Experimental investigation of flow field behind two tandem square cylinders with oscillating upstream cylinder

Experimental Thermal and Fluid Science 68 (2015) 339–358

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Experimental investigation of flow field behind two tandem square cylinders with oscillating upstream cylinder Bhupendra Singh More, Sushanta Dutta ⇑, Manish Kumar Chauhan, Bhupendra Kumar Gandhi Mechanical and Industrial Engineering Department, Indian Institute of Technology Roorkee, U.K., India

a r t i c l e

i n f o

Article history: Received 28 March 2015 Received in revised form 12 May 2015 Accepted 27 May 2015 Available online 6 June 2015 Keywords: Hotwire anemometer Tandem square cylinders Particle image velocimetry Spacing ratio Drag coefficient

a b s t r a c t In this paper, the fluid flow around two identical square cylinders arranged in tandem has been discussed. The upstream cylinder is oscillated in the transverse direction while the downstream cylinder is held stationary. The experiments are conducted at a Reynolds number of 295. Both the influences of spacing between two cylinders, as well as the effect of oscillation, of the upstream cylinder are investigated using Particle image velocimetry, hotwire anemometry and flow visualization techniques. The spacing ratios are varied from 1.5 to 5 while the upstream cylinder is oscillated in harmonics of the vortex shedding frequency of a stationary cylinder at the fixed amplitude. It is observed that there is a strong effect of spacing between the cylinders on vortex shedding mechanism and flow structures. When two cylinders are in tandem there is a critical distance below which vortex shedding of the upstream cylinder is suppressed. Three distinct flow regimes are captured and the detailed investigation of the intricate flow field is done both spatial and temporal domain. The vortex shedding frequency of a single stationary square cylinder is measured with hotwire anemometer and this frequency is being used to oscillate the upstream cylinder with its sub-harmonic, harmonic and super-harmonic frequency ratios. The effect of forcing frequency on flow interference, wake oscillation frequencies, aerodynamic forces and turbulence statistics have been studied for these spacing ratios. Flow fields are investigated in terms of the time-averaged drag coefficient, stream traces, vorticity contours, turbulence statistics and the time-dependent flow field is captured using flow visualization, vorticity contours, and Strouhal number. Ó 2015 Elsevier Inc. All rights reserved.

1. Introduction The flow around oscillating cylinders in tandem arrangement is an important component of numerous engineering applications, such as offshore structures, high rise buildings, trailer trucks, bridge piers, flow around closely spaced electrical power poles, turning vanes in duct elbows, arrays of tubes in heat exchangers and the slender structures in submarines. Nowadays high rise buildings are not isolated but situated close to other building. This leads for two cylinders investigation. Most of the architectural buildings and structures are rigid up to a certain extent; they are flexible in real life. These structures can get energy from surrounded flow and cause flow induced oscillation under certain circumstances. Flow interference between the bodies depends on various factors such as body geometry, spacing ratio, reduced velocity, supports and end conditions of the arrangement. When one of the bodies is subjected to oscillation, the interference becomes more complex and depends on oscillation frequency ⇑ Corresponding author. Tel.: +91 1332 285410; fax: +91 1332 285665. E-mail address: [email protected] (S. Dutta). http://dx.doi.org/10.1016/j.expthermflusci.2015.05.011 0894-1777/Ó 2015 Elsevier Inc. All rights reserved.

and amplitude. Oscillation of a cylinder significantly influences the wake of the downstream side of the bluff bodies. Flow past two identical cylinders in various arrangements has been studied experimentally and numerically in the past by several authors. Zdravkovich [1] has provided an excellent review work in this area of fluid behavior that categorized into three basic categories of interference based on the position of the downstream cylinder. These three categories of interference under which they occur are (1) no interference, (2) wake interference; when one cylinder is completely or partially submerged in the wake of neighbor and (3) proximity interference; when the two cylinders are located close to one another, but neither is submerged in the wake of the other. A similar type of work done by Gu and Sun [2] has also been categorized into shear layer interference and neighborhood interference of the wake region. Sumner [3] has studied the flow around two circular cylinders and identified nine flow patterns depending on the orientation of the cylinder and spacing between cylinders. These flow patterns are categorized as (a) single bluff-body flows; where the two cylinders are close enough to behave as one body (b) small angles of incidence (a = 0–20°) and (c) large angles of incidence (a = 20–90°).

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Nomenclature A AR CD CD0 D f f0 L Re St s

amplitude of oscillation from peak to peak aspect ratio (L/D) drag coefficient based on average upstream velocity and D, = drag per unit length ½qU2D combined drag coefficient for arrangement edge of square cylinder (m) oscillation frequency (Hz) vortex shedding frequency of stationary cylinder (Hz) length of square cylinder (m) Reynolds number qUD=l Strouhal number f o D=U distance between center of two cylinders (m)

Williamson and Roshko [4] studied various spatial modes of vortices which are generated by a cylinder oscillated at different amplitude ratio (A/D) and frequency ratio (f/f0). They classified these modes into three categories; (1) ‘‘2S’’ mode in which two single vortices appear per cycle, (2) ‘‘2P’’ mode in which two pairs of vortices are formed per cycle and (3) an asymmetric ‘‘P + S’’ mode, comprising a pair of vortices and a single vortex per cycle. This work is further extended by Morse and Williamson [5] and found the regime in which the vortex formation is not synchronized with the transverse oscillation at Re = 4000. They also obtained 2S, 2P, P + S and 2Poverlap modes. In 2Poverlap mode, two pairs of vortices are shaded per cycle of oscillation, but the secondary vortex was much weaker. Griffin and Ramberg [6] found the lock-in phenomenon at f = 0.8f0–1.2f0 and a fixed amplitude ratio for transverse oscillation of a body. They also observed that the lateral spacing between vortices decreased as A/D increased due to the forced vibration effect but the longitudinal spacing unchanged. The streamwise distance between the vortices is not constant

U Ucl u u0 urms Vr v v0

vrms l q xz

upstream velocity (m/s) centerline velocity (m/s) x component of velocity (m/s) x component of fluctuating velocity (m/s) root mean square of x component of velocity (m/s) reduced velocity U=fD y component of velocity (m/s) y component of fluctuating velocity (m/s) root mean square of y component of velocity (m/s) dynamic viscosity (Pa s) fluid density (kg/m3) spanwise component of vorticity scaled by U/D

and change inversely with vibration frequency in the lock-in regime. Anagnostopoulos [7] and Placzek et al. [8] reported computational work in the lock-in range and found the variation of drag on a circular cylinder oscillating in the transverse direction. Singh et al. [9] reported, simulation work on flow past a square cylinder oscillating in transverse direction with A/D = 0.2 and frequency ratio range 0.5 6 f/f0 6 3 at 100 and 150 Reynolds numbers. They observed that the vortex shedding frequency matches with excitation frequency in the range of 0.8 < f/f0 < 1.2. At the higher frequency ratio, excitation frequency dominates and multi-polar vortices also exist in the far wake. The literature concerning square cylinders in the tandem arrangement is relatively sparse. Kim et al. [10] studied on two square cylinders in tandem arrangement with changing the s/D ratio from 1.5 to 11 at Re = 5300 and 16,000. They found that the flow patterns at s/D 6 3 are completely different than those at s/D P 3.5, therefore, flow pattern are divided into two modes. In mode 1, shear layers were reattached to the downstream cylinder

Fig. 1. Schematic diagram of the experimental setup.

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0.22

2.4 Okajima (1982); AR=13.3-120 Norberg (1993); AR=51 Sohankar et al. (1999); AR=10 Saha et al. (2003); AR=6-10 Dutta et al. (2007); AR=28 Present; AR=50

0.18 0.16

2.2 2

CD

Strouhal number

0.2

1.8

0.14

1.6

0.12

1.4

0.1 100

200

300

400

500

600

700

800

1.2 200

900

Okajima1995 Yen et al.2008 Present 300

400

500

600

700

Reynolds number

Reynolds number

(a)

(b)

800

900

Fig. 2. Strouhal number and drag coefficient with Reynolds number for flow over a stationary square cylinder comparison with literature.

2 1.8

CD

1.6 1.4 1.2

Lu & Dalton (1996), CC, Re =185, A/D=0.4 Placzek (2009), CC, Re=100, A/D=0.25 Singh (2009), square cyl., Re=150, A/D=0.2 Present (Re=295, A/D=0.1)

1 0

0.5

1

1.5

2

Frequency ratio Fig. 3. Variation of time averaged drag coefficients with frequency ratios of single square cylinder.

2.4

2.2

2

2

1.6

1.8

1.2

CD'

CD'

and in mode 2, shear layers were separately formed from both the cylinders. The critical spacing ratio was 3.5 where the drag was minimum. Yen et al. [11] investigated the two square cylinders in the tandem arrangement by PIV and flow topology. They divided the flow pattern into three different modes; single mode, reattached mode and binary mode at low Reynolds number (Re = 535). In a single mode (s/D = 1.5), the flow pattern over the two square cylinder resembles as a single cylinder pattern. In reattached mode (s/D = 3), the flow separated from the upstream

cylinder and reattached to the lateral surface of the downstream cylinder. In binary mode (s/D = 5), the distance between two cylinders are sufficiently large, so two similar flow patterns are formed from both the cylinders. For multi-cylinder arrangement, Sewatkar et al. [12] studied numerically and limited experimentally to classify the flow around six tandem square cylinders into four regions as synchronous flow (1.5 6 s/D 6 2.1), quasi – periodic-I (2.2 6 s/D 6 2.3), quasi-periodic-II (2.4 6 s/D 6 6) and chaotic regimes (7 6 s/D 6 11). Some researchers reported the flow around the two cylinders with the one cylinder (upstream/downstream) forced to oscillate in the transverse direction. Price et al. [13] investigated the upstream circular cylinder forced to oscillate in transverse direction with s/D = 2 and transverse separation between centers (T/D) = 0.17 in the range of 1440 6 Re 6 1680. Bao et al. [14] have been numerically studied the effect of varying the spacing ratio, frequency ratio and the amplitude ratio on tandem circular cylinders at low Reynolds number (Re = 100). They found that the wake is simple and regular when cylinders are closely spaced and the small amplitude of oscillation. When the space between the cylinders was large and amplitude was high, the flow tends to chaotic. Mithun et al. [15] studied flow past two square cylinders vibrating in transverse direction at Re = 100 and identified the lock-in regime by varying the frequency ratio from 0.4 to 1.6 at the amplitude ratio of 0.4. They also observed the periodic, quasi-periodic and lock-in behavior in the synchronous range at inter cylinder spacings of 2D and 3D. The flow field of two square cylinders in tandem arrangement involves complex interactions between the shear layers, vortices,

0.8

Single Square cylinder s/D = 1.5 s/D = 3 s/D = 5

0.4 0 200

300

400

500

600

700

800

900

s/D = 1.5 s/D = 3 s/D = 5

1.6 1.4 1.2 Re = 295

1

0

0.5

1

Reynolds number

Frequency ratio

(a)

(b)

1.5

2

Fig. 4. Variation of combined time averaged drag coefficient with various spacing ratios (a) at different Re and (b) at different forcing frequency.

