View source for UFR 2-15 Evaluation

= Benchmark on the Aerodynamics of a Rectangular 5:1 Cylinder (BARC) =
{{UFRHeader
|area=2
|number=15
}}
__TOC__
== Flows Around Bodies ==
=== Underlying Flow Regime 2-15 ===    
= Evaluation =
<!--{{LoremIpsum}}-->
== 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
[[UFR_2-15_Evaluation#table7|Tables&nbsp;7]] and [[UFR_2-15_Evaluation#table8|8]]:
''t''&nbsp;-&nbsp;avg(''C<sub>D</sub>'') and ''t''&nbsp;-&nbsp;avg(''C<sub>L</sub>'') are the time- and spanwise-averaged
drag and lift coefficients per unit length, respectively;
''t''&nbsp;-&nbsp;std(''C<sub>L</sub>'')  is the standard deviation of the time variation of the lift coefficient;
St<sub>D</sub>&nbsp;=&nbsp;''f<sub>s</sub>D/U'' is the Strouhal number, where the shedding frequency ''f<sub>s</sub>'' 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&nbsp;[&#8204;[[UFR_2-15___References#53|53]],&nbsp;[[UFR_2-15_References#54|54]]] and
from Bartoli&nbsp;''et&nbsp;al.''&nbsp;[&#8204;[[UFR_2-15_References#5|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 [[UFR_2-15_Evaluation#table7|Table&nbsp;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 [[UFR_2-15_Evaluation#figure4|Fig.&nbsp;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 [[UFR_2-15_Evaluation#table8|Table&nbsp;8]].
The ensemble average over the available data and the standard deviation are also reported in [[UFR_2-15_Evaluation#table8|Table&nbsp;8]].
The data of the 2D LES in&nbsp;[&#8204;[[UFR_2-15_References#1|1]]]
and of the simulations in&nbsp;[&#8204;[[UFR_2-15_References#71|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&nbsp;priori'' expected to give unreliable results, while the simulations in&nbsp;[&#8204;[[UFR_2-15_References#71|71]]]
are probably affected by a too small size of the computational domain.


<div id="figure4"></div>
{|align="center" border="0" width="650"
|[[Image:UFR2-15_figure04.png|640px]]
|-
!align="center" style="text-align: left;"|'''Figure 4: Computational results: histograms of the bulk parameters; (a) <math>{\left.t-avg(C_D)\right.}</math> over 36 realizations, (b)  <math>{\left.t-avg(C_L)\right.}</math> over 36 realizations, (c) <math>{\left.t-std(C_L)\right.}</math> over 30 realizations, (d) <math>{\left.t\right.}</math> over 25 realizations.'''
|}


The values of ''t''&nbsp;-&nbsp;avg(''C<sub>D</sub>'') 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,&nbsp;[&#8204;[[UFR_2-15_References#54|54]]]
obtains ''t''&nbsp;-&nbsp;avg(''C<sub>D</sub>'') equal to 1.029 at Re<sub>D</sub>&nbsp;=&nbsp;26400,
while the measured values vary very little
(0.94&nbsp;&le;&nbsp;''t''&nbsp;-&nbsp;avg(''C<sub>D</sub>'')&nbsp;&le;&nbsp;1.05) for
2&nbsp;&times;&nbsp;10<sup>4</sup>&nbsp;&le;&nbsp;Re<sub>D</sub>&nbsp;&le;&nbsp;2&nbsp;&times;&nbsp;10<sup>6</sup>.
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 [[UFR_2-15_Evaluation#figure5|Fig.&nbsp;5b]]) and the mean drag coefficient, show only small differences.
Only a few data deviate significant from the others: the 2D LES in&nbsp;[&#8204;[[UFR_2-15_References#1|1]]]
shows a discrepancy with the experimental value of&nbsp;[&#8204;[[UFR_2-15_References#54|54]]]
of 35% and the simulations in&nbsp;[&#8204;[[UFR_2-15_References#71|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 ''t''&nbsp;-&nbsp;avg(''C<sub>D</sub>'')&nbsp;&isin;&nbsp;[0.96,&nbsp;1.04],
while the URANS and hybrid simulations give ''t''&nbsp;-&nbsp;avg(''C<sub>D</sub>'')&nbsp;&isin;&nbsp;[0.965,&nbsp;1.295].
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 St<sub>D</sub> 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 <math>{\left.t-std(C_L)\right.}</math> obtained in the different simulations is significantly larger than the
only available wind tunnel value ([[UFR_2-15_Evaluation#table7|Tab.&nbsp;7]]).
In this case, Arslan ''et&nbsp;al.''&nbsp;[&#8204;[[UFR_2-15_References#1|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&nbsp;[&#8204;[[UFR_2-15_References#28|28]]] show a significant impact of numerical dissipation,
[&#8204;[[UFR_2-15_References#10|10]],&nbsp;[[UFR_2-15_References#11|11]]]
and&nbsp;[&#8204;[[UFR_2-15_References#17|17]],&nbsp;[[UFR_2-15_References#18|18]]]
point out a decrease of <math>{\left.t-std(C_L)\right.}</math> with increasing grid resolution,
[&#8204;[[UFR_2-15_References#17|17]],&nbsp;[[UFR_2-15_References#18|18]]]&nbsp;a decrease with increasing Reynolds number
and&nbsp;[&#8204;[[UFR_2-15_References#10|10]],&nbsp;[[UFR_2-15_References#11|11]],&nbsp;[[UFR_2-15_References#27|27]]]
a decrease with increasing the spanwise extent of the computational domain.
Finally, turbulence modeling has also a significant impact on the predictions of <math>{\left.t-std(C_L)\right.}</math>:
lower values are obtained in [&#8204;[[UFR_2-15_References#27|27]]] in DES simulations than in URANS,
while&nbsp;[&#8204;[[UFR_2-15_References#71|71]]] generally find lower values in LES than in IDDES.
Note, however, that the IDDES predictions of <math>{\left.t-std(C_L)\right.}</math> of&nbsp;[&#8204;[[UFR_2-15_References#71|71]]]
are significantly larger than those of the DES in&nbsp;[&#8204;[[UFR_2-15_References#27|27]]].
Finally,&nbsp;[&#8204;[[UFR_2-15_References#17|17]],&nbsp;[[UFR_2-15_References#18|18]]]
and&nbsp;[&#8204;[[UFR_2-15_References#1|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&nbsp;priori'' expected to be zero.
Although values of <math>{\left.t-avg(C_L)\right.}</math> close to zero are obtained in most of the simulations, there are a few cases
in which its absolute value is significant (Bruno ''et&nbsp;al.''&nbsp;[&#8204;[[UFR_2-15_References#10|10]]]
and Wei and Kareem&nbsp;[&#8204;[[UFR_2-15_References#71|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&nbsp;al.''&nbsp;[&#8204;[[UFR_2-15_References#10|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 <math>{\left.t-avg(C_L)\right.}</math> 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.


