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Flows in Complex Systems

# URANS Calculations for Smooth Circular Cylinder Flow in a Wide Range of Reynolds Numbers: Solution Verification and Validation

[+] Author and Article Information
Guilherme F. Rosetti

Numerical Offshore Tank – TPN,
Department of Naval Architecture
and Ocean Engineering,
University of São Paulo,
São Paulo, Brazil 055080-030
e-mail: gfeitosarosetti@usp.br

Guilherme Vaz

Mem. ASME
CFD Projects,
R&D Department,
MARIN,
Wageningen, The Netherlands 6700AA
e-mail: g.vaz@marin.nl

André L. C. Fujarra

Mem. ASME
Numerical Offshore Tank – TPN,
Department of Naval Architecture
and Ocean Engineering,
University of São Paulo,
São Paulo, Brazil 055080-030
e-mail: afujarra@usp.br

For some cases here presented the authors indeed obtained results closer to the experimental values for coarse grids and time-steps. An example can be seen for Re = 1 × 103 in Fig. 7. These are, however, according to us “worst” numerical results than the ones for finer grids and time-steps which are in the numerical error asymptotic range.

This feature was not captured in these calculations.

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the Journal of Fluids Engineering. Manuscript received April 12, 2012; final manuscript received August 10, 2012; published online November 20, 2012. Assoc. Editor: Mark F. Tachie.

J. Fluids Eng 134(12), 121103 (Nov 20, 2012) (18 pages) doi:10.1115/1.4007571 History: Received April 12, 2012; Revised August 10, 2012

## Abstract

The flow around circular smooth fixed cylinder in a large range of Reynolds numbers is considered in this paper. In order to investigate this canonical case, we perform CFD calculations and apply verification & validation (V&V) procedures to draw conclusions regarding numerical error and, afterwards, assess the modeling errors and capabilities of this (U)RANS method to solve the problem. Eight Reynolds numbers between Re = 10 and $Re=5×105$ will be presented with, at least, four geometrically similar grids and five discretization in time for each case (when unsteady), together with strict control of iterative and round-off errors, allowing a consistent verification analysis with uncertainty estimation. Two-dimensional RANS, steady or unsteady, laminar or turbulent calculations are performed. The original 1994 $k-ω$ SST turbulence model by Menter is used to model turbulence. The validation procedure is performed by comparing the numerical results with an extensive set of experimental results compiled from the literature.

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## Figures

Fig. 1

Grid and domain used in the calculations

Fig. 2

Detail of the mesh close to the cylinder. The shapes seen are typical of a nested-refinement technique.

Fig. 3

Infinity and rms norms for evaluating the residuals of the flow quantities in the case Re = 40

Fig. 4

Infinity and rms norms for evaluating the residuals of the flow quantities in the case Re = 1×103. Velocities and pressure. Turbulent kinetic energy (TurbKinE) and turbulent frequency (TurbVar2).

Fig. 5

Surface fit for St and Re = 100. The size of the blocks indicate the uncertainty of each data point. The convergence orders are p = 1.0 for space and p = 1.6 for time.

Fig. 6

Surface fit for CDavg and Re = 200. The size of the blocks indicate the uncertainty of each data point. The convergence orders are p = 2.0 for space and p = 1.4 for time.

Fig. 7

Drag coefficient calculations for Re = 1×103. The size of the blocks indicate the uncertainty of each data point. In this case, the order of convergence of time and space are, respectively, p = 1.5 and p = 1.7.

Fig. 8

Time step refinement for the calculation of Strouhal numbers for Re = 5×105. Oscillatory behavior is identified in this case.

Fig. 9

Surface fit of the calculated Strouhal numbers for Re = 5×105. The size of the blocks indicate the uncertainty of each data point. In this fit, p = 1.48 for space and p = 1.95 for time.

Fig. 10

Surface fit to θsep for Re = 1×104. The size of the blocks indicate the uncertainty of each data point. In this case, p = 1 for time and space.

Fig. 11

Surface fit to Cpb for Re = 1×105. The size of the blocks indicate the uncertainty of each data point. In this case, p = 2 for space and time.

Fig. 12

Sensitivity of the drag coefficient for different space and time discretizations. Different grids with the finest time-steps. Different time step discretization with the finest grid.

Fig. 13

Drag coefficient results from laminar calculations. Experiments from Refs. [50,51-50,51].

Fig. 14

Separation angle results from laminar calculations. Experiments from Ref. [52].

Fig. 15

Base suction coefficient results from laminar calculations. Experiments from Ref. [46].

Fig. 16

Strouhal number results from laminar calculations. Experimental formulas from Ref. [53].

Fig. 17

Drag and lift time traces and power spectrum densities from calculation with finest grid and time step for Re = 100. Permanent-regime traces were used for the statistics.

Fig. 18

Time traces of separation angles and power spectrum densities from calculations with finest grid and time step for Re = 200. Both upper and lower separation angles are shown. Permanent-regime traces were used for the statistics.

Fig. 19

Field plots of normalized velocity at the point of largest lift coefficient. Re = 10. Re = 40. Re = 100. Re = 200.

Fig. 20

Drag coefficient results from turbulent calculations. Experiments from Refs. [50,51,55-51,55].

Fig. 21

Base suction coefficient results from turbulent calculations. Experiments from Ref. [46].

Fig. 22

Strouhal number results from turbulent calculations. Experimental formulas from Ref. [53].

Fig. 23

Separation angle results from turbulent calculations. Experiments from Ref. [52].

Fig. 24

Time traces of separation angles for Re = 1×103 with finest grid and time step. Permanent-regime traces were used for the statistics.

Fig. 25

Time traces of separation angles for Re = 1×104 with finest grid and time step. Permanent-regime traces were used for the statistics.

Fig. 26

Field plots of normalized vorticity, ωD/U1 at the point of largest lift coefficient. Re = 1×103. Re = 1×104. Re = 1×105. Re = 5×105.

Fig. 27

Field plots showing streamlines at the point of largest lift coefficient. Re = 1×103. Re = 1×104. Re = 1×105. Re = 5×105.

Fig. 28

Field plots of normalized eddy viscosity, νt/ν at the point of largest lift coefficient. Re = 1×103. Re = 1×104. Re = 1×105. Re = 5×105.

Fig. 29

Comparison between drag coefficients from present calculations and benchmark results. Experiments from [50,51,55-51,55]. Numerical results: FD - [2-5,57-5,57,58]; SE - [7]; FE - [11,59,60,59-11,59,60]; DNS - [8,13,13]; LES - [14,61,61-63]; RANS - [19,20-19,20].

Fig. 30

Comparison between base suction coefficients from present calculations and benchmark results. Experiments from Ref. [46].

Fig. 31

Comparison between Strouhal number from present calculations and benchmark results. Experimental formulas from Ref. [53]. Numerical results: FE - [11,59,60,59-11,59,60]; DNS - [8,13,13]; LES - [14,61,61-63]; RANS - [20].

Fig. 32

Comparison between separation angles from present calculations and benchmark results. Experimental results from Ref. [52]. Numerical results: FD - [1,2,6,58-2,6,58].

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