UFR 2-15 Description

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

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Description

Introduction

The Benchmark on the Aerodynamics of a Rectangular 5:1 Cylinder, BARC, is aimed at establishing a platform for discussion among scientists working on bluff body aerodynamics, and in particular it concerns the analysis of the turbulent, separated flow around an elongated rectangular cylinder. The characteristics of the flow field around rectangular bodies is of great interest both for fundamental research and for applications. From the fundamental research point of view, {in spite of the simple and nominally two-dimensional geometry, the flow over an elongated rectangular cylinder at high Reynolds numbers is highly complex, being three dimensional, turbulent and characterized by unsteady flow separation and reattachment. On the other hand, thanks to the simple geometry, a detailed analysis of the flow dynamics can be carried out, and different patterns, which can also be found when dealing with more complex geometries, can be identified}. As for applications, this benchmark problem provides useful information on the aerodynamics of a wide range of bluff bodies of interest in civil engineering (e.g. long-span bridge decks or high-rise buildings) as well as in other engineering areas. The 5:1 aspect ratio was chosen because it 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.

BARC is a blind benchmark, which has not adopted a single set of measurements as a reference at its launching. In this sense, the BARC differs, for instance, from the pioneering benchmark on the aerodynamics of the square cylinder [see for a review of the obtained results ‌49, 50, 68], included since the Nineties in the ERCOFTAC classic collection database [‌15] and now in the ERCOFTAC QNET-CFD Knowledge Base Wiki [‌16]. Indeed, this benchmark used as a reference the measurements by [‌24]. Coherently with the BARC aims, the lack of a reference set of measurement is intended to:

1. put the benchmark conditions closer to the common situation in many engineering flow problems;
2. collect as many as possible experimental and numerical data produced by different groups, in different facilities or by means of different numerical models and codes, but all within a common set-up as a-priori specified;
3. clearly describe the set-up uncertainties and the measure or modelling errors which affect both wind tunnel tests and computational simulations;
4. characterize the impact of these uncertainties on the measurements/predictions of the main flow quantities and, when possible, single out and analyse the effects of different set-up parameters;
5. assess the reliability and the dispersion of the measurements or of the numerical predictions of different quantities of practical interest
6. make available at its maturity a statistic database, which is expected to be further enriched and updated by new realisations;
7. give information useful to assess the possibility of developing integrated procedures relying on both wind tunnel and computational outcomes aimed at improving the reliability of the results, and, eventually, to develop Best Practice Advice for wind tunnel tests and computational simulations.

BARC was launched in 2008 with the support of ANIV (Italian National Association for Wind Engineering), IAWE (International Association for Wind Engineering) and ERCOFTAC (European Research Community On Flow, Turbulence And Combustion). The benchmark was announced first at the VI Colloquium on Bluff Body Aerodynamics and Applications (BBAA VI) and in a few international journals. A web site was also made available (http://www.aniv-iawe.org/barc), which provides all the details on the computational and experimental set-ups and on the data to be provided. Contribution to BARC could and can be made on a volunteer basis through registration to the website. During the first five years of activity, thematic sessions have been devoted to BARC at the 5th European and African Conference on Wind Engineering (EACWE, 2009, Florence), at the 5th International Symposium on Computational Wind Engineering (CWE, 2010, Chapel Hill) and at the 13th International Conference on Wind Engineering (ICWE, 2011, Amsterdam). The last thematic session {hosted} 9 contributions and a final synopsis and overview. Besides the contributions to the mentioned conference thematic sessions, five journal papers explicitly referring to BARC have been published up to now [‌8, 11, 12, 26, 27]. In particular, an in-progress overview after the first four years of activity is provided in [‌12].

