct numerical simulation of unstably stratified turbulent channel flow. ASME J. Heat Transfer 119 (1), 53–61.CrossRefGoogle Scholar
Jayaraman, B. & Brasseur, J.G. 2021 Transition in atmospheric boundary layer turbulence structure from neutral to convective, and large-scale rolls. J. Fluid Mech. 913, A42.CrossRefGoogle Scholar
Jelly, T.O., Chin, R.C., Illingworth, S.J., Monty, J.P., Marusic, I. & Ooi, A. 2020 A direct comparison of pulsatile and non-pulsatile rough-wall turbulent pipe flow. J. Fluid Mech. 895, R3.CrossRefGoogle Scholar
Jiang, H., Zhu, X., Wang, D., Huisman, S.G. & Sun, C. 2020 Supergravitational turbulent thermal convection. Sci. Adv. 6 (40), eabb8676.CrossRefGoogle ScholarPubMed
Jiménez, J. 2012 Cascades in wall-bounded turbulence. Annu. Rev. Fluid Mech. 44 (1), 27–45.CrossRefGoogle Scholar
Jin, X.-L. & Xia, K.-Q. 2008 An experimental study of kicked thermal turbulence. J. Fluid Mech. 606, 133–151.CrossRefGoogle Scholar
Kays, W.M. 1994 Turbulent Prandtl number. Where are we? ASME J. Heat Transfer 116 (2), 284–295.CrossRefGoogle Scholar
Kok, J.F., Parteli, E.J.R., Michaels, T.I. & Karam, D.B. 2012 The physics of wind-blown sand and dust. Rep. Prog. Phys. 75 (10), 106901.CrossRefGoogle ScholarPubMed
Komen, E., Shams, A., Camilo, L. & Koren, B. 2014 Quasi-DNS capabilities of OpenFOAM for different mesh types. Comput. Fluids 96, 87–104.CrossRefGoogle Scholar
Komen, E.M.J., Camilo, L.H., Shams, A., Geurts, B.J. & Koren, B. 2017 A quantification method for numerical dissipation in quasi-DNS and under-resolved DNS, and effects of numerical dissipation in quasi-DNS and under-resolved DNS of turbulent channel flows. J. Comput. Phys. 345, 565–595.CrossRefGoogle Scholar
Komen, E.M.J., Mathur, A., Roelofs, F., Merzari, E. & Tiselj, I. 2023 Status, perspectives, and added value of high fidelity simulations for safety and design. Nucl. Engng Des. 401, 112082.CrossRefGoogle Scholar
Komori, S., Ueda, H., Ogino, F. & Mizushina, T. 1982 Turbulence structure in unstably-stratified open-channel flow. Phys. Fluids 25 (9), 1539–1546.CrossRefGoogle Scholar
Kooij, G.L., Botchev, M.A., Frederix, E.M.A., Geurts, B.J., Horn, S., Lohse, D., van der Poel, E.P., Shishkina, O., Stevens, R.J.A.M. & Verzicco, R. 2018 Comparison of computational codes for direct numerical simulations of turbulent Rayleigh–Bénard convection. Comput. Fluids 166, 1–8.CrossRefGoogle Scholar
Li, Y.-Z., Chen, X., Xu, A. & Xi, H.-D. 2022 Counter-flow orbiting of the vortex centre in turbulent thermal convection. J. Fluid Mech. 935, A19.CrossRefGoogle Scholar
Liu, H., He, M., Wang, B. & Zhang, Q. 2014 Advances in low-level jet research and future prospects. J. Meteorol. Res. 28 (1), 57–75.Google Scholar
Lohse, D. 2024 Asking the right questions on Rayleigh–Bénard turbulence. J. Fluid Mech. 1000, F3.CrossRefGoogle Scholar
Lohse, D. & Shishkina, O. 2024 Ultimate Rayleigh–Bénard turbulence. Rev. Mod. Phys. 96 (3), 035001.CrossRefGoogle Scholar
Lohse, D. & Xia, K.-Q. 2010 Small-scale properties of turbulent Rayleigh–Bénard convection. Annu. Rev. Fluid Mech. 42 (1), 335–364.CrossRefGoogle Scholar
Madhusudanan, A., Illingworth, S.J., Marusic, I. & Chung, D. 2022 Navier–Stokes-based linear model for unstably stratified turbulent channel flows. Phys. Rev. Fluids 7 (4), 044601.CrossRefGoogle Scholar
Manna, M., Vacca, A. & Verzicco, R. 2015 Pulsating pipe flow with large-amplitude oscillations in the very high frequency regime. Part 2. Phase-averaged analysis. J. Fluid Mech. 766, 272–296.CrossRefGoogle Scholar
