شبیه سازی عددی انتقال حرارت جابجایی آزاد در یک آنولی افقی با حرارت دهی گسسته با استفاده از روش لاتیس بولتزمن بدون شبکه

نوع مقاله : مقاله پژوهشی

نویسندگان

1 گروه مهندسی مکانیک، دانشگاه صنعتی ارومیه

2 گروه ریاضی کاربردی، دانشگاه صنعتی ارومیه

چکیده

مطالعه حاضر به بررسی انتقال حرارت جابجایی آزاد در یک آنولی استوانه‌ای افقی با حرارت دهی گسسته با استفاده از روش لاتیس بولتزمن بدون شبکه می‌پردازد. روش لاتیس بولتزمن، بعنوان یک روش جایگزین روشهای دینامیک سیالات محاسباتی متداول برای شبیه سازی جریان‌های پیچیده در آمده است. از مزایای مهم این روش، صریح بودن معادله حاکم، سادگی اعمال آن برای محاسبات موازی و نیز سادگی اعمال شرایط مرزی برای مرزهای منحنی‌ وار است. با وجود قابلیت‌های خوب روش شبکه بولتزمن استاندارد برای شبکه‌های یکنواخت، نمی‌توان آن را به طور مستقیم برای هندسه‌های پیچیده و شبکه‌های غیر یکنواخت بکار برد. یک روش مؤثر برای رفع این محدودیت، روش شبکه بولتزمن بر مبنای بسط سری تیلور و روش حداقل مربعات (TLLBM) است. شکل نهایی فرمولاسیون این روش یک معادله جبری است و هیچ محدودیتی روی ساختار شبکه ندارد. همچنین این روش را می‌توان برای مدل‌های مختلف سرعت ذره به کار برد. در کار حاضر، از این روش با مدل شبکه D2Q9 برای شبیه سازی انتقال حرارت جابجایی آزاد در یک آنولی استوانه‌ای افقی با حرارت دهی گسسته استفاده می شود و تأثیر عدد رایلی و آرایش‌های مختلف دو جفت چشمه- چاه حرارتی روی نرخ انتقال حرارت بررسی می‌گردد.
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کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Numerical simulation of natural convection heat transfer in a horizontal annulus with discrete heating using mesh-free lattice-Boltzmann method

نویسندگان [English]

  • Abdolrahman Dadvand 1
  • Ahmad Haghighi 2
  • Hamideh Hoseini Ghejlo 2
1 Department of Mechanical Engineering, Urmia University of Technology
2 Department of Mathematics, Urmia University of Technology
چکیده [English]

This study investigates the natural convection heat transfer in a horizontal annulus with discrete heating using a mesh-free lattice Boltzmann method. The lattice Boltzmann method has become an alternative to the conventional computational fluid dynamics methods for simulation of complex fluid flows. The major advantages of the lattice Boltzmann method are the explicit feature of the governing equation, easy for parallel computation, and simple implementation of boundary conditions on curved boundaries. Despite well viability of standard LBM for the uniform mesh, it cannot be directly applied to problems with complex geometry and non-uniform mesh. An efficient method for removing this limitation is to use Taylor series expansion and least squares-based LBM (TLLBM). The final form of the TLLBM is an algebraic formulation with no limitation on the mesh structure. This method can also be applied to any lattice velocity model. In the present work, the TLLBM with D2Q9 lattice model is used to simulate natural convection heat transfer in a horizontal annulus with discrete heating. The effects of Rayleigh number and different arrangement of two heat source-sink pairs on the fluid flow and heat transfer characteristics are investigated.

کلیدواژه‌ها [English]