Review of UFR studies and choice of test case

It is well known that two-dimensional (2D) rectangular cylinders are characterized by one single geometric parameter, i.e. the ratio of the alongwind dimension (Breadth) to the crosswind dimension (Depth), ${B/D}$, which} governs their aerodynamic behaviour (see e.g. [‌32, 60]). Other geometric (e.g. surface roughness, corner sharpness) and flow parameters (e.g. Reynolds number, turbulence intensity and scale) play a major or minor role, depending on the ${B/D}$ value and on their range of variability. For small ${B/D}$ ratios (${<2.5}$), the flow separates from the upstream corners and does nor reattach to the side faces of the cylinder, with vortex shedding occurring only from the upstream corners. For larger ${B/D}$ ratios, the shear layer impinges on the side faces of the cylinder. For moderate ${B/D}$ ratios (roughly between 2.5 and 3.5), reattachment is intermittent, and vortex shedding still occurs only from the leading edge. For ${B/D}$ ratios greater than 3.5, reattachment is permanent, and vortex shedding occurs from both the leading and the trailing edges. Under this circumstance, the flow patterns depends on ${B/D}$ in a discontinuous fashion. Trailing edge shedding is {influenced by the dynamics of the shear layer detaching at the upstream corners and impinging on the side face downstream of the separation bubble}; the breadth-based Strouhal number is a multiple of 0.55 ÷ 0.60, depending on the number of vortices simultaneously attached to each face of the cylinder (see e.g. [‌36, 60]). For B/D < 6 the Strouhal number is 1 ×(0.55 ÷ 0.60), for 6 < B/D < 9 the Strouhal number is 2 × (0.55 ÷0.60), for 9 < B/D < 12 it is 3 × (0.55 ÷ 0.60). It follows that the choice made for the BARC of a B/D ratio of 5 brings a completely reattached flow (B/D > 3.5), and simultaneously one single attached vortex on each face of the cylinder (B/D < 6).

In the following, the studies published prior to the BARC announcement are briefly reviewed in order to provide the context in which the BARC benchmark was launched. The overview is limited to the aerodynamics of rectangular cylinders with ${B/D}$ ratio equal to 5 or close to it, i.e. 3.5 ≤ B/D ≤ 6. Bearing in mind that BARC addresses both the wind tunnel and the computational approaches, they are discussed separately.

Review of previous experimental studies

The reviewed wind/water tunnel studies are chronologically listed in Table 1. For the sake of clarity, the listed references can be grouped in two subsets by referring to both the chronological and thematic criteria. The studies developed in the eighties and nineties mainly investigated the variability of the aerodynamic behaviour versus the ${B/D}$ ratio by means of force and/or velocity measurements. The more recent works focus their attention on the ratio ${B/D=5}$ and on the spanwise coherence of the flow by means of pressure measurements over the cylinder surface. From the results of wind and water tunnel experiments on rectangular prisms with ${B/D}$ = 1, 2, 3 and 4, at Reynolds numbers in the range of 70 to 20,000, the variation of the Strouhal number and flow characteristics with the Reynolds number was investigated in [‌41]. This study concluded that the minimum aspect ratio giving rise to flow reattachment is Reynolds number dependent, and tends to 2.8 at high Reynolds number. Conversely, the minimum Reynolds number giving rise to fully separated flow depends on the aspect ratio.

Table 1: Wind/water tunnel studies around rectangular cylinders {prior} to BARC. {B is the cylinder breadth, D the depth and L the spanwise length; I_u is the turbulence intensity of the oncoming flow}

