# Experimental investigation of flow regimes and Strouhal number in a pair of side-by-side square cylinders.

IntroductionStudying flow around the cylinders is considered one of the most important classical and fluid mechanics issues. Scince theoretical methods and computational are still far from practical engineering design, test with wind tunnel is often the only way for determining exact flow parameters, especially for drag models. For this reason, an experimental investigation was carried out about the flow around a pair of side by side square cylinder, and interaction consequences upon flow parameters has been discussed in this research. When cylinders are considerably close to each other or downstream cylinder is close to the upstream cylinder, Interaction effects in pair cylinder begin. Investigation and study about the flow around the cylinder can help for understanding of the vortex dynamics, pressure distribution and aerodynamic forces like lift and drag [1].

Created wakes in behind of tubes in the heat exchangers or in the guiding rods in nuclear reactors, buildings, cooling towers and suspension bridges are the examples of the application of side by side cylinders.

Created wakes through cylinders usually come from interaction consequences of the number of simple wakes [2]. Flow in behind of pair cylinders with side by side arrangement depend on T/d ratio and other parameters such as pressure gradient, initial conditions and Reynolds number [3].

Zhou, Xu had been investigated Reynolds number effects on the structure of flow behind of two side by side cylinder [4] and observed that flow structure was asymmetric in T/d=1.2-1.6 and in T/d>2.2-2.5 two separated vortex paths were created and also observed that same structures remained between distance of two cylinders when Reynolds number changed, and two separated paths created as well, that had same Strouhal number.

Ishigai and his colleagues concluded that the flow regimes at T/d<1.2- 1.3 behave as a single massive objects and produce just one Strouhal number [5].

Sumner and his co-operatives categorized measured quantities in previous experiments with experimental condition such as Reynolds number, T/d and measurement type and revealed that; there are three kind of flow for cylinders with side by side arrangement which also observed by the previous researchers [6].The first flow regime is the single massive object that produce a vortex and one Strouhal number in distances between two cylinders at 1<T/d<1.2 .And wide and narrow wake patterns constitute in the middle distance with 1.2<T/d<2.2 . The third flow regime with in- phase or anti--phase symmetric vortices form at T/d>2.2 that create two wakes with same frequencies.

Williamson observed that constituted vortices in distances between two cylinders were in-phase or anti-phase[7].In-phase paths in downstream, eventually compose with each other in order to create single path, while anti-phase paths remain separate and different in downstream. He also observed that anti--phase vortices are dominant in 2<T/d<6.

Experiment Details

The open circuit and blower wind tunnel testing machine has been used in this research which consists of hot- wire flow measuring equipment (figl) and has the ability of measuring turbulent flow mean and oscillatory velocity. A centrifuge electric motor with 7KW power used in this machine for creating air flow which has the ability of creating air with 30 meter per hour speed. The maximum free stream turbulence intensity for this machine is 0.1%. This amount of turbulence intensity in free stream is infinitesimal so the machine has a great accuracy in this regard. Material of machine room's is Plexiglas with 168cm length, 40cm width and 40cm height. Air flow tested with 20m/s speed, as result, Reynolds number should be 18800 if we consider cylinder diameter. In addition to hot-wire sensor, air flow speed measured with Pitot tube. Also temperature parameter measured for considering temperature effects and calibration measured with other sensors.

The material of selected cylinders in this research was Plexiglas which prevented the effects of surface roughness on the results. Cylinders had same diameter and was 15mm and cylinder length was selected 40cm.

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Schematics of this test and directions and parameters definition can be seen in fig2.

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Discussion of experiment result

This paper investigated how wake formed between a pair of square cylinder with side by side arrangement and drag coefficient and Strouhal number in Reynolds number 18800. The Strouhal number can be obtained by the following equation:

St = fd/U[infinity]

Where St is Strouhal number, f is vortices frequency, d is cylinders diameter and U[infinity] is the free stream velocity. Strouhal number is indicator of small vortices frequencies inside wake behind the cylinders. Data extraction has been carried out in 6 station in behind of cylinders x/d=0.51,1.5,2.5,3.5,4.5,5.5 with free stream velocity U[infinity] = 20m/s by the one dimension hot-wire flow meter.

Through the figures it can be observed that distance between two cylinders plays key role in creation of wakes and through these distances it can be seen that following three sample flows happened between two cylinders with side by side arrangement:

From fig.3 it can be observed that at T/d=1.1, two cylinders act as single one and create a wake which there are one maximum and two minimum velocity inside the wake at x/d=0.51 and became more steady in higher x/d.

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From the fig.4 and fig.5, it can be observed that at T/d=1.5, 2 and x/d=0.51,1.5,2.5 and x/d=0.51,1.5 asymmetric double separated narrow and wide wakes were created which repeated alternatively that means, when wide wake at T/d=1.5 happened in upstream, at T/d=2, wide wake happened in downstream and also it can be seen that wake edges velocity was more than free stream velocity in the first station because of pressure reduction in behind of two side by side cylinders. Velocity at the point that wakes changes is more than free stream velocity because of interacting between jet and wakes. Created jet increases with decreasing of T/d and with increasing distance from cylinders, jet loses its energy and double separated wakes converted to the single one.

