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Pressure drop in a channel with cylinders in tandem arrangement
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International Communications in Heat and Mass Transfer 35 (2008) 76 – 83 www.elsevier.com/locate/ichmt
Pressure drop in a channel with cylinders in tandem arrangement ☆ Alican Daloglu Department of Mechanical Engineering, Karadeniz Technical University, 61080 Trabzon, Turkey Available online 3 July 2007
Abstract This paper presents the results of an experimental study conducted on pressure drop for flow in a square channel with two cylinders in tandem arrangement. In the study special attention is paid to the effects of the shape and size of the upstream cylinder and the separation between the upstream and downstream cylinders. In the experiments two types of upstream cylinders, one having a circular cross-section and the other having a square cross-section in three different sizes; D = d, D = 2d, and D = 3d, respectively were used. The size of the downstream circular cylinder was kept constant at d and the distance between the tandem cylinders was varied in the interval 1.0 ≤ S/d ≤ 10.0. The effect of Reynolds number on pressure drop was also studied in the range of 52,100 ≤ Re ≤ 156,000. Results show that the distance between the cylinders significantly affects the pressure drop in the channel. At certain range of distance between the cylinders, the pressure drop takes smaller values comparing to pressure drop in a channel with single upstream cylinder. © 2007 Elsevier Ltd. All rights reserved. Keywords: Tandem cylinders; Channel flow; Pressure drop
1. Introduction Flow in channels occurs in many engineering applications. Prediction of pressure drop in channel flow is important to obtain required flow conditions. The pressure drop can be easily calculated for empty channel flow by using the equations given in the literature. For many engineering applications, some bluff bodies are placed in channel such as a cylinder, two cylinders in various arrangements, or tube bundles in different configurations. For this situation, the prediction of the pressure drop in channel becomes difficult and the pressure drop can be experimentally obtained. There are numerous experimental and numerical studies on flow past bluff bodies in different configurations. Previous work on the flow pattern around two identical cylinders for different orientations was extensively reviewed by Zdravkovich [1]. An experimental investigation of the flow and heat transfer around two identical cylinders in tandem was performed by Kostic and Oka [2] for different distances between the cylinders. They found that there were two different characteristic flow patterns depending on distance between the cylinders. Hiwada et al. [3] experimentally investigated fluid flow and heat transfer around two cylinders of different diameters. They placed the small diameter cylinder as an upstream cylinder. Igarashi [4] experimentally studied flow characteristics around two tandem circular cylinders in the Reynolds number range of 8.7 × 103–5.2 × 104 and dimensionless spacing, S/d, in the interval 1.03–5.0. He performed similar study for tandem circular cylinders of different diameters [5]. Ljungkrona and Sunden ☆
Communicated by W.J. Minkowycz. E-mail address: [email protected].
0735-1933/$ - see front matter © 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.icheatmasstransfer.2007.05.011
A. Daloglu / International Communications in Heat and Mass Transfer 35 (2008) 76–83
77
Nomenclature d D fapp fo H L Le P ▵P ▵Pus ▵Pmin ▵Pmax Re S Uo ν
diameter of downstream cylinder, m diameter (side length for square) of upstream cylinder, m apparent friction coefficient friction coefficient for the channel without cylinder channel height, m channel length, m entrance length, m dimensionless distance, S/d pressure drop, Pa pressure drop in the channel with upstream cylinder, Pa minimum pressure drop in the channel with tandem cylinders, Pa maximum pressure in the channel with tandem cylinders, Pa Reynolds number, UoH / ν separation between two cylinders, m average velocity at the inlet, m/s kinematic viscosity, m2/s
[6] experimentally investigated the flow pattern and pressure distribution for flow past two tandem circular cylinders. Flow visualizations were carried out in the Reynolds number range, 3.3 × 103 b Re b 1.2 × 104 and for dimensionless spacing, S/D, ranging from 1.25 to 4.0. Pressure measurements were performed in the Reynolds number range of 3 × 103 b Re b 4 × 104 and for three different spacings, S/D = 1.25, 2.0 and 4.0. Results showed that the flow pattern exhibits a strong dependence on the Reynolds number and cylinder spacing. The flow visualization and numerical study to investigate the effects of the spacing between two tandem square cross-sectional cylinders on the flow pattern and heat transfer from the downstream cylinder were performed by Tatsutani et al. [7]. They found that the flow behavior and heat transfer from the downstream cylinder are affected by the spacing between the cylinders. The effects of the two rectangular bars placed in tandem normal to flow in a channel on pressure drop and heat transfer were investigated by Valencia [8]. Numerical computations were carried out in the entrance region for three different cylinder separation distances and five different Reynolds numbers. Daloglu and Ünal [9] conducted an experimental study on heat transfer from a downstream cylinder placed behind an upstream cylinder in a channel. From their results, it is observed that the shape and size of the upstream cylinder, and the spacing between the cylinders significantly affects the heat transfer from the downstream cylinder. Alvarez et al. [10] computed the flow and heat transfer in a channel with square bars. They investigated the effects of two bars on pressure drop and heat transfer in a channel for tandem and side by side arrangements. The Reynolds number Re based on channel height was 104 and the ratio of