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

Flows Around Bodies

Underlying Flow Regime 2-15

Test Case Study

Brief Description of the Study Test Case

As previously mentioned, BARC addresses the high Reynolds number, external, unsteady flow over a stationary, sharp-edged smooth rectangular cylinder, and the associated aerodynamic loads [‌2]. The breadth ${(B)}$ to depth ${(D)}$ ratio is set equal to 5. A sketch of the configuration is shown in Fig. 2. The BARC test case gathered new wind tunnel tests in four different facilities [‌5, 7, 54, 56, 57] and computational simulations from six different teams [‌1, 8, 10, 11, 17, 26–28, 46, 71]; the UFR is mainly based on these contributions.

The following common requirements are set for both wind tunnel tests and numerical simulations:

the depth-based Reynolds number ${\left.{\text{Re}}_{D}=UD/\nu \right.}$ has to be in the range of ${2\times 10^{4}}$ to ${6\times 10^{4}}$ ;
the incoming flow has to be set parallel to the breadth of the rectangle, i.e. ${\left.\alpha =0\right.}$ , ${\left.\alpha \right.}$ being the angle of attack;
the maximum intensity of the longitudinal component of the freestream turbulence is set to ${\left.I_{x}=0.01\right.}$ ;
the minimum spanwise length of the cylinder for wind tunnel tests and 3D numerical simulations is set to ${\left.L/D=3\right.}$ .

The following additional requirements are specified for wind tunnel tests:

the maximum acceptable radius of curvature of the edges of wind tunnel models is set to ${\left.R/D=0.05\right.}$ ;
the maximum wind tunnel blockage is set to 5%;
all the points of measurement have to be outside the boundary layers developed at the tunnel walls;
uniformity of the flow at all measurement points must be checked in the empty tunnel and appropriately documented.

In addition to the main setup described above, sensitivity studies are strongly encouraged. The following additional values of the parameters are suggested for both wind tunnel tests and numerical simulations:

angles of incidence ${\left.\alpha =1^{\circ },3^{\circ },6^{\circ }\right.}$ ;
Reynolds number ${\left.{\text{Re}}_{D}=10^{3},10^{4},10^{5},10^{6}\right.}$ ;
turbulence intensity ${\left.I_{x}=0.02,0.05,0.10\right.}$ .

The flow quantities presented in the following are made dimensionless by using the undisturbed flow field velocity ${U}$ , the cylinder depth ${D}$ and the fluid density ${\rho }$ , unless specified otherwise.

Data can be uploaded to the BARC website by registered participants. Setup information and output data requested for numerical simulations and wind tunnel tests are set in Requests for Computational Simulations [‌3] and Requests for Wind Tunnel Tests [‌4], respectively. To summarize, statistics of pressure over the cylinder central section and at other give sections along the spanwise direction are required both in experiments and in computational contributions. Velocity statistics and time-histories of the aerodynamic loads are required in numerical studies and encouraged in wind-tunnel tests.

Most of the studies adopt incoming flow characteristics in accordance with the range prescribed by the BARC main setup (see above) and/or with the ones suggested for the sensitivity studies [e.g. turbulence intensity and length scale in 56, 57]. The adopted incoming flow features are summarized in Figure 1. As for the freestream turbulence intensity, all the computational studies using Large-Eddy Simulation (LES) or Detached Eddy Simulation (DES) turbulence approaches adopt perfectly smooth incoming flow, mainly because of the difficulties involved in the generation of realistic incoming turbulence features within these approaches. Conversely, perfectly smooth flow conditions cannot be obtained in wind tunnels, where a residual turbulence always exists; on the other hand, grid turbulence generation is a relatively easy and inexpensive task in wind tunnel tests. Hence, the mentioned differences among computational and wind tunnel approach do not allow to compare flowfields obtained exactly in the same conditions, but the complementary features of each approach allow the effects of incoming turbulence to be investigated in a collaborative framework. Figure 1b also shows that another parameter significantly varying among the different contributions is the freestream Reynolds number, even if it keeps the same order of magnitude and most of the values fall in the range specified in the BARC main setup.

