# LES and Wind Tunnel Test of Flow around Two Tall Buildings in Staggered Arrangement

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Simulation on Shear Stress/Friction Velocity on Roofs

#### 2.1. Governing Equations

_{s}is computed at each time step with a test-filter and clipped to the range of 0 to 0.23 to avoid numerical instabilities. This imposed maximum value of 0.23 for C

_{s}follows the default value in Ansys Fluent and is found to be appropriate for flow around an isolated bluff body [21].

#### 2.2. Computational Domain and Boundary Conditions

^{6}hexahedral meshes, which is refined near the target building and ground surface. The height of the first layer of cells around the building models was small enough (y+ < 1) to solve the viscous sublayer. Stretching ratios between neighboring cells were kept below 1.3 in accordance with the best practice guidelines [23,24].

_{μ}is a model constant of 0.09. The amount of vorticity was set to 50.

_{init}= 3.0 s, the statistics were sampled for 20 s, corresponding to 38.7 flow-through times (T

_{ft}= L

_{x}/U

_{H}, where L

_{x}is the length of the computational domain), which are longer than the sampling duration suggested by Gousseau [21] who found that 21.8 flow-through times are sufficiently long to achieve statistical convergence.

## 3. Description of Wind Tunnel Test

_{H}= 5.8 m/s and 0.089, respectively. The measured mean wind velocity and the turbulence intensity profiles in the wind tunnel test and the simulated profiles in the numerical simulation are presented in Figure 3. The longitudinal integral scale of turbulence was about 0.39 m at the roof height in the wind tunnel. This corresponds to a full-scale integral scale of 390 m at 180 m height.

^{2}. With this configuration, the measurement uncertainty of individual velocity vector was estimated at about ±0.02U

_{H}[28,29].

## 4. Result Analysis and Discussion

#### 4.1. Time-Averaged Wind Flow Characteristics

#### 4.2. LES Validation by Wind Tunnel Result

#### 4.3. Vortex Structures of Tall Buildings under Interference

#### 4.4. Excitation of Across-Wind Forces on Buildings

_{peak}, where f

_{peak}is the averaged dominant frequency of the quasi-periodic components in the across-wind force signal (Figure 16). This means that a quasi-cycle of the across-wind force on the downstream building has the strongest correlation with that on the upstream building happened one period earlier. The reason for this becomes evident from the flow excitation mechanism revealed in Figure 13. When a vortex is shed from the upstream building and subsequently convects downstream, the vortex dynamics causes flow oscillations in the building wake. When these oscillations reach the downstream building, they act to enhance flow separations on the building which is then responsible for the magnification of the across-wind force on it. As a result, the across-wind force signal on the downstream building relates to vortex shedding activities occurring earlier from the upstream building. In other works, the characteristics of the upstream building wake such as strength and regularity of vortex shedding strongly affect the generation of a peak across-wind force acting on the downstream building later.

