非牛顿流体在环管中流动与换热特性的数值研究
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摘要
工业生产中经常遇到充分发展的轴向层流在环管中的流动与热交换，很多情况下这些流体表现出非牛顿流体的性质。
本文研究了表观粘度函数为幂律形式的幂律流体在环管中的流动与换热情况，考虑不同的边界条件，在结构化网格和非结构化网格中数值模拟出不同流动指数的流体在不同流通区域中的速度场和温度场，给出雷诺数、摩擦因子、努谢尔数等。特别对于环管产生偏心的情况，给予了更深入的研究。区域的不对称性和非牛顿流体的本身性质，严重影响了速度及温度分布。考虑环管偏心率和半径率的影响，研究圆环半径比在0.2和0.8之间，偏心率在0和0.6之间的情况，复杂的流通区域使流动和换热的分布严重不均，引起了反常的水力及热力性质。同时对于结构化网格的计算结果和非结构化网格的计算结果进行比较，也与部分精确解进行比较，得出了比较理想的结果。上述有关方法和结论将为工程上的设计与更深入地研究提供有利的依据。
Many laminar fully developed flows, that are processed in many heat exchange andflow devices with annular channels, exhibit a viscous, non-Newtonian behavior.
This paper referred to the flows and the forced convection heat transfer of thepower-law fluids, and the different boundary conditions were considered. Numericalsolutions for the velocity and temperature distributions, Reynolds number, isothermalfrictions factors, and Nusselt numbers for different ducts were presented. And the instanceof inner core eccentricity was analyzed. The geometric asymmetry of the eccentric annularcross-section and the performance of the non-Newtonian were seen to have a stronginfluence on the velocity and temperature distributions. The annular ducts of varyingaspect ratios from 0.2 to 0.8, and inner core eccentricity from 0 to 0.6 were considered. Thecomplex ducts induced the non-uniformity in the velocity and the temperature field, whichproduced a significantly anomalous thermal-hydraulic performance. And the resultscomputed on unstructured grids and the solutions computed on structured grids werecontrasted, also compared with some results shown in the reference. All of these prove thatthe method and the program are correct and perfect. The methods and the conclusions ofthis paper can be helpful to the design in industry and the improved research.
本文研究了表观粘度函数为幂律形式的幂律流体在环管中的流动与换热情况，考虑不同的边界条件，在结构化网格和非结构化网格中数值模拟出不同流动指数的流体在不同流通区域中的速度场和温度场，给出雷诺数、摩擦因子、努谢尔数等。特别对于环管产生偏心的情况，给予了更深入的研究。区域的不对称性和非牛顿流体的本身性质，严重影响了速度及温度分布。考虑环管偏心率和半径率的影响，研究圆环半径比在0.2和0.8之间，偏心率在0和0.6之间的情况，复杂的流通区域使流动和换热的分布严重不均，引起了反常的水力及热力性质。同时对于结构化网格的计算结果和非结构化网格的计算结果进行比较，也与部分精确解进行比较，得出了比较理想的结果。上述有关方法和结论将为工程上的设计与更深入地研究提供有利的依据。
Many laminar fully developed flows, that are processed in many heat exchange andflow devices with annular channels, exhibit a viscous, non-Newtonian behavior.
This paper referred to the flows and the forced convection heat transfer of thepower-law fluids, and the different boundary conditions were considered. Numericalsolutions for the velocity and temperature distributions, Reynolds number, isothermalfrictions factors, and Nusselt numbers for different ducts were presented. And the instanceof inner core eccentricity was analyzed. The geometric asymmetry of the eccentric annularcross-section and the performance of the non-Newtonian were seen to have a stronginfluence on the velocity and temperature distributions. The annular ducts of varyingaspect ratios from 0.2 to 0.8, and inner core eccentricity from 0 to 0.6 were considered. Thecomplex ducts induced the non-uniformity in the velocity and the temperature field, whichproduced a significantly anomalous thermal-hydraulic performance. And the resultscomputed on unstructured grids and the solutions computed on structured grids werecontrasted, also compared with some results shown in the reference. All of these prove thatthe method and the program are correct and perfect. The methods and the conclusions ofthis paper can be helpful to the design in industry and the improved research.