In the following sections, the setup and objectives of both wind tunnel tests and computational simulations are shortly summarized.

Test Case Experiments

The main characteristics of the set-ups of the wind tunnel contributions to BARC are given in table 3. All the experimental contributions are aimed at reproducing as much as possible an unconfined 2D nominal flow, as in the requirements of the BARC benchmark: the ratio between the cylinder spanwise length, ${\left.L\right.}$ and ${\left.B\right.}$ ranges from 3 to 10.8, i.e. ${\left.L/D=15-54\right.}$ , and the blockage is generally lower than 2%, except for one case in Shirato et al. [‌57]. Three of the experimental contributions [‌5, 7, 54] are aimed at obtaining measurements for freestream conditions that are as smooth as possible. A different approach is that of the paper of Shirato et al. (2011), [‌57], in which the characteristics of the spanwise coherence of the aerodynamic action of rectangular cylinders with ${\left.B/D\right.}$ ratios ranging from 2.2 to 10 is investigated, for different intensity and scale of the incoming turbulence, obtained by means of three grid arrangements placed upstream of the model.

As for reduced scale models, it is worth pointing out that the tests performed by [‌5] are characterised by an ad hoc conceived, aluminum model shaped through a countersink procedure in order to obtain very accurate prismatic shape and sharp edges. The model adopted by [‌7] consists of plastic and wooden parts including interchangeable edge elements with radii of curvature of R/D = 0, 0.01, 0.02 and 0.5 to investigate the influence of edge sharpness on the flow. The model in [‌54] was originally used as a generic H-shaped section in a previous investigation and it has been adapted to obtain a rectangular 5:1 cylinder. All details concerning the model and the experimental arrangement can be found in [‌52]. The model used in [‌56, 57] is made of thin aluminum plate in its ${\left.B/D=5\right.}$ main set-up, while an additional frame made of foamed styrol is inserted between one side surface aluminum plate and the remaining open box-shape model in order to investigate further ${\left.B/D\right.}$ ratios.

As for measurement techniques and outputs, pressure taps placed on the model surface are used in [‌5, 7, 57] to provide the statistics of the pressure distribution at the body surface. The sampling frequency of pressure measurements was between 350 and 500Hz and in all cases it was found to be adequate to capture the flow fluctuations (we refer to [‌5, 7, 57] for more details). Unsteady aerodynamic loads are measured in [‌54] by means of a high-stiffness piezoelectric balance. Experiments are carried out in [‌54] for different angles of attack and for a wide range of Reynolds numbers ${(2\times 10^{4}\leq {\text{Re}}_{D}\leq 2\times 10^{6})}$ . In the following, only the case at ${\left.\alpha =0\right.}$ will be considered and the values of the forces measured for ${\left.{\text{Re}}_{D}=26400\right.}$ will be used for comparison, as also done in [‌27, 28], while the effects of Reynolds number will be briefly discussed in the following.

**Table 3: Wind tunnel tests: set-up characteristics. *L_x* is the streamwise integral length scale of oncoming flow turbulence.**
${\left.{\text{Source}}\right.}$	${\left.{\text{Re}}_{D}\right.}$	${\left.L/B\right.}$	${\left.{\text{Blockage}}\ (\%)\right.}$	${\left.I_{x}\ \%\right.}$	${\left.L_{x}/D\right.}$
Schewe [‌54]	${\left.26400\right.}$	${\left.10.8\right.}$	${\left.1.83\right.}$	${\left.0.4\right.}$	—
Bronkhorst et al. [‌7]	${\left.50000-100000\right.}$	${\left.4\right.}$	${\left.3.5\right.}$	${\left.0.32-0.56\right.}$	—
Bartoli et al. [‌5]	${\left.20000-80000\right.}$	${\left.7.93\right.}$	${\left.3.75\right.}$	${\left.1.6-2.1\right.}$	${\left.1.27-1.87\right.}$
Shirato et al. [‌57]	—	${\left.3.6\right.}$	—	${\left.10.5,11.5,14\right.}$	${\left.0.92-3.16\right.}$

