Non-linear dynamics in thermal and reactive fluid flows

Fundamentals of non-linear dynamics in thermal and reactive fluid flows are presented with some recent topics. The concept of phase space, attractor, dimension, Poincare section will be summarized. The mixing and reaction in a high viscous fluid in an eccentric flow system of outer cylindrical vessel and inner cylindrical rod is discussed experimentally and numerically. The very slow alternative motion of the outer vessel and inner rod induces the chaotic motion with stretching and holding of fluid element without any turbulence and perturbations which enhances the mixing. The results show that there are two regions: one is a well-mixed region, that is a chaotic region, and the other is hardly mixed island region, that is a regular region. The experimental results of complex mixing and reaction patterns coincide well with numerical results not only qualitatively but quantitatively. This indicates that the complex phenomena observed is not a random one but the deterministic one even though the phenomena observed is very complex. The mixing in the static mixer, Kenics type static mixer, is discussed which shows the chaotic mixing in the steady state flow system by elements installed in the mixer. The results show that the elements with simple structure make stretching and holding effectively and then the mixing is enhanced extensively. The non-element mixing devices are discussed as well. The results show that the periodic flow variation makes the similar effect of the elements in the static mixer. A short term forward prediction is also demonstrated, using a Bunsen flame with burner rotation. When the burner is rotated, the flame tip starts to oscillate significantly because of the effect of the centrifugal force. When the rotating speed is increased, the oscillating motion becomes complex from a limit cycle to chaotic motion. The results demonstrated that the short term forward prediction can be done by using a concept of the chaotic dynamics. Through these interesting topics, I would like to emphasize the importance of non-linear dynamics, especially chaotic dynamics, in the thermal and reactive systems.