UFR 2-15 Evaluation

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

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Comparison of CFD Calculations with Experiments

Bulk parameters

The main flow bulk parameters obtained in the different wind tunnel and numerical studies are reported in Tables 7 and 8: ${\left.t-avg(C_{D})\right.}$ and ${\left.t-avg(C_{L})\right.}$ are the time- and spanwise-averaged drag and lift coefficients per unit length, respectively; ${\left.t-std(C_{L})\right.}$ is the standard deviation of the time variation of the lift coefficient; ${\left.St_{D}=f_{s}D/U\right.}$ is the Strouhal number, where the shedding frequency ${\left.f_{s}\right.}$ is evaluated from the time fluctuations of the lift coefficient or from pressure or velocity time signals (we refer to the single cited articles for more details).

First of all, we remark that at present, among the different wind tunnel tests carried out in the framework of the BARC benchmark, bulk parameters are available only from Schewe [‌53, 54] and from Bartoli et al. [‌5] (only the Strouhal number). In general, several wind tunnel data are available in the literature for the flow around the same body geometry as far as the Strouhal number is concerned and only a few for the mean drag coefficient; these data are also reported in Table 7 for comparison. Conversely, bulk-parameter values computed in 25-36 simulations of the BARC configuration are available. The histograms of the bulk parameters obtained by computational simulations are plotted in Fig. 4. For the sake of brevity, detailed values are not given herein (we refer to the cited papers which may be made available upon request to the interested readers) and only the range of the results obtained in all the simulations carried out in each single contribution is reported in Table 8. The ensemble average over the available data and the standard deviation are also reported in Table 8. The data of the 2D LES in [‌1] and of the simulations in [‌71] have been excluded from the computation of the ensemble average and of the standard deviations, since they deviate significantly from the other data (see also the discussion below). Moreover, 2D LES is a priori expected to give unreliable results, while the simulations in [‌71] are probably affected by a too small size of the computational domain.

Figure 4: Computational results: histograms of the bulk parameters; (a) ${\left.t-avg(C_{D})\right.}$ over 36 realizations, (b) ${\left.t-avg(C_{L})\right.}$ over 36 realizations, (c) ${\left.t-std(C_{L})\right.}$ over 30 realizations, (d) ${\left.t\right.}$ over 25 realizations.

The values of ${\left.t-avg(C_{D})\right.}$ obtained in most of the simulations are very close to 1 and this is in good agreement with the available wind tunnel data. In particular, [‌54] obtains ${\left.t-avg(C_{D})\right.}$ equal to ${\left.1.029\right.}$ at ${\left.{\text{Re}}_{D}=26400\right.}$, while the measured values vary very little ${\left.(0.94\leq t-avg(C_{D})\leq 1.05)\right.}$ for ${\left.2\times 10^{4}\leq {\text{Re}}_{D}\leq 2\times 10^{6}\right.}$. Moreover, an overall good agreement is observed between the predictions obtained in the various numerical studies, in spite of the previously outlined differences in numerics, modelling and simulation set-up. Indeed, the standard deviation of the data remains lower than 5% of the ensemble-averaged prediction. It will be shown in the following that, although the characteristics of flow on the cylinder sides significantly vary among the different simulations, the near-wake structure and, consequently, both the base mean pressure (see Fig. 5b) and the mean drag coefficient, show only small differences. Only a few data deviate significant from the others: the 2D LES in [‌1] shows a discrepancy with the experimental value of [‌54] of 35% and the simulations in [‌71] a maximum discrepancy of 28%. Therefore, it appears that the choice of the computational domain may significantly affect also the prediction of quantities which are rather insensitive to modeling and to the other simulation parameters. By excluding these data, the LES contributions to BARC give ${\left.t-avg(C_{D})\in [0.96,1.04]\right.}$, while the URANS and hybrid simulations give ${\left.t-avg(C_{D})\in [0.965,1.295]\right.}$. The Strouhal number is another quantity for which the predictions given in the different simulations are rather close to each other and in good agreement with the available wind tunnel data. Since ${\left.St_{D}\right.}$ gives the dimensionless frequency of the vortex shedding behind the cylinder, this is a further confirmation that the dynamics of the near wake is satisfactorily captured in all the simulations in spite of the differences in the flow features on the cylinder lateral sides.

