Eventos Anais de eventos
COBEM 2021
26th International Congress of Mechanical Engineering
MODELLING AND THEORETICAL ANALYSIS OF THE FLOW OF A ELECTRICALLY CONDUCTING FLUID IN THE PRESENCE OF HIGH FREQUENCY WAVES
Submission Author:
Leonardo Afonso da Silva Inácio , DF
Co-Authors:
Leonardo Afonso da Silva Inácio, Francisco Ricardo Cunha
Presenter: Leonardo Afonso da Silva Inácio
doi://10.26678/ABCM.COBEM2021.COB2021-1481
Abstract
The aim of this work is to model and analyze a compressible flow of a electrically conducting fluid in the presence of an expansional viscosity (i.e. high frequency flows). The non-dimensional form of the governing equations are obtained in terms of the fundamental physical parameters of the flow. The governing equations represent a coupling between hydrodynamics and Maxwell's equations in the context of magnetohydrodynamics, where the density of free charges is invariably very small in electrically conducting fluids. The set of governing equations are then linearized when considering the hydrodynamics and magnetic variables as the sum of their equilibrium value with an associated fluctuation of small amplitude around it. The resulting linearized equations has oscillatory nature and can be written in the form of a set of equations in the frequency-wave number space (i.e. Fourier space), from which, combined in a particular way, we obtain the dispersion relations for Alfvén and magnetoacoustic waves in the presence of a expansional viscosity effect and in terms of the main physical parameters of the flow. By the present analysis, we show how the dispersion relations of the different types of magnetic waves investigated are influenced by the extensional viscosity at high frequency compressible flows. In addition, the stability of the waves are examined, verifying if the fluctuations around the equilibrium state are stable or unstable disturbances. A rigours study in terms of the growth rate and of the phase velocities in Fourier space is presented as well as a discussion on the effects of the expansional high frequency effects in the growth rate and in the phase velocities of the waves. A model to determine or calibrate material constants of the constitutive relations using experimental measures of the wave properties is also proposed.
Keywords
Magnetohydrodynamics, Expansional Viscosity, Linear Stability Analysis, Magnetoacoustic Waves
