Features of Transition to Turbulence in Sudden Expansion Pipe Flows

TL;DR

This study uses direct numerical simulations to analyze the transition to turbulence in sudden expansion pipe flows, revealing a power law threshold, a new shear-driven instability, and hysteresis effects in flow behavior.

Contribution

It identifies a new shear instability and characterizes the transition thresholds and hysteresis phenomena in sudden expansion pipe flows through detailed DNS analysis.

Findings

Power law scaling of transition threshold with -3 exponent

Discovery of a new shear-driven instability

Hysteresis in flow states depending on Reynolds number

Abstract

The complex flow features resulting from the laminar-turbulent transition (LTT) in a sudden expansion pipe flow, with expansion ratio of 1:2 subjected to an inlet vortex perturbation is investigated by means of direct numerical simulations (DNS). It is shown that the threshold for LTT described by a power law scaling with -3 exponent that links the perturbation intensity to the subcritical transitional Reynolds number. Additionally, a new type of instability is found within a narrow range of flow parameters. This instability originates from the region of intense shear rate which is a result of the flow symmetry breakdown. Unlike the fast transition, usually reported in the literature, the new instability emerges gradually from a laminar state and appears to be chaotic and strongly unsteady. Additionally, the simulations show a hysteresis mode transition due to the reestablishment of the recirculation zone in a certain range of Reynolds numbers. The latter depends on (i) the initial and final quasi-steady states, (ii) the observation time and (iii) the number of intermediate steps taken when increasing and decreasing the Reynolds number.