# Visualization of Turbulent Flow Fields Around a Circular Cylinder at Reynolds Number 1.4×10^{5} Using PIV

## Article information

## Abstract

This study investigates the experimental parameters of particle image velocimetry (PIV) to enhance the measurement technique for turbulent flow fields around a circular cylinder at a Reynolds number (Re) of 1.4×10^{5}. At the Korea Research Institute of Ships & Ocean Engineering (KRISO), we utilized the cavitation tunnel and PIV system to capture the instantaneous flow fields and statistically obtained the mean flow fields. An aspect ratio and blockage ratio of 16.7% and 6.0%, respectively, were considered to minimize the tunnel wall effect on the cylinder wakes. The optimal values of the pulse time and the number of flow fields were determined by comparing the contours of mean streamlines, velocities, Reynolds shear stresses, and turbulent kinetic energy under their different values to ensure accurate and converged results. Based on the findings, we recommend a pulse time of 45 μs corresponding to a particle moving time of 3–4 pixels, and at least 3,000 instantaneous flow fields to accurately obtain the mean flow fields. The results of the present study agree well with those of previous studies that examined the end of the subcritical flow regime.

**Keywords:**Circular cylinder; Turbulent flow fields; PIV (Particle image velocimetry); High Reynolds number; Cavitation tunnel

## 1. Introduction

Circular cylinders, one of the shapes that are commonly used to represent bluff bodies, are targets that provide the most fundamental physical insight to improve the hydrodynamic performance’ of engineering systems. Since the 1960s, many studies have been conducted to understand the load and flow characteristics of cylinders (Roshko, 1961; James et al., 1980; Schewe, 1983; Williamson, 1996; Zdravkovich, 1997; Chen, 2022).

Although the study of flow characteristics around a cylinder is a traditional problem, research on this subject has been conducted until recently because in spite of the simple geometry, the flow characteristics are extremely complex and highly dependent on the Reynolds number (*Re*). These characteristics are very important for evaluating the fluid performance of marine structures or risers that have basic cylinder geometry because they are the direct cause of the scale effect that may occur between a model and a full-scale ship.

Most previous studies have considered the subcritical flow regime, where the wakes are turbulent while the boundary layers are laminar on the object surface, in the range 10^{3} ≤ *Re* ≤ 10^{4}.

In recent years, several studies have focused on flow with *Re* ≥ 10^{5} as well as in the critical and supercritical regimes (van Hinsberg, 2015; van Hinsberg et al., 2018). The highest Reynolds number in the sub-critical regime, i.e., 10^{5}, has engineering significance and can be actually observed when a riser or marine structure column support is considered with its characteristic length.

The Strouhal number is maintained at 0.2 in the sub-critical regime (Blevins, 1977) because the vortex shedding period decreases due to rapid turbulent transition in wakes with increase in the velocity. Therefore, the flow characteristics at a relatively higher Reynolds number of 10^{5} can be predicted through existing flow field measurement studies within 10^{3} ≤ *Re* ≤ 10^{4}. However, actual flow field measurements can provide direct clues to understand the flow characteristics in wakes according to the change in position of turbulent transition. This may hold importance as an experimental data base (DB) for validation with recent developments in computational fluid dynamics. Most studies conducted at a Reynolds number of approximately 10^{5} (Schewe, 1983, van Hinsberg, 2015, van Hinsberg et al., 2018) were focused on changes in load characteristics. However, there is insufficient experimental data on flow characteristics around a cylinder, which are the fundamental cause of load change. In this regard, particle image velocimetry (PIV) is a very useful method for measuring the flow field around a cylinder. Due to a lack of related studies at *Re* ≈ 10^{5}, research on PIV measurement techniques is required for the accurate measurement of flow fields in cylinder wakes.

In this study, we focused on the PIV technique and visualization to accurately measure the flow fields in cylinder wakes prior to constructing the flow field DB at a Reynolds number of 10^{5}. The flow field measurement characteristics were evaluated in great detail according to the measurement times of particle images (which were experiment variables) and the number of instantaneous flow fields used to obtain mean flow fields. This helped to investigate the basic characteristics of the PIV technique for precise flow field measurement. The reliability of the PIV technique established in this study was verified through a comparison with previous studies at the same Reynolds number.

