Flow Patterns Providing Maximum Speed-Up Ratio and Maximum Speed-Up Area of Pedestrian-Level Winds

1. Introduction

It is known that wind speed increase in pedestrian-level spaces around high-rise buildings tend to cause uncomfortable and even unsafe wind conditions for pedestrians [1,2]. Especially, instantaneous strong winds can have a significant impact on the body sensation of pedestrians, because they provide an indication of the maximal speed that a pedestrian might experience due to unsteady wind flow, and its unexpected nature can affect pedestrian wind comfort more and easily catch people off guard [3,4,5]. Instantaneous strong winds at pedestrian level are usually related to complex flow patterns around buildings. Therefore, a detailed examination of flow patterns corresponding to instantaneous strong wind events around high-rise buildings is essential to understand the physical mechanism of this phenomenon.

Referring to some previous studies on airflows around buildings and pedestrian wind environments, the physical mechanisms of wind speed increase at pedestrian level around buildings are considered to be Venturi effect and the downwash effect. The former originally states that a fluid’s velocity increases when the cross section of a certain mass of fluid decreases along with its passage in fluid dynamics and is usually only used for confined flow in closed channels. Currently, Venturi effect is also used in wind engineering and urban aerodynamics with the meaning of increase in wind speed due to flow constriction [6,7,8] and is typically associated with passages between buildings. In a broad sense, the term “Venturi effect” can be used even for isolated buildings, since narrower paths on two sides of an isolated building than the upstream region causes speed-up phenomenon [9,10].

The latter, downwash effect, generally happens when the approaching boundary layer flows are blocked by the windward surface of a building, causing downwash (or downward flows) on the front and two sides of the building and then accelerate the near-ground flows. Cook [11] concluded that the downward movement of the airflow is mainly due to the pressure gradient between different heights within the windward surface of the building because of wind speed difference in the approaching boundary layer flow, based on comparison of the distribution of surface wind pressure and flow field around a two-dimensional rectangular building model between a uniform turbulence flow (UTF) and a boundary layer flow (BLF). Blocken and Carmeliet [12] explained that two pressure systems determined the flow patterns around a single rectangular building based on the wind tunnel measurement results of Beranek [13]. The first one acts on the windward surface of the building with maximum pressure at the stagnation point and lower pressures on the rest of the surface due to approaching wind speed increase with height and causes a standing vortex that feeds the corner streams. The second one consists of an overpressure zone on the windward side of the building and an under-pressure zone on the leeward side, which causes reverse flow and also contributes to the corner streams [12,13]. It is obvious that the distribution characteristics of surface wind pressure are closely related to flow patterns, especially downwash effect, around buildings. Therefore, it is also necessary to examine the distribution characteristics of a building’s surface wind pressure along with flow patterns corresponding to instantaneous strong winds at pedestrian level around the building.

To quantitatively evaluate the pedestrian-level wind environment around a high-rise building, two important indices, speed-up ratio and speed-up area, have usually been introduced. The concept of speed-up ratio was introduced by Sexton [14] and defined as the ratio between the wind speed at a point around a building and the wind speed at the same point without the existence of a building. Speed-up area is the area of regions where wind speeds increase or speed-up ratio is larger than 1 and is usually near the building corners of the windward side. The magnitude of speed-up ratio reflects the influence degree of a building on the near-ground flow at a certain position. In contrast, the magnitude of speed-up area shows the actual area of high wind speed at pedestrian level around a high-rise building. Tamura et al. [9] found that downwash effect has a greater impact on the expansion of mean speed-up area around an isolated building than Venturi effect, but is comparable to Venturi effect for the maximum mean speed-up ratio, based on measured mean pedestrian-level wind speeds around square-section high-rise buildings with different dimensions (height, width, size) under BLF (Boundary layer flow) and UTF (Uniform turbulence flow) in a wind tunnel.

In this study, Large Eddy Simulation (LES) was performed for isolated high-rise buildings with different heights/aspect ratios to further examine flow patterns around buildings and distribution characteristics of building surface pressure corresponding to instantaneous strong wind events at pedestrian level providing two conditions of “maximum speed-up ratio” and “maximum speed-up area”.

