Characterizing the Vibrational Modes of a Cavitating Bubble Immersed in a Magnetic Fluid

Sara Malvar¹; Rafael Gabler Gontijo¹; Francisco Ricardo Cunha¹

¹ UnB

doi:10.20906/CPS/COB-2015-0514

Resumo

The main goal of this article is to identify the vibrational patterns of an oscillating spherical bubble using Neural Networks. The gas bubble is immersed on a Newtonian fluid and subjected to an harmonic pressure excitation. The classical 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 motio, 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.

Palavras-chave: bubble dynamics; neural networks; cavitation; nonlinear dynamics; ferrofluids