Hostname: page-component-5d59c44645-lfgmx Total loading time: 0 Render date: 2024-02-28T04:09:53.675Z Has data issue: false hasContentIssue false

On the energy transport and heat transfer efficiency in radiatively heated particle-laden Rayleigh–Bénard convection

Published online by Cambridge University Press:  14 December 2022

Wenwu Yang
Affiliation:
Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, and Shanghai Key Laboratory of Mechanics in Energy Engineering and Shanghai Frontier Science Center of Mechanoinformatics, Shanghai University, Shanghai 200072, PR China
Zhen-Hua Wan
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, PR China
Quan Zhou
Affiliation:
Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, and Shanghai Key Laboratory of Mechanics in Energy Engineering and Shanghai Frontier Science Center of Mechanoinformatics, Shanghai University, Shanghai 200072, PR China
Yuhong Dong*
Affiliation:
Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, and Shanghai Key Laboratory of Mechanics in Energy Engineering and Shanghai Frontier Science Center of Mechanoinformatics, Shanghai University, Shanghai 200072, PR China
*
Email address for correspondence: dongyh@shu.edu.cn

Abstract

We investigate the energy transport and heat transfer efficiency in turbulent Rayleigh–Bénard (RB) convection laden with radiatively heated inertial particles. Direct numerical simulations combined with the Lagrangian point-particle mode were carried out in the range of density ratio $854.7\le \rho _p/\rho _0 \le 8547$ and radiation intensity $1\le \phi /\phi _{solar}\le 100$ for both two-dimensional (2-D) and three-dimensional (3-D) simulations. The Rayleigh number ranges from $2\times 10^6$ to $10^8$ for 2-D cases, and is $10^7$ for 3-D cases for $Pr=0.71$. It is found that particles with small density ratio that encounter strong radiation significantly alter the flow momentum transport and fluid heat transfer, so the fluid temperature of bulk is remarkably heated. We then derived the theoretical relation of the Nusselt number for interphase heat transfer in the heated particle-laden RB convection, which reveals that the heat transfer difference between the top and bottom plates stems from the interphase heat transfer. We further found that both the interphase heat transfer and the interphase thermal energy transport exhibit universal properties. They are both increased linearly with the reciprocal of the normalized density ratio. Additionally, both the interphase heat transfer and the interphase thermal energy transport increase linearly with the increase of radiation intensity. The growth rates exhibit specific scaling relations versus Rayleigh number and density ratio. Two different regimes distinguished by the critical density ratio, i.e. the exothermic particle regime and the endothermic particle regime, are observed. We further derived the power-law relation of the critical density ratios versus Rayleigh number and radiation intensity, i.e. $\rho _p/\rho _c \sim (\phi /\phi _{solar})^{1/2}\,Ra^{1/3}$, which is in remarkable agreement with the 3-D simulations.

Type
JFM Papers
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Ahlers, G., Grossmann, S. & Lohse, D. 2009 Heat transfer and large scale dynamics in turbulent Rayleigh–Bénard convection. Rev. Mod. Phys. 81, 503537.CrossRefGoogle Scholar