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Strouhal number

0.25

cylinder is transversely oscillated at a frequency of sub-harmonic (f/f0 = 0.5), harmonic (f/f0 = 1) and super harmonic (f/f0 = 2) with fixed A/D = 0.1. The results for the isolated square cylinder are first obtained. Then interference studies have been carried out at a reduced velocity (Vr = U/fD) of 11.7 which is in the range of 7.3 < U/fD < 14.0, obtained by Kumar et al. [17].

s/D = 1.5 s/D = 3 s/D = 5

0.2 0.15 0.1

2. Experimental setup and procedure

0.05 0

0

0.5

1

1.5

All experiments are performed in a horizontal open-ended wind tunnel. The schematic diagram of the experimental setup is shown in Fig. 1. The test section has a length of 1800 mm long and 300  200 mm in cross-section. Maximum turbulence intensity in the test section measured is less than 0.08% and a nearly uniform velocity profile (uniformity better than 95%) observed by digital micro-manometer, hotwire anemometer and PIV. The free stream velocity U was measured using pitot-tube equipped with digital micro-manometer (Furness Controls, 19.99 mm H2O). The experiments are conducted over two square cylinders arranged in tandem at various spacing ratios as shown in Fig. 1. The upstream cylinder is subjected to forced oscillation in the transverse direction whereas the downstream cylinder is kept stationary. Two cylinders are placed horizontally in the test section. These are constructed from aluminum and the square cross section of 6 mm sides. Both identical square cylinders have an aspect ratio (AR) of 50 and solid blockage ratio of 3%. The upstream cylinder is mounted on electromagnetic actuators (Spranktronics) for enabling forced oscillation to the cylinder. These electromagnetic actuators are located outside the test section. A small gap is maintained between the cylinder and the test section wall for smooth

2

Frequency ratio Fig. 5. Variation of Strouhal number with spacing ratio and forcing frequency at Re = 295.

wakes and Karman Vortex Street. This complexity further increases when the upstream cylinder is oscillated in the transverse direction. In the present study, the experiments are performed over the two tandem square cylinders for finding drag, observing the flow pattern and the lock-in regime at Re = 295. The effect of variation of s/D in the range of 1.5–5 is also studied with or without oscillation. Three spacing have been selected to capture the three distinct flow regime such as extended-body regime, reattachment regime, and co-shedding regime by Xu and Zhou [16]. These three regimes are important due to the fact that three distinct flow phenomena are observed at these three s/D ratios. Also the upstream

(a)

y/D

3

f/f0 = 0

3

s/D = 1.5

2

2

2

1

1

1

0

0

0

-1

-1

1

-2

-2

2

-3

-3

0

1

2

3

4

5

6

7

8

0

1

2

3

x/D 3

f/f0 = 0

3

s/D = 1.5

y/D

-3.2

-0.2

-2.2

6

7

8

3

s/D = 3

2.2

3.2

-0.2

-3.2

0.2

2

3

4

2

3

5

6

7

8

-3

1.7

3

6

7

8

3.2 2.7 2.2 1.7 1.2 0.7 0.2 -0.2 -0.7 -1.2 -1.7 -2.2 -2.7 -3.2

s/D = 5

0

1

2

3

4

5

6

7

-0.7 0. 7

2 8

3

0

1

2

3

x/D s/D = 1.5

5

2.7

1

0.2

x/D f/f0 = 0

4

-2.7

0 0 .2

-2 1

1

f/f0 = 0

1

-1.7

3.2

-1

-2 0

0

2

0

-1

3

x/D

f/f0 = 0

1

0

3

5

2

1

-3

4

s/D = 5

f/f0 = 0

x/D

2

(b)

3

s/D = 3

f/f0 = 0

4

5

6

7

8

x/D

f/f0 = 0

3

s/D = 3

f/f0 = 0

0.10

s/D = 5

2

2

2

0.08

1

1

1

0.04

0

0

0

-1

-1

1

-2

-2

2

(c)

y/D

0.06 0.02 -0.02 -0.04 -0.06

-3

0

1

2

3

4

x/D

5

6

7

8

-3

0

1

2

3

4

x/D

5

6

7

8

3

-0.08 -0.10

0

1

2

3

4

5

6

7

8

x/D

Fig. 6. Time-averaged (a) Stream traces, (b) Span-wise vorticity and (c) Reynolds stresses for stationary cylinders at spacing ratio (s/D) = 1.5, 3, and 5.

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oscillation of the cylinder. This gap is filled with soft rubber to minimize the leakage of air. The cylinder motion is pure sine wave over a wide range of frequencies (1–1000 Hz). It is excited at different harmonics of the vortex shedding frequency (frequency ratio 0.5, 1 and 2) of a stationary cylinder. The amplitude of oscillation is fixed as 10% of cylinder diameter (0.1D). The downstream square cylinder which is held stationary varies its position with respect to an oscillating cylinder for a different spacing ratio studied. The spacing ratio is the streamwise distance between centers of two cylinders as shown in Fig. 1. The forcing frequency to the upstream cylinder in the transverse direction is provided by power oscillator. The oscillation amplitude of the electromagnetic actuator is calibrated by laser Vibrometer (Polytec). The actuator frequency and amplitude are adjustable through a power oscillator. The PIV measurements are taken in some selected planes of interest. The PIV system consisting of double pulsed, Nd-YAG laser (Evergreen, 532 nm) of 200 mJ, a 4 MP camera (power view, 2048  2048 pixels) with frame speed 15 Hz, a synchronizer, a frame grabber and a dual processor PC. Minimum frame straddling time for PIV capture is 200 ns. The pulse separation distance (Dt) varied between 15 and 150 ls based on incoming velocity and the resolution requires the measurements. A Nikon 60 mm manual lens is attached with the camera to observe the field of view of 92 mm  92 mm. The FFT-based cross-correlation algorithm is used to make computations faster. It is then coupled with a two-dimensional Gaussian fit to find the correlation peak positions in each interrogation region. A total of 127  127 vectors are

(a)

y/D

3

f/f0 = 0.5

3

s/D = 1.5

obtained after analysis with a spatial resolution of 0.718 mm. A total of 200 images are captured for time-averaging the velocity field from raw data. These images are sufficient to get the steady time-averaged vectors field. The vorticity field is being calculated from the circulation value measured from 3  3 surrounding grid points. Olive oil is used for seeding the particles through a six-jet atomizer (TSI model 9306) connected with an automatic air compressor. Flow seeding is done uniformly in the test section with a customized seeding arrangement which is given at the entrance of the wind tunnel. The average seeding particle size estimated of 2 lm. The velocity measured using PIV are matches quite well with a digital micro-manometer (Furness Controls Limited) reading and hotwire anemometer (Dantec Dynamics) reading for different Reynolds numbers. Hotwire anemometer has been used for measuring the fluctuating velocity signal. A cross wire probe is used for measuring the velocity in two planes. The long time signal of 20,000 samples with 1000 Hz sample frequency is taken to obtain the better results. A band pass filter (0.1 Hz–1 kHz) is used additionally to avoid unwanted noise in the signal. The voltage signal collected from hotwire anemometer is converted to the velocity signal through calibration curve using the pitot-static tube. A fifth order polynomial is fitted for calibration purpose. The velocity is resolved into u and v-velocity components using calibration curve. The power spectrum from the velocity signal (v-velocity) is obtained by using Fast Fourier Transform (FFT) algorithm. The long time signal divided into a number of parts and fast Fourier transform is done

f/f0 = 0.5

2

2

2

1

1

1

0

0

0

-1

-1

1

-2

-2

2

-3

0

1

2

3

4

5

6

7

8

-3

0

1

2

3

x/D

y/D

3

(b)

5

6

7

8

3

3

s/D = 1.5

f/f0 = 1

f/f0 = 1

3

s/D = 3

2

1

1

1

0

0

0

-1

-1

1

-2

-2

2

0

1

2

3

4

x/D

5

6

f/f0 = 2

7

8

-3

1

2

3

4

5

6

7

8

3

3

s/D = 3

f/f0 = 2

2

1

1

1

0

0

0

-1

-1

1

-2

-2

2

1

2

3

4

x/D

2

3

5

6

7

8

-3

0

1

2

3

4

x/D

4

5

6

7

8

s/D = 5

f/f0 = 1

0

1

2

3

4

5

6

7

8

x/D

2

0

1

x/D 3

s/D = 1.5

0

2

-3

0

s/D = 5

x/D

2

3

y/D

4

f/f0 = 0.5

x/D

2

-3

(c)

3

s/D = 3

5

6

7

8

3

s/D = 5

f/f0 = 2

0

1

2

3

4

5

6

7

8

x/D

Fig. 7. Time-averaged stream traces for (a) sub-harmonic (f/f0 = 0.5), (b) harmonic (f/f0 = 1) and (c) super-harmonic frequency (f/f0 = 2) oscillation at spacing ratio (s/D) = 1.5, 3, and 5.