引文
1 袁龙蔚．流变力学．北京：科学出版社，1986
2 陈文芳．非牛顿流体力学．北京：科学出版社，1984
3 陶文铨．计算传热学的近代发展．北京：科学出版社，2000
4 A.V. Piercy. Viscous Flow Through Pipes with Cores. Edinburgh, Dublin Philos. Mag. J. Sci, 1993.15:647-676
5 C. Stevenson. The Center of Flexure of a Hollow Shaft. Proc. London Math. Soc, 1949. 50:536
6 T. Snyder and G. A. Goldstein. An Analysis of Fully Developed Flow in an Eccentric Annulus. AIChE J, 1965.11:462-467
7 沈崇棠，刘鹤年．非牛顿流体力学及其应用．北京：高等教育出版社，1989
8 L. Trombetta. Laminar Forced Convection in Eccentric Annuli. Int. J. Heat Mass Transfer, 1971.14:1161-1173
9 W. Tiedt. Berechnung des Laminaren und Turbulent Reibungswiderstandes Konzentrischer Exzentrisher Ringspalte, Part Ⅰ, Chem. -Ztg., Chem. Appar, 1966.90:813-821
10 W. Tiedt. Berechnung des Laminaren und Turbulenten Reibungswiderstandes Konzentrischer und Exzentrisher Ringspalte, Part Ⅱ, Chem. -Ztg., Chem. Appar, 1967.91:17-25
11 P. Fang. Characteristics of laminar viscous shear-thinning fluid flows in eccentric annular channels, Journal of Non-Newtonian Fluid Mechanics, 1999.17:9-26
12 M. P. Escudier. I. W. Gouldson. Effect of centerbody rotation on laminar flow through an eccentric annulus, in: R. J. Adrian et al.(Eds), Developments in Laser Techniques and Nuclear Engineering, University of Cincinnati, OH, 1998
13 A. G. Fredrickson and R. B. Bird. Non-Newtonian Flow in Annuli. Ind. Eng. Chem, 1958.50:347-352
14 A.H.P.Skelland. Non-Newtonian Flow and Heat Transfer, 1967
15 T. K. Tuoc and J. M. McGiven. Laminar Flow of Non-Newtonian Fluids in Annuli. Trans. I. Chem. E, 1994.72:669-676
16 M. P. Escudier. Flowof Shear-Thinning Fluids in a Concentric Annulus. Exp. Fluids. 1995.18:225-238
17 T. L. Guckes. Laminar Flow of Non-Newtonian Fluids in an Eccentric Annulus. J. Eng. Ind. 1975.97:498-506
18 D. Uner, C. Ozgen, and I. Tosun. An Approximate Solution for Non-Newtonian Flow in Eccentric Armuli. Ind. Eng. Chem. Res. 1988.27:698-701
19 I. C. Walton and S. H. Bittleston. The Axial Flow of a Bingham Plastic in a Narrow Eccentric Annulus. J. Fluid Mech.. 1991.222:39-60
20 P. Szabo and O. Hassager. Flow of Viscoplastic Fluids in Eccentric Annular Geometries. J. Non-Newtonian fluid Mech, 1992.45:149-169
21 N. Mitsuishi and Y. Aoyagi. Non-Newtonian Fluid Flow in an Eccentric Annulus. J. Chem. Eng. Japan, 1973,6:402-408
22 Capobianchi, M.and Irvine. T.F.Jr. Predictions of pressure drop and heat transfer in concentric annular ducts with modified power law fluids. Warme stoffubertr, 1992.27:209-215
23 I. Cho and J. P. Hartnett. Non-Newtonian Fluids in Circular Pipe Flow. Advances in Heat Transfer, 1982.15:59-141
24 Lundberg, R.E., McCuen, P.A.and Reynolds,W.C. Heat transfer in annular passages: Hydrodynamically developd laminar flow with arbitrarily prescribed wall temperatures or heat fluxes. Int.J.Heat Mass Transfer, 1963.6:495-529
25 Cheng, K, C. and Hwang, G. J. Laminar forced convection in eccentric annuli. AIChE J.,1968.14:510-512