Ahmed, A.M. & Elghobashi, S. 2000 On the mechanisms of modifying the structure of turbulent homogeneous shear flows by dispersed particles. Phys. Fluids 12 (11), 29062930.CrossRefGoogle Scholar
Balachandar, S. & Eaton, J.K. 2010 Turbulent dispersed multiphase flow. Annu. Rev. Fluid Mech. 42, 111133.CrossRefGoogle Scholar
Banko, A.J., Villafñe, L., Kim, J.H. & Eaton, J.K. 2020 Temperature statistics in a radiatively heated particle-laden turbulent square duct flow. Intl J. Heat Fluid Flow 84, 108618.CrossRefGoogle Scholar
Bec, J., Homann, H. & Ray, S.S. 2014 Gravity-driven enhancement of heavy particle clustering in turbulent flow. Phy. Rev. Lett. 112 (18), 184501.CrossRefGoogle ScholarPubMed
Boivin, M., Simonin, O. & Squires, K.D. 1998 Direct numerical simulation of turbulence modulation by particles in isotropic turbulence. J. Fluid Mech. 375, 235263.CrossRefGoogle Scholar
Bosse, T., Kleiser, L. & Meiburg, E. 2006 Small particles in homogeneous turbulence: settling velocity enhancement by two-way coupling. Phys. Fluids 18, 027102.CrossRefGoogle Scholar
Boussinesq, J. 1903 Theorie Analytique de la Chaleur, vol. 2. Gauthier-Villars.Google Scholar
Bragg, A.D., Richter, D.H. & Wang, G. 2021 Mechanisms governing the settling velocities and spatial distributions of inertial particles in wall-bounded turbulence. Phys. Rev. Fluids 6, 064302.CrossRefGoogle Scholar
Briggs, W.L., Henson, V.E. & McCormick, S.F. 2000 A Multigrid Tutorial, vol. 72. SIAM.CrossRefGoogle Scholar
Carbone, M., Bragg, A.D. & Iovieno, M. 2019 Multiscale fluid–particle thermal interaction in isotropic turbulence. J. Fluid Mech. 881, 679721.CrossRefGoogle Scholar
Chen, H., Chen, Y., Hsieh, H.-T. & Siegel, N. 2007 Computational fluid dynamics modeling of gas-particle flow within a solid-particle solar receiver. J. Sol. Energy Engng 129 (2), 160170.CrossRefGoogle Scholar
Cherukat, P., Mclaughlin, J.B. & Dandy, D.S. 1998 A computational study of the inertial lift on a sphere in a linear shear flow field. Intl J. Multiphase Flow 25, 1533.CrossRefGoogle Scholar
Chillà, F. & Schumacher, J. 2012 New perspectives in turbulent Rayleigh–Bénard convection. Eur. Phys. J. E 35 (7), 58.CrossRefGoogle ScholarPubMed
Chinnici, A., Arjomanidi, M., Tian, Z.F., Lu, Z. & Nathan, G.J. 2015 A novel solar expanding-vortex particle reactor: influence of vortex structure on particle residence times and trajectories. Solar Energy 122, 5875.CrossRefGoogle Scholar
Chung, J.N. & Troutt, T.R. 1988 Simulation of particle dispersion in an axisymmetric jet. J. Fluid Mech. 186, 199222.CrossRefGoogle Scholar
Crowe, C.T. 1982 Review: numerical models for dilute gas-particle flows. Trans. ASME J. Fluids Engng 104, 297303.CrossRefGoogle Scholar
Crowe, C.T., Gore, R. & Troutt, T.R. 1985 Particles dispersion by coherent structures in free shear flows. Particul. Sci. Tech. 3, 149158.CrossRefGoogle Scholar
Crowe, C.T., Troutt, T.R. & Chung, J.N. 1996 Numerical models for two-phase turbulent flows. Annu. Rev. Fluid Mech. 28, 1143.CrossRefGoogle Scholar
Davis, D., Jafarian, M., Chinnici, A., Saw, W.L. & Nathan, G.J. 2019 Thermal performance of vortex-based solar particle receiver for sensible heating. Solar Energy 177, 163177.CrossRefGoogle Scholar
Dong, Y. & Chen, L. 2011 The effect of stable stratification and thermophoresis on fine particle deposition in a bounded turbulent flow. Intl J. Heat Mass Transfer 54, 11681178.CrossRefGoogle Scholar
