搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

非正交多松弛系数轴对称热格子Boltzmann方法

王佐 张家忠 王恒

引用本文:
Citation:

非正交多松弛系数轴对称热格子Boltzmann方法

王佐, 张家忠, 王恒

Non-orthogonal multiple-relaxation-time lattice Boltzmann method for axisymmetric thermal flows

Wang Zuo, Zhang Jia-Zhong, Wang Heng
PDF
导出引用
  • 提出了一种模拟轴对称热流动的非正交多松弛系数格子Boltzmann(MRT-LB)模型.通过采用非正交转换矩阵,建立了基于D2Q9离散速度的求解流场的MRT-LB模型和基于D2Q5离散速度的求解温度场的MRT-LB模型.Chapman-Enskog分析表明,该模型可以恢复对应的柱坐标下的宏观连续方程、动量方程和能量方程.与现有的轴对称MRT-LB模型相比,本文采用的非正交转换矩阵中含有更多的零元素,因而具有更高的计算效率.采用本文模型对几种典型的轴对称热流动问题,包括热Womersley流动、竖直圆柱体内的Rayleigh-Bnard对流和环形柱体内的自然对流进行了数值模拟,通过等温线图和流线图以及定量数据的对比,验证了本文模型的可行性和可靠性.并且数值模拟结果表明,相对现有模型,本文模型具有更好的数值稳定性和计算效率.
    Axisymmetric thermal flows in cylindrical systems are widely encountered in engineering practices. Typically, axisymmetric thermal flows belong in three-dimensional (3D) problems. However, taking advantage of the axisymmetric condition, the 3D axisymmetric flows can be reduced to quasi two-dimensional (2D) problems in the meridian plane, which significantly reduces the computational requirements and avoids treating the curved boundary. In recent years, various 2D lattice Boltzmann (LB) models, including single relaxation time LB (SRT-LB, or LBGK) and multiple relaxation time LB (MRT-LB) models, for axisymmetric thermal flows have been proposed. In the LB community, it is well accepted that the MRT-LB is superior to the LBGK in terms of numerical stability. The existing MRT-LB model for axisymmetric thermal flows are developed based on orthogonal basis vectors obtained from the combination of the lattice velocity components, i.e., the transform matrix in the existing MRT-LB is an orthogonal one. Unlike the existing MRT-LB model, in this paper, a non-orthogonal multiple-relaxation-time lattice Boltzmann (MRT-LB) method of simulating axisymmetric thermal flows is proposed. In the proposed MRT-LB method, the velocity field is solved by a D2Q9 discrete velocity set while the temperature by a D2Q5 discrete velocity set. The main advantage of the present MRT-LB model is that the transform matrix of the model is a non-orthogonal one, which is comprised of some proper non-orthogonal basis vectors obtained from the combination of the lattice velocity components. The non-orthogonal transform matrix of the present MRT-LB model contains more zero elements than the classical orthogonal transform matrix, and thus the present MRT-LB model is expected to be more efficient than the existing orthogonal-based MRT-LB model. The equilibrium velocity and temperature moments of the present MRT-LB model are expressed by mapping the equilibrium distribution functions onto their moment spaces through using the non-orthogonal transformation matrix. Also the vectors in the forcing term are modified according to the matrix mapping. Through the Chapman-Enskog analysis, it is demonstrated that the macroscopic governing equations in the cylindrical coordinate can be recovered from the present MRT-LB model. Then several numerical tests, including thermal Womersley flow, Rayleigh-Bnard convection in a vertical cylinder and natural convection in a vertical annulus, are conducted to validate the present model. It is found that the present numerical results are in good agreement with the analytical solutions and/or other numerical results reported in the literature. Numerical stability is also tested, and the results suggest that the present MRT model shows better numerical stability than its LBGK counterpart. Moreover, the numerical results also indicate that the present MRT-LB model is more computationally efficient than the existing MRT-LB model for axisymmetric thermal flow. These findings indicate that the present MRT-LB model can serve as a powerful method of computing the axisymmetric thermal flows.
      通信作者: 张家忠, jzzhang@mail.xjtu.edu.cn
    • 基金项目: 国家重点基础研究发展计划(批准号:2012CB026002)和国家重点科技支撑项目(批准号:2013BAF01B02)资助的课题.
      Corresponding author: Zhang Jia-Zhong, jzzhang@mail.xjtu.edu.cn
    • Funds: Project supported by the National Fundamental Research Program of China (Grant No.2012CB026002) and the National Key Technology Research and Development Program of China (Grant No.2013BAF01B02).
    [1]

