1 Introduction

Velocity field measurements using particle image velocimetry (PIV) can only be performed from locations where seeding particles are made visible, typically using laser light illumination. However, PIV also has an intrinsic limitation that stems from how the laser light is introduced into the flow test rig. With conventional PIV methods, the laser light sheet is first formed externally. The laser light sheet is then introduced into the flow. If an optically opaque test body is placed in the path of the light sheet, a “shadow” is formed as shown by Fig. 1. The seeding particles that are in the shadow region created by the test body cannot be illuminated, which implies that they are not visible on the PIV recordings. Hence, investigators have been limited to regions of the flow field where there are no shadows to obtain PIV velocity field measurements (Sumner et al. 1999; Xu et al. 2003; Wang and Zhou 2005).

Fig. 1
figure 1

External light sheet with a shadow below the test body (cylinder)

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This paper introduces a new method for the illumination of the seeding particles where the shadow region is eliminated for a particular test setup. Hence, particles that would have previously entered into a shadow are now illuminated and, therefore, recorded. This new configuration generates the thin laser light sheet internally through the transparent walls embedded with the test body in all radial directions into the flow field. This illumination is isotropic planar where the laser light is planar and radiates outwards from inside the test body, creating the so called laser disk of light or laser light disk. Depending on individual configurations, there is a 360° illumination.

Particle image velocimetry (PIV) measurements of the velocity field around five side-by-side circular cylinders immersed in uniform flow have been taken (Fig. 2). While taking the PIV measurements, it was found that the conventional configuration is inadequate. Some regions of the flow field, including the gap region, always has a shadow even if the position of the laser is adjusted in an attempt to eliminate it.

Fig. 2
figure 2

Schematics of the test section with five side-by-side circular cylinders (side view)

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The new method, with 360° illumination around the central cylinder, has allowed the upstream, gap and downstream flow fields to be measured simultaneously. Using this illumination technique, we aim to provide physical insight of (1) the development of the upstream flow ahead of the cylinders into gap flow passing between the cylinders and (2) the interaction of the gap flow with the wake created by the row of cylinders. This configuration has engineering significance that allows for an improved understanding of the flow behavior that affects the performance of certain fluidic devices, including heat exchangers where flow mixing is important.

Ishigai et al. (1975) and Moretti and Cheng (1988) have reported that the gap flow behaves like a two-dimensional jet flow that penetrates into the wake region downstream of the row of cylinders. When the spacing ratio is T/D < 2.0 ~ 2.3, instability of the jet has been observed to alter the wake pattern where T is the center-to-center spacing between cylinders and D is the cylinder diameter. The nature of the jet instability is such that the gap flow or jet is deflected toward or away from a particular cylinder in the row. Depending on the direction of the jet deflection, a narrow or a wide wake is formed behind the cylinder in question.

Sumner et al. (1999) reported on the wake patterns created by three side-by-side circular cylinders (with T/D = 1.5) as summarized in Fig. 3. They measured the non-dimensional shedding frequency (S = fD/U ∞ ) immediately behind the row of cylinders where f is the shedding frequency and U ∞ is the free-stream velocity. They found that the narrow near wake had a higher shedding frequency (S n ~ 0.31–0.33) than the wide near wake (S w ~ 0.05–0.06) that developed behind the central cylinder. The resulting wake pattern is symmetrical about the axis of the central cylinder, and the adjacent gap flows are deflected away from the central cylinder, which is classified as the symmetric-biased flow pattern.

Fig. 3
figure 3

Schematic of symmetric-biased wake pattern behind three side-by-side circular cylinders (Sumner et al. 1999)

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The PIV measurement also conducted by Sumner et al. (1999) showed the wake of the row of three circular cylinders, varied with the spacing between the cylinders. However, the flow in the upstream and gap regions was not linked to the observed downstream wake pattern, which may play an important role in affecting the wake pattern. Such a deficiency is primarily due to the shadow region that is created by the cylinders. The PIV measurement setup used by Sumner et al. (1999) may be classified as an external illumination configuration. Simultaneous measurement of the upstream, gap and wake regions around the row of cylinders may provide further insight into the jet instability that leads to jet deflection.