26 Suzuki, K., Szmyd, J. S. and Ohtsuka, H. Laminar forced Convection heat transfer in eccentric annuli. Heat Transfer-Jpn. Res., 1991.20:169-183
27 R. M. Manglik and P. P. Fang. Effect of Eccentricity and Thermal Boundary Conditions on Laminar Flow in Annular Ducts. Int. J. Heat Fluid Flow, 1995.16:298-306
28 M. Tanaka, N. Mitsuishi. Non-Newtonian laminar heat transfer in concentric annuli. Heat Transfer-Jpn. Res.,1975.4:26-36
29 黄善波，李兆敏．幂律流体管内充分发展的对流换热分析．石油大学学报，2004．28：71-74
30 王艳辉．偏心环空非牛顿流体紊动场特性的研究．水动力学研究与进展，1997．12(2)：150-156
31 刘明新，沈平平，袁江如．幂律非牛顿流体平面流动的数值计算．石油学报，2004．25(3)：75-78
32 谭军，葛培琪，张鹏顺．非牛顿流体圆模型弹流的数值计算．哈尔滨工业大学学报，1997．29(2)：84-86
33 陶文铨．数值传热学．西安：西安交通大学出版社，2001
34 Suhas V.Patankar. Computation of Conduction and Duct Flow Heat Transfer.Innovative Research, Inc.7846 Ithaca Lane North Maple Grove, MN55369-8549, USA
35 宇波，林明杰，王秋旺，陶文铨．一种非结构化同位网格算法．工程热物理学报，1998．19(4)：475-479
36 任安禄．不可压缩粘性流场计算方法．北京：国防工业出版社，2003
37 Zhang. M. "Modeling of Radiative Heat Transfer and Diffusion Processes Using Unstructured Grid", Ph.D. Dissertation, 2000, Tennessee Technological University, USA.
38 S.R.Mathur, J.Y.Murthy. A Pressure-Based Method for Unstructured Meshes, Numerical Heat Transfer, Part B, 1997, 31:195-215
39 J. Prusa, L.S. Yao. Natural convection heat transfer between eccentric horizontal cylinders. J. Heat Transfer, 1983.105:108-115
40 J. Prusa, L.S. Yao. Numerical solution for fully developed flow in heated curved tubes. J.Fluid Mech, 1982.123:503-522
41 R.M. Manglik, A.E. Bergles. Fully developed laminar heat transfer in circular segment ducts with uniform wall temperature. Heat Transfer, 1994.Part A 26:499-519
42 J.M. Nouri, J.H. Whitelaw. Flow of Newtonian and non-Newtonian fluids in a concentric annulus with rotation of the inner cylinder. J. Fluids Eng. 1994.116,821-827
43 M.P. Escudier, I.W. Gouldson. 1997
44 M. Capobianchi, T.E Irvine, Jr., Predictions of pressure drop and heat transfer in concentric annular ducts with modified power law fluids. Warme Stoffubertr, 1992.27:209-215
45 R.K. Shah, A.L. London, Laminar flow forced convection in ducts, supplement 1,in:T.F. Irvine Jr., J.P. Hartnett(Eds.), Advances in Heat Transfer, Academic Press, New York,1978
46 P.Fang, R.M. Manglik, M.A. Jog, Characteristics of laminar viscous shear-thinning fluid flows in eccentric annular channesl, J. Non-Newtonian Fluid Mech, 1999.84:1-17
47 商立英．非结构网格上非稳态导热问题的应用，2005
48 章熙民，任泽霈．传热学．北京：中国建筑工业出版社，2001
49 杨世铭，陶文铨．传热学．北京：高等教育出版社，1998
50 徐明海．非结构网格的扩散通量计算方法评价．工程热物理学报，2005，26(2)：316-315
51 景思瑞，张鸣远．流体力学．西安：西安交通大学出版社，2001
52 R. M. Manglik and P. Fang. Thermal processing of viscous non-Newtonian fluids in annular ducts. Heat and Mass Transfer, 2002.45:803-814
53 柏威，鄂学全．用非结构网格研究旋转振荡圆柱绕流．力学学报，2004．36(4)：466-472
54 杨晓洪，张政．幂律流体在半圆及扁圆形通道中充分发展流动数值分析与阻力计算．北京化工学院学报，1992．19(2)：1-6
55 W. Kozicki, C. H. Chou and C. Yiu. Non-Newtonian Flow in Ducts of Arbitrary Cross-Sections. Chemical Engineering Science, 1966.21:665-679.
