Geometry optimization of elemental flow channels with asymmetric bifurcations

This dissertation investigates the optimal geometric characteristics of elemental flow channels with asymmetries due to geometry and mass distribution. The optimization techniques used follow the constructal approach [26]. The elemental flow channels considered in this dissertation include channels on circular discs, T-shaped channels in 2D and 3D and Y-shaped channels in 2D. Symmetric channel configurations have flow dividing into equal proportions at the junction and the source placed equidistantly between the outlets. Mass asymmetry is introduced by creating imbalance in the division of flow at the junction. Geometric asymmetry is introduced by moving the source away from the equidistant point between the outlets. During the optimization the local junction losses are assumed to be negligible and the inner walls of the channels are assumed to be smooth. The pressure drop across the channels is non-dimensionalized into flow resistance with respect to mass flow rate, the volume occupied by the channels and the area/volume influenced by the channels. The non-dimensional flow resistance is minimized to obtain optimal geometric characteristics in the form of length and diameter ratios of the channels sections. The dimensionless results can be applied in a broad range of length scales without losing generality of the optimization. The optimization results brought up important observations in both 2D and 3D channels. The optimal diameter ratio of symmetric channel sections is observed to depend only upon the number of branch sections. The optimal bifurcating angle in symmetric 2D Y-shaped channels is found to be a constant. Mass induced asymmetry is observed to reduce the flow resistance in all channel configurations where as geometric asymmetry tend to increase the flow resistance.