## 2. Experimental Setup and Method

Fig. 1 shows the experimental setup of the cavitation tunnel in the Korea Research Institute of Ships & Ocean Engineering (KRISO). The test section of the tunnel had a size of 0.6^{W} m × 0.6^{H} m × 2.6^{L} m. The maximum flow velocity in the section was 12 m/s, and the static pressure in the section was varied from 10.1 kPa to 202 kPa. The uniformity of the free flow introduced into the test section had an error rate less than 1%.

The cylinder diameter (*D*) was 36 mm and the aspect ratio (*L/D*; L is the cylinder span length) was 16.7. The blockage ratio (*D/H)*, which is the ratio of the diameter of the horizontally placed circular cylinder to the height of the tunnel test section (*H*), was 6.0%. First, we identified the pulse time (△*t*) and number of instantaneous flow fields suitable to measure the characteristics of flow fields around the cylinder in order to investigate the basic characteristics of the PIV technique and obtain the mean velocity fields. Table 1 summarizes the experimental conditions to examine the basic characteristics of the PIV technique.

In PIV, the velocity vector is obtained by calculating the pulse time (△*t*) of two particle images and the distance traveled by a scattering particle. The change in △*t* is strongly related to the accuracy of calculation of the particle velocity vector according to the length and time scale of rapidly moving turbulence. In general, a pulse time that corresponds to less than one-tenth of the time required for a scattering particle to pass through the measurement area is adopted. The selection of scattering particles in the measurement area of the cylinder wake (according to the research objective) affects the measurement of flow fields (Park and Kwak, 2004; Paik et al., 2007; Paik et al., 2010). Fig. 2 shows a schematic on the generation of velocity vectors according to the pulse time. In the figure, when a fluid particle is assumed to flow from point 1 to point 4, it is possible to identify its movement path and obtain accurate velocity vectors according to the pulse time. In this study, we selected scattering particles in the wake area, where the velocity was decreased by the generation of Kármán vortex street. The pulse time corresponding to a scattering particle traveling one-tenth (three to four pixels) of the interrogation window was applied, and its value was 45.0 μs. In addition, pulse times that were 0.25 and 4 times of the pulse time of 45.0 μs (11.25 and 180.0 μs) were considered to examine the dependency of flow field measurement on the pulse time at *Re* = 1.4 × 10^{5}.

Fig. 3 shows the PIV system installed to measure the flow in the cylinder wakes. The two-dimensional (2D) PIV system for velocity field measurement consisted of Dantec’s dual-pulsed Nd:Yag laser (200 mJ/pulse), a high-resolution charge-coupled device (CCD) camera with 2048 × 2048 pixels, a camera transport system, an image processing system, and computers for control and computation. Titanium dioxide (TiO_{2}) scattering particles were used. A laser light sheet was irradiated from the bottom of the cavitation tunnel and the camera was placed on the left side of the tunnel to capture particle images in the measurement area of 140 × 140 mm^{2} (Fig. 3); 16,129 velocity vectors were obtained from the velocity fields calculated using a PIV algorithm (adaptive correlation). The size of the interrogation window was 32 × 32 pixels, and the spatial resolution of the velocity fields was increased using the 50% overlapping technique. The effective spatial resolution was 0.907 mm, which represents the distance between velocity vectors. During PIV postprocessing, the error vector was treated using the dynamic mean value operator, a representative algorithm (Lee, 1999). As shown in Fig. 3, a laser light sheet was irradiated from the bottom of the test section. Thus, it was deemed difficult to accurately calculate the velocity vector in a few areas at the top of the cylinder because the light sheet was not formed. Therefore, a flat mirror was installed on the upper plate window of the test section to induce reflection of the laser light sheet and form the light sheet in the upper part of the cylinder. This made it possible to calculate the velocity vector in the upper part. In this study, the Reynolds number was fixed at 1.4 × 10^{5} for comparison with previous studies. To implement the corresponding flow conditions, a flow velocity of 4.5 m/s was considered in the tunnel.