2 陈文芳．非牛顿流体力学．北京：科学出版社，1984
3 陶文铨．计算传热学的近代发展．北京：科学出版社，2000
4 A.V. Piercy. Viscous Flow Through Pipes with Cores. Edinburgh, Dublin Philos. Mag. J. Sci, 1993.15:647-676
5 C. Stevenson. The Center of Flexure of a Hollow Shaft. Proc. London Math. Soc, 1949. 50:536
6 T. Snyder and G. A. Goldstein. An Analysis of Fully Developed Flow in an Eccentric Annulus. AIChE J, 1965.11:462-467
7 沈崇棠，刘鹤年．非牛顿流体力学及其应用．北京：高等教育出版社，1989
8 L. Trombetta. Laminar Forced Convection in Eccentric Annuli. Int. J. Heat Mass Transfer, 1971.14:1161-1173
9 W. Tiedt. Berechnung des Laminaren und Turbulent Reibungswiderstandes Konzentrischer Exzentrisher Ringspalte, Part Ⅰ, Chem. -Ztg., Chem. Appar, 1966.90:813-821
10 W. Tiedt. Berechnung des Laminaren und Turbulenten Reibungswiderstandes Konzentrischer und Exzentrisher Ringspalte, Part Ⅱ, Chem. -Ztg., Chem. Appar, 1967.91:17-25
11 P. Fang. Characteristics of laminar viscous shear-thinning fluid flows in eccentric annular channels, Journal of Non-Newtonian Fluid Mechanics, 1999.17:9-26
12 M. P. Escudier. I. W. Gouldson. Effect of centerbody rotation on laminar flow through an eccentric annulus, in: R. J. Adrian et al.(Eds), Developments in Laser Techniques and Nuclear Engineering, University of Cincinnati, OH, 1998
13 A. G. Fredrickson and R. B. Bird. Non-Newtonian Flow in Annuli. Ind. Eng. Chem, 1958.50:347-352
14 A.H.P.Skelland. Non-Newtonian Flow and Heat Transfer, 1967
15 T. K. Tuoc and J. M. McGiven. Laminar Flow of Non-Newtonian Fluids in Annuli. Trans. I. Chem. E, 1994.72:669-676
16 M. P. Escudier. Flowof Shear-Thinning Fluids in a Concentric Annulus. Exp. Fluids. 1995.18:225-238
17 T. L. Guckes. Laminar Flow of Non-Newtonian Fluids in an Eccentric Annulus. J. Eng. Ind. 1975.97:498-506
18 D. Uner, C. Ozgen, and I. Tosun. An Approximate Solution for Non-Newtonian Flow in Eccentric Armuli. Ind. Eng. Chem. Res. 1988.27:698-701
19 I. C. Walton and S. H. Bittleston. The Axial Flow of a Bingham Plastic in a Narrow Eccentric Annulus. J. Fluid Mech.. 1991.222:39-60
20 P. Szabo and O. Hassager. Flow of Viscoplastic Fluids in Eccentric Annular Geometries. J. Non-Newtonian fluid Mech, 1992.45:149-169
21 N. Mitsuishi and Y. Aoyagi. Non-Newtonian Fluid Flow in an Eccentric Annulus. J. Chem. Eng. Japan, 1973,6:402-408
22 Capobianchi, M.and Irvine. T.F.Jr. Predictions of pressure drop and heat transfer in concentric annular ducts with modified power law fluids. Warme stoffubertr, 1992.27:209-215
23 I. Cho and J. P. Hartnett. Non-Newtonian Fluids in Circular Pipe Flow. Advances in Heat Transfer, 1982.15:59-141
24 Lundberg, R.E., McCuen, P.A.and Reynolds,W.C. Heat transfer in annular passages: Hydrodynamically developd laminar flow with arbitrarily prescribed wall temperatures or heat fluxes. Int.J.Heat Mass Transfer, 1963.6:495-529
25 Cheng, K, C. and Hwang, G. J. Laminar forced convection in eccentric annuli. AIChE J.,1968.14:510-512