bar height to channel height was 0.152. Five arrangements with the bars placed in tandem along the channel axis and four cases with the bars arranged side by side to the flow were studied. The results show that the ratio of the apparent friction factors for tandem arrangement increases as the separation distance between the bars increases. Rosales et al. [11] conducted a numerical investigation to analyze the unsteady flow field and heat transfer characteristics for a tandem pair of square bars in a laminar channel flow. The drag, lift and heat transfer coefficients from the downstream heated cylinder due to inline and offset upstream cylinder were studied. It is observed that the drag coefficient and Nusselt number decreases as the heated cylinder approaches the wall. Buyruk [12] carried out numerical analyses to predict heat transfer characteristics for flow past tandem, inline and staggered circular cylinders configurations by using finite element method. Effect of the spacing between the tandem cylinders was investigated at small Reynolds number, Re = 400. Valencia and Paredes [13] computed the flow and heat transfer in a channel with two square bars mounted side by side in an approaching flow. The dimensionless spacing between the bars is varied from 0 to 5, whereas the bar height to channel height is d/H = 0.125 and the channel length is L = 5H. It is observed that the pressure drop in the channel and heat transfer from the channel surfaces are strongly dependent on the spacing between the bars and the Reynolds number. The aerodynamic characteristics of flow past a square cylinder with an upstream rod experimentally studied for different Reynolds numbers by Sarioglu et al. [14] and by Zhang et al. [15]. The results
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A. Daloglu / International Communications in Heat and Mass Transfer 35 (2008) 76–83
Fig. 1. Channel dimensions and arrangement of the tandem cylinders.
show that the value of the drag on square cylinder with an upstream rod decreases comparing to the drag on square without rod at certain spacing. Zhou and Yiu [16] experimentally investigated flow structure, momentum and heat transfer in the wake of two tandem circular cylinders. Flow measurements were carried out at three sections away from the downstream cylinder, x/d = 10, 20 and 30, at a Reynolds number of 7000 and at four different spacing ratios, L/d = 1.3, 2.5, 4.0 and 6.0, respectively. They proposed a new classification of the flow in four different categories as 1 b L/d b 2, 2 b L/d b 3, 3 b L/d b 5 and 5 b L/d. This paper presents the results of an experimental investigation conducted on the pressure drop in a channel flow past tandem cylinders. The downstream cylinder has circular cross-section, and the size of this cylinder is kept constant. Two types of upstream cylinder geometries, one type having a circular cross-section and the other type having a square cross-section, are used in the experiments in order to investigate the shape effect. The experiments are performed for three different upstream cylinder sizes by varying the Reynolds number in the range of 5.21 × 104 b Re b 1.56 × 105 and the dimensionless distance between the cylinders in the interval 1.0 b S/d b 10.0, in order to examine the effects of cylinder size, Reynolds number and the spacing, respectively. 2. Experimental apparatus Fig. 1 shows the experimental set-up used in the present study. Experiments were conducted in an open circuit wind tunnel with a square cross-sectional test section (125 mm × 125 mm) of 2 m long. Measurement of the mean air velocity in the tunnel was performed using a pitot tube placed in a cross-section near the channel entrance, and an inclined manometer was used for dynamic pressure readings in ± 0.5 Pa accuracy. An upstream cylinder (square or circular) was placed at channel axis at a location 750 mm down from the entrance. The diameter of the upstream cylinder was set 12.5, 25.0 and 37.5 mm, the blockage ratios ranging from 0.1 to 0.3. A circular cylinder with a diameter d = 12.5 mm (d/H = 0.1) is used as the downstream cylinder. The pressure drop was measured for L = 600 mm channel length (L/H = 4.8) starting at Le = 625 mm (Le/H = 6.0) away from the entrance by using a micro manometer with 1% uncertainty. First the pressure drop in the empty channel was measured for various values of Reynolds number. In defining Reynolds number and friction factor, channel height H was used as the characteristic length and the related equations are Re ¼ fo ¼
Uo H v
DPH : 1=2qUo2 L
ð1Þ ð2Þ
After obtaining the pressure drop in the channel with single upstream cylinder, the pressure drop was measured in the channel with two tandem cylinders. The distance between the tandem cylinders was changed in the range of 1.0 b S/d b 10.0. The apparent friction factor for the channel with cylinder is defined by using Eq. (2) similar to Alvarez's definition [10]. 3. Results and discussion The effects of upstream cylinder on heat transfer from downstream cylinder placed in a channel have been investigated depending on upstream cylinder geometry, spacing and Reynolds number in previous study by Daloglu and Ünal [9]. In this study, experimental measurements of pressure drop in a square channel with tandem cylinders are presented. Experiments are carried out for two types of upstream cylinders, one type having a circular cross-section (circular cylinder), and the other type a square cross-section (square cylinder), and three different sizes of each type, namely D = d, D = 2d and D = 3d in diameter in the case of circular upstream cylinder
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Fig. 2. Variations of pressure drop with spacing.
and in side length in the case of square upstream cylinder are used. For each type and size upstream cylinder the effects of both spacing between the tandem cylinders and Reynolds number on pressure drop are investigated in the interval of 1.0 b P b 10.0 and by varying Reynolds number from 52,100 to 156,000.
