Simultaneous optimization of topology and geometry of flow networks

摘要

We consider a problem of minimizing a pressure drop due to a flow of a fluid or gas through an interconnected system of pipes. We show that simultaneous optimization of pipe diameters and nodal positions (topology and geometry optimization) results for fluid networks in a better optimization strategy than traditionally used ground-structure approach (topology optimization only), as opposed to the linear truss case. We also show how the results for linear flow networks can be easily carried out to nonlinear transient and turbulent cases. Stating the optimality conditions for the latter types of flow, we give an alternative derivation of generalized Murray's law, which is well-known in physiology. We illustrate our theoretical findings with numerical examples.