Druzhinin, O.A. & Elghobashi, S. 1999 On the decay rate of isotropic turbulence laden with microparticles. Phys. Fluids 11 (3), 602610.CrossRefGoogle Scholar
Elghobashi, S. 1991 Particle-laden turbulent flows: direct simulation and closure models. Appl. Sci. Res. 48, 301314.CrossRefGoogle Scholar
Elghobashi, S. 1994 On predicting particle-laden turbulent flows. Appl. Sci. Res. 52, 309329.CrossRefGoogle Scholar
Elghobashi, S. 2019 Direct numerical simulation of turbulent flows laden with droplets or bubbles. Annu. Rev. Fluid Mech. 51, 217244.CrossRefGoogle Scholar
Elghobashi, S. & Truesdell, G.C. 1992 Direct simulation of particle dispersion in a decaying isotropic turbulence. J. Fluid Mech. 242, 655700.CrossRefGoogle Scholar
Elghobashi, S. & Truesdell, G.C. 1993 On the two-way interaction between homogeneous turbulence and dispersed solid particles. I. Turbulence modification. Phys. Fluids A 5 (7), 17901801.CrossRefGoogle Scholar
Ferrante, A. & Elghobashi, S. 2003 On the physical mechanisms of two-way coupling in particle-laden isotropic turbulence. Phys. Fluids 15 (2), 315329.CrossRefGoogle Scholar
Frankel, A., Iaccarino, G. & Mani, A. 2017 Optical depth in particle-laden turbulent flows. J. Quant. Spectrosc. Radiat. Transfer 201, 1016.CrossRefGoogle Scholar
Frankel, A., Pouransari, H., Coletti, F. & Mani, A. 2016 Settling of heated particles in homogeneous turbulence. J. Fluid Mech. 792, 869893.CrossRefGoogle Scholar
Gereltbyamba, B. & Lee, C. 2019 Flow modification by inertial particles in a differentially heated cubic cavity. Intl J. Heat Fluid Flow 78, 108445.CrossRefGoogle Scholar
Good, G., Gerashchenko, S. & Warhaft, Z. 2012 Intermittency and inertial particle entrainment at a turbulent interface: the effect of the large-scale eddies. J. Fluid Mech. 694, 371398.CrossRefGoogle Scholar
Grabowski, W.W. & Wang, L.-P. 2013 Growth of cloud droplets in a turbulent environment. Annu. Rev. Fluid Mech. 45, 293324.CrossRefGoogle Scholar
Grossmann, S. & Lohse, D. 2000 Scaling in thermal convection: a unifying theory. J. Fluid Mech. 407, 2756.CrossRefGoogle Scholar
Guha, A. 2008 Transport and deposition of particles in turbulent and laminar flow. Annu. Rev. Fluid Mech. 40, 311341.CrossRefGoogle Scholar
Hanna, S.R. 1969 The formation of longitudinal sand dunes by large helical eddies in the atmosphere. J. Appl. Meteorol. 8 (6), 874883.2.0.CO;2>CrossRefGoogle Scholar
Ho, C.K. 2016 A review of high-temperature particle receivers for concentrating solar power. Appl. Therm. Engng 109 (B), 958969.CrossRefGoogle Scholar
Huang, S.-D., Kaczorowski, M., Ni, R. & Xia, K.-Q. 2013 Confinement-induced heat-transport enhancement in turbulent thermal convection. Phys. Rev. Lett. 111, 104501.CrossRefGoogle ScholarPubMed
Hunt, J.C.R. 1991 Industrial and environmental fluid mechanics. Annu. Rev. Fluid Mech. 23, 141.CrossRefGoogle Scholar
Ireland, P.J., Bragg, A.D. & Collins, L.R. 2016 The effect of Reynolds number on inertial particle dynamics in isotropic turbulence. Part 1. Simulations without gravitational effects. J. Fluid Mech. 796, 617658.CrossRefGoogle Scholar
Jellinek, A.M. & Kerr, R.C. 2001 Magma dynamics, crystallization, and chemical differentiation of the 1959 Kilauea Iki lava lake, Hawaii, revisited. J. Volcanol. Geotherm. Res. 110, 235263.CrossRefGoogle Scholar