2. Description of Numerical Simulation

2.1. Model Configurations

LES was conducted for three square-section buildings with the same width ($B=B_0=50\mathrm{m}$ in full-scale) but different heights ($H=100\mathrm{m}$, 200m and 400m in full-scale), giving aspect ratios $H/B_0=2$, 4 and 8, as shown in Table 1. Here, the building model with height $H=200\mathrm{m}\equiv H_0$ is defined as “reference building model (RBM)”.

2.2. Numerical Setting

The open-source Computational Fluid Dynamic (CFD) code, OpenFOAM (v8), was used. Table 2 lists the calculation conditions for LES. Referring to the commonly used CFD guidelines [15,16], the building width was uniformly discretized into 20 grids, and sufficient distances between building surfaces and boundaries of the computational domain were ensured, in which the cross-section of the computational domain corresponds to the wind tunnel section ($1.2\mathrm{m}\left(y\right)\times 1.5\mathrm{m}\left(z\right)=6.0H_0\times 7.5H_0$) of the PIV (Particle Image Velocimetry) test in Lin et al. [17], as shown in Figure 1(a). The mesh stretching ratio was set to 1.08 or less.

The inflow fluctuations were generated by an artificial generation method [18]. Figure 1(b) shows the approaching flow profiles obtained from LES results in an empty computational domain. It can be seen that the turbulence characteristics of the inflow boundary condition were sufficiently maintained and they show good agreement at both the inlet boundary and the origin “O”. The mean wind speed at pedestrian-level ($z=2.5\mathrm{m}$) and the top of the RBM ($z=200\mathrm{m}=H_0$) are equal to ${\overline{U}}_{2.5\mathrm{m}}=2.2\mathrm{m}/\mathrm{s}$ and ${\overline{U}}_{H_0}=5.0\mathrm{m}/\mathrm{s}$, and will be used for normalization in the latter analysis. The power-law exponent of mean wind speed profile was $\alpha =0.27$, representing the urban terrain condition. For more information on detailed numerical settings and validation of flow fields around building models from LES based on PIV (Particle Image Velocimetry) measurements, readers can refer to Lin et al. [17].

2.3. Validation of Surface Pressure from LES

Validation of flow fields around building models from LES have been conducted based on PIV measurements in Lin et al. [17], but where building surface pressures were not measured simultaneously. Therefore, in order to validate the accuracy of surface pressures obtain from LES, the pressure coefficients $C_{p,d}$ are compared with the wind tunnel experimental results for a square-section building model (Full-scale height $H=200\mathrm{m}=H_d$, Width $B=40\mathrm{m}=B_d$) from the TPU (Tokyo Polytechnic University) database [19]. In this Section 2.3, the subscript “$d$” is added to the parameters to represent the LES results corresponding to the target building model in the TPU database to distinguish them from the LES results used for the latter formal analysis. The pressure coefficient $C_{p,d}$ is defined as

$$C_{p,d}={\displaystyle \frac{p-p_{\mathrm{r}\mathrm{e}\mathrm{f}}}{1/2\rho {\overline{U}}_{H_d}^2}},$$

(1)

where $\rho$ is air density, $p_{\mathrm{r}\mathrm{e}\mathrm{f}}$ is the reference pressure set to zero at the outlet boundary and ${\overline{U}}_{H_d}=11.1\mathrm{m}/\mathrm{s}$ is the mean wind speed at the top of the building model. Mean and standard deviation (std) of statistics of wind pressure coefficients is denoted as ${\overline{C}}_{p,d}$ and $C_{p,d}^{\mathrm{\text{'}}}$.