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in each part of the signal and then averaged out. Drag coefficient is indirectly calculated by the momentum balance method using velocity profile at 12D downstream from the center of the upstream cylinder. For finding the vortex shedding frequency (Strouhal number), the highest peak of power spectra is used. Flow visualization is carried out using a light sheet generated from the laser used for PIV measurements in the same test cell. The seeding density adjusted to get the intricate flow structure.

by Yen et al. [11]. The comparison of our work with other published data in terms of different flow patterns, Strouhal number, and drag coefficient agrees well with the results reported in the literature. Before performing the experiments using PIV, the standard criteria like particle image-to-pixel ratio, the number of particles in a interrogation spot and average in-plane displacement of the particle as discussed by Keane and Adrian [22] are taken into consideration. These criteria help in reducing the bad vectors as well as reduce uncertainty in finding the peak of the cross-correlation function. The best PIV images also give 1–2% bad or spurious vectors (also called outliers). These are due to the missing particle image pair, insufficient particle in interrogation spots and high-velocity gradient. These vectors can be identified by its abrupt deviation in magnitude and direction compare to neighborhood vectors. In present experiments, maximum 5% bad vectors are found. These vectors are removed by local median filtering (kernel size 3  3) and then replaced with a vector by using the least square fit curve between neighboring vectors.

3. Validation The present data is validated in terms of Strouhal number and drag coefficient at different Reynolds number. Fig. 2 compares the variation of the Strouhal number and drag coefficient with Reynolds number (Re) over a range from 200 to 800. The Strouhal number measured in the present study matches quite well with that reported by the Dutta et al. [18] and Okajima et al. [19]. Drag coefficient is found by the wake survey method applied at mid-plane of the test section and results compared well with Okajima [20] and Yen et al. [11] as shown in Fig. 2. The variation is within the uncertainty range. The drag coefficient (CD) is also measured at ±10D from the mid-plane in the spanwise direction. The maximum variation of drag coefficient in the spanwise direction was within 2%. CD over a single square cylinder with different frequency ratios at Reynolds number of 295 has shown similar trend as reported earlier by Lu & Dalton [21], Singh et al. [9] and Placzek et al. [8] shown in Fig. 3. Three different types of the mode were observed over two tandem stationary square cylinders at different s/D ratio and these are similar with previous work done

3

f/f0 = 0.5

3

s/D = 1.5

y/D

(a)

-3.2

-0.2

-2.2

1

f/f0 = 0.5

2.2

3.2

-1

-0.2

-3.2

1

2

3

5

4

6

7

8

-3

1.7

3.2

f/f0 = 1

3

s/D = 1.5

y/D

-0.2

-3.2

-2.2 2.2

3.2

1

0

2

3

3

0.2

y/D

(c)

0

1

2

3

4

x/D

5

6

7

8

6

7

8

3

s/D = 3

2

1

1

-3.2

-1.2

-0.2

1.7

3.2

1.7

-3

1

0

2

3

4

x/D

5

6

7

8

-3

4

5

6

2

3

4

5

6

8

7

8

3

3.2 2.7 2.2 1.7 1.2 0.7 0.2 -0.2 -0.7 -1.2 -1.7 -2.2 -2.7 -3.2

-0.2

-3.2

-1.2 1.2

3.2

0.2 0

1

2

3

4

5

6

7

8

x/D

f/f0 = 2

3

s/D = 3

f/f0 = 2

-0.2

1

-1.2

3.2 2.7 2.2 1.7 1.2 0.7 0.2 -0.2 -0.7 -1.2 -1.7 -2.2 -2.7 -3.2

s/D = 5

2

-0.2 -3.2

7

s/D = 5

f/f0 = 1

1

-2.7

-1.2

2.2

1.2

0

1.2

3.2

1

0.2

-2 1

3

x/D

-1

0.2

-2 0

2

2

1

-1.7

3.2

1

0

0

-1

0

x/D

2

-3.2

3

2

3

s/D = 1.5

f/f0 = 2

0

-3

5

-2

2 1

4

f/f0 = 1

-1

-2 -3

0.2

2

0

0 -1

0.7

x/D

2

(b)

-0.7

2.7

1

0.2

x/D

1

-2.7

0

-2 0

-0.2

1

-1.7

3.2 2.7 2.2 1.7 1.2 0.7 0.2 -0.2 -0.7 -1.2 -1.7 -2.2 -2.7 -3.2

s/D = 5

f/f0 = 0.5

2

-1

0.2

-2

3

3

s/D = 3

0

0

-3

In the present study, we have captured the three distinct flow regime based on cylinder spacing combined with cylinder oscillation. The flow is seen to be sensitive to Reynolds number, as well as the spacing ratio between the cylinders. It is also quite complex due to the interaction of shear layer, boundary layer and wake of the cylinders. It becomes even more complex as one of the cylinders is oscillating. The general trend for the three spacing can be

2

2 1

4. Results and discussion

0

1

2

3

4

x/D

5

0.2

2 6

7

8

3

0

1

2

3

4

5

6

7

8

x/D

Fig. 8. Time-averaged span-wise vorticity for (a) sub-harmonic, (b) harmonic and (c) super-harmonic frequency oscillation at spacing ratio (s/D) = 1.5, 3, and 5.

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summarized as follows: When two cylinders are very close to each other (s/D = 1.5), the second cylinder act as an extended body. With an increase in spacing (s/D = 3) a recirculation zone is formed behind the first cylinder but no vortex shedding occurs from the upstream cylinder. A quasi-steady flow condition prevails between the two cylinders. When the cylinders are reasonably apart (s/D = 5), the vortex shedding is also seen from the first cylinder. For all the three cases studied, the incoming flow condition for the downstream cylinder gets modified due to the presence of the upstream cylinder. The flow interference between the cylinders depends upon the spacing of the cylinders and the oscillation frequency. Three spacing ratios and three oscillating frequencies in harmonics of the vortex shedding frequency of the stationary cylinder are studied. The amplitude of oscillation kept constant (A/D = 0.1). Flow details are discussed in the following headings.

CD ¼ 2

y/D

(a)

3

s/D = 1.5

u u 1 dy þ 2 U U

Z

1

1

 v 02  u02 dy U2

ð1Þ

The acquired velocity profile and fluctuating components measured are fed into the extended momentum integral formula (Eq. (1)) to calculate drag. The first term in the above equation is the momentum deficit of the time-averaged velocity field and the second term is due to turbulent fluctuations. The variation of drag coefficient (CD) with respect to Reynolds numbers at various spacing ratios is shown in Fig. 4(a). When the spacing between the cylinder s/D = 1.5, the second cylinder behave as an extended body like a short splitter plate. So the drag coefficient reduced as compared to the single stationary square cylinder for all the Reynolds number studied. The shear layer separation delayed due to the presence of the downstream cylinder. With the increase in spacing (s/D = 3), a quasi-steady bubble forms in the gap between the two cylinders. This bubble formation causes a reduction in base pressure of the upstream cylinder. Simultaneously there is a reduction in recirculation length of the downstream cylinder. This two-counter effect reduces the drag coefficient as a whole compared to the single cylinder. As s/D ratio increases further (s/D = 5) the upstream cylinder shed vortices independently and the downstream cylinder shedding is initiated by the upstream cylinder. The wake of the downstream cylinder becomes three dimensional as seen in flow visualization images (Fig. 16). The total drag coefficient (s/D = 5) increases compare to the single stationary square cylinder. Similar observations are also reported by Bao et al. [14]. The calculated CD for the single square cylinder is validated the trend with the previous literature of single transversally oscillating

The drag coefficient is calculated by the wake survey method. This method is based on momentum balance over a control volume around the cylinders. In the present case, it is calculated from the time-averaged velocity profile taken at 12D from the center of the upstream cylinder. Since at this position the fluctuating velocity component is significant, it has been added to the modified drag coefficient formula. For all, the drag coefficient, a velocity profile is taken at 12D position irrespective of the spacing ratio of the cylinders. Averaging is done over 200 instantaneous PIV images. The drag coefficient is calculated by the following relation:

f/f0 = 0.5

1

1

4.1. Drag coefficient and Strouhal number

3

Z

f/f0 = 0.5

3

s/D = 3

f/f0 = 0.5

0.10

s/D = 5

2

2

2

0.08

1

1

1

0.04

0

0

0

-1

-1

1

-2

-2

2

-3

-3

3

0.06 0.02 -0.02 -0.04 -0.06

0

1

2

3

4

5

6

7

8

0

1

2

3

x/D 3

y/D

5

6

7

8

-0.10

0

1

2

3

x/D

f/f0 = 1

3

s/D = 1.5

4

5

6

7

8

x/D

f/f0 = 1

3

s/D = 3

f/f0 = 1

0.10

s/D = 5

0.08

2

2

2

(b)

4

-0.08

1

1

1

0

0

0

-1

-1

1

-2

-2

2

-3

-3

3

0.06 0.04 0.02 -0.02 -0.04 -0.06

(c)

y/D

3

0

1

2

3

4

x/D

5

6

f/f0 = 2

7

8

1

2

3

4

5

6

7

8

-0.10

0

1

2

3

x/D 3

s/D = 1.5

0

-0.08

4

5

6

7

8

x/D

f/f0 = 2

3

s/D = 3

2

2

2

1

1

1

0

0

0

-1

-1

1

-2

-2

2

f/f0 = 2

0.10

s/D = 5

0.08 0.06 0.04 0.02 -0.02 -0.04 -0.06

-3

0

1

2

3

4

x/D

5

6

7

8

-3

0

1

2

3

4

x/D

5

6

7

8

3

-0.08 -0.10

0

1

2

3

4

5

6

7

x/D

Fig. 9. Reynolds stresses for (a) sub-harmonic, (b) harmonic and (c) super-harmonic frequency oscillation at spacing ratio (s/D) = 1.5, 3, and 5.

