Low Reynolds number flow in rectangular cooling channels provided with low aspect ratio pin fins

Low Reynolds number flow in rectangular cooling channels provided with low aspect ratio pin fins

International Journal of Heat and Fluid Flow 31 (2010) 689–701 Contents lists available at ScienceDirect International Journal of Heat and Fluid Flo...

2MB Sizes 0 Downloads 25 Views

International Journal of Heat and Fluid Flow 31 (2010) 689–701

Contents lists available at ScienceDirect

International Journal of Heat and Fluid Flow journal homepage: www.elsevier.com/locate/ijhff

Low Reynolds number flow in rectangular cooling channels provided with low aspect ratio pin fins Alessandro Armellini, Luca Casarsa, Pietro Giannattasio * Dipartimento di Energetica e Macchine, Università di Udine, Via delle Scienze 208, 33100 Udine, Italy

a r t i c l e

i n f o

Article history: Received 30 July 2009 Received in revised form 27 October 2009 Accepted 3 February 2010 Available online 7 March 2010 Keywords: PIV Pin fin Confined flow Horseshoe vortex Vortex shedding

a b s t r a c t The flow structures around single heat transfer promoters of different shapes (square, circular, triangular and rhomboidal) have been investigated experimentally by means of a 2-D Particle Image Velocimetry (PIV) technique. The geometrical configuration and flow conditions considered are typical of real liquid cooling channels. They include low aspect ratio pin fins confined at both ends by the walls of a rectangular channel, water flow at low Reynolds numbers (Re = 800, 1800, 2800), high core flow turbulence and undeveloped boundary layers at the position of the obstacle. In front of the pin fins the high turbulence level is found to promote a strong instability of the horseshoe vortex system that forms at the wall/obstacle junction. In particular, frequent events of break-away of the primary vortices and inrush of core fluid, which are known to enhance the wall heat transfer, are observed in the cases of square and circular pins already from Re = 1800. The near wake downstream of the obstacles appears to be influenced by streamwise oriented vortical structures produced at the wall/obstacle junction. They give rise to spanwise velocity components (up-wash flow) that lead to a three-dimensional mass recirculation behind the pins. The combination of up-wash flows, low Reynolds number and high core flow turbulence gives rise to a competition between the classical alternate vortex shedding and an irregular shedding mode characterized by the decoupling of the shear layers and the absence of well organized primary structures. At Re = 800, the irregular shedding prevails and the mean wake topology is almost insensitive to the obstacle shape. As the Reynolds number is increased, the junction flow structures reduce in size and strength, their effect on the wake flow weakens and the recirculation structures behind the obstacles differentiate significantly according to the pin shape. Besides investigating complex flow structures in geometrical and flow configurations of practical interest but scarcely covered by the current literature, the present work provides an accurate experimental data-base for the validation of CFD codes under challenging flow conditions. Ó 2010 Elsevier Inc. All rights reserved.

1. Introduction Modern cooling systems such as the heat sinks for electronic components are required to dissipate very high heat fluxes in small size and noiseless devices. To fulfill these requirements it is often necessary to resort to the forced convection of liquid refrigerants flowing in narrow channels. Low Reynolds numbers flows are usually considered in order to reduce the pumping losses and the noise emissions, while arrays of short pin fins of various shapes are installed in between the channel walls to increase the wetted surface and promote turbulence. The flow approaching the obstacles is normally characterized by undeveloped boundary layers and high turbulence content as a consequence of the short entry length and flow separation at the channel entrance. The pursuit of the optimal design of such cooling systems requires a deep knowledge of the complex three-dimensional flow * Corresponding author. Tel.: +39 0432 558012; fax: +39 0432 558027. E-mail address: [email protected] (P. Giannattasio). 0142-727X/$ - see front matter Ó 2010 Elsevier Inc. All rights reserved. doi:10.1016/j.ijheatfluidflow.2010.02.003

that develops around the obstacles, especially in the near wall regions. The flow characteristics are affected by a large number of independent variables, such as obstacle shape and aspect ratio, Reynolds number, core flow turbulence intensity and displacement thickness of the incoming boundary layer. The influence of such variables is only partially treated in the current literature, especially as the interaction is concerned between thick and unstable boundary layers and low aspect ratio obstacles of various shapes. Many works have been devoted to the study of the fundamental case of nominally two-dimensional flow around an infinite or high aspect ratio circular cylinder with uniform incoming flow (see Williamson, 1996, for a thorough review). Even in this apparently simple case several wake flow regimes have been identified at varying Reynolds numbers, which are characterized by complex transitions and strongly three-dimensional effects. Thanks to the use of an advanced time-resolved tomographic PIV technique, an impressive experimental characterization of the vortex structure evolution in the wake of a circular cylinder at Reynolds numbers ranging from 180 to 5540 is provided in a very recent work by Scarano and Poelma (2009).

690

A. Armellini et al. / International Journal of Heat and Fluid Flow 31 (2010) 689–701

Nomenclature AR d Dh d f h I Lc Lf Re ReDh Re*

= h/d, aspect ratio pin fin characteristic diameter hydraulic diameter of the channel pin fin characteristic diameter shedding frequency pin fin height turbulence intensity wake closure length wake formation length Reynolds number based on UB, d Reynolds number based on UB, Dh Reynolds number based on U*, d

As suggested by Bearman and Morel (1983) the free-stream turbulence intensity, length scale and frequency spectrum exert a strong influence on the wake dynamics. Gerrard (1965) and Norberg (1986) showed that, for a circular cylinder in the shear layer transition regime (Re ¼ 103  2  105 ), an increase in the free-stream turbulence shortens the wake formation length and anticipates the occurrence of the transition points. On the contrary, a reduction in the aspect ratio of a cylinder confined between end-plates was reported to shift the transition points to higher Reynolds numbers (Law and Ko, 2001; Norberg, 1994), so enhancing the stability of the wake. When the aspect ratio is very low, the thickness of the boundary layer developing on the confining walls can be comparable with the obstacle height. In these conditions very complex three-dimensional flow structures arise both upstream and downstream of the body. In front of a surface-mounted obstacle the incoming boundary layer separates from the wall, giving rise to a horseshoe vortex system that is diverted symmetrically around the obstacle and advected downstream. In his pioneering work, Baker (1979) showed that the laminar horseshoe vortex topology and dynamics are determined by the Reynolds number and the ratio of boundary layer displacement thickness and cylinder diameter, d =d. The existence of remarkable unsteadiness in the vortex dynamics was evidenced by Baker (1979), Lin et al. (2003), Seal et al. (1995), Thomas (1987), and, for high Reynolds numbers, by Agui and Andreopoulos (1992). Among the different classifications of the horseshoe vortex system available in the literature (Baker, 1979; Khan and Ahmed, 2005; Simpson, 2001) the one proposed by Lin et al. (2002) seems to be the most popular. Four major flow regimes are defined, namely, steady vortex system (Re < 1300), periodic oscillating vortex system with small displacement (1300 6 Re < 1700), periodic break-away vortex system (1700 6 Re < 5000) and turbulent-like vortex system (Re P 5000). The literature on flows around wall-mounted cylinders provides a useful insight into the effects of low aspect ratio and thick incoming boundary layer. In these conditions complex three-dimensional flow structures around the obstacle have been observed and investigated, among the others, by Sakamoto and Arie (1983), Sau et al. (2003), Sumner et al. (2004), and Wang et al. (2006) in the case of fully submerged obstacles, and by Akilli and Rockwell (2002) in shallow water flows. In most cases peculiar flow characteristics, such as streamwise oriented vortical structures and up-wash flow (away from the wall), were observed inside the obstacle near wake. In the cases of submerged bodies the shear layer produced by the flow separation at the obstacle free-end interacts with those from both sides of the obstacle, which results in the formation of symmetric arch-type vortices. Wang et al. (2006) showed that the up-wash flow weakens the arch-type vortices at the free-end and encourages a symmetric vortex shedding in the near wall region.

