Turbulent Kinetic Energy Transport in Oscillatory Pipe Flow

Abstract

Laminar as well as turbulent oscillatory pipe flows occur in many fields of biomedical science and engineering. Pulmonary air flow and vascular blood flow are usually laminar, because shear forces acting on the physiological system ought to be small. However, frictional losses and shear stresses vary considerably with transition to turbulence. This plays an important role in cases of e.g. artificial respiration or stenosis. On the other hand, in piston engines and reciprocating thermal/chemical process devices, turbulent or transitional oscillatory flows affect mixing properties, and also mass and heat transfer. In contrast to the extensively investigated statistically steady wall bounded shear flows, rather little work has been devoted to the onset, amplification and decay of turbulence in pipe flows driven by an unsteady external force. Experiments [1, 3, 6] indicate that transition to turbulence depends on only one parameter, i.e. Re_{\delta} \sim Re/Wo with a critical value of about 550, at least for Womersley numbers Wo > 7. We perform direct numerical simulations (DNS) of oscillatory pipe flows at several combinations of Re and Wo to extend the validity of this critical value to higher Wo. To better understand the physical mechanisms involved during decay and amplification of the turbulent flow, we further analyse the turbulent kinetic energy distribution and its budgets terms.