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Fig.6, 7, 8 reveal that two separated wakes was formed at T/d=3, 4, 5 which are approximately symmetric and at the first stations wake edges velocity was more than free stream velocity but in the following next stations they reached together and also in this distances there is not interaction between jet and wake . Because of suddenly pressure reduction in the first station, flow velocity changes in behind cylinder at first station is much more than the next stations. As can be seen through the figures, with getting far from cylinders, velocity profile become steady for distances between two cylinders and velocity difference will be reduced at inside and outside of the wake.

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We define velocity defect parameter for Giving quantitative to mean velocity profile results. Velocity defect parameter obtains through abstraction of free stream velocity from inside wake minimum velocity. As a result, the larger this parameter, the greater velocity difference inside and outside of cylinder. It can be observed from fig.9 that velocity defect parameter in narrow wakes is less than wide wakes at T/d=1.5, 2 and X/d=1.5 and also the velocity defect parameter in the both (narrow and wide wakes) is less than form T/d=2.

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In fig.10, velocity defect profile presented for T/d=3, 4, 5. Results have shown that at x/d=1.5,3.5 this parameter reduces with increasing distance between two cylinders and also with getting far from cylinders, reduction of this parameter reduces too.

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Fig.11 shows drag coefficient graph's whit wake-survey method in flow between square cylinders with side by side arrangement. Via this graph it can be find that drag coefficient reduces with increasing T/d.

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Fig.12 shows Strouhal number graph's at various T/d for two square cylinders with side by side arrangement, through the fig.12 it can be find that Strouhal number of wide and narrow wakes increases and decreases respectively with increasing of T/d. And at T/d=3, 4, 5 Strouhal numbers in two symmetric wakes are the same and with increasing T/d Strouhal numbers remain unchanged in symmetric wakes. Regard to Strouhal number in single square cylinder is 0.15, it can be find through the fig. that Strouhal number in single cylinder is more than wide wake Strouhal number's and less than narrow wake Strouhal number's.

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Conclusion

In this research we considered flow pattern around a pair square cylinder with side by side arrangement in various distances. Results have shown that distance between two cylinders has key role in wakes creation for which at T/d[greater than or equal to]3 both of wakes are symmetric and have same Strouhal number which approximately is equal with Strouhal number in flow around single cylinder. And at T/d=1.5,2, with decreasing T/d both wide and narrow wakes will be created that Strouhal number in wide wake is less than Strouhal number in single cylinder and for narrow wake is more than that of single cylinder. And also with decreasing T/d,.difference between Strouhal numbers in a pair cylinders and single cylinder increases and ultimately two wakes amalgamated at T/d=1.1 and only a single wake can be observed. Also investigation in velocity profiles at samples with T/d= 1.5,2 which have two kind wakes reveal that, velocity defect in wide wake was more than narrow wake and in other distances, this parameter decreases with increasing distance between two cylinders. And also it can be observed that, with decreasing T/d, drag coefficient increases, and compound drag coefficient in a pair cylinder with side by side arrangement is less than that of two single cylinders in complex.

Symbols

T: distance between cylinder centers

d: cylinder diameter

Uref: free stream velocity

Re: Reynolds number

X: Longitudinal distance

St: Strouhal number

Cd: drag coefficient

References

[1] J. R. Meneghini, F. Saltara, C. L. R. Siqueira, J. A. Ferrari JR, 2001, Numerical simulation of flow interference between two circular cylinders in tandem and side-by-side arrangements, Journal of fluid and structures, vol15, 327-350

[2] Y. Zhou, R. M. C. So, M. H. Liu, H. J. Zhang, 2000, Complex turbulent wakes generated two and three side-by-side cylinders, International Journal of heat and fluid flow, 21, 125-133

[3] Y. Zhou, H. J. Zhang, M. W. Yiu, 2002, The turbulent wake of two side-by-side circular cylinders, J. FluidMech,, Vol. 458, pp 303-332

[4] Xu, S. J, Zhou, Y., 2003, Reynolds number effects on the flow structure behind two side-by-side cylinders, Physics of fluids 15, 1214-1219

[5] Ishigai, S., Nishikaw, E., Nishimura, E., K., 1973, Experimental study of structure of gas flow in tube banks axes normal to flow, Bulletin of the Japan Society Of Mechanical Engineer 15, 949-956

[6] Sumner D, Wong SST, Price SJ, Paidoussis MP, 1999, Fluid behavior of side by side circular cylinders in steady cross-flow, J Fluids structure, 309-338

[7] Williamson, C. H. K, Vortex dynamics in the cylinder wake, 1996, Annual Review of fluid mechanics 28, 477-539.

[8] Bia Lu, Michael B. Bragg, 2002, Experimental investigation of the wake survey Method for a bluff body with a highly turbulent wake, 20th Applied Aerodynamics Conference, 24-26 Jun

Abdol Amir Bak Khoshnevis (1) ; Saber Amiralaie Bonab (2) *, Rahman Karamati (3) and Gh. Jabbari (4)

(1) Dept. of Mechanic Sabzevar Tarbiat Moallem University Sabzevar, Iran (2) Faculty of Science, Dept. of Engineering, Islamic Azad University of Bonab, Iran (3) Faculty of Science, Dept. of Engineering, Islamic Azad University of Bonab, Iran (4) Institute of Energy & Hydro Technology (Azarbyjian Complex) * Correspondence Author E-mail: saber_amiralaie@yahoo.com