St u0 , v0 , w0 U UB U* x, y, z

¼ fd=U  ; Strouhal number r.m.s. velocity fluctuations mean streamwise velocity bulk flow velocity peak flow velocity streamwise, crosswise and spanwise coordinates

Greek symbols boundary layer displacement thickness d h boundary layer momentum thickness xy ; xz crosswise and spanwise vorticity components

Confined short obstacles of different shapes have been investigated from the thermal standpoint by Montelpare and Ricci (2004), and Ricci and Montelpare (2006), who considered geometries and flow regimes that are typical of cooling devices for electronic components. They measured the heat transfer coefficient of liquid cooled pin fins in single and in-line arrangements at low Reynolds numbers and performed flow visualizations that emphasized the need of a deeper knowledge of the complex flow fields around the obstacles. In the present study a 2-D PIV technique is used to investigate the separated flow structures around low aspect ratio (AR = 1.09) pin fins of different shapes (square, circular, triangular and rhomboidal) in a practical configuration of liquid cooling channels. Distinctive features are the confinement of the obstacles at both ends, water flow at low Reynolds numbers (Re = 800, 1800, 2800), high core flow turbulence and undeveloped boundary layers at the position of the obstacle. In a previous study (Armellini et al., 2009) the present authors performed a similar investigation limited to the circular pin, which showed the effects of the incoming flow perturbation on the horseshoe vortex system, the existence of a peculiar mechanism of three-dimensional mass redistribution behind the obstacle, and the occurrence of an irregular shedding mode in the near wake. Besides confirming all these findings also for pin shapes different from the circular one, the present work clarifies the reasons for the different flow behaviors observed at varying obstacle geometries and Reynolds numbers, so providing a rational basis for interpreting the heat transfer mechanisms that determine the performance of pin fins in real cooling channels. 2. Experimental apparatus and procedure 2.1. Test rig The test rig consists of the water circuit shown in Fig. 1. The facility, described in detail in Armellini et al. (2009), allows a precise control of both the temperature (fixed at 25 ± 0.2 °C) and the mass flow rate of the water that feeds the test section. Particular care has been taken in decoupling the circuit branch containing the pump from the test channel, so preventing the pump disturbances from being transmitted to the measurement section. On the basis of the flow rate and temperature measurement errors, the overall uncertainty in the Reynolds number turns out to be less than ±1.5%. The test section consists of a rectangular channel completely machined out of Plexiglas in order to provide full optical access for the application of the PIV technique. The duct is 160 mm wide, 24 mm high and 880 mm long. Its ends are connected by means of flanges to short aluminum ducts having the same internal crosssection of the channel. The aluminum ducts enter inside the cylin-

A. Armellini et al. / International Journal of Heat and Fluid Flow 31 (2010) 689–701

Fig. 1. Schematic of the experimental apparatus.

drical walls of the settling tanks (R1 and R2 in Fig. 1) so as to provide inlet and outlet sections characterized by abrupt contraction and expansion, respectively. The overall channel length is 1156 mm. The obstacles are placed at the centre of the channel (see Fig. 2A) and consist of four prisms having different shapes, i.e., circular, square, rhomboidal and triangular cross-sections. Their height, h = 24 mm, is equal to the channel inner height and they all have characteristic diameter d = 22 mm (see Fig. 2C). The investigated flow regimes (Re = 800, 1800, 2800) and the channel geometry, in particular the obstacle aspect ratio (AR = h/d = 1.09) and the type of inlet and outlet sections, have been selected in order to reproduce a practical configuration of liquid cooling channels, such as the heat sinks used in the electronic devices. 2.2. Particle Image Velocimetry A two-dimensional PIV technique has been used for flow field measurements. The system set-up includes a 125 mJ double cavity Nd:Yag laser operated at a wavelength of 532 nm, a 12-bit CCD camera with a resolution of 1024  1280 pixels and the related synchronization and acquisition systems. The camera was operated at the frequency of 4 Hz. Different spatial resolutions were

A

691

used, depending on the size of the flow structures to be detected. For the measurements in the wake region, resolutions of 11,000 pixels/m and 18,000 pixels/m were used in planes xy and 1xz, respectively (see Section 2.4). Additional measurements upstream of the obstacle in plane 1xz were performed at the higher magnification of 34,000 pixels/m for a more detailed sampling of the instantaneous structures of the horseshoe vortex system. These values were achieved by means of a lens of 60 mm focal length mounted on the camera and set at f  4.8. The tracer particles were hollow glass spheres, silver coated, with a characteristic size of 12 lm and the same density as water. All PIV images were processed using commercial software PIVview, with a first interrogation window of 64  64 pixels, a single step of window size refinement and 50% of window overlapping. Two steps of window distortion-displacement were used for each step of the refinement procedure. Finally, a Gaussian peak-fitting was adopted to perform the sub-pixel interpolation. Vector validation was performed with tests based on a normalized median filter and on criteria of primary to secondary correlation peak and minimum signal-to-noise ratio. The percentage of invalid vectors was typically low, less than 3%, and only the valid vectors were sampled to obtain the mean velocity fields and turbulent statistics. 2.3. Error estimation As PIV is a comparatively complicated experimental technique, there is no simple means available to check the accuracy of PIV measurements. Nevertheless, a careful analysis of the different sources of PIV errors was already performed by Casarsa and Giannattasio (2008) with reference to a flow field with characteristics similar to the present one (three-dimensional shearing flow). The upper bound of the error in the instantaneous flow fields was estimated to be 3%. When looking at statistical quantities such as mean and r.m.s. velocities computed from a limited number of samples, the sampling error must be also considered. As shown by the present authors in Armellini et al. (2009), an overall upper bound estimate of the uncertainty in the mean velocities turns out to be less than 5% (95% confidence level) in the most part of the flow fields, except for limited regions inside the recirculation bubbles affected by very low velocities and high fluctuations. Under the same assumptions, the maximum uncertainty in the estimate of the r.m.s. velocity fluctuations is 6.2%. 2.4. Measurement stations

B

C

Fig. 2. Test section: nomenclature and position of the measurement planes. (A) xy view, (B) xz view, (C) cross-section of the obstacles (measures in mm).

