DIRECT NUMERICAL SIMULATIONS ON THE TURBULENT FLOW PAST A CONFINED CIRCULAR CYLINDER WITH THE INFLUENCE OF THE STREAMWISE MAGNETIC FIELDS1)

doi:10.6052/0459-1879-20-217

Abstract

Abstract:

The flow around a cylinder is a typical flow pattern in the liquid metal blanket in Tokomak fusion device, which reveals significant influence on the relevant flow and heat transfer. In the present work, three-dimensional direct numerical simulations (DNSs) are performed to study the turbulent flows past a circular cylinder at $Re=3900$ under magnetic fields. For the case without magnetic fields, the DNS results are in good agreement with the available experimental and numerical results. With the increase of the flow distance in the downstream wake of the cylinder, the mean streamwise velocity profile varies from U-shaped to V-shaped and flattens out, indicating that the influence of cylinder on the flow structures weakens gradually. Within the shear layers, because of the Kelvin-Helmholtz instability, the shedding of the small-scale shear vortices can be observed clearly through the flow visualization. Taking the results of non-magnetic field as the initial condition, the magnetic fields along the streamwise direction are applied, where the corresponding Hartmann numbers (Ha) are 20, 40 and 80. When the magnetic field is weak, the three-dimensional turbulent properties are still clear, although the magnetic field inhibits the velocity field. As the magnetic field increases, the recirculation zone behind the cylinder is elongated. The shear layers near the cylinder become smoother and the corresponding destabilizing position shift downstream. Since the vortices in the wake are squeezed by Lorentz force in the vertical direction, the Karman vortex street gradually gets narrow with the increase of magnetic field. Meanwhile, the scale of the vortex structures becomes smaller compared with those without magnetic fields because of the dissipation effect of magnetic fields. This research not only extends the parameter range of turbulence under magnetic fields, but also shows important theoretical guiding value and engineering application value for the design and safe operation of the blanket.

Key words: magnetic fields, turbulence, flow around a circular cylinder, DNS

CLC Number:

O361.3

Hao Le, Chen Long, Ni Mingjiu. DIRECT NUMERICAL SIMULATIONS ON THE TURBULENT FLOW PAST A CONFINED CIRCULAR CYLINDER WITH THE INFLUENCE OF THE STREAMWISE MAGNETIC FIELDS¹⁾[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(6): 1645-1654.

Figures/Tables 12

Fig. 1 Schematic diagram of calculation model

Table 1 Effect of grid design on time-averaged flow characteristics

Fig. 2 The distribution of double curvilinear O-type orthogonal grids

Fig. 3 Mean streamwise velocity along the centreline of the cylinder

Fig. 4 Vertical profiles of the mean streamwise and vertical velocity at $x/D=1.06$, 1.54, 2.02

Fig. 5 Vertical profiles of the mean Reynolds stress components at $x/D=1.06$, 1.54, 2.02

Table 2 Experiments and simulations of the turbulent flow past a confined circular cylinder at $Re=3900$

Fig. 6 Two dimensional vortex structures near the cylinder: (a) Two-dimensional instantaneous vorticity magnitude contour; (b) two-dimensional instantaneous velocity vector contour

Fig. 7 Change under different magnetic fields

Fig. 8 Under different magnetic fields, vertical profiles of the mean velocity

Fig. 9 Effect of magnetic field on the mean Reynolds stress components at the different vertical profiles

Fig. 10 The instantaneous streamwise velocity contour and vortical structure, identified by the $Q$-criterion ($Q=1$)