8

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B.S. More et al. / Experimental Thermal and Fluid Science 68 (2015) 339–358 3

3

f/f0 = 0

2

0.07

y/D

1

(a)

0

0.20

0.07

0.10

0.05 0

1

2

3

4

5

6

7

8

-3

1

2

3

x/D f/f0 = 0 0.10

y/D

0.40

0.50

-1

f/f0 = 0

0

1

2

0.10

5

6

7

8

-3

f/f0 = 0

y/D

0.25

0.20

0

1

2

3

0.35

-1

s/D = 1.5 0

1

2

3

4

6

7

8

4

5

7

8

-3

7

6

8

0.60

0.10

0.30

0.15

3

0

1

0.35

0.25

3

4

x/D

0.30

0.10 0.05

2

3

4

5

7

6

8

0.75

0.10

5

6

7

0.65

0.25

0.55

0.65

0.05

8

3

0.45

0.55

0.35

0.45

1

s/D = 3 2

0.30 0.20

f/f0 = 0

2 1

0.40

s/D = 5

0

0

0.50

1

0.45

0.10

0.40

0.50

0.20

0.05

0.50

0.30

0.60

2

0.05

-2 6

5

x/D

f/f0 = 0

x/D

Fig. 10. Time-averaged (a) urms, (b)

5

3

-1

0.15

0.05

4

0

0.55

-2

3

2

s/D = 3

1

0.45

0

2

f/f0 = 0

1

0.05

2

0.10

0.07 0.05

1

x/D 3

1

0

0

0.40

x/D

2

3

0.10

s/D = 5

1

0.30

-2 4

3

0.05

0.10

2

-1

s/D = 1.5

-3

8

0.20

0.30

x/D

0

0.30

0.20

0.05

-2

(c)

7

3

1

0.20

0

3

6

2

1

-3

5

0.30

x/D 3

2

(b)

4

0.40

0.40

2

s/D = 3 0

0.20

0.40

1

0.10

0.05

0.07

1

0.30

-2

s/D = 1.5

0.60 0.50

0

-1

-2

3

0.20

0.40

0

0.30

f/f0 = 0

2

1

-1

-3

3

f/f0 = 0

2

0.25 0.15

0.35

0.15

0.10

s/D = 5 0

1

0.05

2

3

4

5

6

7

8

x/D

vrms and (c) turbulence intensity {(urms2 + vrms2)0.5/U} contours, of stationary cylinders at spacing ratio (s/D) = 1.5, 3, and 5.

square cylinder as shown in Fig. 3. There is a wide band in drag coefficient value in the literature as Reynolds number and flow configuration compares are little different, but the overall trend is same. The variation of combined time-averaged drag coefficient with different forcing frequencies and spacing ratios at this Reynolds number is shown in Fig. 4(b). When the upstream cylinder is oscillated with sub-harmonic frequency (f/f0 = 0.5), the total drag coefficient of two tandem cylinder arrangement are almost equal to that of stationary cylinder arrangements which implies flow structures are not manipulated with this frequency. Although the little increase in drag coefficient observed for s/D = 5. With the further increase in oscillation frequency (f/f0 = 1), synchronization occurs and the combined drag coefficient has increased for s/D = 1.5 and 3. For super-harmonic oscillation, there is maximum variation in CD value. At this frequency, the wake is quite unsteady and flow three-dimensionality is dominant as seen in flow visualization images (Fig. 20). For s/D = 1.5, the wake size reduces quite marginally at this frequency compare to other two spacings. Both spacing and frequency plays a crucial role in overall vortex load measurement. Fig. 5 shows the Strouhal number variation with the spacing ratio as well as the forcing frequency of the upstream cylinder. The Strouhal number is determined from the dominant spectral peak from the spectrum of the velocity signal. For the stationary upstream cylinder, a maximum Strouhal number is seen for spacing ratio s/D = 1.5. It is to be noted that at this spacing ratio the downstream cylinder seen to behave as an extended body mentioned earlier. The vortex roll-up behind the downstream cylinder is closer to the cylinder base. The shedding frequency is higher compared to a single stationary cylinder and consequently higher

Strouhal number as reported by Meneghini et al. [23]. The wake is also narrower compared to the single stationary cylinder. With an increase in spacing the Strouhal number decreases abruptly to a smaller value. It is even smaller than the shedding frequency of the single stationary cylinder. The same observation was made by Sumner [3]. With the forcing frequency of the upstream cylinder, the vortex shedding phenomena modified. For lower forcing frequency (f/f0 = 0.5), the effect of spacing is seen to be reduced. This effect is very strong for f/f0 = 1 and the vortex shedding frequency of the downstream cylinder is coupled with the forcing frequency of the upstream cylinder and lock-on occurs for all spacing ratio. The effect of spacing on the vortex shedding is minimum at this frequency. At the higher forcing frequency (f/f0 = 2), the shedding frequency resembles that of the stationary cylinder. 4.2. Flow around two stationary cylinders in tandem 4.2.1. Time-averaged stream traces The time-averaged stream traces over two stationary square cylinders for different spacing ratios (s/D = 1.5, 3, and 5) are shown in Fig. 6(a). These stream traces are derived from the time-averaged velocity vectors. At s/D = 1.5, the flow separates near the front corners of the upstream cylinder and a pair of minor vortices centered at a position (x/D, y/D  0.8,±0.5) between the gap of the two cylinders. A pair of major vortices centered at (2.8, 0.25) and (2.75, 0.3) are formed in the wake of downstream cylinder and also a four-way saddle point is formed at (3.5, 0). Yen et al. [11] named this as the vortex sheet of single mode for two stationary cylinders. At s/D = 3, the flow separates from the upstream cylinder and two reattached bubbles are centered at

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B.S. More et al. / Experimental Thermal and Fluid Science 68 (2015) 339–358

(2.1, 0.6) and (1.7, 0.28) that reattached to the lateral surface of the downstream cylinder. Two vortices are formed behind the downstream cylinder at (4.0, 0.25), (4.05, 0.25) and a saddle point is formed at (4.7, 0). A quasi- steady equilibrium is seen between the two cylinders. For larger s/D, the shear effect of the upstream cylinder is less pronounced in the downstream cylinder. With the further increase in spacing (s/D = 5) regular vortex shedding occurs from both upstream and downstream cylinder. The shedding from the downstream cylinder is manipulated by the upstream cylinder wake. This is seen clearly in flow visualization images (Fig. 16). At s/D = 5.0, two vortices and a saddle point are formed behind the upstream cylinder at (1.55, 0.35), (1.5, 0.3) and (2.3, 0). Similarly two vortices and a saddle point are formed behind the downstream cylinder at (5.77, 0.22), (5.71, 0.21) and (6.1, 0.15). Two similar types of flow structures are formed in the downstream side of both the cylinders. This flow pattern is called the binary mode of vortex shedding.

proportional to vorticity production. The size of two oppositely oriented vortices is almost same. Normalized vorticity strength of 0.2 are formed up to 6D position in the streamwise direction at s/D = 1.5. When the spacing increases and reaches up to reattach mode (s/D = 3), vorticity strength of 0.2 is formed up to 8D. For binary mode (s/D = 5) this strength is further increased in the downstream side. The vorticity strengths near upstream cylinder are constant for single and reattach mode but decreases for binary mode. This strength near the downstream cylinder is decreased with respect to spacing. 4.2.3. Time-averaged Reynolds stress The Reynolds stress (–u0 v0 ) contours for different s/D ratios are shown in Fig. 6(c). The Reynolds stress can be taken as the mean momentum transport by the fluctuating velocity components. The production of Reynolds stress arises due to the velocity gradient in the flow field. The higher gradient which occurs in the near wake and hence the Reynolds stress. In case of the single stationary cylinder, the maximum Reynolds stress is seen to occur at the leading edge of the cylinder in the shear layer. But with the multi-cylinder arrangement the time-averaged Reynolds stress are seen to occur further downstream location. At s/D = 1.5, Reynolds stress is formed behind the downstream cylinder at a distance of 4–5D from cylinder center. It is concluded that for multi-cylinder arrangement, the momentum transport in the near cylinder occurs by the pressure fluctuation only. With the development of the shear layer downstream the turbulent motion causes the momentum transport. Due to the presence of the downstream cylinder the vortex shedding delays and occurs at a distance from

4.2.2. Time-averaged vorticity field Fig. 6(b) shows the time-averaged spanwise vorticity (xz) contours over two stationary square cylinders. These contours represent the strength of the formed vortex in the wake of cylinder arrangements. Contours are normalized by U/D. Dotted lines are used for negative vorticity in the clockwise direction and solid lines are used for positive vorticity in the counter clockwise direction. Vorticity in the wake is generated where the shear layer separates and its strength decreases with downstream direction due to viscosity effect. With downstream distance, the velocity difference between the centerline and the main flow decreases which is

3

3

f/f0 = 0.5

2

0.10

(a)

y/D

1

0.25

0.35

-3

0

1

2

4

3

5

7

6

8

-3

0.05 0

1

2

3

f/f0 = 1 0.25

y/D

0

-1

-3

3

1

3

4

x/D

5

6

7

8

f/f0 = 2

y/D

(c)

0.10

0.35 0.35

0.10

0.35 -1

0.15

1

2

-2 3

4

x/D

0

1

5

6

7

8

-3

0.10

0.05 2

0.05

3

4

5

6

7

8

0.75

f/f0 = 1

0

1

2

3

4

0.65

5

6

7

8

3

f/f0 = 2

0.55

1

3

0.10

s/D = 5 0

1

0.05

2

3

4

5

6

7

8

0.75

f/f0 = 2

4

x/D

0.65

0.10

0.05

2 5

6

7

8

3

0.55

0.35

0.45

0.45

0.45

1

0.35

0.25 0.55

0

0.55

0.15 2

0.15

0.15

0.05

1

0.45

0

0.25

2

0.25

0.05 s/D = 3

0.35

x/D 3

0.10

0.45

0.45

0.55 0.35

2

s/D = 3

0.55

0.45

1

0.35

0.15

0.05

0.65

0.25

0.10

0

0.55

-1

s/D = 1.5 0

s/D = 5

0.15

0.35

0.15

1

0.45

0

0.25

0.05

-2

0.25

1

0

-3

0.10

2

0.25

0.35 0.25

x/D 3

2 1

-3

0.55

2

-2

0.05

2

8

0.45

x/D

-1

0.15

0

7

3

3

0

0.35

s/D = 1.5

6

f/f0 = 1

1

0.45

0.55

-2

0.55

2 5

0.55

1

2

0.10

1

(b)

0.25

x/D 3

2

4

0.65

0.45

0

0.35

s/D = 3

x/D 3

0.15

0.75

0 0.1

1

0.45

-2

0.05

s/D = 1.5

0.25

-1

0.15

-2

0.10

0

-1

f/f0 = 0.5

2

1

0.45

0.55

0

3

f/f0 = 0.5

2

0.35 0.25

0.15

0.15 0.10

s/D = 5 0

1

0.05

2

3

4

5

6

7

8

x/D

Fig. 11. Turbulence intensity {(urms2 + vrms2)0.5/U} contours for (a) sub-harmonic, (b) harmonic and (c) super-harmonic frequency oscillation at spacing ratio (s/D) = 1.5, 3, and 5.