We compare the velocity fields determined from the conventional external laser light sheet to the new internally generated laser light disk under the same test conditions. In addition, we provide further physical insight into the flow behavior around the row of side-by-side cylinders, specifically linking the upstream and gap flow behavior to the downstream wake pattern.

2 Experimental details

2.1 Test rig and instrumentation

The experiments were conducted in a closed-type wind tunnel with test section dimensions of W × H × L = 0.312 m × 0.32 m × 1.0 m (Fig. 2). The walls of the test section are made from transparent acrylic sheet (Perspex) that is 10.0 mm thick. A glass observation window for the CCD camera was inserted into the side of the test section that was 4.0 mm thick. A single layer of honeycomb is placed ahead of the test section to improve the uniformity of the free-stream flow. The flow velocity in the test section is controlled by a frequency inverter that adjusts the axial fan speed. The flow velocity was set to maintain a subcritical Reynolds number based on the single cylinder diameter of Re D  = 6000. Prior to the actual testing, the free-stream turbulence intensity was measured to be Tu = 1.9 % (Dantec MiniCTA 54T42).

Five side-by-side circular cylinders were mounted in the test section (Fig. 2). Each cylinder was made from transparent acrylic tube with a diameter of 15.0 mm and a span of 0.312 m. However, for the isotropic-planar illumination setup, the central cylinder was made from glass, due to its superior optical properties. The resulting area blockage was 23.5 %. The spacing ratio T/D = 1.7 was selected where T is the transverse center-to-center spacing and D is the cylinder diameter that is 15.0 mm.

To measure the free-stream flow conditions, the velocity profile was traversed at a distance L u = 15.0D upstream of the cylinders (see Fig. 2). The axial velocity was measured using a Pitot probe mounted on a linear traverse system (along the y-axis) that was positioned at the mid-span of the cylinders. The pressure data from the Pitot probe were read by a differential pressure transducer (DSA 3217, Scanivalve Inc).

2.2 External illumination

The conventional externally illuminated PIV setup is shown in Fig. 4. We note from Fig. 4a that the plane of the laser light sheet is parallel to the x–z plane because the base of the laser source is mounted horizontally on a table secured to the floor of the test facility. Consequently, the five side-by-side circular cylinders were mounted so that the cylinder axis is perpendicular to the x–z plane. The optical axis of the CCD camera is also perpendicular to the x–z plane (or parallel to the cylinder axis) for 2D PIV experiments (Fig. 4b).

Fig. 4
figure 4

Experimental setup of the test section for the conventional external illumination; a plan view; b side view

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To create the laser light sheet as shown in Fig. 4a, light sheet optics is connected to the laser source to transform the emitted laser beam into the laser light sheet. The schematic of the typical light sheet optics shown in Fig. 5 illustrates the arrangement of multiple lens necessary to form a thin laser light sheet. The light sheet thickness (Δy) is manually adjusted (i.e., Δy ~ 1.0 mm), and the laser source energy was approximately (30 mJ/pulse).

Fig. 5
figure 5

Light sheet optics, detailing the arrangement of the optical lens required to transform the laser beam into a light sheet (Dantec Dynamics 2002)

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The objective of the present case study was to quantify the velocity field of the upstream, gap and downstream regions of the cylinders simultaneously. However, it is not achievable using an external light sheet due to the large shadow regions that form (see Fig. 4a). The upstream region was, therefore, illuminated to observe how the upstream flow field behaves as it approaches the cylinders. The laser is offset by, e.g., 37°, which is measured from the transverse z-axis of the five side-by-side cylinder (Fig. 4a). This is the maximum angle that could be obtained within the confines of the test facility. Naturally, the angular offset of the laser means that the majority of the gap region and the downstream regions were obstructed by the shadows created by the cylinders as illustrated in Fig. 4a.

To circumvent the lack of illumination in these regions, transparent cylinders were also tested to allow the laser light to be transmitted into the shadow regions. However, a significant proportion of the light sheet intensity was attenuated while passing through the transparent cylinders, due to refraction and reflection. Consequently, insufficient intensity remained within the light sheet to illuminate the downstream seeding particles.

