THE 8th INTERNATION

Interactionand the Voin a Turbul

Nicoleta Oct1Politehnica University, REORO

notanase@yaho Abstract - The study and modeling of flow coa cylinder is a benchmark CFD problem in fapplications are multiple, from micro-fluifrom fluid-structure interaction to geophpaper is concerned with a particular motion rthe interaction between the free surface cylinder in an open channel turbulent flow. Tto the investigations of the vortical structurethe cylinder and their dependence on the dissurface. Numerical simulations in 2D performed with VOF code and k-ε turbcalculations of the free surface and the directdisclose a good correlation. The results eminfluence on the flow dynamics of the vorticthe free surface to the cylinder. The locatpoints on the immersed surface are determinedistribution around cylinder is computed.

Keywords: vortices, cylinder, free surface, tur

I. INTRODUCTION

The flow dynamics around immersed bwith free surface is an important topic of sand hydraulics, in the design of water turbshore development projects, [1], [2]. The mthe modeling of free surface hydrodynamictwo factors: (i) the boundary of the flow d(the free surface and the local configuratiobottom are normally not given), (ii) the floalmost all regimes, so only the numericaReynolds equation of motion might description of the flow configuration. Oproblem in obtaining the solutions of the immersed body is created by the influence on the vortical pattern around the body, directly related to a more complex and dynamics of fluid - solid interaction, see e.g

To develop and improve the computaticompulsory to establish a benchmark tesparticular phenomena under investigation. Ithe benchmark problem is the flow conficylinder in an infinite domain, see [5], [6proper boundary conditions, the solutionsequations are dependent of one single flow

NAL SYMPOSIUM ON ADVANCED TOPICS IN ELECTMay 23-25, 2013

Bucharest, Romania

n Between the Free Surortical Structures Develent Flow Around a Cy

avia Tănase1, Diana Broboană1 and Corneliu BălanOM Laboratory, Splaiul Independentei 313, 060042 Boo.com, diana.broboana@upb.ro, corneliu.balan@upb

onfiguration around fluid mechanics; the idics to hydrology, ysics. The present related to this topic: and the immersed

The study is focused es developed around stance from the free configurations are

bulent models. The t flow visualizations mphasis the major city transport from tions of the critical ed and the flow rate

rbulence

N

odies in a channel study in hydrology

bines plant and off-main difficulties in cs are generated by domain is unknown on of the channel's ow is turbulent for al solutions of the

offers a proper One of the main flow field around of the free surface

a subject which is general topic: the

g. [3], [4]. ional techniques is st problem for the In fluid mechanics,

figuration around a 6]. In this case, for s of Navier-Stokes

w parameter, i.e. the

Reynolds number - Re, which dstresses distributions and the pashown the numerical solution cylinder in a symmetric finite do

For a laminar and stable flow

formed down-stream the cylinddependent on the value of Re-nu< Recr < 100, depends on the ma

The flow spectrum disclosecylinder: (i) the impact point ((D1 and D2); for the case frsymmetrically located against tthe infinite flow direction.

We propose as a benchmarimmersed body - free surfacconfiguration with Fig. 1: the pla channel with free surface. Suin [7] and [8], but the investigathe study and modeling of the wake behind the cylinder and thfree surface into the fluid.

Fig. 1. Planar flow pattern around Re = 50. The steady stream lines avorticity (maximum being red, minimusymmetric for Re < Recr; boundary co(entrance), 1-2 and 3-4, respectively thon the cylinder.

A

D1

D2

θ o

1

3

TRICAL ENGINEERING

rface loped linder 1

Bucharest, Romania .ro

determines the flow spectrum, atterns of vortices. In Fig. 1 is of the steady flow around a

omain.

w, two symmetric vortices are der, the length L being linearly umber for Re < Recr (where 50 agnitude of the flow domain). s three critical points on the (A) and the separation points rom Fig. 1, D1 and D2 are the horizontal axis defined by

rk problem for the study of e interaction a similar flow lanar flow around a cylinder in uch flow was previous studied ations were mainly directed to

free surface influence on the he vorticity transport from the

a cylinder at Reynolds number -are colored with the magnitude of um is blue). The vortices are perfect

onditions: the velocity v = V0 on 1-3 he pressure p = p0 on 2-4 (exit); v = 0

L

2

4

978-1-4673-5980-1/13/$31.00 ©2013 IEEE

The present paper is concerned with the numerical simulations of the incipient turbulent flows around the cylinder located in vicinity of a free surface. We calculate the flows spectrum for different immersed depths and the variations of the wall shear stress (WSS) distribution around the cylinder. The aim of the work is to determine the locations of the critical points on the cylinder surface and to compute the flow rate distribution around the cylinder. The influence of surface tension on the free surface topology is also briefly discussed.