    Vynnycky M, Maeno N 2012 Int. J. Heat Mass Transfer 55 7297

    [2]

    Grosan T, Pop I 2011 Int. J. Heat Mass Transfer 54 3139

    [3]

    Huang H, Hong N, Liang H, Shi B C, Chai Z H 2016 Acta Phys. Sin. 65 084702 (in Chinese)[黄虎, 洪宁, 梁宏, 施保昌, 柴振华 2016 物理学报 65 084702]

    [4]

    Aidun C K, Clausen J R 2009 Annu. Rev. Fluid Mech. 42 439

    [5]

    Li Q, Luo K H, Kang Q J, He Y L, Chen Q, Liu Q 2015 Prog. Energy Combust. Sci. 52 62

    [6]

    Lallemand P, Luo L S 2000 Phys. Rev. E 61 6546

    [7]

    d'Humières D, Ginzburg I, Krafczyk M, Lallemand P, Luo L S 2002 Philos. Trans. R. Soc. London A 360 437

    [8]

    Halliady I, Hammond L A, Care C M, Good K, Stevens A 2001 Phys. Rev. E 64 011208

    [9]

    Lee T S, Huang H, Shu C 2006 Int. J. Mod. Phys. C 17 645

    [10]

    Reis T, Phillips T N 2007 Phys. Rev. E 75 056703

    [11]

    Reis T, Phillips T N 2008 Phys. Rev. E 2008 77 026703

    [12]

    Guo Z L, Han H F, Shi B C, Zheng C G 2009 Phys. Rev. E 79 046708

    [13]

    Li Q, He Y L, Tang G H, Tao W Q 2010 Phys. Rev. E 81 056707

    [14]

    Zhou J G 2011 Phys. Rev. E 84 036704

    [15]

    Peng Y, Shu C, Chew Y T, Qiu J 2003 J. Comput. Phys. 186 295

    [16]

    Huang H, Lee T S, Shu C 2007 Int. J. Numer. Methods Fluids 53 1707

    [17]

    Li Q, He Y L, Tang G H, Tao W Q 2009 Phys. Rev. E 80 037702

    [18]

    Zheng L, Shi B C, Guo Z L, Zheng C G 2010 Comput. Fluids 39 945

    [19]

    Meng X, Guo Z L 2015 Phys. Rev. E 92 043305

    [20]

    Liu Q, He Y L 2015 Physica A 429 215

    [21]

    Li Q, He Y L, Tang G H, Tao W Q 2011 Microfluid. Nanofluid. 10 607

    [22]

    Wang L, Guo Z L, Zheng C G 2010 Comput. Fluids 39 1542

    [23]

    Premnath K N, Banerjee S 2009 Phys. Rev. E 80 036702

    [24]

    Geier M, Schönherr M, Pasquali A, Krafczyk M 2015 Comput. Math. Appl. 70 507

    [25]

    Liu Q, He Y L, Li D, Li Q 2016 Int. J. Heat Mass Transfer 102 1334

    [26]

    Guo Z L, Shi B C, Zheng C G 2002 Chin. Phys. B 11 366

    [27]

    Lemembre A, Petit J P 1998 Int. J. Heat Mass Transfer 41 2437

    [28]

    Li L K, Mei R W, Klausner J F 2013 Int. J. Heat Mass Transfer 67 338

    [29]

    Kumar R, Kalam M A 1991 Int. J. Heat Mass Transfer 34 513

    [30]

    Venkatachalappa M, Sankar M, Natarajan A A 2001 Acta Mech. 147 173

  • [1]

    Vynnycky M, Maeno N 2012 Int. J. Heat Mass Transfer 55 7297

    [2]

    Grosan T, Pop I 2011 Int. J. Heat Mass Transfer 54 3139

    [3]