The positions of the PIV measurement planes within the test section are shown in Fig. 2A and B, together with the co-ordinate system adopted. The number and the location of these planes have been selected in order to obtain a quasi-3D description of the flow field with a reasonable experimental effort. In order to characterize the unperturbed flow at the position of the obstacle (x = y = z = 0), velocity measurements were performed in symmetry planes xy-s and xz-s of the smooth channel, i.e., without the obstacle. In view of the short entry length (Le/h = 24.1), the flow is still developing at the obstacle location (Armellini et al., 2009). Consequently, in order to provide an inflow condition useful for numerical simulations, velocity measurements were also performed in symmetry planes xz-in and xy-in around the streamwise position x/ d = 14.5, which is sufficiently upstream of the obstacle to avoid any blockage effect. In the region of the obstacle, measurements were performed in the channel symmetry planes, 1xy and 1xz, and in other two horizontal planes, 3xy and 4xy, located at distances h/3 and 5/12h from plane 1xy, respectively. Only for the circular cylinder measurements were carried out also in plane 2xy, h/ 4 away from plane 1xy. All five planes extend up to 2d upstream of

692

A. Armellini et al. / International Journal of Heat and Fluid Flow 31 (2010) 689–701

the obstacle and about 4d downstream of it. To maximize the spatial resolution, each plane was divided in two or more measurement windows acquired separately.

3. Results and discussion

Reynolds number. On the other hand, it is hard to ascribe the large value of I/UB in Table 1 to a high core flow turbulence. It would be more reasonable to simply define the inlet flow at Re = 800 as a highly perturbed one. 3.2. Flow upstream of the obstacles

3.1. Incoming flow Table 1 provides a summary of the flow characteristics at the position of the obstacle obtained by means of PIV measurements performed in planes xz-s and xy-s. For the smooth channel the Reynolds number should be referred to the hydraulic diameter of the channel (Dh = 41.74 mm) rather than to the pin diameter. For this reason Table 1 reports also the values of ReDh . Complete velocity and fluctuation profiles at both locations x/d = 0 and x/d = 14.5 of the smooth channel can be found in Armellini et al. (2009). Those data show high values of the velocity fluctuations at the position of the obstacle, which were ascribed to the strong flow perturbation induced by the abrupt channel entrance and to the short entry length of the duct. For Re = 1800 and 2800 a comparison with DNS data concerning a fully developed turbulent flow between flat plates (Iwamoto et al., 2002; Tsukahara et al., 2005), not reported for brevity, showed a reasonable agreement between computed and measured mean velocity and fluctuation profiles, the main differences being due to the incomplete flow development in the present channel. The values of turbulence intensity at the centre of the channel predicted by DNS turned out to be comparable to the ones reported in Table 1, which confirms the turbulent nature of the measured velocity fluctuations, at least at Re = 1800 and 2800 (ReDh ¼ 3415; 5312). For Re = 800 (ReDh ¼ 1518) the classification of the flow regime turns out to be a more difficult task. Although a laminar flow condition would be expected in this case, both shapes and levels of the velocity fluctuation profiles turn out to be comparable to those at the higher Reynolds numbers. It is argued that the strong perturbation due to the flow separation and reattachment at the channel inlet does not allow the development of a pure laminar flow at this

Table 1 Boundary layer characteristics, peak streamwise velocity and core flow turbulence intensity at the position of the obstacle in the smooth channel. x = 0, y = 0

x = 0, y = 0, z = 0

Re

ReDh

d =d

#=d

U  =U B

I=U B ð%Þ

800 1800 2800

1518 3415 5312

0.136 0.100 0.081

0.0545 0.0454 0.0409

1.39 1.29 1.24

7.58 6.66 6.58

Upstream of the obstacles the approaching fluid separates and gives rise to a horseshoe vortex system that turns out to be remarkably unsteady also at the lowest Reynolds number. In Armellini et al. (2009) the present authors showed that the separated structures upstream of the circular pin are strongly perturbed by vorticity bursts from the incoming boundary layers. These bursts are a distinctive feature of the highly perturbed inlet flow, having been observed also in the smooth channel. They cause the vortex system to oscillate aperiodically at Re = 800 and to produce an even stronger instability at Re = 1800 and 2800. In particular, break-away of the primary vortices and frequent eruptions of secondary vorticity from the channel walls were observed at the higher Reynolds numbers. In the present contribution the effect of the different obstacle shapes is investigated. Changing the pin geometry results in strong variations in the intensity and size of the separated structures, whereas the dynamics of the horseshoe vortex system remains substantially unaltered. The square pin produces the most intense separation structure and the vortices are remarkably larger than in the other cases. The unstable behavior of the horseshoe vortex system is documented quite well in Figs. 3 and 4, which report examples of instantaneous flow fields in plane 1xz for Re = 800 and Re = 1800, respectively. Frame A of Fig. 3 shows the unperturbed horseshoe vortices just before the appearance of an incoming vorticity burst; a dashed line marks the initial position of the first primary vortex. Frame B, 6 s after frame A, shows the effect of the perturbation: the horseshoe system has grown in size and strength, the vortices have moved upstream and a counter-rotating secondary structure has got clearly visible in between the two primary ones. Moving further in time (frame C, 9 s after frame A), the additional vorticity is dissipated and the vortex system comes back to almost its original size and position. The amplitude of the streamwise oscillation of the primary vortex core reaches a maximum value of about 0.25 d. Fig. 4A shows the horseshoe vortex system for Re = 1800 at the time when the incoming vorticity burst is going to impinge on the obstacle. In frame B, 1 s after frame A, the effects of the perturbation are quite evident: differently from the case at Re = 800, the secondary vortex is erupted from the channel surface, the main primary vortex moves closer to the obstacle and an intense inrush of core fluid to the wall region takes place. These phenomena have been well documented in the literature (Praisner and Smith, 2006)

Fig. 3. Instantaneous vorticity fields and stream-tracers in the upper half of plane 1xz in front of the square obstacle for Re = 800: (A) t = 0 s, before the vorticity burst; (B) t = 6 s, effect of the perturbation, (C) t = 9 s, restoring of the initial condition.

