Turbulence Modeling for Oscillatory Pipe Flow

Oscillating pipe flows, with zero mean velocity, are common in engineering systems and particularly in Stirling-based engines and heat pumps, e.g. pulse-tube cryogenic coolers. These flows are particularly challenging to model because their flow state depends on both the Reynolds number and the dimensionless frequency or Womerlsey number. A central challenge in modeling these systems is that the Reynolds number varies greatly within the cycle, often crossing from laminar to turbulent flow regimes. Indeed, flows that have super-critical Reynolds numbers may pass between states a total of four times; two laminar-turbulent transitions and two turbulent-laminar transitions. Contrary to a steady flow in which the transition between the laminar and the turbulent regimes is affected only by the Reynolds number, for oscillating flow the transition is affected by a combination of Reos and a dimensionless frequency-based number such as Womersley (Wo). The objective of this work is to develop and validate a computational method that solves the incompressible oscillating flow equations for different combinations of Reos and Wo