Numerical analysis of laminar and transitional flow in a planar sudden expansion

The laminar and transitional flow through a planar sudden expansion with various expansion ratios is studied using two-dimensional direct numerical simulations at flow Reynolds numbers up to 5000 and expansion ratios in the range of 1.33 to 4.00. Results show the relationship between the reattachment length and the flow Reynolds number and expansion ratio. Correlations are developed for the non-dimensional reattachment length and the maximum velocity magnitude in the reverse-flow region in terms of Reynolds numbers and expansion ratios. The correlations and computed results achieve excellent agreement with published literature. Bifurcation phenomena resulting in the loss of flow symmetry downstream of the sudden expansion is observed and critical Reynolds numbers for the onset of bifurcation for various expansion ratios are identified. The initiation mechanism for bifurcation is attributed to the amplification of streamwise velocity disturbances at a spatial location that depends on the flow Reynolds number. For Reynolds numbers near the critical value for bifurcation onset, the disturbances grow from the sudden expansion, while for Reynolds numbers well above the critical value, the disturbances grow from the location of flow reattachment that occurred in the symmetric condition prior to bifurcation. Finally, the effect of the bifurcation phenomena on the development of flow unsteadiness and transition to turbulence downstream of the sudden expansion is linked to the successive formation of smaller-scale, steady recirculation zones. Transition is initiated by inviscid instability of the inflectional velocity profiles associated with these smaller-scale zones.