The numerical simulation uses the same geometrical scale of 1/400 as the TPU wind tunnel test. It is worth mentioning that the numerical settings for LES are the same as those in Lin at al. [17] except in the computational domain that is equal to $13H_d\left(x\right)\times 3H_d\left(y\right)\times 4H_d\left(z\right)$, where the cross section is equal to that of the TPU wind tunnel ($1.5\mathrm{m}\left(y\right)\times 2.0\mathrm{m}\left(z\right)$). Figure 2 compares the approaching flow conditions with those in the TPU wind tunnel test. It can be seen that mean wind speed and turbulence intensity show good agreement, as shown in Figure 2(a). The power spectrum density functions of fluctuating velocities were not reported and are assumed to follow the von Karman spectrum model for the TPU database results. Therefore, the non-dimensional power spectrum density of $u$ velocity component at building height ${\displaystyle \frac{f{S}_u}{{\sigma }_u^2}}$ obtained from LES is compared with the Karman spectrum (Figure 2(b)), where $f$, $S_u$, $L_u$ and ${\sigma }_u$ denote frequency, power spectral density, turbulence scale and standard deviation (std) of $u$ velocity component. LES results for ${\displaystyle \frac{f{S}_u}{{\sigma }_u^2}}$ generally show good agreement where the normalized frequency ${\displaystyle \frac{f{L}_u}{{\overline{U}}_{H_d}}}$ is smaller than about 1, which is determined by the computational mesh size.

Figure 3 shows variations of mean and fluctuating (std) wind pressure coefficients, ${\overline{C}}_{p,d}$ and $C_{p,d}^{\mathrm{\text{'}}}$, around the perimeter of a building at $z=2H/3$ obtained from LES and wind tunnel experiment (Exp.). It is observed that LES results are basically in agreement with experimental results, although LES results on the windward surface are slightly overestimated for mean pressure coefficients ${\overline{C}}_{p,d}$ and slightly underestimated for fluctuating wind pressure coefficients $C_{p,d}^{\mathrm{\text{'}}}$. Figure 4 compares mean and fluctuating wind pressure coefficients for all the pressure monitoring taps on building surfaces (windward, side, and leeward surfaces) from LES and experimental results in the form of scatter plots. It can be seen that for the mean and fluctuating wind pressure coefficients, the differences between the results from LES and wind tunnel experiment are almost all in the range of $\pm 20\mathrm{\%}$. The contour plots in Figure 5 also demonstrate the good agreement and acceptable accuracy for LES results compared with experimental results.

. (a) Mean ${\overline{C}}_{p,d}$; (b) Fluctuating $C_{p,d}^{\mathrm{\text{'}}}.$; (b) Fluctuating $C_{p,d}^{\mathrm{\text{'}}}.$; (b) Fluctuating $C_{p,d}^{\mathrm{\text{'}}}.$

3. Definition of Instantaneous Strong Wind Events

In this study, we focus on two instantaneous strong wind events at pedestrian level $(z=2.5\mathrm{m}$ in full-scale) around buildings providing “maximum speed-up ratio” and “maximum speed-up area”. Instantaneous speed-up ratio at time $t$ is defined as $R^{*}\left(t\right)=\sqrt{{U_{2.5m}\left(t\right)}^2+{V_{2.5m}\left(t\right)}^2+W_{2.5m}{\left(t\right)}^2}/{\overline{U}}_{2.5\mathrm{m}}$,where $U_{2.5m}\left(t\right)$, $V_{2.5m}\left(t\right)$ and $W_{2.5m}\left(t\right)$ represent instantaneous velocity components in the x, y and z directions at pedestrian level around a building.

Maximum instantaneous speed-up ratio $R_{max}^{*}$ at pedestrian level around a building occurs at a point near the building corner denoted as Point “G”, as shown in Figure 6(a). Figure 7(a) further shows the time history of instantaneous speed-up ratio at Point “G”, $R_G^{*}\left(t\right)$. Instantaneous strong wind events at pedestrian level around a building generally coincide with considerably low-occurrence frequencies. Meanwhile, wind speeds larger than 90th percentile values are generally considered to represent rare but instantaneous strong wind events in pedestrian wind environmental studies (e.g., [20,21,22]). Meanwhile, in order to reduce the risk caused by instantaneous strong wind at pedestrian-level, several wind environment criteria [3,23,24,25] have also been proposed based on a combination of threshold wind speeds and the probabilities of exceeding the corresponding thresholds. In the present study, to capture strong wind events at pedestrian level and to avoid too few data to be lack of representation, the moments when $R_G^{*}\left(t\right)$ fall within the top 2% of all time-history data (red line in Figure 7(a)) are extracted. Averaged value for the top 2% approximately represent the strong wind event providing “maximum speed-up ratio” of pedestrian-level wind around a building and is denote as $R_{G,max}^{*}$.