There are alternative methods that can be used to eliminate the shadow region such as laser beam splitting. With laser beam splitting, the laser beam is split using an optical element and illuminates the row of cylinders from opposite sides. The two separate beams would be directed using planar turning mirrors, and light sheet optics placed in the optical path of the beams would transform the laser beam into two opposing light sheets and hence eliminate the shadow region. The expected limitations of this configuration were primarily due to the complexity of setting up the optical arrangement. A large number of optical elements would be necessary to create the illumination. With an increased number of optical elements, the task of aligning the laser beams and overlapping the opposing light sheets becomes quite difficult and time-consuming. There may also be a limit on the available laser source energy as a given amount of laser energy would now need to be distributed over a wider area. Hence, the overall scattered light intensity would be reduced. To compensate, higher laser pulse energy would be needed to create the required levels of exposure on the CCD detector and create visible particle images.

In light of these considerations, internal isotropic-planar illumination was deemed to be the most viable option for removing the shadow region in the field of view. In addition, the new method could potentially illuminate the space between multiple rows of staggered cylinders, which would not be possible with any form of external illumination.

2.3 Internal isotropic-planar illumination

Internal isotropic-planar illumination is a new optical configuration that was designed and manufactured in-house. The purpose is to eliminate the shadow so that the upstream, gap and downstream velocity fields of the five side-by-side cylinders can be measured simultaneously using PIV.

The shadow is eliminated by introducing the laser light internally through the middle cylinder and radiating the light outwards through the cylinder. To achieve this, (1) the optical axis of the laser beam must be coincident with the axis of the middle cylinder, (2) there must be laser optics inside the middle cylinder to create the laser light disk, (3) the two beams from the dual-cavity laser must have a circular shape with the same beam diameters and energy, and (4) the middle cylinder needs to be transparent, ideally manufactured from optical glass.

Figure 6 illustrates the experimental setup for the internal isotropic-planar illumination. The optical axis of the laser and the CCD camera is perpendicular to the plane of the laser light disk where the laser light disk is parallel to the x–y plane. The laser source is connected by an “adaptor” to the end of the middle cylinder. As shown in Fig. 6b, the middle cylinder is the illuminated cylinder where the planar laser light disk is created and radiates outwards in all directions, resulting in 360° laser light coverage around the middle cylinder. Therefore, the upstream, gap and downstream flow regions are now illuminated simultaneously.

Fig. 6
figure 6

Experimental setup for the internal isotropic-planar illumination; a plan view; b side view

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A schematic of the laser light disk optics is provided in Fig. 7. A circular, collimated laser beam is emitted from the laser source. This beam is transformed into a laser light disk with a 360° illumination, using a cone mirror with a 90° cone angle.

Fig. 7
figure 7

Laser light disk optics, detailing the arrangement of the adaptor, inner tube, optical shroud, cone mirror and the transparent outer cylinder which are required to transform the laser beam into a light disk

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The fluence of the pulsed laser and the beam profile were characterized and controlled to ensure that the energy density limit or damage threshold of the cone mirror (0.2 J/cm2) was not exceeded. Applying excessive laser energy to increase the illumination of the seeding particles would result in permanent damage to the cone mirror reflective surface. The diameter of the collimated laser beam was approximately 5.5 mm, based on the criteria that the beam diameter is located at the e −2 value of the peak intensity. Therefore, the laser source energy was limited to 20 mJ/pulse.

The cone mirror is placed inside an optical shroud. The assembly of the cone mirror and the shroud are then placed inside the outer clear glass circular cylinder that has a 12.5 mm internal diameter. The optical shroud functions to house the cone mirror and to control the light disk thickness and brightness. The light disk thickness (Δz) is controlled by varying the aperture size.