## 3. Experimental Results

To examine the effects of change in pulse time (△*t*) on the measurement of mean streamlines, streamwise velocity, crosswise velocity, *u*′*v*′ Reynolds shear stress, and the turbulent kinetic energy distribution field, the measurement results according to the pulse time are shown in Fig. 4. The aforementioned physical quantities were obtained using 3,000 instantaneous velocity fields and the Reynolds number was 1.4 × 10^{5}. The observation of the mean streamlines is shown in Fig. 4(a). The recirculation length, *l _{C}*, is approximately 1.3

*D*± 0.05

*D*regardless of the change in pulse time, but the central positions of the upper and lower vortices of the separation bubble differ depending on the pulse time. In particular, the central positions of the upper and lower vortices are asymmetric when △

*t*is 11.25 μs and 180 μs, but the difference decreases and a symmetric tendency is observed at a pulse time of 45.0 μs. As no particular trend is observed according to the increase in pulse time, it is necessary to further examine the relationships among the spatial distribution of the flow velocity in the test section, the formation of the light sheet in the upper part of the cylinder due to the installation of the mirror, and the pulse time in order to analyze the cause of the results. In addition, from Figs. 4(b) and 4(c), it is evident that the pulse time (△

*t*) also affects the mean streamwise velocity and mean crosswise velocity distribution characteristics. Due to the formation of the separation bubble, negative and positive velocity changes are observed in the streamwise direction. For pulse times of 11.25 μs and 45.0 μs, a negative velocity that corresponds to 25% of the free flow velocity is measured inside the separation bubble, which is in agreement with the result of a previous study by Braza et al. (2006). However, at 180 μs, a negative velocity that corresponds to approximately 10% of the free flow velocity is measured. This indicates that the velocity change in the separation bubble as a result of the time average of the Kármán vortex street could not be properly measured at the pulse time of 180 μs. From Fig. 4(c), it is also evident that the rapid crosswise velocity change in the range −0.25 ≤

*v/U*≤ 0.25 could not be correctly measured at a pulse time of 180 μs compared to the results of the other pulse times.

Unlike the streamwise and crosswise velocity distributions for which the time average values are important, the *u*′*v*′ Reynolds shear stress and turbulent kinetic energy depend on the perturbation of the turbulent velocity. As shown in Figs. 4(d) and 4(e), the pulse time affects the mean flow fields to which the velocity perturbation information is reflected. The occurrence of the Kármán vortex street with turbulent characteristics complicates the movement paths of the scattering particles by causing interactions of time-dependent multi-scale vortices. In such instances, an increase in the pulse time leads to an increase in the calculation error of the velocity vector and hence, failure to accurately capture the velocity perturbation change within a short period of time. In particular, the pulse time of 180.0 μs, which is approximately 16 times and 4 times larger than 11.25 μs and 45.0 μs, makes it difficult to accurately measure flow fields in the Kármán vortex street area where anisotropic vortices are generated and strong momentum exchange occurs. This causes positive and negative mean velocities. The turbulent kinetic energy is measured lower than the actual value and the *u*′*v*′ Reynolds shear stress distribution is longer in the downstream direction in the flow field results obtained through the average of 3,000 instantaneous flow fields.

Fig. 5 shows the streamwise and crosswise velocity, Reynolds shear stress, and turbulent kinetic energy distributions in the centerline of the cylinder according to the pulse time for a quantitative comparison. Here, for *x/D*, which corresponds to the boundary of the separation bubble, changes in physical quantities are considered at 1.2 and 1.4 according to *y/D*. Interestingly, from Fig. 5, it is evident that convergence is achieved at 45 μs for all the physical quantities. This indicates that an appropriate pulse time in consideration of the flow characteristics is required in PIV measurement. Fig. 5(a) shows the streamwise velocity distribution. The recirculation length, which is the distance between the center of the cylinder and the position where the velocity changes to zero, is consistent regardless of the pulse time, △*t*, but there is a significant difference in the velocity distribution. In particular, when the pulse time is lower than the time of approximately one-tenth of the interrogation window, the dimensionless negative velocity in the recirculation area increases to 0.25 and rapidly recovers positive velocity at *x* = 1.3*D* or higher, which exceeds the recirculation area. However, at a pulse time of 180 μs, relatively small negative and positive velocity distribution is observed in Fig. 5(a), confirming that the correct velocity distribution could not be measured. For the other physical quantities, the least favorable results are observed for a pulse time of 180 μs. In particular, there are significant differences in the turbulent kinetic energy distribution compared to the results for other pulse times. For a pulse time of 45.0 μs, the movement speed of scattering particles corresponds to one-tenth of the interrogation window (three to four pixels). Consequently, a particle moving distance of three to four pixels, which was proposed in previous studies (Park and Kwak, 2004; Paik et al., 2007; Paik et al., 2010), is adhered to in this study.

