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Detached-eddy and large-eddy simulations of wind effects on a high-rise structure
Accepted Manuscript
Detached-eddy and large-eddy simulations of wind effects on a high-rise structure B.W. YAN , Q.S. LI PII: DOI: Reference:
S0045-7930(17)30054-3 10.1016/j.compfluid.2017.02.009 CAF 3398
To appear in:
Computers and Fluids
Received date: Revised date: Accepted date:
23 July 2014 9 February 2017 9 February 2017
Please cite this article as: B.W. YAN , Q.S. LI , Detached-eddy and large-eddy simulations of wind effects on a high-rise structure, Computers and Fluids (2017), doi: 10.1016/j.compfluid.2017.02.009
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Highlight Carry out a combined wind tunnel test and CFD study on the wind effects on an elliptical cylinder
Investigate the surface roughness effects on the wind loading of an elliptical cylinder using DES
DES and LES models and numerical treatments adopted in this study can provide reasonably good correspondence with wind tunnel tests
DES model can reproduce the effects of surface roughness effects on the wind loading with the modified wall function
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Detached-eddy and large-eddy simulations of wind effects on a high-rise structure B.W. YANa,b, Q.S. LIb,* School of Civil Engineering, Chongqing University, Chongqing 400045, China a
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a
Dept. of Architecture and Civil Engineering, City University of Hong Kong, Kowloon, Hong Kong
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*Corresponding Author: [email protected]
Abstract
In this study, detached-eddy simulations (DES) and large-eddy simulations (LES)
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of wind effect on a high-rise structure with elliptical shape are performed. The aim of
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this study is to examine the accuracy of the numerical simulations for wind flow around a complex high-rise structure and investigate the effects of surface roughness
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on the wind loading. In order to reproduce appropriate inflow turbulence, the
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improved recycling method combined with the weighted amplitude wave
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superposition (WAWS) method is used to generate the inflow turbulence in the streamwise direction. Also, to study the surface roughness effects on the wind loading, the rough wall boundary conditions are adopted in the DES models. Typical results including the mean and fluctuating pressure coefficients, force spectra, Reynolds stresses and wind-induced top-floor response are obtained and compared with the 2
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corresponding wind tunnel experimental data. Through the cross-comparisons, the numerical results by the DES and LES models are found to be comparable with the experimental results. Additionally, the surface roughness effects on the wind loading is well reproduced with the DES models, such as the slow pressure recovery in the
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separation regions and the increased mean drag force coefficients. It is demonstrated through the validations that the DES and LES models and the numerical treatments adopted in this study can provide reasonably good results.
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Key words: Large-eddy simulation; Detached-eddy simulation; Elliptical cylinder; Surface roughness; Wind tunnel experiment
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1. Introduction
High-rise structures, such as chimneys, cooling towers and aero control towers,
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are usually built with circular and elliptical cross-sections, which are commonly
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slender, light-weighted and with low damping ratio. It is of significance to investigate the wind effects on these wind-sensitive structures for the wind-resistant design.
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Isyumov et al. (1984) presented an overview of the comprehensive wind tunnel study
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for a TV tower with a height of 555m (Toronto, Canada), in comparison with full-scale measurements. Kwok and Macdonald (1990) conducted an on-site measurement of the Sydney Tower and found that the wind-induced response was greatly reduced after installation of a tuned mass damper (TMD) system. Kareem et al. (1998) investigated the wind-induced response of Nanjing Tower with a height of 3
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310m numerically and experimentally. In fluids mechanics, the cross-flow around a circular or elliptical cylinder has been the subject of intense scrutiny. As is well known, the flow around a circular cylinder is dependent on Reynolds number, surface roughness, blockage, and
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free-stream turbulence (Simiu and Scanlan, 1996). Scruton (1971) revealed the dependence of drag force of a circular cylinder on the surface roughness through wind tunnel experiments for rough surface with sand and grain. For the effects of surface
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roughness on mean wind loading, Farell et al. (1976) measured the mean pressure distributions on a cooling tower model with different roughness configurations. Güven et al. (1980) used sandpaper to model rough wall of a circular cylinder in
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boundary wind tunnel laboratory and discussed the results together with previous measurements using the boundary layer theory. Through the experimental
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investigations, the base wind pressure was demonstrated to be independent of surface
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roughness, while the pressure differences between the minimum pressure and base pressure was closely related to the roughness, i.e. the surface roughness was inversely
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proportional pressure recovery. However, the experiments on the surface roughness
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were quite cumbersome and limited to a moderate Reynolds number (Re) range 7×104 and 5.5×105 (Güven et al., 1980) due to the spatial restriction in wind tunnel experiments. With the rapid development of improved turbulence models, numerical techniques and increasing computational power, numerical simulations of flow field 4
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around a circular cylinder have become feasible in the past decades. Catalano et al. (2003) examined the accuracy of LES for high-Reynolds number flow (0.5×106~2×106) around a circular cylinder and the wall boundary were modelled with a simple wall stress model. They suggested that the LES solutions were much
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more accurate than the RANS results and the mean pressure distribution was predicted reasonably well at high-Reynolds number. Breuer (2000) scrutinized the capabilities of LES for flow around a circular cylinder at supercritical regime and
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investigated the influences of two subgrid scale (SGS) models at different grids. The dynamic SGS model was shown to perform well for complex flow at high-Reynolds number, particularly in the near wake region. Travin et al. (2000) examined the applicability of Detached eddy simulation (DES) for transitional (Re=5×104 and
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1.4×105) and turbulent (Re=1.4×105 and 3×106) flows around a circular cylinder and
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the coefficients of pressure and drag force showed better agreement with the
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experimental results at medium refined grid than those at finest grid, while discrepancies existed for skin friction coefficients and wake statistics including
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Reynolds stresses and mean recirculation bubble. Squires et al. (2008) used the
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delayed detached eddy simulation (DDES) to predict the supercritical flow around a circular cylinder (Re=8×106) and the agreement with the basic DES is reasonably good for mean drag coefficient, Strouhal number, skin friction and separation angle. For flow around an elliptical cylinder, Mittal et al. (1996) studied the flow separation and wake structures using Direct Numerical Simulation (DNS). Li et al. (2005) 5
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investigated the effect of minor to major axis ratio on the drag and convective heat transfer with 2D unsteady k-ω SST model. To the best knowledge of the authors, there is still absence of studies on flow around an elliptical cylinder in supercritical and upper transition regimes, particularly
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for practical applications with high Reynolds number and effects of surface roughness on flows around an elliptical cylinder. Additionally, numerical simulations have the merits over the experimental measurements such as without limit of similarity criteria
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and “whole flow field data” (Blocken, 2014). Therefore, in this study, DES and LES of atmospheric boundary layer (ABL) flow around a high-rise structure with elliptical shape are performed at high Reynolds number (>106). The main purpose of this study
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is to assess the validity and accuracy of DES and LES for simulating the wind effects
the wind loading.
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on a complex high-rise structure and to investigate the effects of surface roughness on
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2. Details of the aero control tower
As shown in Fig. 1(a), the aero control tower is characterized by an elliptical
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cross section with the typical axis ratio of 1.35 and aspect ratio of 14. Moreover, the
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aero control tower consists of two parts which are the concrete shaft and control tower, and the architectural shape is similar to a golf club mounted on the ground. 1.1 Concrete shaft
The concrete shaft of the aero control tower is placed from height level of 0m to height of 84.45m, and the cross-section is typically elliptical along the height, with the 6
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dimensions of major axis (Ll) of 11.8 m and minor axis (Ls) of 6 m, respectively. 1.2 Control tower The control tower begins at the height level of 84.45 m and ends at the height level of 114 m. Although its cross-section is elliptical, the dimension varies gradually
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with height as shown in Fig. 1(a) which provides the architectural view of the aero control tower. The maximum major axis is of 29.2 m, while the minimum is of 20 m. 1.3 Dynamic characteristics
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Using the finite element model of the aero control tower, its dynamic characteristics are obtained through the modal analysis (Clough and Penzien, 2003) that the natural frequencies in the x-direction fx and in the y-direction fy are 0.225 Hz
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and 0.341 Hz, respectively. The damping ratio of the aero control tower is adopted as 2% in this study.
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3 METHODOLOGY
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3.1 Numerical simulation
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3.1.1 Computational domain and mesh scheme
As shown in Fig. 2(a), the computational domain covers 40Dy (Dy is the typical
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major axis of 11.6 m at the base of the structure) in the streamwise direction (-8
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inflow and outflow boundary conditions. For the mesh generation, taking into account the irregular geometric shape of the aero control tower, its computational mesh arrangement is not straightforward with respect to the boundary-layer conditions and wind attack angle, while another requirement is to reduce the mesh number as low as
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possible to achieve the efficient numerical computation. As shown in Fig. 2(b) is the mesh on x-z plane at y=0, in which the nesting style mesh is adopted that the high-rise structure is nested in a rectangular cylinder that is four times larger than the tower and
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the whole computational domain is divided into two parts, the inner and outer zones. Additionally, in the inner nesting rectangular cylinder, the inner zone is composed of two subdomains, for which the upper part is filled with the unstructured elements and
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the neighborhood of the wall surface is discretized using a viscous boundary layer of 20 grid nodes and stretched with the ratio of 1.03. The structured mesh is generated in
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the lower part, while for the external zones outside the nesting rectangular cylinder
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the structured mesh is also applied. The advantage of the nesting style mesh offers the fine mesh in the neighborhood of the complex tower while keeping the mesh in zones
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far away from the building unchanged or in a properly coarser manner. Moreover, the
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mesh scheme for the DES model follows the guideline suggested by Spalart (2001), in which the mesh grids were divided into RANS region and LES region from the windward to leeward sides around the bluff body. The RANS region in the windward part requires the coarser grid nodes than the very fine mesh needed for the LES region in the leeward part. Therefore, the minimal grid size in the neighborhood of the aero 8
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control tower is nearly Dy/250 for LES-1 as shown in Fig. 2(b) and the minimal grid size of Dy/150 on the windward side and Dy/200 on the leeward side was set for DES-1. For the purpose of the grid-independence check, the refined mesh schemes of both LES-2 and DES-2 are generated and the grid cells around the high-rise structure
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are refined with the coarsening factor of 2 (the refined mesh scheme divided by the initial one). Table 1 shows the minimal grid size, total mesh number, and the computing costs for the cases with different mesh scheme and turbulence models. The
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non-dimensional wall distances y+ (y+=u*y/ν, y denotes the distance between the first near-wall grid node and the surface, u* represents the friction velocity at the nearest wall and ν indicates the local kinematic viscosity of the fluid) of the first near-wall
3.1.2 Turbulence models
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grid node are less than 10.