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Fig. 3. Variations of the ratio of apparent friction coefficients with spacing.
The results of the experiments conducted using circular cross-sectional upstream cylinders of size 1d, 2d and 3d are shown in Fig. 2a, c and e, respectively. Fig. 2b, d and f shows the experimental results obtained using similar size square cylinders. In this figure, the pressure drop is plotted against the dimensionless spacing, as a function of Reynolds numbers. The points marked at P = 0 in the same
A. Daloglu / International Communications in Heat and Mass Transfer 35 (2008) 76–83
Fig. 4. Variations of pressure drop with Reynolds number.
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figures correspond to the values of pressure drop, ▵Pus, measured in a channel with single front (upstream) cylinder of the corresponding size. The data presented in Fig. 2a shows that, typically for all values of the Reynolds number studied, the pressure drop in the channel decreases first as the separation increases from P = 0 to P = 1, makes a minimum ▵Pmin at P = 1, then a sharp increase occurs in the interval 1 b P b 2, and then a monotonic increase takes place from P = 2 to P b P b 1 occurs. The other characteristic regions observed in Fig. 2a agree well with the ones in [17]; the sharp increase in ▵P corresponding to W–T2 regime, the monotonic increase corresponding to W–T regimes in general and finally ▵Pmax = constant region corresponding to the uncoupled eddy shedding regime behind both cylinders. Pressure drops measured using D = d size square cylinder as upstream cylinder are presented in Fig. 2b.The results show similarity with circular cylinder, but the spacing between the cylinders at which ▵Pmin is achieved moves 1 to 1.4. Comparing the results for circular cylinder and square cylinder, it can be seen that pressure drops for single square upstream cylinder are higher than for circular cylinder at same Reynolds numbers. Fig. 2c and d shows pressure drops against the dimensionless spacing for D = 2d size circular and square cylinders giving the blockage ratio as 0.2, respectively. Similar to D = d size cylinder, pressure drop decreases after placing the downstream cylinder, and the minimum pressure drop is obtained around P = 2.5. With increasing spacing, it increases gradually and becomes constant around P = 5.5, Fig. 2c. The results for square cylinder show some differences, Fig. 2d. As it is expected pressure drop for square upstream cylinder takes higher values than for circular cylinder. The pressure drop in the channel with single front cylinder have smaller values than with tandem cylinders at P = 1.5, in that case cylinders touch each other, After this point the pressure drop decreases with increasing dimensionless distance, and shows a minimum at P = 2.0. After increasing gradually, pressure drop takes constant value for all Reynolds numbers around P = 5.5. Comparing to the pressure drops in the channel with tandem cylinders and with single front cylinder for Re = 156,000, the decrease in pressure drop for tandem cylinders are around 11% for circular and square cylinders. Pressure drops for D = 3d size upstream cylinder are shown in Fig. 2e and f. The minimum pressure drop occurs around at P = 2.4 but decrease in pressure drop is small comparing to smaller size upstream cylinders. The pressure drop gradually increases with increasing spacing and becomes constant around P = 7.5. The smallest effect of the spacing on pressure drop is seen for D = 3d size square upstream cylinder, Fig. 2f. As it is expected, pressure drop for square bar is higher than for circular cylinder all the cases tested. Comparing the maximum pressure drops obtained for circular cylinder and square bar as upstream cylinder at Re= 116,000, the pressure drops for square bar are 9.8% higher than for circular cylinder for D = 1d size, 57.8% for D = 2d size and 62% for D = 3d size. Fig. 3 shows the ratio of apparent friction factor in channel with tandem cylinders, defined similar to empty channel by Alvarez et al. [10], to apparent friction factor in empty channel against the dimensionless spacing. The ratio of apparent friction factors obtained for circular and square cylinders show similarity with the pressure drop results. It is noticed that the ratio of apparent friction factors for square cylinder take higher values than the same size circular cylinder in the same manner with pressure drop. For Re = 116,000, the ratio of apparent friction factors is around 2.9 in the channel with single D = d size circular upstream cylinder. After placing downstream cylinder it drops to 2.1 giving the minimum. It increases again with increasing dimensionless spacing and reaches to 4.5 as the maximum, Fig. 3a. From the results given in Fig. 3b for D = d size square cylinder, it is noticed that the values of the ratio of apparent friction factors take the values of 3.8, 2.5 and 4.8, respectively for Re = 116,000. Although the maximum value of the ratio of apparent friction factors for D = 2d size circular upstream cylinder is 7.7 at Re = 116,000, it takes a value of 12.2 for same size square upstream cylinder, Fig. 3c and d. From Fig. 3e, it can be seen that the ratio of apparent friction factors shows small changes for P N 3.5 and Re N 116,000. For circular cylinder, the ratio of apparent friction factors increases, decreases and again increases with increasing spacing at small Reynolds numbers. But these changes in ratio of apparent friction factors are seen for square cylinder at all Reynolds numbers tested, Fig. 3f. From this figure it can be seen that the ratio of apparent friction factors does not change too much with dimensionless spacing. For example, the maximum value of this ratio is 18.9 for single square upstream cylinder and 20.8 for tandem cylinders at Re = 156,000. In order to see clearly the effect of the spacing on the pressure drop Fig. 4 is given. In Fig. 4, the pressure drops are plotted against Reynolds number for different dimensionless spacings using circular and square upstream cylinders. As it is expected the variation of pressure drop with Reynolds number exhibits a parabolic character. From Fig. 4a and b plotted for D = d size upstream cylinder, it can be clearly seen that pressure drop in channel with tandem cylinders takes smaller values than in channel with single upstream cylinder for P b 2 and for all Reynolds numbers. Comparing subpanels c and d of Fig. 4 for D = 2d size upstream cylinder, the effect of the spacing on pressure drop is stronger for circular upstream cylinder. For two types of upstream cylinders, pressure drops in channel with tandem cylinders are lower than in channel with single upstream cylinder for P b 2.5. The effect of spacing on pressure drop becomes less important for D = 3d size upstream cylinders with a blockage ratio of 0.3, Fig. 4e and f. Especially for square upstream cylinder the variation in pressure drop with spacing takes place in a narrow band.
