MHD reaction wheel for spacecraft attitude control: configuration analysis and numerical models

A novel actuator for spacecraft attitude control with liquid flywheel is presented. The main characteristic of this new concept of reaction wheel is that a conductive liquid rather than a solid mass is accelerated to change the angular momentum of the equipment and, as a consequence, to provide torque to the spacecraft. The conductive liquid is accelerated using a distributed Magneto-Hydro-Dynamic (MHD) conductive pump. Two different configurations of the device have been studied on the base of the optimization of the dimensionless moment of inertia and the minimization of the viscous shear. A 2-dimensional Finite Differences Hybrid Model (FDHM) has been developed on the base of the MHD set of equations under the hypothesis of low Magnetic Reynolds. The model solves numerically the time dependent axially symmetric problem of a conductive liquid rotating in a torus with rectangular cross section due to the interaction of a radial magnetic field and an axial electric field. The electric side of the problem has been solved by means of the node method applied to a network of electric resistances and voltage generators representing the back electromotive voltage induced by the spinning liquid through the magnetic field. The fluid-dynamics side of the problem has been solved using a Crank-Nicolson method over a non uniform and collocated grid. The grid generator has been written to be sensitive to the Hartmann number of the problem. A Lumped Parameter Model (LPM) has been then derived using a stationary and mono-dimensional analytical solution of the MHD set of equations under the hypothesis of low Magnetic Reynolds number. The LPM has been compared with the results obtained with the FDHM, showing good agreement in the estimation of the coefficients of the model. Finally, in order to understand the room for improvement of the performances of the device, a simplified lumped parameter model has been applied to a device with concentrated MHD conductive pumps.