<div id="table7"></div>
{|border="1" cellpadding="5" align="center" width = 720
|+ style="text-align: center;"|'''Table 7:  Bulk parameters: wind tunnel data'''
|align="left"|<math>{\left. \right.}</math>
|align="center"|<math>{\left.t-avg(C_D)\right.}</math>
|align="center"|<math>{\left.t-avg(C_L)\right.}</math>
|align="center"|<math>{\left.t-std(C_L)\right.}</math>
|align="center"|<math>{\left.St_D\right.}</math>
|-
|align="left"|Bartoli ''et al.'' [&#8204;[[UFR_2-15_References#5|5]]]
|align="center"|&mdash;
|align="center"|&mdash;
|align="center"|&mdash;
|align="center"|<math>{\left.0.12\right.}</math>
|-
|align="left" style="border-bottom:3px solid black;"|Schewe [&#8204;[[UFR_2-15_References#53|53]],&nbsp;[[UFR_2-15_References#54|54]]]
|align="center" style="border-bottom:3px solid black;" |<math>{\left.1.029\right.}</math>
|align="center" style="border-bottom:3px solid black;"|<math>{\left.\sim 0\right.}</math>
|align="center" style="border-bottom:3px solid black;"|<math>{\left.\sim 0.4\right.}</math>
|align="center" style="border-bottom:3px solid black;"|<math>{\left.0.111\right.}</math>
|-
|align="left" style="border-top:3px solid black;"|Nakamura and Mizota [&#8204;[[UFR_2-15_References#33|33]]]
|align="center" style="border-top:3px solid black;"|<math>{\left.\sim 1\right.}</math>
|align="center" style="border-top:3px solid black;"|&mdash;
|align="center" style="border-top:3px solid black;"|&mdash;
|align="center" style="border-top:3px solid black;"|&mdash;
|-
|align="left"|Nakamura and Yoshimura [&#8204;[[UFR_2-15_References#34|34]]]
|align="center"|<math>{\left.\sim 1\right.}</math>
|align="center"|&mdash;
|align="center"|&mdash;
|align="center"|&mdash;
|-
|align="left"|Nakamura and Nakashima [&#8204;[[UFR_2-15_References#35|35]]]
|align="center"|&mdash;
|align="center"|&mdash;
|align="center"|&mdash;
|align="center"|<math>{\left.0.115\right.}</math>
|-
|align="left"|Nakamura ''et al.'' [&#8204;[[UFR_2-15_References#36|36]]]
|align="center"|&mdash;
|align="center"|&mdash;
|align="center"|&mdash;
|align="center"|<math>{\left.0.118\right.}</math>
|-
|align="left"|Okajima [&#8204;[[UFR_2-15_References#41|41]]]
|align="center"|&mdash;
|align="center"|&mdash;
|align="center"|&mdash;
|align="center"|<math>{\left.0.115\right.}</math>
|-
|align="left"|Okajima [1983]<ref name="fn1">Reported in Mannini ''et al.'' [&#8204;[[UFR_2-15_References#27|27]]]</ref>
|align="center"|&mdash;
|align="center"|&mdash;
|align="center"|&mdash;
|align="center"|<math>{\left.0.105\right.}</math>
|-
|align="left"|Parker and Welsh [&#8204;[[UFR_2-15_References#43|43]]]
|align="center"|&mdash;
|align="center"|&mdash;
|align="center"|&mdash;
|align="center"|<math>{\left.0.105\right.}</math>
|-
|align="left"|Stokes and Welsh [&#8204;[[UFR_2-15_References#60|60]]]
|align="center"|&mdash;
|align="center"|&mdash;
|align="center"|&mdash;
|align="center"|<math>{\left.0.105\right.}</math>
|-
|align="left"|Knisely [&#8204;[[UFR_2-15_References#22|22]]]
|align="center"|&mdash;
|align="center"|&mdash;
|align="center"|&mdash;
|align="center"|<math>{\left.0.106\right.}</math>
|-
|align="left"|Matsumoto [2005]<ref name="fn1" />
|align="center"|&mdash;
|align="center"|&mdash;
|align="center"|&mdash;
|align="center"|<math>{\left.0.132\right.}</math>
|-
|align="left"|Ricciardelli and Marra [&#8204;[[UFR_2-15_References#47|47]]]
|align="center"|&mdash;
|align="center"|&mdash;
|align="center"|&mdash;
|align="center"|<math>{\left.0.116\right.}</math>
|}
<references />