4. Conclusion From the experimental data presented in this paper it is observed that the pressure drop in a channel with two tandem cylinders inline exhibits a strong dependence on the spacing between tandem cylinders. The most important result that should be extracted from this paper is that, for all the parameters considered in the study, there exists a critical spacing between the two cylinders at which the pressure drop takes a minimum value, ▵Pmin, which is even less than the
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pressure drop obtained for the case of in the channel with single upstream cylinder. The value of this critical spacing varies considerably with the shape and size of the upstream cylinder, but it is almost independent of the Reynolds number. The percent reduction in ▵P from ▵Pus to ▵Pmin is more important for the same size upstream and down stream cylinders than the one for D = 2d and D = 3d size upstream cylinders. It must be pointed out that flow in the same channel with square cross-sectional upstream cylinders yields higher pressure drops when compared with the circular cylinders, as it is expected. Acknowledgement The author gratefully thanks Professor Ahmet Ünal for his helpful advices. References [1] M.M. Zdravkovich, Review of flow interference between two circular cylinders in various arrangements, Journal of Fluids Engineering 99 (1977) 618–633. [2] Z.G. Kostic, N. Oka, Fluid flow and heat transfer with two cylinders in cross flow, International Journal of Heat and Mass Transfer 15 (1972) 279–299. [3] M. Hiwada, T. Taguchi, I. Mabuchi, M. Kumada, Fluid flow and heat transfer around two cylinders of different diameters in cross flow, Bulletin of the JSME 22 (167) (1979) 715–723. [4] T. Igarashi, Characteristics of a flow around two circular cylinders arranged in tandem, Bulletin of the JSME 24 (1981) 323–331. [5] T. Igarashi, Characteristics of a flow around two circular cylinders of different diameters arranged in tandem, Bulletin of the JSME 25 (1982) 349–357. [6] L. Ljungkrona, B. Sunden, Flow visualization and surface pressure measurement on two tubes in an in-line arrangement, Experimental Thermal and Fluid Science 6 (1) (1993) 15–27. [7] K. Tatsutani, R. Devarakonda, J.A.C. Humphrey, Unsteady flow and heat transfer for cylinder pairs in a channel, International Journal of Heat and Mass Transfer 36 (13) (1993) 3311–3328. [8] A. Valencia, Unsteady flow and heat transfer in a channel with a built-in tandem of rectangular cylinders, Numerical Heat Transfer 29 (1996) 613–623. [9] A. Daloglu, A. Ünal, Heat transfer from a cylinder in the wake flow, International Communication in Heat and Mass Transfer 27 (4) (2000) 355–366. [10] J. Alvarez, M. Pap, A. Valencia, Turbulent heat transfer in a channel with bars in tandem and in side by side arrangements, International Journal of Numerical Methods for Heat & Fluid Flow 10 (8) (2000) 877–896. [11] J.L. Rosales, A. Ortega, J.A.C. Humphrey, A numerical simulation of the convective heat transfer in confined channel flow past square cylinders: comparison of inline and offset tandem pairs, International Journal of Heat and Mass Transfer 44 (2001) 587–603. [12] E. Buyruk, Numerical study of heat transfer characteristics on tandem cylinders, inline and staggered tube banks in cross-flow of air, International Communications in Heat and Mass Transfer 29 (3) (2002) 355–366. [13] A. Valencia, R. Paredes, Laminar flow and heat transfer in confined channel flow past square bars arranged side by side, Heat and Mass Transfer 39 (2003) 721–728. [14] M. Sarioglu, Y.E. Akansu, T. Yavuz, Control of flow around square cylinders at incidence by using a rod, AIAA Journal 43 (7) (2005) 1419–1426. [15] P.F. Zhang, J.J. Wang, S.F. Lu, J. Mi, Aerodynamic characteristics of a square cylinder with a rod in a staggered arrangement, Experiments in Fluids 38 (4) (2005) 494–502. [16] Y. Zhou, M.W. Yiu, Flow structure, momentum and heat transport in a two-tandem-cylinder wake, Journal of Fluid Mechanics 548 (2006) 17–48. [17] M.M. Zdravkovich, Flow Around Circular Cylinders, Oxford Science Publication, 2003, pp. 998–1018.
