Benchmark on the Aerodynamics of a Rectangular 5:1 Cylinder (BARC)

Flows Around Bodies

Underlying Flow Regime 2-15

Best Practice Advice

Key physics and summary of the results

The flow past a rectangular cylinder of breadth to depth ratio equal to 5 is characterized by shear-layers detaching at the upstream cylinder corners and reattaching on the cylinder side rather close to the downstream corners. This leads to a complex dynamics and topology of the flow on the cylinder side, which adds to the vortex shedding from the rear corners and to the complex unsteady dynamics of the wake. Wind tunnel measurements and computational simulations provided by 10 research teams within the BARC benchmark and obtained from nominally common setups have been collected in a single ensemble of realizations in order to obtain statistics of several flow quantities, such as bulk parameters and chordwise pressure distributions. Some bulk parameters (e.g. the ${\left.St\right.}$ number) show narrow histograms, while others (e.g. the ${\left.t-std(C_{L})\right.}$ ) are significantly dispersed. The ${\left.t-std(C_{L})\right.}$ dispersion is recognized to be due to the high sensitivity of the flow along the side surface to small differences in the wind tunnel setup and in the simulation parameters. Consequently, the statistics of the pressure distribution on the cylinder lateral surfaces also show significant dispersion, both in wind tunnel measurements and in numerical simulations. Therefore, although it is not yet clear which results may be considered as the "most accurate", we assume as reasonable those results which do not deviate too much from the ensemble average of both the experimental and numerical contributions. Conversely, the wind tunnel measurements and the numerical predictions of base pressure, and, hence, of the drag have been found to be in overall very good agreement.

Finally, an asymmetry of the time-averaged flow has been recognized in both preliminary wind tunnel tests and in computational simulations. This may be again explained by the extreme sensitivity of the flow to small uncontrolled uncertainties which can, in some cases, trigger the asymmetry of the mean flow.

Flow conditions

As for the freestream turbulence intensity, perfectly smooth incoming flow is recommended for the computational studies using LES or DES, mainly because of the difficulties involved in the generation of realistic incoming turbulence features within these approaches. For wind tunnel tests, it is recommended to maintain the freestream turbulence intensity as low as possible and in any case lower than 2%, unless specific sensitivity studies to freestream turbulence are carried out.

The effect of Reynolds number has been investigated in LES simulations of a single contribution ${\left(2\times 10^{4}\leq Re_{D}\leq 4\times 10^{4}\right)}$ ; it has been shown that the impact is definitely limited compared to the overall dispersion of the results.

Turbulence modelling

URANS, LES and hybrid RANS/LES simulations were carried out. None of these approaches seems to reduce the result dispersion. For URANS, as expected the largest sensitivity is to turbulence model; the realizable k – ε model and the LEA k$ – &\omega; model give a mean pressure distribution on the cylinder very close to the ensemble average of the predictions of all the approaches. SGS modeling in LES has been found to have a limited impact on the results. As it could have been anticipated, 2D LES does not give reliable results. On the other hand, properly carried out 3D LES give reasonable results independently of the SGS model. Clearly, in general, the computational costs of LES are significantly larger than those of URANS. However, in VMS-LES on unstructured grids analogous accuracy is obtained with a coarse grid having a number of cells seven times lower than the ones adopted in other classical LES and this obviously leads to a significant reduction of the computational costs. As for hybrid RANS/LES approaches, no general conclusion can be drawn for the moment, due to the many different parameters involved and to the few contributions using this approach.

Computational domain

The streamwise and lateral dimensions of the computational domain should be larger than 20 ${\left.B\right.}$ . A significantly undersized domain introduces a basic source of discrepancy with respect to the BARC set-up, which frustrates further efforts in grid refinement and turbulence modeling. Sensitivity studies indicated that a spanwise domain size equal to ${\left.B\right.}$ , together with periodic boundary conditions in the spanwise direction, is adequate.

Grid resolution and topology

Grid independence has been established only for the RANS contributions. In LES the impact of grid resolution depends on closure modeling, on grid topology and on the numerical method. For instance, very close results have obtained in LES with a hybrid hexahedral grid and in Variational Multiscale LES on a completely unstructured tetrahedral grid, the latter having a number of cells seven times lower than that used in LES simulations. A striking impact of grid resolution in the spanwise direction has been highlighted in a single contribution; however, the results obtained for the finest considered grid resolution deviate significantly from the other contributions, including the experimental ones. The reasons for this behaviour are not clear at the moment and this point definitely deserves further investigation.

Numerical issues

The sensitivity to the numerical method, and, in particular, to the numerical dissipation has been investigated only in the DES simulations of a single contribution, in which it is shown that the length of the main recirculation zone becomes smaller with decreasing numerical dissipation. Note, however, that the sensitivity is likely to depend on the specific used numerical scheme.

Application uncertainties

The uncertainty sources in numerical simulations are different than in experiments, but all produce similar dispersion. This confirms the difficulty in identifying a reference experiment or simulation for the considered flow configuration, while ensemble statistics over a sufficiently large number of realizations seem to be more suitable to characterize at least some of the flow properties and of the aerodynamic loads. The main sources of uncertainties in experiments are the model quality and, in particular, the sharpness of the corners, the homogeneity and two-dimensionality of the incoming flow and the alignment between the model and the incoming flow. Sources of uncertainties in numerical simulations are {related to turbulence modeling}, numerical accuracy and dissipation, grid resolution and computational domain size and boundary location (together with boundary conditions).

Recommendations for Future Work

Propose further studies which will improve the quality or scope of the BPA and perhaps bring it up to date. For example, perhaps further calculations of the test-case should be performed employing more recent, highly promising models of turbulence (e.g Spalart and Allmaras, Durbin's v2f, etc.). Or perhaps new experiments should be undertaken for which the values of key parameters (e.g. pressure gradient or streamline curvature) are much closer to those encountered in real application challenges.

Contributed by: Luca Bruno, Maria Vittoria Salvetti — Politecnico di Torino, Università di Pisa