After fixing the pulse time at 45.0 μs, the flow field measurement characteristics were compared by additionally considering 500, 1,000, and 2,000 instantaneous velocity field samples for the time average. First, for a qualitative comparison, similar to the comparison of physical quantities in Fig. 4, the mean streamlines, streamwise and crosswise velocity distributions, *u*′*v*′ Reynolds stress distributions, and turbulent kinetic energy were compared according to the number of samples as shown in in Fig. 6. When the number of samples is 100, the spatial distributions of all measured physical quantities are asymmetric and uneven with respect to *y/D* = 0, indicating that more samples are required to accurately estimate the mean flow fields. When the number of samples increases from 500 to 1,000, the spatial distributions improve. In particular, the results of the streamwise and crosswise velocity fields converge more rapidly than those of the Reynolds shear stress and turbulent kinetic energy. When the number of samples is 3,000 or larger, there is no difference in results depending on the number of samples for all physical quantities as shown in Fig. 6. For a quantitative comparison, each physical quantity was compared according to the change in *y/D* at *x* = 1.2*D*. The physical trends observed in Fig. 6 can be clearly confirmed in Fig. 7. In other words, as the number of samples increases, convergence is observed for 3,000 samples. The streamwise and crosswise velocity fields converge when the number of samples is at least 1,000, but the Reynolds stress and turbulent kinetic energy distributions, which are related to turbulent fluctuations, converge for 3,000 samples. Thus, the optimum number of samples to obtain mean flow fields is 3,000, which leads to consistent results.

To verify the experimental technique developed in this study, the results of this study were compared with the results of Braza et al. (2006). The experimental conditions of the two studies are listed in Table 2. The mean flow fields were acquired using approximately 4,600 and 3,000 instantaneous velocity vector fields in Braza et al. (2006) and the present study, respectively.

Fig. 8(a) compares the mean streamline distributions. Based on *y/D* = 0, the upper and lower parts represent the results of Braza et al. (2006) and the present study, respectively. The results of the two studies are generally consistent for the size and geometry of the separation bubble. For a quantitative comparison, the recirculation length (*l _{C}*) is compared, and there is no significant difference (1.28

*D*± 0.03

*D*in Braza et al. (2006) and 1.29

*D*± 0.005

*D*in the present study). Fig. 8(b) and Fig. 8(c) compare the streamwise and crosswise velocity distributions, respectively. When the periodic occurrence of the Kármán vortex street in the sub-critical regime is averaged over time, the commonly observed velocity distributions are identical in the results of the two studies. The negative and positive switching positions of the streamwise velocity caused by the separation bubble and the maximum value position of the vertical velocity (

*x/D*= 1.2) also show good agreement. Fig. 8(d) and Fig. 8(e) show the

*u*′

*v*′ Reynolds shear stress distributions and turbulent kinetic energy. First, a slight difference in the

*y/D*position is observed for the position at which the maximum Reynolds shear stress is caused by the release of the Kármán vortex street (

*x/D*= 1.4 and

*y/D*= ±0.3 in Braza et al. (2006) and

*x/D*= 1.388 and

*y/D*= ±0.367 in the present study). The measurements of the present study differ from those of Braza et al. (2006) by approximately 11%. The turbulent kinetic energy is maximum at