${\left.{\text{Authors}}\right.}$	${\left.B/D\right.}$	${\left.{\text{Re}}_{D}\right.}$	${\left.L/D\right.}$	${\left.{\text{Blockage}}(\%)\right.}$	${\left.I_{u}(\%)\right.}$
Nakamura and Yoshimura [‌34]	${\left.0.2-5\right.}$	${\left.5500-140000\right.}$	${\left.10;25\right.}$	${\left.2;5\right.}$	${\left.0.1\right.}$
Okajima [‌41]	${\left.1-4\right.}$	${\left.200-20000\right.}$	${\left.13.3-100\right.}$	${\left.<2.5\right.}$	${\left.<0.5\%\right.}$
Okajima et al. [‌42]	${\left.1-9\right.}$	${\left.42000\right.}$	—	${\left.1\right.}$	${\left.0.4\right.}$
Parker and Welsh [‌43]	${\left.<52\right.}$	${\left.15000-31000\right.}$	${\left.203\right.}$	${\left.0.25\right.}$	${\left.0.2\right.}$
Stokes and Welsh [‌60]	${\left.<16\right.}$	${\left.8000-44300\right.}$	${\left.203-407\right.}$	${\left.0.25-0.49\right.}$	${\left.0.2\right.}$
Nakamura and Nakshima [‌35]	${\left.1-10\right.}$	${\left.2500-300000\right.}$	${\left.3-30\right.}$	${\left.\leq 6\right.}$	—
Nakamura et al. [‌36]	${\left.3-16\right.}$	${\left.1000-3000\right.}$	${\left.100\right.}$	${\left.0.17\right.}$	${\left.0.3\right.}$
Matsumoto et al. [‌29]	${\left.5\right.}$	—	${\left.15\right.}$	${\left.3\right.}$	—
Ricciardelli and Marra [‌47]	${\left.5\right.}$	${\left.63600\right.}$	${\left.38.7\right.}$	${\left.3.5\right.}$	${\left.\simeq 1\right.}$
Le et al. [‌23]	${\left.1;5\right.}$	${\left.18000-54000\right.}$	${\left.10.4\right.}$	—	${\left.9.5-11.5\right.}$
Ricciardelli [‌48]	${\left.5\right.}$	${\left.64000\right.}$	${\left.38.7\right.}$	${\left.3.5\right.}$	${\left.\simeq 1\right.}$

In [‌42] the variation of the drag and lift coefficients and of the Strouhal number with the aspect ratio was investigated, and the existence of an unsteady reattachment of the separated shear layer on the side surfaces for values of the aspect ratio in the range of 2.0 to 2.8 was pointed out. The effects that the application of sound has on the characteristics of the shear layer and of the separation bubble of rectangular cylinders with ${B/D}$ ratios up to 52 were analysed in [‌43] and [‌60]. Nakamura and Nakshima [‌35] suggested that for rectangular cylinders with ${B/D}$ in the range 3 – 15 the vortex shedding mechanism is not of Karman type, i.e. triggered directly by the interaction between upper and lower shear layers, but it is due to the impinging shear layer instability. They also showed that shear layer instability, vortex shedding and vortex excitation were possible also in the presence of a splitter plate, and observed that vortex excitation was possible for elastically suspended models for which hot-wire measurements had not shown sharp spectra at rest. Successively, in [‌36] the characteristics of vortex shedding from rectangular cylinders with ${\left.3<B/D<13\right.}$ was investigated, and the discontinuous variation of the Strouhal number earlier pointed out was found. In [‌29] the spanwise coherence of pressure fluctuations on a rectangular cylinder with ${\left.B/D=5\right.}$ was investigated through wind tunnel tests in smooth and turbulent flow. It was found that: (i) the pressure coherence is higher than that of the longitudinal component of the oncoming turbulence; (ii) the pressure fluctuation slightly upstream the reattaching point plays the most significant role in the evaluation of buffeting force. [‌47] discussed the sectional distribution of the statistics (mean, standard deviation, skewness and kurtosis) of the pressure coefficients on a rectangular stationary and vibrating cylinder with ${\left.B/D=5\right.}$, as derived from wind tunnel experiments. In addition the spanwise correlation of pressure fluctuations was also discussed, in the cases of smooth and turbulent incoming flow. In [‌48], the effects of the vibration regime on the spanwise correlation of aerodynamic forces and of stagnation and base pressure for a rectangular cylinder with ${\left.B/D=5\right.}$ were discussed, as derived from wind tunnel tests. [‌23] analysed the results obtained by means of wind tunnel tests for a highly turbulent incoming flow ($10\%\leq I_{x}\leq 12\%$) around a square and a rectangular 5:1 cylinder. First, statistics on chordwise pressure distribution were discussed. Second, Fourier and wavelet spectra of spanwise coherent turbulent structures and of pressure were analysed. The differences from the case of the fully separated and reattached flow were pointed out, and the larger coherence of pressures with respect to turbulent fluctuations was confirmed. [‌19] examined turbulence effects on the self-excited and buffeting forces on an oscillating rectangular prism having ${\left.B/D=6.67\right.}$.