The time history of instantaneous normalized speed-up area $A_R^{*}\left(t\right)=A_R\left(t\right)/B_0^2$ is shown in Figure 7(b), where $A_{\mathrm{R}}\left(t\right)$ represents the total area surrounded by the contour line of wind speed ratio $R$ (Figure 6(b)). In the present study, a moderate value of $R=1.5$ was selected and correspondingly, the time history of instantaneous normalized speed-up area is denoted as $A_{1.5}^{*}\left(t\right)(=A_{1.5}(t)/B_0^2)$. Similarly, the moments when $A_{1.5}^{*}\left(t\right)$ falls within the top 2% of all the time-history data (red line in Figure 7(b)) are extracted. The averaged value for the top 2% approximately represents the strong wind event providing “maximum speed-up area” around a building and is denoted as $A_{1.5,max}^{*}$. Correspondingly, three-dimensional flow fields around buildings and wind pressure coefficients on building surfaces for the two strong wind events are extracted to obtain a conditional average.

4. Simulation Results and Analysis

In this section, conditional-average results will be discussed in detail. It is worth mentioning that the definition of pressure coefficient $C_p$ used in the following analysis is a little different from that in Section 2.3. Here, for convenience of comparison between buildings with different height $H$ or aspect ratio $H/B_0$, the pressure coefficient $C_p$ is defined as

$$C_p={\displaystyle \frac{p-p_{ref}}{1/2\rho {\overline{U}}_{H_0}^2}},$$

(2)

where ${\overline{U}}_{H_0}=5.0\mathrm{m}/\mathrm{s}$ is the mean wind speed at the top of the “refence building model (RBM)” with aspect ratio $H/B_0=4$, and $H=200\mathrm{m}\equiv H_0$.

4.1. Determination of Data Acquisition Period

In numerical simulation, the data acquisition period is usually determined based on the statistical stability of the data of interest and the computational cost of the simulation. In this paper, in order to determine the appropriate data acquisition period, the effect of data acquisition period on the probability density distributions and percentile values of $R_G^{*}\left(t\right)$ and $A_{1.5}^{*}\left(t\right)$ is mainly discussed and shown in Appendix A. It is shown that a data acquisition period of 20min or 1200s in full scale is sufficient to ensure acceptable uncertainty.

4.2. Conditional-Average Results

As shown in Figure 7, it can be seen that the moments corresponding to “maximum speed-up ratio” event and “maximum speed-up area” event mostly do not coincide for the building model with aspect ratio $H/B_0=2$. A similar phenomenon can also be seen for other building models with different heights H or aspect ratios $H/B_0=4$ and 8, as shown in Figures. 8 and 9. This phenomenon indicates that the two strong wind events do not occur simultaneously.

Figure 9. Extraction of maximum-level of speed-up ratio $R_G^{*}\left(t\right)$ and normalized speed-up area $A_{1.5}^{*}\left(t\right)$ at pedestrian level around the building model with aspect ratio $H/B_0=8$. (a) “Maximum speed-up ratio” event, $R_{G,max}^{\mathrm{*}}$; (b) “Maximum speed-up area” event $A_{1.5,max}^{\mathrm{*}}.$

Figure 9. Extraction of maximum-level of speed-up ratio $R_G^{*}\left(t\right)$ and normalized speed-up area $A_{1.5}^{*}\left(t\right)$ at pedestrian level around the building model with aspect ratio $H/B_0=8$. (a) “Maximum speed-up ratio” event, $R_{G,max}^{\mathrm{*}}$; (b) “Maximum speed-up area” event $A_{1.5,max}^{\mathrm{*}}.$

Figure 10 first shows conditional-average results for speed-up ratio vector $R$, pressure coefficient $C_p$ on building surfaces and three-dimensional streamlines for the building model with aspect ratio $H/B_0=2$. For the “maximum speed-up ratio” event, the area with high wind speeds (yellow to red) at pedestrian level is relatively narrow, but values of $R$ are large. Meanwhile, positive pressure on the windward surface is generally smaller and the streamlines mostly show two-dimensional characteristics.

In contrast, for the “maximum speed-up area” event, the area with high wind speeds becomes wider (yellow to red). The positive pressure on the upper part of the windward surface is quite large and the difference for the surface pressure with the lower part of windward surface and the negative pressure on the side, i.e., the pressure gradient, is also large. Accordingly, a three-dimensional flow pattern where the wind at higher level descends to near ground level is shown and a strong influence of downwash can be seen.

