Influence of Inflow Turbulence on the Flow Characteristics around a Circular Cylinder

Featured Application

The results obtained in this paper such as C_D, C_L and the distribution of the wind pressure can provide the reference for the wind load design of cylindrical structure.

Abstract

To study the influence of turbulence on the wind pressure and aerodynamic behavior of smooth circular cylinders, wind tunnel tests of a circular cylinder based on wind pressure testing were conducted for different wind speeds and turbulent flows. The tests obtained the characteristic parameters of mean wind pressure coefficient distribution, drag coefficient, lift coefficient and correlation of wind pressure for different turbulence intensities and of Reynolds numbers. These results were also compared with those obtained by previous researchers. The results show that the minimum drag coefficient in the turbulent flow is basically constant at approximate 0.4 and is not affected by the turbulence intensity. When the Reynolds number is in the critical regime, the lift coefficient increased sharply to 0.76 in the smooth flow, indicating that flow separation has an asymmetry; however, the asymmetry does not appear in the turbulent flow. Drag coefficient decreases sharply at a lower critical Reynolds number in the turbulent flow than in the smooth flow. In the smooth flow, the separation point is about 80° in the subcritical regime; it suddenly moves backwards in the critical regime and remains almost unchanged at about 140° in the supercritical regime. However, the angular position of the separation point will always be about 140° for turbulent flow for the Reynolds number in these three regimes. Turbulence intensity and Reynolds number have a significant effect on the correlation of wind pressures around the circular cylinder. Turbulence will weaken the positive correlation of the same side and also reduce the negative correlation between the two sides of the circular cylinder.

1. Introduction

The flow characteristics over circular cylindrical structures have always been a classic problem in the field of wind engineering. Tubular steel parts are often used in many structures such as TV and transmission towers, steel poles and bridges. Compared to bluff structures (such as square columns) and streamlined structures (such as aerofoils), circular cylinders are usually defined as semi-pneumatic [1], with their flow characteristics and aerodynamic parameters affected by factors such as Reynolds number, flow turbulence and surface roughness [2,3].

Previous studies have mainly focused on the Reynolds number effect of the drag coefficients of smooth circular cylinders. In the pioneering work of Roshko [4], a Strouhal-Reynolds number relationship for the laminar shedding regime was presented for Reynolds numbers from about 50 to 150. Based on the pressure tests of circular cylinders, Achenbach [5] divided the measured Reynolds number into four regimes: subcritical, critical, supercritical and transcritical. However, not all studies use the same terminology for regimes above the critical [6,7,8,9]. In this study, the terminology for the regimes is as defined by Achenbach [5]. The different phenomena of the different stages of transition from subcritical to transcritical have been clarified in more detail by Schewe [10]. Norberg [11] measured the wind pressure at the mid-span position of the circular cylinder and found that the flow around circular cylinders appears to be a switching between regular and irregular vortex shedding in a critical Reynolds number regime. Grove et al. [12] studied the flow characteristics of circular cylinders in the regime of the transcritical Reynolds number by artificially stabilizing the steady wake, finding that the drag coefficient is about 0.7. Liu et al. [13] studied the drag coefficient and lift coefficient of a circular cylinder whose diameter was 30 cm under different regimes of Reynolds numbers and found that asymmetric wind pressure distribution appears at a certain wind speed at the regime of the critical Reynolds number. With advances in computer technology, in addition to the study of wind tunnel tests, computational fluid dynamics (CFD) has been applied to the study of the problem by some researchers. Franke et al. [14] presented numerical calculations of laminar vortex-shedding flows past circular cylinders and they found that the Strouhal number and the drag coefficient agreed better with experiments and previous numerical results at the lower Reynolds numbers comparing to these at the higher Reynolds numbers. It is blamed on the initial influence of stochastic fluctuations for the difference between the calculations and measurements for higher Reynolds numbers. Anagnostopoulos [15] provided a numerical solution of vortex-excited oscillations of a circular cylinder based on numerical simulation and found that the results of this investigation agreed well with the experimental evidence, except for the reduced velocities in the lock-in region. Michael [16] studied the three-dimensional flow characteristics of a circular cylinder with a Reynolds number of 1.4 × 10⁵ based on large eddy simulation (LES) and found that the importance of the subgrid scale model significantly increased in the case of the high Reynolds number in comparison with a low Reynolds number. Catalano et al. [17] studied the mean pressure distribution by LES for high Reynolds number complex turbulent flows and found that the mean pressure distribution is predicted reasonably well over the Reynolds number regime from 5 × 10⁵ to 1 × l0⁶.