Conversely, the oscillations in time of the lift coefficient are very sensitive to the complex dynamics of the flow on the lateral cylinder sides. Indeed, a large spread of the numerical predictions is observed for the standard deviation of the lift coefficient. Note how the ensemble average of ${\left.t-std(C_{L})\right.}$ obtained in the different simulations is significantly larger than the only available wind tunnel value (Tab. 7). In this case, Arslan et al. [‌1] does not observe a significant difference between 2D and 3D simulations. However, in general, this quantity seems to be sensitive to many numerical, modeling and simulation parameters. Mannini and Schewe [‌28] show a significant impact of numerical dissipation, [‌10, 11] and [‌17, 18] point out a decrease of ${\left.t-std(C_{L})\right.}$ with increasing grid resolution, [‌17, 18] a decrease with increasing Reynolds number and [‌10, 11, 27] a decrease with increasing the spanwise extent of the computational domain. Finally, turbulence modeling has also a significant impact on the predictions of ${\left.t-std(C_{L})\right.}$: lower values are obtained in [‌27] in DES simulations than in URANS, while [‌71] generally find lower values in LES than in IDDES. Note, however, that the IDDES predictions of ${\left.t-std(C_{L})\right.}$ of [‌71] are significantly larger than those of the DES in [‌27]. Finally, [‌17, 18] and [‌1] also observe remarkable effects of the SGS model in the predictions of this quantity obtained in LES simulations.

Finally, the mean lift coefficient is a priori expected to be zero. Although values of ${\left.t-avg(C_{L})\right.}$ close to zero are obtained in most of the simulations, there are a few cases in which its absolute value is significant (Bruno et al. [‌10] and Wei and Kareem [‌71]). This might be due to the fact that the time interval used to compute the averaged quantities is not large enough to obtain statistical convergence. Nonetheless, in Bruno et al. [‌10], a careful check of the convergence of the averaged quantities is made, and, hence, at least in that case, the statistical sample may be assumed to be adequate. Therefore, it may be argued that a ${\left.t-avg(C_{L})\right.}$ value significantly different from zero is an indication of an asymmetry of the mean flow {which may be triggered by very small perturbations of different nature}. This point will be more deeply analysed in the following.

Table 7: Bulk parameters: wind tunnel data

${\left.\right.}$	${\left.t-avg(C_{D})\right.}$	${\left.t-avg(C_{L})\right.}$	${\left.t-std(C_{L})\right.}$	${\left.St_{D}\right.}$
Bartoli et al. [‌5]	—	—	—	${\left.0.12\right.}$
Schewe [‌53, 54]	${\left.1.029\right.}$	${\left.\sim 0\right.}$	${\left.\sim 0.4\right.}$	${\left.0.111\right.}$
Nakamura and Mizota [‌33]	${\left.\sim 1\right.}$	—	—	—
Nakamura and Yoshimura [‌34]	${\left.\sim 1\right.}$	—	—	—
Nakamura and Nakashima [‌35]	—	—	—	${\left.0.115\right.}$
Nakamura et al. [‌36]	—	—	—	${\left.0.118\right.}$
Okajima [‌41]	—	—	—	${\left.0.115\right.}$
Okajima [1983]	—	—	—	${\left.0.105\right.}$
Parker and Welsh [‌43]	—	—	—	${\left.0.105\right.}$
Stokes and Welsh [‌60]	—	—	—	${\left.0.105\right.}$
Knisely [‌22]	—	—	—	${\left.0.106\right.}$
Matsumoto [2005]	—	—	—	${\left.0.132\right.}$
Ricciardelli and Marra [‌47]	—	—	—	${\left.0.116\right.}$