<div id="table8"></div>
{|border="1" cellpadding="5" align="center" width = 720
|+ style="text-align: center;"|'''Table 8:  Bulk parameters: numerical results'''
|align="left"|<math>{\left. \right.}</math>
|align="center"|<math>{\left.t-avg(C_D)\right.}</math>
|align="center"|<math>{\left.t-avg(C_L)\right.}</math>
|align="center"|<math>{\left.t-std(C_L)\right.}</math>
|align="center"|<math>{\left.St_D\right.}</math>
|-
|align="left"|Arslan ''et al.'' [&#8204;[[UFR_2-15_References#1|1]]] 2D LES
|align="center"|<math>{\left.1.39\right.}</math>
|align="center"|&mdash;
|align="center"|<math>{\left.0.82\right.}</math>
|align="center"|<math>{\left.0.16\right.}</math>
|-
|align="left"|Arslan ''et al.'' [&#8204;[[UFR_2-15_References#1|1]]] 3D LES
|align="center"|<math>{\left.0.984 \text{ -- } 1.04\right.}</math>
|align="center"|&mdash;
|align="center"|<math>{\left.0.59 \text{ -- } 0.84\right.}</math>
|align="center"|<math>{\left.0.107 \text{ -- } 0.113\right.}</math>
|-
|align="left"|Mannini ''et al.'' [&#8204;[[UFR_2-15_References#27|27]]]
|align="center"|<math>{\left.0.968 \text{ -- } 1.071\right.}</math>
|align="center"|<math>{\left.0.0032 \text{ -- } 0.047\right.}</math>
|align="center"|<math>{\left.0.42 \text{ -- } 1.075\right.}</math>
|align="center"|<math>{\left.0.094 \text{ -- } 0.102\right.}</math>
|-
|align="left"|Mannini ''et al.'' [&#8204;[[UFR_2-15_References#26|26]]]
|align="center"|<math>{\left.1.015 \text{ -- } 1.172\right.}</math>
|align="center"|&mdash;
|align="center"|<math>{\left.0.108 \text{ -- } 1.12\right.}</math>
|align="center"|<math>{\left.0.087 \text{ -- } 0.105\right.}</math>
|-
|align="left"|Mannini and Schewe [&#8204;[[UFR_2-15_References#28|28]]]
|align="center"|<math>{\left.0.965 \text{ -- } 1.016\right.}</math>
|align="center"|<math>{\left.-0.087 \text{ -- } 0.085\right.}</math>
|align="center"|<math>{\left.0.173 \text{ -- } 0.553\right.}</math>
|align="center"|<math>{\left.0.087 \text{ -- } 0.119\right.}</math>
|-
|align="left"|Ribeiro [&#8204;[[UFR_2-15_References#46|46]]]
|align="center"|<math>{\left.1.17\right.}</math>
|align="center"|&mdash;
|align="center"|<math>{\left.0.9\right.}</math>
|align="center"|<math>{\left.0.073\right.}</math>
|-
|align="left"|Grozescu ''et al.'' [&#8204;[[UFR_2-15_References#18|18]]]
|align="center"|<math>{\left.0.97 \text{ -- } 0.98\right.}</math>
|align="center"|<math>{\left.-0.097 \text{ -- } 0.0043\right.}</math>
|align="center"|<math>{\left.0.52 \text{ -- } 0.65\right.}</math>
|align="center"|<math>{\left.0.107 \text{ -- } 0.11\right.}</math>
|-
|align="left"|Grozescu ''et al.'' [&#8204;[[UFR_2-15_References#17|17]]]
|align="center"|<math>{\left.0.96\right.}</math>
|align="center"|<math>{\left.0.0022\right.}</math>
|align="center"|<math>{\left.0.35\right.}</math>
|align="center"|<math>{\left.0.122\right.}</math>
|-
|align="left"|Bruno ''et al.'' [&#8204;[[UFR_2-15_References#10|10]]]<ref>Also in Grozescu ''et al.'' [&#8204;[[UFR_2-15_References#17|17]]]</ref>
|align="center"|<math>{\left.0.96 \text{ -- } 1.03\right.}</math>
|align="center"|<math>{\left.-0.315 \text{ -- } -0.0024\right.}</math>
|align="center"|<math>{\left.0.2 \text{ -- } 0.73\right.}</math>
|align="center"|<math>{\left.0.112 \text{ -- } 0.122\right.}</math>
|-
|align="left"|Bruno ''et al.'' [&#8204;[[UFR_2-15_References#8|8]]]
|align="center"|<math>{\left.1.03\right.}</math>
|align="center"|&mdash;
|align="center"|<math>{\left.0.73\right.}</math>
|align="center"|<math>{\left.0.112\right.}</math>
|-
|align="left" style="border-bottom:3px solid black;"|Wei and Kareem [&#8204;[[UFR_2-15_References#71|71]]]
|align="center" style="border-bottom:3px solid black;"|<math>{\left.1.165 \text{ -- } 1.305\right.}</math>
|align="center" style="border-bottom:3px solid black;"|<math>{\left.-0.33 \text{ -- } 0.42\right.}</math>
|align="center" style="border-bottom:3px solid black;"|<math>{\left.0.495 \text{ -- } 1.465\right.}</math>
|align="center" style="border-bottom:3px solid black;"|&mdash;
|-
|align="left" style="border-top:3px solid black;"|ensemble average<ref name="fn2">The data of the 2D LES
in&nbsp;[&#8204;[[UFR_2-15_References#1|1]]] and those in&nbsp;[&#8204;[[UFR_2-15_References#71|71]]]
have not been included in the computation of the ensemble average and of the standard deviation</ref>
|align="center" style="border-top:3px solid black;"|<math>{\left.1.002\right.}</math>
|align="center" style="border-top:3px solid black;"|<math>{\left.-0.04\right.}</math>
|align="center" style="border-top:3px solid black;"|<math>{\left.0.54\right.}</math>
|align="center" style="border-top:3px solid black;"|<math>{\left.0.107\right.}</math>
|-
|align="left" style="border-bottom:3px solid gray;"|standard deviation<ref name="fn2" />
|align="center" style="border-bottom:3px solid gray;"|<math>{\left.0.047\right.}</math>
|align="center" style="border-bottom:3px solid gray;"|<math>{\left.0.10\right.}</math>
|align="center" style="border-bottom:3px solid gray;"|<math>{\left.0.25\right.}</math>
|align="center" style="border-bottom:3px solid gray;"|<math>{\left.0.011\right.}</math>
|-
|align="left" style="border-top:3px solid gray;"|Shimada and Ishihara [&#8204;[[UFR_2-15_References#55|55]]]
|align="center" style="border-top:3px solid gray;"|<math>{\left.0.975\right.}</math>
|align="center" style="border-top:3px solid gray;"|&mdash;
|align="center" style="border-top:3px solid gray;"|<math>{\left.0.03\text{ -- }0.12\right.}</math>
|align="center" style="border-top:3px solid gray;"|<math>{\left.0.103\text{ -- }0.119\right.}</math>
|}
<references />