## 5. Conclusions

- The results of wind flow around two buildings, including time-averaged mean and fluctuating streamwise and transverse velocity distributions obtained by LES agree well with the wind tunnel measurements. A better agreement is found for time-averaged mean flow field than the fluctuating velocity distributions.
- The large scale coherent patterns are successfully revealed by numerical simulation and wind tunnel test. A distinct relationship between the across-wind peak forces and the phases of alternating vortex shedding is observed. Three-dimensional flow structures are further observed by LES.
- An in-phase synchronization of the vortex shedding from both buildings is observed and confirmed by the wind forces analysis. This would be the cause of largely amplified across-wind excitation of the downstream building.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Bailey, P.A.; Kwok, K.C.S. Interference excitation of twin tall buildings. J. Wind Eng. Ind. Aerodyn.
**1985**, 21, 323–338. [Google Scholar] [CrossRef] - Taniike, Y.; Inaoka, H. Aeroelastic behavior of tall buildings in wakes. J. Wind Eng. Ind. Aerodyn.
**1988**, 28, 317–327. [Google Scholar] [CrossRef] - Xie, Z.N.; Gu, M. Simplified formulas for evaluation of wind-induced interference effects among three tall buildings. J. Wind Eng. Ind. Aerodyn.
**2007**, 95, 31–52. [Google Scholar] [CrossRef] - Lam, K.M.; Zhao, J.G.; Leung, M.Y.H. Wind-induced loading and dynamic responses of a row of tall buildings under strong interference. J. Wind Eng. Ind. Aerodyn.
**2011**, 99, 573–583. [Google Scholar] [CrossRef] [Green Version] - Khanduri, A.C.; Stathopoulos, T.; Bedard, C. Wind-induced interference effects on buildings—A review of the state-of-the-art. Eng. Struct.
**1998**, 20, 617–630. [Google Scholar] [CrossRef] - English, E.C.; Fricke, F.R. The interference index and its prediction using a neural network analysis of wind-tunnel data. J. Wind Eng. Ind. Aerodyn.
**1999**, 83, 567–575. [Google Scholar] [CrossRef] - Kim, W.; Tamura, Y.; Yoshida, A. Interference effects on local peak pressures between two buildings. J. Wind Eng. Ind. Aerodyn.
**2011**, 99, 584–600. [Google Scholar] [CrossRef] - Yu, X.F.; Xie, Z.N.; Zhu, J.B.; Gu, M. Interference effects on wind pressure distribution between two high-rise buildings. J. Wind Eng. Ind. Aerodyn.
**2015**, 142, 188–197. [Google Scholar] [CrossRef] - Taniike, Y. Interference mechanism for enhanced wind forces on neighboring tall buildings. J. Wind Eng. Ind. Aerodyn.
**1992**, 42, 1073–1083. [Google Scholar] [CrossRef] - Sakamoto, H.; Haniu, H. Aerodynamic forces acting on two square prisms placed vertically in a turbulent boundary-layer. J. Wind Eng. Ind. Aerodyn.
**1988**, 31, 41–66. [Google Scholar] [CrossRef] - Gowda, B.H.L.; Sitheeq, M.M. Interference effects on the wind pressure distribution on prismatic bodies in tandem arrangement. Indian J. Technol.
**1993**, 31, 485–495. [Google Scholar] - Hui, Y.; Tamura, Y.; Yoshida, A.; Kikuchi, H. Pressure and flow field investigation of interference effects on external pressures between high-rise buildings. J. Wind Eng. Ind. Aerodyn.
**2013**, 115, 150–161. [Google Scholar] [CrossRef] - Blocken, B.; Stathopoulos, T. CFD simulation of pedestrian-level wind conditions around buildings: Past achievements and prospects. J. Wind Eng. Ind. Aerodyn.
**2013**, 121, 138–145. [Google Scholar] [CrossRef] - Sohankar, A. A LES study of the flow interference between tandem square cylinder pairs. Theor. Comp. Fluid Dyn.
**2014**, 28, 531–548. [Google Scholar] [CrossRef] - Tamura, T. Towards practical use of LES in wind engineering. J. Wind Eng. Ind. Aerodyn.
**2008**, 96, 1451–1471. [Google Scholar] [CrossRef] - Mara, T.G.; Terry, B.K.; Ho, T.C.E.; Isyumov, N. Aerodynamic and peak response interference factors for an upstream square building of identical height. J. Wind Eng. Ind. Aerodyn.
**2014**, 133, 200–210. [Google Scholar] [CrossRef] - Zu, G.B.; Lam, K.M. Interference mechanism of two tall buildings in staggered arrangement. In Proceedings of the 9th Asia-Pacific Conference on Wind Engineering, Auckland, New Zealand, 3–8 December 2017. [Google Scholar]
- Ansys Inc. Ansys Fluent 13.0, User’s Guide; Ansys Inc.: Canonsburg, PA, USA, 2010. [Google Scholar]
- Lilly, D.K. A proposed modification of the Germano subgrid-scale closure model. Phys. Fluids
**1992**, 4, 633–635. [Google Scholar] [CrossRef] - Germano, M.; Piomelli, U.; Moin, P.; Cabot, W.H. A dynamic subgrid scale eddy viscosity model. Phys. Fluids
**1991**, A3, 1760–1765. [Google Scholar] [CrossRef] - Gousseau, P.; Blocken, B.; Vanheijst, G.J.F. Quality assessment of large-eddy simulation of wind flow around a high-rise building: Validation and solution verification. Comput. Fluids
**2013**, 79, 120–133. [Google Scholar] [CrossRef] - Franke, J. Recommendations of the COST action C14 on the use of CFD in predicting pedestrian wind environment. In Proceedings of the Fourth International Symposium on Computational Wind Engineering, Yokohama, Japan, 16–19 July 2006. [Google Scholar]
- Franke, J.; Hellsten, A.; Schlünzen, H.; Carissimo, B. COST 732. Best Practice Guideline for the CFD Simulation of Flows in the Urban Environment; University of Hamburg, Meteorological Inst.: Hamburg, Germany, 2007. [Google Scholar]
- Tominaga, Y.; Mochida, A.; Yoshie, R.; Kataoka, H.; Nozu, T.; Yoshikawa, M.; Shirasawa, T. AIJ guidelines for practical applications of CFD to pedestrian wind environment around buildings. J. Wind Eng. Ind. Aerodyn.
**2008**, 96, 1749–1761. [Google Scholar] [CrossRef] - Lam, K.M.; Leung, M.Y.H.; Zhao, J.G. Interference effects on wind loading of a row of closely spaced tall buildings. J. Wind Eng. Ind. Aerodyn.
**2008**, 96, 562–583. [Google Scholar] [CrossRef] - Theunissen, R.; Scarano, F.; Riethmuller, M.L. Spatially adaptive PIV interrogation based on data ensemble. Exp. Fluids
**2010**, 48, 875–887. [Google Scholar] [CrossRef] - Willert, C.E.; Gharib, M. Digital particle image velocimetry. Exp. Fluids
**1991**, 10, 181–193. [Google Scholar] [CrossRef] - Adrian, R.J. Multi-point optical measurements of simultaneous vectors in unsteady flow—A review. Int. J. Heat Fluid Flow
**1986**, 7, 127–145. [Google Scholar] [CrossRef] - Adrian, R.J.; Westerweel, J. Particle Image Velocimetry; Cambridge University Press: Cambridge, UK, 2011. [Google Scholar]
- Wang, H.F.; Zhou, Y. The finite-length square cylinder near wake. J. Fluid Mech.
**2009**, 638, 453–490. [Google Scholar] [CrossRef] - To, A.P.; Lam, K.M.; Xie, Z.N. Effect of a through-building gap on wind-induced loading and dynamic responses of a tall building. Wind Struct.
**2012**, 15, 531–553. [Google Scholar] [CrossRef] - Lam, K.M.; Zhao, J.G. Occurrence of peak lifting actions on a large horizontal cantilevered roof. J. Wind Eng. Ind. Aerodyn.
**2002**, 90, 897–940. [Google Scholar] [CrossRef] [Green Version]