B.S. More et al. / Experimental Thermal and Fluid Science 68 (2015) 339–358

the downstream cylinder as happens in the case of a splitter plate attached to the cylinder. When spacing ratio increases to s/D = 3, strength of Reynolds stresses increases in downstream side and with the further increase in the distance (s/D = 5), these contours are formed for both the cylinders with enhancement in strength. At far downstream locations for all spacing ratio these opposite sign Reynolds stress component essentially merged on averaging.

pressure reduces which ultimately increases the drag coefficient of the downstream cylinder. But the combined effects of both the cylinders decrease the overall drag coefficient (Fig. 4b). With the increase in spacing (s/D = 3) two encapsulated recirculation bubble form between these two cylinders. This phenomenon is observed for all oscillation frequencies studied. The recirculation bubble length between the cylinders decreases with an increase in forcing frequency. At higher frequency, this is detached from the downstream cylinder and get concentrated near the base of the upstream cylinder. The downstream cylinder wake shows a noticeable change with respect to the frequency of oscillation. At f/f0 = 0.5, recirculation zone is formed behind the downstream cylinder which diminishes with higher frequency ratios. At s/D = 5, interestingly the recirculation bubble formed behind the upstream cylinder are of almost equal size. When a cylinder is forced to oscillate in either streamwise or transverse direction there is a reduction in recirculation length, and hence increases in base pressure as Dutta et al. [18].

4.3. Flow around oscillating upstream and stationary downstream cylinder 4.3.1. Time-averaged stream traces When one of the cylinders is set in motion, it modifies the whole wake structure and reduces momentum deficit in the wake. The effect of oscillation is prominent at the higher frequency. Fig 7(a) shows the time-averaged stream traces of sub-harmonic oscillation for spacing ratios, s/D = 1.5, 3, and 5. Due to the oscillation of the upstream cylinder the wake becomes more unstable. The shear layer developed on the upstream cylinder interacts with the shear layer of the downstream cylinder due to which the wake of the downstream cylinder modifies. Similarly, the upstream wake is affected by the presence of the downstream cylinder up to a certain spacing ratio. The recirculation length and base pressure of the cylinder are mostly affected by forcing frequency. For the unlocked situation (f/f0 = 0.5 and 2), the wake structures are different for each cylinder and so the time-averaged flow structure is different. At s/D = 1.5 and all frequencies studied, the flow separates only from the downstream cylinder. The recirculation length is seen to increase significantly at f/f0 = 2. At this frequency, the base 3

f/f0 = 0

3

s/D = 1.5

2

y/D

-0.35

0.1

0.35

-1

1

-0.15

0

-1

-0.02

-0.25

-0.15

0.3

0.15

1

2

3

4

5

6

7

8

-3

s/D = 1.5

f/f0 = 0

5

y/D

0.08

0

1

2

3

0.01

0

1

2

3

4

5

8

6

7

8

-3

3

s/D = 1.5

1

0.04

0.1 0.04

0

1

0.04

2

3

1

4

5

6

7

8

1

2

3

4

x/D

3

3

0.01

-0.35 0

2

1

5

6

7

8

-3

4

3

5

6

7

8

s/D = 5

f/f0 = 0

0.10

0.01 0.10

0.08

0.10 0.08

0.1

0.10

0.06 0.04

0

0.02

0.01

0.01 0

1

2

3

4

5

6

f/f0 = 0

7

8

s/D = 5

0.10 -0.10 0.01

-0.10

1

-0.06

0.10

0.10

0 1

0.04

-2 0

-0.15

2

-1

-2

-0.05 -0.25

2

s/D = 3

0

4 0.0

-1

0.15

x/D

f/f0 = 0

1

-0.04 0.06 -0.03

0.05

0.02

0

0.01 0

0.15

-0.02

5

2

0.04

0.25

2

x/D 3

2

0

3

0.35

0.02

0.2

0.35

x/D

f/f0 = 0

1

y/D

7

-2

2

-3

6

s/D = 3

x/D

(c)

5

f/f0 = 0

-1

-2

3

4

0

0.10

-1

-3

1

0.02

-0.15

2

1

0.10

0

-0.25

-0.35

0

2

1

-0. 0

x/D 3

2

(b)

1

-2 0

s/D = 5

f/f0 = 0

2

x/D 3

3

s/D = 3

0

5

-2 -3

f/f0 = 0

2

1

(a)

4.3.2. Time-averaged vorticity field Fig. 8 shows the time-averaged spanwise vorticity (xz) contours for spacing ratios s/D = 1.5, 3 and 5 with different frequency ratios. For smaller spacing ratio (s/D = 1.5), the shear layer from the upstream cylinder reattached on the top and bottom surface of the downstream cylinder. The vortex shedding and reattachment process synchronized which is observed in the flow visualization as well as instantaneous vorticity contours. The effect of sub-harmonic forcing frequency on the time-averaged, as well as instantaneous flow field is nominal for two cylinder case, as

0. 08

348

-0.04

0.10

-0.04

2 0

1

2

3

4

x/D

5

6

7

8

3

0

1

2

3

4

5

6

7

0.10 0.08 0.06 0.04 0.02 0.01 -0.01 -0.02 -0.04 -0.06 -0.08 -0.10

8

x/D

Fig. 12. Dimensionless (a) production, (b) dissipation and (c) diffusion of turbulent kinetic energy (normalized by U3/D) for stationary cylinders at spacing ratio (s/D) = 1.5, 3, and 5.

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B.S. More et al. / Experimental Thermal and Fluid Science 68 (2015) 339–358

compared to a single cylinder. There is a stabilization effect in the wake due to the presence of another cylinder. The wake is not manipulated at this frequency. To compare the relative spreading of vortices due to oscillation non-dimensional vorticity contours of strength 0.2 are compared. The streamwise distance over which these vortices are formed varies from 6D to maximum 9D for these frequencies. Maximum spreading in the streamwise direction is observed for f/f0 = 2 as maximum energy influx in the near wake at this frequency. At s/D = 3, these vorticity contours are formed up to 8D position for sub-harmonic oscillation and it reduces to 7D position for harmonic and super-harmonic oscillation cases. At s/D = 5, these contours of strength 0.2 further increase in the downstream side for all three frequency ratios. Which implies the diffusion mechanism is also stronger at the higher frequency and spacing ratios. The wake is broader and three dimensional which is observed in flow visualization images as well. Vorticity production is proportional to the velocity difference between a main stream and center line velocity.

stationary cylinder at sub-harmonic oscillation. It moves more closely to the cylinder at harmonic oscillation with an increase in strength. But at a higher frequency (f/f0 = 2) it is diminished in the near wake of the cylinder. When spacing ratio increases to s/D = 3, the strength of Reynolds stresses increases and formed around the downstream cylinder for harmonic and superharmonic frequency ratio, but it decreases for sub-harmonic oscillation. At s/D = 5, these stresses are formed separately from both the cylinders with an increase in strength. 4.4. Velocity fluctuations & turbulence characteristics Fig. 10 shows the urms, vrms and non-dimensional turbulence intensity contours at the different spacing ratio for stationary cylinders. The streamwise (urms), transverse (vrms) velocity fluctuation, and the turbulence intensity strength increases with an increase of spacing ratio. The minimum velocity fluctuation between the cylinders is obtained at s/D = 1.5 for two stationary cylinders and it further increases at s/D = 3 and 5. The urms can be related with the transverse gradient of the streamwise velocity whereas vrms can be related with the pressure gradient within and outside the wake. The magnitude of transverse fluctuating velocity (vrms) is higher than the streamwise velocity (urms). The fluctuating components of forces are directly related with the fluctuating flow field since they affect the base pressure distribution on the cylinder surface. The downstream spreading of the fluctuating flow field affects the pressure variation of the suction side of the cylinder hence the drag coefficient. Fig. 11 shows the time-averaged turbulence intensity at different forcing frequency

4.3.3. Time-averaged Reynolds stress Reynolds stresses contours with different frequency and s/D ratios are shown in Fig. 9. The base pressure and the recirculation bubble length are directly linked with Reynolds stress [24]. It is seen that the increase in recirculation length is related to decrease maximum Reynolds stress value (Fig. 10). The higher values of Reynolds stress allow the boundary layer to survive an adverse pressure gradient and delay the transition in the boundary layer. At s/D = 1.5, Reynolds stresses are formed behind the downstream cylinder and these moves closer to the cylinder as compared to the

f/f0 = 0.5

3

s/D = 1.5

2

(a)

y/D

1

-0.25

1

-0.15 0.15

0.25

-1

-2

-0.35

1

2

3

4

5

6

7

8

-3

3

s/D = 1.5

1

y/D

(b)

-0.02 -0.25

.35

0 -1

1

0

1

2

3

1

2

3

4

5

7

6

8

-3

y/D

(c)

f/f0 = 2

s/D = 1.5

-0.35

-0.0

0

0.3

1

-0.02 5

-1

0.02

-2 -3

7

8

1

-0.15

1

2

3

4

x/D

0.15

5

6

7

8

-3

-0.05 -0.15

0.02

-0.25 -0.35

0

1

2

3

4

5

6

7

f/f0 = 1

8

1

0.02

0.35

s/D = 5

0.25

-0.02 -0.35

0

0.15

0.35

-0.25

0.25

0.35

0.15 0.05

-0.15

0.02 -0.02

0.15

-0.05

0.02

-0.15

2 0

1

2

3

4

5

6

7

8

3

-0.25 -0.35

0

1

2

3

f/f0 = 2

s/D = 3

-0. 2

1

5

6

f/f0 = 2

7

8

0.35

s/D = 5

0.25

-0.02 -0.35 -0.35

0

0.25

0.35

5

2

-0.02 -0.35

4

x/D 3

1

0.02

-2 0

3

3

-0.02

-0.35

0

0.05

5

-0.02

x/D

2

-1

0.02

0.35

x/D 3

2 1

6

s/D = 3

x/D 3

5

-2 0

0.05

-0.15

2

-1

0.02

-2 -3

4

f/f0 = 1

0

0.25

0.35

-0.35

2

2

2

-0

0.25 0.15

-0.02

x/D

f/f0 = 1

0.35

s/D = 5

0

0.15

0.35

x/D

1

1

-0.15

-2 0

f/f0 = 0.5

2

0

-1

3

3

s/D = 3

2

0

-3

f/f0 = 0.5

0.35

0.35

0.15 0.05

-0 .2 5

3

0.02 -0.02

0.25

-0.05

0.02

-0.15

2 0

1

2

3

4

x/D

5

6

7

8

3

-0.25 -0.35

0

1

2

3

4

5

6

7

8

x/D

Fig. 13. Dimensionless production of turbulent kinetic energy (normalized by U3/D) for (a) sub-harmonic, (b) harmonic and (c) super-harmonic frequency oscillation at spacing ratio (s/D) = 1.5, 3, and 5.

