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Mesh-adaptive LES for wind load estimation of a high-rise building in a city
J. Wind Eng. Ind. Aerodyn. 144 (2015) 62–69
Contents lists available at ScienceDirect
Journal of Wind Engineering and Industrial Aerodynamics journal homepage: www.elsevier.com/locate/jweia
Mesh-adaptive LES for wind load estimation of a high-rise building in a city Tsuyoshi Nozu a, Tetsuro Tamura b, Kishida Takeshi c, Katsumura Akira c a
Institute of Technology, Shimizu Corporation, 3-4-17 Etchujima, Koto-ku, Tokyo, Japan Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama, Japan c Wind engineering Institute, Co., Ltd, 3-29 Kanda-Jinbocho, Chiyoda-ku, Tokyo, Japan b
art ic l e i nf o
Keywords: LES Urban canopy Wind pressure coefficient Turbulent structure Wind load estimation
a b s t r a c t This paper discusses the applicability of large eddy simulation (LES) to the wind-resistant design of buildings in cities. In order to accurately predict wind pressures and forces on actual buildings with complicated shapes, we partially introduce the unstructured grid system, which is formulated on the open-source CFD code. Applying the LES method for modeling the urban flow, where a specified highrise building focuses on safety under wind loading, the combined model is employed to investigate aerodynamic characteristics. This model uses overset grids, consisting of the Cartesian grid and the unstructured-grids. According to previous studies, the Cartesian grid method can accurately generate the turbulent structures in the urban canopy, whereas the unstructured grid method can reproduce detailed patterns of the near-wake flows around a specified building inside a densely built-up area. In this study, we have applied the combined model consisting of the Cartesian grid and unstructured grid for wind load estimation of a high-rise building in a city. Particularly, at inclined wind direction to the main streets, there is a presumption of different effects of wind impact at each vertical level of a high-rise building along the street. Accordingly, relatively a large torsional force tends to be present. On the basis of the results obtained, their accuracy is checked in comparison with the previous data by wind tunnel experiment, and wind pressure distributions on the surfaces as well as wind force coefficients of a highrise building are estimated and discussed in view of structural safety. & 2015 Elsevier Ltd. All rights reserved.
1. Introduction To date, urban winds have often been simulated by the Reynolds-averaged Navier–Stokes (RANS) model from an environmental point of view, wherein the average wind velocity prediction is essential. The RANS model generally shows good performance (Blocken et al., 2004) (Yoshie et al., 2007) (Blocken and Persoon, 2009). Applying the large eddy simulation (LES) for modeling the urban wind, the Cartesian grid system is mainly employed, and its accuracy is generally good enough for the wind velocity prediction. However, in previous studies, the grid resolution could not accurately represent the actual building shape, but we have shown the success of the LES prediction for the flow field. Accordingly, the Cartesian grid-based method, in spite of including main streets in a direction different from wind or grid line, can simulate the gap flows among the buildings and transport phenomena of mass and gas in cities (Tamura et al., 2010) (Nozu and Tamura, 2012). However, the predictive accuracy of the abovementioned method is ambiguous for the estimation of the wind pressures and forces on a specified building in a city. Particularly, in order to deal with the wind-resistant design for a high-rise http://dx.doi.org/10.1016/j.jweia.2015.05.007 0167-6105/& 2015 Elsevier Ltd. All rights reserved.
building in a city, the numerical model must reproduce not only the approaching flow to the urban area but also the flow around a target building and surrounding buildings with a high degree of accuracy. Therefore, we have introduced the combined model with finer mesh for the near region of the specified building by employing the unstructured grid system, which is formulated on the open-source code OpenFOAM. The present method consists of the Cartesian structured grid for accurately reproducing the turbulent structures in the urban canopy and the unstructured grid for resolving the exact wake patterns around the specified building inside the densely built-up area. The authors realized the accurate aerodynamic prediction of a high-rise building in a city at wind direction parallel to the main streets by LES (Tamura et al., 2012). However, in order to assure the establishment of LES prediction for the wind-resistant design of a building, we must validate the LES model for various wind directions of an approaching flow. In this study, we have applied the LES method for the wind load estimation of a high-rise building in a city at inclined wind direction to the main streets. In this situation, the flows are sensitively deformed within the urban canopy; accordingly, the
T. Nozu et al. / J. Wind Eng. Ind. Aerodyn. 144 (2015) 62–69
63
Domain2 (for developing TBL)
Driver region Domain3 (Main region)
Domain1 (for turbulence generation) 1280m
z
y
2400m
x
1080m
Fig. 1. Numerical model for urban wind on Cartesian grid.
Table 1 The number of grid points for each Cartesian domains. Streamwise(x) Domain 1 Grid points
156
Domain 2 þ 151
Spanwise (y)
Vertical (z)
270
100
Domain 3 þ 600
achievement of appropriate numerical discretization and wellbalanced model construction becomes very difficult. There is a possibility of an extreme local pressure peak due to the unexpected behavior of the separated shear layer. We have also confirmed the accuracy of the calculation results in comparison with the previous experimental data. On the basis of the computed results, wind pressure distributions on the surfaces as well as wind force coefficients of high-rise buildings are estimated and discussed in view of structural safety.