Kim, K., Siegel, N., Kolb, G., Rangaswamy, V. & Moujaes, S.F. 2009 A study of solid particle flow characterization in solar particle receiver. Solar Energy 83, 17841793.CrossRefGoogle Scholar
Kok, J.F., Parteli, E.J., Michaels, T.I. & Karam, D.B. 2012 The physics of wind-blown sand and dust. Rep. Prog. Phys. 75, 106901.CrossRefGoogle ScholarPubMed
Kraichnan, R.H. 1967 Inertial ranges in two-dimensional turbulence. Phys. Fluids 10 (7), 14171423.CrossRefGoogle Scholar
Kulick, J.D., Fessler, J.R. & Eaton, J.K. 1994 Particle response and turbulence modification in fully developed channel flow. J. Fluid Mech. 277 (1), 109134.CrossRefGoogle Scholar
Kurose, R. & Komori, S. 1999 Drag and lift forces on a rotating sphere in a linear shear flow. J. Fluid Mech. 384, 183206.CrossRefGoogle Scholar
Landau, L.D. & Lifshitz, E.M. 1987 Fluid Mechanics. Pergamon.Google Scholar
Lázaro, B.J. & Lasheras, J.C. 1992 Particle dispersion in the developing free shear layer. Part 2. Forced flow. J. Fluid Mech. 235, 179211.CrossRefGoogle Scholar
Liu, C., Tang, S., Dong, Y. & Shen, L. 2018 Heat transfer modulation by inertial particles in particle-laden turbulent channel flow. Trans. ASME J. Heat Transfer 140 (11), 112003.CrossRefGoogle Scholar
Liu, S., Xia, S.-N., Yan, R., Wan, Z.-H. & Sun, D.-J. 2018 Linear and weakly nonlinear analysis of Rayleigh–Bénard convection of perfect gas with non-Oberbeck–Boussinesq effects. J. Fluid Mech. 845, 141169.CrossRefGoogle Scholar
Lohse, D. & Xia, K.-Q. 2010 Small-scale properties of turbulent Rayleigh–Bénard convection. Annu. Rev. Fluid Mech. 42, 335364.CrossRefGoogle Scholar
Longmire, E.K. & Eaton, J.K. 1992 Structure of a particle-laden round jet. J. Fluid Mech. 236, 217257.CrossRefGoogle Scholar
Loth, E. 2000 Numerical approaches for motion of dispersed particles, droplets and bubbles. Prog. Energy Combust. Sci. 26, 161223.CrossRefGoogle Scholar
Maxey, M.R. 1987 The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields. J. Fluid Mech. 174, 441465.CrossRefGoogle Scholar
Maxey, M.R. & Corrsin, S. 1986 Gravitational settling of aerosol particles in randomly oriented cellular flow fields. J. Atmos. Sci. 43, 11121134.2.0.CO;2>CrossRefGoogle Scholar
Mei, R. 1992 An approximate expression for the shear lift force on a spherical particle at finite Reynolds number. Intl J. Multiphase Flow 18, 145147.CrossRefGoogle Scholar
Momenifar, M. & Bragg, A.D. 2020 Local analysis of the clustering, velocities and accelerations of particles settling in turbulence. Phys. Rev. Fluids 5, 034306.CrossRefGoogle Scholar
Monchaux, R., Bourgoin, M. & Cartellier, A. 2010 Preferential concentration of heavy particles: a Voronoï analysis. Phys. Fluids 22, 11121134.CrossRefGoogle Scholar
Nielsen, P. 1993 Turbulence effects on the settling of suspended particles. J. Sedim. Petrol. 63, 835838.Google Scholar
Oresta, P. & Prosperetti, A. 2013 Effects of particle settling on Rayleigh–Bénard convection. Phys. Rev. E 87, 063014.CrossRefGoogle ScholarPubMed
Paolucci, S. 1982 Filtering of sound from the Navier–Stokes equations. NASA STI Tech. Rep. Recon Tech. Rep. N, 83, 26036.Google Scholar
Park, H.J., O'Keefe, K. & Richter, D.H. 2018 Rayleigh–Bénard turbulence modified by two-way coupled inertial, nonisothermal particles. Phys. Rev. Fluids 3, 034307.CrossRefGoogle Scholar