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According to the characteristic dimension of the aero control tower (Ls) and
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reference velocity (Uref), the Reynolds number Re=UrefH/ν is 5.95×106 and it is critical to choose an appropriate turbulence model for such a high Reynolds-number
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problem. Several turbulence models, including dynamic Sub-grid Scale (SGS) model
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proposed by Germano et al. (1991) and Lily (1992) in LES, the Spalart-Allmaras (S-A) (Spalart and Allmaras, 1994) and k-ω Shear-Stress-Transport (SST) (Mentor et al., 2003) models in DES (Shur et al., 1999) are used in the present simulations. For the dynamic SGS model in LES, it has some advantages over the standard Smagorinsky SGS model in two aspects (Murakami, 1999): 1) the Smagorinsky 9
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model constant Cs is determined based on space and time of the properties of local flow fields. 2) since the value of Cs automatically becomes zero in the laminar region just near the wall, the empirical damping function for νSGS is no longer necessary in the near-wall region as that adopted in the standard Smagorinsky model .
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In addition, two different DES models including the S-A and k-ω SST based models are adopted in this study to investigate the effects of the roughened wall surfaces. The S-A model uses the distance to the closest wall as the definition of the
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length scale d. However, the DES based S-A model revises the length scale to avoid the ambiguous grid definition. Provided that ∆max <δ ( δ is the boundary layer thickness), the undesired case occurs that the LES model is activated inside the
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boundary layer, where the grid is not fine enough to resolve the turbulence. Therefore, alternative DES model is provided, which is known as the delayed DES model
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(DDES) (Spalart et al. 2006), in order to preserve the RANS model throughout the
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boundary layer. In the DDES model, the revised DES length dddes is given in the
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following form (Spalart et al. 2006), dddes=d-Fdmax(0, (d -CdesΔmax))
(1)
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where Cdes is a model constant with the value of 0.61 and the defer function Fd is defined as
Fd 1 tanh((8rd )3 )
and the specific length scale rd is given by
10
(2)
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rd
t U i , jU i , j 2 d
(3)
For the k-ω SST based DES, compared with the SST model, the dissipation term in the k (turbulence kinetic energy) transport equation is revised as suggested by
Dissipation term *k FDES
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Mentor et al. (2003) in the following form: (4)
where β* is a constant of the SST model and the function FDES is expressed as Lt ,1) Cdes max
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FDES max(
(5)
The turbulence length scale, Lt, is defined as that in the RANS model
Lt
k
*
(6)
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3.1.3 Inflow boundary conditions
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For the approaching wind flows in the wind tunnel testing and the numerical simulations for the aero control tower, the mean longitudinal wind speed and
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turbulence intensity profiles are shown in Fig. 3. As recognized in the wind
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engineering community, the mean wind speed profile should follow the power-law as
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shown in Fig. 3:
U ( z) z h uref ref
(7)
where Uref is the reference mean wind speed at the reference height, which is 7.5 m/s in this study. href is 0.6m in the wind tunnel testing. α is the exponential value of the wind speed profile with the value of 1.5, which is best fitted from the measurements 11
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at the wind tunnel, and z is the height above the ground. The upstream terrain in the wind tunnel testing is regarded as Category Ⅰstipulated in AIJ and exposure C specified in the ASCE7-02 (Flat open grassland). Fig. 3 presents the fitted turbulence intensity profile in the following form (AIJ, 2004),
I ref
z h ref
0.05
3.1.4 Inlet turbulence
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I
(8)
For the unsteady simulation of computational wind engineering problems, one of
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the important issues is to reproduce the realistically time-evolving inflow boundary. As revealed by Huang et al. (2010), the turbulence superimposed at the inlet has a significant effect on the numerical simulation of the wind loading on buildings and
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structures, especially for the fluctuating components. In a previous study of the
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authors (Yan and Li, 2015), several inflow turbulence generation methods have been examined in details, suggesting that the recycling method may provide inadequate
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turbulence level in the upper part of the computational domain. In this study, since the
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roughness element arrangement in the wind tunnel experiment is available, the recycling method over a rough wall is used to reproduce the physically realistic
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inflow turbulence. In order to overcome the shortcoming of the recycling method, additional synthetic turbulence is superposed in the upper part of the computational domain with the weighted amplitude wave superposition (WAWS) method. The equation of the WAWS for the fluctuating streamwise velocity u’(t) is given as (Iannuzzi and Spinelli, 1987), 12
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N
u ' (t ) 2 Su (ni )n cos(2 ni t i )
(9)
i 1
where ni, i=1,…N are the sampled frequencies, φii is a uniformly distributed random phase angle between 0 and 2π, and S(ni) is the sampled von Karman spectrum. With
I add I targ
(t ) U recy urecy U recy
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the WAWS method, the additional turbulence level is given in the following form, (10)
where the subscript “add” and “targ” stand for the additional and target turbulence
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intensity, respectively, and the target turbulence level is specified according to Eq. (8).
(t ) and Urecy indicate the instantaneous and mean wind speeds Moreover, urecy generated by the recycling method, respectively.
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3.1.5 Wall function
near-wall treatment.
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Another issue concerned in the high-Reynolds number flow simulation is the
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For the LES, the near-wall treatment adopted here is based on the work of Werner and Wengle (1991) as described in the following, in which the wall shear
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stresses are estimated by the analytical integration of the power-law near-wall velocity
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distribution.
|𝜏𝜔 | =
𝜌[ {
2𝜇|𝑢𝑝 | 𝑦𝑝 1−𝐵 2
𝐴
1+𝐵 1−𝐵
2
𝜇
|𝑢𝑝 | ≤ 2𝜌𝑦 𝐴1−𝐵 𝑝
1+𝐵
𝜇
(𝜌𝑦 ) 𝑝
+
1+𝐵 𝐴
𝐵
𝜇
2 1+𝐵
(𝜌𝑦 ) |𝑢𝑝 |] 𝑝
𝜇
|𝑢𝑝 | > 2𝜌𝑦 𝐴
2 1−𝐵
(11)
𝑝
where A=8.3, B=1/7, and yp is the near-wall control volume length scale. The “non-slip” boundary condition in the first formula of Eq. (11) is only used in low 13
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velocity regions such as leeward sides, while the second formula is generally activated for most wall boundary conditions. In the present simulations, the near-wall length scales are usually between 0.05 and 0.1m, indicating that the first formula can rarely be used, which represents a real “non-slip” boundary condition.
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The wall roughness effects are included in the study through the law-of-the-wall modified for roughness. Based on the experiments in roughened pipes and channels, the mean velocity distribution near rough walls when plotted in the usual
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semi-logarithmic scale, has the same slope (1/κ) but a different intercept (additive constant B in the log-law). Thus, the law-of-the-wall for mean velocity modified for roughness has the form as follows:
u y p ln( E ) B K s u 1
(12)
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up
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where Ks is the physical sand-grain roughness height, E is equal to eκB with the integration constant B=5.0~5.4 (Schlichting, 1968; White, 1991)) and Ks+ is the
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dimensionless sand-grain roughness height ( u K s / ). Based on the work conducted
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by Nikuradse (1933), Cebeci and Bradshaw (1977) subdivided the whole domain into three regimes: hydro-dynamically smooth regime ( 𝐾𝑠 + < 2.25 ), transitional
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(2.25 ≤ 𝐾𝑠 + ≤ 90), fully rough (𝐾𝑠 + > 90). For surface roughness, according to AIJ specifications for the surface roughness of circular cylinder (AIJ. 2004), two different heights in the present simulation is considered, which are 1% and 5% of the characteristic dimension, Lc (in the present simulation, Lc Ll Ls where Ll and Ls are respectively major and minor axis length at the base of the structure). According 14
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to Cebeci and Bradshaw (1977), the roughness effects are evaluated by the formula as follows:
B
1
ln(1 Cs K s )
(13)
(Hargreaves and Wright, 2006; Blocken et al., 2007). 3.1.6 Numerical algorithm
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where Cs is fixed in the range [0, 1] and the value of 0.5 was adopted in this study
Wind flow concerned in wind engineering applications is usually regarded as
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incompressible flow. In this study, all the discretized equations are solved in a segregated manner. All the discretized equations are solved in a segregated manner. The Pressure Implicit with Splitting of Operators algorithm (PISO) is used in the
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pressure-velocity calculation procedure, which involves one predictor step and two
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corrector steps. PISO is an extension of Semi-Implicit Method for Pressure-Linked Equations (SIMPLE), with an additional corrector step and developed for the
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non-iterative computation of unsteady compressible flows. Therefore, PISO is more
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suitable for the unsteady simulation than the SIMPLE algorithm. In addition, the second order discretization schemes are adopted for spatial discretization. Bounded
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central differencing is used to discretize the convective terms of momentum equations. The time derivative is discretized using the implicit second order backward differences. The Green-Gauss node based method is used for numerical approximation of pressure gradients. The LES is performed a high performance cluster (HPC) at City University of 15
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Hong Kong with the general purpose commercial code ANSYS/Fluent 14.0. A total of 32 CPUs are used in parallel for the simulations. And the time step Δt are restricted to 1×10−3 for computational stability purposes. The initial flow fields of LES and DES cases are established with the convergent RANS results. Meanwhile, the transient
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inflow turbulence generation methods including the DSRFG method and the recycling method are embedded via paralleled user-defined function (UDF) in the ANSYS/Fluent code. All the results from the LES and DES are sampled after an
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initialization period of 5.2 flow-through times (Tft=Lx/UH, where Lx is the length of the computational domain in the longitudinal direction (x) and UH is the reference mean wind speed). The total computational time is equivalent to 20.8Tft, which is
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sufficiently long to reach the statistical convergence for LES and DES (Gousseau et al., 2013). Table 1 shows the computing time costs of LES and DES cases and the
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longest computing time for LES and DES cases are 510 CPU hours with the mesh
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number of 6.7 million and 445 CPU hours with the mesh number of 4.8 million 3.2 Wind tunnel testing
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Wind tunnel experiment is carried out in a boundary layer wind tunnel laboratory
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and the pressure field on the external surfaces of a 1:200 scale model of the aero control tower is measured by means of a Synchronous multi-pressure sensing system (SMPSS). In the testing, the sample frequency is 312.5 Hz and the sampling time length is 32 seconds. In the experiment, the rigid model of the tower as shown in Fig. 1(b) is divided 16
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into twelves measurement levels along the vertical direction and the height of the 12th measurement level is 0.95H (H is the height of the tower model), a total of 285 taps are installed on the surface of the model to measure the time-dependent surface wind pressures. The measured pressures at the taps are integrated to estimate the global and
CD
FD H
1/ 2 U ( z ) 2 dz
CD
FD H
1/ 2 U ( z ) 2 dz
0
0
FL H
1/ 2 U ( z )2 dz
CL
FL H
1/ 2 U ( z )2 dz
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CL
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local aerodynamic forces acting on the tower as defined as,
0
(14)
(15)
0
where ρ is the air density, U(z) is the mean wind speed corresponding to the height z.
