Direct Numerical Simulation Of Turbulent Taylor-Couette Flow In The Presence Of Axial Magnetic Field

As a classical flow of fluid dynamics,Taylor-Couette flow is widely investigated in hydrodynamics and magnetohydrodynamics,and also used as prototypes in the study of turbulence,due to its inherent features of wall-bounded and rotating turbulence.This kind of flow,or similar apparatus has various applications in industry and in astrophysics,especially in a strong magnetic field which making the scenario more complicated.However,with the limitation of current experimental technology,including the measurement of the turbulent velocity field,flow visualization of the optical liquid metal,and the manufacting of the strong magnetic field,it is difficult to implement such experiment.With low magnetic Reynolds number,which is suitable for most industrial applications,no experimental study has been reported.So,on this occasion,the direct numerical simulation(DNS)is introduced to investigate the MHD turbulence here.The analytical solution of Taylor-Couette flow in the presence of an axial magnetic field is deduced theoretically.It not only reveals the special effect of boundary conditions on the flow,but also verifies the DNS results and assists the data analysis.Then,the highly conservative finite difference scheme with second order accuracy is employed to perform the investigation of the effect of magnetic field on turbulent Taylor-Couette flow.Via comparing the turbulent statistic properties,the magnetic effect and their relations with the mean flow are studied.The turbulent coherent structures and streaks shown by using the visualization technology provides a deep insight to the flow for the readers.Combining with the variation of statistic properties,the formation of the flow field is also analyzed.In order to investigate the effect of the velocity and electrical boundaries on the flow,the following models are considered here.In the studies of infinitely long cylinders,three kinds of cylinder conditions are considered(equal-potential,perfectly insulating,and perfectly conducting).Since the rotation difference of the cylinders,the induced currents pass through the gap width,and generate negative Lorentz force with the interaction of magnetic field.When at small Hartmann number,the increased mean shear rate leads to the enhancement of turbulence.And then,increasing Hartmann numbers,the inner potential is offset by the outer part caused by the negative velocity,accompanying with the decreasing net current and the formation of saturation state.Since the effect of turbulent suppression effect is always enforced with increasing magnetic field,finally,the flow is relaminarized completely.Then,in insulating and conducting cylinders,since no closed electrical current circuit is formed between cylinders,the magnetic field will not affect the mean flow.But via the Joule dissipation of eddy currents,the turbulent kinetic energy is dissipated proportional to the strength of magnetic field,and finally the flow approaches to the laminar state.With increasing Hartmann numbers,the numbers of Taylor vortices decrease,showing consistence with the flow in longer cylinders.These results also present the stronger suppression effect while the cylinders are conducting,despite the evolution tendency in insulating and conducting cylinders are similar.At last,the turbulence confined between fixed endwalls and the corresponding Hartmann wall is studied.The Hartmann layers affect the flow properties by redistributing the current densities.In the bulk flow,at small and moderate Hartmann numbers(Ha<80),the variation tendency is consistent with the flow in infinitely long cylinders.When at great Hartmann number(Ha? 80),since the Hartmann layers are bearing on most of the currents,the main flow is changed obviously;and different scenarios are presented with different electrical boundary conditions.In the present works,the suppression effect of axial magnetic field on the turbulent Taylor-Couette flow,and the relaminarization tendency are revealed;and the suppression effect could be described by the Stuart number.In the equal-potential cylinders,the critical Stuart number is in the range between 1.8 and 3.6;in the insulating cylinders the critical Stuart number is greater than 3.6.The electrical boundary condition and the Hartmann layer will also affect the turbulence.Innovation in present work:(1)The effect of an strong magnetic field on turbulent Taylor-Couette flow is investigated;the effect on turbulent properties is analyzed with the evolutions of coherent structures and streaks.(2)The theoretical solutions of the considered flows are deduced here and employed to verify the DNS results in the strong magnetic field;and both of them indicate the significant impacts on the flow.(3)The Stuart number is found to be the proper parameter to estimate the effect of magnetic field on Taylor-Couette flow.(4)The formation of Hartmann layer is studied,accompanying with unique influence of electrical boundary on the turbulent behaviors.