===Main flow features and statistics===
The distribution of the pressure coefficient <math>{\left.Cp\right.}</math>, averaged in time (<math>{\left.t-avg\right.}</math>
in the following), in the spanwise direction (<math>{\left.z-avg\right.}</math> in the following)
and between the upper and lower half perimeters (<math>{\left.side-avg\right.}</math> in the following),
is plotted in [[UFR_2-15_Evaluation#figure5|Fig.&nbsp;5]].
[[UFR_2-15_Evaluation#figure5|Figure&nbsp;5(a)]]
collects the wind tunnel measurements, while [[UFR_2-15_Evaluation#figure5|Figure&nbsp;5(b)]] collects the computational results.
The abscissa <math>{\left.s\right.}</math> denotes the distance from the cylinder leading edge measured along the cylinder side
(see also [[UFR_2-15_Test_Case#figure2|Fig.&nbsp;2]]).
For the sake of completeness [[UFR_2-15_Evaluation#figure5|Figure&nbsp;5(a)]]
(and [[UFR_2-15_Evaluation#figure8|Fig.&nbsp;8(a)]] in the following) also
includes the data obtained in high turbulent incoming flows by Le ''et&nbsp;al.''&nbsp;[&#8204;[[UFR_2-15_References#23|23]]],
even if the experimental setup significantly differs from the BARC main one.
The data of Galli&nbsp;(2005) and Matsumoto&nbsp;(2005) are taken from Mannini ''et&nbsp;al.''&nbsp;[&#8204;[[UFR_2-15_References#27|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, <math>{\left.5.5 \le s/D \le 6\right.}</math>, are very close to each other
and in good agreement with the experimental data available in the literature
(also reported in [[UFR_2-15_Evaluation#figure5|Fig.&nbsp;5(a)]]),
with the only exception of the RANS computation with the RSM model in Ribeiro&nbsp;[&#8204;[[UFR_2-15_References#46|46]]].
As already mentioned, this leads to very similar predictions of the time averaged drag.


<div id="figure5"></div>
{|align="center" border="0" width="650"
|[[Image:UFR2-15_figure05.png|640px]]
|-
!align="center" style="text-align: left;"|'''Figure 5: Side-averaged, spanwise-averaged and time-averaged <math>{\left.Cp\right.}</math> distributions: wind tunnel (a) and computational (b) results.'''
|}


Conversely, a significant spread of both wind tunnel and computational pressure values is observed
in [[UFR_2-15_Evaluation#figure5|Fig.&nbsp;5]] on the lateral side of the cylinder.
[[UFR_2-15_Evaluation#figure6|Figure&nbsp;6]] summarizes the ensemble statistics of the <math>{\left.C_p\right.}</math>
distributions on the lateral cylinder side;
in particular, the range of the wind tunnel and numerical <math>{\left.C_p\right.}</math> values is reported for
24 locations over the cylinder
lateral side, together with the median, the 25-th and the 75-th percentile values <math>{\left.p_{25}\right.}</math>
and <math>{\left.p_{75}\right.}</math>, respectively, whiskers and outliers, if any.
Points are drawn as outliers if they are larger than <math>{\left.p_{75} + w\left(p_{75} - p_{25}\right)\right.}</math> or
smaller than <math>{\left.p_{25} - w\left(p_{75} - p_{25}\right)\right.}</math>, being <math>{\left.w=1.5\right.}</math>
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&nbsp;[&#8204;[[UFR_2-15_References#23|23]]], because such measurements
do not belong to the same ensemble of smooth conditions.