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FD and FL are the steady forces acting parallel and transverse to the streamwise direction, respectively.
H
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In order to account for the wind shear profile,
U ( z) dz is considered herein. 2
0
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Substituting the velocity profile given in Eq. (7) into the integration, one has: H
U ( z) dz 0.25U 2
2 H
H
(13)
0
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where UH is the wind speed atop the high-rise structure. 3.3 Wind-induced response analysis
In this study, the wind-induced responses of the aero control tower are estimated
by the spectral analysis method (Tschanz and Davenport, 1983). In the dynamic response analysis of the high-rise structure, only the contribution of the first order 17
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r z, t z q t
(14)
where z is the generalized mode shape and q t is the top-floor displacement. Henceforth, the relationship between the power spectrum of displacement and the
S r z, n 2 z S q n
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principal coordinate power spectrum is given as follows: (15)
in which, Sr z, n and Sq n are the generalized and principal coordinate
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displacement power spectrum, respectively, and n is the frequency of the wind pressure fluctuation. Based on the random vibration theory, the principal coordinate power spectrum Sq z, n is given by
S q n H n S p n 2
(16)
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where S p n is the generalized force power spectrum determined from the time
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sequence of the wind force, H n is the structural frequency response function, and
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the root-mean-square of structural acceleration a z is obtained as follows: 1
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2 2 2 a z (2 ) z H n S p n dn 0
(17)
4 Results and discussion
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4.1 Inflow velocity characteristics
Fig. 5 shows inflow characteristics of the generated wind speeds by the recycling
method. Fig. 5(a) presents the mean wind speed and turbulence intensity profiles which agree well with the experimental results and fitted power-law and the turbulence intensities in the upper part of the computational domain are improved to a 18
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satisfactory level with the WAWS method. Also, the simulated longitudinal velocity spectrum sampled at the top of the aero control tower matches the von Karman spectrum model and that created in the model testing until the reduced frequency reaches approximately 1 Hz and then rapidly decays in high-frequency range
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(dissipation range) due to the filter operation according to the grid resolution at the driver section. Given the fundamental frequency of the aero control tower (fy=0.341 Hz), the upper reduced frequency fxLu/UH=1 Hz as shown in Fig. 5(b) provides a
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lower limit of design wind speed as 2.845 m/s, which is lower than the wind speed of 10-year return period (20 m/s) which is usually adopted for serviceability consideration of high-rise structures, indicating that the current grid resolution is
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adequate for occupant comfort analysis.
4.2 Wind pressure distribution
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Figs. 6 and 7 present the mean and fluctuating wind pressure coefficients
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predicted by the different numerical approaches compared with the results from the wind tunnel testing. In general, the mean pressure coefficients agree well with the
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experimental results on the windward and leeward faces. However, obvious
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discrepancies are observed for the prediction of negative pressures in the separation region which are overestimated by the numerical simulations. This discrepancy might be attributed to the defects of the wall functions in the flow separation region with the inverse pressure gradients. Moreover, the consistent results are provided by the numerical cases “SST-DES-1rough” and “SST-DES-5rough”, which refer to the cases 19
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with rough walls of 1% and 5% roughness heights by DES based k-ω SST model, respectively. Meanwhile, the agreement between the cases “SST-DES-smooth” and “S-A-DES-smooth” is reasonably good, which refer to the cases with smooth walls by DES based k-ω SST model and DES based S-A model, respectively. Furthermore, it is
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noteworthy that the values of negative pressure coefficients in the separation region are reduced when taking into account the surface roughness, which is in consistence with the experimental study conducted by Farell et al. (1976) on rough-walled cooling
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tower. And the smaller pressure recovery was due to the earlier flow separation induced by the surface roughness (Güven et al., 1980).
For the fluctuating components of the pressure coefficients, the agreement
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between all the numerical predictions is fairly good. Nevertheless, they are slightly larger than the experimental results, particularly for those under the wind incident
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angle α=270o. Similar to the results of mean pressure coefficients, the discrepancy of
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RMS pressure coefficients is observed in the flow separation region, and the numerical simulations with the LES and DES models produce relatively larger
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fluctuating pressures as compared to the experimental results. Generally speaking, the
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LES and DES models with rough walls can provide satisfactory predictions of the surface pressures, while the values of negative pressures in the separation region are reduced by the DES models with rough walls in comparison with those with smooth wall. It is clear that the surface roughness has obvious effects on the numerical evaluations of the surface pressures by DES models. Meanwhile, the influence of 20
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different roughness heights seems to be less significant to the numerical simulations. 4.3 Aerodynamic forces As aforementioned, the aerodynamic forces such as the lift and drag coefficients are compared among the numerical predictions and the experimental results, as listed
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in Table 2. The grid-independence check was conducted using LES-1 and LES-2 for LES, while for DES using DES-1 and DES-2. The comparisons show that the basic grid schemes of LES-1 and DES-2 can provide the grid-convergent results for the
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case considered in this study with the fractional errors of less than 3%. Hence, the results from the LES-1 and DES-1 are adopted for the following analysis in this study. For the mean drag force coefficient CD, there exist obvious differences between the cases with smooth walls by the DES based S-A and k-ω SST models and the
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experimental results, while the values calculated by the LES and the k-ω SST DES
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models with rough wall are in good agreement with the experimental data. For the
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fluctuating drag and lift force coefficients, the results by the DES models agree well with those by the LES. However, the discrepancies between all the numerical
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predictions and the experimental results are observed from Table 2, while the LES and
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DES S-A model provide relatively improved fluctuating surface pressure coefficients. As discussed by Breuer et al. (2003), the S-A model with minor modification is consistent with the Smagorinsky SGS model. In summary, when the surface roughness is considered in simulations with DES approaches, the mean drag force coefficients of the rough-walled aero control tower are significantly increased 21
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compared with the smooth-walled case. 4.4 Wind force spectra For the assessment of occupant comfort using spectral analysis, it is necessary to accurately predict the wind force spectra. Fig. 8 presents the along-wind and
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across-wind force spectra obtained from the numerical simulations in comparison with the experimental results. For the along-wind force spectra as shown in Fig. 8(a), the agreement between the numerical predictions and the experimental measurements
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is fairly good and the energy contained in the along-wind force covers a quite wide frequency range. For the across-wind force spectra as shown in Fig. 8(b), the typical narrow-band spectra are provided by all the numerical simulations, which is mainly
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initiated by the vortex-shedding. However, the position of the single spectral peak by the DES based k-ω SST model with rough walls matches that of the measured
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across-wind spectrum, while there exist differences between the numerical predictions
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by the LES and DES models with smooth walls and the experimental results that the single peak of the across-wind spectra are shifted to higher and lower frequency range,
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respectively. It is clear that the DES model considering the surface roughness can
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provide improved across-wind force spectrum over the smooth-walled cases. 4.5 Response analysis
In this study, the wind-induced accelerations atop the tower are calculated using
the method described in section 3.3. As listed in Table 3 are the numerical predictions compared with the wind tunnel test results. For the acceleration in the along-wind 22
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direction, the agreement among the numerical results by the different approaches is quite good, which is in accordance with the consistent along-wind force spectra. However, all the numerical simulations provide slightly larger predictions than the experimental results. For the across-wind acceleration, the LES and DES models with
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rough walls provide quite larger results compared with the experimental results under α=270o (along the major axis), while the agreement for α=0o (along the minor axis) is fairly good. Also, when the surface roughness is taken into account, the across-wind
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peak acceleration predicted by the DES model is increased to a conservative extent compared with the smooth-walled case, since the improved agreement is achieved by the cases with rough walls as shown in Fig. 8(b). It is worth noting that the maximum wind-induced acceleration occurs in the along-wind direction when the wind flow
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approaches along the minor axis (α=0o). On the other hand, the across-wind response
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is dominant when the wind flow approaches along the major axis (α=270o).
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4.6 Wind flow field
Fig. 9 presents the mean and instantaneous velocity contours with streamlines on
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x-y plane at z=0.5 m high by various numerical approaches. As shown in Fig. 9(a), (c)
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and (e) for mean velocity contours, there exist two counter-rotating vortices behind the aero control tower and the LES gives the largest recirculation zone, while the DES based k-ω SST model provides the smallest one. For the instaneous velocity contours as illustrated in Fig. 9(b), (d) and (f), quite strong turbulent vortex sheddings are captured by all the numericla models and fairly long wake zone is predicted by the 23
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LES. Fig. 10 shows turbulence statistics including the resolved Reynolds stresses uv and uw on x-y plane at z=0.5 m high. As shown in Fig. 10(a), (c) and (e) are the shear stress uv contours from -3 to 3 with an increment 0.3 and the results
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calculated by the different numerical models are quite similar, while the differences still exist. For the shear stress uw contours from -1 to 1 with an increment 0.05 as illustrated in Fig. 10(b), (d) and (f), the agreement of the results predicted by the LES
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and DES models is reasonably good.