International Communications in Heat and Mass Transfer 35 (2008) 76 – 83 www.elsevier.com/locate/ichmt
Pressure drop in a channel with cylinders in tandem arrangement ☆ Alican Daloglu Department of Mechanical Engineering, Karadeniz Technical University, 61080 Trabzon, Turkey Available online 3 July 2007
Abstract This paper presents the results of an experimental study conducted on pressure drop for flow in a square channel with two cylinders in tandem arrangement. In the study special attention is paid to the effects of the shape and size of the upstream cylinder and the separation between the upstream and downstream cylinders. In the experiments two types of upstream cylinders, one having a circular cross-section and the other having a square cross-section in three different sizes; D = d, D = 2d, and D = 3d, respectively were used. The size of the downstream circular cylinder was kept constant at d and the distance between the tandem cylinders was varied in the interval 1.0 ≤ S/d ≤ 10.0. The effect of Reynolds number on pressure drop was also studied in the range of 52,100 ≤ Re ≤ 156,000. Results show that the distance between the cylinders significantly affects the pressure drop in the channel. At certain range of distance between the cylinders, the pressure drop takes smaller values comparing to pressure drop in a channel with single upstream cylinder. © 2007 Elsevier Ltd. All rights reserved. Keywords: Tandem cylinders; Channel flow; Pressure drop
1. Introduction Flow in channels occurs in many engineering applications. Prediction of pressure drop in channel flow is important to obtain required flow conditions. The pressure drop can be easily calculated for empty channel flow by using the equations given in the literature. For many engineering applications, some bluff bodies are placed in channel such as a cylinder, two cylinders in various arrangements, or tube bundles in different configurations. For this situation, the prediction of the pressure drop in channel becomes difficult and the pressure drop can be experimentally obtained. There are numerous experimental and numerical studies on flow past bluff bodies in different configurations. Previous work on the flow pattern around two identical cylinders for different orientations was extensively reviewed by Zdravkovich [1]. An experimental investigation of the flow and heat transfer around two identical cylinders in tandem was performed by Kostic and Oka [2] for different distances between the cylinders. They found that there were two different characteristic flow patterns depending on distance between the cylinders. Hiwada et al. [3] experimentally investigated fluid flow and heat transfer around two cylinders of different diameters. They placed the small diameter cylinder as an upstream cylinder. Igarashi [4] experimentally studied flow characteristics around two tandem circular cylinders in the Reynolds number range of 8.7 × 103–5.2 × 104 and dimensionless spacing, S/d, in the interval 1.03–5.0. He performed similar study for tandem circular cylinders of different diameters [5]. Ljungkrona and Sunden ☆
Communicated by W.J. Minkowycz. E-mail address: [email protected].
0735-1933/$ - see front matter © 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.icheatmasstransfer.2007.05.011
A. Daloglu / International Communications in Heat and Mass Transfer 35 (2008) 76–83
77
Nomenclature d D fapp fo H L Le P ▵P ▵Pus ▵Pmin ▵Pmax Re S Uo ν
diameter of downstream cylinder, m diameter (side length for square) of upstream cylinder, m apparent friction coefficient friction coefficient for the channel without cylinder channel height, m channel length, m entrance length, m dimensionless distance, S/d pressure drop, Pa pressure drop in the channel with upstream cylinder, Pa minimum pressure drop in the channel with tandem cylinders, Pa maximum pressure in the channel with tandem cylinders, Pa Reynolds number, UoH / ν separation between two cylinders, m average velocity at the inlet, m/s kinematic viscosity, m2/s
[6] experimentally investigated the flow pattern and pressure distribution for flow past two tandem circular cylinders. Flow visualizations were carried out in the Reynolds number range, 3.3 × 103 b Re b 1.2 × 104 and for dimensionless spacing, S/D, ranging from 1.25 to 4.0. Pressure measurements were performed in the Reynolds number range of 3 × 103 b Re b 4 × 104 and for three different spacings, S/D = 1.25, 2.0 and 4.0. Results showed that the flow pattern exhibits a strong dependence on the Reynolds number and cylinder spacing. The flow visualization and numerical study to investigate the effects of the spacing between two tandem square cross-sectional cylinders on the flow pattern and heat transfer from the downstream cylinder were performed by Tatsutani et al. [7]. They found that the flow behavior and heat transfer from the downstream cylinder are affected by the spacing between the cylinders. The effects of the two rectangular bars placed in tandem normal to flow in a channel on pressure drop and heat transfer were investigated by Valencia [8]. Numerical computations were carried out in the entrance region for three different cylinder separation distances and five different Reynolds numbers. Daloglu and Ünal [9] conducted an experimental study on heat transfer from a downstream cylinder placed behind an upstream cylinder in a channel. From their results, it is observed that the shape and size of the upstream cylinder, and the spacing between the cylinders significantly affects the heat transfer from the downstream cylinder. Alvarez et al. [10] computed the flow and heat transfer in a channel with square bars. They investigated the effects of two bars on pressure drop and heat transfer in a channel for tandem and side by side arrangements. The Reynolds number Re based on channel height was 104 and the ratio of bar height to channel height was 0.152. Five arrangements with the bars placed in tandem along the channel axis and four cases with the bars arranged side by side to the flow were studied. The results show that the ratio of the apparent friction factors for tandem arrangement increases as the separation distance between the bars increases. Rosales et al. [11] conducted a numerical investigation to analyze the unsteady flow field and heat transfer characteristics for a tandem pair of square bars in a laminar channel flow. The drag, lift and heat transfer coefficients from the downstream heated cylinder due to inline and offset upstream cylinder were studied. It is observed that the drag coefficient and Nusselt number decreases as the heated cylinder approaches the wall. Buyruk [12] carried out numerical analyses to predict heat transfer characteristics for flow past tandem, inline and staggered circular cylinders configurations by using finite element method. Effect of the spacing between the tandem cylinders was investigated at small Reynolds number, Re = 400. Valencia and Paredes [13] computed the flow and heat transfer in a channel with two square bars mounted side by side in an approaching flow. The dimensionless spacing between the bars is varied from 0 to 5, whereas the bar height to channel height is d/H = 0.125 and the channel length is L = 5H. It is observed that the pressure drop in the channel and heat transfer from the channel surfaces are strongly dependent on the spacing between the bars and the Reynolds number. The aerodynamic characteristics of flow past a square cylinder with an upstream rod experimentally studied for different Reynolds numbers by Sarioglu et al. [14] and by Zhang et al. [15]. The results
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A. Daloglu / International Communications in Heat and Mass Transfer 35 (2008) 76–83
Fig. 1. Channel dimensions and arrangement of the tandem cylinders.