References 40

[1]	杨明, 刘巨保, 岳欠杯等. 涡激诱导并列双圆柱碰撞数值模拟研究. 力学学报, 2019,51(6):1785-1796
	( Yang Ming, Liu Jubao, Yue Qianbei, et al. Numerical simulation on the vortex-induced collision of two side-by-side cylinders. Chinese Journal of Theoretical and Applied Mechanic, 2019,51(6):1785-1796 (in Chinese))
[2]	涂佳黄, 谭潇玲, 邓旭辉等. 平面剪切来流作用下串列布置三圆柱流致运动特性研究. 力学学报, 2019,51(3):787-802
	( Tu Jiahuang, Tan Xiaoling, Deng Xuhui, et al. Study of flow-induced motion characteristics of three tandem circular cylinders in planar shear flow. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(3):787-802 (in Chinese))
[3]	陈威霖, 及春宁, 许栋. 不同控制角下附加圆柱对圆柱涡激振动影响. 力学学报, 2019,51(2):432-440
	( Chen Weilin, Ji Chunning, Xu Dong. Effects of the added cylinders with different control angles on the vortex-induced vibrations of an circular cylinder. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(2):432-440 (in Chinese))
[4]	Dong S, Karniadakis GE, Ekmekci A, et al. A combined direct numerical simulation-particle image velocimetry study of the turbulent near wake. Journal of Fluid Mechanics, 2006,569:185-207 DOI URL
[5]	Parnaudeau P, Carlier J, Heitz D, et al. Experimental and numerical studies of the flow over a circular cylinder at Reynolds number 3900. Physics of Fluids, 2008,20(8):085-101
[6]	Norberg C. An experimental investigation of the flow around a circular cylinder: influence of aspect ratio. Journal of Fluid Mechanics, 1994,258:287-316
[7]	涂程旭, 王昊利, 林建忠. 圆柱绕流的流场特性及涡脱落规律研究. 中国计量学院学报, 2008,136:98-102
	( Tu Chengxu, Wang Haoli, Lin Jianzhong. Experimental research on the flow characteristics and vortex shedding in the flow around a circular cylinder. Journal of China Jiliang University, 2008,136:98-102 (in Chinese))
[8]	Gerrard JH. The wakes of cylindrical bluff bodies at low Reynolds number. Philosophical Transactions of the Royal Society of London Series A, Mathematical and Physical Sciences, 1978,288:351-382
[9]	王勇, 郝南松, 耿子海等. 基于时间解析PIV的圆柱绕流尾迹特性研究. 实验流体力学, 2018,141(1):66-72
	( Wang Yong, Hao Nansong, Geng Zihai, et al. Measurements of circular cylinder's wake using time-resolved PIV. Journal of Experiments in Fluid Mechanics, 2018,141(1):66-72 (in Chinese))
[10]	张玮, 王元, 徐忠等. 圆柱绕流涡系演变的DPIV测试. 空气动力学学报, 2002,20(4):8-16
	( Zhang Wei, Wang Yuan, Xu Zhong, et al. Experimental investigation of vortex evlovement around a circular cylinder by digital particle image velocimetry (DPIV). Acta Aerodynamic Sinica, 2002,20(4):8-16 (in Chinese))
[11]	Wu J, Sheridan J, Hourigan K, et al. Shear layer vortices and longitudinal vortices in the near wake of a circular cylinder. Experimental Thermal & Fluid Science, 1996,12(2):169-174
[12]	Thompson M, Hourigan K, Sheridan J. Three-dimensional instabilities in the wake of a circular cylinder. Experimental Thermal & Fluid Science, 1996,12(2):190-196
[13]	Hammache M, Gharib M. An experimental study of the parallel and oblique vortex shedding from circular cylinders. Journal of Fluid Mechanics, 1991,232:567-590 DOI URL
[14]	Tremblay F. Direct and large-eddy simulation of flow around a circular cylinder at subcritical Reynolds numbers. [PhD Thesis]. Technische Universität München, 2002
[15]	Breuer M. Large eddy simulation of the subcritical flow past a circular cylinder: numerical and modeling aspects. International Journal for Numerical Methods in Fluids, 1998,28(9):1281-1302 DOI URL
[16]	Lysenko DA, Ertesvåg IS, Rian KE. Large-eddy simulation of the flow over a circular cylinder at Reynolds number $2\times 10^{4}$. Flow, Turbulence and Combustion, 2014,92(3):673-698
[17]	Ma X, Karamanos GS, Karniadakis GE. Dynamics and low-dimensionality of a turbulent near wake. Journal of Fluid Mechanics, 2000,410:29-65
[18]	Mittal R, Moin P. Suitability of upwind-biased finite difference schemes for large-eddy simulation of turbulent flows. AIAA Journal, 1997,35(8):1415-1417
[19]	Fröhlich J, Rodi W, Kessler P, et al. Large eddy simulation of flow around circular cylinders on structured and unstructured grids. Numerical Flow Simulation I, 1998,12:319-338