Fig. 11 shows the mean and instantaneous velocity contours on x-y planes at z=0.1m, 0.2 m, 0.3 m, 0.4 m, 0.5 m and 0.55 m, x-z plane at y=0 and y-z plane at x=0
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by both LES and DES modes for α=0o. Figs. 11(a) and (c) present the three-dimensional mean wind flow field around the aero control tower by LES and
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DES, and both the shear flow and recirculation regions in the leeside are well
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reproduced. Also, the turbulent vortex shedding due to the obstacle and random-like vortices in the upstream flow can be obviously observed in Figs. 11(b) and (d). From
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Fig. 11, it can be found that the LES and DES models can provide similar
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visualizations of the flow field around the aero control tower.
5 Conclusions
This study focuses on the investigation of the influence of surface roughness on
the wind effects on a high-rise structure with elliptical shape. The pressure distribution, drag and lift forces calculated by the LES and DES models are presented 24
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and compared with the experimental results. Moreover, the wind flow fields including the turbulence structures and flow recirculation zones are also revealed and discussed. The main conclusions of the combined numerical and experimental study are summarized as follows:
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(1) The inflow characteristics including the mean and fluctuating speed profiles and the streamwise velocity spectrum can be properly reproduced using the recycling method in combination with the WAWS method. The inadequate turbulence in the
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upper part of the computational domain is improved to a satisfactory level with the use of the WAWS method to generate additional synthetic turbulence. Also, as far as the assessment for occupant comfort is concerned, the grid resolution at the driver
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section is fine enough to provide the upper spectral bound for the wind-induced response analysis using the spectral method.
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(2) The mean pressure coefficients by the LES and DES models are in good
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agreement with the experimental results on the windward and leeward faces; while obvious discrepancies exist in the prediction of negative pressures. Additionally, all
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the numerical simulations slightly overestimate the fluctuating pressure coefficients
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compared with the experimental measurements. It is also noted that the values of negative pressure coefficients in the separation region are reduced when taking into account the surface roughness, but, the effects of different surface roughness heights are less significant. (3) The mean drag force coefficients by the LES and DES models with rough 25
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walls are in reasonable agreement with the experimental results, while the LES and DES based S-A model provide improved fluctuating lift and drag force coefficients. Moreover, the mean drag force coefficient of the rough-walled aero control tower is significantly increased compared with the smooth-walled case.
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(4) The agreement of the numerically predicted along-wind force spectra by the LES and DES models and the experimental data is reasonably good for a wide frequency range. Although the typical narrow band across-wind spectrum is provided
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by all the numerical approaches, the DES based k-ω SST models with rough walls can give consistent prediction of the spectral peak position with the experimental results. (5) For wind-induced response analysis, the across-wind peak acceleration by the
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DES model is increased as far as the surface roughness is concerned, and the LES and DES can provide consistent results compared with the wind tunnel testing.
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(6) Both the LES and DES models can well reproduce the turbulent vortex
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shedding behind the cylinder, while the largest recirculation zone is given by the LES and the smallest by the DES based k-ω SST model. Also, the resolved Reynolds
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stresses in wake regions by the LES and DES models macth each other.
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Acknowledgement
The work described in this paper was fully supported by a grant from the
Research Grants Council of Hong Kong Special Administrative Region, China (Project No: CityU11256416) and a research grant from the National Natural Science Foundation of China (Project No. 51478405). 26
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N. Isyumov, A.G. Davenport and J. Monbaliu, CN Tower, Toronto: Model and full-scale response to wind. Proceedings, 12th Congress, International Association for Bridge and Structural Engineering, Vancouver, Canada, 3-7 September, 1984, p. 737-46. O. Guven, C. Farell and V.C. Patel, Surface-roughness effects on the mean flow past 29
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circular cylinders. Journal of Fluid Mechanics, 1980, 98 (4): p. 673-701. P. Catalano, M. Wang G. Iaccarinob and P. Moinb, Numerical simulation of the flow around a circular cylinder at high Reynolds numbers, International Journal of Heat and Fluid Flow. 2003, 24(4):p. 463-469.
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P. R. Spalart, S. Deck, M. L. Shur, K. D. Squires, M. K. Strelets, and A. Travin, A new version of detached-eddy simulation, resistant to ambiguous grid densities. Theoretical and Computational Fluid Dynamics, 2006, 20: p.181–195.
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P.R. Spalart and S.R. Allmaras, A one-equation turbulence model for aerodynamic flows. La Rech. Aérospatiale, 1994, 1: p. 5-21.
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P.R. Spalart, Young-person's Guide to Detached-eddy Simulation for Bluff Bodies,
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NASA Center for Aerospace Information, USA, 2001. R. Mittal and S. Balachandar, Direct numerical simulation of low past elliptic
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cylinders, Journal of Computational Physics, 1996, 124: p.351-367.
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R.W. Clough and J. Penzien, Dynamics of structures, 3rd edition, Computers & Structures, Inc., Berkeley, USA, 2003.
S. Murakami and A. Mochida, Past, present, and future of CWE: the view from 1999. 10th International conference on wind engineering (ICWE), 1999, p. 91-104. S.H. Huang, Q.S. Li and J.R. Wu, A general inflow turbulence generator for large 30
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eddy simulation, Journal of Wind Engineering and Industrial Aerodynamics, 2010, 98: p. 600-617. T. Cebeci and P. Bradshaw, Momentum Transfer in Boundary Layers. Hemisphere Publishing Corporation, New York, 1977.
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T. Tschanz and A.G. Davenport, The base balance technique for the determination of dynamic wind loads, Journal of Wind Engineering and Industrial Aerodynamics, 1983, 13: p. 429–439.
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Y. Tominaga, A. Mochida, S. Murakami and S. Sawaki, Comparison of various revised k–ε models and LES applied to flow around a high-rise building model with 1:1:2 shape placed within the surface boundary layer. Journal of Wind
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Engineering and Industrial Aerodynamics, 2008, 96:p.389-411. Z.H. Li, J. Davidson and S. Mantell, Numerical simulation of flow field and heat
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transfer of streamlined cylinders in cross flow, ASME Summer Heat Transfer
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CE
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Conference, USA, 2005.
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a.
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b.
c.
Fig. 1 (a) Architectural view; (b) Physical modelling in wind tunnel test; (c)
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a.
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Geometric model in the numerical simulation.
32
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b.
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Fig. 2 (a) Computational domain; (b) standard mesh scheme on x-z plane at y=0
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Fig. 3 Mean velocity and turbulence intensity profiles at the inflow
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(a) Mean velocity and turbulence intensity profiles
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Fig. 4 Aerodynamic forces
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(b) Streamwise wind speed spectrum
(a) mean wind pressure coefficients
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Fig. 5 Inflow velocity characteristics by the recycling method
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(b) RMS wind pressure coefficients
Fig. 6 Comparisons of wind pressure coefficients between the numerical simulations
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and the wind tunnel testing for α=0O
(a) mean wind pressure coefficients
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(b) RMS wind pressure coefficients
Fig. 7 Comparisons of wind pressure coefficients between the numerical simulations
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and the wind tunnel testing for α=270O
(a) Along-wind force spectra
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(b) Across-wind force spectra
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Fig. 8 Along-wind and across-wind spectra estimated from the LES for α=270o
(b) Instaneous wind velocity by LES
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(a) Mean wind velocity by LES
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(c) Mean wind velocity by DES
(d) Instaneous wind velocity by DES based S-A model
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based S-A model
(f) Instaneous wind velocity by DES
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(e) Mean wind velocity by DES based k-ω SST model
based k-ω SST model
Fig. 9 Mean and instaneous velocity contours with streamlines on x-y plane at
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z=100 m for α=270o
(b) Resolved Reynolds stress uw
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(a) Resolved Reynolds stress uv
by LES
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by LES
(c) Resolved Reynolds stress uv
(d) Resolved Reynolds stress uw
39
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by DES based S-A model
by DES based S-A model
(f) Resolved Reynolds stress uw
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(e) Resolved Reynolds stress uv by DES based k-ω SST model
by DES based k-ω SST model
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Fig. 10 Resolved Reynolds stresses uv and uw for α=270o
(a) Mean velocity contours by LES
(b) Instaneous velocity contours by LES
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(d) Instaneous velocity contours by DES
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(c) Mean velocity contours by DES
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Fig. 11 Mean and instantaneous wind velocity fields for α=0o by LES and DES Table 1 Mesh arrangement description and computing costs Mesh
Minimal grid size
Mesh numbers (M)
y+
Computing cost (CPU hours)
1
LES-1
Dy/250
4.2
3~8
432
2
LES-2
Dy/500
6.7
2~5
510
3
DES-1
Dy/250
3.5
5~10
366
4
DES-2
Dy/500
4.8
2~8
445
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Cases
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Table 2 Aerodynamic force coefficients by the numerical simulations and the wind tunnel testing Cases
Mesh
Roughness α
1
LES-1
smooth
0o
LES
2
LES-2
smooth
0o
LES
3
DES-1
smooth
0o
SST DES
4
DES-2
smooth
0o
SST DES
5
DES-1
1%
0o
SST DES
6
DES-1
5%
0o
7
LES-1
smooth
270o
8
DES-1
smooth
270o
9
DES-1
smooth
270
10
DES-1
1%
11
DES-1
Turbulence model CD
C’L
0.060
0.1508
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0.514
C’D
0.054 7
0.1531
0.362
0.048
0.1785
0.375 8
0.047 9
0.1733
0.510 5
0.066
0.1829
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0.517 3
0.517 7
