UFR 3-33 Test Case

Turbulent flow past a smooth and rigid wall-mounted hemisphere

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Test Case Study

Brief Description of the geometrical model

Fig. 1: Geometrical configuration of the wall-mounted hemisphere.

Description of the wind channel

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

Fig. 2: Wind tunnel applied for the experimental investigations.

Fig. 3: Dimensions and position of the hemisphere in the test section.

Measuring Techniques

Laser-Doppler anemometer

Fig 4: LDA configuration and measurement grid resolution of the symmetry x-z-plane.

Generation of artificial turbulent boundary layer

Fig. 5: Generation of a turbulent boundary layer with turbulence generators mounted onto the bottom wall of the wind tunnel's nozzle.

Fig. 6: Close view on the position of the vortex generators inside the nozzle.

Fig. 7: Inflow properties of the turbulent boundary layer at the inlet of the test section.

Numerical Simulation Methodology

CFD solver

To predict the turbulent flow around the hemisphere based on the large-eddy simulation technique, the three-dimensional finite-volume fluid solver FASTEST-3D is used. This in-house code is an enhanced version of the original one (Durst and Schäfer, 1996, Durst et al. 1996). To solve the filtered Navier-Stokes equations for LES, the solver relies on a predictor-corrector scheme (projection method) of second-order accuracy in space and time (Breuer et al., 2012). The discretization relies on a curvilinear, block-structured body-fitted grid with a collocated variable arrangement. The surface and volume integrals are calculated based on the midpoint rule. Most flow variables are linearly interpolated to the cell faces leading to a second-order accurate central scheme. The convective fluxes are approximated by the technique of flux blending (Khosla and Rubin, 1974, Ferziger and Peric, 2002) to stabilize the simulation. For the current case the flux blending includes 5% of a first-order accurate upwind scheme and 95% of a second-order accurate central scheme. A preliminary study shows that these settings are a good compromise between accuracy and stability. The momentum interpolation technique of Rhie and Chow (1983) is applied to couple the pressure and the velocity fields on non-staggered grids.

FASTEST-3D is efficiently parallelized based on the domain decomposition technique relying on the Message-Passing-Interface (MPI). Non-blocking MPI communications are used and offer a non negligible speed-up compared to blocking MPI communications (Scheit et al. 2014).

Numerical setup

Since LES is used, the large scales of the turbulent flow field are resolved directly, whereas the non-resolvable small scales have to be taken into account by a subgrid-scale (SGS) model. Different SGS models based on the eddy-viscosity concept are available in FASTEST-3D: The well-known and most often used Smagorinsky model (Smagorinsky, 1963), the dynamic Smagorinsky model according to Germano et al. (Germano et al., 1991) and Lilly (1992), and the WALE model (Nicoud and Ducros, 1999). Owing to the moderate Reynolds number considered and the fine grid applied, the SGS model is expected to have a limited influence on the results. Nevertheless, in order to investigate and verify this issue, simulations of the flow around the hemisphere are carried out applying the above mentioned SGS models. For this purpose, a constant inflow velocity profile (1/7 power law) without any turbulent fluctuations is assumed. The results are analyzed in Wood et al. (2016). This SGS investigation shows that the Smagorinsky model with $0.065\leq C_{s}\leq 0.1$ or the dynamic Smagorinsky model basically leads to the same results. The WALE model with $C_{W}=0.33$ (value corresponding to the classical Smagorinsky model with $C_{s}=0.1$ (Nicoud and Ducros, 1999)) produces a nearly identical flow except for the region upstream to the hemisphere. Therefore, as the best compromise between accurate results and fast computations, the standard Smagorinsky model with the constant set to $C_{s}=0.1$ is used for the present case.

Synthetic turbulent inflow generator

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:

• What numerical procedures were used (discretisation scheme and solver)?

• What grid resolution was used? Were grid sensitivity studies carried out?

• Did any of the analyses check or demonstrate numerical accuracy?

• Were sensitivity tests carried out to explore the effect of uncertainties in boundary conditions?

• If separate calculations of the assessment parameters using the same physical model have been performed and reported, do they agree with one another?

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Contributed by: Jens Nikolas Wood, Guillaume De Nayer, Stephan Schmidt, Michael Breuer — Helmut-Schmidt Universität Hamburg

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