# Influence of Inflow Turbulence on the Flow Characteristics around a Circular Cylinder
## 3 Characteristic Parameters of Mean Wind Pressure Coefficient Distribution  
### In the Smooth Flow  
The wind pressure coefficient is given by:  
\[C_{p}=\frac{p(\theta)-p_{\infty}}{0.5\rho U_{\infty}^{2}} \tag{1}\]  
where \(p(\theta)\) is the measured wind pressure at any azimuthal angle \(\theta\), \(p_{\infty}\) and \(U_{\infty}\) denote the freestream static pressure and uniform velocity, respectively, and \(\rho\) 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 \(\theta_{m}\) 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 \(\theta_{b}\) 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 [PERSON] and [PERSON] [24] in the subcritical regime; the varying trend in the measured Reynolds number regime is consistent with [PERSON] and [PERSON] [22]. \begin{table}
\begin{tabular}{c c c c} \hline \(I_{u}\) & **Wind Speed \(v\) (m/s)** & **Reynolds Number** & **Integral Scale (mm)** \\ \hline
0\% & 3–36 & \(6.21\times 10^{4}\)–\(7.45\times 10^{5}\) & 111 \\
4\% & 3–29 & \(6.21\times 10^{4}\)–\(6.00\times 10^{5}\) & 214 \\
8\% & 3–19 & \(6.21\times 10^{4}\)–\(3.93\times 10^{5}\) & 360 \\
12\% & 3–15 & \(6.21\times 10^{4}\)–\(3.11\times 10^{5}\) & 323 \\ \hline \end{tabular}
\end{table} 
Table 1: Test wind speed and Reynolds number in the tests. Figure 3: Definition of the characteristic parameters of mean wind pressure coefficients’ distribution curve. Figure 5 shows the position of the separation point \(\theta_{b}\) at different Reynolds numbers in the smooth flow. When the Reynolds number is in the subcritical regime, \(\theta_{b}\) is basically around \(80^{\circ}\). When the Reynolds number is in the critical regime, \(\theta_{b}\) increases rapidly, indicating that turbulent separation causes the separation point to move backwards, with the angular position close to \(160^{\circ}\). When the Reynolds number is in the supercritical regime, \(\theta_{b}\) falls back to \(142^{\circ}\)-\(144^{\circ}\). The experimental results in this paper are basically consistent with the results of [PERSON] [28] and [PERSON] and [PERSON] [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 [PERSON] and [PERSON] [24]. Figure 4: The mean wind pressure coefficient within the base region \(C_{pb}\) in the smooth flow.