Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-28T04:03:34.110Z Has data issue: false hasContentIssue false
  • English
  • Français

Effects of Reynolds and Prandtl Numbers on Heat Transfer Around a Circular Cylinder by the Simplified Thermal Lattice Boltzmann Model

Published online by Cambridge University Press:  30 April 2015

Qing Chen ,
Xiaobing Zhang  and
Junfeng Zhang
Qing Chen*
Affiliation:
School of Energy and Power Engineering, Nanjing University of Science & Technology, Jiangsu, 210094, China Bharti School of Engineering, Laurentian University, 935 Ramsey Lake Road, Sudbury, Ontario, P3E 2C6, Canada
Xiaobing Zhang
Affiliation:
School of Energy and Power Engineering, Nanjing University of Science & Technology, Jiangsu, 210094, China
Junfeng Zhang
Affiliation:
Bharti School of Engineering, Laurentian University, 935 Ramsey Lake Road, Sudbury, Ontario, P3E 2C6, Canada
*
*Corresponding author. Email addresses: chenqing86878@gmail.com (Q. Chen), zhangxb680504@163.com (X. Zhang), jzhang@laurentian.ca (J. Zhang)
Get access

Abstract

In this paper, the fluid flow and heat transfer around a circular cylinder are studied under various conditions (Reynolds number 10 < Re < 200; Prandtl number, 0.1 ≤ Pr ≤ 2). To solve the governing equations, we use the simplified thermal lattice Boltzmann model based on double-distribution function approach, and present a corresponding boundary treatment for both velocity and temperature fields. Extensive numerical results have been obtained to the flow and heat transfer behaviors. The vortices and temperature evolution processes indicate that the flow and temperature fields change synchronously, and the vortex shedding plays a determinant role in the heat transfer. Furthermore, the effects of Reynolds and Prandtl number on the flow and isothermal patterns and local and averaged Nusselt numbers are discussed in detail. Our simulations show that the local and averaged Nusselt numbers increase with the Reynolds and Prandtl numbers, irrespective of the flow regime. However, the minimum value of the local Nusselt number can shift from the rear point at the back of the cylinder with higher Prandtl number even in the steady flow regime, and the distribution of the local Nusselt number is almost monotonous from front stagnation point to rear stagnation point with lower Prandtl number in the unsteady flow regime.

Keywords

47.11.-j44.05.+eHeat transferReynolds numberPrandtl numbersimplified thermal lattice Boltzmann modelcurved boundary
Type
Research Article
Information
Communications in Computational Physics , Volume 17 , Issue 4 , April 2015 , pp. 937 - 959
Copyright
Copyright © Global-Science Press 2015 

