THE PRIMARY STABILITY ANALYSIS OF HARTMANN BOUNDARY LAYER

Dong Shuai; Lin Dianji; Lü Yukun

doi:10.6052/0459-1879-15-179

Volume 48 Issue 2

Turn off MathJax

Article Contents

Abstract

References

Chinese Journal of Theoretical and Applied Mechanics > 2016 > 48(2): 327-335. > DOI: 10.6052/0459-1879-15-179 CSTR: 32045.14.0459-1879-15-179

Dong Shuai, Lin Dianji, Lü Yukun. THE PRIMARY STABILITY ANALYSIS OF HARTMANN BOUNDARY LAYER[J]. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(2): 327-335. DOI: 10.6052/0459-1879-15-179

Citation:

PDF (2731 KB)

THE PRIMARY STABILITY ANALYSIS OF HARTMANN BOUNDARY LAYER

North China Electric Power University, School of Energy Power and Mechanical Engineering, Baoding 071003, Hebei, China

Received Date: May 17, 2015
Revised Date: November 26, 2015

Graphical Abstract

Abstract

Abstract

A thin Hartmann boundary layer will be formed near the wall when the conducting fluid is passing through a vertical magnetic field.The property of Hartmann boundary layers is vital to design and operation of equipments in electromagnetic metallurgy and thermonuclear fusion cooling system.This stability problem is investigated by non-modal stability analysis method.Through solving the governing equations of disturbances and adjoint field variables iteratively, the amplification and spatial distributions of primary perturbations are obtained.The effects of magnetic field on the optimal perturbation amplification G_max, spanwise wavenumber β_opt and time t_opt are analyzed, and the interaction between two opposite Hartmann boundary layers is considered as well.Results indicate that the optimal initial perturbations are in the form of streamwise vortices, which is symmetric or antisymmetric with respect of the normal direction.When the Hartmann number Ha is larger(Ha>10), the initial perturbations of symmetric and antisymmetric vortices are amplified equally, and the two opposite Hartmann boundary layers can be considered as independent from each other.In this case, the dependence of optimal perturbation amplification G_max on the square of local Reynolds number R is obtained, and the corresponding optimal spanwise wavenumber β_opt and time t_opt are proportional to the Hartmann number Ha.When the Hartmann number Ha is smaller(Ha<10), the antisymmetric vortices are more unstable, and the perturbation amplifications G_max is larger than that of symmetric vortices.There is still a kind of interaction between the two opposite Hartmann boundary layers to influence the stability of the flow field.
- Hartmann boundary layers,
- primary perturbation,
- stability analysis,
- non-normal mode,
- numerical simulation

FullText(HTML)

References (31)

References

1 Mukhopadhyay S, Layek GC, Samad SA. Study of MHD boundary layer flow over a heated stretching sheet with variable viscosity. International Journal of Heat and Mass Transfer, 2005, 48(21):4460-4466

2 Sharma R, Bhargava R, Bhargava P. A numerical solution of unsteady MHD convection heat and mass transfer past a semi-infinite vertical porous moving plate using element free Galerkin method. Computational Materials Science, 2010, 48(3):537-543

3 Rao JS, Sankar H. Numerical simulation of MHD effects on convective heat transfer characteristics of flow of liquid metal in annular tube. Fusion Engineering and Design, 2011, 86(2):183-191

4 Molokov S, Moreau R, Moffatt HK. Magnetohydrodynamics-Historical Evolution and Trends. New Yorker:Springer, 2007:231-233

5 Moreau R. Magnetohydrodynamics. New York:Springer, 1990:1-4

6 周本谋, 范宝春, 陈志华等. 流体边界层上电磁力的控制效应研究. 力学学报, 2004, 36(4):472-478(Zhou Benmou, Fan Baochun, Chen Zhihua, et al. Flow control effects of electromagnetic force in the boundary layer. Chinese Journal of Theoretical and Applied Mechanics, 2004, 36(4):472-478(in Chinese))

7 陈耀慧, 范宝春, 周本谋等. 翼型绕流的电磁力控制. 力学学报, 2008, 40(1):121-127(Chen Yaohui, Fan Baochun, Zhou Benmou, et al. Electro-magnetic control of hydrofoil wake. Chinese Journal of Theoretical and Applied Mechanics, 2008, 40(1):121-127(in Chinese))