grid points. Table 1 shows the number of grid points for each Cartesian domain. The governing equations for the LES model are the filtered forms for continuity and the incompressible Navier–Stokes, which are as follows: ∂ui ¼0 ∂xi ∂ui ∂u ∂p ∂ þuj i ¼ þ τij þ 2νSij ∂xi ∂xj ∂t ∂xj where ui , p, τij , and ν stand for filtered velocity, filtered pressure, sub-grid scale (SGS) Reynolds stress ðui uj ui uj Þ, and molecular viscosity coefficient, respectively. The overbar indicates spatial filtering. Concerning the sub-grid scale modeling, the Smagorinsky-type eddy viscosity model is employed for representing the flow. The turbulent eddy viscosity coefficient νe can be estimated by the constant C S , the filter size Δ, and the strain velocity tensor Sij as follows: 1 3
τij δij τkk ¼ 2νe Sij νe ¼ C S Δ
2. Problem formulation 2.1. Numerical model for urban wind For the LES analysis of the specified building in the city, it is important to resolve the flow around the building and its near region or the urban area consisting of many other buildings. According to the prediction of wind velocity, it is not so significant to reproduce the precise shape of the building because local small eddies do not change the essential properties of urban canopy flows. The Cartesian grid method with higher-order accurate scheme has been applied to this problem. Fig. 1 illustrates the numerical model for urban wind (Cartesian grid). This model consists of two driver regions (Domain1 and Domain2) for the approaching turbulent flow. Domain1 is for generating the turbulent boundary layer over rough surface by the rescaling technique (Lund et al. 1998) (Nozawa and Tamura, 2002). Domain2 is for arranging the boundary layer so that it can develop along the fetch on the urban roughness and for stabilizing the turbulent structures over the urban type of the area. This numerical model has one more driver region – Domain3 (main region), which is used for the flow over an actual urban area and the boundary shape at the ground, and building surfaces are set by geographic information system (GIS) data. The domain size of Domain3 is 2.40 km x 1.08 km x 1.28 km, with uniform grid resolution of 4.0 m in the horizontal direction and the stretching grid upward with sufficiently fine grid near the ground. Therefore, the building shapes are represented by discretizing the building width with several ten
2
2Sij Sij 1 ∂ui ∂uj Sij ¼ þ 2 ∂xj ∂xi
1=2
where δij is the Kronecker delta and C S is the Smagorinsky constant. The value of C S is set to be 0.10. The coupling algorithm of the velocity and pressure fields is based on the marker-and-cell method (MAC) method, with the Adams–Bashforth scheme for time integration. For the spatial discretization in the governing equation of the flow field, variables such as velocity and pressure are defined by the staggered mesh method, and the fourth-order accurate central difference and interpolation schemes are employed for the convection terms (Kajishima, 1993). For the near-ground region, van Driest damping function is used in relation to the wall normal distance to the nearest ground surface. 2.2. Combined model We have applied the combined model (Tamura and Nozu, 2012) to predict the wind pressures and forces on the specified building in the city. On the basis of the mesh-adaptive concept, the combined model consists of an outer area, which is discretized by the Cartesian grid to obtain the appropriate turbulent structure without numerical damping in time and space over roughened urban surface, and an inner area, which represents the complexity of urban geometry including the buildings and houses. Fig. 2 illustrates the combined model, in which the area including the specified building and its surroundings are clipped for the unstructured grid area obtained by the mesh generation software
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T. Nozu et al. / J. Wind Eng. Ind. Aerodyn. 144 (2015) 62–69
Target building
Overset grid Cartesian grid
Unstructured grid
Δx=2m
Δx=1m
Δx=4m
Δx=1m
Δx=4m
y
Δx=2m
x Fig. 2. Combined model on the specified building in the city. (a) Combined model for the area including the specified building and its surroundings. (b) Calculation grid of unstructured grid area.
Cartesian grid Unstructured grid Fig. 3. Instantaneous wind velocity field on Cartesian grid and unstructured grid.
(SnappyHex). The domain size of the unstructured grid area is 1.4 km x 0.7 km x 0.6 km. The utility generates three-dimensional (3D) meshes containing hexahedra and split hexahedra, which is refined near the target building and ground surface with the grid resolution between 1 m and 16 m in the horizontal direction. It can be confirmed that the complicated configurations of buildings are correctly reproduced. On the inflow boundary condition of the unstructured grid area, turbulent flow is given by one-way method, which is obtained using LES on the Cartesian coordinate grid system, as shown in Fig. 1. The simulation of the unstructured grid area is carried out using OpenFOAM (Ver. 1.7.1), which is widely used as an open-source code, on a shared-memory type workstation with 12 CPU cores. The target city has the aspect with widespread layout of high-rise buildings, including the specified tall
building (target building in Fig. 2). The calculated wind direction is northwest (NW), which is slightly inclined to the main streets. For representation of actual buildings in the city, we used two different GIS data for the urban area (Cartesian grid domain) and the near region of the target building (unstructured grid domain). Therefore, the building configurations at the leeward region are slightly different from each other, but this difference does not affect the computational results around the specified building at all. OpenFOAM uses the finite volume method to solve the systems of partial differential equations ascribed on any 3D unstructured grid. The temporal term of the governing equations is treated by using the Crank-Nicolson scheme, which is the second-order difference in time. Other terms of the governing equations are
T. Nozu et al. / J. Wind Eng. Ind. Aerodyn. 144 (2015) 62–69
discretized using the second-order limited central difference. The governing equations are solved sequentially using the resulting Pressure-Implicit Splitting Operation (PISO) algorithm. The solution is performed implicitly by matrix inversion using the incomplete Cholesky conjugate gradient method. The standard Smagorinsky model is applied for turbulence modeling.