II. EXPERIMENTAL AND FLOW PARAMETERS

The open channel test geometry is shown in Fig. 2. Downstream the cylinder of diameter D = 50 mm is a hydraulic weir which controls the transported flow rate. The average velocity is V0 measured upstream the cylinder where the height H0 is maintained constant.

0

Fig. 2. The geometry of the open channel, (a), and the free surface developed in vicinity of the immersed cylinder: b) numerical simulation and c) direct visualization of the free surface. The separation points D1, (d), and the flow patter downstream the cylinder, (e), are visualized with streak line method The center of the cylinder is located at x = 303 mm, the flow parameters are: Re = 7500, Fr = 0.22.

The channel width is 15 mm and the total length from the entrance to the weir is x = 613 mm. During a measurement the height H0 (at x = 0) is kept constant, 90 mm < H0 < 120 mm, which corresponds to a mean velocity range 0.1 m/s < V0 < 0.2 m/s, with H = 60 mm for all cases.

The flow is characterized by the non-dimensional Reynolds, respectively Froude numbers: Re DV , Fr V D (1)

and by the non-dimensional parameters:

D , H , (2)

where h the minimum distance between the unperturbed upstream free surface (corresponds to x = 180 mm) and the cylinder, see Fig. 2 and Tab. 1. In (1) 1000 / is mass density and 1 is the viscosity (working fluid is water at 20oC). The experiments and corresponding simulations were performed in the region of weak turbulence (5000 < Re < 12000) at Fr < 0.5 (subcritical gravitational flow regime). In experiments the free surface downstream the cylinder is unstable for all tested flow regimes, the amplitude of oscilation being proportional to the magnitude of the Reynolds number (same phenomena was observed and investigated in [8]). In the present study the phenomena is modelled as a steady flow and, as consequence, the surface waves generated downstream the cylinder are considered steady in the average. The influence of surface tension is relevant only at small values, where the free surface is in the very vicinity of the cylinder. However, the presence of surface tension damps the oscillations, which is observed better in numerical simulations.

TABLE 1 MEASURED FLOW PARAMETERS (EXCEPT Q1/Q2 WHICH IS COMPUTED)

No. H0

[mm]

[mm]

[mm] Re [-]

Fr [-]

[-]

⁄ [-]

1 92 6.4 21.2 5400 0.154 0.128 0.0676 2 105 18.76 32.3 7500 0.22 0.375 0.47 3 115 29.2 40.9 10500 0.3 0.584 0.704

III. NUMERICAL SIMULATIONS

Numerical solutions are obtained using the specialized code Fluent 6.3 for solving the continuity and the Reynolds equations for turbulence:

0, (3) ∆ (4)

where is the Reynolds turbulent stress tensor. In (3) is the time average velocity, is the time average pressure, is the turbulent fluctuation of velocity and is the viscosity. The present simulations were performed using the classical and models (SIMPLE pressure-velocity coupling and QUICK scheme as interpolation method for convective terms), where k is the specific turbulent kinetic energy and ε is the specific turbulent dissipation rate, the closure relation being:

2 (5)

a)

air

water interface

b) c)

H

h

D free surface

310 mm

h0 V0

H0

instabilities of free surface

x

a)

d)

e)

D1

where

⁄

is the turbulent (eddy) viscosity, is a time average stretching, and being givequations, [9], [10]. The turbulent solversthe whole computation domain, which in both fluids, i.e. air and water. No other subused for the special treatment of the regionsolid walls (e.g. the boundary layer profiFLUENT, [10]).

The numerical computations of the freeperformed using the VOF code implemenmixture of water and air being solved simulsame turbulent solver in a 2D geometry. mixture, the fluids are considered inimmiscible (no real diffusion between the aallowed), see for details [10]. The sepaobtained by connecting the cells of equausing the modified HRIC (High ResCapturing) scheme. However, in the papthe corresponding interfaces obtained for volume fractions, see Fig. 6 - detail.