The results of Bartoli ''et&nbsp;al.''&nbsp;[&#8204;[[UFR_2-15_References#5|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 ([[UFR_2-15_Evaluation#figure6|Figure&nbsp;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 [[UFR_2-15_Evaluation#figure7|Fig.&nbsp;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&nbsp;[&#8204;[[UFR_2-15_References#8|8]]]), whose size and shape significantly vary in the different contributions.
To give a more precise quantification of this variability, [[UFR_2-15_Evaluation#table9|Table&nbsp;9]] shows the
<math>{\left.x\right.}</math> coordinate at which
the mean recirculation zone ends (mean reattachment location <math>{\left.x_r\right.}</math>) 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 [[UFR_2-15_Evaluation#table9|Table&nbsp;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 <math>{\left.x_r\right.}</math> deduced by Matsumoto ''et&nbsp;al.''&nbsp;[&#8204;[[UFR_2-15_References#29|29]]]
from wind tunnel pressure measurements is also shown for
reference {both in [[UFR_2-15_Evaluation#table9|Table&nbsp;9]] and in [[UFR_2-15_Evaluation#figure7|Fig.&nbsp;7]] (red line).
The data in [[UFR_2-15_Evaluation#table9|Tab.&nbsp;9]] confirm a significant variability of the length
and of the <math>{\left.x\right.}</math> 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&nbsp;al.''&nbsp;[&#8204;[[UFR_2-15_References#61|61]]]
and the 2D LES by Arsan ''et&nbsp;al.''&nbsp;[&#8204;[[UFR_2-15_References#1|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&nbsp;[&#8204;[[UFR_2-15_References#8|8]]]
(see in particular Fig. 11 of&nbsp;[&#8204;[[UFR_2-15_References#8|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.


<div id="figure6"></div>
{|align="center" border="0" width="650"
|[[Image:UFR2-15_figure06.png|640px]]
|-
!align="center" style="text-align: left;"|'''Figure 6: Statistics of the side-averaged, spanwise-averaged and time-averaged <math>{\left.Cp\right.}</math> distributions: wind tunnel (a) and computational (b) results. The data of the 2D LES in&nbsp;[&#8204;[[UFR_2-15_References#1|1]]] and those in&nbsp;[&#8204;[[UFR_2-15_References#71|71]]] have not been included.'''
|}


The distribution of the standard deviation of the time variation of the <math>{\left.Cp\right.}</math> pressure coefficient,
averaged also spanwise and between the upper and lower half perimeters, is plotted in [[UFR_2-15_Evaluation#figure8|Fig.&nbsp;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 face of the cylinder the <math>{\left.C_p\right.}</math> 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&nbsp;[&#8204;[[UFR_2-15_References#23|23]]], obtained for high levels of
oncoming flow turbulence and reported in [[UFR_2-15_Evaluation#figure8|Fig.&nbsp;8]], show very large values of the
<math>{\left.C_p\right.}</math> standard deviation in the upstream part of the cylinder side. 
As for its mean value, the largest variability <math>{\left.C_p\right.}</math> 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 <math>{\left.Cp\right.}</math> increases.
On 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 <math>{\left.C_p\right.}</math> 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 <math>{\left.C_p\right.}</math> 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.  


<div id="figure7"></div>
{|align="center" border="0" width="650"
|[[Image:UFR2-15_figure07.png|640px]]
|-
!align="center" style="text-align: center;"|'''Figure 7: Time and spanwise-averaged streamlines'''
|}



