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 ${8.52H}$ . In the simulations, the flow is assumed to be spanwise homogeneous, with the spanwise slab being ${3.7H}$ . 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 ${25H}$ . 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:

{\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

The experimental working section is 5.49m long and 1.2m wide. The ramp height is 31.5mm, with an upstream section 660m long. The incoming flow velocity is fixed at 6.5m/s. Thirty-six pressure tapings are made along the ramp between ${x=-400mm}$ and 90mm with a spacing of 10mm or 20mm. To prevent an interference with the LDA measurement on the central streamwise plane of the ramp, the pressure tapings are located 25mm off this plane. Combined with the existing pressure tapings on the ceiling of the working section downstream of the ramp (150mm in spacing), the coverage of the pressure measurement is extended further up to 600mm. The velocity at the inlet of the test section is monitored using a Pitot tube. The pressure measurement system consists of a low-range pressure transducer and a scani-valve with forty-eight ports. The pressure sensor has a pressure range of -2.5mbar to 2.5mbar and an accuracy of 0.25% full scale span. The system is remotely controlled by a computer equipped with a data acquisition card. The pressure data are sampled at 1kHz and 10,000 data points are used to produce the time-averaged pressure at each tapping.

A three-component Dantec LDA system is used to measure the boundary layer development around the ramp-down section in both the streamwise and the spanwise direction. The laser beam generated by the 5W Argon ion laser is separated by a series of beam separators and colour filters inside the optic transmitter box to produce three pairs of beams with a wavelength of 512nm, 488nm and 476nm respectively. The averaged sampling rate in the freestream is about 1kHz and a lower rate of about 100Hz is obtained in the near-wall region. The number of realisations used to obtain the time-averaged velocity and turbulence fluctuations is set at 10K, and the time threshold for acquiring the data at each point is 30 seconds. The Dantec 3D traverse specially designed for this LDA system has a resolution of 6.25μm in the three directions. The uncertainty of measurements is about 4 ×10^-4 m/s in the freestream and 1.6 ×10^-3 m/s 1.6$\times 10^{-3}$ m/s in the near-wall region. All velocity components and all Reynolds stresses have been obtained, and the skin-friction is deduced from the LDA velocity measurements, assuming the first point being in the viscous sub-layer.

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: