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为准确、有效地模拟非等温非牛顿黏性流体的流动问题,本文基于一种不含核导数计算的核梯度修正格式和不可压缩条件给出了一种改进光滑粒子动力学(SPH)离散格式,它较传统SPH离散格式具有较高精度和较好稳定性. 同时,为准确地描述温度场的演化过程,建立了非牛顿黏性的SPH温度离散模型. 通过对等温Poiseuille流、喷射流和非等温Couette流、4:1收缩流进行模拟,并与其他数值结果作对比,分别验证了改进SPH方法模拟非牛顿黏性流动问题的可靠性和提出的SPH温度离散模型求解非等温流动问题的有效性和准确性. 随后,运用改进SPH方法结合SPH温度离散模型对环形腔和C形腔内非等温非牛顿黏性流体的充模过程进行了试探性模拟研究,分析了数值模拟的收敛性,讨论了不同位置处热流参数对温度和流动的影响.In this paper, a corrected smoothed particle hydrodynamics (SPH) method is proposed to solve the problems of non-isothermal non-Newtonian viscous fluid. The proposed particle method is based on the corrected kernel derivative scheme under no kernel derivative and incompressible conditions, which possesses higher accuracy and better stability than the traditional SPH method. Meanwhile, a temperature-discretization scheme is deduced by the concept of SPH method for the purpose of precisely describing the evolutionary process of the temperature field. Reliability of the corrected SPH method for simulating the non-Newtonian viscous fluid flow is demonstrated by simulating the isothermal Poiseuille flow and the jet fluid of filling process; and the validity and accuracy of the proposed SPH discrete scheme in a temperature model for solving the non-isothermal fluid flow are tested by solving the non-isothermal Couette flow and 4:1 contraction flow. Subsequently, the proposed corrected SPH method combined with the SPH temperature-discretization scheme is tentatively extended to include the simulation of the non-isothermal non-Newtonian viscous free-surface flows in the ring-shaped and C-shaped cavities. Especially, the convergence of numerical simulations is analyzed, and the influences of heat flow parameters on the temperature and fluid flow at different positions are discussed.
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Keywords:
- non-isothermal /
- viscosity fluid /
- smoothed particle hydrodynamics /
- thermo-viscosity model
[1] Hieber C A, Shen S F 1980 Journal of Non-Newtonian Fluid Mechanics 7 1
[2] Tao W Q 2006 Heat Transfer (Fourth Edition) (Beijing: Higher Education Press) (in Chinese) [陶文铨2006传热学 (第四版)(北京: 高等教育出版社)]
[3] Han X H, Li X K 2007 International Journal of Heat Mass Transfer 50 847
[4] Yang B X, Ouyang J 2012 Acta Phys. Sin. 61 234602 (in Chinese) [杨斌鑫, 欧阳洁 2012 61 234602]
[5] Lewis R W, Nithiarasu P, Seetharamu K N 2004 Fundamentals of the Finite Element Method for Heat and Fluid Flow (Chichester: John Wiley)
[6] Pan Y, Suga K 2005 Phys. Fluids 17 082105
[7] Jiang X, James A J 2007 J. Engineer. Math. 59 99
[8] Tomé M F, Grossia L, Casteloa A, Cuminatoa J A, Mangiavacchia N, Ferreiraa V G, de Sousaa F S, McKeeb S 2004 Journal of Non-Newtonian Fluid Mechanics 123 85
[9] Zhong C W, Xie J F, Zhuo C S, Xiong S W, Yin D C 2009 Chin. Phys. B 18 4083
[10] Cheng R J, Cheng Y M, Ge H X 2009 Chin. Phys. B 18 4059
[11] Chen R J, Ge H X 2010 Chin. Phys. B 19 090201
[12] Liu G R, Liu M B 2003 Smoothed Particle Hydrodynamics: A Mesh-free Particle Method (Singapore: World Scientific)
[13] Liu M B, Liu G R 2010 Archives of Computational Methods in Engineering 17 25
[14] Zhou G Z, Ge W, Li J H 2010 Chemical Engineering Science 65 2258
[15] Su T X, Ma L Q, Liu M B, Chang J Z 2013 Acta Phys. Sin. 62 064702 (in Chinese) [苏铁熊, 马理强, 刘谋斌, 常建忠 2013 62 064702]
[16] Han X H 2007 Ph. D. Dissertation (Dalian: Dalian University of Technology) (in Chinese) [韩先洪2007博士学位论文(大连: 大连理工大学)]
[17] Jiang F, Oliveira M S A, Sousa A C M 2005 M. T-wias. U. Werkstofftech 10 613
[18] Cleary P W, Ha J, Prakash M, Nguyen T 2010 Applied Mathematical Modelling 34 2018
[19] Jiang T, Ouyang J, Li X J, Zhang L, Ren J L 2011 Acta Phys. Sin. 60 090206 (in Chinese) [蒋涛, 欧阳洁, 栗雪娟, 张林, 任金莲 2011 60 090206]