show that the value of the drag on square cylinder with an upstream rod decreases comparing to the drag on square without rod at certain spacing. Zhou and Yiu [16] experimentally investigated flow structure, momentum and heat transfer in the wake of two tandem circular cylinders. Flow measurements were carried out at three sections away from the downstream cylinder, x/d = 10, 20 and 30, at a Reynolds number of 7000 and at four different spacing ratios, L/d = 1.3, 2.5, 4.0 and 6.0, respectively. They proposed a new classification of the flow in four different categories as 1 b L/d b 2, 2 b L/d b 3, 3 b L/d b 5 and 5 b L/d. This paper presents the results of an experimental investigation conducted on the pressure drop in a channel flow past tandem cylinders. The downstream cylinder has circular cross-section, and the size of this cylinder is kept constant. Two types of upstream cylinder geometries, one type having a circular cross-section and the other type having a square cross-section, are used in the experiments in order to investigate the shape effect. The experiments are performed for three different upstream cylinder sizes by varying the Reynolds number in the range of 5.21 × 104 b Re b 1.56 × 105 and the dimensionless distance between the cylinders in the interval 1.0 b S/d b 10.0, in order to examine the effects of cylinder size, Reynolds number and the spacing, respectively. 2. Experimental apparatus Fig. 1 shows the experimental set-up used in the present study. Experiments were conducted in an open circuit wind tunnel with a square cross-sectional test section (125 mm × 125 mm) of 2 m long. Measurement of the mean air velocity in the tunnel was performed using a pitot tube placed in a cross-section near the channel entrance, and an inclined manometer was used for dynamic pressure readings in ± 0.5 Pa accuracy. An upstream cylinder (square or circular) was placed at channel axis at a location 750 mm down from the entrance. The diameter of the upstream cylinder was set 12.5, 25.0 and 37.5 mm, the blockage ratios ranging from 0.1 to 0.3. A circular cylinder with a diameter d = 12.5 mm (d/H = 0.1) is used as the downstream cylinder. The pressure drop was measured for L = 600 mm channel length (L/H = 4.8) starting at Le = 625 mm (Le/H = 6.0) away from the entrance by using a micro manometer with 1% uncertainty. First the pressure drop in the empty channel was measured for various values of Reynolds number. In defining Reynolds number and friction factor, channel height H was used as the characteristic length and the related equations are Re ¼ fo ¼
Uo H v
DPH : 1=2qUo2 L
ð1Þ ð2Þ
After obtaining the pressure drop in the channel with single upstream cylinder, the pressure drop was measured in the channel with two tandem cylinders. The distance between the tandem cylinders was changed in the range of 1.0 b S/d b 10.0. The apparent friction factor for the channel with cylinder is defined by using Eq. (2) similar to Alvarez's definition [10]. 3. Results and discussion The effects of upstream cylinder on heat transfer from downstream cylinder placed in a channel have been investigated depending on upstream cylinder geometry, spacing and Reynolds number in previous study by Daloglu and Ünal [9]. In this study, experimental measurements of pressure drop in a square channel with tandem cylinders are presented. Experiments are carried out for two types of upstream cylinders, one type having a circular cross-section (circular cylinder), and the other type a square cross-section (square cylinder), and three different sizes of each type, namely D = d, D = 2d and D = 3d in diameter in the case of circular upstream cylinder
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Fig. 2. Variations of pressure drop with spacing.
and in side length in the case of square upstream cylinder are used. For each type and size upstream cylinder the effects of both spacing between the tandem cylinders and Reynolds number on pressure drop are investigated in the interval of 1.0 b P b 10.0 and by varying Reynolds number from 52,100 to 156,000.