0.061 9
0.1827
LES
1.577 0
0.168 5
0.1360
S-A DES
1.285
0.198 4
0.1480
SST DES
1.386
0.214 2
0.1414
270o
SST DES
1.615
0.237 4
0.1339
5%
270o
SST DES
1.659 6
0.216 6
0.1358
Exp
smooth
0o
---
0.524 9
0.058 9
0.1370
Exp
smooth
270o
---
1.718 4
0.157 4
0.0948
6
3
AC
CE
PT
ED
M
SST DES
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Table 3 Wind-induced acceleration assessment atop the tower Roughness Along-wind peak
Across-wind peak
acceleration (m/s2)
acceleration (m/s2) 0.0564
0o
smooth
0.3039
SST DES
0o
smooth
0.2784
SST DES
0o
1%
0.3137
SST DES
0o
5%
0.3212
LES
270o smooth
0.1086
0.1997
DES S-A
270o smooth
0.0913
0.1411
SST DES
270o smooth
0.0931
0.1453
SST DES
270o 1%
0.0967
0.1874
SST DES
270o 5%
0.0992
0.1911
smooth
0.285
0.055
0.084
0.155
0.0313 0.0583
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0.0579
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Experiment 0o
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LES
M
α
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Cases
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Experiment 270o smooth
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Detached-eddy and large-eddy simulations of wind effects on a high-rise structure B.W. YAN , Q.S. LI PII: DOI: Reference:
S0045-7930(17)30054-3 10.1016/j.compfluid.2017.02.009 CAF 3398
To appear in:
Computers and Fluids
Received date: Revised date: Accepted date:
23 July 2014 9 February 2017 9 February 2017
Please cite this article as: B.W. YAN , Q.S. LI , Detached-eddy and large-eddy simulations of wind effects on a high-rise structure, Computers and Fluids (2017), doi: 10.1016/j.compfluid.2017.02.009
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Highlight Carry out a combined wind tunnel test and CFD study on the wind effects on an elliptical cylinder
Investigate the surface roughness effects on the wind loading of an elliptical cylinder using DES
DES and LES models and numerical treatments adopted in this study can provide reasonably good correspondence with wind tunnel tests
DES model can reproduce the effects of surface roughness effects on the wind loading with the modified wall function
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1
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Detached-eddy and large-eddy simulations of wind effects on a high-rise structure B.W. YANa,b, Q.S. LIb,* School of Civil Engineering, Chongqing University, Chongqing 400045, China a
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a
Dept. of Architecture and Civil Engineering, City University of Hong Kong, Kowloon, Hong Kong
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*Corresponding Author: [email protected]
Abstract
In this study, detached-eddy simulations (DES) and large-eddy simulations (LES)
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of wind effect on a high-rise structure with elliptical shape are performed. The aim of
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this study is to examine the accuracy of the numerical simulations for wind flow around a complex high-rise structure and investigate the effects of surface roughness
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on the wind loading. In order to reproduce appropriate inflow turbulence, the
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improved recycling method combined with the weighted amplitude wave
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superposition (WAWS) method is used to generate the inflow turbulence in the streamwise direction. Also, to study the surface roughness effects on the wind loading, the rough wall boundary conditions are adopted in the DES models. Typical results including the mean and fluctuating pressure coefficients, force spectra, Reynolds stresses and wind-induced top-floor response are obtained and compared with the 2
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corresponding wind tunnel experimental data. Through the cross-comparisons, the numerical results by the DES and LES models are found to be comparable with the experimental results. Additionally, the surface roughness effects on the wind loading is well reproduced with the DES models, such as the slow pressure recovery in the
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separation regions and the increased mean drag force coefficients. It is demonstrated through the validations that the DES and LES models and the numerical treatments adopted in this study can provide reasonably good results.
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Key words: Large-eddy simulation; Detached-eddy simulation; Elliptical cylinder; Surface roughness; Wind tunnel experiment
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1. Introduction
High-rise structures, such as chimneys, cooling towers and aero control towers,
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are usually built with circular and elliptical cross-sections, which are commonly
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slender, light-weighted and with low damping ratio. It is of significance to investigate the wind effects on these wind-sensitive structures for the wind-resistant design.
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Isyumov et al. (1984) presented an overview of the comprehensive wind tunnel study
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for a TV tower with a height of 555m (Toronto, Canada), in comparison with full-scale measurements. Kwok and Macdonald (1990) conducted an on-site measurement of the Sydney Tower and found that the wind-induced response was greatly reduced after installation of a tuned mass damper (TMD) system. Kareem et al. (1998) investigated the wind-induced response of Nanjing Tower with a height of 3
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310m numerically and experimentally. In fluids mechanics, the cross-flow around a circular or elliptical cylinder has been the subject of intense scrutiny. As is well known, the flow around a circular cylinder is dependent on Reynolds number, surface roughness, blockage, and
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free-stream turbulence (Simiu and Scanlan, 1996). Scruton (1971) revealed the dependence of drag force of a circular cylinder on the surface roughness through wind tunnel experiments for rough surface with sand and grain. For the effects of surface
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roughness on mean wind loading, Farell et al. (1976) measured the mean pressure distributions on a cooling tower model with different roughness configurations. Güven et al. (1980) used sandpaper to model rough wall of a circular cylinder in
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boundary wind tunnel laboratory and discussed the results together with previous measurements using the boundary layer theory. Through the experimental
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investigations, the base wind pressure was demonstrated to be independent of surface
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roughness, while the pressure differences between the minimum pressure and base pressure was closely related to the roughness, i.e. the surface roughness was inversely
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proportional pressure recovery. However, the experiments on the surface roughness
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were quite cumbersome and limited to a moderate Reynolds number (Re) range 7×104 and 5.5×105 (Güven et al., 1980) due to the spatial restriction in wind tunnel experiments. With the rapid development of improved turbulence models, numerical techniques and increasing computational power, numerical simulations of flow field 4
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around a circular cylinder have become feasible in the past decades. Catalano et al. (2003) examined the accuracy of LES for high-Reynolds number flow (0.5×106~2×106) around a circular cylinder and the wall boundary were modelled with a simple wall stress model. They suggested that the LES solutions were much
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more accurate than the RANS results and the mean pressure distribution was predicted reasonably well at high-Reynolds number. Breuer (2000) scrutinized the capabilities of LES for flow around a circular cylinder at supercritical regime and
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investigated the influences of two subgrid scale (SGS) models at different grids. The dynamic SGS model was shown to perform well for complex flow at high-Reynolds number, particularly in the near wake region. Travin et al. (2000) examined the applicability of Detached eddy simulation (DES) for transitional (Re=5×104 and
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1.4×105) and turbulent (Re=1.4×105 and 3×106) flows around a circular cylinder and
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the coefficients of pressure and drag force showed better agreement with the
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experimental results at medium refined grid than those at finest grid, while discrepancies existed for skin friction coefficients and wake statistics including
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Reynolds stresses and mean recirculation bubble. Squires et al. (2008) used the
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delayed detached eddy simulation (DDES) to predict the supercritical flow around a circular cylinder (Re=8×106) and the agreement with the basic DES is reasonably good for mean drag coefficient, Strouhal number, skin friction and separation angle. For flow around an elliptical cylinder, Mittal et al. (1996) studied the flow separation and wake structures using Direct Numerical Simulation (DNS). Li et al. (2005) 5
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investigated the effect of minor to major axis ratio on the drag and convective heat transfer with 2D unsteady k-ω SST model. To the best knowledge of the authors, there is still absence of studies on flow around an elliptical cylinder in supercritical and upper transition regimes, particularly
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for practical applications with high Reynolds number and effects of surface roughness on flows around an elliptical cylinder. Additionally, numerical simulations have the merits over the experimental measurements such as without limit of similarity criteria
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and “whole flow field data” (Blocken, 2014). Therefore, in this study, DES and LES of atmospheric boundary layer (ABL) flow around a high-rise structure with elliptical shape are performed at high Reynolds number (>106). The main purpose of this study
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is to assess the validity and accuracy of DES and LES for simulating the wind effects
the wind loading.
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on a complex high-rise structure and to investigate the effects of surface roughness on
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2. Details of the aero control tower
As shown in Fig. 1(a), the aero control tower is characterized by an elliptical
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cross section with the typical axis ratio of 1.35 and aspect ratio of 14. Moreover, the
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aero control tower consists of two parts which are the concrete shaft and control tower, and the architectural shape is similar to a golf club mounted on the ground. 1.1 Concrete shaft
The concrete shaft of the aero control tower is placed from height level of 0m to height of 84.45m, and the cross-section is typically elliptical along the height, with the 6
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dimensions of major axis (Ll) of 11.8 m and minor axis (Ls) of 6 m, respectively. 1.2 Control tower The control tower begins at the height level of 84.45 m and ends at the height level of 114 m. Although its cross-section is elliptical, the dimension varies gradually
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with height as shown in Fig. 1(a) which provides the architectural view of the aero control tower. The maximum major axis is of 29.2 m, while the minimum is of 20 m. 1.3 Dynamic characteristics
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Using the finite element model of the aero control tower, its dynamic characteristics are obtained through the modal analysis (Clough and Penzien, 2003) that the natural frequencies in the x-direction fx and in the y-direction fy are 0.225 Hz
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and 0.341 Hz, respectively. The damping ratio of the aero control tower is adopted as 2% in this study.
