# Flow over curved backward-facing step

## Key Physics

The key physical features of this UFR that need to be correctly modelled are the position and the extent of the separation region. Both are very much a function of the performance of the model in three distinct regions: the turbulent boundary layer upstream of the separation (correct rise of turbulence level even upstream of nominal separation point), sufficient level of turbulent activity in the separated shear layer, and correct representation of the stabilizing effect of curvature to turbulence in separated shear layer.

## Numerical Issues and Boundary Conditions

• As the separation region is very thin, a fine wall-normal resolution is necessary everywhere in the flow domain.
• The flow is also very sensitive to the streamwise location of the separation point: a too late separation will lead to a too short bubble, and a too early one will lead to a too late reattachment. A precise prediction of the separation point is crucial, and this requires a fine mesh (of order ${\displaystyle {\ \Delta x^{+}\sim 8-10}}$) close to the theoretical separation region.
• The flow behaviour in the separated region is less sensitive to the correct prediction of the upper-wall boundary layer, and either a high-Re (ie. wall-function) formulation or a free-slip conditions can be used there, if computational cost is an issue.
• The inflow boundary condition is also important for consistency, and two possible definitions are detailed in the CFD section.

## Physical Modelling

• Both LES approaches, with dynamic SGS and mixed time-scale modelling, yield good results,
• Low-Reynolds number models are better at predicting the attached boundary layer upstream of separation and should thus be preferred to high-Reynolds number models with wall-functions. The effect of curvature is also important in this respect and specific treatment are needed if not using a Reynolds-stress model.

## Application Uncertainties

A careful assessment of the effect of the inflow condition on the results is necessary. The advice is to use the mean flow and turbulent kinetic energy extracted from the LES database if possible, but the length-scale should be extracted from a preliminary computation with the same model as the one tested, in order to match the boundary layer thickness and the wall-shear stress up to the separation point.

## Recommendations for Future Work

Unsteady methods, such as Hybrid RANS-LES are probably better suited to predict this type of flow separation than steady statistical models, Second-moment closure is also certainly attractive to predict this type of flows, from an industrial point-of-views and an example of how the database can be used for a priori testing of low-Reynolds-number Reynolds-stress models can be found in [‌2].

Contributed by: Sylvain Lardeau — CD-adapco, London, UK