Network numerical analysis of hydromagnetic squeeze film flow dynamics between two parallel rotating disks with induced magnetic field effects

摘要

We study numerically the hydromagnetic squeeze film between two rotating disks using the numerical network simulation method. The external magnetic field, H, generates an induced magnetic field, B, with radial (B_r), tangential (B_θ) and axial (B_z) components between the two disks, which rotate with different angular velocities, Ω_1 and Ω_2, and at time tare separated by a distance D(l - αt)~(1/2). The applied magnetic field at the lower disk is assumed to be zero. The conservation equations for mass, momentum and induced magnetic field are reduced to a set of ordinary differential equations using a series of transformations, in terms of four dependent variables, f (axial velocity), g (azimuthal velocity), m (axial magnetic field component) and n (azimuthal magnetic field component) and a single independent variable, η (dimensionless disk separation), with appropriate boundary conditions. The transformed ordinary differential equations have collective order of 10 and are shown to be controlled by rotational Reynolds number (R_1), squeeze Reynolds number (R_2 = Re_m/Bt), dimensionless parameter based on the magnetic force in the axial direction (R_3), dimensionless parameter based on magnetic force strength in the azimuthal (tangential) direction (R_4), magnetic Reynolds number (Re_m), disk rotational velocity ratio (S) and Batchelor number (Bt). In the present study we examine the flow regime at various Batchelor numbers (for the case of unity value of the squeeze Reynolds number, Re_m = Bt). Excellent comparison of NSM solutions is achieved with earlier analytical and shooting solutions. The present study finds applications in hydromagnetic lubrication of braking devices, slider bearings, rotating machinery, etc. Applications also arise in hydraulic shock absorbers employing electrically conducting liquids such as sodium where electro-magnetical braking of streams can be achieved in liquid metal cooled nuclear reactors for arresting control rods. Finally in the context of astronautical vehicles, the present study has applications in electromagnetic braking for potential spacecraft in planetary orbits.