Simulation-based optimization of driving waveforms in turbulent pipe flow

In practical applications, flows through pipes predominantly exhibit multi-scale eddying motion patterns, referred to as turbulence. Turbulence is responsible for the majority of the encountered friction and, therefore, accounts for vast amounts of the power input associated with steadily pumping fluids. Remarkably, in pulsatile driven flows, like for example aortic blood flows, features of turbulence are widely suppressed despite relatively large peak flow velocities during systolic phases. In the context of cardiovascular health, reducing turbulence levels and their accompanying phenomena, such as large shear stresses, is essential. From an energy perspective, compared to steady conditions, pulsatile driving can reduce the power input required to satisfy a desired mass flux. However, the specific shape of pulsation is a crucial factor when addressing the question if at all and to what extent, shear stress or power input can be reduced. In this regard, this thesis aims to identify periodic driving waveforms that are optimal in terms of reducing drag and saving power by, overall, diminishing features of turbulence. A simulation-based framework, guided by gradient-free black-box optimization routines, for identifying drag- or energy-optimal driving patterns is developed and applied to turbulent pipe flow. At Reynolds numbers comparable to those of aortic blood flow in large mammals, drag-optimal waveforms reduce shear by roughly up to 30%, whereas energy-optimal waveforms of different shape save up to 13% of energy. At higher flow velocities, the identical driving is capable of reducing drag by approximately 39% and power input by 21% when compared to steady driving. The results demonstrate that the predominant operation mode of steadily pumping fluids through pipes — responsible for an estimated 20% of the global electricity consumption — is far from top-tier effciency.