Laminar, Isothermal Backward Facing Step Benchmark

In a flow system, where the flow cross-section expands too rapidly for the flow to follow, flow separation and subsequent reattachment may occur. There are numerous examples in engineering applications e.g. a wide angle diffuser, a sharp bend, or simply a junction between two channels with different cross-sections. Flow separation is associated with local flow direction reversal that manifests itself in a vortex formation. Such a flow anomaly causes additional pressure losses in the system.

Flow across a backward facing step is one of most studied validation cases in Computational Fluid Dynamics (CFD), mostly because of its simple geometrical arrangement and lack of adequate analytical solution of the flow field. Pressure and flow velocity although strongly coupled do experience significant changes.

The case of backward facing step tests coupling between the pressure field and the flow velocity. Due to rapid expansion of the flow cross-section, the pressure locally increases, causing flow variations across the channel crosssection, separation and subsequent flow recirculation.

Any modelling deficiency and/or numerical error (e.g. discretization inadequacy, numerical diffusion, equation under-relaxation) inevitably leads to inaccurate prediction of the extent of the recirculation region. Comparing computed velocity profiles and the flow reattachment location with the available experimental data [1], [2] should expose these deficiencies.

The inflow velocity profile consistent with the laminar flow regime is set at the inlet:

The fluid properties that correspond to incompressible and isothermal air shall be used: \(\rho\) is density of \(1.23 \mathrm{kg} / \mathrm{m}^{3}\)

\(\mu\) is dynamic viscosity of \(1.79 \cdot 10^{-5} \mathrm{Pa}\) s.

Steady-state problem, initial conditions can be arbitrary.

Vertical profiles of the velocity shall be extracted from the CFD simulation results and compared with the experimental data [1]

The diagrams below present two sets of such data for Reynolds number \(\left(\rho u_{\text {ave}} 2 h / \mu\right) 389\) and \(1095,\) respectively. Only a small subset of the experimental data is presented. The coordinate \(x\) represents the downstream distance from the step location and has been normalised with the step height \((S)\)

Another important parameter is the flow reattachment, which is characterised by the change in the flow velocity gradient: \(\partial_{y} u<0 \rightarrow \partial_{y} u>0\)

The reattachment length, which is the distance from the step to the location of the flow direction reversal, shall be calculated and compared to the experimental results \([6.1 \& 6.2\)]

Data summarises the experimental data in a table form to simplify the validation process. The quadratic mean (or RMS) of deviation can be used to quantify the level of agreement between both sets of results.