Patočka, V., Calzavarini, E. & Tosi, N. 2020 Settling of inertial particles in turbulent Rayleigh–Bénard convection. Phys. Rev. Fluids 5, 114304.CrossRefGoogle Scholar
van der Poel, E.P., Stevens, R.J. & Lohse, D. 2013 Comparison between two- and three-dimensional Rayleigh–Bénard convection. J. Fluid Mech. 736, 117197.CrossRefGoogle Scholar
Pouransari, H. & Mani, A. 2017 Effects of preferential concentration on heat transfer in particle-based solar receivers. J. Solar Energy Engng 139, 021008.CrossRefGoogle Scholar
Pouransari, H. & Mani, A. 2018 Particle-to-fluid heat transfer in particle-laden turbulence. Phys. Rev. Fluids 3, 074304.CrossRefGoogle Scholar
Puragliesi, R., Dehbi, A., Leriche, E., Soldati, A. & Deville, M.O. 2011 DNS of buoyancy-driven flows and Lagrangian particle tracking in a square cavity at high Rayleigh numbers. Intl J. Heat Fluid Flow 32, 915931.CrossRefGoogle Scholar
Rahmani, M., Geraci, G., Iaccarino, G. & Mani, A. 2018 Effects of particle polydispersity on radiative heat transfer in particle-laden turbulent flows. Intl J. Multiphase FLow 104, 4259.CrossRefGoogle Scholar
Ranz, W. & Marshall, W. 1952 Evaporation from drops. Chem. Engng Prog. 48, 142180.Google Scholar
Reeks, M.W. 1983 The transport of discrete particles in inhomogeneous turbulence. J. Aerosol Sci. 14, 729739.CrossRefGoogle Scholar
Saffman, P.G. 1965 The lift on a small sphere in a slow shear flow. J. Fluid Mech. 22, 385400.CrossRefGoogle Scholar
Sahu, S., Hardalupas, Y. & Tayler, A.M.K.P. 2014 Droplet–turbulence interaction in a confined polydispersed spray: effect of droplet size and flow length scales on spatial droplet–gas velocity correlations. J. Fluid Mech. 741, 98138.CrossRefGoogle Scholar
Shaw, R.A. 2003 Particle–turbulence interactions in atmospheric clouds. Annu. Rev. Fluid Mech. 35, 183227.CrossRefGoogle Scholar
Shotorban, B., Mashayek, F. & Pandya, R. 2003 Temperature statistics in particle-laden turbulent homogeneous shear flow. Intl J. Multiphase Flow 29 (8), 117153.CrossRefGoogle Scholar
Shraiman, B.I. & Siggia, E.D. 1990 Heat transport in high-Rayleigh number convection. Phys. Rev. A 43, 36503653.CrossRefGoogle Scholar
Siggia, E.D. 1994 High Rayleigh number convection. Annu. Rev. Fluid Mech. A 26, 137168.CrossRefGoogle Scholar
Squires, K.D. & Eaton, J.K. 1991 Preferential concentration of particles by turbulence. Phys. Fluids 3, 19891993.CrossRefGoogle Scholar
Stevens, R.J.A.M., Verzicco, R. & Lohse, D. 2010 Radial boundary layer structure and Nusselt number in Rayleigh–Bénard convection. J. Fluid Mech. 643, 495507.CrossRefGoogle Scholar
Suslov, S.A. 2010 Mechanism of nonlinear flow pattern selection in moderately non-Boussinesq mixed convection. Phys. Rev. E 81 (2), 026301.CrossRefGoogle ScholarPubMed
Suslov, S.A. & Paolucci, S. 1999 Nonlinear stability of mixed convection flow under non-Boussinesq conditions. Part 1. Analysis and bifurcations. J. Fluid Mech. 398, 6185.CrossRefGoogle Scholar
Sutherland, W. 1893 The viscosity of gases and molecular force. Lond. Edinb. Dublin Phil. Mag. J. Sci. 36, 507531.CrossRefGoogle Scholar
Talbot, L., Cheng, R.K., Schefer, R.W. & Willis, D.R. 1980 Thermophoresis of particles in a heated boundary layer. J. Fluid Mech. 101, 737758.CrossRefGoogle Scholar
Tan, T. & Chen, Y. 2010 Review of study on solid particle solar receivers. Renew. Sust. Energ. Rev. 14, 256276.CrossRefGoogle Scholar
