In this paper we address the problem of wall-shape optimization for axially symmetric corrugated pipes. The main objective is, to increase the flow rate in a periodic section of a pipe, by modifying the wall-shape from the traditional cylindrical shape. We tackle this problem by numerically solving the Navier-Stokes equations for the periodic section of the pipe. The numerical model is validated by comparing our numerical results with available experimental data on the pressure drop and friction factor.
The wall-shape optimization problem is tackled by considering a family of periodic pipes, in which the wall-shape is characterized by the amplitude, and the ratio between the lengths of expansion and contraction of the periodic section. We first study the effects of varying these parameters and then we show that for small Reynolds numbers the optimal shape turns out to be symmetric, while for large Reynolds numbers, a configuration with a large expansion region, followed by a short contraction region, performs better. The dependency of the optimal ratio on the pressure gradient is studied, and at the same time, we quantify the improvement in terms of flow rate (reduction in friction). Depending on the kind of geometry and the applied pressure gradient, the flow rate can be increased by 8%, for a geometry with small period. In the case of a geometry with large period, the flow rate increases by 35%, for large Reynolds number, and even 120% for small Reynolds numbers.