Two-Objective Shape Optimization of Sewers

Hydraulic characteristics of different sewer shapes are studied. The sewer must carry a very large flow rate for example in storm conditions, but most of the time there is very little flow at the bottom. This causes sedimentation of particles, which is avoided by having a high flow velocity. These are contradicting objectives in sewer design and therefore yield a multi-objective optimization problem. It is shown using a shape optimization procedure, that hydraulic characteristics of existing sewers can be improved. Using the optimization scheme, the Pareto-optimal solution of a shape optimization problem is found, for which the objectives are maximizing the flow velocity at low flow rates and maximizing the volume flow rate when the sewer is full. If the volume flow rate is to be maximized, almost a square cross-section is the best and the lower part of the sewer is very narrow if the velocity at the bottom is to be maximized. Hydraulic characteristics of sewers of different shapes are compared. In order to obtain optimal results in a reasonable time, an analytical treatment using the Manning formula is adopted and its results are compared with a numerical solution. Traditionally, in this kind of analysis the friction factor in the Manning formula is assumed constant. The validity of this assumption is confirmed using numerical modeling of flow (CFD).