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B.S. More et al. / Experimental Thermal and Fluid Science 68 (2015) 339–358

"    0 2  0 2  0 2 # 2 @u0 @u @v @v Dissipation ¼ t  þ2 þ2 þ8 @x @y @x @y

and spacing ratios. It is non-dimensionalized with incoming velocity. Turbulence intensity contours are plotted in the range from 0.05 to 0.75 with an interval of 0.05. Due to the imposed oscillation on the cylinder there is a constant energy flux near the cylinder. The total turbulence intensity strength increases with an increase in spacing between the cylinders mainly in the gap between the cylinders. At higher frequency, the maximum intensity value shifted in the gap between the cylinders and reduces behind the downstream cylinder. The turbulent kinetic energy budget is useful for examining how the turbulence is spatially distributed. The development of cascade processes which give the kinetic energy of velocity fluctuations from large scale to small scales, ultimately dissipated by molecular level processes. Under simplification of transport of the turbulent kinetic energy equation by Wilcox [25], we derive the three important component of the turbulent kinetic energy equation. It is assumed that the total kinetic energy is 1.33 times that of measured from two dimensions as Panigrahi et al. [26]. The production, dissipation and diffusion terms are simplified and defined as:

      @u @v @u þ ðv 0 v 0 Þ þ ðu0 v 0 Þ @x @y @x   @ v : þ ðu0 v 0 Þ @x

Fig. 12 shows the production, dissipation and diffusion of kinetic energy for the stationary cylinder arrangement for three spacing ratios. Production, dissipation, and diffusion are non-dimensionalized by U3/D. All the three budget quantities are stronger in the near field region compare to the far field region. Production of kinetic energy mainly due to shear in the flow therefore considering the normal and shear stresses. The kinetic energy dissipated to the internal energy of the fluid. Diffusion of kinetic energy is very less in magnitude as compared to the production of kinetic energy. Fig. 13 shows dimensionless production of kinetic energy of fluctuating velocity at three forcing frequency and three spacing ratios. The contours of turbulent kinetic energy production are similar with time-averaged vorticity contour. Dissipation and diffusion of kinetic energy of fluctuating velocity are represented in Figs. 14 and 15. It is observed that in the synchronization range (f/f0 = 1), the cascade is faster compare to other situations. The sign of diffusion reverses between the near field and the far field region. As the wake evolves with distance, it approaches equilibrium in the sense that production and dissipation terms become close to each other.

Production ¼ ðu0 u0 Þ

Diffusion ¼

3

3

s/D = 1.5

y/D

1

1

0.10 0.08

0

Instantaneous spanwise vorticity contours for two stationary tandem cylinders is shown in Fig. 17. This is being compared with

ð3Þ

f/f0 = 0.5

-1

0.01

0

1

2

4

3

5

6

7

8

-3

f/f0 = 1

s/D = 1.5

0.08

y/D

(b)

1

0.08

0 -1

0.10

0.10

0.10

-1

0.01

1

2

3

1

2

3

4

5

7

6

8

-3

f/f0 = 2

s/D = 1.5

y/D

8

0.04

-1

0.01

-2

0.0

1

2

3

4

x/D

1

2

3

5

6

7

8

-3

4

6

5

f/f0 = 1

7

8

s/D = 5

0.10

0.06

0.10

0

0.08

1

8

0.10

0.01

0.10

0.08

0

0.10 .08

0.04

0.10

0. 01

2 0

1

2

3

4

5

6

7

8

3

0.06

0.04

0.10

1

0.02 0.01

0

1

2

3

4

5

6

7

8

x/D

f/f0 = 2

3

s/D = 3

f/f0 = 2

s/D = 5

0.10

2

0.08

1

0.10 0.10

0.06 0.10

0.04

0.10

0.10

0.10

0.10

0

0.01

1

-2 0

0.01

0

x/D 3

s/D = 3

0.10

0

0.10

-1

3

2

1

0.10

0

-3

7

6

2

1

0.02

0.01

x/D 3

2

(c)

5

f/f0 = 1

x/D 3

4

-2 0

0.04

0.10

0.10

2 0

0.06

0.06

0.08

1

0

-2 -3

0

2

0.10

0.10

0.10

0.10

x/D 3

2

0.10

s/D = 5

0.08

1

0.10

x/D

1

f/f0 = 0.5

2

-2

-2

3

3

s/D = 3

0

0.10

-1

-3

4.5. Instantaneous flow field and flow visualization

2

2

(a)

ð2Þ

@ 1 02 0 @ @ 1 03 @ ðu v Þ þ ðv 03 Þ þ ðu Þ þ ðu0 v 02 Þ @y 2 @y @x 2 @x

f/f0 = 0.5

ð4Þ

0.06

0.10

0.04

0.10

0.10

0.01

0.02

2 0

1

2

3

4

x/D

5

6

7

8

3

0.01

0

1

2

3

4

5

6

7

8

x/D

Fig. 14. Dimensionless dissipation of turbulent kinetic energy (normalized by U3/D) for (a) sub-harmonic, (b) harmonic and (c) super-harmonic frequency oscillation at spacing ratio (s/D) = 1.5, 3, and 5.

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B.S. More et al. / Experimental Thermal and Fluid Science 68 (2015) 339–358

2

-0 .0 4

y/D

0.08 -0.08

0

-0.01

0.10

1

-2

-2

2

-3

-3

3

2

1

3

4

5

6

7

8

0

1

2

3

x/D f/f0 = 1

3

s/D = 1.5

2

-0.04

06 0.

-

2

1

3

4

-0.01

5

6

8

7

-3

0.01

1

y/D

-0.0

8

04 0.

0

0.10

-0.01

.0 -0

0

1

2

3

4

f/f0 = 2

5

6

0

3

4

x/D

5

6

7

8

-3

5

6

7

8

0.10 0.08 0.06 0.04 0.02 0.01 -0.01 -0.02 -0.04 -0.06 -0.08 -0.10

s/D = 5

0.1 -0.10 0.10

0

-0.01

3

0

1

2

3

0

1

2

3

4

5

6

7

8

x/D 3

f/f0 = 2

10 -0. 10 0.

0.10 0.08 0.06 0.04 0.02 0.01 -0.01 -0.02 -0.04 -0.06 -0.08 -0.10

s/D = 5

2 1

0.01

-2 2

8

s/D = 3

-1

-2 1

7

-0.10 0.10

1

4

4

0.01

1

2

0

3

f/f0 = 1

0

-0.1 0 0. 10

3

s/D = 1.5

2

-3

2

x/D

f/f0 = 2

-0.10

1

2

x/D

-1

0

1

-0.10

-2 0

0.10

0.01

2

0.01

10 0.

-1

-2

3

s/D = 3

0

0. 04

y/D

f/f0 = 1

1

-1

(c)

8

-0.08

x/D

0. 10

6 -0.0

0

3

7

2

1

-3

6

-0.10

0.10

x/D

0.10

3

5

4

-0.10

0

-0.08

-1

0

0.10 0.08 0.06 0.04 0.02 0.01 -0.01 -0.02 -0.04 -0.06 -0.08 -0.10

s/D = 5

1

-0.06

0

0.04

f/f0 = 0.5

2

1

-0.04

-0.04

-1

(b)

3

s/D = 3

2

1

(a)

f/f0 = 0.5

-0 .1 0

3

s/D = 1.5

0. 10

f/f0 = 0.5

0. 10

3

0 1

-0.01

0.10

-0.10

10 .10 0. -0

-0.08

2 4

x/D

5

6

7

8

3

0

1

2

3

4

5

6

7

8

x/D

Fig. 15. Dimensionless diffusion of turbulent kinetic energy (normalized by U3/D) for (a) sub-harmonic, (b) harmonic and (c) super-harmonic frequency oscillation at spacing ratio (s/D) = 1.5, 3, and 5.

(a)

(b)

(c)

(d)

Fig. 16. Instantaneous flow visualization images in x–y plane for (a) single stationary cylinder and two cylinders in tandem with spacing ratio (b) s/D = 1.5, (c) s/D = 3, and (d) s/D = 5, at Re = 295.

352

B.S. More et al. / Experimental Thermal and Fluid Science 68 (2015) 339–358 4

(a)

y/D

3 1

1

1

0

0

0

-1

-1

-1

-2

-2

-2

-3

-3

-3

y/D

2

4

6

8

10

f/f0 = 0

12

14

-4

0

4

s/D =1.5

2

4

6

8

10

f/f0 = 0

3

12

14

-4

1

1

0

0

-1

-1

-1

-2

-2

-2

-3

-3

3

4

6

8

10

f/f0 = 0

12

14

-4

4

s/D = 3

3

2

4

6

8

10

12

14

2

1

1

0

0

0

-1

-1

-1

-2

-2

-2

-3

-3

4 3

4

6

8

10

f/f0 = 0

12

14

-4 4

s/D = 5

3

2

4

6

8

10

f/f0 = 0

12

14

-4

1

1

1

0

0

0

-1

-1

-1

-2

-2

-2

-3

-3

-3

4

6

x/D

8

10

12

14

-4

0

2

4

6

x/D

8

10

12

0

12

14

4.5 3.5 2.5 1.5 0.5 -0.5 -1.5 -2.5 -3.5 -4.5

s/D = 1.5

2

4

6

8

10

12

14

4.5 3.5 2.5 1.5 0.5 -0.5 -1.5 -2.5 -3.5 -4.5

s/D = 3

14

-4

2

4

6

8

10

f/f0 = 0

3 2

2

10

f/f0 = 0

4

s/D = 5

2

0

8

-3 0

2

-4

0

3

2

2

6

f/f0 = 0

4

s/D = 3

f/f0 = 0

-4

1

0

4

-3 0

2

-4

2

2

0

2

0

3

1

0

4.5 3.5 2.5 1.5 0.5 -0.5 -1.5 -2.5 -3.5 -4.5

f/f0 = 0

4

s/D = 1.5

2

4

y/D

0

2

-4

y/D

3 2

3

(d)

4

f/f0 = 0

2

4

(c)

3

2

-4

(b)

4

f/f0 = 0

0

2

12

14

4.5 3.5 2.5 1.5 0.5 -0.5 -1.5 -2.5 -3.5 -4.5

s/D = 5

4

6

x/D

8

10

12

14

Fig. 17. Instantaneous spanwise vorticity contours for (a) single stationary cylinder and two cylinders in tandem with spacing ratio (b) s/D = 1.5, (c) s/D = 3, and (d) s/D = 5.

