Iterative solvers and inflow boundary conditions for plane sudden expansion flows

Abstract

Incompressible laminar flow in a symmetric plane sudden expansion is studied numerically. The flow is known to exhibit a stable symmetric solution up to a critical Reynolds number above which symmetry-breaking bifurcation occurs. The aim of the present study is to investigate the effect of using different iterative solvers on the calculation of the bifurcation point. For this purpose, the governing equations for steady two-dimensional incompressible flow are written in terms of a stream function-vorticity formulation. A second order finite volume discretization is applied. Explicit and implicit solvers are used to solve the resulting system of algebraic equations. It is shown that the explicit solver recovers the stable asymmetric solution, while the implicit solver can recover both the unstable symmetric solution or the stable asymmetric solution, depending on whether the initial guess is symmetric or not. It is also found that the type of inflow velocity profile, whether uniform or parabolic, has a significant effect on the onset of bifurcation as uniform inflows tend to stabilize the symmetric solution by delaying the onset of bifurcation to a higher Reynolds number as compared to parabolic inflows.

New contributions on laminar flow of inelastic non-Newtonian fluid in the two-dimensional symmetric expansion: Creeping and slowly moving flow conditions

“…3 provides another interesting feature for the Re → 0.0 case, as it shows that the point of separation along the wall in expansion plane does not coincide with the sharp corner, but lies at a point along the vertical wall at some distance away from the sharp corner. A similar behaviour is reported for the Newtonian fluid flow at Re = 0 [16] and Re = 5 [17] as well as viscoelastic UCM and Oldroyd-B fluid [18,19], where the separation point is found to lay at some distance along the vertical wall from the sharp corner.…”

“…These corner regions are found to increase in length (in the direction of flow) as value of Re is increased. Clear presence of finite sized eddies for the creeping flow limit (Re = 0) of Newtonian fluid is also pointed out in the work of Wahba [16]. In addition, it is observed [16] that the separation point does not coincide with the sharp corner, but rather lies at a point along the vertical wall at some distance away from the sharp corner.…”

“…Clear presence of finite sized eddies for the creeping flow limit (Re = 0) of Newtonian fluid is also pointed out in the work of Wahba [16]. In addition, it is observed [16] that the separation point does not coincide with the sharp corner, but rather lies at a point along the vertical wall at some distance away from the sharp corner. Similar findings for the flow separation along the vertical wall in expansion plane were reported by Hawa and Rusak [17].…”

Planar sudden symmetric expansion flows and bifurcation phenomena of purely viscous shear-thinning fluids

“…Eq. (16) predicts the non-zero (finite) size vortices that are clearly present in creeping flows of Newtonian fluid through 1:3 [6] as well as 1:4 sudden expansions [24]. Of course, for more accurate predictions of finite size vortices with Eq.…”

Parallel pseudo-transient Newton–Krylov–Schwarz continuation algorithms for bifurcation analysis of incompressible sudden expansion flows

“…[14] 40.45(S), 44(E) Shapira et al (1990) [41] 107.5(L) 41.3(L) Durst et al (1993) [13] 62.5(S) Drikakis (1997) [12] 108(S) 40(S) 20.5(S) Foumeny et al (1996) [15] 40(S) Alleborn et al (1997) [1] 109(S)(L) 40(S) Battaglia et al (1997) [3] 112 [11] 92.5(S) 44(S) Mizushima and Shiotani (2000) [34] 40.23(S) Schreck and Schäfer (2000) [40] 40.7(S) Hawa and Rusak (2001) [22] 40.35(S)(L) Kadja and Bergeles (2002) [27] 100(S) Mishra and Jayaraman (2002) [33] 40.5(S) Wahba (2007) [45] 108 …”