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3 METHODOLOGY
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3.1 Numerical simulation
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3.1.1 Computational domain and mesh scheme
As shown in Fig. 2(a), the computational domain covers 40Dy (Dy is the typical
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major axis of 11.6 m at the base of the structure) in the streamwise direction (-8
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inflow and outflow boundary conditions. For the mesh generation, taking into account the irregular geometric shape of the aero control tower, its computational mesh arrangement is not straightforward with respect to the boundary-layer conditions and wind attack angle, while another requirement is to reduce the mesh number as low as
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possible to achieve the efficient numerical computation. As shown in Fig. 2(b) is the mesh on x-z plane at y=0, in which the nesting style mesh is adopted that the high-rise structure is nested in a rectangular cylinder that is four times larger than the tower and
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the whole computational domain is divided into two parts, the inner and outer zones. Additionally, in the inner nesting rectangular cylinder, the inner zone is composed of two subdomains, for which the upper part is filled with the unstructured elements and
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the neighborhood of the wall surface is discretized using a viscous boundary layer of 20 grid nodes and stretched with the ratio of 1.03. The structured mesh is generated in
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the lower part, while for the external zones outside the nesting rectangular cylinder
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the structured mesh is also applied. The advantage of the nesting style mesh offers the fine mesh in the neighborhood of the complex tower while keeping the mesh in zones
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far away from the building unchanged or in a properly coarser manner. Moreover, the
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mesh scheme for the DES model follows the guideline suggested by Spalart (2001), in which the mesh grids were divided into RANS region and LES region from the windward to leeward sides around the bluff body. The RANS region in the windward part requires the coarser grid nodes than the very fine mesh needed for the LES region in the leeward part. Therefore, the minimal grid size in the neighborhood of the aero 8
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control tower is nearly Dy/250 for LES-1 as shown in Fig. 2(b) and the minimal grid size of Dy/150 on the windward side and Dy/200 on the leeward side was set for DES-1. For the purpose of the grid-independence check, the refined mesh schemes of both LES-2 and DES-2 are generated and the grid cells around the high-rise structure
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are refined with the coarsening factor of 2 (the refined mesh scheme divided by the initial one). Table 1 shows the minimal grid size, total mesh number, and the computing costs for the cases with different mesh scheme and turbulence models. The
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non-dimensional wall distances y+ (y+=u*y/ν, y denotes the distance between the first near-wall grid node and the surface, u* represents the friction velocity at the nearest wall and ν indicates the local kinematic viscosity of the fluid) of the first near-wall
3.1.2 Turbulence models
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grid node are less than 10.
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According to the characteristic dimension of the aero control tower (Ls) and
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reference velocity (Uref), the Reynolds number Re=UrefH/ν is 5.95×106 and it is critical to choose an appropriate turbulence model for such a high Reynolds-number
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problem. Several turbulence models, including dynamic Sub-grid Scale (SGS) model
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proposed by Germano et al. (1991) and Lily (1992) in LES, the Spalart-Allmaras (S-A) (Spalart and Allmaras, 1994) and k-ω Shear-Stress-Transport (SST) (Mentor et al., 2003) models in DES (Shur et al., 1999) are used in the present simulations. For the dynamic SGS model in LES, it has some advantages over the standard Smagorinsky SGS model in two aspects (Murakami, 1999): 1) the Smagorinsky 9
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model constant Cs is determined based on space and time of the properties of local flow fields. 2) since the value of Cs automatically becomes zero in the laminar region just near the wall, the empirical damping function for νSGS is no longer necessary in the near-wall region as that adopted in the standard Smagorinsky model .
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In addition, two different DES models including the S-A and k-ω SST based models are adopted in this study to investigate the effects of the roughened wall surfaces. The S-A model uses the distance to the closest wall as the definition of the
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length scale d. However, the DES based S-A model revises the length scale to avoid the ambiguous grid definition. Provided that ∆max <δ ( δ is the boundary layer thickness), the undesired case occurs that the LES model is activated inside the
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boundary layer, where the grid is not fine enough to resolve the turbulence. Therefore, alternative DES model is provided, which is known as the delayed DES model
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(DDES) (Spalart et al. 2006), in order to preserve the RANS model throughout the
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boundary layer. In the DDES model, the revised DES length dddes is given in the
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following form (Spalart et al. 2006), dddes=d-Fdmax(0, (d -CdesΔmax))
(1)
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where Cdes is a model constant with the value of 0.61 and the defer function Fd is defined as
Fd 1 tanh((8rd )3 )
and the specific length scale rd is given by
10
(2)
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rd
t U i , jU i , j 2 d
(3)
For the k-ω SST based DES, compared with the SST model, the dissipation term in the k (turbulence kinetic energy) transport equation is revised as suggested by
Dissipation term *k FDES
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Mentor et al. (2003) in the following form: (4)
where β* is a constant of the SST model and the function FDES is expressed as Lt ,1) Cdes max
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FDES max(
(5)
The turbulence length scale, Lt, is defined as that in the RANS model
Lt
k
*
(6)
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3.1.3 Inflow boundary conditions
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For the approaching wind flows in the wind tunnel testing and the numerical simulations for the aero control tower, the mean longitudinal wind speed and
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turbulence intensity profiles are shown in Fig. 3. As recognized in the wind
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engineering community, the mean wind speed profile should follow the power-law as
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shown in Fig. 3:
U ( z) z h uref ref
(7)
where Uref is the reference mean wind speed at the reference height, which is 7.5 m/s in this study. href is 0.6m in the wind tunnel testing. α is the exponential value of the wind speed profile with the value of 1.5, which is best fitted from the measurements 11
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at the wind tunnel, and z is the height above the ground. The upstream terrain in the wind tunnel testing is regarded as Category Ⅰstipulated in AIJ and exposure C specified in the ASCE7-02 (Flat open grassland). Fig. 3 presents the fitted turbulence intensity profile in the following form (AIJ, 2004),
I ref
z h ref
0.05
3.1.4 Inlet turbulence
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I
(8)
For the unsteady simulation of computational wind engineering problems, one of
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the important issues is to reproduce the realistically time-evolving inflow boundary. As revealed by Huang et al. (2010), the turbulence superimposed at the inlet has a significant effect on the numerical simulation of the wind loading on buildings and
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structures, especially for the fluctuating components. In a previous study of the
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authors (Yan and Li, 2015), several inflow turbulence generation methods have been examined in details, suggesting that the recycling method may provide inadequate
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turbulence level in the upper part of the computational domain. In this study, since the
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roughness element arrangement in the wind tunnel experiment is available, the recycling method over a rough wall is used to reproduce the physically realistic
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inflow turbulence. In order to overcome the shortcoming of the recycling method, additional synthetic turbulence is superposed in the upper part of the computational domain with the weighted amplitude wave superposition (WAWS) method. The equation of the WAWS for the fluctuating streamwise velocity u’(t) is given as (Iannuzzi and Spinelli, 1987), 12
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N
u ' (t ) 2 Su (ni )n cos(2 ni t i )
(9)
i 1
where ni, i=1,…N are the sampled frequencies, φii is a uniformly distributed random phase angle between 0 and 2π, and S(ni) is the sampled von Karman spectrum. With
I add I targ
(t ) U recy urecy U recy
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the WAWS method, the additional turbulence level is given in the following form, (10)
where the subscript “add” and “targ” stand for the additional and target turbulence
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intensity, respectively, and the target turbulence level is specified according to Eq. (8).
(t ) and Urecy indicate the instantaneous and mean wind speeds Moreover, urecy generated by the recycling method, respectively.
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3.1.5 Wall function
near-wall treatment.
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Another issue concerned in the high-Reynolds number flow simulation is the
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For the LES, the near-wall treatment adopted here is based on the work of Werner and Wengle (1991) as described in the following, in which the wall shear
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stresses are estimated by the analytical integration of the power-law near-wall velocity
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distribution.
|𝜏𝜔 | =
𝜌[ {
2𝜇|𝑢𝑝 | 𝑦𝑝 1−𝐵 2
𝐴
1+𝐵 1−𝐵
2
𝜇
|𝑢𝑝 | ≤ 2𝜌𝑦 𝐴1−𝐵 𝑝
1+𝐵
𝜇
(𝜌𝑦 ) 𝑝
+
1+𝐵 𝐴
𝐵
𝜇
2 1+𝐵
(𝜌𝑦 ) |𝑢𝑝 |] 𝑝
𝜇
|𝑢𝑝 | > 2𝜌𝑦 𝐴
2 1−𝐵
(11)
𝑝
where A=8.3, B=1/7, and yp is the near-wall control volume length scale. The “non-slip” boundary condition in the first formula of Eq. (11) is only used in low 13
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velocity regions such as leeward sides, while the second formula is generally activated for most wall boundary conditions. In the present simulations, the near-wall length scales are usually between 0.05 and 0.1m, indicating that the first formula can rarely be used, which represents a real “non-slip” boundary condition.