    Huang H, Hong N, Liang H, Shi B C, Chai Z H 2016 Acta Phys. Sin. 65 084702 (in Chinese)[黄虎, 洪宁, 梁宏, 施保昌, 柴振华 2016 物理学报 65 084702]

    [4]

    Aidun C K, Clausen J R 2009 Annu. Rev. Fluid Mech. 42 439

    [5]

    Li Q, Luo K H, Kang Q J, He Y L, Chen Q, Liu Q 2015 Prog. Energy Combust. Sci. 52 62

    [6]

    Lallemand P, Luo L S 2000 Phys. Rev. E 61 6546

    [7]

    d'Humières D, Ginzburg I, Krafczyk M, Lallemand P, Luo L S 2002 Philos. Trans. R. Soc. London A 360 437

    [8]

    Halliady I, Hammond L A, Care C M, Good K, Stevens A 2001 Phys. Rev. E 64 011208

    [9]

    Lee T S, Huang H, Shu C 2006 Int. J. Mod. Phys. C 17 645

    [10]

    Reis T, Phillips T N 2007 Phys. Rev. E 75 056703

    [11]

    Reis T, Phillips T N 2008 Phys. Rev. E 2008 77 026703

    [12]

    Guo Z L, Han H F, Shi B C, Zheng C G 2009 Phys. Rev. E 79 046708

    [13]

    Li Q, He Y L, Tang G H, Tao W Q 2010 Phys. Rev. E 81 056707

    [14]

    Zhou J G 2011 Phys. Rev. E 84 036704

    [15]

    Peng Y, Shu C, Chew Y T, Qiu J 2003 J. Comput. Phys. 186 295

    [16]

    Huang H, Lee T S, Shu C 2007 Int. J. Numer. Methods Fluids 53 1707

    [17]

    Li Q, He Y L, Tang G H, Tao W Q 2009 Phys. Rev. E 80 037702

    [18]

    Zheng L, Shi B C, Guo Z L, Zheng C G 2010 Comput. Fluids 39 945

    [19]

    Meng X, Guo Z L 2015 Phys. Rev. E 92 043305

    [20]

    Liu Q, He Y L 2015 Physica A 429 215

    [21]

    Li Q, He Y L, Tang G H, Tao W Q 2011 Microfluid. Nanofluid. 10 607

    [22]

    Wang L, Guo Z L, Zheng C G 2010 Comput. Fluids 39 1542

    [23]

    Premnath K N, Banerjee S 2009 Phys. Rev. E 80 036702

    [24]

    Geier M, Schönherr M, Pasquali A, Krafczyk M 2015 Comput. Math. Appl. 70 507

    [25]

    Liu Q, He Y L, Li D, Li Q 2016 Int. J. Heat Mass Transfer 102 1334

    [26]

    Guo Z L, Shi B C, Zheng C G 2002 Chin. Phys. B 11 366

    [27]

    Lemembre A, Petit J P 1998 Int. J. Heat Mass Transfer 41 2437

    [28]

    Li L K, Mei R W, Klausner J F 2013 Int. J. Heat Mass Transfer 67 338

    [29]

    Kumar R, Kalam M A 1991 Int. J. Heat Mass Transfer 34 513

    [30]