693

A. Armellini et al. / International Journal of Heat and Fluid Flow 31 (2010) 689–701

Fig. 4. Instantaneous vorticity fields and stream-tracers in the upper half of plane 1xz in front of the square obstacle for Re = 1800: (A) t = 0 s, incoming perturbation; (B) t = 1 s, effect of the vorticity burst, (C) t = 1.25 s, break-away of the primary vortex.

increased, the mean separation structure is observed to reduce in size and to change into a single stretched vortex. The progressively lower blockage effect produced by the circular, rhomboidal and triangular pins with respect to the square obstacle is well underlined by the corresponding reduction of both the size of the vortex system and the distance between the obstacle and the main primary vortex. In the cases of square and circular pins at Re = 800 two relative maxima of u0 are observed at the mean positions of the two primary vortex cores. At increasing Reynolds number, the occurrence of phenomena such as break-away, vorticity eruption and inrush leads to a more spread area of intense streamwise velocity fluctuations. The highest fluctuations w0 are detected at the positions where the secondary vortex and the eruption phenomena are observed. Remarkable levels of w0 are also found in the flow regions immediately adjacent to the obstacle, due to the spanwise oscillations of the stagnation point on the pin surface. A clear evidence of the lower intensity and size of the horseshoe vortex system in front of the rhomboidal and triangular pins is provided by the significantly smaller velocity fluctuations, in particular w0 .

as a driving mechanism of heat transfer enhancement at the obstacle/channel wall junction. Finally, in frame C, the main primary vortex undergoes stretching and subsequent break-away and the second primary vortex takes its place. Similar observations have been made also at Re = 2800, but the time and length scales of the flow structures are smaller as expected in view of the higher Reynolds number. In front of the circular pin the horseshoe vortices show a quite similar evolution (see Armellini et al., 2009), the only difference being the smaller size of the flow structures due to the lower blockage effect produced by the cylindrical obstacle. More relevant differences are observed in front of the other two pins, which present a sharp edge on the frontal surface. Their blockage effect is quite moderate and the separation structures are very small. Adopting the same spatial resolution as for the square pin, the instantaneous flow fields capture only a main primary vortex located very close to the obstacle in the case of rhomboidal pin and Re = 800. In the remaining cases, small primary vortices have been observed only under perturbed conditions as a consequence of the amplifying effect of the vorticity bursts. Recognizable cases of break-away and inrush have been documented for the rhomboidal pin at Re = 1800 and 2800. Figs. 5–8 show the stream-tracers of the time-averaged flow fields and r.m.s. velocity fluctuations u0 and w0 in front of the obstacles for Re = 800, 1800 and 2800. As the Reynolds number is

3.3. Flow downstream of the obstacles A detailed analysis of the PIV measurements around the circular pin presented in Armellini et al. (2009) showed that the combination of low Reynolds number, low aspect ratio and thick incoming

Re=800

0.6

Re=1800

Re=2800

z/d

0.4 0.2 0 0.6 24

2

9

12

21

24

33 30

15 18

27 30

33

9

2

15

12 15

9

-1.25

-1

x/d

-0.75

-0.5 -1.75

33

21

3

9

-1.5

-1.25

-1

x/d

18

-1.5

18

15

33

6

15

6

12

3

12

9

-0.75

12

6 9 12

12

-0.5

-1.75

-1.5

15

-1.25

30

-1

x/d

Fig. 5. Time-averaged flow fields and r.m.s. velocity fluctuations in plane 1xz in front of the square obstacle.

15

6

0.4

-1.75

21 24

12

12

0.2

0.6

18

27

18

w’/UB⋅10

15

12

15

u’/UB⋅10

6

z/d

6

18

0.2 0

3

24 21

30

Square

27 30

12

0.4

-0.75

-0.5

694

A. Armellini et al. / International Journal of Heat and Fluid Flow 31 (2010) 689–701

Re=800

0.6

Re=1800

Re=2800

z/d

0.4 0.2 0 0.6

15

18 12

9

2

w’/UB⋅10

18

21

24

12

12

15

u’/UB⋅10

15

18

9

9 9

Circular

21

12

z/d

24 21

21

6

24

0.2 0

21

21

21

6

0.4

2

0.2

-1.75

6

-1.5

-1.25

-1

9 12

6

-0.75

6

9

9

0.6

3

15 12

0.4

15

-0.5 -1.75

-1.5

-1.25

x/d

-1

9

12

-0.75

-0.5

12 18

3

-1.75

-1.5

-1.25

x/d

-1

-0.75

-0.5

x/d

Fig. 6. Time-averaged flow fields and r.m.s. velocity fluctuations in plane 1xz in front of the circular obstacle.

Re=800

0.6

Re=1800

Re=2800

z/d

0.4 0.2 0 0.6 24

z/d

0.2

21

24

18

w’/UB⋅10

12 12

12

18

21

24

9

9

2

15

12

15

15

u’/UB⋅10

21

Rhomboidal

18

0

21

21

21

9

9 2

6

0.2

9

0.4

3

0.6

3

6 9

6

-1.75

-1.5

-1.25

-1

-0.75

-0.5 -1.75

-1.5

-1.25

x/d

-1

x/d

-0.75

6

9

0.4

9

3

-0.5

-1.75

-1.5

-1.25

-1

-0.75

9

-0.5

x/d

Fig. 7. Time-averaged flow fields and r.m.s. velocity fluctuations in plane 1xz in front of the rhomboidal obstacle.

boundary layers produces a highly three-dimensional wake downstream of the obstacle. A sketch of the conjectured mass transport mechanism in the near wake is shown in Fig. 9. Streamwise oriented vortical structures, consistent with the base vortices described by Wang et al. (2006), develop at the obstacle/wall junction in between and adjacent to the advected branches of the horseshoe vortex system. In this region outer flow is entrained into the mean recirculation bubbles and is transported from the channel walls towards the horizontal symmetry plane (up-wash flow). A portion of the fluid is returned to the wall region just behind the obstacle, the remaining is transferred to the shear layers at the wake sides and is transported to the wall by the spanwise velocity component of the horseshoe vortex. For continuity, the outer flow entrained into the recirculation bubbles in the wall region is restituted by the shear layers downstream of the near wake in the central portion of the channel. The three-dimensional mean flow recirculation behind the obstacle is particularly evident at

Re = 800, where it extends over almost the whole channel height. At the other two flow regimes the smaller size of the base and horseshoe vortices leads to weaker three-dimensional effects in the central portion of the channel. The measurements performed downstream of the square, rhomboidal and triangular obstacles are consistent with the interpretation of the flow mechanism derived for the circular pin. Fig. 10 shows the time-averaged stream-tracers and normalized vorticity fields downstream of the obstacles in planes 1xy and 4xy at Re = 800. Important topological differences between the two flow planes can be observed for all the geometrical configurations. In particular, the path of the stream-tracers in the recirculation bubbles, centripetal in the wall region and centrifugal in the channel mid-plane, gives evidence of the spanwise fluid transport from the wall to the horizontal symmetry plane. Moreover, in plane 4xy the effects of the advected branch of the horseshoe vortex are well documented by both the crosswise deviation of the

695

A. Armellini et al. / International Journal of Heat and Fluid Flow 31 (2010) 689–701

Re=800

0.6

Re=1800

Re=2800

z/d

0.4 0.2 0 0.6 18

21

0.4

18

9

12

u’/UB⋅102

21

Triangular

z/d

0

18

12

12

15

0.2

15

15

18

9

9

w’/UB⋅102

0.2 6

3

0.4 0.6

3

-1.75

-1.5

-1.25

-1

-0.75

-0.5 -1.75

-1.5

3

-1.25

x/d

-1

x/d

-0.75

-0.5

-1.75

-1.5

-1.25

-1

-0.75

-0.5

x/d

Fig. 8. Time-averaged flow fields and r.m.s. velocity fluctuations in plane 1xz in front of the triangular obstacle.