Among factors influencing the flow around the circular cylinder—in addition to the Reynolds number—the turbulence intensity also plays an important role. The effect of freestream turbulence in crossflow around a circular cylinder in delaying the separation and reducing its drag at subcritical Reynolds numbers has long been recognized. This was initially reported by Fage and Warsap [18]. Fage and Falkner [19] used an experimental setup in a wind tunnel and at subcritical Reynolds numbers and found that the drag reduction and a delay in the separation angle were caused by turbulence. Bearman [20] studied the flow around a circular cylinder over a Reynolds number regime from 1 × 10⁵ to 7.5 × 10⁵ and observed narrow-band vortex shedding up to a Reynolds number of 5.5 × 10⁵. Surry [21] experimentally studied the effect of high-intensity, large-scale, free-stream turbulence on the flow past a rigid circular cylinder at subcritical Reynolds numbers, finding that the turbulent intensity of the flow mainly increased vortex frequency in the circular cylinder’s wake but did not weaken the vortex shedding of the wake. Cheung and Melbourne [22] conducted wind tunnel tests of circular cylinders with two different diameters under different turbulence intensities and obtained the variation curve of aerodynamic coefficients with Reynolds numbers under different turbulence intensities. They found that the critical Reynolds number under turbulence appeared earlier than the smooth flow and that the area of the critical Reynolds number in the turbulent flow was also not obvious. So and Savkar [23] studied the steady and unsteady forces induced by a cross flow over a smooth circular cylinder and found that turbulence will cause the critical Reynolds number regime to move to a smaller Reynolds number regime. Sadeh and Saharon [24] conducted a wind tunnel test on a smooth circular cylinder at subcritical Reynolds numbers from 5.2 × 10⁴ to 2.09 × 10⁵; measurements showed that turbulence induces an aft shift in the separation point ranging from 5° to 50° beyond the laminar separation angle of 80°.

Based on the above analysis, the previous research has mainly discussed the variation of the drag coefficient of circular cylinders with the Reynolds number; however, research on the aerodynamic coefficient and the wind pressure distribution of the smooth circular cylinder surface in the turbulent flow is deficient. Except some review articles [25], there have been few recent studies on this problem. In this paper, a smooth flow and three different turbulent flows for different wind speeds were measured for a smooth circular cylinder with a diameter of 0.3 m. The characteristic parameters of the mean wind pressure distribution curves in different turbulent flows were studied. The mean and fluctuating values of the drag coefficient and lift coefficient in different turbulent flows were obtained and then compared with the results obtained by other researchers. Furthermore, the correlation characteristics of the wind pressure coefficients on the circular cylinder surface in different turbulent flows were analyzed. The results in this paper can serve as a reference for related basic research and engineering applications.

2. Setup of the Wind Tunnel Test

To study the effect of turbulence on the surface flow of the circular cylinder, a cylindrical model made of plexiglass was designed with a diameter of 0.3 m and height of 0.5 m. A total of 180 measuring points were arranged in the middle section of the model, with the angle between adjacent measuring points being 2°. The test model in the wind tunnel test is shown in Figure 1. Kubo et al. [26] found that as the size of the end plate increases, the absolute values of the drag coefficient and the leeward pressure coefficient gradually increase and finally tend to a constant value. Meanwhile, they suggested that the diameter of the end plate should be larger than 8.5 times the model depth. Zheng et al. [27] showed that the end effect of the flow field around the model was suppressed when the end plate is four times the diameter of the test model’s diameter. Therefore, in order to suppress the end effect of the flow field of the test model, two square end plates with a side length of 1.5 m were used above and below the model for creating two-dimensional flow conditions between the two end plates. The tests were conducted in the ZJU-1 wind tunnel at Zhejiang University, China. The testing section is 4.0 m wide and 3.0 m high and the testing wind speed regimes range from 0.0 to 50.0 m/s. The maximum blocking ratio of this wind tunnel test is 2.4%.

