Perturbation threshold and hysteresis associated with the transition to turbulence in sudden expansion pipe flow

Minh Quan Nguyen (1) , Mostafa Safdari Shadloo (2) , Abdellah Hadjadj (2) , Benoit Lebon (3) , Jorge Peixinho (3)

1 LMFA - Laboratoire de Mecanique des Fluides et d'Acoustique
2 CORIA - Complexe de recherche interprofessionnel en aérothermochimie
3 LOMC - Laboratoire Ondes et Milieux Complexes

The complex flow resulting from the laminar-turbulent transition in a sudden expansion pipe flow, with expansion ratio of 1:2, subjected to an inlet parabolic velocity profile and a vortex perturbation, is investigated by means of direct numerical simulations. It is shown that the threshold amplitude for disordered motion is described by a power law scaling, with -3 exponent, as a function of the subcritical Reynolds number. The instability originates from a region of intense shear rate, which results on the flow symmetry breakdown. Above the threshold, several unsteady states are identified using space-time diagrams of the centreline axial velocity fluctuation and their energy. In addition, the simulations show a small hysteresis transition mode due to the reestablishment of the recirculation region in the subcritical range of Reynolds numbers, which 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.

Domaines: Milieux fluides et réactifs; Science non linéaire [physics]; Mécanique des fluides [physics.class-ph]

Minh Quan Nguyen, Mostafa Safdari Shadloo, Abdellah Hadjadj, Benoit Lebon, Jorge Peixinho. Perturbation threshold and hysteresis associated with the transition to turbulence in sudden expansion pipe flow. International Journal of Heat and Fluid Flow, 2019, 76, pp.187-196. ⟨10.1016/j.ijheatfluidflow.2019.01.018⟩. ⟨hal-02084275⟩