8 Hartmann J. Hg-Dynamics I, Theory of the laminar flow of an electrically conductive liquid in a homogeneous magnetic field. Kongelige Danske Videnskabernes Selskab, Matematisk-Fysiske Meddelelser, 1937, 15(6):1-28

9 Hartmann J,Lazarus F. Hg-dynamics Ⅱ:Experimental investigation on the flow of mercury in a homogeneous magnetic field. Kongelige Danske Videnskabernes Selskab, Matematisk-Fysiske Meddelelser, 1937, 15(7):1-45

10 Ha MY, Lee HG, Seong SH. Numerical simulation of threedimensional flow, heat transfer, and solidification of steel in continuous casting mold with electromagnetic brake. Journal of Materials Processing Technology, 2003, 133(3):322-339

11 Fujisaki K. In-Mold electromagnetic stirring in continuous casting. IEEE Transactions on Industry Applications, 2001, 37(4):1098-1104

12 Dold P, Benz KW. Rotating magnetic fields:Fluid flow and crystal growth applications. Progress in Crystal Growth and Characterization of Materials, 1999, 38(1):39-58

13 Smolentsev S, Moreau R, Buhler L, et al. MHD thermofluid issues of liquid-metal blankets:Phenomena and advances. Fusion Engineering and Design, 2010, 85(7):1196-1205

14 Lundquist S. Studies in magnetohydrodynamics. Arkiv für Fysik, 1952, 5(4):297-347

15 Murgatroyd W. Experiments on magnetohydrodynamic channel flow. Philosophical Magazine, 1953, 44(359):1348-1354

16 Moresco P, Alboussiére T. Experimental study of the instability of the Hartmann layer. Journal of Fluid Mechanics, 2004, 504(10):167-181

17 Lingwood RJ, Alboussiére T. On the stability of the Hartmann layer. Physics of Fluids, 1999, 11(8):2058-2068

18 Krasnov D, Zienicke E, Zikanov O, et al. Numerical study of the instability of the Hartmann layer. Journal of Fluid Mechanics, 2004, 504(10):183-211

19 Gerard-Varet D. Amplification of small perturbations in a Hartmann layer. Physics of Fluids, 2002, 14(4):1458-1467

20 Airiau C, Castets M. On the amplification of small disturbances in a channel flow with a normal magnetic field. Physics of Fluids, 2004, 16(8):2991-3005

21 Krasnov D, Zikanov O, Boeck T. Numerical study of magnetohydrodynamic duct flow at high Reynolds and Hartmann numbers. Journal of Fluid Mechanics, 2012, 704(2):421-446

22 Davidson PA. An Introduction to Magnetohydrodynamics. Cambridge:Cambridge University Press, 2001:117-119

23 Dong S, Krasnov D, Boeck T. Secondary energy growth and turbulence suppression in conducting channel flow with streamwise magnetic field. Physics of Fluids, 2012, 24(7):074101

24 李春曦, 陈朋强, 叶学民. 含活性剂液滴在倾斜粗糙壁面上的铺展稳定性. 物理学报, 2015, 64(1):014702(Li Chunxi, Chen Pengqiang, Ye Xuemin. Stability of surfactant-laden droplet spreading over an inclined heterogeneous substrate. Acta Physica Sinica, 2015, 64(1):014702(in Chinese))

25 Luchini P. Reynolds-number-independent instability of the boundary layer over a flat surface:optimal perturbations. Journal of Fluid Mechanics, 2000, 404(2):298-309

26 Butler KM, Farrell BF. Three-dimensional optimal perturbations in viscous shear flow. Physics of Fluids A:Fluid Dynamics, 1992, 4(8):1637-1650

27 Andersson P, Berggren M, Henningson DS. Optimal disturbances and bypass transition in boundary layers. Physics of Fluids, 1999, 11(1):134-150

28 Schmid PJ, Henningson DS. Stability and Transition in Shear Flows. New Yorker:Springer, 2001:515-519

29 Reddy SC, Schmid PJ, Baggett JS, et al. On stability of streamwise streaks and transition thresholds in plane channel flows. Journal of Fluid Mechanics, 1998, 365:269-303