As suggested in the guidelines of the BARC benchmark, the contributions by [‌7] and [‌5] report calibration studies of the model and of the wind tunnel set-up, and both point out the difficulties associated with obtaining a perfectly symmetric configuration. In particular several causes of asymmetry in the experiment conditions are identified and investigated, the main ones being the disturbances in the incoming flow, misalignment of the model with the incoming flow and inaccuracies in the model geometry. These three causes are separately analyzed in [‌7]. The two research teams use different approaches when aligning the model in the wind tunnel. [‌5] use a trial and error approach, by rotating the model, horizontally placed in the wind tunnel, around its axis, and checking the value of the stagnation pressure coefficient. The tests are then carried out for the angle giving the largest value of the stagnation pressure coefficient, which turns out to be equal to 1. This approach allows compensating for possible flow non symmetries. [‌7], on the other hand, align the model, vertically placed in the wind tunnel, such to have its faces perpendicular to the tunnel walls (a turntable permits an accuracy of 0.05°). This configuration brings a stagnation pressure coefficient of 1. In spite of the attention paid to the alignment of the model, both studies show a clear non symmetry in the mean and RMS pressure coefficients between the upper and lower faces. Conversely, [‌54], for all the considered Reynolds numbers and ${\left.\alpha =0\right.}$ , obtains values of the mean lift coefficient practically equal to zero, which indicate a symmetry of the mean flow. Asymmetries in the mean flow have also been observed in some of the numerical contributions and this issue will be discussed in detail in the Evaluation section.

CFD Methods

The various numerical contributions differ for physical modeling, numerical methods and simulation set-up. We refer to the original papers for a complete description, while an overview is herein given of those aspects which have been the object of extensive sensitivity studies by the contributors.

A first issue is clearly turbulence modeling. The different numerical studies cover a wide range of approaches to turbulence (see Tab. 4), even if the studies based on LES and DES prevail over the ones using Unsteady Reynolds Average (URANS) models, the latter being restricted to the works of Mannini et al. [‌26] and Ribeiro [‌46]. LES simulations represent the 51% of the numerical contributions, the DES ones the 30% and, finally, URANS computations the 29%. Nevertheless, a significant number of URANS models have been applied to the test case, thanks to the affordable computational cost of each simulation: 1-equation Spalart–Allmaras model (SA), Linearized Explicit Algebraic Wilcox k – ω model (LEA k – ω), Menter k – ω model (SST k – ω), realizable and RNG k – ε models, Reynolds Stress Model (RSM). Testing the performance of the URANS approach is surely useful in an engineering perspective, as industrial applications often require simple and cheap 2D URANS simulations to investigate a large number of flow parameters and geometry configurations [e.g. in 46]. As for LES, both the classical formulation and the Variational Multi Scale one (VMS-LES)} are tested in conjunction with a number of sub-grid models: Standard and Dynamic Smagorinsky Model (SM and DSM, respectively), Kinetic Energy one-equation model (KET), Wall-Adapting Local Eddy-viscosity (WALE) model. Finally, as for hybrid methods, both classical DES and Improved Delayed Detached Eddy Simulation (IDDES) are employed, where the SA model is adopted in the URANS part of the model. A more detailed description and the precise references for the adopted turbulence approaches and models can be found in the papers cited in Tab 4.

**Table 4: Computational studies: turbulence modeling**
		${\left.{\text{turbulence model}}\right.}$		${\left.L/B\right.}$	${\left.{\text{Blockage}}\ (\%)\right.}$	${\left.I_{x}\ \%\right.}$	${\left.L_{x}/D\right.}$