On the origin of wave patterns in fluidized beds

摘要: In this report, a model designed for the description of flow two miscible phases in fluidized bed is discussed. Apart from basic problems modelling accurately such multi-phase flows, little analytical progress had been achieved investigation certain standard based on theory interacting continua. It turns out, however, that under consideration can be investigated with help bifurcation theory. particular, methods symmetry applied owing to symmetries system. general, stationary homogeneous state exists beds which become unstable when physical parameters system are varied. Then pattern formation takes place, e.g. form one- and/or two-dimensional waves, bubbles, or convection patterns; also turbulent behaviour has observed. order understand occurrence wave patterns and other phenomena as an inherent feature system, finite, but periodically continued investigated. While suppresses boundary effects, it gives us thorough insight into principal complicated allows not only perform easily linear stability analysis uniform fluidization, conclude travelling waves occurs becomes unstable. Well-known like vertical oblique (OTW) $u(x,y,t) = \tilde{u}(x-\omega t\pm ky)$ , k [ges ] 0, discovered. Owing symmetry, existence standing (STW) t, y)$ expected, regrettably no mathematically rigorous proof last conjecture presently available. Bubble approached via instability plane train transverse perturbations. secondary another kind place. This scenario agreement experimental observations. addition, bifurcations higher order, lead more complex found route turbulence, deduced.