Error analysis of theoretical model of angular velocity sensor based on magnetohydrodynamics at low frequency

• 3D unsteady motion in closed rectangular channel has been deduced.
• Effects of secondary flow cannot be ignored in the theoretical model derivation.
• Inhomogeneity of magnetic field leads to the error of the simplified model.
• Magnetic field generated by the induced current is almost negligible.

The angular velocity sensor is commonly used in the navigation of aircrafts, ships and satellites, which can accurately determine the orientation of the moving objects. The angular velocity sensor based on magnetohydrodynamics (MHD) has a wide bandwidth, long life, impact resistance and other excellent properties. However, this sensor has poor performance at low frequency, and there are errors in the theoretical model. This paper presents the derivation of the simplified model by MHD governing equations and analyzes the three-dimensional unsteady motion of conducting fluid in the cylindrical container with a closed rectangular flow channel by the finite volume method. And then simulations and experiments are conducted in the amplitude-frequency and phase-frequency characteristics test, calibration experiment and slope test. Comparing the simplified model, the simulations and experiments, the conclusion can be drawn that the efforts of the secondary flow and the inhomogeneity of the magnetic field cannot be ignored; magnetic field generated by the induced current is almost negligible. The research results of this paper will provide a reference for improving low frequency performance of the sensor.