Figure 11 and Figure 12 further show speed-up ratio vector $R$, pressure coefficient $C_p$ on building surfaces and three-dimensional streamlines for other building models with different heights or aspect ratios $H/B_0=4$ and $8$. A similar phenomenon to those for the building model with aspect ratio $H/B_0=2$ can also be seen in the building models with different heights or aspect ratios. The difference is that the values of speed-up ratio $R$, the positive pressure on the upper part of the windward surface and its difference with the lower part of the windward surface and the negative pressure on the side, i.e., the pressure gradients, are larger for building models with higher heights $H$ or larger aspect ratios $H/B_0$. Meanwhile, building models tend to be slender with increase of building height or aspect ratio. The incoming flows easily pass by the sides of the building and the flow around the building tends to be two dimensional [9,26]. Therefore, the difference between conditional average results for two strong events providing “maximum speed-up ratio” and “maximum speed-up area” is more obvious at the lower part for building models with higher heights $H$ or larger aspect ratios $H/B_0$.

Figure 13 quantitatively summarizes the conditional average results shown in Figures 10~12 for the normalized speed-up ratio at point “G”, $R_G^{*}$ and normalized speed-up area $A_{1.5}^{*}$ at pedestrian level corresponding to the two strong events providing “maximum speed-up ratio” and “maximum speed-up area”. It is obvious that compared to the situation providing “maximum speed-up area” (red color), $R_G^{*}$ is larger and $A_{1.5}^{*}$ is smaller for the situation providing “maximum speed-up ratio” (blue color). Conversely, $A_{1.5}^{*}$ is larger and $R_G^{*}$ is smaller for the situation providing “maximum speed-up area”. Meanwhile, with an increase of aspect ratio $H/B_0$, the difference in both $R_G^{*}$ and $A_{1.5}^{*}$ between the two situations providing “maximum speed-up ratio” and “maximum speed-up area” becomes larger.

In addition, instantaneous flow patterns around all building models corresponding to the moments $t_{R_{max}^{*}}$ and $t_{A_{max}^{*}}$, when actual maximum speed-up ratio at pedestrian-level$R_{max}^{*}$ and maximum speed-up area $A_{max}^{*}$ happen, are also checked as a reference and shown in Figure 14. Similar phenomena can be seen by comparing conditional average results in Figure 10, Figure 11 and Figure 12 and actual instantaneous results, where downwash flows at the moment $t_{A_{max}^{*}}$ for the building model with $H/B_0=4$ are most obvious and it may be due to relatively higher approaching flow at front stagnation level and the mediate slenderness of the building model. This also suggests the reasonableness of using the conditional average results to discuss the flow patterns corresponding to the two strong wind events.

In summary, the results above indicate that flow patterns around buildings for strong wind events providing “maximum speed-up ratio” and “maximum speed-up area” are different: the contribution of downwash tends to be larger for “maximum speed-up area” event showing more three-dimensional flow characteristics.

5. Conclusions

LES was conducted for square-section building models with different heights$H=100\mathrm{m},200\mathrm{m}\mathrm{a}\mathrm{n}\mathrm{d}400\mathrm{m}$in full-scale or aspect ratios $H/B_0=2$, $4$ and $8$, focusing on two instantaneous strong wind events providing “maximum speed-up ratio” and “maximum speed-up area” of pedestrian-level wind. The following findings were obtained.

Two strong wind events do not occur simultaneously.

Conditional-average flow patterns around buildings for the two instantaneous strong wind events are different: the contribution of downwash tends to be larger for the strong wind event providing “maximum speed-up area” of pedestrian-level wind, showing more three-dimensional flow characteristics.

For building models with different heights $H$ or aspect ratios $H/B_0$, a similar phenomenon as described above can also be seen. The difference is that the values of speed-up ratio $R^{\mathrm{*}}$, the positive pressure on the upper part of the windward surface and its difference with the lower part of windward surface and the negative pressure on the side, i.e., the pressure gradient, are larger for building models with higher heights $H$ or larger aspect ratios $H/B_0$.