For each case from Tab. 1 the calculus different boundary conditions at the entran(x = 0, H0 = constant), respectively: (i) con(ii) constant height with linear pressureboundary condition at the exit is alwa. Differences between the two typboundary conditions are observed, mainly fdeveloped downstream the cylinder, see Fig

Numerical solutions give the insight of

one of the most important being the WSS cylinder, see Fig. 4. Plotting the compofunction of the θ ο - angle, one can determcritical points and the separation line betwlower translated flow rates, see Fig. 5.

One possibility to validate the numericalcomparison of the computed free surface wone, see Fig. 6. The VOF model assumes the grid might be present both phases, aratio of the phases is computed and the sepcase the free surface) is tracked through cells where concentration has the value of 5line is just an approximation, since at the fr

Fig. 3. Flow spectrum and free surface geometry (Re = 7500): a) constant velocity imposed at the edistribution imposed at the entrance (location of c

cylinder: A, respectively D1, B and D2, see

a) b)

A

(6)

constant, is the ven by the transport s were applied for this case contains

broutines have been n in the vicinity of ile implemented in

e surface flows are nted in Fluent, the ltaneously with the In VOF model of

ncompressible and air and water being aration interface is al volume fraction solution Interface

per are also shown different air-water

was made for two nce of the geometry nstant velocity and e distribution (the ays the same, i.e. pes of solvers and for the flow pattern g. 3.

all flow quantities, distribution on the

onents of WSS as mine the location of ween the upper and

l simulations is the with the visualized that in each cell of s consequence the

paration line (in our the centers of the

50%, [10]. But this ree surface we have

also to find the pressure valueThis is not always the case, so surface is actually located in a“spatial representation” of the cfrom Fig. 6 we can observe thalocated in the band between course, a refined mesh is a soluof the computations, but alwaysbalance between precision, com

Fig. 4. The wall shear stress distributioFr = 0.22 – case b) in Fig

All simulation were perfor

(489297 nodes with 487222 elserver Dual 2.66 GHz with simulation takes on average 3 imposed convergence criteria and 10-5 for velocities) and a staThe presence of surface tensquantitatively the results, bqualitatively changes. The majosimulations is to reproduce the downstream the cylinder. Thperformed with steady 2D solvaverage free surface. Thereforereproduce with accuracy the rewith the computing resources:surface tension implemented immiscible fluids are required. The validation of numerical work are limited and depends of the free surface. In the fut

for case 2 in Tab. 1

entrance; b) pressure critical points on the e also Fig. 1).

Fig.5. Flow rate distribution around thm3/s, Q2 = 139.44⋅10-6 m3/s, (Re = 54flow spectrum, b) flow separation arou

a)

b)

a)

b)

0 3 0 6 0 9 0 1 20 1 50 1 8-0 .6

-0 .4

-0 .2

0 .0

0 .2

0 .4

0 .6

0 .8

1 .0

1 .2

WSS

[Pa]

A n g l

x y

A D 1

D1

B D2

e p0 and the zero shear stress. the prediction of the real free

a “band”, its width being the calculation error. In the detail at the experimental points are 10% and 90% of water. Of

ution to improve the precision s has to be established a proper

mputation time and resources.

on around the cylinder at Re = 7500, g. 3 and no. 2 in Tab. 1.

rmed using the same mesh lements) and run on a 64-bit 16 GB RAM memory. One days of working to reach the (10-3 for continuity equation

ationary free surface. sion in simulations improves but does not bring major or difficulties of the numerical oscillations of the free surface

he present computations are vers, so the final result is an

e, to decrease the errors and to eal flow field is direct related : 3D unsteady solutions with

at the boundary between

simulations presented in this exclusively on the calculation ture studies is compulsory to

he immersed cylinder: Q1 = 9.86⋅10-6

400, Fr = 0.15 – no. 1 in Tab. 1); a) und the cylinder.

Q2

Q1

8 0 21 0 24 0 2 70 3 00 3 30 36 0

BD 2

e θ ο

x - W S Sy - W S S

compare the numerical results also quantitatively with experiments, so a PIV system is required to obtain the velocity field around the cylinder.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.30.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

0.11

90% water

cylinder center

10% water

Hei

ght o

f the

free

surf

ace

prof

ile [m

]

x - coordinate [m]

Phase water/air concentration 0.1 (10% water) 0.2 0.5 (50% water) 0.8 0.9 (90% water)

experiments

Case 2: Re = 7500

weir

DETAIL

Fig. 6. The free surface geometry (computed and measured, see Fig. 2); simulations performed with solver and constant velocity imposed

as the entrance boundary condition.