(a)

(b)

(c)

(d)

Fig. 18. Instantaneous flow visualization images in x–y plane for (a) single oscillating cylinder and two cylinders in tandem with different spacing ratio (b) s/D = 1.5, (c) s/ D = 3, and (d) s/D = 5, when the upstream cylinder is oscillating at sub-harmonic frequency.

353

B.S. More et al. / Experimental Thermal and Fluid Science 68 (2015) 339–358 4

y/D

(a)

2

1

1

1

0

0

0

-1

-1

-1

-2

-2

-2

-3

-3

-3

-4

-4

0

y/D

2

4

6

8

10

12

14

6

8

10

4

f/f0 = 0.5

s/D = 1.5

14

-4 4

s/D = 1.5

f/f0 = 0.5

3

12

3

2

2

1

1

0

0

0

-1

-1

-1

-2

-2

-2

-3

-3

3

0

2

4

6

8

10

f/f0 = 0.5

12

1 0 -1 -2 -3 -4 4 3

0

2

4

6

8

10

12

s/D = 5

6

8

10

12

14

-4

2

4

6

8

10

12

14

0

-1

-1

-2

-2

-2

-3

-3

-3

14

-4

0

2

0

2

4

6

8

10

12

14

4.5 3.5 2.5 1.5 0.5 -0.5 -1.5 -2.5 -3.5 -4.5

s/D = 3

4

6

x/D

8

10

12

14

-4

2

4

6

8

10

f/f0 = 0.5

3

-1

12

4.5 3.5 2.5 1.5 0.5 -0.5 -1.5 -2.5 -3.5 -4.5

s/D = 1.5

f/f0 = 0.5

4

s/D = 5

f/f0 = 0.5

-4

1

10

14

-2

0

8

12

-3

1

x/D

10

0

0

6

8

-1

1

4

6

1

2

2

0

3

2

0

4

f/f0 = 0.5

4 s/D = 3

2

-4

2

2

0

3

4

f/f0 = 0.5

14 4

f/f0 = 0.5

2

0

4 3 2 1 0 -1 -2 -3 -4

s/D = 3

0

-3

-4

14

2

y/D

4

2

4

y/D

2

1

-4

(d)

0

4.5 3.5 2.5 1.5 0.5 -0.5 -1.5 -2.5 -3.5 -4.5

f/f0 = 0.5

3

2

3

(c)

4

f/f0 = 0.5

3

2

4

(b)

4

f/f0 = 0.5

3

0

2

12

14

4.5 3.5 2.5 1.5 0.5 -0.5 -1.5 -2.5 -3.5 -4.5

s/D = 5

4

6

x/D

8

10

12

14

Fig. 19. Instantaneous vorticity contours for (a) single oscillating cylinder and two cylinders in tandem with different spacing ratio (b) s/D = 1.5, (c) s/D = 3, and (d) s/D = 5, when the upstream cylinder is oscillating at sub-harmonic frequency.

(a)

(b)

(c)

(d)

Fig. 20. Instantaneous flow visualization images in x–y plane for (a) single oscillating cylinder and two cylinders in tandem with different spacing ratio (b) s/D = 1.5, (c) s/ D = 3, and (d) s/D = 5, when the upstream cylinder is oscillating at harmonic frequency.

354

B.S. More et al. / Experimental Thermal and Fluid Science 68 (2015) 339–358 4

y/D

(a)

4

f/f0 = 1

3

2

2

1

1

1

0

0

0

-1

-1

-1

-2

-2

-2

-3

-3

-3

4 3

0

2

4

6

8

10

12

14

s/D = 1.5

3

y/D

y/D

2

4

6

8

10

f/f0 = 1

12

14

-4

1

1 0

-1

-1

-1

-2

-2

-2

-3

-3

-3

-4

-4

2

4

6

8

10

f/f0 = 1

12

14

4

s/D = 3

3

0

2

4

6

8

10

f/f0 = 1

12

14

-4

s/D = 3

2

2

1

1

0

0

0

-1

-1

-1

-2

-2

-2

-3

-3

4

4

2

6

8

10

f/f0 = 1

12

14

s/D = 5

3

-4 4 3

2

4

6

8

10

12

14

4

s/D = 5

f/f0 = 1

-4

3

2

2

1

1

1

0

0

0

-1

-1

-1

-3 -4 0

2

4

6

8

x/D

10

12

14

-2

-2

-3

-3

-4

6

8

10

12

14

s/D = 1.5

2

4

6

8

10

f/f0 = 1

12

14

s/D = 3

-3 0

2

-2

0

3

1

0

4

f/f0 = 1

4

2

-4

2

2

0

0

0

3

2

4.5 3.5 2.5 1.5 0.5 -0.5 -1.5 -2.5 -3.5 -4.5

f/f0 = 1

4

s/D = 1.5

0

3

y/D

0

1

4

(d)

-4 4

f/f0 = 1

2

(c)

3

2

-4

(b)

4

f/f0 = 1

3

0

2

4

8

6

x/D

10

12

14

-4

0

2

4

6

8

10

f/f0 = 1

0

12

14

4

6

8

10

12

4.5 3.5 2.5 1.5 0.5 -0.5 -1.5 -2.5 -3.5 -4.5

4.5 3.5 2.5 1.5 0.5 -0.5 -1.5 -2.5 -3.5 -4.5

s/D = 5

2

4.5 3.5 2.5 1.5 0.5 -0.5 -1.5 -2.5 -3.5 -4.5

14

x/D

Fig. 21. Instantaneous vorticity contours for (a) single oscillating cylinder and two cylinders in tandem with different spacing ratio (b) s/D = 1.5, (c) s/D = 3, and (d) s/D = 5, when the upstream cylinder is oscillating at harmonic frequency.

(a)

(b)

(c)

(d)

Fig. 22. Instantaneous flow visualization images in x–y plane for (a) single oscillating cylinder and two cylinders in tandem with different spacing ratio (b) s/D = 1.5, (c) s/ D = 3, and (d) s/D = 5, when the upstream cylinder is oscillating at super harmonic frequency.

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B.S. More et al. / Experimental Thermal and Fluid Science 68 (2015) 339–358 4

(a)

y/D

3

2

1

1

0

0

0

-1

-1

-1

-2

-2

-2

-3

-3 0

2

4

6

8

10

12

14

f/f0 = 2

s/D = 1.5

2

4

6

8

10

12

14

-4 4

f/f0 = 2

s/D = 1.5

3

1

1

1

0

0

0

-1

-1

-1

-2

-2

-2

3

2

4

6

8

10

12

14

4

s/D = 3

f/f0 = 2

-4

3

0

2

4

6

8

10

f/f0 = 2

12

14

-4

4

s/D = 3

3

2

2

2

1

1

1

0

0

0

-1

-1

-1

-2

-2

-2

-3

-3

-4 4 3

0

2

4

6

8

10

12

14

4

s/D = 5

f/f0 = 2

-4

3

2

4

6

8

10

f/f0 = 2

12

14

-4 4

s/D = 5

3

2

2

1

1

1

0

0

0

-1

-1

-1

-2

-2

-2

-3

-3

-3

0

2

4

6

8

10

12

14

-4

4

6

8

10

f/f0 = 2

12

14

s/D = 1.5

0

2

4

6

8

10

12

14

0

2

4

x/D

6

x/D

8

10

12

14

-4

0

2

4

6

8

10

f/f0 = 2

0

12

14

4.5 3.5 2.5 1.5 0.5 -0.5 -1.5 -2.5 -3.5 -4.5

s/D = 5

2

4

6

8

10

12

4.5 3.5 2.5 1.5 0.5 -0.5 -1.5 -2.5 -3.5 -4.5

4.5 3.5 2.5 1.5 0.5 -0.5 -1.5 -2.5 -3.5 -4.5

s/D = 3

f/f0 = 2

-3 0

2

-4

2

-3

-3 0

0

2

2

4

y/D

3

4.5 3.5 2.5 1.5 0.5 -0.5 -1.5 -2.5 -3.5 -4.5

f/f0 = 2

-3 0

2

-4

y/D

-4 4

-3

(d)

3

2

3

(c)

4

f/f0 = 2

1

4

y/D

3

2

-4

(b)

4

f/f0 = 2

14

x/D

Fig. 23. Instantaneous vorticity contours for (a) single oscillating cylinder and two cylinders in tandem with different spacing ratio (b) s/D = 1.5, (c) s/D = 3, and (d) s/D = 5, when the upstream cylinder is oscillating at super harmonic frequency.