3. Wind velocity field on the Cartesian grid domain and unstructured grid domain Fig. 3 depicts the LES results for the instantaneous wind velocity distributions among the densely arrayed tall buildings on the Cartesian grid area and unstructured grid area. It can be recognized that the flow with fully developed turbulence comes from the inflow boundary (driver region) into the main region on the Cartesian grid. Furthermore, it can be confirmed that the turbulent structures flow into the unstructured grid domain from the Cartesian grid domain. At the inflow boundary of the unstructured grid domain, the reverse flows occur in several areas in consequence of the buildings’ wake flow, but LES could be performed without any trouble. In addition, although we use different algorithm in each domain, a numerical instability in the unstructured domain does not occur because of using the one-way method. Fig. 4 indicates the power spectra and time histories of wind velocity on the Cartesian grid and the unstructured grid. The time series have been sampled at 650 m windward of the target building. In a previous study, the authors confirmed that LES on the Cartesian grid system could reproduce the flow patterns and the turbulent structures in the wake region of high-rise buildings measured by digital particle image velocimetry (DPIV) experiment (Nozu and Tamura, 2012). As the effect of numerical dissipation is ambiguous for the unstructured grid system of OpenFOAM, the results on the unstructured grid system are compared with the results on the Cartesian grid system with sufficient accuracy under the same computational conditions as in the previous case. It can be found that the high-frequency energy of the unstructured grid is a little lower than that of the Cartesian grid, whereas the lowfrequency energy of the unstructured grid corresponds to that of the Cartesian grid. The reason is that we apply the higher-order accurate scheme on the Cartesian grid in spite of using the same resolution grid at the measurement point (at 650 m windward of the target building) in each calculation domain (Cartesian grid
65
area and unstructured grid area). However, in terms of time history of wind velocity, the difference between the Cartesian grid area and unstructured grid area cannot be found. Fig. 5 shows the LES results for flow patterns obtained by using the unstructured grid system embedded in the near region of the specified building. It can be found that the finer mesh of the unstructured grid in the limited area around the specified building can reproduce the fine turbulent structures as well as the shape of the complicated building. On the other hand, the vortex structures in the coarse-mesh region away from the specified building become smoother and dissipative compared with those in the fine-mesh region. Fig. 6 represents the time-averaged streamlines and timeaveraged wind velocity contours around the specified building. In the higher region around the building, the streamlines go straight along the inflow wind direction. On the other hand, in the lower region, the streamlines are bent depending on the flow into the main street in front of the specified building. Therefore, it can be recognized that the wake at the 66-m height of the specified building has different pattern from that at the 143-m height because of a vertical change of a local wind direction.
4. Comparison with the wind tunnel test 4.1. Wind tunnel test Fluctuating pressures acting on a tall building were measured in wind tunnel experiments. The wind pressure model of the target building used in the experiments had a width of 135 mm, a depth of 107 mm, and a height of 360 mm. The geometric scale was 1/500. A total of 250 wind pressure measurement points were arranged on the building surface. Fluctuating wind pressures were measured simultaneously at all the 250 points sampled at 800 Hz. Wind forces were calculated by integration of the surface pressures. With regard to the oncoming flow in the experiments, the power exponent αof the vertical profile for the mean wind speed was 0.27 and the turbulence intensity I uH at the building height was about 12%. The wind speed at the building height was set at U H ¼ 6.4 m/s.
Cartesian grid
1.5
0
-1
1.0 0.5 0.0 700
nS(n)/σ 2
10
Velocity (-)
10
800
900
1000
1100
1200
time(s)
Cartesian grid -2
Velocity (-)
10
Cartesian grid Unstructured grid 10
Unstructured grid
1.5
-3 -2
10
-1
10
10 nLx/U
0
1
10
1.0 0.5 0.0 700
800
900
1000
1100
1200
time(s)
Unstructured grid
Fig. 4. Power spectra and time histories of wind velocity on Cartesian grid and unstructured grid. (a) Power spectra. (b) Time histories of wind velocity.
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T. Nozu et al. / J. Wind Eng. Ind. Aerodyn. 144 (2015) 62–69
Fig. 5. LES result obtained by using the unstructured grid system embedded in the region of the specified building.
z=143m
z=66m
Target building Fig. 6. Computed averaged stream lines and time-averaged velocity fields around the specified building (a) stream lines, and (b) wind velocity contours.
The measured pressures were expressed in dimensionless form by pressure coefficient C p C p ¼ p ps = 1=2ρU 2H where p, pS , and ρ stand for the measured pressure, static pressure, and air density, respectively. 4.2. Wind pressures for wind load estimation Fig. 7 illustrates the comparison of mean wind pressure coefficients of the target building between LES results (LES) and experimental results (Exp.). It can be confirmed that there are two stagnation points at the edges on the north and west surfaces because the approaching flow comes into the building at an angle of almost 45 degrees. As the central part of the north surface is pulled out forward and the local flow leads to slightly separated or almost attached flow pattern from the corner of this pulled part, the pressure coefficients have very small values at the surface of the pulled part. Therefore, the pressure distribution of LES has unsymmetrical shape on the north and west surfaces, and this
tendency is in good agreement with experimental data. Moreover, it can be found that the pressure coefficients at the central position on the north surface at the height of 143 m have small positive values and those at the height of 66 m have small negative values (Fig. 7(b)). This tendency is consistent with the changing pattern of a wind direction in the vertical direction. In short, the flow at the height of 66 m completely separates at the northpulled part because of a variation in the local wind direction due to flow penetrating into the main street (Fig. 6). Fig. 8 illustrates the comparison of root mean square (RMS) wind pressure coefficients of the building between LES results (LES) and experimental results (Exp.). According to the experimental results, it can be confirmed that RMS values become larger near the corner on the north and west surfaces of the building because the approaching wind flows with inclined angle to the building. Particularly, the largevalue area appears near the corner on the central part of the north surface. On the other hand, the LES results can reproduce the large value near the corner on the north and west surfaces, but cannot reproduce that near the corner on the central part of the north surface. In this region, it is found that the grid resolution is not enough because the separating shear layer is close to the building surface (Fig. 6(b)).
