Variation of the Sectional Drag Coefficient of a Group of Buildings with Packing Density

Santiago, José Luis; Coceal, Omduth; Martilli, Alberto; Belcher, Stephen E.

doi:10.1007/s10546-008-9294-x

Cited by 72 publications

(85 citation statements)

References 16 publications

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“…The roughness length results, in figure 8(a), closely follow the skin friction trends as a function of both the solidities, as shown in table 1. The drag-peak location herein is partially in contrast with previous studies, for which it was found at λ P ≡ λ F ≈ 0.15 (Hagishima et al 2009;Leonardi & Castro 2010;Kanda et al 2004) and λ P ≡ λ F ≈ 0.16 (Santiago et al 2008;Coceal & Belcher 2004). These differences are perhaps not surprising giving the high uncertainty in the fitting procedure which results in the visible scatter of the data for different studies in figure 8(a), even when values of similar frontal and plan solidity are considered.…”

Section: Effect Of Surface Morphology On Aerodynamic Parameterscontrasting

confidence: 99%

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Effects of frontal and plan solidities on aerodynamic parameters and the roughness sublayer in turbulent boundary layers

Placidi

Ganapathisubramani

2015

J. Fluid Mech.

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Citation: Placidi, M. & Ganapathisubramani, B. (2015). Effects of frontal and plan solidities on aerodynamic parameters and the roughness sublayer in turbulent boundary layers. Journal of Fluid Mechanics, 782, pp. 541-566. doi: 10.1017Mechanics, 782, pp. 541-566. doi: 10. /jfm.2015 This is the accepted version of the paper.This version of the publication may differ from the final published version. Experiments were conducted in the fully-rough regime on surfaces with large relative roughness height (h/δ ≈ 0.1, where h is the roughness height and δ is the boundary layer thickness). The surfaces were generated by distributed LEGO TM bricks of uniform height, arranged in different configurations. Measurements were made with both floating-element drag-balance and high-resolution particle image velocimetry on six configurations with different frontal solidity, λ F , at fixed plan solidity, λ P , and vice versa, for a total of twelve rough-wall cases. Results indicate that the drag reaches a peak value λ F ≈ 0.21 or a constant λ P = 0.27, whilst it monotonically decreases for increasing values of λ P for a fixed λ F = 0.15. This is in contrast with previous studies in the literature based on cube roughness that show a peak in drag for both λ F and λ P variations. The influence of surface morphology on the depth of the roughness sublayer (RSL) is also investigated. Its depth is found to be inversely proportional to the roughness length, y 0 . A decrease in y 0 is usually accompanied by a thickening of the the RSL and vice-versa. Proper orthogonal decomposition analysis was also employed. The shapes of the most energetic modes calculated using the data across the entire boundary layer are found to be selfsimilar across the twelve rough-walls cases, however, when the analysis is restricted to the roughness sublayer, differences that depend on the wall morphology are apparent. Moreover, the energy content of the POD modes within the RSL suggest that the effect of increased frontal solidity is to redistribute the energy towards the larger-scales (i.e. larger portion of energy is within the first few modes) whilst the opposite is found for variation of plan solidity. Permanent

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Section: Effect Of Surface Morphology On Aerodynamic Parameterscontrasting

confidence: 99%

“…These studies include both numerical and physical experiments (Cheng & Castro 2002b;Coceal & Belcher 2004;Kanda et al 2004;Cheng et al 2007;Hagishima et al 2009;Santiago et al 2008;Leonardi & Castro 2010 among various others). Open symbols in figure 2(a) show the cases examined in these studies.…”

Section: Introductionmentioning

confidence: 99%

Effects of frontal and plan solidities on aerodynamic parameters and the roughness sublayer in turbulent boundary layers

Placidi

Ganapathisubramani

2015

J. Fluid Mech.

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“…5a), consistent with the trend reported for rigid canopies (Poggi et al 2004b;Santiago et al 2008). As suggested by DNS results of Santiago et al (2008), the instantaneous drag coefficient (C d ) for a canopy of rigid cubes is approximately a constant, and most of the variability in the mean drag coefficient ( C d ) is attributed to the contribution from the components of TKE and DKE. Removing the variability in C d caused by variability in TKE and DKE is critical for investigating the drag-wind relationships.…”