Marusic, I., Chandran, D., Rouhi, A., Fu, M.K., Wine, D., Holloway, B., Chung, D. & Smits, A.J. 2021 An energy-efficient pathway to turbulent drag reduction. Nat. Commun. 12 (1), 5805.CrossRefGoogle ScholarPubMed
Marusic, I., McKeon, B.J., Monkewitz, P.A., Nagib, H.M., Smits, A.J. & Sreenivasan, K.R. 2010 Wall-bounded turbulent flows at high Reynolds numbers: recent advances and key issues. Phys. Fluids 22 (6), 065103.CrossRefGoogle Scholar
Moser, R.D., Kim, J. & Mansour, N.N. 1999 Direct numerical simulation of turbulent channel flow up to
$Re_\tau = 590$
. Phys. Fluids 11 (4), 943–945.CrossRefGoogle Scholar
$Re_\tau = 590$
. Phys. Fluids 11 (4), 943–945.CrossRefGoogle ScholarNiemela, J.J. & Sreenivasan, K.R. 2008 Formation of the “superconducting” core in turbulent thermal convection. Phys. Rev. Lett. 100 (18), 184502.CrossRefGoogle ScholarPubMed
Nieuwstadt, F.T.M. 1984 The turbulent structure of the stable, nocturnal boundary layer. J. Atmos. Sci. 41 (14), 2202–2216.2.0.CO;2>CrossRefGoogle Scholar
Pirozzoli, S., Bernardini, M., Verzicco, R. & Orlandi, P. 2017 Mixed convection in turbulent channels with unstable stratification. J. Fluid Mech. 821, 482–516.CrossRefGoogle Scholar
Podvin, B. & Sergent, A. 2015 A large-scale investigation of wind reversal in a square Rayleigh–Bénard cell. J. Fluid Mech. 766, 172–201.CrossRefGoogle Scholar
Ricco, P., Ottonelli, C., Hasegawa, Y. & Quadrio, M. 2012 Changes in turbulent dissipation in a channel flow with oscillating walls. J. Fluid Mech. 700, 77–104.CrossRefGoogle Scholar
Scagliarini, A., Einarsson, H., Gylfason, Á. & Toschi, F. 2015 Law of the wall in an unstably stratified turbulent channel flow. J. Fluid Mech. 781, R5.CrossRefGoogle Scholar
Sharifnezhadazizi, Z., Norouzi, H., Prakash, S., Beale, C. & Khanbilvardi, R. 2019 A global analysis of land surface temperature diurnal cycle using MODIS observations. J. Appl. Meteorol. Climatol. 58 (6), 1279–1291.CrossRefGoogle Scholar
Shishkina, O., Stevens, R.J.A.M., Grossmann, S. & Lohse, D. 2010 Boundary layer structure in turbulent thermal convection and its consequences for the required numerical resolution. New J. Phys. 12 (7), 075022.CrossRefGoogle Scholar
Smits, A.J., McKeon, B.J. & Marusic, I. 2011 High-Reynolds number wall turbulence. Annu. Rev. Fluid Mech. 43 (1), 353–375.CrossRefGoogle Scholar
Soucasse, L., Podvin, B., Rivière, P. & Soufiani, A. 2019 Proper orthogonal decomposition analysis and modelling of large-scale flow reorientations in a cubic Rayleigh–Bénard cell. J. Fluid Mech. 881, 23–50.CrossRefGoogle Scholar
Stevens, R.J.A.M., Hartmann, R., Verzicco, R. & Lohse, D. 2024 How wide must Rayleigh–Bénard cells be to prevent finite aspect ratio effects in turbulent flow? J. Fluid Mech. 1000, A58.CrossRefGoogle Scholar
Stull, R.B. 2015 Practical Meteorology: an Algebra-Based Survey of Atmospheric Science. University of British Columbia.Google Scholar
Teimurazov, A., Singh, S., Su, S., Eckert, S., Shishkina, O. & Vogt, T. 2023 Oscillatory large-scale circulation in liquid-metal thermal convection and its structural unit. J. Fluid Mech. 977, A16.CrossRefGoogle Scholar
Urban, P., Hanzelka, P., Králik, T., Musilová, V. & Skrbek, L. 2022 Thermal waves and heat transfer efficiency enhancement in harmonically modulated turbulent thermal convection. Phys. Rev. Lett. 128 (13), 134502.CrossRefGoogle ScholarPubMed