Review of previous computational studies

Computational studies on the aerodynamics of rectangular cylinders available prior to the announcement of BARC are chronologically listed in Table 2. Both 2D and three-dimensional (3D) features of the low-Reynolds number flow ${(10^{2}\leq Re\leq 10^{3})}$ around rectangular cylinders have been clarified in several studies, e.g. [‌37, 39], [‌21, 65]. However, these Reynolds numbers being much lower than those of interest for BARC, these studies are not reviewed herein, and interested readers can refer to the cited papers and to their references. On the other hand, the high-Reynolds number flow conditions (i.e. ${Re\geq 10^{4}}$) have been investigated using computational techniques with special emphasis on the dependence of the aerodynamic behaviour on the chord-to-depth ratio, e.g. in [‌53, 63, 70]. In particular, Shimada and Ishihara [‌55] also investigated, among others, the rectangular 5:1 cylinder in a 2D domain with a two-layer modified k ε RANS turbulence model. Their computations succeeded in reproducing a smooth and periodic vortex shedding also at high Reynolds numbers, as well as the discontinuity in the Strouhal number at ${\left.B/D=2.8\right.}$ and ${\left.B/D=6.0\right.}$. Nonetheless, the pressure and force fluctuations were underestimated. The authors argued that this is due to Reynolds averaging of the Navier-Stokes equations. More recently, [‌69] carried out a numerical parametric study of the flow around rectangular cylinders having ${\left.B/D\right.}$ ranging from 0.3 to 7, by means of large-eddy simulations at ${\left.Re_{D}=10^{5}\right.}$. They found the reattachment of the separated flow on the cylinder side faces for ${\left.B/D\right.}$ from 3 and greater. The numerical results for aerodynamic forces and Strouhal numbers reproduced the trends observed in the experiments.

Table 2: Computational studies around rectangular elongated cylinders previous to BARC. Re_D is the Reynolds number based on the cylinder depth and the freestream velocity; the remaining symbols are the same as in Table 1

${\left.{\text{Authors}}\right.}$	${\left.{\text{Turbulence model}}\right.}$	${\left.B/D\right.}$	${\left.{\text{Re}}_{D}\right.}$	${\left.L/D\right.}$
Tamura et al. [‌61]	${\left.{\text{no model}}\right.}$	${\left.5\right.}$	${\left.10^{4}\right.}$	${\left.2\right.}$
Tamura and Ito [‌63]	${\left.{\text{no model}}\right.}$	${\left.0.6\leq B/D\leq 8\right.}$	${\left.10^{4}\right.}$	${\left.2\right.}$
Yu and Kareem [‌70]	${\left.{\text{LES}}\right.}$	${\left.1\leq B/D\leq 4\right.}$	${\left.10^{5}\right.}$	${\left.2\right.}$
Shimada and Ishihara [‌55]	${\left.{\text{URANS}}\right.}$	${\left.0.6\leq B/D\leq 8\right.}$	${\left.2\times 10^{4}\right.}$	${\left.0\ {\text{(2D)}}\right.}$

Tamura and Ito [‌63] discretized the 3D Navier–Stokes equations through a finite-difference technique at ${\left.Re=10^{4}\right.}$ and studied the mechanism of vortex formation for several rectangular cylinders with different ${\left.B/D\right.}$ ratios. To our knowledge, only Tamura et al. [‌61] focused on the rectangular 5:1 cylinder by using a finite-difference discretisation of the Navier–Stokes equations on structured O-grids in 2D and 3D. A third-order upwind scheme was adopted for the convective terms and no turbulence model was employed. The separation bubble was recognized to be responsible for irregularly fluctuating pressure patterns around the reattachment area on the side surface. The dynamic characteristics of the shear layer separated from the leading edge and the instability of the strong shear region to form the wake vortices were discussed by comparing two- and three-dimensional computed flows. In a successive work [‌62] also the forced oscillating cylinder was studied at the same incoming flow conditions by means of a 2D model. Finally, we recall that the aspect ratio ${\left.B/D=5\right.}$ was selected for the BARC benchmark with the specifications described in the study test case.

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

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