The brightness is varied by changing the depth that the cone mirror rests inside the shroud. For a given laser beam diameter and energy level, adjusting the depth of the cone mirror inside the shroud varies the energy intensity of the laser light that is reflected from the cone mirror. If it is assumed that the energy intensity distribution of the laser beam has a Gaussian profile (Raffel et al. 1998; Westerweel 2000), the maximum energy intensity is located at the center of the beam, which then decays exponentially with increasing distance away from the beam center. The brightness of the light disk can be increased if the light that passes through the aperture is reflected from a section of the incident beam that has the highest energy intensity (i.e., the beam center). Consequently, the reflected light intensity profile across the light disk is not symmetrical. As shown in Fig. 8, the internal isotropic-planar illumination has a normalized intensity profile that is biased toward the side of the laser source. In contrast, the external illumination configuration has a typically symmetrical light intensity profile. However, the biased intensity profile does not appear to affect the recording of the particle images, as high image contrast (i.e., visible particle images) is still obtainable.

Fig. 8
figure 8

Normalized laser light intensity profile relating to the external illumination configuration (square box) and internal isotropic-planar illumination (x). The intensity (pixel gray value) is normalized by the peak gray value

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The aperture size is defined by the gap between the sharp edges of the optical shrouds. The sharp edges have a 30° wedge angle (Fig. 7). The wedge angle minimized diffraction of the light disk. A high degree of diffraction is associated with the spreading of the light disk where the thickness increases rapidly as the distance from the central light source increases. The boundaries of the light disk are also blurred, which is undesirable for PIV measurements. The addition of the optical shroud with sharp edges created a desirable light disk for PIV measurements where the boundaries of light disk are more sharply defined. This can be confirmed from the steep increase in light intensity (normalized gray value), particularly on the laser source side shown in Fig. 8. The aperture size should be less than half the incident beam diameter if the masking caused by the sharp edges is to be effective. In addition, the sharp edges should be positioned so that they “cut” the laser light reflected from the cone mirror. The laser light disk thickness was adjusted so that Δz ~ 1.0 mm.

The laser beam was concealed by an opaque inner tube. The inner tube was necessary to prevent the laser light reflecting from the walls of the outer glass cylinder as the light was transmitted along the cylinder axis. When the inner tube was absent, laser light was reflected and refracted from the transparent walls of the outer tube. The laser effectively illuminated the entire length of the central cylinder, which then caused severe blooming of the CCD camera. Blooming rendered some regions of the PIV recordings unsuitable for interrogation. The end of the inner tube near to the mirror–shroud assembly is supported by a hollow optical shroud with the same internal diameter and wedge angle as the optical shroud that houses the cone mirror. The concealed laser beam also has laser safety benefits, as the laser light is introduced directly into the test section. In contrast, there are significant health and safety risks to the PIV/laser operator that are associated with the external laser light sheet reflecting from the walls of the test rig.

The optical shroud that supports the end of the inner tube also provides a way of supporting additional optical elements, such as beam reducer or expander lens. Alternatively, an arrangement of cylindrical lens may be added to further condition the laser beam before the cone mirror (i.e., create a uniform, circular profile).

The experimental configuration (Fig. 7) opted not to use additional optical elements (although they have been tested) for the following reasons: (1) the profile of the pulsed laser beams was largely symmetrical (i.e., circular) and (2) the beam divergence angle was small enough to assume that the beam is collimated over the distance that the beam travels to meet the cone mirror.

2.4 Velocity field measurement using particle image velocimetry (PIV)

In both the external and internal illumination configurations, the flow field was seeded with an atomized mineral oil with a mean particle diameter of 1 μm. The particles carried by the flow are then illuminated by a frequency-doubled, dual-cavity Nd:YAG laser (New Wave Research™), with a light wavelength of 532 nm (i.e., green light). It is assumed that the measured flow field is predominately two dimensional so that the majority of particles entering into the thin light sheet remain within the light sheet during the measurement period. The measurement period is defined by two sequential pulses of the laser light sheet that are separated by a finite time interval (33 μs).

The recorded flow field is represented by the random pattern of particle images that are mapped onto the image plane of the CCD sensor. The images are recorded on the sensor frame that has a 2048 × 2048 pixel resolution and a pixel pitch of 7.4 μm. The field of view that is set up within the light sheet is shown in Fig. 2 where the PIV measurement area is 100 mm × 100 mm. The magnification factor is M 0 = 0.15, and the CCD camera lens (60 mm focal length) f-number is set as f # = 2.8. The maximum aperture size of the camera lens was used to create the highest pixel exposure and keep the laser pulse energy as low as possible. Due to the damage threshold constraint of the cone mirror, increasing the camera aperture size increases the pixel exposure without risking damage to the mirror. However, a trade-off exists where the depth of field is reduced. To compensate, a sharply defined thin light sheet is needed so the particle images are well focused and visible on the PIV images.