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Fig. 3. Variations of the ratio of apparent friction coefficients with spacing.
The results of the experiments conducted using circular cross-sectional upstream cylinders of size 1d, 2d and 3d are shown in Fig. 2a, c and e, respectively. Fig. 2b, d and f shows the experimental results obtained using similar size square cylinders. In this figure, the pressure drop is plotted against the dimensionless spacing, as a function of Reynolds numbers. The points marked at P = 0 in the same
A. Daloglu / International Communications in Heat and Mass Transfer 35 (2008) 76–83
Fig. 4. Variations of pressure drop with Reynolds number.
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figures correspond to the values of pressure drop, ▵Pus, measured in a channel with single front (upstream) cylinder of the corresponding size. The data presented in Fig. 2a shows that, typically for all values of the Reynolds number studied, the pressure drop in the channel decreases first as the separation increases from P = 0 to P = 1, makes a minimum ▵Pmin at P = 1, then a sharp increase occurs in the interval 1 b P b 2, and then a monotonic increase takes place from P = 2 to P b P b 1 occurs. The other characteristic regions observed in Fig. 2a agree well with the ones in [17]; the sharp increase in ▵P corresponding to W–T2 regime, the monotonic increase corresponding to W–T regimes in general and finally ▵Pmax = constant region corresponding to the uncoupled eddy shedding regime behind both cylinders. Pressure drops measured using D = d size square cylinder as upstream cylinder are presented in Fig. 2b.The results show similarity with circular cylinder, but the spacing between the cylinders at which ▵Pmin is achieved moves 1 to 1.4. Comparing the results for circular cylinder and square cylinder, it can be seen that pressure drops for single square upstream cylinder are higher than for circular cylinder at same Reynolds numbers. Fig. 2c and d shows pressure drops against the dimensionless spacing for D = 2d size circular and square cylinders giving the blockage ratio as 0.2, respectively. Similar to D = d size cylinder, pressure drop decreases after placing the downstream cylinder, and the minimum pressure drop is obtained around P = 2.5. With increasing spacing, it increases gradually and becomes constant around P = 5.5, Fig. 2c. The results for square cylinder show some differences, Fig. 2d. As it is expected pressure drop for square upstream cylinder takes higher values than for circular cylinder. The pressure drop in the channel with single front cylinder have smaller values than with tandem cylinders at P = 1.5, in that case cylinders touch each other, After this point the pressure drop decreases with increasing dimensionless distance, and shows a minimum at P = 2.0. After increasing gradually, pressure drop takes constant value for all Reynolds numbers around P = 5.5. Comparing to the pressure drops in the channel with tandem cylinders and with single front cylinder for Re = 156,000, the decrease in pressure drop for tandem cylinders are around 11% for circular and square cylinders. Pressure drops for D = 3d size upstream cylinder are shown in Fig. 2e and f. The minimum pressure drop occurs around at P = 2.4 but decrease in pressure drop is small comparing to smaller size upstream cylinders. The pressure drop gradually increases with increasing spacing and becomes constant around P = 7.5. The smallest effect of the spacing on pressure drop is seen for D = 3d size square upstream cylinder, Fig. 2f. As it is expected, pressure drop for square bar is higher than for circular cylinder all the cases tested. Comparing the maximum pressure drops obtained for circular cylinder and square bar as upstream cylinder at Re= 116,000, the pressure drops for square bar are 9.8% higher than for circular cylinder for D = 1d size, 57.8% for D = 2d size and 62% for D = 3d size. Fig. 3 shows the ratio of apparent friction factor in channel with tandem cylinders, defined similar to empty channel by Alvarez et al. [10], to apparent friction factor in empty channel against the dimensionless spacing. The ratio of apparent friction factors obtained for circular and square cylinders show similarity with the pressure drop results. It is noticed that the ratio of apparent friction factors for square cylinder take higher values than the same size circular cylinder in the same manner with pressure drop. For Re = 116,000, the ratio of apparent friction factors is around 2.9 in the channel with single D = d size circular upstream cylinder. After placing downstream cylinder it drops to 2.1 giving the minimum. It increases again with increasing dimensionless spacing and reaches to 4.5 as the maximum, Fig. 3a. From the results given in Fig. 3b for D = d size square cylinder, it is noticed that the values of the ratio of apparent friction factors take the values of 3.8, 2.5 and 4.8, respectively for Re = 116,000. Although the maximum value of the ratio of apparent friction factors for D = 2d size circular upstream cylinder is 7.7 at Re = 116,000, it takes a value of 12.2 for same size square upstream cylinder, Fig. 3c and d. From Fig. 3e, it can be seen that the ratio of apparent friction factors shows small changes for P N 3.5 and Re N 116,000. For circular cylinder, the ratio of apparent friction factors increases, decreases and again increases with increasing spacing at small Reynolds numbers. But these changes in ratio of apparent friction factors are seen for square cylinder at all Reynolds numbers tested, Fig. 3f. From this figure it can be seen that the ratio of apparent friction factors does not change too much with dimensionless spacing. For example, the maximum value of this ratio is 18.9 for single square upstream cylinder and 20.8 for tandem cylinders at Re = 156,000. In order to see clearly the effect of the spacing on the pressure drop Fig. 4 is given. In Fig. 4, the pressure drops are plotted against Reynolds number for different dimensionless spacings using circular and square upstream cylinders. As it is expected the variation of pressure drop with Reynolds number exhibits a parabolic character. From Fig. 4a and b plotted for D = d size upstream cylinder, it can be clearly seen that pressure drop in channel with tandem cylinders takes smaller values than in channel with single upstream cylinder for P b 2 and for all Reynolds numbers. Comparing subpanels c and d of Fig. 4 for D = 2d size upstream cylinder, the effect of the spacing on pressure drop is stronger for circular upstream cylinder. For two types of upstream cylinders, pressure drops in channel with tandem cylinders are lower than in channel with single upstream cylinder for P b 2.5. The effect of spacing on pressure drop becomes less important for D = 3d size upstream cylinders with a blockage ratio of 0.3, Fig. 4e and f. Especially for square upstream cylinder the variation in pressure drop with spacing takes place in a narrow band.