30 Zikanov O. On the instability of pipe Poiseuille flow. Physics of Fluids, 1996, 8(11):2923-2932

31 Gustavsson LH. Energy growth of three-dimensional disturbances in plane Poiseuille flow. Journal of Fluid Mechanics, 1991, 224:241-260

[1]	Yu Enyi, Di Yuan, Wu Hui, Cao Xiaopeng, Zhang Qingfu, Zhang Chuanbao. NUMERICAL SIMULATION ON RISK ANALYSIS OF CO₂ GEOLOGICAL STORAGE UNDER MULTI-FIELD COUPLING: A REVIEW[J]. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(9): 2075-2090. DOI: 10.6052/0459-1879-23-127
[2]	Guan Xinyan, Fu Qingfei, Liu Hu, Yang Lijun. NUMERICAL SIMULATION OF OLDROYD-B VISCOELASTIC DROPLET COLLISION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(3): 644-652. DOI: 10.6052/0459-1879-22-020
[3]	Chen Jianqiang, Chen Qi, Yuan Xianxu, Xie Yufei. NUMERICAL SIMULATION STUDY ON DYNAMIC RESPONSE UNDER RUDDER CONTROL[J]. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(2): 302-306. DOI: 10.6052/0459-1879-12-222
[4]	Geng Yunfei Chao Yan. Numerical investigation of self-aligning spiked bodies at hypersonic speeds[J]. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(3): 441-446. DOI: 10.6052/0459-1879-2011-3-lxxb2010-732
[5]	Zhenpeng Liao, Heng Liu, Zhinan Xie. An explicit method for numerical simulation of wave motion---1-D wave motion[J]. Chinese Journal of Theoretical and Applied Mechanics, 2009, 41(3): 350-360. DOI: 10.6052/0459-1879-2009-3-2007-635
[6]	Yaling Wang, Hongsheng Zhang. Numerical simulation of nonlinear wave propagation on non-uniform current[J]. Chinese Journal of Theoretical and Applied Mechanics, 2007, 23(6): 732-740. DOI: 10.6052/0459-1879-2007-6-2006-410
[7]	Z.Y. Gao, Tongxi Yu, D. Karagiozova. Finite element simulation on the mechanical properties of MHS materials[J]. Chinese Journal of Theoretical and Applied Mechanics, 2007, 23(1): 65-75. DOI: 10.6052/0459-1879-2007-1-2006-198
[8]	Zheng Wu. On the numerical simulation of perturbation's propagation and development in traffic flow[J]. Chinese Journal of Theoretical and Applied Mechanics, 2006, 38(6): 785-791. DOI: 10.6052/0459-1879-2006-6-2005-392
[9]	NUMERICAL SIMULATION OF CONVECTIVE BIFURCATION FOR A SQUARE POROUS CAVITY[J]. Chinese Journal of Theoretical and Applied Mechanics, 1993, 25(6): 721-725. DOI: 10.6052/0459-1879-1993-6-1995-698
[10]	CRACK TIP SUPERBLUNTING: EXPERIMENT, THEORY AND NUMERICAL SIMULATION[J]. Chinese Journal of Theoretical and Applied Mechanics, 1993, 25(4): 468-478. DOI: 10.6052/0459-1879-1993-4-1995-667

Cited By

Cited by

Periodical cited type(5)

1.	董帅，李爽，叶学民. 低强度磁场作用下Hunt流的稳定性分析. 系统仿真学报. 2019(08): 1605-1616 .
2.	陈永，贺红，张薇，周宁. 基于场力的驾驶员影响因素交通流动力学模型. 力学学报. 2018(05): 1219-1234 . 本站查看
3.	毛洁，王彦利，王浩. 倾斜非均匀磁场下导电方管磁流体管流的数值模拟研究. 力学学报. 2018(06): 1387-1395 . 本站查看
4.	董帅，李爽，刘立帅，叶学民. 磁场作用下导电流体的流动稳定性研究进展. 化工进展. 2017(S1): 17-26 .
5.	董帅，刘立帅，叶学民. 磁场作用下平行平板内导电流体的流动稳定性. 系统仿真学报. 2017(08): 1762-1771 .

Other cited types(3)

Get Citation

PDF

XML

Article Metrics

Article views (1523) PDF downloads (743) Cited by(8)

THE PRIMARY STABILITY ANALYSIS OF HARTMANN BOUNDARY LAYER