Image masking was also implemented prior to the velocity field calculations where regions of the flow field that were not suitable for interrogation were excluded from the analysis. These regions are (1) regions in the field of view that were obstructed by the cylinders and (2) areas of the flow field that were poorly illuminated or cast into shadow.

Acquisition of the velocity field depends on first estimating the displacement field. This is achieved when the PIV images are interrogated using an imaging software (Dantec DynamicStudio version 1.45). The PIV images are divided into subregions referred to as interrogation windows that are 32 × 32 pixels in size and overlapped by 50 %. The spatial resolution is 1.6 mm or 0.107D, and the velocity map contains 127 × 127 vectors. The interrogation window offset technique was employed. This used the results from prior interrogation and validation runs to determine the offset amount of each interrogation window. Each window was offset by the discrete mean particle displacement (units: pixel) measured in a specific interrogation window. Window offsetting improves the strength of the displacement correlation peak relative to the random correlation peaks, which improved the reliability of the velocity field estimate. This process was repeated until the estimated velocity field was converged.

A number of validation procedures were implemented on the raw velocity vector maps to remove outliers. (1) Peak detection validation removes invalid velocity vector estimates. Vectors are rejected when the ratio of the amplitude of the displacement correlation peak (signal) is <1.2 times the amplitude of the noise correlation peak. In addition, the correlation peak width must be within the range of 2–7 pixel units. (2) Range validation was then implemented to remove velocity vectors with a magnitude that was greater than a predetermined maximum value (i.e., 12.0 m/s1). (3) Moving average validation then followed where the averaging area consisted of 3 × 3 interrogation windows, and the acceptance factor was 0.1 carried out over three iterations. Less than 1 % of the vectors were rejected after image masking eliminated regions that were not suitable for interrogation due to poor illumination, shadows and obstructions in the field of view.

The evaluation of the vector field between two successive frames yields an instantaneous vector map. The time-averaged velocity field for a specific location in the flow field is then evaluated over an ensemble of eighty instantaneous vector maps sampled at a frequency of 5 Hz.

2.5 Data reduction parameters and measurement uncertainties

The Reynolds number based on the single cylinder diameter D and the upstream mean flow velocity U ∞ is defined as:

$$Re_{D} = \frac{{\rho_{\infty } U_{\infty } D}}{{\mu_{\infty } }}$$
(1)

where ρ ∞ and μ ∞ are the density and dynamic viscosity of air, respectively. The Reynolds number was fixed at 6000 (subcritical flow regime).

The experimental uncertainty of the Reynolds number and axial flow velocity were estimated using a method reported by Holman and Gajda (1978) based on 20:1 odds and were within 1.1 %. Uncertainty of the cylinder dimensions and the transverse center-to-center cylinder spacing are within ±0.015 mm. Pitot probe traverse positions along the y-axis are measured using a digital caliper with a resolution of 0.01 mm.

The uncertainty of the instantaneous PIV velocity measurements is primarily related to the estimation of the average particle displacement within an interrogation area. The uncertainty regarding the timing of the light sheet pulses, camera synchronization and particle lag is not considered as significant sources of error. The determination of measurement uncertainty relating to particle displacement has been quantified analytically and by the generation of synthetic images with known parameter values (Westerweel 1997, 2000, 2008). In order to provide a reasonable estimate of measurement error, the results given in Westerweel (2000) are considered to be applicable to the PIV algorithm used in this investigation. The displacement measurement error based on the mean particle image diameter of 2–3 pixels is 0.05 pixels. Therefore, the full scale relative measurement error is 0.6 %.