4. Conclusion From the experimental data presented in this paper it is observed that the pressure drop in a channel with two tandem cylinders inline exhibits a strong dependence on the spacing between tandem cylinders. The most important result that should be extracted from this paper is that, for all the parameters considered in the study, there exists a critical spacing between the two cylinders at which the pressure drop takes a minimum value, ▵Pmin, which is even less than the
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pressure drop obtained for the case of in the channel with single upstream cylinder. The value of this critical spacing varies considerably with the shape and size of the upstream cylinder, but it is almost independent of the Reynolds number. The percent reduction in ▵P from ▵Pus to ▵Pmin is more important for the same size upstream and down stream cylinders than the one for D = 2d and D = 3d size upstream cylinders. It must be pointed out that flow in the same channel with square cross-sectional upstream cylinders yields higher pressure drops when compared with the circular cylinders, as it is expected. Acknowledgement The author gratefully thanks Professor Ahmet Ünal for his helpful advices. References [1] M.M. Zdravkovich, Review of flow interference between two circular cylinders in various arrangements, Journal of Fluids Engineering 99 (1977) 618–633. [2] Z.G. Kostic, N. Oka, Fluid flow and heat transfer with two cylinders in cross flow, International Journal of Heat and Mass Transfer 15 (1972) 279–299. [3] M. Hiwada, T. Taguchi, I. Mabuchi, M. Kumada, Fluid flow and heat transfer around two cylinders of different diameters in cross flow, Bulletin of the JSME 22 (167) (1979) 715–723. [4] T. Igarashi, Characteristics of a flow around two circular cylinders arranged in tandem, Bulletin of the JSME 24 (1981) 323–331. [5] T. Igarashi, Characteristics of a flow around two circular cylinders of different diameters arranged in tandem, Bulletin of the JSME 25 (1982) 349–357. [6] L. Ljungkrona, B. Sunden, Flow visualization and surface pressure measurement on two tubes in an in-line arrangement, Experimental Thermal and Fluid Science 6 (1) (1993) 15–27. [7] K. Tatsutani, R. Devarakonda, J.A.C. Humphrey, Unsteady flow and heat transfer for cylinder pairs in a channel, International Journal of Heat and Mass Transfer 36 (13) (1993) 3311–3328. [8] A. Valencia, Unsteady flow and heat transfer in a channel with a built-in tandem of rectangular cylinders, Numerical Heat Transfer 29 (1996) 613–623. [9] A. Daloglu, A. Ünal, Heat transfer from a cylinder in the wake flow, International Communication in Heat and Mass Transfer 27 (4) (2000) 355–366. [10] J. Alvarez, M. Pap, A. Valencia, Turbulent heat transfer in a channel with bars in tandem and in side by side arrangements, International Journal of Numerical Methods for Heat & Fluid Flow 10 (8) (2000) 877–896. [11] J.L. Rosales, A. Ortega, J.A.C. Humphrey, A numerical simulation of the convective heat transfer in confined channel flow past square cylinders: comparison of inline and offset tandem pairs, International Journal of Heat and Mass Transfer 44 (2001) 587–603. [12] E. Buyruk, Numerical study of heat transfer characteristics on tandem cylinders, inline and staggered tube banks in cross-flow of air, International Communications in Heat and Mass Transfer 29 (3) (2002) 355–366. [13] A. Valencia, R. Paredes, Laminar flow and heat transfer in confined channel flow past square bars arranged side by side, Heat and Mass Transfer 39 (2003) 721–728. [14] M. Sarioglu, Y.E. Akansu, T. Yavuz, Control of flow around square cylinders at incidence by using a rod, AIAA Journal 43 (7) (2005) 1419–1426. [15] P.F. Zhang, J.J. Wang, S.F. Lu, J. Mi, Aerodynamic characteristics of a square cylinder with a rod in a staggered arrangement, Experiments in Fluids 38 (4) (2005) 494–502. [16] Y. Zhou, M.W. Yiu, Flow structure, momentum and heat transport in a two-tandem-cylinder wake, Journal of Fluid Mechanics 548 (2006) 17–48. [17] M.M. Zdravkovich, Flow Around Circular Cylinders, Oxford Science Publication, 2003, pp. 998–1018.