<div id="table9"></div>
{|border="1" cellpadding="5" align="center" width = 720
|+ style="text-align: center;"|'''Table 9:  Mean reattachment location <math>{\left(x_r\right)}</math> and coordinates of the centre of the mean recirculation zone <math>{\left(x_c, y_c\right)}</math>'''
|align="left"|<math>{\left. \right.}</math>
|align="center"|<math>{\left.x_r\right.}</math>
|align="center"|<math>{\left.x_c\right.}</math>
|align="center"|<math>{\left.y_c\right.}</math>
|-
|align="left"|Arslan ''et al.'' [&#8204;[[UFR_2-15_References#1|1]]] 2D LES
|align="center"|<math>{\left.0.66\right.}</math>
|align="center"|<math>{\left.-1.24\right.}</math>
|align="center"|<math>{\left.0.78\right.}</math>
|-
|align="left"|Arslan ''et al.'' [&#8204;[[UFR_2-15_References#1|1]]] 3D LES
|align="center"|<math>{\left.2.07\div 2.29\right.}</math>
|align="center"|<math>{\left.0.34\div 0.75\right.}</math>
|align="center"|<math>{\left.0.81\div 0.82\right.}</math>
|-
|align="left"|Mannini ''et al.'' [&#8204;[[UFR_2-15_References#27|27]]]<ref>Reported in Arslan ''et al.'' [&#8204;[[UFR_2-15_References#1|1]]]</ref>
|align="center"|<math>{\left.2.25\right.}</math>
|align="center"|&mdash;
|align="center"|&mdash;
|-
|align="left"|Mannini ''et al.'' [&#8204;[[UFR_2-15_References#25|25]]]
|align="center"|<math>{\left.1.72 \div 2.06\right.}</math>
|align="center"|<math>{\left.-1.44 \div -0.05\right.}</math>
|align="center"|<math>{\left.0.77 \div 0.88\right.}</math>
|-
|align="left"|Grozescu ''et al.'' [&#8204;[[UFR_2-15_References#17|17]]]
|align="center"|<math>{\left.1.65 \div 2.1\right.}</math>
|align="center"|<math>{\left.-0.97 \div 0.09\right.}</math>
|align="center"|<math>{\left.0.76 \div 0.805\right.}</math>
|-
|align="left"|Grozescu ''et al.'' [&#8204;[[UFR_2-15_References#18|18]]]
|align="center"|<math>{\left.1.64\right.}</math>
|align="center"|<math>{\left.-0.17\right.}</math>
|align="center"|<math>{\left.0.35,\ 0.82\right.}</math>
|-
|align="left"|Bruno ''et al.'' [&#8204;[[UFR_2-15_References#8|8]]]
|align="center"|<math>{\left.2.18\right.}</math>
|align="center"|<math>{\left.0.04\right.}</math><ref name="fn2">In percent of the ensemble-average value</ref>
|align="center"|<math>{\left.0.8\right.}</math><ref name="fn2" />
|-
|align="left"|Ensemble average
|align="center"|<math>{\left.2.25\right.}</math>
|align="center"|<math>{\left.-0.23\right.}</math>
|align="center"|<math>{\left.0.804\right.}</math>
|-
|align="left" style="border-bottom:3px solid gray;"|Standard deviation
|align="center" style="border-bottom:3px solid gray;"|<math>{\left.0.45\right.}</math>
|align="center" style="border-bottom:3px solid gray;"|<math>{\left.0.73\right.}</math>
|align="center" style="border-bottom:3px solid gray;"|<math>{\left.0.038\right.}</math>
|-
|align="left" style="border-top:3px solid gray;"|Matsumoto ''et al.'' [&#8204;[[UFR_2-15_References#29|29]]]
|align="center" style="border-top:3px solid gray;"|<math>{\left.1.875\right.}</math>
|align="center" style="border-top:3px solid gray;"|&mdash;
|align="center" style="border-top:3px solid gray;"|&mdash;
|}
<references />


<div id="figure8"></div>
{|align="center" border="0" width="650"
|[[Image:UFR2-15_figure08.png|640px]]
|-
!align="center" style="text-align: left;"|'''Figure 8: Side-averaged, spanwise-averaged distributions of the standard deviation in time of the <math>{\left.Cp\right.}</math>: wind tunnel (a) and computational (b) results'''
|}



====Sensitivity to modelling and simulation parameters====
Let us analyze herein in more detail the sensitivity of the numerical predictions of the pressure distribution and
of the mean flow on the cylinder lateral surface to different modelling and simulation parameters, in order to possibly
identify some trends or explanations of the result dispersion.

Let us consider first the mean pressure distribution, which has been previously shown to be linked to the mean flow topology.
The approach to turbulence, viz. URANS, LES or hybrid RANS/LES, is expected to play a key role.
However, none of these approaches seem to reduce the result dispersion, i.e. results significantly deviating from the
ensemble average are found for LES, URANS and hybrid simulations.
 
For URANS, as expected, the largest sensitivity is to turbulence model; in particular, [&#8204;[[UFR_2-15_References#46|46]]]
obtains a mean ''C<sub>p</sub>'' distribution very close to the ensemble average for the
realizable k&nbsp;-&nbsp;&epsilon; and the RSM models (the latter, however, giving a wrong prediction of the base pressure),
while the distributions obtained with the RNG k&nbsp;-&nbsp;&epsilon; and the SST k&nbsp;-&nbsp;&omega; models
largely overestimate the pressure increase in the downwind zone of the cylinder side.
Finally, the URANS simulation of&nbsp;[&#8204;[[UFR_2-15_References#28|28]]],
which uses the LEA k&nbsp;-&nbsp;&omega; model, provides a mean ''C<sub>p</sub>'' distribution close to the ensemble average.
 