The reference wind speed in the wind tunnel is measured and monitored using a pitot tube and a micromanometer. The wind pressures of the 180 testing points were measured by Scanivalve electronic pressure scanning valve system DSM3400 with ZOC33 modules. The measuring range of the system is ±2500 Pa, the precision of the system is 0.1% (full-scale) and the highest sampling frequency is 625 Hz. The wind pressures of all the testing points were measured simultaneously and the sampling frequency is 333 Hz.

By adjusting the spires and grids in the wind tunnel, three turbulent flows, which are nominally 4%, 8% and 12%, were generated. The turbulent intensity I_u and average wind speed U of the four flow fields simulated by the wind tunnel are shown in Figure 2, in which H is defined as the vertical height above the wind tunnel ground. It was found that the smooth flow and the three turbulent flow fields are well simulated in the wind tunnel.

The test wind speed of the smooth flow in the wind tunnel is 3–36 m/s and the corresponding Reynolds number is 6.2 × 10⁴–7.5 × 10⁵. Due to the blockage of the spires and grids in the wind tunnel test, the maximum testing speed decreases in high turbulent flow. The working conditions of this test are shown in

Table 1. Test wind speed and Reynolds number in the tests.

Iu	Wind Speed v (m/s)	Reynolds Number	Integral Scale (mm)
0%	3–36	6.21 × 104–7.45 × 105	111
4%	3–29	6.21 × 104–6.00 × 105	214
8%	3–19	6.21 × 104–3.93 × 105	360
12%	3–15	6.21 × 104–3.11 × 105	323

.

3. Characteristic Parameters of Mean Wind Pressure Coefficient Distribution

3.1. In the Smooth Flow

The wind pressure coefficient is given by:

$$C_p=\frac{p\left(\theta \right)-p_{\infty }}{0.5\rho U_{\infty }^2}$$

(1)

where p(θ) is the measured wind pressure at any azimuthal angle θ, p_∞ and U_∞ denote the freestream static pressure and uniform velocity, respectively, and ρ is the density of the air.

Similarly to the previous research, the characteristic parameters of mean wind pressure distribution on the smooth cylindrical surface will be discussed in this paper and are shown in Figure 3. C_pm is the minimum wind pressure coefficient on the surface of circular cylinder and θ_m is the angular position of the minimum wind pressure coefficient. C_pb is the mean wind pressure coefficient within the base region of the circular cylinder and θ_b is the angular position where the base region starts. The wind pressure rise coefficient C_pb − C_pm is defined as the difference between the mean wind pressure coefficient in the base region and the minimum wind pressure coefficient.

Figure 4 shows C_pb at different Reynolds numbers in the smooth flow. When the Reynolds number is in the subcritical regime, C_pb increases slowly with a higher Reynolds number. When the Reynolds number is in the critical regime, C_pb increases rapidly, which indicates that the flow on both sides of the circular cylinder changes from laminar to turbulent separation. When the Reynolds number is in the supercritical regime, C_pb is basically near −0.4 due to the complete turbulent separation on both sides of the circular cylinder, exhibiting a slight decrease. They are consistent with the results of Sadeh and Saharon [24] in the subcritical regime; the varying trend in the measured Reynolds number regime is consistent with Cheung and Melbourne [22].

Figure 5 shows the position of the separation point θ_b at different Reynolds numbers in the smooth flow. When the Reynolds number is in the subcritical regime, θ_b is basically around 80°. When the Reynolds number is in the critical regime, θ_b increases rapidly, indicating that turbulent separation causes the separation point to move backwards, with the angular position close to 160°. When the Reynolds number is in the supercritical regime, θ_b falls back to 142°–144°. The experimental results in this paper are basically consistent with the results of Achenbach [28] and Sadeh and Saharon [24] in the measured Reynolds number regime.

Figure 6 shows the minimum wind pressure coefficient C_pm at different Reynolds numbers in the smooth flow. When the Reynolds number is in the subcritical regime, C_pm increases slowly from less than −1.0 to greater than −1.0 as the Reynolds number increases. When the Reynolds number is in the critical regime, C_pm rapidly decreases to −2.4. When the Reynolds number is in the supercritical regime, C_pm decreases slightly due to the completely turbulent separation on both sides of the circular cylinder. As with C_pb, the results in the subcritical regime are basically consistent with the results of Sadeh and Saharon [24].