26 Suzuki, K., Szmyd, J. S. and Ohtsuka, H. Laminar forced Convection heat transfer in eccentric annuli. Heat Transfer-Jpn. Res., 1991.20:169-183
27 R. M. Manglik and P. P. Fang. Effect of Eccentricity and Thermal Boundary Conditions on Laminar Flow in Annular Ducts. Int. J. Heat Fluid Flow, 1995.16:298-306
28 M. Tanaka, N. Mitsuishi. Non-Newtonian laminar heat transfer in concentric annuli. Heat Transfer-Jpn. Res.,1975.4:26-36
29 黄善波，李兆敏．幂律流体管内充分发展的对流换热分析．石油大学学报，2004．28：71-74
30 王艳辉．偏心环空非牛顿流体紊动场特性的研究．水动力学研究与进展，1997．12(2)：150-156
31 刘明新，沈平平，袁江如．幂律非牛顿流体平面流动的数值计算．石油学报，2004．25(3)：75-78
32 谭军，葛培琪，张鹏顺．非牛顿流体圆模型弹流的数值计算．哈尔滨工业大学学报，1997．29(2)：84-86
33 陶文铨．数值传热学．西安：西安交通大学出版社，2001
34 Suhas V.Patankar. Computation of Conduction and Duct Flow Heat Transfer.Innovative Research, Inc.7846 Ithaca Lane North Maple Grove, MN55369-8549, USA
35 宇波，林明杰，王秋旺，陶文铨．一种非结构化同位网格算法．工程热物理学报，1998．19(4)：475-479
36 任安禄．不可压缩粘性流场计算方法．北京：国防工业出版社，2003
37 Zhang. M. "Modeling of Radiative Heat Transfer and Diffusion Processes Using Unstructured Grid", Ph.D. Dissertation, 2000, Tennessee Technological University, USA.
38 S.R.Mathur, J.Y.Murthy. A Pressure-Based Method for Unstructured Meshes, Numerical Heat Transfer, Part B, 1997, 31:195-215
39 J. Prusa, L.S. Yao. Natural convection heat transfer between eccentric horizontal cylinders. J. Heat Transfer, 1983.105:108-115
40 J. Prusa, L.S. Yao. Numerical solution for fully developed flow in heated curved tubes. J.Fluid Mech, 1982.123:503-522
41 R.M. Manglik, A.E. Bergles. Fully developed laminar heat transfer in circular segment ducts with uniform wall temperature. Heat Transfer, 1994.Part A 26:499-519
42 J.M. Nouri, J.H. Whitelaw. Flow of Newtonian and non-Newtonian fluids in a concentric annulus with rotation of the inner cylinder. J. Fluids Eng. 1994.116,821-827
43 M.P. Escudier, I.W. Gouldson. 1997
44 M. Capobianchi, T.E Irvine, Jr., Predictions of pressure drop and heat transfer in concentric annular ducts with modified power law fluids. Warme Stoffubertr, 1992.27:209-215
45 R.K. Shah, A.L. London, Laminar flow forced convection in ducts, supplement 1,in:T.F. Irvine Jr., J.P. Hartnett(Eds.), Advances in Heat Transfer, Academic Press, New York,1978
46 P.Fang, R.M. Manglik, M.A. Jog, Characteristics of laminar viscous shear-thinning fluid flows in eccentric annular channesl, J. Non-Newtonian Fluid Mech, 1999.84:1-17
47 商立英．非结构网格上非稳态导热问题的应用，2005
48 章熙民，任泽霈．传热学．北京：中国建筑工业出版社，2001
49 杨世铭，陶文铨．传热学．北京：高等教育出版社，1998
50 徐明海．非结构网格的扩散通量计算方法评价．工程热物理学报，2005，26(2)：316-315
51 景思瑞，张鸣远．流体力学．西安：西安交通大学出版社，2001
52 R. M. Manglik and P. Fang. Thermal processing of viscous non-Newtonian fluids in annular ducts. Heat and Mass Transfer, 2002.45:803-814
53 柏威，鄂学全．用非结构网格研究旋转振荡圆柱绕流．力学学报，2004．36(4)：466-472
54 杨晓洪，张政．幂律流体在半圆及扁圆形通道中充分发展流动数值分析与阻力计算．北京化工学院学报，1992．19(2)：1-6
55 W. Kozicki, C. H. Chou and C. Yiu. Non-Newtonian Flow in Ducts of Arbitrary Cross-Sections. Chemical Engineering Science, 1966.21:665-679.