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

[1]Zdravkovich, M. M., Flow Around Circular Cylinders, Vol.1 Fundamentals, Oxford University Press, New York, 1997.CrossRefGoogle Scholar
[2]Zdravkovich, M. M., Flow Around Circular Cylinders, Vol. 2 Applications, Oxford University Press, New York, 2003.CrossRefGoogle Scholar
[3]Williamson, C. H. K., Vortex dynamics in the cylinder wake, Annu. Rev. Fluid Mech., 28 (1996), 477–539.CrossRefGoogle Scholar
[4]Karniadakis, G. E., Numerical simulation of forced convection heat transfer from a cylinder in cross flow, Int. J. Heat Mass Transfer, 31 (1988), 107–118.CrossRefGoogle Scholar
[5]Lange, C. F., Durst, F. and Breuer, M., Momentum and heat transfer from cylinder in laminar cross-flow at 10−4 < Re < 200, Int. J. Heat Mass Transfer, 41 (1998), 3409–3430.CrossRefGoogle Scholar
[6]Baranyi, L., Computation of unsteady momentum and heat transfer from a fixed circular cylinder in laminar flow, Comput, J.. Appl. Mech., 4 (2003), 13–25.Google Scholar
[7]Bharti, R. P., Chhabra, R. P. and Eswaran, V., A numerical study of the steady forced convection heat transfer from an unconfined circular cylinder, Heat Mass Transfer, 41 (2005), 824–833.Google Scholar
[8]Bao, S., Chen, S., Liu, Z. and Zheng, C., Lattice Boltzmann simulation of the convective heat transfer from a stream-wise oscillating circular cylinder, Int. J. Heat Fluid Flow, 37 (2012), 147–153.CrossRefGoogle Scholar
[9]Liao, C. C., and Lin, C. A., Simulations of natural and forced convection flows with moving embedded object using immersed boundary method, Comput. Methods Appl. Mech. Engrg., 213–216 (2012), 58–70.CrossRefGoogle Scholar
[10]Zu, Y. Q., Yan, Y. Y., Shi, W. P. and Ren, L. Q., Numerical method of lattice Boltzmann simulation for flow past a rotating circular cylinder with heat transfer, Int. J. Numer. Method H., 18 (2008), 766–782.CrossRefGoogle Scholar
[11]Chen, S. and Doolen, G. D., Lattice Boltzmann method for fluid flows, Annu. Rev. Fluid Mech., 30 (1998), 329364.CrossRefGoogle Scholar
[12]Succi, S., The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, Oxford University Press, New York, 2001.CrossRefGoogle Scholar
[13]Aidun, C. K. and Clausen, J. R., Lattice Boltzmann method for complex flows, Annu. Rev. Fluid Mech., 42 (2010), 439472.CrossRefGoogle Scholar
[14]Zhang, J., Lattice Boltzmann method for microfluidics: Models and applications, Microfluid Nanofluid, 10 (2011), 1–28.CrossRefGoogle Scholar
[15]Shan, X. and Chen, H., Lattice Boltzmann model for simulating flows with multiple phases and components, Phys. Rev. E, 47 (1993), 18151819.CrossRefGoogle Scholar
[16]Zhang, J., Li, B. and Kwok, D. Y., Mean-field free-energy approach to the lattice Boltzman method for liquid-vapor and solid-fluid interfaces, Phys. Rev. E, 69 (2004), 032602.CrossRefGoogle Scholar
[17]Dawson, S. P., Chen, S. and Doolen, G. D., Lattice Boltzmann computations for reactiondiffusion equations, J. Chem. Phys., 98 (1993), 15141523.CrossRefGoogle Scholar
[18]Guo, Z. and Zhao, T. S., Lattice Boltzmann model for incompressible flows through porous media, Phys. Rev. E, 66 (2002), 036304.CrossRefGoogle Scholar
[19]Li, Q., He, Y. L., Wang, Y. and Tao, W. Q., Coupled double-distribution-function lattice Boltzmann method for the compressible Navier-Stokes equations, Phys. Rev. E, 76 (2007), 056705.CrossRefGoogle Scholar
[20]Chen, Q. and Zhang, X., A novel less dissipation finite-difference lattice Boltzmann scheme for compressible flows, Int. J. Modern Phys. C, 23 (2012), 1250074.CrossRefGoogle Scholar
[21]Wang, L., Guo, Z., Shi, B. and Zheng, C., Evalution of three lattice Boltzmann models for particulate flows, Commun. Comput. Phys., 13 (2013), 1151–1172.CrossRefGoogle Scholar
[22]Tian, F. B., Luo, H., Zhu, L. and Lu, X. Y., Interaction between a flexible filament and a downstream rigid body, Phys. Rev. E, 82 (2010), 026301.CrossRefGoogle Scholar
[23]Tian, F. B., Luo, H., Zhu, L., Liao, J. C. and Lu, X. Y., An immersed boundary lattice Boltzmann method for elastic boundaries with mass, J. Comput. Phys., 230 (2011), 7266–7283.CrossRefGoogle Scholar
[24]Zhang, J., Johnson, P. C. and Popel, A. S., Red blood cell aggregation and dissociation in shear flows simulated by lattice Boltzmann method, J. Biomech, 41 (2008), 47–55.CrossRefGoogle ScholarPubMed