IV. FINAL REMARKS AND CONCLUSIONS

The main aim of our study is to investigate and to model the interaction between the free surface and the flow spectrum in the vicinity of the body, for a subcritical flow regime with weak turbulence. The major goal of the research is to establish as precisely as possible the location of the critical points (impact and separation points) on the body and the separation line between the upper and lower transported flow rates, as function of the distance h (or geometrical parameter , see Fig. 2) from the free surface, see Fig. 5 and also Fig. 7.

The vorticity magnitude is the major kinematic quantity

which characterizes the flow under investigation, see Fig. 8, the transport of vorticity from the free surface into the fluid being responsible with the location of the critical points. With increasing of h the vorticity transport from free surface to the cylinder becomes less important, as consequence the flow becomes closer to the symmetric pattern, see Fig. 7.

Fig. 8. Vorticity magnitude distribution at the free surface, see Tab. 1. The intensity of vorticity ( 1 2⁄ | | is higher at lower h-depth (which corresponds to low Re-numbers). It is also observed that the pick of is moved downstream the cylinder with increasing the Re-number. This paper was focused on the numerical computations of the flow; in particular, to test the capabilities of several solvers and boundary conditions to reproduce the motion under investigation (i.e. the flow around a circular cylinder). The turbulent model , with pressure imposed as entrance boundary condition was found the most appropiate to reproduce our flows. The experimental investigations were limited up to now only to the direct visualization of the free surface. Further experimental studies are needed to obtain the quantitative data of velocities in vicinity of the cylinder, so to compare directly the numerical results with computation. It is the authors intentions to progress with this study in the direction to develop a CFD benchmark application for the flows around immersed bodies in an open channel.

ACKNOWLEDGMENT

The authors acknowledge the support of dr. ing. Tiberiu Barbat for his assistance and advice regarding the numerical simulations. Drd. Nicoleta Octavia Tanase acknowledges the financial support of the grant POSDRU/6/1.5/S/16 ID5159.

REFERENCES [1] L. P. Chamorro, C. Hill, S. Morton, C. Ellis, R. E. A. Arndt and F.

Sotiropoulos, "On the interaction between a turbulent open channel flow and an axial-flow turbine," J. Fluid Mech., vol. 716, pp. 658-670, 2013.

[2] J. I. Whelan, J. M. R. Grahamand and J. Peiró, "A free-surface and blockage correction for tidal turbines," J. Fluid Mech,. vol. 624, pp. 281-291, 2009.

[3] D. J. Lee and Daichin, "Flow past a circular cylinder over a free surface: Interaction between the near wake and the free surface deformation," J. Fluids and Structures, vol. 19, pp. 1049–1059, 2004.

[4] Y. Bazilevs, K. Takizawa and T. Tezduyar, Computational fluid-structure interaction: methods and applications, Wiley, 2013, pp.171-190.

[5] S. W. Churchill, Viscous flows: the practical use of theory, Butterworths, 1988, pp. 317-357.

[6] H. Schlichting and K. Gersten, Boundary layer theory, 8th ed., Springer, 2000, pp. 555-680.

[7] J. Sheridan, J.-C. Lin and D. Rockwell, "Flow past a cylinder close to a free surface," J. Fluid Mech., vol. 330, pp. 1-30, 1997.

[8] P.Reichl, K. Hourigan and M. C. Thompson, "Flow past a cylinder close to a free surface," J. Fluid Mech., vol. 533, pp. 269–296, 2005.

[9] S. Dănăilă and C. Berbente, C. Metode Numerice în Dinamica Fluidelor, Ed. Academiei, 2003 (in Romanian).

[10] *** Fluent Inc., Fluent 6.3 user's guide, 2006.

0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42

0

10

20

30

40

50

60

Vor

ticity

mag

nitu

de [1

/s]

x - coord inate [m ]

N o. R e 1 5400 2 7500 3 10500

center

4 6 8 10 12 14 16 18 20 22 24 26 28 30 320

20406080

100120140160180200220240

Ang

le -

θ

h [mm]

Impact point A Separation point D1 Separation point D2

Fig. 7. The dependence θ(h) for the points A, D1 and D2, see Fig. 1 and Fig. 4. The diagram also disclose the critical value of h where D1and D2 start to take different values.