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The wall roughness effects are included in the study through the law-of-the-wall modified for roughness. Based on the experiments in roughened pipes and channels, the mean velocity distribution near rough walls when plotted in the usual
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semi-logarithmic scale, has the same slope (1/κ) but a different intercept (additive constant B in the log-law). Thus, the law-of-the-wall for mean velocity modified for roughness has the form as follows:
u y p ln( E ) B K s u 1
(12)
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up
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where Ks is the physical sand-grain roughness height, E is equal to eκB with the integration constant B=5.0~5.4 (Schlichting, 1968; White, 1991)) and Ks+ is the
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dimensionless sand-grain roughness height ( u K s / ). Based on the work conducted
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by Nikuradse (1933), Cebeci and Bradshaw (1977) subdivided the whole domain into three regimes: hydro-dynamically smooth regime ( 𝐾𝑠 + < 2.25 ), transitional
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(2.25 ≤ 𝐾𝑠 + ≤ 90), fully rough (𝐾𝑠 + > 90). For surface roughness, according to AIJ specifications for the surface roughness of circular cylinder (AIJ. 2004), two different heights in the present simulation is considered, which are 1% and 5% of the characteristic dimension, Lc (in the present simulation, Lc Ll Ls where Ll and Ls are respectively major and minor axis length at the base of the structure). According 14
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to Cebeci and Bradshaw (1977), the roughness effects are evaluated by the formula as follows:
B
1
ln(1 Cs K s )
(13)
(Hargreaves and Wright, 2006; Blocken et al., 2007). 3.1.6 Numerical algorithm
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where Cs is fixed in the range [0, 1] and the value of 0.5 was adopted in this study
Wind flow concerned in wind engineering applications is usually regarded as
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incompressible flow. In this study, all the discretized equations are solved in a segregated manner. All the discretized equations are solved in a segregated manner. The Pressure Implicit with Splitting of Operators algorithm (PISO) is used in the
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pressure-velocity calculation procedure, which involves one predictor step and two
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corrector steps. PISO is an extension of Semi-Implicit Method for Pressure-Linked Equations (SIMPLE), with an additional corrector step and developed for the
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non-iterative computation of unsteady compressible flows. Therefore, PISO is more
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suitable for the unsteady simulation than the SIMPLE algorithm. In addition, the second order discretization schemes are adopted for spatial discretization. Bounded
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central differencing is used to discretize the convective terms of momentum equations. The time derivative is discretized using the implicit second order backward differences. The Green-Gauss node based method is used for numerical approximation of pressure gradients. The LES is performed a high performance cluster (HPC) at City University of 15
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Hong Kong with the general purpose commercial code ANSYS/Fluent 14.0. A total of 32 CPUs are used in parallel for the simulations. And the time step Δt are restricted to 1×10−3 for computational stability purposes. The initial flow fields of LES and DES cases are established with the convergent RANS results. Meanwhile, the transient
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inflow turbulence generation methods including the DSRFG method and the recycling method are embedded via paralleled user-defined function (UDF) in the ANSYS/Fluent code. All the results from the LES and DES are sampled after an
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initialization period of 5.2 flow-through times (Tft=Lx/UH, where Lx is the length of the computational domain in the longitudinal direction (x) and UH is the reference mean wind speed). The total computational time is equivalent to 20.8Tft, which is
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sufficiently long to reach the statistical convergence for LES and DES (Gousseau et al., 2013). Table 1 shows the computing time costs of LES and DES cases and the
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longest computing time for LES and DES cases are 510 CPU hours with the mesh
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number of 6.7 million and 445 CPU hours with the mesh number of 4.8 million 3.2 Wind tunnel testing
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Wind tunnel experiment is carried out in a boundary layer wind tunnel laboratory
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and the pressure field on the external surfaces of a 1:200 scale model of the aero control tower is measured by means of a Synchronous multi-pressure sensing system (SMPSS). In the testing, the sample frequency is 312.5 Hz and the sampling time length is 32 seconds. In the experiment, the rigid model of the tower as shown in Fig. 1(b) is divided 16
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into twelves measurement levels along the vertical direction and the height of the 12th measurement level is 0.95H (H is the height of the tower model), a total of 285 taps are installed on the surface of the model to measure the time-dependent surface wind pressures. The measured pressures at the taps are integrated to estimate the global and
CD
FD H
1/ 2 U ( z ) 2 dz
CD
FD H
1/ 2 U ( z ) 2 dz
0
0
FL H
1/ 2 U ( z )2 dz
CL
FL H
1/ 2 U ( z )2 dz
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CL
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local aerodynamic forces acting on the tower as defined as,
0
(14)
(15)
0
where ρ is the air density, U(z) is the mean wind speed corresponding to the height z.
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FD and FL are the steady forces acting parallel and transverse to the streamwise direction, respectively.
H
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In order to account for the wind shear profile,
U ( z) dz is considered herein. 2
0
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Substituting the velocity profile given in Eq. (7) into the integration, one has: H
U ( z) dz 0.25U 2
2 H
H
(13)
0
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where UH is the wind speed atop the high-rise structure. 3.3 Wind-induced response analysis
In this study, the wind-induced responses of the aero control tower are estimated
by the spectral analysis method (Tschanz and Davenport, 1983). In the dynamic response analysis of the high-rise structure, only the contribution of the first order 17
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r z, t z q t
(14)
where z is the generalized mode shape and q t is the top-floor displacement. Henceforth, the relationship between the power spectrum of displacement and the
S r z, n 2 z S q n
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principal coordinate power spectrum is given as follows: (15)
in which, Sr z, n and Sq n are the generalized and principal coordinate
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displacement power spectrum, respectively, and n is the frequency of the wind pressure fluctuation. Based on the random vibration theory, the principal coordinate power spectrum Sq z, n is given by
S q n H n S p n 2
(16)
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where S p n is the generalized force power spectrum determined from the time
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sequence of the wind force, H n is the structural frequency response function, and
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the root-mean-square of structural acceleration a z is obtained as follows: 1
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2 2 2 a z (2 ) z H n S p n dn 0
(17)
4 Results and discussion
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4.1 Inflow velocity characteristics
Fig. 5 shows inflow characteristics of the generated wind speeds by the recycling
method. Fig. 5(a) presents the mean wind speed and turbulence intensity profiles which agree well with the experimental results and fitted power-law and the turbulence intensities in the upper part of the computational domain are improved to a 18
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satisfactory level with the WAWS method. Also, the simulated longitudinal velocity spectrum sampled at the top of the aero control tower matches the von Karman spectrum model and that created in the model testing until the reduced frequency reaches approximately 1 Hz and then rapidly decays in high-frequency range
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(dissipation range) due to the filter operation according to the grid resolution at the driver section. Given the fundamental frequency of the aero control tower (fy=0.341 Hz), the upper reduced frequency fxLu/UH=1 Hz as shown in Fig. 5(b) provides a
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lower limit of design wind speed as 2.845 m/s, which is lower than the wind speed of 10-year return period (20 m/s) which is usually adopted for serviceability consideration of high-rise structures, indicating that the current grid resolution is
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adequate for occupant comfort analysis.
4.2 Wind pressure distribution
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Figs. 6 and 7 present the mean and fluctuating wind pressure coefficients
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predicted by the different numerical approaches compared with the results from the wind tunnel testing. In general, the mean pressure coefficients agree well with the
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experimental results on the windward and leeward faces. However, obvious
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discrepancies are observed for the prediction of negative pressures in the separation region which are overestimated by the numerical simulations. This discrepancy might be attributed to the defects of the wall functions in the flow separation region with the inverse pressure gradients. Moreover, the consistent results are provided by the numerical cases “SST-DES-1rough” and “SST-DES-5rough”, which refer to the cases 19
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with rough walls of 1% and 5% roughness heights by DES based k-ω SST model, respectively. Meanwhile, the agreement between the cases “SST-DES-smooth” and “S-A-DES-smooth” is reasonably good, which refer to the cases with smooth walls by DES based k-ω SST model and DES based S-A model, respectively. Furthermore, it is
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noteworthy that the values of negative pressure coefficients in the separation region are reduced when taking into account the surface roughness, which is in consistence with the experimental study conducted by Farell et al. (1976) on rough-walled cooling
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tower. And the smaller pressure recovery was due to the earlier flow separation induced by the surface roughness (Güven et al., 1980).
For the fluctuating components of the pressure coefficients, the agreement
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between all the numerical predictions is fairly good. Nevertheless, they are slightly larger than the experimental results, particularly for those under the wind incident
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angle α=270o. Similar to the results of mean pressure coefficients, the discrepancy of
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RMS pressure coefficients is observed in the flow separation region, and the numerical simulations with the LES and DES models produce relatively larger
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fluctuating pressures as compared to the experimental results. Generally speaking, the
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LES and DES models with rough walls can provide satisfactory predictions of the surface pressures, while the values of negative pressures in the separation region are reduced by the DES models with rough walls in comparison with those with smooth wall. It is clear that the surface roughness has obvious effects on the numerical evaluations of the surface pressures by DES models. Meanwhile, the influence of 20
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different roughness heights seems to be less significant to the numerical simulations. 4.3 Aerodynamic forces As aforementioned, the aerodynamic forces such as the lift and drag coefficients are compared among the numerical predictions and the experimental results, as listed
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in Table 2. The grid-independence check was conducted using LES-1 and LES-2 for LES, while for DES using DES-1 and DES-2. The comparisons show that the basic grid schemes of LES-1 and DES-2 can provide the grid-convergent results for the
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case considered in this study with the fractional errors of less than 3%. Hence, the results from the LES-1 and DES-1 are adopted for the following analysis in this study. For the mean drag force coefficient CD, there exist obvious differences between the cases with smooth walls by the DES based S-A and k-ω SST models and the
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experimental results, while the values calculated by the LES and the k-ω SST DES
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models with rough wall are in good agreement with the experimental data. For the
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fluctuating drag and lift force coefficients, the results by the DES models agree well with those by the LES. However, the discrepancies between all the numerical
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predictions and the experimental results are observed from Table 2, while the LES and
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DES S-A model provide relatively improved fluctuating surface pressure coefficients. As discussed by Breuer et al. (2003), the S-A model with minor modification is consistent with the Smagorinsky SGS model. In summary, when the surface roughness is considered in simulations with DES approaches, the mean drag force coefficients of the rough-walled aero control tower are significantly increased 21
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compared with the smooth-walled case. 4.4 Wind force spectra For the assessment of occupant comfort using spectral analysis, it is necessary to accurately predict the wind force spectra. Fig. 8 presents the along-wind and
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across-wind force spectra obtained from the numerical simulations in comparison with the experimental results. For the along-wind force spectra as shown in Fig. 8(a), the agreement between the numerical predictions and the experimental measurements
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is fairly good and the energy contained in the along-wind force covers a quite wide frequency range. For the across-wind force spectra as shown in Fig. 8(b), the typical narrow-band spectra are provided by all the numerical simulations, which is mainly
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initiated by the vortex-shedding. However, the position of the single spectral peak by the DES based k-ω SST model with rough walls matches that of the measured
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across-wind spectrum, while there exist differences between the numerical predictions
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by the LES and DES models with smooth walls and the experimental results that the single peak of the across-wind spectra are shifted to higher and lower frequency range,
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respectively. It is clear that the DES model considering the surface roughness can
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provide improved across-wind force spectrum over the smooth-walled cases. 4.5 Response analysis
In this study, the wind-induced accelerations atop the tower are calculated using
the method described in section 3.3. As listed in Table 3 are the numerical predictions compared with the wind tunnel test results. For the acceleration in the along-wind 22
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direction, the agreement among the numerical results by the different approaches is quite good, which is in accordance with the consistent along-wind force spectra. However, all the numerical simulations provide slightly larger predictions than the experimental results. For the across-wind acceleration, the LES and DES models with
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rough walls provide quite larger results compared with the experimental results under α=270o (along the major axis), while the agreement for α=0o (along the minor axis) is fairly good. Also, when the surface roughness is taken into account, the across-wind
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peak acceleration predicted by the DES model is increased to a conservative extent compared with the smooth-walled case, since the improved agreement is achieved by the cases with rough walls as shown in Fig. 8(b). It is worth noting that the maximum wind-induced acceleration occurs in the along-wind direction when the wind flow
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approaches along the minor axis (α=0o). On the other hand, the across-wind response
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is dominant when the wind flow approaches along the major axis (α=270o).