    Venkatachalappa M, Sankar M, Natarajan A A 2001 Acta Mech. 147 173

  • [1] 赖瑶瑶, 陈鑫梦, 柴振华, 施保昌. 基于格子Boltzmann方法的钉扎螺旋波反馈控制. 物理学报, 2024, 73(4): 040502. doi: 10.7498/aps.73.20231549
    [2] 刘程, 梁宏. 三相流体的轴对称格子 Boltzmann 模型及其在 Rayleigh-Plateau 不稳定性的应用. 物理学报, 2023, 72(4): 044701. doi: 10.7498/aps.72.20221967
    [3] 张恒, 任峰, 胡海豹. 基于格子Boltzmann方法的幂律流体二维顶盖驱动流转捩研究. 物理学报, 2021, 70(18): 184703. doi: 10.7498/aps.70.20210451
    [4] 臧晨强, 娄钦. 复杂微通道内非混相驱替过程的格子Boltzmann方法. 物理学报, 2017, 66(13): 134701. doi: 10.7498/aps.66.134701
    [5] 周光雨, 陈力, 张鸿雁, 崔海航. 基于格子Boltzmann方法的自驱动Janus颗粒扩散泳力. 物理学报, 2017, 66(8): 084703. doi: 10.7498/aps.66.084703
    [6] 顾娟, 黄荣宗, 刘振宇, 吴慧英. 一种滑移区气体流动的格子Boltzmann曲边界处理新格式. 物理学报, 2017, 66(11): 114701. doi: 10.7498/aps.66.114701
    [7] 张娅, 潘光, 黄桥高. 疏水表面减阻的格子Boltzmann方法数值模拟. 物理学报, 2015, 64(18): 184702. doi: 10.7498/aps.64.184702
    [8] 刘邱祖, 寇子明, 贾月梅, 吴娟, 韩振南, 张倩倩. 改性疏水固壁润湿性反转现象的格子Boltzmann方法模拟. 物理学报, 2014, 63(10): 104701. doi: 10.7498/aps.63.104701
    [9] 任晟, 张家忠, 张亚苗, 卫丁. 零质量射流激励下诱发液体相变及其格子Boltzmann方法模拟. 物理学报, 2014, 63(2): 024702. doi: 10.7498/aps.63.024702
    [10] 解文军, 滕鹏飞. 声悬浮过程的格子Boltzmann方法研究. 物理学报, 2014, 63(16): 164301. doi: 10.7498/aps.63.164301
    [11] 史冬岩, 王志凯, 张阿漫. 任意复杂流-固边界的格子Boltzmann处理方法. 物理学报, 2014, 63(7): 074703. doi: 10.7498/aps.63.074703
    [12] 黄桥高, 潘光, 宋保维. 疏水表面滑移流动及减阻特性的格子Boltzmann方法模拟. 物理学报, 2014, 63(5): 054701. doi: 10.7498/aps.63.054701
    [13] 刘邱祖, 寇子明, 韩振南, 高贵军. 基于格子Boltzmann方法的液滴沿固壁铺展动态过程模拟. 物理学报, 2013, 62(23): 234701. doi: 10.7498/aps.62.234701
    [14] 郭亚丽, 徐鹤函, 沈胜强, 魏兰. 利用格子Boltzmann方法模拟矩形腔内纳米流体Raleigh-Benard对流. 物理学报, 2013, 62(14): 144704. doi: 10.7498/aps.62.144704
    [15] 曾建邦, 李隆键, 蒋方明. 气泡成核过程的格子Boltzmann方法模拟. 物理学报, 2013, 62(17): 176401. doi: 10.7498/aps.62.176401
    [16] 曾建邦, 李隆键, 廖全, 蒋方明. 池沸腾中气泡生长过程的格子Boltzmann方法模拟. 物理学报, 2011, 60(6): 066401. doi: 10.7498/aps.60.066401
    [17] 曾建邦, 李隆键, 廖全, 陈清华, 崔文智, 潘良明. 格子Boltzmann方法在相变过程中的应用. 物理学报, 2010, 59(1): 178-185. doi: 10.7498/aps.59.178
    [18] 卢玉华, 詹杰民. 三维方腔温盐双扩散的格子Boltzmann方法数值模拟. 物理学报, 2006, 55(9): 4774-4782. doi: 10.7498/aps.55.4774
    [19] 吕晓阳, 李华兵. 用格子Boltzmann方法模拟高雷诺数下的热空腔黏性流. 物理学报, 2001, 50(3): 422-427. doi: 10.7498/aps.50.422
    [20] 李华兵, 黄乒花, 刘慕仁, 孔令江. 用格子Boltzmann方法模拟MKDV方程. 物理学报, 2001, 50(5): 837-840. doi: 10.7498/aps.50.837
计量
  • 文章访问数:  4931
  • PDF下载量:  224
  • 被引次数: 0
出版历程
  • 收稿日期:  2016-09-03
  • 修回日期:  2016-11-22
  • 刊出日期:  2017-02-05

/

返回文章
返回