Characterization Of Oscillation Instability Of A Three-dimensional Cubic Lid-driven Cavity Magnetohydrodynamic Flow Using SCM-ACM

In recent years,magnetohydrodynamics(MHD)has been widely applied in the fields of astrophysics,liquid metal cooling and flow control in nuclear reactions,magnetic fluid power generation,metal electromagnetic casting and so on.Industrial application of MHD involves flow instability and other basic theoretical problems,such as the MHD instability of the transition from steady flow to periodic oscillating flow.Due to the coupling of multiple physical fields and the complex physical mechanism,the study of MHD instability has become a hot and difficult topic in this field.In this paper,the MHD oscillation instability in a three-dimensional cubic cavity is studied.The high-precision numerical method SCM-ACM,which combines spectral collocation method and artificial compressibility method,is utilized to solve the control equations under the subcritical flow state.The instability transforms from a steady state to a periodic oscillating unsteady state of three-dimensional MHD lid-driven cavity(LDC)flow in a cube by the Hopf bifurcation is investigated with low intensity of magnetic flied.The influence of the external magnetic field on the critical Reynolds number(Re_cr)and critical dimensionless angular frequency(?_cr)when the flow state changes is analyzed.Under the condition of a certain direction of the magnetic field,the influence of the magnetic field strength on the velocity evolution,the decay of amplitude and oscillation frequency in the subcritical flow state is studied by increasing the magnetic field strength(Hartman number Ha=0?6).Under the condition of the same magnetic field intensity(Ha=4),the influence of the magnetic field direction on the velocity evolution,the decay of amplitude and oscillation frequency in the subcritical flow state is studied by changing the direction of the magnetic field(x-axis direction,y-axis direction and z-axis direction).The research results show that the velocity amplitude of the flow decays exponentially with time in the subcritical flow state under a certain intensity of magnetic field,and the decay rate decreases with the increase in the Reynolds number.The velocity oscillation has a single angular frequency,and value does not change with Reynolds number.The Re_cr number of the flow for the transition from steady to periodic oscillatory state is 1921.81,and?_cr is 0.5752 with the magnetic field strength is zero.With increase in Ha number,the Re_cr number of the transition becomes larger and larger,indicating that the magnetic field stabilizes the flow.When Ha=0?4,the increase of magnetic field intensity does not change the?_cr.However,it can be seen from the results that?_cr will decrease when Ha?5.The Ha number and Re_cr number that characterize the magnetic field strength accord with the strict parabolic relationship(Re_cr?1916.71+7.26Ha+3.79Ha²).When the magnetic field strength is constant(Ha=4),different magnetic field directions have different suppression effects on the oscillation instability of flow.When the direction of the magnetic field is along the z-axis,the suppression effect on the flow instability is the strongest,and the Re_cr number and?_crfor unstable transition is 2068.42 and 0.5513.The following is the x-axis direction,and the Re_cr number and?_cr for the unstable transition of oscillation is 2008.33 and 0.5752.The magnetic field in the direction of y-axis has the worst inhibitory effect on the oscillation instability of flow,and its corresponding Re_cr number and?_cris 2007.16 and 0.5752.