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4.6 Wind flow field
Fig. 9 presents the mean and instantaneous velocity contours with streamlines on
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x-y plane at z=0.5 m high by various numerical approaches. As shown in Fig. 9(a), (c)
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and (e) for mean velocity contours, there exist two counter-rotating vortices behind the aero control tower and the LES gives the largest recirculation zone, while the DES based k-ω SST model provides the smallest one. For the instaneous velocity contours as illustrated in Fig. 9(b), (d) and (f), quite strong turbulent vortex sheddings are captured by all the numericla models and fairly long wake zone is predicted by the 23
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LES. Fig. 10 shows turbulence statistics including the resolved Reynolds stresses uv and uw on x-y plane at z=0.5 m high. As shown in Fig. 10(a), (c) and (e) are the shear stress uv contours from -3 to 3 with an increment 0.3 and the results
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calculated by the different numerical models are quite similar, while the differences still exist. For the shear stress uw contours from -1 to 1 with an increment 0.05 as illustrated in Fig. 10(b), (d) and (f), the agreement of the results predicted by the LES
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and DES models is reasonably good.
Fig. 11 shows the mean and instantaneous velocity contours on x-y planes at z=0.1m, 0.2 m, 0.3 m, 0.4 m, 0.5 m and 0.55 m, x-z plane at y=0 and y-z plane at x=0
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by both LES and DES modes for α=0o. Figs. 11(a) and (c) present the three-dimensional mean wind flow field around the aero control tower by LES and
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DES, and both the shear flow and recirculation regions in the leeside are well
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reproduced. Also, the turbulent vortex shedding due to the obstacle and random-like vortices in the upstream flow can be obviously observed in Figs. 11(b) and (d). From
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Fig. 11, it can be found that the LES and DES models can provide similar
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visualizations of the flow field around the aero control tower.
5 Conclusions
This study focuses on the investigation of the influence of surface roughness on
the wind effects on a high-rise structure with elliptical shape. The pressure distribution, drag and lift forces calculated by the LES and DES models are presented 24
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and compared with the experimental results. Moreover, the wind flow fields including the turbulence structures and flow recirculation zones are also revealed and discussed. The main conclusions of the combined numerical and experimental study are summarized as follows:
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(1) The inflow characteristics including the mean and fluctuating speed profiles and the streamwise velocity spectrum can be properly reproduced using the recycling method in combination with the WAWS method. The inadequate turbulence in the
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upper part of the computational domain is improved to a satisfactory level with the use of the WAWS method to generate additional synthetic turbulence. Also, as far as the assessment for occupant comfort is concerned, the grid resolution at the driver
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section is fine enough to provide the upper spectral bound for the wind-induced response analysis using the spectral method.
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(2) The mean pressure coefficients by the LES and DES models are in good
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agreement with the experimental results on the windward and leeward faces; while obvious discrepancies exist in the prediction of negative pressures. Additionally, all
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the numerical simulations slightly overestimate the fluctuating pressure coefficients
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compared with the experimental measurements. It is also noted that the values of negative pressure coefficients in the separation region are reduced when taking into account the surface roughness, but, the effects of different surface roughness heights are less significant. (3) The mean drag force coefficients by the LES and DES models with rough 25
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walls are in reasonable agreement with the experimental results, while the LES and DES based S-A model provide improved fluctuating lift and drag force coefficients. Moreover, the mean drag force coefficient of the rough-walled aero control tower is significantly increased compared with the smooth-walled case.
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(4) The agreement of the numerically predicted along-wind force spectra by the LES and DES models and the experimental data is reasonably good for a wide frequency range. Although the typical narrow band across-wind spectrum is provided
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by all the numerical approaches, the DES based k-ω SST models with rough walls can give consistent prediction of the spectral peak position with the experimental results. (5) For wind-induced response analysis, the across-wind peak acceleration by the
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DES model is increased as far as the surface roughness is concerned, and the LES and DES can provide consistent results compared with the wind tunnel testing.
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(6) Both the LES and DES models can well reproduce the turbulent vortex
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shedding behind the cylinder, while the largest recirculation zone is given by the LES and the smallest by the DES based k-ω SST model. Also, the resolved Reynolds
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stresses in wake regions by the LES and DES models macth each other.
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Acknowledgement
The work described in this paper was fully supported by a grant from the
Research Grants Council of Hong Kong Special Administrative Region, China (Project No: CityU11256416) and a research grant from the National Natural Science Foundation of China (Project No. 51478405). 26
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eddy simulation, Journal of Wind Engineering and Industrial Aerodynamics, 2010, 98: p. 600-617. T. Cebeci and P. Bradshaw, Momentum Transfer in Boundary Layers. Hemisphere Publishing Corporation, New York, 1977.
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Y. Tominaga, A. Mochida, S. Murakami and S. Sawaki, Comparison of various revised k–ε models and LES applied to flow around a high-rise building model with 1:1:2 shape placed within the surface boundary layer. Journal of Wind
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Engineering and Industrial Aerodynamics, 2008, 96:p.389-411. Z.H. Li, J. Davidson and S. Mantell, Numerical simulation of flow field and heat
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transfer of streamlined cylinders in cross flow, ASME Summer Heat Transfer
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Conference, USA, 2005.
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a.
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b.
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Fig. 1 (a) Architectural view; (b) Physical modelling in wind tunnel test; (c)
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Geometric model in the numerical simulation.
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b.
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Fig. 2 (a) Computational domain; (b) standard mesh scheme on x-z plane at y=0
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Fig. 3 Mean velocity and turbulence intensity profiles at the inflow
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(a) Mean velocity and turbulence intensity profiles
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Fig. 4 Aerodynamic forces
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(b) Streamwise wind speed spectrum
(a) mean wind pressure coefficients
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Fig. 5 Inflow velocity characteristics by the recycling method
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(b) RMS wind pressure coefficients
Fig. 6 Comparisons of wind pressure coefficients between the numerical simulations
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and the wind tunnel testing for α=0O
(a) mean wind pressure coefficients
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(b) RMS wind pressure coefficients
Fig. 7 Comparisons of wind pressure coefficients between the numerical simulations
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and the wind tunnel testing for α=270O
(a) Along-wind force spectra
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(b) Across-wind force spectra
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Fig. 8 Along-wind and across-wind spectra estimated from the LES for α=270o
(b) Instaneous wind velocity by LES
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(a) Mean wind velocity by LES
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(c) Mean wind velocity by DES
(d) Instaneous wind velocity by DES based S-A model
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based S-A model
(f) Instaneous wind velocity by DES
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(e) Mean wind velocity by DES based k-ω SST model
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Fig. 9 Mean and instaneous velocity contours with streamlines on x-y plane at
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z=100 m for α=270o
(b) Resolved Reynolds stress uw
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(a) Resolved Reynolds stress uv
by LES
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by LES
(c) Resolved Reynolds stress uv
(d) Resolved Reynolds stress uw
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by DES based S-A model
by DES based S-A model
(f) Resolved Reynolds stress uw
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(e) Resolved Reynolds stress uv by DES based k-ω SST model
by DES based k-ω SST model
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Fig. 10 Resolved Reynolds stresses uv and uw for α=270o
(a) Mean velocity contours by LES
(b) Instaneous velocity contours by LES
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(d) Instaneous velocity contours by DES
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(c) Mean velocity contours by DES
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Fig. 11 Mean and instantaneous wind velocity fields for α=0o by LES and DES Table 1 Mesh arrangement description and computing costs Mesh
Minimal grid size
Mesh numbers (M)
y+
Computing cost (CPU hours)
1
LES-1
Dy/250
4.2
3~8
432
2
LES-2
Dy/500
6.7
2~5
510
3
DES-1
Dy/250
3.5
5~10
366
4
DES-2
Dy/500
4.8
2~8
445
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Cases
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Table 2 Aerodynamic force coefficients by the numerical simulations and the wind tunnel testing Cases
Mesh
Roughness α
1
LES-1
smooth
0o
LES
2
LES-2
smooth
0o
LES
3
DES-1
smooth
0o
SST DES
4
DES-2
smooth
0o
SST DES
5
DES-1
1%
0o
SST DES
6
DES-1
5%
0o
7
LES-1
smooth
270o
8
DES-1
smooth
270o
9
DES-1
smooth
270
10
DES-1
1%
11
DES-1
Turbulence model CD
C’L
0.060
0.1508
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0.514
C’D
0.054 7
0.1531
0.362
0.048
0.1785
0.375 8
0.047 9
0.1733
0.510 5
0.066
0.1829
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0.517 3
0.517 7
0.061 9
0.1827
LES
1.577 0
0.168 5
0.1360
S-A DES
1.285
0.198 4
0.1480
SST DES
1.386
0.214 2
0.1414
270o
SST DES
1.615
0.237 4
0.1339
5%
270o
SST DES
1.659 6
0.216 6
0.1358
Exp
smooth
0o
---
0.524 9
0.058 9
0.1370
Exp
smooth
270o
---
1.718 4
0.157 4
0.0948
6
3
AC
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PT
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M
SST DES
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Table 3 Wind-induced acceleration assessment atop the tower Roughness Along-wind peak
Across-wind peak
acceleration (m/s2)
acceleration (m/s2) 0.0564
0o
smooth
0.3039
SST DES
0o
smooth
0.2784
SST DES
0o
1%
0.3137
SST DES
0o
5%
0.3212
LES
270o smooth
0.1086
0.1997
DES S-A
270o smooth
0.0913
0.1411
SST DES
270o smooth
0.0931
0.1453
SST DES
270o 1%
0.0967
0.1874
SST DES
270o 5%
0.0992
0.1911
smooth
0.285
0.055
0.084
0.155
0.0313 0.0583
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0.0579
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Experiment 0o
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α
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Experiment 270o smooth
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