Figure 7 is the position of the minimum wind pressure coefficient θ_m at different Reynolds numbers in the smooth flow. When the Reynolds number is in the subcritical regime, θ_m slowly decreases from 70° to about 64° as the Reynolds number increases. When the Reynolds number is in the critical regime, θ_m increases rapidly and the minimum wind pressure coefficient C_pm appears at an approximate angle of 84°. When the Reynolds number is in the supercritical regime, θ_m slowly increases to about 94°. In the subcritical regime, θ_m obtained in this paper is less than that obtained by Sadeh and Saharon [24], indicating that the measured minimum wind pressure coefficient in this paper appears at a more forward angular position of the circular cylinder.

Figure 8 shows the wind pressure rise coefficient C_pb-C_pm at different Reynolds numbers in the smooth flow. When the Reynolds number is in the subcritical regime, C_pb-C_pm is around 0.2, which is basically consistent with the results of Sadeh and Saharon [24]. When the Reynolds number is in the critical regime, the wind pressure coefficient C_pb suddenly increases and the minimum wind pressure coefficient C_pm decreases rapidly, resulting in a sudden increase of C_pb-C_pm. When the Reynolds number is in the supercritical regime, the increasing value of the wind pressure coefficient is basically stable at nearly 2.0.

3.2. In the Turbulent Flow

In order to further analyze the influence of turbulence intensity and the Reynolds number on certain factors, the following are plotted in Figure 9, Figure 10, Figure 11, Figure 12 and Figure 13: the characteristics of wind pressure distribution on the circular cylinder surface, the mean wind pressure coefficient within the base region C_pb, the angular position of where the base region starts θ_b, the minimum wind pressure C_pm, the angular position of minimum wind pressure coefficient θ_m and the wind pressure rise coefficient C_pb-C_pm of different turbulent flows and Reynolds numbers.

Figure 9 shows C_pb of different turbulent flows and Reynolds numbers. In the smooth flow, C_pb increases with the increase in Reynolds number, and C_pb is basically unchanged in the supercritical regime. In the turbulent flow, C_pb increases first and then decreases with the increase in Reynolds number. When the Reynolds number is less than 1 × 10⁵, C_pb increases with the increasing turbulence intensity. There is no significant difference between C_pb in different turbulent flows when the Reynolds number is larger than 2 × 10⁵. When the turbulence intensity is larger than 8%, C_pb in all regimes is basically the same at the same Reynolds number. In the supercritical regime, C_pb in the smooth flow is larger than the C_pb under turbulence.

Figure 10 shows θ_b for different turbulence intensities and Reynolds numbers. In the smooth flow, θ_b is about 80° in the subcritical regime, suddenly moves backwards in the critical regime and it is basically stable at 140° in the supercritical regime. In the turbulent flow, θ_b is about 140° in the measured Reynolds number regime and is independent of the turbulence intensity. When the Reynolds number is in the supercritical regime, θ_b in the smooth flow and the turbulent flows are both approximately 140°—that is, in the supercritical regime. The position of the flow separation point is then basically independent of the flow state.

Figure 11 shows C_pm for different turbulence intensities and Reynolds numbers. In the smooth flow, C_pm is almost unchanged in the subcritical regime and suddenly decreases in the critical regime. However, it changes little in the supercritical regime. In the turbulent flow, when the Reynolds number is less than 2 × 10⁵, C_pm decreases with the increasing Reynolds number and decreases with stronger turbulence intensity at the same Reynolds number. When the Reynolds number is larger than 2 × 10⁵, C_pm has very minor changes. When the Reynolds number is greater than 3.3 × 10⁵, C_pm is basically unchanged and is close to the value in the smooth flow.

Figure 12 is θ_m for different turbulence intensities and Reynolds numbers. In the subcritical regime, turbulence leads to an increase of θ_m. In every turbulent flow in this paper, within the regime of measured Reynolds number, θ_m is basically unchanged when the Reynolds number reaches a certain value—such as 1.9 × 10⁵—in turbulent flows of 8% and 12%. There is a significant difference in θ_m when the Reynolds number is between 1 × 10⁵ and 3 × 10⁵.