T. Nozu et al. / J. Wind Eng. Ind. Aerodyn. 144 (2015) 62–69
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Fig. 7. Distributions of the computed and experimental mean pressure coefficients at each height on the specified building.
Fig. 8. Distributions of the computed and experimental RMS pressure coefficients at each height on the specified building.
Fig. 9 indicates the correlations between the wind pressure coefficients of experimental results and those of LES results obtained at the measurement points on the building surfaces. In regard to the correlations of the mean and maximum values, the LES results agree very well with the experimental results. However, in regard to those of RMS and minimum values, there are some points where the LES results do not correspond to the
experimental results. These points are located near the corner on the central part of the north surface. Fig. 10 represents the vertical profiles of the wind force coefficients of the experimental results and those of the LES results. It can be found that the profile characteristics of the mean wind force coefficients in the x-direction of the building axis change approximately at the height of 80 m. This height almost coincides with the height of the surrounding buildings. Therefore, we can assume that
T. Nozu et al. / J. Wind Eng. Ind. Aerodyn. 144 (2015) 62–69
ave_315_820s_rev
1.0
Exp.
Exp.
0.0
0.3
max_315_820s_rev
2.0
0.4
0.5
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rms_315_820s_rev
0.5
min_315_820s_rev
1.0
1.5
0.5
1.0
0.0 Exp.
68
0.5
-0.5
0.2 -0.5
-1.0 -1.0
0.1
-0.5
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0.0 0.0
0.1
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0.4
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-1.0
-0.5
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LES
1.0
1.5
-2.0 -2.0 -1.5 -1.0 -0.5 0.0
2.0
0.5
1.0
LES
LES
Fig. 9. Correlations between the pressure coefficients of experimental results and those of LES results (a) mean value, (b) RMS value, (c) maximum value .and (d) minimum value.
150
125
125
height(m)
height(m)
150
100 75
100 75 50
50 25
920s_rev
175
920s_rev
175
ave(Exp.) rms(Exp.)
0 -1
-0.5
25
ave(LES) rms(LES) 0
ave(Exp.) rms(Exp.)
0 -0.5
0.5
0
ave(LES) rms(LES) 0.5
1
CFyave, CFyrms
CFxave, CFxrms
Fig. 10. Vertical profiles of computed and experimental wind force coefficients at each height (a) x-direction, and (b) y-direction.
0
10
-1
10
-2
10
-3
10
fScfx, fScfy
fScfx, fScfy
10
0
10
-1
10
-2
10
-3
Cfx Cfy 10
Cfx Cfy
-4
10
-2
-1
10
0
10
fD/U
10
-4
10
-2
-1
10
0
10
fD/U
Fig. 11. Power spectra of wind force coefficients of the building obtained by LES (a) z¼ 143m, and (b) z¼ 66m.
the local wind direction around the specified building varies at this height. On the whole, it can be recognized that LES results are in good agreement with the experimental results.
Fig. 11 illustrates the power spectra of wind force coefficients on the building obtained by LES. It can be confirmed that the energy around the Strouhal frequency in the y-direction is higher than that in the x-direction at the height of 143 m and lower than
T. Nozu et al. / J. Wind Eng. Ind. Aerodyn. 144 (2015) 62–69
that in the x-direction at the height of 66 m. These tendencies can be explained by the wake position behind the target building at every height. 5. Conclusions We have applied the combined model consisting of the Cartesian grid and the unstructured grid to the wind load estimation of a high-rise building in a city at inclined wind direction to the main streets and confirmed the accuracy of the LES results. We can demonstrate that the mesh-adaptive concept has an advantage for the LES prediction of the complicated flows around buildings and houses in a city. The conclusions of this study can be summarized as follows: (1) On the basis of the LES method using the numerical model overlaid by the unstructured grid system, the appropriate turbulent structures at inflow and among a pack of tall buildings can be simulated. Moreover, we have confirmed that regarding wind velocity fluctuations on the unstructured grid area with sufficient grid resolution, the appropriate time histories and power spectra can be reproduced without excessive damping of high-frequency energy. (2) In urban areas, surrounding buildings around a target building have the potential for causing a vertical change to a local wind direction. However, it is confirmed that we can accurately calculate the wind pressure distributions on a high-rise building at inclined wind direction to the main streets by using the unstructured grid system embedded in the near region of the building. (3) The present LES results cannot reproduce completely large RMS values at a limited location where the separating shear
69
layer approaches close to the building surface due to the local change of the oncoming flow direction. This inconsistency is because of the insufficient grid resolution, and the demand of a grid resolution becomes more severe inside and around these areas where the wind flow is much affected by the surrounding obstacles.