Table 8: Bulk parameters: numerical results

${\left.\right.}$	${\left.t-avg(C_{D})\right.}$	${\left.t-avg(C_{L})\right.}$	${\left.t-std(C_{L})\right.}$	${\left.St_{D}\right.}$
Arslan et al. [‌1] 2D LES	${\left.1.39\right.}$	—	${\left.0.82\right.}$	${\left.0.16\right.}$
Arslan et al. [‌1] 3D LES	${\left.0.984{\text{ -- }}1.04\right.}$	—	${\left.0.59{\text{ -- }}0.84\right.}$	${\left.0.107{\text{ -- }}0.113\right.}$
Mannini et al. [‌27]	${\left.0.968{\text{ -- }}1.071\right.}$	${\left.0.0032{\text{ -- }}0.047\right.}$	${\left.0.42{\text{ -- }}1.075\right.}$	${\left.0.094{\text{ -- }}0.102\right.}$
Mannini et al. [‌26]	${\left.1.015{\text{ -- }}1.172\right.}$	—	${\left.0.108{\text{ -- }}1.12\right.}$	${\left.0.087{\text{ -- }}0.105\right.}$
Mannini and Schewe [‌28]	${\left.0.965{\text{ -- }}1.016\right.}$	${\left.-0.087{\text{ -- }}0.085\right.}$	${\left.0.173{\text{ -- }}0.553\right.}$	${\left.0.087{\text{ -- }}0.119\right.}$
Ribeiro [‌46]	${\left.1.17\right.}$	—	${\left.0.9\right.}$	${\left.0.073\right.}$
Grozescu et al. [‌18]	${\left.0.97{\text{ -- }}0.98\right.}$	${\left.-0.097{\text{ -- }}0.0043\right.}$	${\left.0.52{\text{ -- }}0.65\right.}$	${\left.0.107{\text{ -- }}0.11\right.}$
Grozescu et al. [‌17]	${\left.0.96\right.}$	${\left.0.0022\right.}$	${\left.0.35\right.}$	${\left.0.122\right.}$
Bruno et al. [‌10]	${\left.0.96{\text{ -- }}1.03\right.}$	${\left.-0.315{\text{ -- }}-0.0024\right.}$	${\left.0.2{\text{ -- }}0.73\right.}$	${\left.0.112{\text{ -- }}0.122\right.}$
Bruno et al. [‌8]	${\left.1.03\right.}$	—	${\left.0.73\right.}$	${\left.0.112\right.}$
Wei and Kareem [‌71]	${\left.1.165{\text{ -- }}1.305\right.}$	${\left.-0.33{\text{ -- }}0.42\right.}$	${\left.0.495{\text{ -- }}1.465\right.}$	—
ensemble average	${\left.1.002\right.}$	${\left.-0.04\right.}$	${\left.0.54\right.}$	${\left.0.107\right.}$
standard deviation	${\left.0.047\right.}$	${\left.0.10\right.}$	${\left.0.25\right.}$	${\left.0.011\right.}$
Shimada and Ishihara [‌55]	${\left.0.975\right.}$	—	${\left.0.03{\text{ -- }}0.12\right.}$	${\left.0.103{\text{ -- }}0.119\right.}$

Main flow features and statistics

The distribution of the pressure coefficient ${\left.Cp\right.}$, averaged in time (${\left.t-avg\right.}$ in the following), in the spanwise direction (${\left.z-avg\right.}$ in the following) and between the upper and lower half perimeters (${\left.side-avg\right.}$ in the following), is plotted in Fig. 5. Figure 5(a) collects the wind tunnel measurements, while Figure 5(b) collects the computational results. The abscissa ${\left.s\right.}$ denotes the distance from the cylinder leading edge measured along the cylinder side (see also Fig. 2). For the sake of completeness Figure 5(a) (and Fig. 8(a) in the following) also includes the data obtained in high turbulent incoming flows by Le et al. [‌23], even if the experimental setup significantly differs from the BARC main one. The data of Galli (2005) and Matsumoto (2005) are taken from Mannini et al. [‌27]. As a first remark, the mean pressure values given by the different wind tunnel and computational contributions to BARC on the rear side of the cylinder, ${\left.5.5\leq s/D\leq 6\right.}$, are very close to each other and in good agreement with the experimental data available in the literature (also reported in Fig. 5(a)), with the only exception of the RANS computation with the RSM model in Ribeiro [‌46]. As already mentioned, this leads to very similar predictions of the time averaged drag.