For LES and hybrid URANS/LES approaches, the analysis is more complicated, since different parameters seem to have a comparable impact.
As a first remark, it is pointed out once again that the 2D LES in&nbsp;[&#8204;[[UFR_2-15_References#1|1]]]
yields results significantly different from the 3D ones, and, in particular, a main recirculation zone much shorter than in 3D simulations.
The effects of SGS modeling in LES have been investigated in
Grozescu&nbsp;''et&nbsp;al.''&nbsp;[&#8204;[[UFR_2-15_References#17|17]],&nbsp;[[UFR_2-15_References#18|18]]]
and in&nbsp;[&#8204;[[UFR_2-15_References#1|1]]].
Both these studies show that the SGS model has a limited impact, in spite of the quite coarse grid resolution.
As for the hybridization strategy in hybrid simulations, the mean ''C<sub>p</sub>'' distributions obtained in the IDDES
simulations of Wei and Kareem&nbsp;[&#8204;[[UFR_2-15_References#71|71]]] deviate much more from the ensemble average than
those of the DES simulations in [&#8204;[[UFR_2-15_References#28|28]]];
this is probably due to the large difference in the domain size adopted in the studies.
The sensitivity to grid refinement has been investigated in LES simulations by
Grozescu&nbsp;''et&nbsp;al.''&nbsp;[&#8204;[[UFR_2-15_References#17|17]],&nbsp;[[UFR_2-15_References#18|18]]],
Bruno&nbsp;''et&nbsp;al.''&nbsp;[&#8204;[[UFR_2-15_References#10|10]],&nbsp;[[UFR_2-15_References#11|11]]]
and Wei and Kareem&nbsp;[&#8204;[[UFR_2-15_References#71|71]]];
in Grozescu&nbsp;''et&nbsp;al.''&nbsp;[&#8204;[[UFR_2-15_References#17|17]],&nbsp;[[UFR_2-15_References#18|18]]]
and Wei and Kareem&nbsp;[&#8204;[[UFR_2-15_References#71|71]]] the refinement is carried out in all directions,
while Bruno&nbsp;''et&nbsp;al.''&nbsp;[&#8204;[[UFR_2-15_References#10|10]],&nbsp;[[UFR_2-15_References#11|11]]] focus on refinement
in the spanwise direction.
All these studies agree on the qualitative behaviour, i.e. grid refinement leads to a decrease of the main vortex length
and to an upstream displacement of its centre with the previously highlighted consequences on the pressure distribution.
However, from a quantitative viewpoint, the effect of grid refinement is more limited in
Grozescu&nbsp;''et&nbsp;al.''&nbsp;[&#8204;[[UFR_2-15_References#17|17]],&nbsp;[[UFR_2-15_References#18|18]]]
than in Bruno&nbsp;''et&nbsp;al.''&nbsp;[&#8204;[[UFR_2-15_References#10|10]],&nbsp;[[UFR_2-15_References#11|11]]]
and Wei and Kareem&nbsp;[&#8204;[[UFR_2-15_References#71|71]]]; this is rather surprising since the grid resolution
in Grozescu&nbsp;''et&nbsp;al.''&nbsp;[&#8204;[[UFR_2-15_References#17|17]],&nbsp;[[UFR_2-15_References#18|18]]]
is significantly coarser than in the other studies and it might be due to the use of unstructured grids, which allows
more local refinements, and of the VMS-LES approach, which has been shown in previous studies to give more accurate results of
classical LES on coarse grids.
In particular, Bruno&nbsp;''et&nbsp;al.''&nbsp;[&#8204;[[UFR_2-15_References#10|10]],&nbsp;[[UFR_2-15_References#11|11]]]
carried out a systematic investigation of the effects of the grid resolution in the spanwise direction for a spanwise domain
size <math>{\left.L/D=5\right.}</math>, by considering <math>{\left.\delta_z/D=0.21,\ 0.1,\ 0.05\right.}</math>.
The results show a striking impact of the spanwise grid resolution on the flow features on the cylinder side and on
the related quantities; however, for the finest considered grid a very short length of the main recirculation zone is obtained,
close to that of the 2D LES in&nbsp;[&#8204;[[UFR_2-15_References#1|1]]], and, consequently
the mean pressure distribution becomes quite far from the ensemble average of the numerical predictions.
The reasons of this behaviour are not clear at the moment and this point definitely deserves further investigation.
The sensitivity to the numerical method, and, in particular, to the numerical dissipation is investigated only in the DES
simulations of Mannini and Schewe&nbsp;[&#8204;[[UFR_2-15_References#28|28]]],
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 (see also the discussion
in [[UFR_2-15_Test_Case#CFD_Methods|CFD methods]]).
The effect of the Reynolds number has finally been investigated in
Grozescu&nbsp;''et&nbsp;al.''&nbsp;[&#8204;[[UFR_2-15_References#17|17]],&nbsp;[[UFR_2-15_References#18|18]]],
in which it is shown that the main recirculation region becomes shorter as the Reynolds number is increased; however, the impact
is definitely limited compared to the overall dispersion of the results.

Finally, the analysis of the distribution of pressure standard deviation is even more complex.
In general, since the peak location is related to the length of the mean recirculation region, reference can be made to the discussion above.
As for the intensity of the peak and of the pressure fluctuations in general, differences in the results obtained by different
turbulence approaches, which capture different amounts of turbulence fluctuations, can be expected; for instance, larger
fluctuations are expected in LES simulations, especially those associated with very fine grid resolutions, than in URANS.
The impact of the approach to turbulence has been previously discussed, pointing out that the observed behaviours do not completely
fulfill the expectations and are not fully understood at present.

====Symmetry of the mean flow====
Pressure coefficient distributions previously commented result from the averaging between the upper and lower half perimeters,
so that possible asymmetries with respect to the <math>{\left.x\right.}</math> axis can not be pointed out.
In fact, the pressure measurements in wind tunnel
tests&nbsp;[&#8204;[[UFR_2-15_References#5|5]],&nbsp;[[UFR_2-15_References#7|7]]]
and some computational simulations&nbsp;[&#8204;[[UFR_2-15_References#11|11]],&nbsp;[[UFR_2-15_References#17|17]]]
have systematically, independently and explicitly discussed unexpected emerging differences in the statistics of
pressure fields over the upper and lower lateral surfaces.
Significant differences between the upper and lower surfaces (up to
&Delta;(''t''&nbsp;-&nbsp;avg(''C<sub>p</sub>''))&nbsp;&asymp;&nbsp;0.1 and &Delta;(''t''&nbsp;-&nbsp;std(''C<sub>p</sub>''))&nbsp;&asymp;&nbsp;0.05
are obtained in wind tunnel measurements and in some computational simulations.