References Blocken, B., Roels, S., Charmeliet, J., 2004. Modification of pedestrian wind comfort in the Silvertop Tower passages by an automatic control system. J. Wind Eng. Ind. Aerodyn. 92, 849–873. Blocken, B., Persoon, J., 2009. Pedestrian wind comfort around a large football stadium in an urban environment: CFD simulation, validation and application of the new Dutch wind nuisance standard. J. Wind Eng. Ind. Aerodyn. 97 (5-6), 255–270. Nozawa, K., Tamura, T, 2002. Large eddy simulation of the flow around a low-rise building in a rough-wall turbulent boundary layer OpenFOAM. J. Wind Eng. Ind. Aerodyn. 90, 1151–1162. Yoshie, R., Mochida, A., Tominaga, Y., Kataoka, H., Harimoto, K., Nozu, T., Shirasawa, T., 2007. Cooperative project for CFD prediction of pedestrian wind environment in the Architectural Institute of Japan. Journal of Wind Engineering and Industrial Aerodynamics 95 (9-11), 1551–1578. Kajishima, T., 1993. A Higher-Order Finite Difference Methods for Wall-Bounded Incompressible flows. Proceedings of the Fifth International Symposium on Computational Fluid Dynamics 1, 414–419. Lund, T., Wu, X., Squires, D., 1998. Generation of turbulent inflow data for spatially developing boundary layer simulation. Journal of Computational Physics 140, 233–258. Nozu, T., Tamura, T., 2012. LES of turbulent wind and gas dispersion in a city. J. Wind Eng. Ind. Aerodyn. 104-106, 492–499. T. Tamura, Y. Okuda, T. Kishida, O. Nakamura, K. Miyashita, A. Katsumura, M. Tamari, 2010. LES for aerodynamic characteristics of a tall building inside a dense city district, CWE2010. T. Tamura, T. Nozu, 2012. Introduction of unstructured-grid system on LES for wind pressure estimation on a building in cities, BBAA7.
Contents lists available at ScienceDirect
Journal of Wind Engineering and Industrial Aerodynamics journal homepage: www.elsevier.com/locate/jweia
Mesh-adaptive LES for wind load estimation of a high-rise building in a city Tsuyoshi Nozu a, Tetsuro Tamura b, Kishida Takeshi c, Katsumura Akira c a
Institute of Technology, Shimizu Corporation, 3-4-17 Etchujima, Koto-ku, Tokyo, Japan Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama, Japan c Wind engineering Institute, Co., Ltd, 3-29 Kanda-Jinbocho, Chiyoda-ku, Tokyo, Japan b
art ic l e i nf o
Keywords: LES Urban canopy Wind pressure coefficient Turbulent structure Wind load estimation
a b s t r a c t This paper discusses the applicability of large eddy simulation (LES) to the wind-resistant design of buildings in cities. In order to accurately predict wind pressures and forces on actual buildings with complicated shapes, we partially introduce the unstructured grid system, which is formulated on the open-source CFD code. Applying the LES method for modeling the urban flow, where a specified highrise building focuses on safety under wind loading, the combined model is employed to investigate aerodynamic characteristics. This model uses overset grids, consisting of the Cartesian grid and the unstructured-grids. According to previous studies, the Cartesian grid method can accurately generate the turbulent structures in the urban canopy, whereas the unstructured grid method can reproduce detailed patterns of the near-wake flows around a specified building inside a densely built-up area. In this study, we have applied the combined model consisting of the Cartesian grid and unstructured grid for wind load estimation of a high-rise building in a city. Particularly, at inclined wind direction to the main streets, there is a presumption of different effects of wind impact at each vertical level of a high-rise building along the street. Accordingly, relatively a large torsional force tends to be present. On the basis of the results obtained, their accuracy is checked in comparison with the previous data by wind tunnel experiment, and wind pressure distributions on the surfaces as well as wind force coefficients of a highrise building are estimated and discussed in view of structural safety. & 2015 Elsevier Ltd. All rights reserved.
1. Introduction To date, urban winds have often been simulated by the Reynolds-averaged Navier–Stokes (RANS) model from an environmental point of view, wherein the average wind velocity prediction is essential. The RANS model generally shows good performance (Blocken et al., 2004) (Yoshie et al., 2007) (Blocken and Persoon, 2009). Applying the large eddy simulation (LES) for modeling the urban wind, the Cartesian grid system is mainly employed, and its accuracy is generally good enough for the wind velocity prediction. However, in previous studies, the grid resolution could not accurately represent the actual building shape, but we have shown the success of the LES prediction for the flow field. Accordingly, the Cartesian grid-based method, in spite of including main streets in a direction different from wind or grid line, can simulate the gap flows among the buildings and transport phenomena of mass and gas in cities (Tamura et al., 2010) (Nozu and Tamura, 2012). However, the predictive accuracy of the abovementioned method is ambiguous for the estimation of the wind pressures and forces on a specified building in a city. Particularly, in order to deal with the wind-resistant design for a high-rise http://dx.doi.org/10.1016/j.jweia.2015.05.007 0167-6105/& 2015 Elsevier Ltd. All rights reserved.
building in a city, the numerical model must reproduce not only the approaching flow to the urban area but also the flow around a target building and surrounding buildings with a high degree of accuracy. Therefore, we have introduced the combined model with finer mesh for the near region of the specified building by employing the unstructured grid system, which is formulated on the open-source code OpenFOAM. The present method consists of the Cartesian structured grid for accurately reproducing the turbulent structures in the urban canopy and the unstructured grid for resolving the exact wake patterns around the specified building inside the densely built-up area. The authors realized the accurate aerodynamic prediction of a high-rise building in a city at wind direction parallel to the main streets by LES (Tamura et al., 2012). However, in order to assure the establishment of LES prediction for the wind-resistant design of a building, we must validate the LES model for various wind directions of an approaching flow. In this study, we have applied the LES method for the wind load estimation of a high-rise building in a city at inclined wind direction to the main streets. In this situation, the flows are sensitively deformed within the urban canopy; accordingly, the
T. Nozu et al. / J. Wind Eng. Ind. Aerodyn. 144 (2015) 62–69
63
Domain2 (for developing TBL)
Driver region Domain3 (Main region)
Domain1 (for turbulence generation) 1280m
z
y
2400m
x
1080m
Fig. 1. Numerical model for urban wind on Cartesian grid.