Figure 5: Side-averaged, spanwise-averaged and time-averaged ${\left.Cp\right.}$ distributions: wind tunnel (a) and computational (b) results.

Conversely, a significant spread of both wind tunnel and computational pressure values is observed in Fig. 5 on the lateral side of the cylinder. Figure 6 summarizes the ensemble statistics of the ${\left.C_{p}\right.}$ distributions on the lateral cylinder side; in particular, the range of the wind tunnel and numerical ${\left.C_{p}\right.}$ values is reported for 24 locations over the cylinder lateral side, together with the median, the 25-th and the 75-th percentile values ${\left.p_{25}\right.}$ and ${\left.p_{75}\right.}$, respectively, whiskers and outliers, if any. Points are drawn as outliers if they are larger than ${\left.p_{75}+w\left(p_{75}-p_{25}\right)\right.}$ or smaller than ${\left.p_{25}-w\left(p_{75}-p_{25}\right)\right.}$, being ${\left.w=1.5\right.}$ the maximum whisker length. It is worth pointing out that the subset of wind tunnel pressure data over which statistics are evaluated does not include the realizations obtained in high turbulent incoming flows [‌23], because such measurements do not belong to the same ensemble of smooth conditions.

The results of Bartoli et al. [‌5] are rather away from the remaining ones, which conversely well agree with each other. As for the numerical results, although most of the distributions are contained in a narrower range than the wind tunnel one (Figure 6), the shape of the mean pressure distribution significantly varies among the different simulations. The spread in the predictions of the mean pressure distribution is strictly linked with the differences in the mean flow topology obtained in the various simulations (see Fig. 7). Therefore, before analyzing in more detail the behaviour of the mean pressure coefficient on the cylinder lateral size, let us briefly describe the main features of the mean flow topology. The mean flow on the cylinder lateral side is characterized by a main recirculation zone (or main vortex as in [‌8]), whose size and shape significantly vary in the different contributions. To give a more precise quantification of this variability, Table 9 shows the ${\left.x\right.}$ coordinate at which the mean recirculation zone ends (mean reattachment location ${\left.x_{r}\right.}$) and the coordinates of the centre of the main recirculation zone. Only a subset of the contributions to BARC, for which these data were made available, is considered; as previously for the bulk coefficients, detailed values are not given in Table 9 for the sake of brevity (we refer to the cited papers), and only the range of the results obtained in all the simulations carried out in each single contribution is reported, together with the ensemble average and the standard deviation over all the available data. The value of ${\left.x_{r}\right.}$ deduced by Matsumoto et al. [‌29] from wind tunnel pressure measurements is also shown for reference {both in Table 9 and in Fig. 7 (red line). The data in Tab. 9 confirm a significant variability of the length and of the ${\left.x\right.}$ position of the centre of the mean vortex, while the normal distance from the cylinder of its centre remains almost constant. This leads to very different shapes and curvature of the mean streamlines at the edge of this main recirculation zone. Note how both the 2D simulation with no turbulence model by Tamura et al. [‌61] and the 2D LES by Arsan et al. [‌1] significantly underestimate the size of the main recirculation region. This again confirms that these kinds of 2D simulations, as it could have been anticipated, do not give reliable results. In most of the numerical contributions to BARC, a smaller recirculation is also visible very close to the lateral wall and immediately downstream of the upstream corner, which was already detected in [‌8] (see in particular Fig. 11 of [‌8]}, in which the mean flow structures are sketched). Again, its dimensions and shape vary significantly among the different simulations; in fact, in some cases it is hardly visible.

Figure 6: Statistics of the side-averaged, spanwise-averaged and time-averaged ${\left.Cp\right.}$ distributions: wind tunnel (a) and computational (b) results. The data of the 2D LES in [‌1] and those in [‌71] have not been included.