3 Discussion of results

A comparison of the raw PIV images using the external and the internal isotropic-planar illumination configurations is shown in Fig. 9. For both cases, the CCD camera is focused at the gap region between the third (central) cylinder and the fourth (lower) cylinder. The camera’s object plane that is coincident with the laser light sheet is at the mid-span of the cylinders. The camera lens is a conventional, non-telecentric type. Consequently, due to perspective (parallax) effects, the ends of the cylinders that are closest to the camera will obstruct the field of view. The cylinders will also appear to converge to single point in the background of the image. The obstruction prevents seeding particles from being captured in the PIV images close to the cylinder walls. Unfortunately, this problem is unavoidable, with conventional (non-telecentric) lens, but efforts were made to minimize the parallax effect. The CCD camera was positioned as far from the object plane as possible without deteriorating the focus of the particle images in the object plane/light sheet. However, a level of compromise was necessary, and the obstructed regions were masked before interrogation. Therefore, no velocity field information could be obtained from these regions.

Fig. 9
figure 9

Raw PIV images of the flow around five side-by-side circular cylinders where all the cylinders are transparent. a External illumination and b internal isotropic illumination where the central cylinder houses the laser optics and radiates laser illumination outwards from the cylinder center

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Figure 9a shows a raw PIV image from the external illumination configuration. Multiple shadow regions are created by the cylinders, despite the cylinders being made from transparent acrylic tube. The illumination transmitted through cylinders created caustic patterns in the shadow that appear as “streak” lines.

Isotropic-planar illumination is shown in Fig. 9b where the laser light radiates outwards from the central cylinder with 360° coverage. The thickness of the light disk does not change significantly throughout the field of view. Therefore, the variation in the light intensity in the radial direction is roughly inversely proportional to the distance away from the center of the cylinder. The seeding particles in the flow also attenuate the transmission of the light due to scattering.

To illuminate the outer regions of the field of view, a relatively high light intensity is necessary. Consequently, regions close to the cylinder surface would have high levels of exposure that may cause localized blooming on the PIV image as shown in Fig. 9b. At a certain distance from the central cylinder, the light intensity will become too low to adequately illuminate the seeding particles. With insufficient illumination, the reliability of the velocity estimates will deteriorate as the signal-to-noise ratio will reduce.

Surface flaring and streaks in the light disk were also caused when seeding material accumulated on the cylinder surface. Occasionally, the deposited material increased light scattering which saturated the CCD detector (blooming). The rate of material accumulation was dependent on the experimental conditions and seeding concentration. This limited the total time of the measurement run, and the cylinder had to be wiped clean when the buildup became too severe. Measurement runs ranged between 16 and 30 s.

Implementing internal isotropic-planar illumination requires a balance between a large field of view and blooming or pixel saturation around the illuminating cylinder. With the current experimental setup, it was possible to obtain full illumination of the field of view, with limited blooming near the central cylinder.

Figure 10a shows the velocity field measured using the external illumination. The gap and downstream regions provide no velocity field information, which is a direct consequence of having these regions cast in a shadow. Because the laser was offset by 37° with respect to the transverse plane of the cylinders and the spacing ratio between the cylinders is relatively large (e.g., T/D = 1.7), partial illumination of the downstream region occurs where “strips” of laser light appear. Incomplete illumination of the downstream region creates spurious vectors or outliers due to the inadequate number of seeding particle pairs appearing within the interrogation areas during the PIV interrogation process. However, due to the angular offset, the upstream velocity field ahead of the cylinders has been well resolved.

Fig. 10
figure 10

Time-averaged velocity vector field of the flow around five side-by-side circular cylinder at Re D  = 6000 where T/D = 1.7; a external illumination configuration; b internal isotropic-planar illumination and the filled cylinder is the middle, illuminated cylinder

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In contrast, Fig. 10b shows the velocity field measured using the internal isotropic-planar illumination where the entire flow field around the illuminated (middle) cylinder is revealed. The gap flow, the flow passing between the cylinders, above and below the middle cylinder is deflected toward the adjacent cylinders. Consequently, the near wake structure behind the middle cylinder is wide, whereas the near wake behind the adjacent cylinders is narrow.