Table 1 The number of grid points for each Cartesian domains. Streamwise(x) Domain 1 Grid points
156
Domain 2 þ 151
Spanwise (y)
Vertical (z)
270
100
Domain 3 þ 600
achievement of appropriate numerical discretization and wellbalanced model construction becomes very difficult. There is a possibility of an extreme local pressure peak due to the unexpected behavior of the separated shear layer. We have also confirmed the accuracy of the calculation results in comparison with the previous experimental data. On the basis of the computed results, wind pressure distributions on the surfaces as well as wind force coefficients of high-rise buildings are estimated and discussed in view of structural safety.
grid points. Table 1 shows the number of grid points for each Cartesian domain. The governing equations for the LES model are the filtered forms for continuity and the incompressible Navier–Stokes, which are as follows: ∂ui ¼0 ∂xi ∂ui ∂u ∂p ∂ þuj i ¼ þ τij þ 2νSij ∂xi ∂xj ∂t ∂xj where ui , p, τij , and ν stand for filtered velocity, filtered pressure, sub-grid scale (SGS) Reynolds stress ðui uj ui uj Þ, and molecular viscosity coefficient, respectively. The overbar indicates spatial filtering. Concerning the sub-grid scale modeling, the Smagorinsky-type eddy viscosity model is employed for representing the flow. The turbulent eddy viscosity coefficient νe can be estimated by the constant C S , the filter size Δ, and the strain velocity tensor Sij as follows: 1 3
τij δij τkk ¼ 2νe Sij νe ¼ C S Δ
2. Problem formulation 2.1. Numerical model for urban wind For the LES analysis of the specified building in the city, it is important to resolve the flow around the building and its near region or the urban area consisting of many other buildings. According to the prediction of wind velocity, it is not so significant to reproduce the precise shape of the building because local small eddies do not change the essential properties of urban canopy flows. The Cartesian grid method with higher-order accurate scheme has been applied to this problem. Fig. 1 illustrates the numerical model for urban wind (Cartesian grid). This model consists of two driver regions (Domain1 and Domain2) for the approaching turbulent flow. Domain1 is for generating the turbulent boundary layer over rough surface by the rescaling technique (Lund et al. 1998) (Nozawa and Tamura, 2002). Domain2 is for arranging the boundary layer so that it can develop along the fetch on the urban roughness and for stabilizing the turbulent structures over the urban type of the area. This numerical model has one more driver region – Domain3 (main region), which is used for the flow over an actual urban area and the boundary shape at the ground, and building surfaces are set by geographic information system (GIS) data. The domain size of Domain3 is 2.40 km x 1.08 km x 1.28 km, with uniform grid resolution of 4.0 m in the horizontal direction and the stretching grid upward with sufficiently fine grid near the ground. Therefore, the building shapes are represented by discretizing the building width with several ten
2
2Sij Sij 1 ∂ui ∂uj Sij ¼ þ 2 ∂xj ∂xi
1=2
where δij is the Kronecker delta and C S is the Smagorinsky constant. The value of C S is set to be 0.10. The coupling algorithm of the velocity and pressure fields is based on the marker-and-cell method (MAC) method, with the Adams–Bashforth scheme for time integration. For the spatial discretization in the governing equation of the flow field, variables such as velocity and pressure are defined by the staggered mesh method, and the fourth-order accurate central difference and interpolation schemes are employed for the convection terms (Kajishima, 1993). For the near-ground region, van Driest damping function is used in relation to the wall normal distance to the nearest ground surface. 2.2. Combined model We have applied the combined model (Tamura and Nozu, 2012) to predict the wind pressures and forces on the specified building in the city. On the basis of the mesh-adaptive concept, the combined model consists of an outer area, which is discretized by the Cartesian grid to obtain the appropriate turbulent structure without numerical damping in time and space over roughened urban surface, and an inner area, which represents the complexity of urban geometry including the buildings and houses. Fig. 2 illustrates the combined model, in which the area including the specified building and its surroundings are clipped for the unstructured grid area obtained by the mesh generation software
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Target building
Overset grid Cartesian grid
Unstructured grid
Δx=2m
Δx=1m
Δx=4m
Δx=1m
Δx=4m
y
Δx=2m
x Fig. 2. Combined model on the specified building in the city. (a) Combined model for the area including the specified building and its surroundings. (b) Calculation grid of unstructured grid area.
Cartesian grid Unstructured grid Fig. 3. Instantaneous wind velocity field on Cartesian grid and unstructured grid.
(SnappyHex). The domain size of the unstructured grid area is 1.4 km x 0.7 km x 0.6 km. The utility generates three-dimensional (3D) meshes containing hexahedra and split hexahedra, which is refined near the target building and ground surface with the grid resolution between 1 m and 16 m in the horizontal direction. It can be confirmed that the complicated configurations of buildings are correctly reproduced. On the inflow boundary condition of the unstructured grid area, turbulent flow is given by one-way method, which is obtained using LES on the Cartesian coordinate grid system, as shown in Fig. 1. The simulation of the unstructured grid area is carried out using OpenFOAM (Ver. 1.7.1), which is widely used as an open-source code, on a shared-memory type workstation with 12 CPU cores. The target city has the aspect with widespread layout of high-rise buildings, including the specified tall
building (target building in Fig. 2). The calculated wind direction is northwest (NW), which is slightly inclined to the main streets. For representation of actual buildings in the city, we used two different GIS data for the urban area (Cartesian grid domain) and the near region of the target building (unstructured grid domain). Therefore, the building configurations at the leeward region are slightly different from each other, but this difference does not affect the computational results around the specified building at all. OpenFOAM uses the finite volume method to solve the systems of partial differential equations ascribed on any 3D unstructured grid. The temporal term of the governing equations is treated by using the Crank-Nicolson scheme, which is the second-order difference in time. Other terms of the governing equations are
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discretized using the second-order limited central difference. The governing equations are solved sequentially using the resulting Pressure-Implicit Splitting Operation (PISO) algorithm. The solution is performed implicitly by matrix inversion using the incomplete Cholesky conjugate gradient method. The standard Smagorinsky model is applied for turbulence modeling.