Tom, J. & Bragg, A.D. 2019 Multiscale preferential sweeping of particles settling in turbulence. J. Fluid Mech. 871, 244270.CrossRefGoogle Scholar
Verzicco, R. & Orlandi, P. 1996 A finite-difference scheme for three-dimensional incompressible flows in cylindrical coordinates. J. Comput. Phys. 123 (2), 402414.CrossRefGoogle Scholar
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
Wang, G. & Richter, D. 2020 Multiscale interaction of inertial particles with turbulent motions in open channel flow. Phys. Rev. Fluids 5, 044307.CrossRefGoogle Scholar
Wang, L.-P. & Maxey, M.R. 1993 Settling velocity and concentration distribution of heavy particles in homogeneous isotropic turbulence. J. Fluid Mech. 256, 2768.CrossRefGoogle Scholar
Wang, Q., Xia, S.-N., Yan, R., Sun, D.-J. & Wan, Z.-H. 2019 Non-Oberbeck–Boussinesq effects due to large temperature differences in a differentially heated square cavity filled with air. Intl J. Heat Mass Transfer 128, 479491.CrossRefGoogle Scholar
Whitehead, J.P. & Doering, C.R. 2011 Ultimate state of two-dimensional Rayleigh–Bénard convection between free-slip fixed-temperature boundaries. Phys. Rev. Lett. 106, 244501.CrossRefGoogle ScholarPubMed
Xia, K.-Q. 2013 Current trends and future directions in turbulent thermal convection. Theor. Appl. Mech. Lett. 3, 052001.CrossRefGoogle Scholar
Xia, S.-N., Wan, Z.-H., Liu, S., Wang, Q. & Sun, D.-J. 2016 Flow reversals in Rayleigh–Bénard convection with non-Oberbeck–Boussinesq effects. J. Fluid Mech. 798, 628642.CrossRefGoogle Scholar
Xu, A., Tao, S., Shi, L. & Xi, H.-D. 2020 Transport and deposition of dilute microparticles in turbulent thermal convection. Phys. Fluids 32, 083301.CrossRefGoogle Scholar
Xu, W., Wang, Y., He, X., Wang, X., Schumacher, J., Huang, S. & Tong, P. 2021 Mean velocity and temperature profiles in turbulent Rayleigh–Bénard convection at low Prandtl numbers. J. Fluid Mech. 918, A1.CrossRefGoogle Scholar
Yang, J.-L., Zhang, Y.-Z., Jin, T.-C., Dong, Y., Wang, B.-F. & Zhou, Q. 2021 The $Pr$-dependence of the critical roughness height in two-dimensional turbulent Rayleigh–Bénard convection. J. Fluid Mech. 911, A52.CrossRefGoogle Scholar
Yang, W., Wang, B.-F., Tang, S., Zhou, Q. & Dong, Y. 2022 a Transport modes of inertial particles and their effects on flow structures and heat transfer in Rayleigh–Bénard convection. Phys. Fluids 34, 043309.CrossRefGoogle Scholar
Yang, W., Zhang, Y.-Z., Wang, B.-F., Dong, Y. & Zhou, Q. 2022 b Dynamic coupling between carrier and dispersed phases in Rayleigh–Bénard convection laden with inertial isothermal particles. J. Fluid Mech. 930, A24.CrossRefGoogle Scholar
Zamansky, R., Coletti, F., Massot, M. & Mani, A. 2014 Radiation induces turbulence in particle-laden fluids. Phys. Fluids 26 (7), 111133.CrossRefGoogle Scholar
Zamansky, R., Coletti, F., Massot, M. & Mani, A. 2016 Turbulent thermal convection driven by heated inertial particles. J. Fluid Mech. 809, 390437.CrossRefGoogle Scholar
Zhang, Y., Zhou, Q. & Sun, C. 2017 Statistics of kinetic and thermal energy dissipation rates in two-dimensional turbulent Rayleigh–Bénard convection. J. Fluid Mech. 814, 165184.CrossRefGoogle Scholar
Zonta, F., Marchioli, C. & Soldati, A. 2008 Direct numerical simulation of turbulent heat transfer modulation in micro-dispersed channel flow. Acta Mechanica 195 (1–4), 304326.CrossRefGoogle Scholar