Figure 12 shows θ_m for different turbulence intensities and Reynolds numbers. In the subcritical regime, turbulence leads to an increase of θ_m. In every turbulent flow in this paper, within the regime of measured Reynolds number, θ_m is basically unchanged when the Reynolds number reaches a certain value—such as 1.9 × 10⁵—in turbulent flows of 8% and 12%. There is a significant difference in θ_m when the Reynolds number is between 1 × 10⁵ and 3 × 10⁵.

Figure 13 shows the wind pressure rise coefficient C_pb-C_pm for different turbulence intensities. C_pb-C_pm in the subcritical regime is stable at about 0.2 in the smooth flow, but sharply increases in the critical regime. For different turbulent flows, C_pb-C_pm increases with the increasing turbulence intensity at the same Reynolds number. When the Reynolds number is in the critical regime, C_pb-C_pm increases suddenly in the smooth flow, which does not happen in the turbulent flows. There is a significant difference about C_pb-C_pm in smooth and turbulent flows. In the supercritical regime, C_pb-C_pm is basically stable at 2.0 in the smooth flow and 1.75 in the turbulent flow.

Figure 14 shows the wind pressure distribution on the cylindrical surface at typical Reynolds numbers under four different flows. In the uniform flow, as the Reynolds number increases, both θ_b and C_pb increases. Significant differences can be found between the wind pressure coefficient distribution at a lower Reynolds number and that at a higher Reynolds number. When Re = 3.52 × 10⁵, the wind pressure distribution is asymmetrical because one side of the cylinder underwent a turbulent separation while the other side is underwent a laminar separation. The wind pressure distributions under the three turbulent flows are almost the same at higher Reynolds numbers. When the Reynolds number is 1.04 × 10⁵, as the turbulent intensity increases, C_pm gradually decreases and C_pb increases.

4. Drag Coefficient

The drag coefficient C_D of the circular cylinder was estimated based on the measured wind pressure coefficient. The drag coefficient was then computed for both smooth and turbulent incident flows by integrating the measured pressure distribution according to the relationship:

$$C_D=\underset{0}{\overset{2\pi }{{\displaystyle \int }}}{C}_{p}cos\theta d\theta$$

(2)

where C_P is the wind pressure coefficient measured in the wind tunnel test and θ is the angle between the test point and wind direction.

Figure 15 shows the mean drag coefficient C_D of the circular cylinder in the smooth flow as well as the results of previous studies. When the Reynolds number is less than 1.0 × 10⁵, C_D is basically unchanged; C_D then decreases with the increase of the Reynolds number. When the Reynolds number is between 3.0 × 10⁵ and 3.6 × 10⁵, C_D decreases rapidly, then increases gradually when the Reynolds number is between 3.6 × 10⁵ and 4.0 × 10⁵. When the Reynolds number is between 5.0 × 10⁵–8.0 × 10⁵, C_D gradually becomes stable. The test results in this paper are closer to those obtained by Wieselsberger [29], Delany and Sorensen [30] and Sadeh and Saharon [24] when the Reynolds number is less than 2.0 × 10⁵, and smaller than the results obtained by Liu et al. [13]. When the Reynolds number is between 2.0 × 10⁵ and 3.0 × 10⁵, the test results in this paper are smaller than the results obtained by Wieselsberger [29], Güven et al. [31] and Liu et al. [13]. In the region of rapid decline in the drag coefficient, the results are very close to other results. When the Reynolds number is greater than 4.0 × 10⁵, the test results are greater than the results obtained by Wieselsberger [29], Güven et al. [31] and Liu et al. [13]; however, it is closer to the result obtained by Achenbach and Heinecke [32].