3. Wind velocity field on the Cartesian grid domain and unstructured grid domain Fig. 3 depicts the LES results for the instantaneous wind velocity distributions among the densely arrayed tall buildings on the Cartesian grid area and unstructured grid area. It can be recognized that the flow with fully developed turbulence comes from the inflow boundary (driver region) into the main region on the Cartesian grid. Furthermore, it can be confirmed that the turbulent structures flow into the unstructured grid domain from the Cartesian grid domain. At the inflow boundary of the unstructured grid domain, the reverse flows occur in several areas in consequence of the buildings’ wake flow, but LES could be performed without any trouble. In addition, although we use different algorithm in each domain, a numerical instability in the unstructured domain does not occur because of using the one-way method. Fig. 4 indicates the power spectra and time histories of wind velocity on the Cartesian grid and the unstructured grid. The time series have been sampled at 650 m windward of the target building. In a previous study, the authors confirmed that LES on the Cartesian grid system could reproduce the flow patterns and the turbulent structures in the wake region of high-rise buildings measured by digital particle image velocimetry (DPIV) experiment (Nozu and Tamura, 2012). As the effect of numerical dissipation is ambiguous for the unstructured grid system of OpenFOAM, the results on the unstructured grid system are compared with the results on the Cartesian grid system with sufficient accuracy under the same computational conditions as in the previous case. It can be found that the high-frequency energy of the unstructured grid is a little lower than that of the Cartesian grid, whereas the lowfrequency energy of the unstructured grid corresponds to that of the Cartesian grid. The reason is that we apply the higher-order accurate scheme on the Cartesian grid in spite of using the same resolution grid at the measurement point (at 650 m windward of the target building) in each calculation domain (Cartesian grid
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area and unstructured grid area). However, in terms of time history of wind velocity, the difference between the Cartesian grid area and unstructured grid area cannot be found. Fig. 5 shows the LES results for flow patterns obtained by using the unstructured grid system embedded in the near region of the specified building. It can be found that the finer mesh of the unstructured grid in the limited area around the specified building can reproduce the fine turbulent structures as well as the shape of the complicated building. On the other hand, the vortex structures in the coarse-mesh region away from the specified building become smoother and dissipative compared with those in the fine-mesh region. Fig. 6 represents the time-averaged streamlines and timeaveraged wind velocity contours around the specified building. In the higher region around the building, the streamlines go straight along the inflow wind direction. On the other hand, in the lower region, the streamlines are bent depending on the flow into the main street in front of the specified building. Therefore, it can be recognized that the wake at the 66-m height of the specified building has different pattern from that at the 143-m height because of a vertical change of a local wind direction.
4. Comparison with the wind tunnel test 4.1. Wind tunnel test Fluctuating pressures acting on a tall building were measured in wind tunnel experiments. The wind pressure model of the target building used in the experiments had a width of 135 mm, a depth of 107 mm, and a height of 360 mm. The geometric scale was 1/500. A total of 250 wind pressure measurement points were arranged on the building surface. Fluctuating wind pressures were measured simultaneously at all the 250 points sampled at 800 Hz. Wind forces were calculated by integration of the surface pressures. With regard to the oncoming flow in the experiments, the power exponent αof the vertical profile for the mean wind speed was 0.27 and the turbulence intensity I uH at the building height was about 12%. The wind speed at the building height was set at U H ¼ 6.4 m/s.
Cartesian grid
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Fig. 4. Power spectra and time histories of wind velocity on Cartesian grid and unstructured grid. (a) Power spectra. (b) Time histories of wind velocity.
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Fig. 5. LES result obtained by using the unstructured grid system embedded in the region of the specified building.
z=143m
z=66m
Target building Fig. 6. Computed averaged stream lines and time-averaged velocity fields around the specified building (a) stream lines, and (b) wind velocity contours.
The measured pressures were expressed in dimensionless form by pressure coefficient C p C p ¼ p ps = 1=2ρU 2H where p, pS , and ρ stand for the measured pressure, static pressure, and air density, respectively. 4.2. Wind pressures for wind load estimation Fig. 7 illustrates the comparison of mean wind pressure coefficients of the target building between LES results (LES) and experimental results (Exp.). It can be confirmed that there are two stagnation points at the edges on the north and west surfaces because the approaching flow comes into the building at an angle of almost 45 degrees. As the central part of the north surface is pulled out forward and the local flow leads to slightly separated or almost attached flow pattern from the corner of this pulled part, the pressure coefficients have very small values at the surface of the pulled part. Therefore, the pressure distribution of LES has unsymmetrical shape on the north and west surfaces, and this
tendency is in good agreement with experimental data. Moreover, it can be found that the pressure coefficients at the central position on the north surface at the height of 143 m have small positive values and those at the height of 66 m have small negative values (Fig. 7(b)). This tendency is consistent with the changing pattern of a wind direction in the vertical direction. In short, the flow at the height of 66 m completely separates at the northpulled part because of a variation in the local wind direction due to flow penetrating into the main street (Fig. 6). Fig. 8 illustrates the comparison of root mean square (RMS) wind pressure coefficients of the building between LES results (LES) and experimental results (Exp.). According to the experimental results, it can be confirmed that RMS values become larger near the corner on the north and west surfaces of the building because the approaching wind flows with inclined angle to the building. Particularly, the largevalue area appears near the corner on the central part of the north surface. On the other hand, the LES results can reproduce the large value near the corner on the north and west surfaces, but cannot reproduce that near the corner on the central part of the north surface. In this region, it is found that the grid resolution is not enough because the separating shear layer is close to the building surface (Fig. 6(b)).