The distribution of the standard deviation of the time variation of the ${\left.Cp\right.}$ pressure coefficient, averaged also spanwise and between the upper and lower half perimeters, is plotted in Fig. 8. As an overall remark, a large spread among the different experimental and numerical predictions of this quantity is evident. In this case the variability is larger for the numerical results than for the wind tunnel measurements. More particularly, on the upstream side of the cylinder the ${\left.C_{p}\right.}$ standard deviation is very low in all the numerical simulations, while in most of the experiments is roughly around 0.05. This may be explained by the difference in the free-stream conditions, which are smooth in most of the numerical simulations, while turbulent fluctuations are present in the experiments, although the turbulence intensity is kept low. This is confirmed also by the fact that the data of [‌23], obtained for high levels of oncoming flow turbulence and reported in Fig. 8, show very large values of the ${\left.C_{p}\right.}$ standard deviation in the upstream part of the cylinder side. As for its mean value, the largest variability ${\left.C_{p}\right.}$ standard deviation is observed on the cylinder lateral side. In all cases there is a peak located slightly upstream of the reattachment of the main mean recirculation vortex, in the zone where the mean ${\left.Cp\right.}$ increases. In average, the peak is located more downstream and is more intense in numerical simulations than in experiments. By comparing the distributions of the standard deviation of ${\left.C_{p}\right.}$ obtained on the cylinder lateral surface in DES and LES simulations to those given by URANS models, quite surprisingly the differences in the intensity and location of the main peak are rather small; therefore, it seems that turbulence modeling has an effect on the dynamics of the flow over the lateral cylinder sides which is comparable to that of other sources of uncertainties present in the simulations and experiments. The main difference is that in DES and LES simulations, consistently with the wind tunnel measurements, the value of the standard deviation of ${\left.C_{p}\right.}$ has an unique peak along the cylinder side, while in the RANS ones a minimum is also found at a distance of approximately 2D from the upstream corner. The reasons {for} this behaviour are not clear at this stage.

Figure 7: Time and spanwise-averaged streamlines

Table 9: Mean reattachment location ${\left(x_{r}\right)}$ and coordinates of the centre of the mean recirculation zone ${\left(x_{c},y_{c}\right)}$

${\left.\right.}$	${\left.x_{r}\right.}$	${\left.x_{c}\right.}$	${\left.y_{c}\right.}$
Arslan et al. [‌1] 2D LES	${\left.0.66\right.}$	${\left.-1.24\right.}$	${\left.0.78\right.}$
Arslan et al. [‌1] 3D LES	${\left.2.07\div 2.29\right.}$	${\left.0.34\div 0.75\right.}$	${\left.0.81\div 0.82\right.}$
Mannini et al. [‌27]	${\left.2.25\right.}$	—	—
Mannini et al. [‌25]	${\left.1.72\div 2.06\right.}$	${\left.-1.44\div -0.05\right.}$	${\left.0.77\div 0.88\right.}$
Grozescu et al. [‌17]	${\left.1.65\div 2.1\right.}$	${\left.-0.97\div 0.09\right.}$	${\left.0.76\div 0.805\right.}$
Grozescu et al. [‌18]	${\left.1.64\right.}$	${\left.-0.17\right.}$	${\left.0.35,\ 0.82\right.}$
Bruno et al. [‌8]	${\left.2.18\right.}$	${\left.0.04\right.}$	${\left.0.8\right.}$
ensemble average	${\left.2.25\right.}$	${\left.-0.23\right.}$	${\left.0.804\right.}$
Wei and Kareem [‌71]	${\left.1.165{\text{ -- }}1.305\right.}$	${\left.-0.33{\text{ -- }}0.42\right.}$	${\left.0.495{\text{ -- }}1.465\right.}$	—
ensemble average	${\left.1.002\right.}$	${\left.-0.04\right.}$	${\left.0.54\right.}$	${\left.0.107\right.}$
standard deviation	${\left.0.047\right.}$	${\left.0.10\right.}$	${\left.0.25\right.}$	${\left.0.011\right.}$
Shimada and Ishihara [‌55]	${\left.0.975\right.}$	—	${\left.0.03{\text{ -- }}0.12\right.}$	${\left.0.103{\text{ -- }}0.119\right.}$

Figure 8: Side-averaged, spanwise-averaged distributions of the standard deviation in time of the ${\left.Cp\right.}$: wind tunnel (a) and computational (b) results

Symmetry of the mean flow

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

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