horseshoe vortex

base vortex

Fig. 9. Mass transport mechanism downstream of the obstacle.

stream-tracers and the negative vorticity region at the side of the wake. These effects are observed also downstream of the rhomboidal and triangular pins, in spite of the very small separation structures that form upstream of such obstacles. In fact, the shape of the frontal part of these latter pins produces a constant deviation of the approaching flow along the lateral surfaces, which effectively promotes the growth of the horseshoe vortices due to the distortion of the incoming boundary layer. Experimental results similar to those in Fig. 10 are presented in Fig. 11 for the case Re = 2800. Compared to the data at Re = 800 the results obtained at the higher Reynolds number show a general reduction in the wake closure length (the distance between the obstacle centre and the wake saddle point) and a weaker impact of the three-dimensional effects on the mean flow field. However, strong differences are observed in the sensitivity of each geometry to the change in the Reynolds number. In particular, the recirculation region behind the rhomboidal and triangular obstacles shows significant variations in size and topology, whereas only minor changes are observed in the wake after the square pin. The reasons for such a behavior will be clarified later. An additional support to the understanding of the mean topology of the near wake is provided by the measurements performed in the vertical symmetry plane. Fig. 12 shows the time-averaged stream-tracers and normalized streamwise velocity contours in the lower half of plane 1xz for all the considered pin geometries and Reynolds numbers. The end of the mean flow recirculation behind the obstacles appears as an in-plane reattachment line (it is

actually the locus of saddle points corresponding to contour-line U = 0). Consistently with the observations in planes xy (Figs. 10 and 11), this line moves closer to the obstacle as the Reynolds number is increased, except for the square pin. In all cases the streamwise extension of the mean recirculation region (where U < 0) exhibits significant variations along z-direction. In particular, the wake closure length is maximum in the vicinity of the channel wall. This behavior is explained in Armellini et al. (2009), where the saddle points close to the wall are shown to be produced by streamlines coming from the outside of the shear layers, so that they can no longer be considered as reattachment points of the flow that separates at the obstacle sides. Fig. 12 shows that the backflow starting from the wake closure line is at first attached to the channel wall, then it separates and rolls up in a vortical structure that develops at the rear junction between the obstacle and the channel wall. This mean flow structure is well defined at Re = 800, whereas at Re = 2800 it is too small to be resolved by the present measurements, except for the square pin. The stream-tracers in plane 4xy (see Figs. 10 and 11) clearly show that this recirculation structure is a three-dimensional one, being characterized by a spiral motion directed towards the shear layers. Indeed, it is the actual representation of the conjectured mechanism of three-dimensional mass transport in the near wake. A more exhaustive summary of the time-averaged characteristics of the wake in all the flow cases is presented in Fig. 13 and Table 2. The plots in the first, second and third column of Fig. 13 show the profiles along the channel axis of streamwise velocity, r.m.s. velocity fluctuation u0 and fluctuations v0 and w0 , respectively, for Re = 800, 1800 and 2800. The rows refer to the four different obstacles, the shape of which is shown in the lower right side of each plot. Table 2 reports a summary of the wake characteristic lengths, namely, the wake closure length, Lc, and the vortex formation length, Lf, defined as the distance between the obstacle axis and the point on the wake centerline where fluctuation u0 is at a maximum (Griffin and Ramberg, 1974). In order to allow an easier comparison with data in the literature based on the free-stream velocity, Table 2 reports also the values of Re*, i.e., the Reynolds number based on streamwise velocity U* measured at the origin, ðx; y; zÞ  ð0; 0; 0Þ, without the obstacle. At Re = 800 all the obstacles produce very long wakes, as already observed in Fig. 10, and the three r.m.s. velocity fluctuations on the channel axis turn out

696

A. Armellini et al. / International Journal of Heat and Fluid Flow 31 (2010) 689–701

Fig. 10. Time-averaged vorticity fields and stream-tracers in planes 1xy and 4xy at Re = 800.

Fig. 11. Time-averaged vorticity fields and stream-tracers in planes 1xy and 4xy at Re = 2800.

to be small and of comparable magnitude. Both Lc and Lf have rather large values and their relative differences are remarkably larger than expected on the basis of data in the literature concerning obstacles with higher aspect ratios and two-dimensional flow

fields (Norberg, 1998; Zdravkovich, 1997). As the Reynolds number is increased, the circular, rhomboidal and triangular obstacles exhibit a significant shortening of the wake, smaller differences between Lc and Lf, and a strong increase in fluctuation v0 compared

697

z/d 3.5

4

0.5

1

0.2 0.3 0.4 0. 5

1.5

2

5

05 -0.

-0. 35

0.7

0 -0 .15

0 -0.2 -0.4 -0.6

Re=2800 0

-0 .05

0 -0.2 -0.4 -0.6 0.5

1

1.5

2

2.5

3

0.6

-0.6 -0.4 -0.2

0 0.1 0.2 0.3 0.4 0.5

0.4

z/d z/d 4

Re=1800

-0.6 -0.4 -0.2

-0.2

z/d

-0.05 -0.15

z/d z/d

0.5 0.5

0.3

0.1

0.2

0.4

3.5

0.3

3

-0.3

0.2 0.1 0

2.5

x/d

25 -0.

-0.15

0.2 0.1

z/d

4

Triangular

0

2

-0.05

-0.4

1.5

U/UB

-0.2 -0.3

1

3.5

0 -0.2 -0.4 -0.6

-0.35

0 -0.2 -0.4 -0.6 0.5

3

0

-0.25 5 -0.1

0

-0 .2

1 -0.

-0.35

.3 -0

5 -0.2

0.8

1 -0. .2

Re=2800 0

Re=800

-0.6 -0.4 -0.2

-0.3

0 -0.2 -0.4 -0.6

-0.6 -0.4 -0.2

2.5

-0.1 -0.2

0.2

0.3

0

-0 .3

-0.35

0. 1

5

1 -0.

2 -0.

0 .7

-0

0.4

0.5

0 .3

0.2 1

Re=1800 0 .2 -0

-0.6 -0.4 -0.2

-0. -0.2 3

5 .3 -0

Square

0.

0 -0.2 -0.4 -0.6

U/UB .1 -0

15 -0. .25 -0

0.6

0 -0.2 -0.4 -0.6

x/d

Re=800 0

0.6

Re=2800 0

5

-0.6 -0.4 -0.2

x/d -0.6 -0.4 -0.2

0 .3 0.4 0.5

-0.25 -0.35

0 -0.2 -0.4 -0.6

-0.3

z/d z/d

5

-0.35

-0.25

0 .7

3

-0 .3

Re=1800

0

2.5

-0.4

0

-0.3 -0.4

0.6

2

0.5

1.5

0.4

1

0

0.5

0.2

-0.05 -0.1 5

z/d

-0 .2

Re=2800 0

35

Rhomboidal 0 .5

5

. -0

0.2 0.1 0

3 -0.