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Fig. 7. Distributions of the computed and experimental mean pressure coefficients at each height on the specified building.
Fig. 8. Distributions of the computed and experimental RMS pressure coefficients at each height on the specified building.
Fig. 9 indicates the correlations between the wind pressure coefficients of experimental results and those of LES results obtained at the measurement points on the building surfaces. In regard to the correlations of the mean and maximum values, the LES results agree very well with the experimental results. However, in regard to those of RMS and minimum values, there are some points where the LES results do not correspond to the
experimental results. These points are located near the corner on the central part of the north surface. Fig. 10 represents the vertical profiles of the wind force coefficients of the experimental results and those of the LES results. It can be found that the profile characteristics of the mean wind force coefficients in the x-direction of the building axis change approximately at the height of 80 m. This height almost coincides with the height of the surrounding buildings. Therefore, we can assume that
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Fig. 9. Correlations between the pressure coefficients of experimental results and those of LES results (a) mean value, (b) RMS value, (c) maximum value .and (d) minimum value.
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Fig. 10. Vertical profiles of computed and experimental wind force coefficients at each height (a) x-direction, and (b) y-direction.
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Fig. 11. Power spectra of wind force coefficients of the building obtained by LES (a) z¼ 143m, and (b) z¼ 66m.
the local wind direction around the specified building varies at this height. On the whole, it can be recognized that LES results are in good agreement with the experimental results.
Fig. 11 illustrates the power spectra of wind force coefficients on the building obtained by LES. It can be confirmed that the energy around the Strouhal frequency in the y-direction is higher than that in the x-direction at the height of 143 m and lower than
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that in the x-direction at the height of 66 m. These tendencies can be explained by the wake position behind the target building at every height. 5. Conclusions We have applied the combined model consisting of the Cartesian grid and the unstructured grid to the wind load estimation of a high-rise building in a city at inclined wind direction to the main streets and confirmed the accuracy of the LES results. We can demonstrate that the mesh-adaptive concept has an advantage for the LES prediction of the complicated flows around buildings and houses in a city. The conclusions of this study can be summarized as follows: (1) On the basis of the LES method using the numerical model overlaid by the unstructured grid system, the appropriate turbulent structures at inflow and among a pack of tall buildings can be simulated. Moreover, we have confirmed that regarding wind velocity fluctuations on the unstructured grid area with sufficient grid resolution, the appropriate time histories and power spectra can be reproduced without excessive damping of high-frequency energy. (2) In urban areas, surrounding buildings around a target building have the potential for causing a vertical change to a local wind direction. However, it is confirmed that we can accurately calculate the wind pressure distributions on a high-rise building at inclined wind direction to the main streets by using the unstructured grid system embedded in the near region of the building. (3) The present LES results cannot reproduce completely large RMS values at a limited location where the separating shear
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layer approaches close to the building surface due to the local change of the oncoming flow direction. This inconsistency is because of the insufficient grid resolution, and the demand of a grid resolution becomes more severe inside and around these areas where the wind flow is much affected by the surrounding obstacles.
References Blocken, B., Roels, S., Charmeliet, J., 2004. Modification of pedestrian wind comfort in the Silvertop Tower passages by an automatic control system. J. Wind Eng. Ind. Aerodyn. 92, 849–873. Blocken, B., Persoon, J., 2009. Pedestrian wind comfort around a large football stadium in an urban environment: CFD simulation, validation and application of the new Dutch wind nuisance standard. J. Wind Eng. Ind. Aerodyn. 97 (5-6), 255–270. Nozawa, K., Tamura, T, 2002. Large eddy simulation of the flow around a low-rise building in a rough-wall turbulent boundary layer OpenFOAM. J. Wind Eng. Ind. Aerodyn. 90, 1151–1162. Yoshie, R., Mochida, A., Tominaga, Y., Kataoka, H., Harimoto, K., Nozu, T., Shirasawa, T., 2007. Cooperative project for CFD prediction of pedestrian wind environment in the Architectural Institute of Japan. Journal of Wind Engineering and Industrial Aerodynamics 95 (9-11), 1551–1578. Kajishima, T., 1993. A Higher-Order Finite Difference Methods for Wall-Bounded Incompressible flows. Proceedings of the Fifth International Symposium on Computational Fluid Dynamics 1, 414–419. Lund, T., Wu, X., Squires, D., 1998. Generation of turbulent inflow data for spatially developing boundary layer simulation. Journal of Computational Physics 140, 233–258. Nozu, T., Tamura, T., 2012. LES of turbulent wind and gas dispersion in a city. J. Wind Eng. Ind. Aerodyn. 104-106, 492–499. T. Tamura, Y. Okuda, T. Kishida, O. Nakamura, K. Miyashita, A. Katsumura, M. Tamari, 2010. LES for aerodynamic characteristics of a tall building inside a dense city district, CWE2010. T. Tamura, T. Nozu, 2012. Introduction of unstructured-grid system on LES for wind pressure estimation on a building in cities, BBAA7.