[20]	Mück B, Günther C, Müller U, et al. Three-dimensional MHD flows in rectangular ducts with internal obstacles. Journal of Fluid Mechanics, 2000,418:265-295 DOI URL
[21]	Rhoads JR, Edlund EM, Ji H. Effects of magnetic field on the turbulent wake of a cylinder in free-surface magnetohydrodynamic channel flow. Journal of Fluid Mechanics, 2014,742:446-465 DOI URL
[22]	Dousset V, Pothérat A. Numerical simulations of a cylinder wake under a strong axial magnetic field. Physics of Fluids, 2008,20(1):017104
[23]	Sommeria J, Moreau R. Why, how, and when, MHD turbulence becomes two-dimensional. Journal of Fluid Mechanics, 1982,118:507-518 DOI URL
[24]	Hussam WK, Thompson MC, Sheard GJ. Dynamics and heat transfer in a quasi-two-dimensional MHD flow past a circular cylinder in a duct at high Hartmann number. International Journal of Heat and Mass Transfer, 2011,54:1091-1100 DOI URL
[25]	Hussam WK, Sheard GJ. Heat transfer in a high Hartmann number MHD duct flow with a circular cylinder placed near the heated side-wall. International Journal of Heat and Mass Transfer, 2013,67:944-954 DOI URL
[26]	Gajbhiye NL, Eswaran V. Numerical simulation of MHD flow and heat transfer in a rectangular and smoothly constricted enclosure. International Journal of Heat and Mass Transfer, 2015,83:441-449 DOI URL
[27]	Beaudan P, Moin P. Numerical experiments on the flow past a circular cylinder at sub-critical Reynolds number. No. TF-62. Stanford Univ CA Thermosciences Div, 1994
[28]	Mittal R, Moin P. Large-eddy simulation of flow past a circular cylinder. APS Bulletin, 49th DFD Meeting, 1996,41(9)
[29]	Kravchenko AG, Moin P. Numerical studies of flow over a circular cylinder at $Re_{D} = 3900$. Physical. Fluids, 2000,12:403-417 DOI URL
[30]	Chen L, Smolentsev S, Ni MJ. Toward full simulations for a liquid metal blanket: MHD flow computations for a PbLi blanket prototype at $Ha\sim 10^{4}$. Nuclear Fusion, 2020, in press
[31]	Ni MJ, Munipalli R, Morley NB, et al. A current density conservative scheme for incompressible MHD flows at a low magnetic Reynolds number. Part I: On a rectangular collocated grid system. Journal of Computational Physics, 2007,227(1):174-204
[32]	Ni MJ, Munipalli R, Huang P, et al. A current density conservative scheme for incompressible MHD flows at a low magnetic Reynolds number. Part II: On an arbitrary collocated mesh. Journal of Computational Physics, 2007,227(1):205-228
[33]	Ong L, Wallace J. The velocity field of the turbulent very near wake of a circular cylinder. Experiments in Fluids, 1996,20(6):441-453 DOI URL
[34]	Moin P, Mahesh K. Direct numerical simulation: a tool in turbulence research. Annual Review of Fluid Mechanics, 1998,30(1):539-578 DOI URL
[35]	Grötzbach G. Revisiting the resolution requirements for turbulence simulations in nuclear heat transfer. Nuclear Engineering and Design, 2011,241(11):4379-4390 DOI URL
[36]	Vreman AW, Kuerten JGM. Comparison of direct numerical simulation databases of turbulent channel flow at $Re_{\tau} = 180$. Physics of Fluids, 2014,26(1):015102 DOI URL
[37]	Lourenco LM. Characteristics of the plate turbulent near wake of a circular cylinder. A particle image velocimetry study. In Unpublished, results taken from Beaudan and Moin, 1994
[38]	Wissink JG, Rodi W. Numerical study of the near wake of a circular cylinder. International Journal of Heat and Fluid Flow, 2008,29(4):1060-1070 DOI URL
[39]	D'Alessandro V, Montelpare S, Ricci R. Detached-eddy simulations of the flow over a cylinder at $Re=3900$ using OpenFOAM. Computers & Fluids, 2016,136:152-169
[40]	Govardhan R, Williamson CHK. Modes of vortex formation and frequency response of a freely vibrating cylinder. Journal of Fluid Mechanics, 2000,420:85-130

DIRECT NUMERICAL SIMULATIONS ON THE TURBULENT FLOW PAST A CONFINED CIRCULAR CYLINDER WITH THE INFLUENCE OF THE STREAMWISE MAGNETIC FIELDS¹⁾

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