Two-dimensional modal and non-modal instabilities in straight-diverging-straight channel flow

Abstract

A systematic study of a two-dimensional viscous flow through the straight-diverging-straight (SDS) channel defined by two straight-walled sections of different widths and a divergent section in-between is presented here. It has the plane Poiseuille flow (PPF) and the symmetric sudden expansion flow as the limiting cases. The topology of steady laminar flows and its bifurcations are characterized in the multi-parametric space formed by the divergence angle, the expansion ratio, and the Reynolds number. Three different steady flow regimes with two symmetric zones of recirculation, two asymmetric zones of recirculation, and the one with an additional third recirculation zone are observed with increasing Reynolds number. Modal stability analysis shows that the asymmetric flows remain stable at least up to Re = 300, regardless of the divergence angle and expansion ratio. Non-modal stability analyses are applied to SDS flows in the three topology regimes. A remarkable potential for transient amplification due to the Orr mechanism is found even for relatively low Reynolds numbers, which is related to the flow topology. The optimal energy amplification grows exponentially with the Reynolds number, as opposed to the substantially weaker Re2 scaling known for the lift-up mechanism dominant for PPF. This scaling holds for all divergence angles and is further increased by the expansion ratio, resulting in energy amplifications Gmax ∼ 104 for Reynolds numbers as low as Re ∼ 300. Present results suggest that the sub-critical transition due to transient growth is the most likely scenario for SDS flows at low Reynolds numbers.

Characterization of base bleed effects on subsonic trailing edge flows

“…The deflection of the flow in channel sudden expansion geometries is well documented [33,34,35,36], however, to the authors knowledge, only the references mentioned above include the appearance of a non-symmetrical configuration on two-dimensional base bleed configurations.…”

Direct numerical simulations of laminar and transitional flows in diverging pipes

“…Two-dimensional axisymmetric Navier–Stokes simulations also reported the effect of the diverging angle and Re on the onset of the laminar recirculations (Peixinho and Besnard, 2013). In diverging channel flow, Jobkar et al (Jotkar and Govindarajan, 2019; Jotkar et al , 2015) further showed the effect of the angle and the expansion ratio. Small angles delay the onset of the critical Re and small expansion ratios also delay the critical Re .…”

Study of the reverse transition in pipe flow

“…The reverse transitions did not depend on the ratio of pipe diameter to length. Various studies have examined divergent pipe flow or sudden expansion pipe flow 12 – 14 , 17 – 20 . If those studies had examined flow condition farther downstream, the reverse transition would have been observed.…”