The drag coefficients C_D of the smooth circular cylinder with a Reynolds number for different turbulence intensities and Reynolds numbers are shown in Figure 16 and the results were compared with those obtained by Cheung and Melbourne [22]. In the three different turbulent flows, the critical Reynolds number moves to a smaller Reynolds number and the critical regime of the Reynolds number is inconspicuous compared to that number in the smooth flow. This is consistent with the result of Cheung and Melbourne [22]. In the supercritical regime, the influence of turbulence intensity on C_D of the circular cylinder is not obvious and C_D is basically the same in the four different flows, all of which are approximately 0.5. In the smooth flow, the results in this paper are close to those obtained by Cheung and Melbourne [22]. In the subcritical and critical regimes, however, the results in supercritical are larger than those obtained by Cheung and Melbourne [22]. In the case of similar turbulence, the test results in this paper are slightly smaller than those obtained by Cheung and Melbourne [22], but the varying trends with the Reynolds number are consistent.

The standard deviations of the drag coefficient $C_D^{\prime }$ of the smooth circular cylinder for different turbulence intensities and Reynolds numbers are shown in Figure 17. In different turbulent flow, $C_D^{\prime }$ decreases with the increase in Reynolds number, which is consistent with the results obtained by Cheung and Melbourne [22]. In the smooth flow, there is a sudden change in $C_D^{\prime }$ at Re = 3.5 × 10⁵ because there is no simultaneous transition of laminar separation to turbulent separation on both sides of the circular cylinder. When Re = 1 × 10⁵–2.7 × 10⁵, $C_D^{\prime }$ in the smooth flow is generally larger than that in the turbulent flow, consistent with the results of Cheung and Melbourne [22]. In different turbulent flows, $C_D^{\prime }$ is basically unchanged when Re > 4.0 × 10⁵ and the values are close, consistent with the results of Cheung and Melbourne [22].

5. Lift Coefficient

As with the drag coefficient, the lift coefficient C_L was computed for both smooth and turbulent incident flows by integrating the measured pressure distribution according to the relationship:

$$C_L=\underset{0}{\overset{2\pi }{{\displaystyle \int }}}{C}_{p}sin\theta d\theta$$

(3)

Figure 18 shows the mean lift coefficient C_L of the circular cylinder in the smooth flow. It can be seen that, in general, C_L is almost in the vicinity of 0 in the measured Reynolds number regime, which is in accordance with the force characteristics of the circular cylinder. However, when Re = 3.52 × 10⁵, C_L sharply increases to 0.76 because there is no simultaneous transition of laminar separation to turbulent separation on both sides of the circular cylinder. The test results in this paper are close to those of Liu et al. [13]; C_L in both sharply increases near Re = 3.5 × 10⁵.

The lift coefficients C_L of the smooth circular cylinder for different turbulence intensity and Reynolds numbers are shown in Figure 19. C_L values of the three turbulent flows are all near zero, indicating that the wind field is symmetrically distributed. Being different from the sudden change of C_L in the smooth flow in the critical regime, there is no obvious sudden change in C_L in the critical regime in the turbulent flow.

The standard deviations of lift coefficient $C_L^{\prime }$ of the smooth circular cylinder for different turbulence intensity and Reynolds number are shown in Figure 20. Overall, with the increase of Reynolds number, $C_L^{\prime }$ in different turbulent flows decreases, which is consistent with the results of Cheung and Melbourne [22]. As with C_L, when Re = 3.5 × 10⁵, there is also a sudden change of $C_L^{\prime }$ in the smooth flow and the maximum value is increased to 0.47. However, there is no obviously sudden change in C_L in the critical regime in the turbulent flow. $C_L^{\prime }$ in the smooth flow is larger than that in the turbulent flow. Compared with $C_D^{\prime }$, $C_L^{\prime }$ is larger than $C_D^{\prime }$, indicating that the crosswind excitation caused by the vortex is more intense than the along-wind excitation caused by the turbulence. When the Reynolds number is in the supercritical regime, $C_L^{\prime }$ in various turbulent flows are basically unchanged, indicating that the vortex of the circular cylinder has stabilized.

6. Correlation of Wind Pressure

6.1. In the Smooth Flow

Figure 21 shows the correlation coefficients between the wind pressure of each measuring point around the cylindrical surface and the wind pressure at the angular position of 2°. For the measuring point on the same side of the circular cylinder whose angular position ranges from 0° to 180°, the correlation coefficients are almost positive. For the measuring point on the opposite side whose angular position ranges from 180° to 360°, the correlation coefficients are almost negative.