*x/D*= 1.25 in Braza et al. (2006) and at

*x/D*= 1.41 in the present study. The qualitative distributions of both physical quantities are in good agreement in the results of both studies, but there is a slight difference in the quantitative size compared to the mean velocity distribution. This appears to be due to the different turbulence intensities as well as difference in aspect ratio. Regarding previous studies on turbulence intensity, Blackburn and Melbourne (1996) observed the characteristics of the lift force acting on the cross section of a cylinder according to the turbulence intensity in the Reynolds number range of 1×10

^{5}to 5×10

^{5}. They found that the standard deviation of the lift coefficient was dependent on the Reynolds number at the turbulence intensities of 0.6% and 4.2%, and increased as the turbulence intensity decreased. Cheung and Melbourne (1980) examined the characteristics of the drag coefficient when the turbulence intensity varied from 0.4% to 9.1% for Reynolds number between 7×10

^{4}and 6×10

^{5}. The drag coefficient decreased with increase in the turbulence intensity before the Reynolds number reached the critical regime. Regarding the effect of aspect ratio, Achenbach and Heinecke (1981) identified vortex shedding at an aspect ratio of 6.75, but not at 3.38. Blackburn and Melbourne (1996) reported that vortex shedding with a period did not occur when the aspect ratio was 4.5. To summarize, the aspect ratio and turbulence intensity affect the lift and drag coefficients, which are closely related to the characteristics of flow fields. Table 2 shows the experimental values of the blockage ratio and aspect ratio considered by Braza et al. (2006) and in the present study. A relatively low blockage ratio and high aspect ratio are considered in the present study. In addition, although the turbulence intensity considered in the present study is only 0.5% lower than that in Braza et al. (2006), the difference in tunnel environment and geometric conditions leads to a difference in the measurement results between the two studies. The test conditions of the present study are more favorable for observing flow around a cylinder than those of Braza et al. (2006).

## 4. Conclusions

Cylindrical geometry is common in marine structures, and hence, it is important to investigate the flow characteristics of full-scale cylinders. For full scale flow, it is important to utilize accurate flow visualization techniques to identify the flow characteristics up to the critical regime of high Reynolds numbers. Hence, in this study, we identified the basic characteristics of particle image velocimetry (PIV) and compared the results with those of previous studies. The visualization study of the flow past cylinder performed using the cavitation tunnel and PIV system of the Korea Research Institute of Ships & Ocean Engineering (KRISO). Due to the nature of PIV in which velocity vectors are calculated by acquiring particle images, the time interval of two particle images and the number of instantaneous flow fields are important parameters.

First, regarding the effect of the time interval, the pulse time of the laser was adjusted and a particle moving time of three to four pixels in two particle images was adopted because the flow velocity of particles is known to decrease in cylinder wakes. When the pulse time was long, vortices in the wake area could not be properly measured and the velocity vector size was exaggerated in the flow direction.

Next, we evaluated the effect of number of instantaneous flow fields on the measurement of mean velocities. To obtain more accurate results of mean flow fields, at least 1,000 instantaneous flow fields must be used to measure the mean velocities and at least 3,000 instantaneous flow fields are required to measure the Reynolds shear stress and turbulent kinetic energy distributions.

Consequently, it is necessary to select the pulse time of the laser according to the flow characteristics that correspond to experimental conditions, and good results can be achieved by adopting a pulse time that allows particles to have a distance of three to four pixels. It is also observed that turbulence properties have constant values when at least 3,000 instantaneous velocity fields are acquired and averaged.

Hence, based on the established PIV technique, satisfactory results are confirmed through a comparison with previous studies, but there are quantitative differences. This appears to be due to the difference in experimental environment, such as the tunnel shape, blockage ratio, and aspect ratio. Finally, the flow fields around a circular cylinder were analyzed according to the Reynolds number. Further research is required to observe changes in flow in the critical regime more closely.

## Notes

We declare no potential conflict of interests relevant to this article.

This work was supported by the Korea Research Institute of Ships & Ocean Engineering Project (“Development of CFD Technology for Global Performance Analysis of Offshore Structure”) funded by the Ministry of Oceans and Fisheries (PES4780).

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