The calculation of derived quantities based on the velocity vector field such as streamlines reveals, with a greater degree of clarity, how the entire flow field around the cylinders develops. As shown in Fig. 11a (external illumination), only the upstream streamlines can be calculated due to the upstream flow region being illuminated. No physical insight of the flow behavior in front of the cylinders can be linked to the gap and downstream wake behaviors.

Fig. 11
figure 11

Time-averaged streamlines of the flow around five side-by-side circular cylinder at Re D  = 6000 where T/D = 1.7 and St denotes the stagnation point on the cylinder surface; a external illumination configuration and b internal isotropic-planar illumination

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In contrast, streamlines measured using the internal isotropic-planar illumination in Fig. 11b demonstrate that the upstream streamlines disperse ahead of the cylinders. The dispersion indicates that the flow velocity ahead of the cylinder decreases relative to the free stream. From the flow images, it is also possible to determine the approximate location of the stagnation points on the cylinder surface. The stagnation point (St) is the point on the cylinder surface where the oncoming flow is divided either side of the cylinders. Hence, as the approaching flow is divided, the streamlines bifurcate ahead of the cylinders. Furthermore, there is a high degree of flow acceleration in the gap region between the cylinders as the streamlines now bunch together when the flow passes between the cylinders.

Figure 12 maps the strength of velocity fluctuations (V rms) in the flow by calculating the RMS of the measured velocity field (Wernet 2000). Hence, it also indicates turbulence intensity levels in the flow field if we assume that random fluctuations in the measurements are small in relation to the turbulence levels. From Fig. 12a, b, it can be seen that the (V rms) values corresponding to the upstream flow region ahead of the cylinders is similar for the external and internal illumination configurations. However, the internal illumination setup (Fig. 12b) also reveals information about the gap flow and the downstream regions simultaneously. Again, no such information can be retrieved with external illumination (Fig. 12a).

Fig. 12
figure 12

RMS map of the velocity field; a external illumination and b internal isotropic-planar illumination

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The overall degree of fluctuation in the upstream and gap regions shown in Fig. 12b is quite low compared to the downstream region due to natural wake shedding behavior. It appears that the wide wake behind the central cylinders has far lower velocity fluctuation (V rms) values compared to the narrower wake emanating from behind the adjacent cylinders. This result may support the hot film measurements of Sumner et al. (1999) who reported that the wider wake has a lower shedding frequency compared to narrow wake.

The overall flow pattern around the row of five side-by-side cylinders is symmetrical about the central cylinder (Fig. 13). The stagnation points on the adjacent cylinders corresponding to the upstream flow are inclined toward the middle cylinder by similar amounts, whereas the stagnation point of the middle cylinder is aligned with the nominal free-stream flow. The gap flows in the wake of the adjacent cylinders are deflected away from the central cylinder, indicating a symmetric-biased flow pattern, similar to the case of three side-by-side circular cylinders reported by Sumner et al. (1999).

Fig. 13
figure 13

Schematic of symmetric-biased wake pattern behind five side-by-side circular cylinders that depicts the stagnation points of the adjacent cylinders inclined toward the central cylinder and the gap flows are biased away from the same cylinder

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4 Conclusions

A new laser illumination configuration “isotropic-planar” illumination has been introduced. This new method illuminates regions of the flow field that were previously cast into shadow by creating a 360° disk of light that is generated from a new optical arrangement, placed inside a transparent test body. The test body is, therefore, utilized as a means of introducing the laser light internally into the test section. This is in contrast to an externally introduced light sheet. A comparison between the conventional external and the internal isotropic-planar illumination configurations has been presented in this paper, using five side-by-side circular cylinders in cross-flow as a test case.

The results indicate that there is an overall symmetrical flow pattern about the central cylinder where the stagnation points of the adjacent cylinders are inclined toward the middle cylinder. The gap flows in the wake are then deflected away from the central cylinder. Such symmetrical flow behavior could indicate that there is a possible link between the upstream flow and the downstream wake where the gap flow has biased behavior.

The new illumination method may also be applied to study the velocity fields of other configurations, such as multi-row tube bundles. Employing external illumination, the region directly between the rows of cylinders typically would have been obstructed by the surrounding cylinders. Internal isotropic-planar illumination offers an alternative method to overcome some of the limitations of the conventional illumination methods.