In the smooth flow, the wind pressure distribution in different Reynolds number regimes is different and the correlation of the wind pressure coefficient is different. The correlation of the wind pressure coefficient with each other at three typical Reynolds numbers is plotted in Figure 22. When the Reynolds number is in the subcritical regime (Re = 1.04 × 10⁵), the wind pressure on the same side has a strong positive correlation and the wind pressure has a strong negative correlation between the two sides. When the Reynolds number is in the critical regime (Re = 3.52 × 10⁵), one side has laminar separation while the other side has turbulent separation; wind pressures in the region of about 0°–120° and 120°–180° on the same side have strong correlations but the correlation between the two regions is weak. However, the correlation between the region of about 120°–180° and 180°–210° is relatively weak. When the Reynolds number is in the supercritical regime (Re = 7.25 × 10⁵), the wind pressure correlation is strong before the separation point and the correlation at other locations is weak. The correlation of the wind pressure in the region before the separation point is stronger on the same side and the correlation of the wind pressure in the region after the separation point is weaker. Overall, the correlation on the same side is generally strong at the three wind speeds, while the two sides of the circular cylinder show a significantly negative correlation.

6.2. In the Turbulent Flow

The distribution of wind pressure coefficients in different turbulent flows is different and the correlation of wind pressure coefficients is also different. The correlation of wind pressure coefficients of four turbulence degrees at Re = 3.11 × 10⁵ is shown in Figure 23. In the smooth flow, the wind pressure on the same side of the cylinder shows a strong positive correlation and the wind pressure shows a strong negative correlation between the two sides. When I_u = 4%, the correlation of wind pressure between adjacent points is still strong but the correlation of wind pressure between the distant points drops sharply. Compared with the correlation of wind pressure when I_u = 4%, the correlation of wind pressure between the points on the base region is much stronger when I_u = 8% and 12%. In general, turbulence will weaken the positive correlation of the same side and also reduce the negative correlation between the two sides of the circular cylinder.

7. Conclusions

This paper has studied the characteristic parameters of mean wind pressure coefficient distribution on cylindrical surface, drag coefficient and lift coefficient for different Reynolds numbers and turbulence intensities. The results are compared with the results obtained by other researchers. The correlation of wind pressure on a cylindrical surface is also studied. In the smooth flow, the wind pressure coefficient of the base region increases with the increase of Reynolds number and remains basically unchanged when the Reynolds number is in the supercritical regime. In the turbulent flow, the wind pressure coefficient of the base region increases first and then decreases with the increase in Reynolds number. This is close to the results in the smooth flow when the Reynolds number is in the supercritical regime and far greater than results in the smooth flow when the Reynolds number is in the subcritical and critical regimes. In the smooth flow, the position of separation point is about 80° when the Reynolds number is in the subcritical regime; it suddenly moves back in the critical regime and is basically stable at about 140° in the supercritical regime. However, in the turbulent flow, the position of the separation point is basically around 140° regardless of the Reynolds number regime. In the smooth flow, the minimum wind pressure coefficient is almost constant in the subcritical regime: the value is about −1.0. It suddenly decreases in the critical regime and is basically constant in the supercritical regime, the value of which is about −2.4. In the turbulent flow, the minimum wind pressure coefficient decreases in the subcritical regime as the Reynolds number increases and remains constant in the critical and supercritical regimes, with a value of approximately −2.3.

Compared with characteristics in the smooth flow, turbulence will cause the critical Reynolds number to move to a smaller Reynolds number while the critical regime of the Reynolds number and its characteristics are not obvious. The minimum drag coefficient in the turbulent flow is basically constant at about 0.4 and is not affected by turbulence intensity. The lift coefficient in turbulent flow is basically zero, however, in a smooth flow; the lift coefficient suddenly increases when the Reynolds number is in the critical regime. The fluctuating values of the lift coefficient of the smooth flow are greater than the values in the turbulent flow under the same Reynolds number.

In the smooth flow, the laminar flow separation shows a strong positive correlation between the wind pressure points on the same side. However, the turbulent separation shows a strong correlation between the measured points in the region of about 0°–120° and 120°–180° on the same side; the correlation between the two regions is weak. The turbulent flow basically shows the correlation characteristics of turbulent separation.