  • Natural convection
  • Discrete heating
  • Rayleigh number
  • Horizontal annulus
  • Mesh-free lattice-Boltzmann method
[1]   Basak T., Roy, S., and Pop, I. (2009), Heat flow analysis for natural convection within trapezoidal enclosure based on heat line concept, International Journal of Heat and Mas Transfer, 52(11), 3818-3828.
[2]   Deng, Q. (2008), Fluid flow and heat transfer characteristics of natural convection in square cavities due to discrete source-sink pairs, International Journal of Heat and Mas Transfer, 51(25), 5949-5957.
[3]   Abu-Nada, E., Masoud, Z., Oztop, H.F. and Campo, A. (2010), Effect of nanofluid variable properties on natural convection in enclosures, International Journal of Thermal Sciences, 49(3), 479-491.
[4]   Soleimani, S., Qajarjazi, A., Bararnia, H., Barari, A. and Domairry, G. (2011), Entropy generation due to natural convection in a partially heated cavity by local RBF-DQ method, Meccanica, 46(5), 1023-1033.
[5]   Oztop, H. F., Abu-Nada, E., Varol, Y. and Chamkha, A. (2011), Natural convection in wavy enclosures with volumetric heat sources, International Journal of Thermal Sciences, 50(4), 502-514.
[6]      Chen, S., Liu, Z., Bao, S. and Zheng, C. (2010), Natural convection and entropy generation in a vertically concentric annular space, International Journal of Thermal Sciences, 49(12), 2439-2452.
[7]   Refai, A. G. and Yovanovich, M. M. (1991), Influence of discrete heat source location on natural convection heat transfer in a vertical square enclosure, Journal of Electronic Packaging, 113(3), 268-274.
[8]      Nelson, E. B., Balakrishnan, A. R. and Murthy, S. S. (1999), Experiments on stratified chilled water tank, Int. J. Refrig., 22(3), 216-234.
[9]   Ho, C. J. and Lin, Y. H. (1989), A numerical study of natural convection in concentric and eccentric horizontal cylindrical annuli with mixed boundary conditions, International Journal of heat and Fluid Flow, 10(1), 40-47.
[10]   Asan, H. (2000), Natural convection in an annulus between two isothermal concentric square ducts, International Communication Heat Mass Transfer, 27(3), 367-376.
[11]   Kumar, De A. and Dalal, A. (2006), A numerical study of natural convection around a square, horizontal, heated cylinder placed in an enclosure, International Journal of Heat and Mass Transfer, 49(23), 4608-4623.  
[12]   Sheikhzadeh, G. A., Ehteram, H. and Aghaei, A. (2013), Numerical study of natural convection in a nanofluid filled enclosure with central heat source and presenting correlations for Nusselt number, Modares Mechanical Engineering, 13(10), 62-74.
[13]   Dixit, H. N. and Babu, V. (2006), Simulation of high Rayleigh number natural convection in a square cavity using the lattice Boltzmann method, International Journal of Heat and Mass Transfer, 49(3), 727-739.
[14]   Mohamad, A. A., El-Ganaoui, M. and Bennacer, R. (2009), Lattice Boltzmann and simulation of natural convection in an open ended cavity, International Journal of Thermal Sciences, 48(10), 1870-1875.
[15]   Bararnia, H., Soleimani, S. and Ganji, D. D. (2011), Lattice Boltzmann simulation of natural convection around a horizontal elliptic cylinder inside a square enclosure, International Communications in Heat and Mass Transfer, 38(10), 1436-1442.
[16]   Fattahi, E., Farhadi, M. and Sedighi, K. (2011), Lattice Boltzmann simulation of mixed convection heat transfer in eccentric annulus, International Communications in Heat and Mass Transfer, 38(8), 1135-1141.
[17]   Shi Y., Zhao T. S., Guo Z. L. (2006), Finite difference-based lattice Boltzmann   simulation of natural convection heat transfer in a horizontal concentric annulus, Computers and Fluids, 35(1), 1-15.
[18]   Nazari, M., Kayhani, M. H. and Bagheri A. A. H. (2013), Comparison of heat transfer in a cavity between vertical and horizontal porous layers using LBM, Modares Mechanical Engineering, 13(8), 93-107.
[19]   Nazari, M. and Shokri, H. (2011), Natural convection in semi-ellipse cavities with variable aspect ratios using lattice Boltzmann method, Modares Mechanical Engineering, 13(10), 1-13.
[20]   Nazari, M. and Ramazani, S. (2013), Natural convection in a square cavity with a heated obstacle using lattice Boltzmann method, Modares Mechanical Engineering, 11(2), 119-133.
[21]   Cao, N., Chen, S., Jin, S. and Martinez, D. (1997), Physical symmetry and lattice symmetry in the lattice Boltzmann method, Phys. Rev. E, 55(1), R21.
[22]   Succi, S., Amati, G. and Benzi, R. (1995), Challenges in lattice Boltzmann computing, J. Stat. Phys. 81(1-2), 5-16.
[23]   He, X., Luo, L. S. and Dembo, M. (1996), Some progress in Lattice Boltzmann method: part I. nonuniform mesh grids, Journal of Computational Physics, 129(2), 357-363.
[24]   Shu, C., Chew, Y. T. and Niu X. D. (2001), Least-Squares-Based Lattice Boltzmann Method: A meshless approach for simulation of flows with complex geometry, Phys. Rev. E, 64(4), 045701.
[25]   Peng, Y., Chew, Y. T. and Shu, C. (2003), Numerical simulation of natural convection in a concentric annulus between a square outer cylinder and a circular inner cylinder using the Taylor-series-expansion and least squares-based lattice Boltzmann method, Phys. Rev. E, 67(2), 026701.
[26]   Niu, X., Chew, Y. T. and Shu C. (2003), Simulation of flow around an impulsively started circular cylinder by Taylor series expansion and least souares-based lattice Boltzmann method, Journal of Computational Physics, 188(1), 176-193.
[27]   Teamah,  M. A. (2007), Numerical simulation of double diffusive laminar mixed convection in a horizontal annulus with hot, solutal and rotating inner cylinder, International journal of thermal sciences, 46(7), 637-648.
[28]   Kuehn, T. H. and Goldstein, R. J. (1976), An experimental and theoretical study of natural convection in the annulus between horizontal concentric cylinders, Journal of Fluid Mechanics, 74(04), 695-719.