-0.6 -0.4 -0.2

U/UB

-0.2 -0.3

15

0.5

. -0

25 -0 .

0 -0.2 -0.4 -0.6

-0.4

05 -0.

0 -0.05 -0.15

0.4 0.3 0.2

Re=1800 0

Re=800

-0.6 -0.4 -0.2

0.1 0 .1 -0 .2 -0

5 .2

0.4 0.3 0.2 0.1 0 -0.1 -0.2 3 -0.

0 -0.2 -0.4 -0.6

-0

0.2 0.1 0

5 -0.1

0 -0.2 -0.4 -0.6

-0.6 -0.4 -0.2

Circular

0

-0.05

0 -0.2 -0.4 -0.6

-0.6 -0.4 -0.2

U/UB

-0.2 -0.3

z/d

Re=800

-0.6 -0.4 -0.2

-0.1 2 -0.

z/d

A. Armellini et al. / International Journal of Heat and Fluid Flow 31 (2010) 689–701

3.5

4

x/d

Fig. 12. Time-averaged stream-tracers and streamwise velocity contour-lines in the lower half of plane 1xz behind the four obstacles for Re = 800, 1800 and 2800.

to u0 and w0 . On the contrary, the wake after the square pin appears to be almost insensitive to the change in the flow regime. Finally, when comparing the wake lengths produced by the various obstacles, the different positions of the separation points have to be considered. In particular, the flow around the square and triangular pins separates one half diameter upstream and downstream of the obstacle centre, respectively, which should be taken into account in the comparison with the circular and rhomboidal obstacles. A satisfactory interpretation of the observations reported above is provided by the analysis of the instantaneous flow fields downstream of the obstacles. In Armellini et al. (2009) the authors showed that a competition between two different vortex shedding modes exists in the wake of the circular pin. The occurrence of up-wash flow at low Reynolds number weakens the alternate shedding of primary vortices behind the obstacle, while the high

turbulence level of the incoming flow enhances the growth of the secondary Bloor-Gerrard vortices in the shear layers. In these flow conditions a destructive interaction between weak primary vortices and large out-of-phase secondary vortices may occur, leading to the inhibition of the alternate shedding and the onset of an irregular shedding mode characterized by a decoupling of the shear layers and the absence of well organized primary structures. The measurements performed downstream of the different obstacles confirm that, especially at Re = 800, the wake is dominated by the alternation of these two shedding modes. Typical examples of alternate and irregular vortex shedding downstream of the rhomboidal pin at Re = 800 are provided in Fig. 14A and B, respectively. An increase in the Reynolds number has been observed to stabilize the regular shedding, which occurs more frequently and is defined much better (see Fig. 14C). A semi-quantitative analysis of the sensitivity of the shedding mode to the variation of the flow regime

698

A. Armellini et al. / International Journal of Heat and Fluid Flow 31 (2010) 689–701

y/d=0 z/d=0

70 2 u’/UB⋅10

0.25 0

28

70

42 28 14

E

0

1

84

84

0.75

70

70

0.5

56

-0.25

(v’, w’) /UB⋅102

0

0.25

42 28 14

B

28

1

84

84

0.75

70

70

0.5

56

0 -0.25

(v’, w’) /UB⋅102

0

2 u’/UB⋅10

-0.5

42 28 14

C

28

0

1

84

84

0.75

70

70

0.5

56

u’/UB⋅10

2

0

0 -0.25

42 28 14

D 1

2

3

4

1

5

2

3

4

5

M

42 28

0

0

-0.5

+ + ++ ++ + + + + + + + + + + + ++ ++ + + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + +

56

14

H

+ + + ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + + + + ++ + + + ++

N

1

2

3

4

5

x/d

x/d

x/d

L

42

-0.5

0.25

+ + + ++ ++ +++ + + +++++ +++ +++ + ++ + + ++ + + + ++ + + + ++ + + + +

56

14

G

I

42

0

0.25

+ + ++ ++ + + + + + + ++ + + + + + + + + + + + + + + + + + + + + + + + + ++ + +

56

14

F

v’/UB⋅102 w’/UB⋅102

+

56

-0.5

0

U/UB

42

14

A

2 u’/UB⋅10

U/UB

-0.25

56

(v’, w’) /UB⋅102

U/UB

0.5

U/UB

Re=800 Re=1800 Re=2800

(v’, w’) /UB⋅102

0.75

84

84

1

Fig. 13. Measured profiles along the channel axis (y = z = 0): (A–D) mean streamwise velocity, (E–H) r.m.s. velocity fluctuation u0 , (I–N) r.m.s. velocity fluctuations v0 and w0 .

Table 2 Normalized wake characteristic lengths. Obstacle shape

Re = 800, Re* = 1112

Re = 1800, Re* = 2322

Lc/d

Lf/d

Lc/d

Lf/d

Lc/d

Lf/d

Circular Square Rhomboidal Triangular

3.01 2.61 3.26 3.76

3.65 3.33 3.63 4.14

2.51 2.47 1.87 3.08

2.83 3.12 2.01 3.28

2.15 2.47 1.60 2.31

2.36 3.20 1.37 2.34

has been carried out by performing a visual inspection of the instantaneous flow fields downstream of the pins in plane 1xy. The number of samples showing alternate shedding was recorded for each obstacle and Reynolds number, and the percentages of regular events reported in the histograms of Fig. 15 were obtained. Although the selection based on a visual inspection is affected by some degree of uncertainty, the different trends observed for the

Re = 2800, Re* = 3472

various obstacles can be considered as reliable results, also in view of the agreement with the data in Fig. 13 and Table 2. At Re = 800 the irregular shedding mode prevails for all the obstacles, leading to scarcely organized and very long wakes. The weak interaction between the two shear layers causes the velocity fluctuations to be quite low and of similar magnitude along all directions. At increasing Reynolds number striking variations occur in the shed-

699

A. Armellini et al. / International Journal of Heat and Fluid Flow 31 (2010) 689–701

circular

square

80 18 0 0 28 0 00

80 18 0 0 28 0 00

rhomboidal

triangular

100 75 50 25

80 18 0 0 28 0 00

0 80 18 0 0 28 0 00

Regular shedding %

Fig. 14. Instantaneous flow fields in plane 1xy downstream of the rhomboidal pin at Re = 800 (A and B) and 2800 (C): examples of alternate (A and C) and irregular (B) vortex shedding. Dashed contours denote negative vorticity.

Re

Fig. 15. Percentage of regular shedding events at varying Reynolds numbers and obstacle shapes.

Re = 2800 Re = 1800 Re = 800

0.1

0.1

Amplitude [m/s]

Amplitude [m/s]

ding phenomenology after the rhomboidal and triangular pins. Starting from Re = 1800 for the rhomboidal obstacle and at Re = 2800 for the triangular pin regular alternate shedding is observed in almost all instantaneous samples. Correspondingly, as documented by Fig. 13 and Table 2, the wake closure gets very close to the obstacle rear surface and strong velocity fluctuations v0 are produced by the alternation of well organized primary vortices from the opposite wake sides.