The causes of the occurrence of single asymmetric flow realizations are at this stage unclear.
Systematic errors due to insufficient sampling window in time and related lack of convergence in evaluating the pressure
statistical moment are avoided by convergence assessment, as described at
[[UFR_2-15_Evaluation#Bulk_parameters|the beginning of the evaluation section]].
In the preliminary wind tunnel studies  by&nbsp;[&#8204;[[UFR_2-15_References#7|7]]]
and&nbsp;[&#8204;[[UFR_2-15_References#5|5]]]
different possible causes of the non-symmetry were identified, the main being the disturbances in the incoming flow
(e.g. by the upstream pitot-static tube), misalignment of the model with the incoming flow
(e.g. misalignment of the model and/or asymmetry in the flow) and inaccuracies in the model geometry
(e.g. degree of sharpness of the four edges, pressure taps disturbances and or quality of the rectangular shape of the model section).
These three causes are separately and systematically addressed in&nbsp;[&#8204;[[UFR_2-15_References#7|7]]],
while &nbsp;[&#8204;[[UFR_2-15_References#5|5]]] focus on the last ones.
Based on the performed investigations,&nbsp;[&#8204;[[UFR_2-15_References#7|7]]]
conjecture that the asymmetry results from an inaccuracy in model shape,
while misalignment of the relative flow is tentatively suspected by&nbsp;[&#8204;[[UFR_2-15_References#5|5]]]. 
In spite of a number of trial re-alignments and model flippings, neither study yields a perfect symmetry of the
time-averaged pressure field along the side surfaces.

The computational models are not affected by the wind tunnel inaccuracies cited above.
In particular, the mathematical model accounts for perfectly rectangular cylinder section with perfectly sharp edges,
while the laminar incoming flow and the other boundary conditions are fully symmetric.
Hence, asymmetric flow can be triggered only by numerical issues.
Local asymmetries exist in the spatial grid generated by&nbsp;[&#8204;[[UFR_2-15_References#11|11]]]
outside the grid boundary layer at the wall, while the mesh generated
by&nbsp;[&#8204;[[UFR_2-15_References#17|17]]]
is fully symmetric with respect to the <math>{\left.x-z\right.}</math> plane.
The procedures adopted for the numerical discretization and numerical solution of the governing equations
(e.g. multigrid partition and parallelisation) can represent further potential causes of an asymmetric solution. 
The computational simulations performed by &nbsp;[&#8204;[[UFR_2-15_References#17|17]]]
provide smaller differences than the ones pointed out by &nbsp;[&#8204;[[UFR_2-15_References#11|11]]].
The systematic grid refinement in the spanwise <math>{\left.z-\right.}</math> direction performed
in &nbsp;[&#8204;[[UFR_2-15_References#11|11]]]
suggests that the asymmetric time and spanwise averaged pressure field can be simulated only by using a dense grid,
while negligible differences take place with the coarsest mesh.
The authors conjecture that small coherent flow structures in the spanwise direction past the trailing edges are responsible
for the whole asymmetric flow field.

In general, the scrutinized studies show that the BARC flow has an high sensitivity to a number of factors which may
trigger a significant asymmetry in the time-averaged flow field.
It is worth recalling that some analogous well known examples of time-averaged asymmetric flows around nominally symmetric
setups exist in bluff body aerodynamics, e.g. the circular cylinder in its critical
regime&nbsp;[&#8204;[[UFR_2-15_References#6|6]],&nbsp;[[UFR_2-15_References#51|51]]],
or the side-by-side arrangement of two rectangular cylinders
[''B/D''&nbsp;=&nbsp;1.28,&nbsp;''S/D''&nbsp;=&nbsp;0.5, where ''S''
is the gap between cylinders,&nbsp;[[UFR_2-15_References#30|30]]].
Another example, which is more similar to the flow setup discussed in this paper, is provided
by&nbsp;[&#8204;[[UFR_2-15_References#39|39]]],
where the flow at Re<sub>D</sub>&nbsp;=&nbsp;''UD/&nu;''&nbsp;=&nbsp;10<sup>3</sup> around rectangular cylinders with
different breadth to depth ratios 3&nbsp;&le;&nbsp;''B/D''&nbsp;&le;&nbsp;9
is simulated by solving the 2D Navier-Stokes equations without turbulence models.
The simulated time-averaged flow is symmetric for all the considered ''B/D'' ratios
(included the one characterized by ''B/D''&nbsp;=&nbsp;5, except for ''B/D''&nbsp;=&nbsp;4.
It is worth noting that this asymmetry is not revealed in previous wind tunnel tests performed by the same
authors&nbsp;[[UFR_2-15_References#36|36]]] under the same incoming flow nominal conditions.

The spanwise correlation of pressure and forces were also provided in one experimental
study&nbsp;[&#8204;[[UFR_2-15_References#56|56]]]
and in two numerical contributions&nbsp;[&#8204;[[UFR_2-15_References#11|11]],&nbsp;[[UFR_2-15_References#27|27]]] to BARC.
They are not discussed here for the sake of brevity.
<br/>
----
{{ACContribs
|authors=Luca Bruno, Maria Vittoria Salvetti
|organisation=Politecnico di Torino, Università di Pisa
}}
{{UFRHeader
|area=2
|number=15
}}


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