the single stationary cylinder. At s/D = 1.5, instantaneous vorticity contours are similar to that of the single stationary cylinder. For small spacing, the two cylinder acts as a single body with an extended surface. Similar shedding phenomena were also observed by Yen et al. [11]. With the increase in spacing the shear layer for both the cylinder interact with each other and the shedding phenomena modified. At s/D = 3, the shear layer from the downstream cylinder is elongated and flow separation delays. The shear layer from the upstream cylinder gets attached to the rear side of the downstream cylinder due to which there is no interaction of upper and lower shear layer of the upstream cylinder and no vortex shedding occur. With the further increase in spacing (s/D = 5), the vortex shedding occurs from both the cylinders. These vortices from the upstream cylinder stimulate the shedding from the downstream cylinder. Figs. 19, 21 and 23 are the vorticity contours for three oscillation frequencies with three spacing ratios. At sub-harmonic frequency, the shedding phenomena more or less similar to that of stationary cylinders arrangement (Fig. 17) in tandem which implies that the forcing frequency is not strong enough to manipulate the flow field. It is to be seen that the vortex shedding is more organized in comparison to the single cylinder at this frequency. Synchronization of vortex shedding occurs at forcing frequency f/f0 = 1. While the vortices are shed in laminar fashion in the near wake for spacing s/D = 1.5 and 3, this vortices breaks down very quickly in the near wake for the higher spacing (s/D = 5). This is constantly seen for all forcing frequencies. At the higher forcing frequency (f/f0 = 2), the vortex breakdown occurs

in the near wake even for spacing ratio s/D = 3. Spacing (s/D = 3) is quite critical as far as vortex shedding is the concern. This is due to the fact that at this spacing, the recirculation between the two cylinders is seen to be very sensitive to forcing frequency (Fig. 7). The same vortex pattern was seen by Assi et al. [27]. Flow visualization images at different spacing and frequency ratios are shown in Figs. 16, 18, 20 and 22. The flow direction is left to right in visualization. These images are taken by the zoomed-in view of the camera to the vortex formation region. Images are taken at three different selected times instant to look into the vortex evolution process. The vortex evolution, vortex interaction and vortex shedding phenomena are clearly visible from the images. The interaction of shear layers and the wake of the cylinders are visible from the images. The shear layers are separated at the sharp edge corners of the upstream cylinder and move in the downstream and form the vortices. From the flow visualization images at different s/D ratios, the flow is divided into three groups; single body flow, reattached flow and separated flow. Single body flow is observed at s/D = 1.5 and this flow is similar to flow over a single square cylinder. At s/D = 1.5, Karman vortex streets are formed in the wake of two cylinders and it consists of a sequence of alternate sign vortices. The vortices are separated from the corners of the upstream cylinder. Upper side vortices rotate in the clockwise direction while the lower corner vortices rotate in the counter-clockwise direction. At s/D = 1.5, vortices form the 2S flow pattern as in case of single square cylinder and at s/D = 3, shear layers are separated from the upstream cylinder and reattach at

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s/D = 3

s/D = 1.5 25 21

0.6

0.2 0 50

23

24 2

Fre

30

20

que ncy

21

0.2

24 21

0 50

1.5

40

14

0.4

40

1 10

0.5

F re

f/f 0

0 0

Power

23

25

Power

0.4

15

0.6

30

20

que ncy

10

8

0.5

00

1

1.5

2

f/f 0

s/D = 5

0.6

21

0.2 0 50

18

40

Fre

17

17

18

30

que 20 10 ncy

00

Power

17

0.4

1

0.5

2

1.5

f/f 0

Fig. 24. Power spectra based on y-component of velocity at Re = 295 with different spacing ratio (s/D) = 1.5, 3 and 5; and forcing frequency (f/f0 = 0.5, 1 and 2).

Power

10-1

f/f0 = 0

s/D = 1.5

10-2

10-2

10-3

10-3

10-4 -5

10

10-6

1

10-4

0.8

10-5

0.6 0.4

0.2

0.4

0.6

0.8

10-6

1

100

10-1

f/f0 = 1

s/D = 1.5

-5

10

-6

10

s/D = 1.5

1 0.8 0.6 0.4

0.2

0.4

0.6

0.8

1

100

10-1

f/f0 = 2

200 300 400

s/D = 1.5

10-2

10-3 10-4

f/f0 = 0.5

200 300 400

10-2

Power

10-1

10-3 1

10-4

0.8

10-5

0.6 0.4

0.2

0.4

0.6

0.8

-6

10

1

100

1 0.8 0.6 0.4

0.2

0.4

0.6

0.8

1

200 300 400

Frequency (Hz)

100

200 300 400

Frequency (Hz)

Fig. 25. Power spectra based on y-component of velocity; inset shows time trace of the transverse component of velocity at s/D = 1.5.

lateral surface of the downstream cylinder. Separated flow patterns are observed at s/D = 5, where separate vortices are formed from the both the cylinders. Fig. 18 shows the effect of sub-harmonic oscillation on near wake flow structure. The images are seen to be identical to stationary cylinder arrangements. With the increase

in oscillation frequency (f/f0 = 1), the periodic shedding saw for all spacing ratios from the downstream cylinder. At this frequency, the pure Karman vortex shedding synchronizes with the cylinder oscillation. For spacing ratio s/D = 5, the vortex shedding from the downstream cylinder is identical to visualization images seen

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Power

10 0

f/f0 = 0

s/D = 3

10

-1

10

-1

10

-2

10

-2

10 -3 10

-4

10

-5

10 -6

10-3

1

10

10

-4

10

-5

0.5

0

0.2

0.4

0.6

0.8

10-6

1

f/f0 = 1

s/D = 3

10 10

-1

10

-2

10

-2

10

-5

10 -6

0

0.2

0.4

0.6

0.8

1

100

10

-4

1

10-3

1

200 300 400

0

-1

10

s/D = 3

200 300 400

0

10 -3

f/f0 = 0.5

0.5

100

Power

100

10

-4

10

-5

0.5

f/f0 = 2

s/D = 3

1

0.5

0

0.2

0.4

0.6

0.8

10-6

1

Frequency (Hz)

100

0

0.2

0.4

0.6

200 300 400

0.8

1

Frequency (Hz)

100

200 300 400

Fig. 26. Power spectra based on y-component of velocity; inset shows time trace of the transverse component of velocity at s/D = 3.

Power

100

f/f0 = 0

s/D = 5

10

10-2

10

10-6

10-3 1

-4

1

-5

0.5

10-6

0

10 0.5

10

0

0.2

0.4

0.6

0.8

1

100

0.2

0.4

0.6

0.8

1

200 300 400

100

200 300 400

0

0

10

s/D = 5

-2

10-3 10-4

f/f0 = 0.5

-1

10-1

10-5

Power

100

f/f0 = 1

s/D = 5

10

f/f0 = 2

s/D = 5

-1

-1

10

10

10-2

10

10-3

10-3

-2

10-4

1

10-5

0.5

10-6

0

-4

1

-5

0.5

10-6

0

10 10 0.2

0.4

0.6

0.8

1

100

0.2

0.4

0.6

0.8

1

200 300 400

Frequency (Hz)

100

200 300 400

Frequency (Hz)

Fig. 27. Power spectra based on y-component of velocity; inset shows time trace of the transverse component of velocity at s/D = 5.

by Ongoren et al. [28]. Several vortex roll-ups in shear layers are seen at this frequency. Similar observations of vortex roll-up are reported by Krishnamurthy et al. [29]. 4.6. Power spectra Figs. 25–27 show the power spectra of transverse velocity components in the wake of a downstream cylinder with different spacing and frequency ratios. The time trace of v-velocity component for 1-s length is inserted in the plot. A consolidated 3-D plot for

these power spectrums are shown in Fig. 24. In the present study, the power spectrum is calculated at a position 3D in streamwise direction and 1D in the transverse direction from the downstream cylinder by using x-wire hotwire probe. For stationary cylinders with a spacing ratio of 1.5, a single sharply defined peak is seen at 24 Hz which is the vortex shedding frequency. With oscillation, multiple peaks are observed at f/f0 = 0.5, one for excitation frequency, and other for harmonics of the vortex shedding. A lock-in is observed at f/f0 = 1 where a single peak of high power is observed. In this condition, the vortex shedding frequency is

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synchronized with the excitation frequency of the upstream cylinder. When f/f0 increases up to 2, multiple peaks are observed near the vortex shedding peak and power of vortex shedding is minimum at this frequency. The time signal implies that there is a nonlinear interaction between the vortex shedding frequency and forcing frequency. Fig. 26 shows the power spectra at different frequency ratios for s/D = 3. No synchronization is observed at this condition except for f/f0 = 0.5, where two peaks are observed first at the excitation frequency and other peaks at vortex shedding frequency. Fig. 27 shows the power spectra at different frequency ratios for s/D = 5. These power spectra are similar to power spectra of a single cylinder and show the synchronization at f/f0 = 1, but the power spectra are noisy compared to the stationary cylinder. Also, the three-dimensionality of flow is seen in the spectrums which follow a definite trend (negative slope) in the inertial sub-range. The flow three-dimensionality is also clearly visible from the flow visualization images. 5. Conclusions An experimental investigation is carried out for uniform flow over two tandem square cylinders. Reynolds number mainly considered for the present study is 295 based on average upstream velocity and cylinder size. Experiments are done for multiple configurations. In one case, two stationary cylinders with three different spacing ratios and in another case, the upstream cylinder is oscillated with harmonics of vortex shedding frequency of the stationary cylinder. Flow field is investigated using PIV, hotwire anemometer and flow visualization techniques. The spacing ratios between the two cylinders are varied from 1.5 to 5.0 and frequency ratio of transverse oscillation of the upstream cylinder varies from 0 to 2 at a fixed amplitude ratio of 0.1. The time-average flow properties are measured using PIV and the temporal flow field by using hotwire anemometer. The following conclusion reveal from the study: 1. For both stationary cylinders, the effect of the spacing ratio is the dominant inflow structure as well as associate load. At the spacing ratio s/D = 1.5, the downstream cylinder acts as an extended body. The vortex shedding is close to the downstream cylinder. The vortex shedding frequency is also higher compared to a single stationary cylinder. The combine time-average drag coefficient of s/D = 1.5 is lower than the single cylinder. When the spacing is in reattachment mode (s/D = 3), the vortex shedding is still periodic, but the shedding delays further downstream. This corresponds to the reduction in Strouhal number. The combined drag coefficient is minimum. With further increase is spacing (s/D = 5), the vortex shedding occurs from both the cylinder. The vortices from the upstream cylinder impinge on the downstream cylinder and stimulate the shedding from the downstream cylinder. Flow three-dimensionality is strong in this arrangement and wakes size increases which cause an increase in drag coefficient. 2. With the oscillation of upstream cylinder the flow becomes much more complex particularly at f/f0 = 1 and 2. For sub-harmonic forcing frequency (f/f0 = 0.5), there are not many changes seen in the flow structure as compared to the stationary cylinder. This forcing frequency is not sufficient to modify the flow structure. At f/f0 = 1, vortex shedding synchronizes with cylinder oscillation and lock-on phenomena observed. This is seen irrespective of spacing ratios. With higher forcing frequency (f/f0 = 2), the vortices break down and flow three-dimensionality starts appearing in the flow structure.

The effect of spacing is prominent at this frequency. When the upstream cylinder is oscillated with different frequency ratios, combined time-averaged drag coefficient (CD0 ) is minimum at (s/D = 1.5, f/f0 = 2), (s/D = 3, f/f0 = 0.5), and (s/D = 5, f/f0 = 2).

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