Abstract
The theoretical and numerical development of capillary networks for water transportation is documented here. The capillary network is made of dendritic structures connecting the sources to a sink (the outlet); water is extracted by capillary suction from those multiple random sources and the flow is conducted to one single outlet. The approach is based on the constructal law of evolutionary design. The development of the network starts with one channel, then sources are connected to the network one by one with the objective of transporting higher and higher flow rates through the network while decreasing the overall friction losses. For a fixed network volume, the capillary network generated in a plate has a higher flow rate compared to the one generated in a sphere. The average bifurcation angle from both cases which leads to a higher flow rate is 71°. The impact of the Hess-Murray’s law is discussed in the work. The higher volumetric flow rates are obtained when the radius exponent ratio between the mother and daughter channels ranges from 2 to 25 whilst the value is 3 according to Hess-Murray’s law. A transient numerical study of the capillary flow in the developed network is performed. The end of the transient regime leads to results equivalent to the ones obtained with the in-house approach, therefore validating it.
