Numerical Study of Bubble Breakup in Fractal Tree-Shaped Microchannels

Hydrodynamic behaviors of bubble stream flow in fractal tree-shaped microchannels is investigated numerically based on a two-dimensional volume of fluid (VOF) method. Bubble breakup is examined in each level of bifurcation and the transition of breakup regimes is discussed in particular. The pressure variations at the center of different levels of bifurcations are analyzed in an effort to gain further insight into the underlying mechanism of bubble breakup affected by multi-levels of bifurcations in tree-shaped microchannel. The results indicate that due to the structure of the fractal tree-shaped microchannel, both lengths of bubbles and local capillary numbers decrease along the microchannel under a constant inlet capillary number. Hence the transition from the obstructed breakup and obstructed-tunnel combined breakup to coalescence breakup is observed when the bubbles are flowing into a higher level of bifurcations. Compared with the breakup of the bubbles in the higher level of bifurcations, the behaviors of bubbles show stronger periodicity in the lower level of bifurcations. Perturbations grow and magnify along the flow direction and the flow field becomes more chaotic at higher level of bifurcations. Besides, the feedback from the unequal downstream pressure to the upstream lower level of bifurcations affects the bubble breakup and enhances the upstream asymmetrical behaviors

Optimization for Interval Type-2 Polynomial Fuzzy Systems:A Deep Reinforcement Learning Approach

It is known that the interval type-2 (IT2) fuzzy controllers are superior compared to their type-1 counterparts in terms of robustness, flexibility, etc. However, how to conduct the type reduction optimally with the consideration of system stability under the fuzzy-model-based (FMB) control framework is still an open problem. To address this issue, we present a new approach through the membership-function-dependent (MFD) and deep reinforcement learning (DRL) approaches. In the proposed approach, the reduction of IT2 membership functions of the fuzzy controller is completing during optimizing the control performance. Another fundamental issue is that the stability conditions must hold subject to different type-reduction methods. It is tedious and impractical to resolve the stability conditions according to different type-reduction methods, which could lead to infinite possibility. It is more practical to guarantee the holding of stability conditions during type-reduction rather than resolving the stability conditions, the MFD approach is proposed with the imperfect premise matching (IPM) concept. Thanks to the unique merit of the MFD approach, the stability conditions according to all the different embedded type-1 membership functions within the footprint of uncertainty (FOU) are guaranteed to be valid. During the control processes, the state transitions associated with properly engineered cost/reward function can be used to approximately calculate the deterministic policy gradient to optimize the acting policy and then to improve the control performance through determining the grade of IT2 membership functions of the fuzzy controller. The detailed simulation example is provided to verify the merits of the proposed approach