Flow over curved backward-facing step

Semi-confined flows

Underlying Flow Regime 3-31

Test Case Study

Brief Description of the Study Test Case

The geometry under consideration is shown in Fig. \ref{fig:geometry}. The rounded ramp of height ${H}$ is placed in a high-aspect-ratio duct with upstream height of 8.52$H$. In the simulations, the flow is assumed to be spanwise homogeneous, with the spanwise slab being 3.7$H$. The assumption of homogeneity is justified by the fact that the experimental ratio of duct depth to the step height was 38. In the experiment \cite{zhang2010experimental}, tripped boundary layers were allowed to develop on both walls for a distance of about 25$H$. The Reynolds number, based on $H$ and the inlet free-stream velocity $U_{in}$, is 13,700. At $x/H$ = -7.4, the computational inlet, the momentum-thickness Reynolds number is $Re_\theta = 1192$, and the boundary-layer thickness is $\delta_{99} = 0.83H$.

The step geometry is based on that used originally by Song and Eaton \cite{song2004reynolds}. In order to enlarge the separated region, the height of the step was increased by a factor of 1.5. This adaptation was undertaken interactively with a parallel experiment by Zhang and Zhong \cite{zhang2010experimental}. The step shape is described by the following three relations, with the origin ${x/H=0}$ being the upstream edge of the ramp:

\displaystyle {y_{wall}=(1-R_{1})+{\sqrt {R_{1}^{2}-x_{2}}}\qquad \mathrm {for} \qquad 0<x/H\leq 2.3}

{\begin{aligned}y_{wall}&=(1-R_{1})+{\sqrt {R_{1}^{2}-x_{2}}}\qquad \mathrm {for} \qquad 0<x/H\leq 2.3\\y_{wall}&=y_{2}-{\sqrt {{\frac {1}{4}}R_{1}^{2}-(x_{2}-x)^{2}}}\qquad \mathrm {for} \qquad 2.3<x/H\leq 2.835\\y_{wall}&=R_{2}-{\sqrt {R_{2}^{2}-(3-x)^{2}}}\qquad \mathrm {for} \qquad 2.835<x/H\leq 2.937\\\end{aligned}}

with ${\ R_{1}=4.03}$ , ${\ R_{2}=0.333}$ , ${\ x_{2}=3.449}$ and ${\ y_{2}=1.936}$ and ${\ y_{wall}=1}$ for ${\ x/H<0}$ , ${\ y_{wall}=0}$ for ${\ x/H>2.937}$ .

Test Case Experiments

Provide a brief description of the test facility, together with the measurement techniques used. Indicate what quantities were measured and where.

Discuss the quality of the data and the accuracy of the measurements. It is recognized that the depth and extent of this discussion is dependent upon the amount and quality of information provided in the source documents. However, it should seek to address:

How close is the flow to the target/design flow (e.g. if the flow is supposed to be two-dimensional, how well is this condition satisfied)?

Estimation of the accuracy of measured quantities arising from given measurement technique

Checks on global conservation of physically conserved quantities, momentum, energy etc.

Consistency in the measurements of different quantities.

Discuss how well conditions at boundaries of the flow such as inflow, outflow, walls, far fields, free surface are provided or could be reasonably estimated in order to facilitate CFD calculations

CFD Methods

Provide an overview of the methods used to analyze the test case. This should describe the codes employed together with the turbulence/physical models examined; the models need not be described in detail if good references are available but the treatment used at the walls should explained. Comment on how well the boundary conditions used replicate the conditions in the test rig, e.g. inflow conditions based on measured data at the rig measurement station or reconstructed based on well-defined estimates and assumptions.

Discuss the quality and accuracy of the CFD calculations. As before, it is recognized that the depth and extent of this discussion is dependent upon the amount and quality of information provided in the source documents. However the following points should be addressed: