BBAA VI International Colloquium on:Bluff Bodies Aerodynamics & Applications

Milano, Italy, July, 20–24 2008

EDGE DEGREE-OF-SHARPNESS AND INTEGRAL LENGTH SCALEEFFECTS ON THE AERODYNAMICS OF A BRIDGE DECK

Luca Bruno? and Davide Fransos†

?Dipartimento di Ingegneria Strutturale e GeotecnicaPolitecnico di Torino, Viale Mattioli 39, 10126 Torino, Italy

e-mail: luca.bruno@polito.it

†Dipartimento di MatematicaPolitecnico di Torino, Corso Duca degli Abruzzi 24, 10126 Torino, Italy

e-mail: davide.fransos@polito.it

Keywords: Bridge deck, degree of sharpness, turbulence integral lenght scale, aerodynamicregimes, Computational Wind Engineering

1 INTRODUCTION

The effects of various incoming flow paramenters on the bluff bodies aerodynamics attractedthe attention of the scientific community since the milestones works of Delany & Sorensen [1]and Roshko [2] about the Reynolds number effects on circular and rounded-edges cylinders.In particular, the work of Roshko introduced the well known nomenclature for the individualRe number regimes of a circular cylinder. More recently, relevant and for a some extent analo-gous Re number effects have been recognized in flow around more-or-less bluff bodies [3] andsharp-edges cylinders [4]. Analogous fundamental studies have been adressed to evaluating theeffects of the incoming turbulence on separated and reattaching flow past the leading separa-tion point of elongated rectangular plates, since the pioneering work of Laneville [5], the onesof Nakamura & Ozono [6], Melbourne and coworkers [7]. The results obtained in the abovementioned works show large differences in the recirculation bubble measured for smooth andturbulent incoming flows and, among the latter, relevant sensitivity to both turbulence intensityand integral length scale. More recently, Tamura & Miyagi [8] focused on the combined effectsof turbulence intensity and corner shape on the overall aerodynamics forces acting on a squarecilynder. However, significant difficulties remain in studying the aerodynamic effects of smalledge radius of curvature and integral length scales at low turbulence intensity, because of therestrictions in wind tunnel practice about the physical model manifacturing and the velocitymeasurements. The purpose of the present paper is to tackle such difficulties by means of thecomputational approach, that allows to set the turbulent incoming flow characteristics and theobstacle geometric features. In particular, the combined effects of the turbulence integral lengthscale at low turbulence intensity and of the lower corner small radius of curvature on the flowfield around a trapezoidal bridge deck cross setion are systematically adressed.

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Luca Bruno, Davide Fransos

2 FLOW MODELLING AND COMPUTATIONAL APPROACH

The turbulent, separated, unsteady flow around the 2D section is modeled by the classicaltime-dependent Navier-Stokes equations, along with the RANS k − ω turbulence model [9].Dirichlet conditions on the velocity field and on the turbulence characteristic quantities (k andω) are imposed at the inlet boundaries. Neumann conditions involving the velocity field and thepressure (null normal component of the stress tensor) as well as the same Dirichlet conditionson k and ω are imposed at the outlet boundaries. No-slip conditions are imposed at the sectionsurface. Impulsive initial conditions are introduced.The Finite Volume solver Fluent is used in the following to numerically evaluate the flowfield.A hybrid quadrilateral/triangular grid is employed. The cell-center values of the variables areinterpolated at face locations using a second order Central Difference Scheme for the diffusiveterms on all the elements and Quadratic Upwind Interpolation for Convective Kinematics andsecond-order Upwind Scheme for the convection terms on quadrilateral and triangular cells,respectively. Advancement in time is accomplished by the second-order implicit Euler scheme.Every computational grid in space consists of about 2.43e + 5 cells. The nondimensionaltimestep needed for an accurate advancement in time is ∆t = 0.01. Each simulation is extendedalong 60 time units in order to overcome transient solution and to allow the statistic analysis ofthe periodic flow. Computations are carried out on a single Intel Xeon X5355 2.66GHz CPUwith 2GB of memory and require about 60 hours of CPU time for each simulation.

3 APPLICATION AND RESULTS

The sensitivity study is applied to the bare deck cross section of the Sunshine Skyway Bridge(Figure 1), for which both experimental and computational studies are reported in [10] and [11].Both wind tunnel test setups are characterized by the same order of magnitude of the Reynolds

Figure 1: Bare Sunshine Skyway Bridge deck cross section

number Re = UB/ν = 3 ÷ 6e + 5, where U is the incoming flow velocity, B the deck chordand ν the kinematic viscosity. Moreover, every test have been performed in low turbulenceincoming flow conditions, i.e. It ≈ 1%, while the turbulence integral length scale Lt has notbeen measured. The computational simulations performed by Mannini et al [11] showed that thediscrepancies in experimental results can be referred to two different aerodynamic behaviourstakeing place for sharp (curvature radius R/B = 0) and round (R/B = 0.05) lower cornersof the trapezoidal box. For the present study, the combined effects of the incoming turbulenceintegral length scale and of the lower corners curvature radius are studied: the former varies inthe range 1.e− 3 ≤ Lt/B ≤ 1, while the latter takes values from R/B = 0.01 to R/B = 0.05.The turbulence intensity and the Reynolds number are kept constant and equal to It = 1% andRe = 5.76e+ 5 respectivelly.Very significant changes in the aerodynamic coefficients and in the Strouhal number followto small changes in Lt/B and R/B, as it is shown as an example in Figure 2(a). The meanvalue of the lift is sensitive to both Lt and R, showing both stepwise and piecewise continuous

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Luca Bruno, Davide Fransos

(a) (b)

Figure 2: Mean lift coefficient: point-wise values, interpolating function (a) and regimes in the R - Lt plane (b)

variations. This trend is explained pointing out four different aerodynamic regimes as in Figure2(b), named in analogy to the individual Re number ones [2]. Such regimes are characterizedon the basis of the flow topology around the deck, of the vortex shedding mechanism and ofthe wake structure (Figure 3). Boundary layer separation and reattachment on the side surfaces

Figure 3: Aerodynamic regimes: null mean velocity isocontour and instantaneous vorticity magnitude fields

takes place in different ways in the four regimes. The higher is the regime, the lower is the extentof the side reversed flow, the less massive the separation, the lower the degree-of-bluffness of thesection. Vortices are alternatelly shed in the wake from the upper and lower trailing edges in thesub-critical and supercritical regimes, while the critical and trans-critical ones are characterizedby vortex shedding from the upper edge only.

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Luca Bruno, Davide Fransos

4 CONCLUSIONS

This study contributes to shed some light on the significant sensitivity of the aerodynamicsof some bluff bodies to very small changes in edges degree-of-sharpness and integral lengthscales. Such geometrical and flow features are hard to be set for both the reduced model and theactual prototype, so that their modelling and manufacturing require special care in design andanalysis stages.

5 ACKNOWLEDGEMENTS

The authors wish to thank Prof. F. Ricciardelli and Dr. C. Mannini for kindly providing thegeometrical properties of the Sunshine Skyway Bridge and the wind-tunnel tests set-up data.Further thanks go to Dr. S. Khris for helpful discussions about the topics of the paper.

REFERENCES

[1] N.B. Delany, N.E. Sorensen. Low speed drag of cylinders of various shapes. NACA TN3038, Washington, USA, 1953.

[2] A. Roshko. Experiments on the flow past a circular cylinder at very high Reynolds number.Journal of Fluid Mechanics, 10, 345–356, 1961.

[3] G. Schewe. Reynolds number effects in flow around more-or-less bluff bodies. Journal ofWind Engineering and Industrial Aerodynamics, 89, 1267–1289, 2001.

[4] G.L. Larose, A. D’Auteuil. On the Reynolds number sensitivity of the aerodynamics ofbluff bodies with sharp edges. Journal of Wind Engineering and Industrial Aerodynamics,94, 365–376, 2006.

[5] A. Laneville, C.D. Williams, The effects of intensity and large scale turbulence on themean pressure and drag coefficients of 2D rectangular cylinders, Proc. 5th Int. Conferenceon Wind Effects on Building and Structures, Fort Collins, Colorado, July 8-14, 1979.

[6] Y. Nakamura, S. Ozono, The effects of turbulence on a separated and reattaching flow,Journal of Fluid Mechanics, 178, 477–490, 1987.

[7] Q.S. Li, W.H. Melbourne. An experimental investigation of the effects of free-stream tur-bulence on streamwise surface pressures in separated and reattaching flows. Journal ofWind Engineering and Industrial Aerodynamics, 54/55, 313–323, 1995.

[8] T. Tamura, T. Miyagi, The effect of turbulence on aerodynamic forces on a square cylinderwith various corner shapes, Journal of Wind Engineering and Industrial Aerodynamics, 83,135–145, 1999.

[9] D.C. Wilcox, Turbulence Modelling for CFD, DCW Industries Inc., La Canada, Califor-nia, 1998.

[10] F. Ricciardelli, H. Hangan. Pressure distribution and aerodynamic forces on stationary boxbridge sections. Wind and Structures, 4(5), 399–412, 2001.

[11] C.Mannini, A. Soda, R. Voss. Computational investigation of flow around bridge sections.Proc. Bridges International Conference, Dubrovnik, Croatia, May 21-24, 2006.

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