[25]Xu, Y. Q., Tian, F. B. and Deng, Y. L., An efficient red blood cell model in the frame of IB-LBM and its application, Int. J. Biomath., 5 (2012), 1250061.CrossRefGoogle Scholar
[26]Alexander, F.J., Chen, S. and Sterling, J. D., Lattice Boltzmann thermodynamics, Phys. Rev. E, 47 (1993), R2249.CrossRefGoogle Scholar
[27]Qian, Y. H., Simulating thermodynamics with lattice BGK models, J. Sci. Comput, 8 (1993), 231–242.CrossRefGoogle Scholar
[28]Lallemand, P. and Luo, L. S., Theory of the lattice Boltzmann method: Acoustic and thermal properties in two and three dimensions, Phys. Rev. E, 165 (2003), 036706.CrossRefGoogle Scholar
[29]He, X., Chen, S. and Doolen, G. D., A novel thermal model for the lattice Boltzmann method in incompressible limit, J. Comput. Phys., 146 (1998), 282–300.CrossRefGoogle Scholar
[30]Peng, Y., Shu, C. and Chew, Y. T., Simplified thermal lattice Boltzmann model for incompressible thermal flows, Phys. Rev. E, 68 (2003), 026701.CrossRefGoogle Scholar
[31]Guo, Z., Zheng, C., Shi, B. and Zhao, T. S., Thermal lattice Boltzmann equation for low Mach number flows: Decoupling model, Phys. Rev. E, 75 (2007), 036704.CrossRefGoogle Scholar
[32]Zhang, W., Chai, Z., Guo, Z. and Shi, B., Lattice Boltzmann study of flow and temperature structures of non-isothermal laminar impinging streams, Commun. Comput. Phys., 13 (2013), 835–850.CrossRefGoogle Scholar
[33]Yin, X. and Zhang, J., An improved bounce-back scheme for complex boundary conditions in lattice Boltzmann method, J. Comput. Phys., 231 (2012), 4295–4303.CrossRefGoogle Scholar
[34]Chen, Q., Zhang, X. and Zhang, J., Improved treatments for general boundary conditions in the lattice Boltzmann for convection-diffusion and heat transfer processes, Phys. Rev. E, 88 (2013), 033304.CrossRefGoogle Scholar
[35]Ladd, A. J. C., Numerical simulations of particulate suspensions via a discretized Boltzmann equation, Part 1. Theoretical foundation, J. Fluid Mech., 271 (1994), 285–310.CrossRefGoogle Scholar
[36]Zhang, T., Shi, B., Guo, Z., Chai, Z. and Lu, J., General bounce-back scheme for concentration boundary condition in the lattice Boltzmann method, Phys. Rev. E, 85 (2012), 016701.CrossRefGoogle Scholar
[37]He, X. and Doolen, G., Lattice Boltzmann method on curvilinear coordinates system: Flow around a circular cylinder, J. Comput. Phys., 134 (1997), 306–315.Google Scholar
[38]Mei, R. W., Yu, D. Z., Shyy, W. and Luo, L. S., Force evaluation in the lattice Boltzmann method involving curved geometry, Phys. Rev. E, 65 (2002), 041203.CrossRefGoogle Scholar
[39]Barkley, D., Linear analysis of the cylinder wake mean flow, Europhys. Lett, 75 (2006), 750–756.CrossRefGoogle Scholar
[40]Gao, T., Tseng, Y. H. and Lu, X. Y., An improved hybrid cartesian/immersed boundary method for fluid-solid flows, Int. J. Numer. Meth. Fluids, 55 (2007), 1189–1211.CrossRefGoogle Scholar
[41]Momose, K. and Kimoto, H., Forced convection heat transfer from a heated circular cylinder with arbitrary surface temperature distributions, Heat Transfer Asian Res., 28 (1999), 484–499.3.0.CO;2-T>CrossRefGoogle Scholar
[42]Chen, S., Luo, K. H. and Zheng, C., A simple enthalpy-based lattice Boltzmann scheme for complicated thermal systems, J. Comput. Phys., 231 (2012), 8278–8294.Google Scholar
[43]Eckert, E. R. G. and Soehngen, E., Distribution of heat transfer coefficients around circular cylinders in cross flow at Reynolds numbers from 20 to 500, Trans. ASME, 74 (1952), 343–347.Google Scholar
[44]Cheng, C. H., Hong, J. L. and Win, A., Numerical prediction of lock-on effect on convective heat transfer from a transversely oscillating circular cylinder, Int. J. Heat Mass Transfer, 40 (1997), 1825–1834.CrossRefGoogle Scholar
[45]Patnana, V. K., Bharti, R. P. and Chhabra, R. P., Two-dimensional unsteady forced convection heat transfer in power-law fluids from a cylinder, Int. J. Heat Mass Transfer, 53 (2010), 4152–4167.CrossRefGoogle Scholar
[46]Soares, A. A., Ferreira, J. M. and Chhabra, R. P., Flow and forced convection heat transfer in crossflow of non-Newtonian fluids over a circular cylinder, Ind. Eng. Chem. Res., 44 (2005), 5815-5827.CrossRefGoogle Scholar
[47]Whitaker, S., Forced convection heat transfer correlations for flow in pipes, past flat plates, single cylinders, single sphere and for flow in packed beds and tube bundles, J. AIChE, 18 (1972), 361–371.CrossRefGoogle Scholar