Further evidence of the different wake dynamics at varying obstacle shapes and Reynolds numbers is provided by the amplitude spectra of r.m.s. velocity fluctuation v0 measured at point x = Lf on the wake axis in plane 1xy. A FFT analysis has been performed on stencils of 256 PIV samples recorded consecutively and the results are reported in Fig. 16. A dominant frequency is hardly captured at all the flow regimes for the square pin and at Re = 800 for the other obstacles, due to the chaotic and aperiodical behavior of the wake under prevailing conditions of irregular shedding. On the contrary, when the alternate shedding occurs for at least 50% of the observation time a well defined peak in the frequency spectrum can be easily identified, according to the cases of high velocity fluctuations v0 in Fig. 13. The Strouhal numbers corresponding to the dominant frequencies and based on velocity U* and characteristic diameter d are reported in Table 3. They turn out to be in-line with the values found in the literature for similar obstacle shapes and flow regimes but referred to a much higher aspect ratio (Djebedjian, 2002; Okajima, 1982; Okamoto et al., 1977; Norberg, 1993, 2003). As commented in Armellini et al. (2009), the stabilizing effect of the very low aspect ratio, observed also by Law and Ko (2001) for a circular cylinder with AR = 1 and Re ¼ 102  103 , could be counterbalanced in the present cases by the high levels of core flow turbulence.

0.08 0.06 0.04 0.02 0 0

0.25

0.5

0.75

1

1.25

1.5

1.75

0.08 0.06 0.04 0.02 0

2

0

0.25

0.5

0.75

f [Hz]

0.1

1.25

1.5

1.75

2

1.25

1.5

1.75

2

0.1

Amplitude [m/s]

Amplitude [m/s]

1

f [Hz]

0.08 0.06 0.04 0.02 0 0

0.25

0.5

0.75

1

f [Hz]

1.25

1.5

1.75

2

0.08 0.06 0.04 0.02 0 0

0.25

0.5

0.75

1

f [Hz]

Fig. 16. Amplitude spectra of r.m.s. velocity fluctuation v0 at x = Lf, y = z = 0.

700

A. Armellini et al. / International Journal of Heat and Fluid Flow 31 (2010) 689–701

Table 3 Strouhal numbers (St ¼ f d=U  ) evaluated from the spectra of velocity fluctuation v0 at point x = Lf, y = z = 0. Values in brackets refer to scarcely recognizable dominant frequencies. Obstacle shape

Re = 800, Re* = 1112

Re = 1800, Re* = 2322

Re = 2800, Re* = 3472

Circular Square Rhomboidal Triangular

(0.223) (0.136) (0.175) (0.209)

0.211 (0.123) 0.179 0.202

0.209 (0.129) 0.180 0.215

Additional measurements have been performed in the vicinity of the lateral surface of the square obstacle in order to clarify the particular behavior of this geometry. Fig. 17 shows two examples of instantaneous flow fields in plane 1xy at Re = 800 and 2800, respectively. In both examples the flow separates abruptly at the sharp frontal edge without reattaching on the lateral side of the obstacle, and strong secondary vortices are observed to grow significantly in the shear layer. Differently from the other pins, the square shape forces the initial portions of the two opposite shear layers to develop uncoupled for a whole diameter, which allows the secondary vortices to coalesce into particularly large structures. On the other hand, the primary vortices in the near wake of the square obstacle are weakened by the strong up-wash flows observed at all the Reynolds numbers. The interaction between large secondary vortices and weak primary structures produces a strong inhibition of the regular shedding at all the flow regimes investigated. 4. Conclusions A detailed and accurate experimental investigation of the flow structures around single heat transfer promoters of different shapes has been performed by using a 2-D PIV technique. The peculiar geometrical and flow conditions, such as low aspect ratio, low Reynolds number, high core flow turbulence and undeveloped boundary layers on the channel walls, resemble the real working conditions of practical liquid cooling devices. These conditions have been shown to give rise to flow structures that are hardly predictable on the basis of the present literature. Both size and strength of such flow structures turned out to be very sensitive to the obstacle shape and Reynolds number. The characteristics of the perturbed inlet flow have been observed to influence significantly the dynamics of the horseshoe vortex system that forms in front of the pin at the wall/obstacle junction. In particular, the vorticity bursts from the incoming boundary layers are responsible for aperiodical oscillations of the horseshoe vortices at Re = 800 and for a stronger instability at Re = 1800 and 2800, where break-away of primary vortices, core fluid inrush and secondary vorticity eruptions are observed. These latter phenomena usually occur at higher Reynolds numbers and

they are reported in the literature to be effective mechanisms of wall heat transfer enhancement. The separation structures in front of the obstacle become progressively larger and stronger as the blockage effect due to the pin shape increases, i.e., passing from triangular to rhomboidal, circular and square pins. Downstream of the obstacles spanwise velocity components directed from the wall regions to the channel mid-plane (up-wash flows) are observed to affect the near wake to various extent, depending on the obstacle shape and Reynolds number. It is argued that the up-wash flows originate from streamwise oriented vortical structures formed at the wall/obstacle junctions (base vortices). A careful analysis of both time-averaged and instantaneous flow fields behind the obstacles allowed the following conclusions to be drawn:  the obstacles provided with a sharp edge on the frontal surface (rhomboidal and triangular pins) give rise to smaller junction flow structures, and hence weaker up-wash flows, than those produced by the square and circular shapes;  the effect of an increase in the Reynolds number is to reduce the size of the junction flow structures, which are thus confined closer to the walls;  the up-wash flows interfere with the formation of well organized primary vortices in the near wake, whereas the high core flow turbulence enhance the growth of secondary vortices in the shear layers;  the interaction between weak primary structures and large outof-phase secondary vortices may lead to the inhibition of the alternate vortex shedding and the onset of an irregular shedding mode characterized by the decoupling of the shear layers and a scarcely organized wake flow. From these points a coherent interpretation of the wake phenomenology results. At Re = 800 up-wash flows extending over the whole channel height give rise to a strongly three-dimensional wake and a prevailing irregular vortex shedding behind all the obstacles. Consequently, the wakes turn out to be very long, weakly turbulent and practically independent of the pin shape. As the Reynolds number is increased the alternate shedding soon prevails over the irregular mode in the cases of rhomboidal and triangular pins, so producing a quick shortening of the near wakes (a favorable condition for high wall heat transfer). On the contrary, in the case of the square pin, and to a lesser extent of the circular pin, the irregular shedding mode dominates all the flow regimes due to the persistently large junction flow structures behind these obstacles. For the square pin an additional contribution to the wake instabilization is provided by the particularly large secondary vortices formed in the shear layer portions that are forced to develop uncoupled at the obstacle sides. As a consequence, at increasing Reynolds number the wake characteristic lengths reduce moderately in the case of circular obstacle, whereas they remain almost constant for the square pin. The results of the present work, when coupled with an appropriate thermal analysis of the configurations investigated, will provide a solid basis for interpreting the heat transfer mechanisms that determine the performance of practical cooling devices, which will be useful to define more rational design criteria. Finally, the present measurements represent a wide and accurate data-base for the validation of numerical codes under challenging flow conditions. In particular, the Reynolds numbers considered here are low enough to allow LES or DNS applications. Acknowledgment

Fig. 17. Instantaneous flow fields in plane 1xy on the lateral side of the square pin at Re = 800 (A) and 2800 (B).

