PATTERN IDENTIFICATION ON THE NONLINEAR MOTION OF AN OSCILLATING BUBBLE

Abstract

THE MAIN GOAL OF THIS ARTICLE IS TO STUDY THE OSCILLATORY MOTION OF AN SPHERICAL GAS BUBBLE IMMERSED IN A NEWTONIAN LIQUID SUBJECTED TO AN HARMONIC PRESSURE EXCITATION. WE USE THE CLASSICAL RAYLEIGH-PLESSET EQUATION TO STUDY THE RADIAL MOTION OF THE BUBBLE UNDERGOING A FORCING ACOUSTIC PRESSURE FIELD. THE SECOND ORDER NONLINEAR ORDINARY DIFFERENTIAL EQUATION THAT GOVERNS THE BUBBLEÂS MOTION IS SOLVED THROUGH A ROBUST FIFTH ORDER RUNGE-KUTTA SCHEME WITH ADAPTIVE TIME-STEP. SEVERAL INTERESTING PATTERNS ARE IDENTIFIED. FIRST WE DEVELOP AN ASYMPTOTIC SOLUTION FOR LOW AMPLITUDES OF EXCITATION PRESSURE TO VALIDATE OUR NUMERICAL CODE. THEN WE DEVELOP A BIFURCATION DIAGRAM IN ORDER TO SHOW HOW THE PARAMETERS OF THE FLOW MODIFY THE VIBRATIONAL PATTERNS OF THE BUBBLE. WE ALSO TRAIN A NEURAL NETWORK TO IDENTIFY THE VIBRATIONAL PATTERN THROUGH ITS FFT DATA. THE COMBINATION OF NEURAL NETWORKS WITH A BIFURCATION DIAGRAM COULD BE USEFUL FOR THE IDENTIFICATION OF THE FLOW PHYSICAL PARAMETERS IN PRACTICAL APPLICATIONS. FOR EACH PATTERN WE ALSO PROVIDE AN ANALYSIS OF THE MOTION OF THE BUBBLE ON THE PHASE-SPACE AND INTERPRET PHYSICALLY THE SYSTEMÂS BEHAVIOR WITH ITS FFT. IN ADDITION WE ANALYSE NONLINEAR PATTERNS USING STANDARD TOOLS OF DYNAMICAL SYSTEMS SUCH AS POINCAR ÌE SECTIONS AND CALCULATING THE LYAPUNOV EXPONENTS OF THE SYSTEM. BASED ON THAT, WE HAVE IDENTIFIED TOPOLOGICAL TRANSITIONS IN PHASE PLANE USING FOR INSTANCE THE ANALYSIS OF POINCAR ÌE SECTIONS AND THE SOLUTION IN THE FREQUENCY SPECTRUM. WE HAVE SEEN THAT THE MECHANISMS THAT DOMINATE THE DYNAMICS OF THE OSCILLATING BUBBLE IS THE COMPETITION OF THE ACOUSTIC FIELD EXCITATION WITH SURFACE TENSION FORCES AND MOMENTUM DIFFUSION THROUGH BY THE ACTION OF THE SURROUDING FLUID VISCOSITY.