Vogt, T., Horn, S., Grannan, A.M. & Aurnou, J.M. 2018 Jump rope vortex in liquid metal convection. Proc. Natl Acad. Sci. USA 115 (50), 12674–12679.CrossRefGoogle ScholarPubMed
Wang, B.-F., Zhou, Q. & Sun, C. 2020 Vibration-induced boundary-layer destabilization achieves massive heat-transport enhancement. Sci. Adv. 6 (21), eaaz8239.CrossRefGoogle ScholarPubMed
Wu, J.-Z., Dong, Y.-H., Wang, B.-F. & Zhou, Q. 2021 Phase decomposition analysis on oscillatory Rayleigh–Bénard turbulence. Phys. Fluids 33 (4), 045108.CrossRefGoogle Scholar
Wu, J.-Z., Wang, B.-F. & Zhou, Q. 2022 Massive heat transfer enhancement of Rayleigh–Bénard turbulence over rough surfaces and under horizontal vibration. Acta Mechanica Sin. 38 (2), 321319.CrossRefGoogle Scholar
Xia, K.-Q., Huang, S.-D., Xie, Y.-C. & Zhang, L. 2023 Tuning heat transport via coherent structure manipulation: recent advances in thermal turbulence. Natl. Sci. Rev. 10 (6), nwad012.CrossRefGoogle ScholarPubMed
Xu, A., Chen, X. & Xi, H.-D. 2021 Tristable flow states and reversal of the large-scale circulation in two-dimensional circular convection cells. J. Fluid Mech. 910, A33.CrossRefGoogle Scholar
Xu, A. & Li, B.-T. 2023 Multi-GPU thermal lattice Boltzmann simulations using OpenACC and MPI. Intl J. Heat Mass Transfer 201, 123649.CrossRefGoogle Scholar
Xu, A., Shi, L. & Xi, H.-D. 2019 Lattice Boltzmann simulations of three-dimensional thermal convective flows at high Rayleigh number. Intl J. Heat Mass Transfer 140, 359–370.CrossRefGoogle Scholar
Xu, A., Shi, L. & Zhao, T.S. 2017 Accelerated lattice Boltzmann simulation using GPU and OpenACC with data management. Intl J. Heat Mass Transfer 109, 577–588.CrossRefGoogle Scholar
Yang, R., Chong, K.L., Wang, Q., Verzicco, R., Shishkina, O. & Lohse, D. 2020 Periodically modulated thermal convection. Phys. Rev. Lett. 125 (15), 154502.CrossRefGoogle ScholarPubMed
Yao, J., Chen, X. & Hussain, F. 2022 Direct numerical simulation of turbulent open channel flows at moderately high Reynolds numbers. J. Fluid Mech. 953, A19.CrossRefGoogle Scholar
Yerragolam, G.S., Howland, C.J., Stevens, R.J.A.M., Verzicco, R., Shishkina, O. & Lohse, D. 2024 Scaling relations for heat and momentum transport in sheared Rayleigh–Bénard convection. J. Fluid Mech. 1000, A74.CrossRefGoogle Scholar
Yerragolam, G.S., Verzicco, R., Lohse, D. & Stevens, R.J.A.M. 2022 How small-scale flow structures affect the heat transport in sheared thermal convection. J. Fluid Mech. 944, A1.CrossRefGoogle Scholar
Young, G.S., Kristovich, D.A.R., Hjelmfelt, M.R. & Foster, R.C. 2002 Rolls, streets, waves, and more: a review of quasi-two-dimensional structures in the atmospheric boundary layer. Bull. Am. Meteorol. Soc. 83 (7), 997–1002.Google Scholar
Zhang, H., Tan, X. & Zheng, X. 2023 Multifield intermittency of dust storm turbulence in the atmospheric surface layer. J. Fluid Mech. 963, A15.CrossRefGoogle Scholar
Zhang, H. 2024 Structure and coupling characteristics of multiple fields in dust storms. Acta Mechanica Sin. 40 (3), 123339.CrossRefGoogle Scholar
Zonta, F., Sichani, P.H. & Soldati, A. 2022 Interaction between thermal stratification and turbulence in channel flow. J. Fluid Mech. 945, A3.CrossRefGoogle Scholar
Xu et al. supplementary material movie 1
Iso-surfaces of the Q-criterion
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Xu et al. supplementary material movie 2
Vertical slices of the temperature field
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