[20] Chen J K, Beraun J E 2000 Comp. Meth. Appl. Mech. Eng. 190 225
[21] Liu M B, Chang J Z 2010 Acta Phys. Sin. 59 3654 (in Chinese) [刘谋斌, 常建忠 2010 59 3654]
[22] Zhou G Z, Ge W, Li B, Li X, Wang P, Wang J, Li J H 2013 Microfluidics and Nanofluidics 15 481
[23] Zhang M, Zhang S, Zhang H, Zheng L 2012 Computers & Fluids 59 61
[24] Han Y W, Qiang H F, Zhao J L, Gao W R 2013 Acta Phys. Sin. 62 044702 (in Chinese) [韩亚伟, 强洪夫, 赵久玲, 高巍然 2013 62 044702]
[25] Jiang T, Lu L G, Lu W G 2013 Acta Phys. Sin. 62 224701 (in Chinese) [蒋涛, 陆林广, 陆伟刚 2013 62 224701]
[26] Fan X J, Tanner R, Zheng R 2010 Journal of Non-Newtonian Fluid Mechanics 165 219
[27] Basa M, Quinlan N J, Lastiwka M 2009 Int. J. Num. Meth. Flu. 60 1127
[28] Shao S, Lo E Y M 2003 Advances in Water Resources 26 787
[29] Molteni D, Colagrossi A 2009 Computer Physics Communications 180 861
[30] Rafiee A, Manzari M T, Hosseini M 2007 International Journal of Non-linear Mechanics 42 1210
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[1] Hieber C A, Shen S F 1980 Journal of Non-Newtonian Fluid Mechanics 7 1
[2] Tao W Q 2006 Heat Transfer (Fourth Edition) (Beijing: Higher Education Press) (in Chinese) [陶文铨2006传热学 (第四版)(北京: 高等教育出版社)]
[3] Han X H, Li X K 2007 International Journal of Heat Mass Transfer 50 847
[4] Yang B X, Ouyang J 2012 Acta Phys. Sin. 61 234602 (in Chinese) [杨斌鑫, 欧阳洁 2012 61 234602]
[5] Lewis R W, Nithiarasu P, Seetharamu K N 2004 Fundamentals of the Finite Element Method for Heat and Fluid Flow (Chichester: John Wiley)
[6] Pan Y, Suga K 2005 Phys. Fluids 17 082105
[7] Jiang X, James A J 2007 J. Engineer. Math. 59 99
[8] Tomé M F, Grossia L, Casteloa A, Cuminatoa J A, Mangiavacchia N, Ferreiraa V G, de Sousaa F S, McKeeb S 2004 Journal of Non-Newtonian Fluid Mechanics 123 85
[9] Zhong C W, Xie J F, Zhuo C S, Xiong S W, Yin D C 2009 Chin. Phys. B 18 4083
[10] Cheng R J, Cheng Y M, Ge H X 2009 Chin. Phys. B 18 4059
[11] Chen R J, Ge H X 2010 Chin. Phys. B 19 090201
[12] Liu G R, Liu M B 2003 Smoothed Particle Hydrodynamics: A Mesh-free Particle Method (Singapore: World Scientific)
[13] Liu M B, Liu G R 2010 Archives of Computational Methods in Engineering 17 25
[14] Zhou G Z, Ge W, Li J H 2010 Chemical Engineering Science 65 2258
[15] Su T X, Ma L Q, Liu M B, Chang J Z 2013 Acta Phys. Sin. 62 064702 (in Chinese) [苏铁熊, 马理强, 刘谋斌, 常建忠 2013 62 064702]
[16] Han X H 2007 Ph. D. Dissertation (Dalian: Dalian University of Technology) (in Chinese) [韩先洪2007博士学位论文(大连: 大连理工大学)]
[17] Jiang F, Oliveira M S A, Sousa A C M 2005 M. T-wias. U. Werkstofftech 10 613
[18] Cleary P W, Ha J, Prakash M, Nguyen T 2010 Applied Mathematical Modelling 34 2018
[19] Jiang T, Ouyang J, Li X J, Zhang L, Ren J L 2011 Acta Phys. Sin. 60 090206 (in Chinese) [蒋涛, 欧阳洁, 栗雪娟, 张林, 任金莲 2011 60 090206]
[20] Chen J K, Beraun J E 2000 Comp. Meth. Appl. Mech. Eng. 190 225
[21] Liu M B, Chang J Z 2010 Acta Phys. Sin. 59 3654 (in Chinese) [刘谋斌, 常建忠 2010 59 3654]
[22] Zhou G Z, Ge W, Li B, Li X, Wang P, Wang J, Li J H 2013 Microfluidics and Nanofluidics 15 481
[23] Zhang M, Zhang S, Zhang H, Zheng L 2012 Computers & Fluids 59 61
[24] Han Y W, Qiang H F, Zhao J L, Gao W R 2013 Acta Phys. Sin. 62 044702 (in Chinese) [韩亚伟, 强洪夫, 赵久玲, 高巍然 2013 62 044702]
[25] Jiang T, Lu L G, Lu W G 2013 Acta Phys. Sin. 62 224701 (in Chinese) [蒋涛, 陆林广, 陆伟刚 2013 62 224701]
[26] Fan X J, Tanner R, Zheng R 2010 Journal of Non-Newtonian Fluid Mechanics 165 219
[27] Basa M, Quinlan N J, Lastiwka M 2009 Int. J. Num. Meth. Flu. 60 1127
[28] Shao S, Lo E Y M 2003 Advances in Water Resources 26 787
[29] Molteni D, Colagrossi A 2009 Computer Physics Communications 180 861
[30] Rafiee A, Manzari M T, Hosseini M 2007 International Journal of Non-linear Mechanics 42 1210
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