The present work has been supported by the Italian Ministry of University and Research (MiUR).

A. Armellini et al. / International Journal of Heat and Fluid Flow 31 (2010) 689–701

References Agui, J.H., Andreopoulos, J., 1992. Experimental investigation of a three-dimensional boundary layer flow in the vicinity of an upright wall-mounted cylinder. J. Fluid Eng. 114, 566–576. Akilli, H., Rockwell, D., 2002. Vortex formation from a cylinder in shallow water. Phys. Fluids 14 (9), 2957–2967. Armellini, A., Casarsa, L., Giannattasio, P., 2009. Separated flow structures around a cylindrical obstacle in a narrow channel. Exp. Therm. Fluid Sci. 33, 604–619. Baker, C.J., 1979. The laminar horseshoe vortex. J. Fluid Mech. 95 (2), 347–367. Bearman, P.W., Morel, T., 1983. Effect of free stream turbulence on the flow around bluff bodies. Prog. Aerospace Sci. 20, 97–123. Casarsa, L., Giannattasio, P., 2008. Three-dimensional features of the turbulent flow through a planar sudden expansion. Phys. Fluids 20 (1), 015103-1–015103-15. Djebedjian, B., 2002. Numerical investigation on vortex shedding flow behind a wedge. In: Proc. ASME FEDSM’02, Montreal, Quebec, Canada, July 14–18. Gerrard, J.H., 1965. A disturbance-sensitive Reynolds number range of the flow past a circular cylinder. J. Fluid Mech. 22, 187–196. Griffin, O.M., Ramberg, S.E., 1974. The vortex street wakes of vibrating cylinders. J. Fluid Mech. 66, 553–576. Iwamoto, K., Suzuki, Y., Kasagi, N., 2002. Reynolds number effect on wall turbulence: toward effective feedback control. Int. J. Heat Fluid Flow 23 (5), 678–689. Khan, M.J., Ahmed, A., 2005. Topological model of flow regimes in the plane of symmetry of a surface-mounted obstacle. Phys. Fluids 17 (4), 045101-1– 045101-8. Law, C.W., Ko, N.W.M., 2001. Bistable flow in lower transition regime of circular cylinder. Fluid Dyn. Res. 29, 313–344. Lin, C., Chiu, P.H., Shieh, S.J., 2002. Characteristics of horseshoe vortex system near a vertical plate-base plate juncture. Exp. Therm. Fluid Sci. 27, 25–46. Lin, C., Lai, W.J., Chang, K.A., 2003. Simultaneous Particle Image Velocimetry and Laser Doppler Velocimetry measurements of periodical oscillatory horseshoe vortex system near square cylinder-base plate juncture. J. Eng. Mech. 129 (10), 1173–1188. Montelpare, S., Ricci, R., 2004. An experimental method for evaluating the heat transfer coefficient of liquid-cooled short pin fins using infrared thermography. Exp. Therm. Fluid Sci. 28 (8), 815–824. Norberg, C., 1986. Interaction between freestream turbulence and vortex shedding for a single tube in cross-flow. J. Wind Eng. Ind. Aerod. 23, 501–514. Norberg, C., 1993. Flow around rectangular cylinders: pressure forces and wake frequencies. J. Wind Eng. Ind. Aerod. 49, 187–196. Norberg, C., 1994. An experimental investigation of the flow around a circular cylinder: influence of aspect ratio. J. Fluid Mech. 258, 287–316.

701

Norberg, C., 1998. LDV-measurements in the near wake of a circular cylinder. In: Proc. Advances in Understanding of Bluff Body Wakes and Vortex-induced Vibration, Washington DC (June). Norberg, C., 2003. Fluctuating lift on a circular cylinder: review and new measurements. J. Fluids Struct. 17, 57–96. Okajima, A., 1982. Strouhal numbers of rectangular cylinders. J. Fluid Mech. 123, 379–398. Okamoto, T., Yagita, M., Ohtsuka, K., 1977. Experimental investigation of the wake of a wedge. Bull. JSME 20 (141), 323–328. Praisner, T.J., Smith, C.R., 2006. The dynamics of the horseshoe vortex and associated endwall heat transfer-Part I: temporal behaviour. J. Turbomach. 128, 747–754. Ricci, R., Montelpare, S., 2006. An experimental infrared thermographic method for the evaluation of the heat transfer coefficient of liquid-cooled short pin fins arranged in line. Exp. Therm. Fluid Sci. 30 (4), 381–391. Sakamoto, H., Arie, M., 1983. Vortex shedding from a rectangular prism and a circular cylinder placed vertically in a turbulent boundary layer. J. Fluid Mech. 126, 147–165. Sau, A., Hwang, R.R., Sheu, T.W.H., Yang, W.C., 2003. Interaction of trailing vortices in the wake of a wall-mounted rectangular cylinder. Phys. Rev. E 68, 056303-1– 056303-15. Scarano, F., Poelma, C., 2009. Three-dimensional vorticity patterns of cylinder wakes. Exp. Fluids 47, 69–83. Seal, C.V., Smith, C.R., Akin, O., Rockwell, D., 1995. Quantitative characteristics of a laminar, unsteady necklace vortex system at a rectangular block-flat plate juncture. J. Fluid Mech. 286, 117–135. Simpson, R.L., 2001. Junction flows. Annu. Rev. Fluid Mech. 33, 415–443. Sumner, D., Heseltine, J.L., Dansereau, O.J.P., 2004. Wake structure of a finite circular cylinder of small aspect ratio. Exp. Fluids 37, 720–730. Thomas, A.S.W., 1987. The unsteady characteristics of laminar juncture flow. Phys. Fluids 30 (1), 283–285. Tsukahara, T., Seki, Y., Kawamura, H., Tochio, D., 2005. DNS of turbulent channel flow at very low Reynolds numbers. In: Proc. Forth International Symposium on Turbulence and Shear Flow Phenomena, Williamsburg, USA, pp. 935–940. Wang, H.F., Zhou, Y., Chan, C.K., Lam, K.S., 2006. Effect of initial conditions on interaction between a boundary layer and wall-mounted finite-length-cylinder wake. Phys. Fluids 18, 065106-1–065106-12. Williamson, C.H.K., 1996. Vortex dynamics in the cylinder wake. Annu. Rev. Fluid Mech. 28, 477–539. Zdravkovich, M.M., 1997. Transition-in-shear-layers state. In: Flow around Circular Cylinders. Fundamentals, vol. 1. Oxford University Press Inc., New York, pp. 94– 162.