On the Sedimentation of a Blob of Particles Suspended in a Viscous Fluid - Cerqueira, Wilber; Gontijo, Rafael Gabler; Malvar, Sara (23rd ABCM International Congress of Mechanical Sciences and Engineering, 2015)
The main goal of this article is to identify the vibrational patterns of an oscillating spherical bubble immersed in a ferroﬂuid using Neural Networks. The gas bubble is immersed on a magnetic ﬂuid and subjected to an harmonic pressure excitation and an applied magnetic ﬁeld. The classical Rayleigh-Plesset equation is modiﬁed and a magnetic version is proposed in order to model the radial motion of the bubble. Being a very non-linear system, the correct identiﬁcation of the vibrational patterns is not possible using linear system tools. In this case, fuzzy logic and neural networks are a good solution for the correct pattern identiﬁcation. The magnetic version of Rayleigh-Plesset equation is a second order non linear ordinary differential equation and it is solved through a ﬁfth order Runge-Kutta scheme with adaptive time step. Four different vibrational patterns are identiﬁed and proposed regarding its frequency response and Lyapunov exponets. Based on the Lyapunov exponents it is possible to analyze its non-chaotic behavior. Those Lyapunov exponents are used in a backpropagation neural network to correctly identify the bubble vibration modes what could lead to the identiﬁcation of the ﬂow physical parameters in practical applications. In order to compare the performance, another neural network is trainned with the amplitude and frequency information of the bubble motion from ω= 0 to ω= 10, based on its Fast Fourier Transform. The new results are compared with previous simulations made with harmonic response in frequency spectrum, in which only the ﬁrst harmonic was considered