**Figure 1.**IF contours of RMS across-wind moment: (

**a**) present study; (

**b**) Mara et al. (with permission from [16]).

**Figure 6.**Wind velocity field for normal wind incidence. (

**a**) Time-averaged mean flow field; (

**b**) RMS flow field.

**Figure 8.**Comparison of wind tunnel (WT) measurements and LES results of mean streamwise velocity $\overline{u}$ in horizontal plane: (

**a**) Level 3 (h = 0.5H) and (

**b**) Level 5 (h = 0.82H). Wind velocity plots transversely with positive value on right side of the dotted axis and negative on left side.

**Figure 9.**Comparison of wind tunnel (WT) measurements and LES results of mean transverse velocity in horizontal plane: (

**a**) Level 3 (h = 0.5H) and (

**b**) Level 5 (h = 0.82H). Wind velocity plots transversely with positive value on right side of the dotted axis and negative on left side.

**Figure 10.**Comparison of wind tunnel (WT) measurements and LES results of fluctuating streamwise velocity u’ in horizontal plane: (

**a**) Level 3 (h = 0.5H) and (

**b**) Level 5 (h = 0.82H). Wind velocity plots transversely with positive value on right side of the dotted axis and negative on left side.

**Figure 11.**Comparison of wind tunnel (WT) measurements and LES results of fluctuating transverse velocity v’ in horizontal plane: (

**a**) Level 3 (h = 0.5H) and (

**b**) Level 5 (h = 0.82H). Wind velocity plots transversely with positive value on right side of the dotted axis and negative on left side.

**Figure 13.**Conditionally sampled wind velocity field at: (

**a**) peak maximum across-wind forces (g = 2) and (

**b**) peak minimum across-wind forces (g = −2).

**Figure 14.**Three-dimensional view of Instantaneous vortex structures represented by spanwise vorticity ω* = ωD/U: (

**a**–

**c**) positive across-wind force (upward) event and (

**d**–

**f**) negative across-wind force (downward) event; (

**a**,

**d**) Iso-surfaces of ω* = −2~−5; (

**b**,

**e**) Iso-surfaces of ω* = 2~5; (

**c**,

**f**) Vector field at mid-height.

**Figure 16.**Simultaneous fluctuating overall across-wind force coefficients on upstream building and downstream building.

**Figure 17.**Simultaneous fluctuating surface pressure coefficient Cross correlation curves between across-wind forces on upstream building and downstream building.

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zu, G.; Lam, K.M.
LES and Wind Tunnel Test of Flow around Two Tall Buildings in Staggered Arrangement. *Computation* **2018**, *6*, 28.
https://doi.org/10.3390/computation6020028

**AMA Style**

Zu G, Lam KM.
LES and Wind Tunnel Test of Flow around Two Tall Buildings in Staggered Arrangement. *Computation*. 2018; 6(2):28.
https://doi.org/10.3390/computation6020028

**Chicago/Turabian Style**

Zu, Gongbo, and Kit Ming Lam.
2018. "LES and Wind Tunnel Test of Flow around Two Tall Buildings in Staggered Arrangement" *Computation* 6, no. 2: 28.
https://doi.org/10.3390/computation6020028