Eddy structures in a transitional backward-facing step flow

Abstract

A quasi-implicit fractional-step method is presented for computing unsteady incompressible flow on unstructured grids. A non-staggered grid system is employed rather than a staggered grid system because of the simplicity and ease of extension to three-dimensional analysis. In this study, the momentum , is applied to problems on unstructured grids to resolve the pressure oscillation problem occurring in a non-staggered grid system. An implicit time advancing scheme is used in order to remove the time step restriction and to reduce the required CPU time for problems with complex geometries. The nonlinear equations resulting from this fully implicit scheme are linearized without deteriorating the overall time accuracy. The system matrices are solved using the CG family method, known with P-BiCGSTAB, for momentum equation and P-CG for pressure Poisson equation. The present numerical method is applied to solve four benchmark problems and the results show good agreement with previous experimental and numerical results.

Particle image velocimetry investigation of steady flow over a backwardfacing step

“…transverse oscillations of the separated streamline) as soon as the secondary separation region appeared (Re ~400-500). The highly energetic shear layer becomes unstable which breaks, leading to the formation of isolated convective vortices [15] and for a steady flow over a BFS, this phenomena can only be seen for Re > ~1500 [6]. The nearly linear increase of X R with Re suggests that the size 02018-p. 3 of the recirculation region scales directly with the circulation flux along the separated shear layer as discussed in the next section.…”

“…The steady flow over a BFS has received much interest over the past decades (e.g. [1][2][3][4][5][6]), mainly due to the abundance of competing physical phenomena (e.g. internal flow separation, shear layer instability, boundary layer growth, flow recirculation, vorticity flow, vortex shedding and flow reattachment) of practical pertinence.…”

“…[2,5,6,9,10,11,12,13,14,15]). Armaly et al [2] performed Laser-Doppler measurements of velocity distribution and reattachment length downstream of a BFS mounted in a 18:1 aspect ratio (step span/step height) channel for a wide range of Reynolds number, 70 < Re < 8000.…”

“…An upper wall recirculation region (secondary vortex) appears for Re > ~400 due to the adverse pressure gradient created by the sudden expansion. The flow field downstream the step becomes unsteady due to the complex interaction between these primary and secondary vortices [6]. These vortices have different sizes and characteristics.…”

Dynamically correct formulations of the linearised Navier–Stokes equations

“…In the context of simulation, the validity of numerical schemes is typically assessed by comparing certain time averaged properties, such as mean velocity profiles, to benchmark data from other simulations or experiments (see, e.g. [35,36,37,4,38]). On the other hand, models derived for control design must correctly capture the continuous time dynamics of both velocity and pressure fields in a single set of differential algebraic equations, and in particular must exhibit the correct frequency response, particularly around the unity gain crossover frequency.…”