Section: Implications For the Models Of Mean Drag-wind Relationshipssupporting

confidence: 87%

“…Thirdly, the work done by the canopy drag is expected to dissipate the total kinetic energy of the flow, whereas only the mean velocity directly appears on the right-hand side of (3). Therefore C d must contain the variability associated with TKE and dispersive kinetic energy (DKE), as confirmed by direct numerical simulation (DNS) of a staggered arrangement of rigid cubes (Santiago et al 2008). Alternatively, the model of the mean canopy drag can be modified to account for the dissipation of TKE and DKE explicitly,…”

Section: Models Of Mean Canopy Drag and Traditional Estimates Of Locamentioning

confidence: 99%

“…First, C d is a constant, an assumption used in many LES studies (e.g., Shaw and Schumann 1992;Su et al 1998;Patton et al 2003;Yue et al 2007b;Dupont and Brunet 2008;Gavrilov et al 2013). DNS results suggest that a constant instantaneous drag coefficient is a good model for rigid canopies (Santiago et al 2008). Second, C d decreases as a power-law function of the magnitude of the instantaneous velocity (|u|), which accounts for the effects of viscous drag and reconfiguration,…”

Section: Approaches To Estimate the Instantaneous Drag-wind Relationshipmentioning

confidence: 99%

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Estimating the Instantaneous Drag–Wind Relationship for a Horizontally Homogeneous Canopy

Pan

Chamecki

Nepf

2016

Boundary-Layer Meteorol

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The mean drag-wind relationship is usually investigated assuming that field data are representative of spatially-averaged metrics of statistically stationary flow within and above a horizontally homogeneous canopy. Even if these conditions are satisfied, large-eddy simulation (LES) data suggest two major issues in the analysis of observational data. Firstly, the streamwise mean pressure gradient is usually neglected in the analysis of data from terrestrial canopies, which compromises the estimates of mean canopy drag and provides misleading information for the dependence of local mean drag coefficients on local velocity scales. Secondly, no standard approach has been proposed to investigate the instantaneous drag-wind relationship, a critical component of canopy representation in LES. Here, a practical approach is proposed to fit the streamwise mean pressure gradient using observed profiles of the mean vertical momentum flux within the canopy. Inclusion of the fitted mean pressure gradient enables reliable estimates of the mean drag-wind relationship. LES data show that a local mean drag coefficient that characterizes the relationship between mean canopy drag and the velocity scale associated with total kinetic energy can be used to identify the dependence of the local instantaneous drag coefficient on instantaneous velocity. Iterative approaches are proposed to fit specific models of velocity-dependent instantaneous drag coefficients that represent the effects of viscous drag and the reconfiguration of flexible canopy elements. LES data are used to verify the assumptions and algorithms employed by these new approaches. The relationship between mean canopy drag and mean velocity, which is needed in models based on the Reynolds-averaged Navier-Stokes equations, is parametrized to account for both the dependence on velocity and the contribution from velocity variances. Finally, velocity-dependent drag coefficients lead to significant variations of the calculated displacement height and roughness length with wind speed. B Marcelo Chamecki

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Canopy edge flow: A momentum balance analysis

Moltchanov

Bohbot-Raviv

Duman

et al. 2015

Water Resources Research

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Canopy flow models are often dedicated to ideal, infinite, homogenous systems. However, real canopy systems have physical boundaries, where the flow enters and leaves patches of vegetation, generating a complex pressure field and velocity variations. Here we focus our study on the canopy entry region by examining the terms involved in the double (space and time) averaged momentum equations and their relative contribution to the total momentum balance. The estimation of each term is made possible by particle image velocimetry (PIV) measurements in a model canopy constructed of randomly distributed thin glass plates. The instantaneous velocity fields were used to calculate the mean velocities, pressure, drag, Reynolds stresses, and dispersive stresses. It was found that within the entry region, the pressure gradient, the drag forces, and dispersive stresses are the three most significant terms that affect the balance in the streamwise momentum equation. In the vertical direction, the dispersive stresses are also significant and their contribution to the total momentum cannot be ignored. The study shows that dispersive stresses are initially formed around canopy edges; at both the entry region and the canopy top boundary. They start as a sink term, extracting momentum from the flow, and then become a source term that contributes momentum to the flow until they eventually decay at some short penetration distance into the canopy. These results reveal a new understanding on the evolution of momentum within the entry region, necessary in any closure modeling of flow in real canopies.

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Variation of the Sectional Drag Coefficient of a Group of Buildings with Packing Density

Cited by 72 publications

References 16 publications

Effects of frontal and plan solidities on aerodynamic parameters and the roughness sublayer in turbulent boundary layers

Effects of frontal and plan solidities on aerodynamic parameters and the roughness sublayer in turbulent boundary layers

Estimating the Instantaneous Drag–Wind Relationship for a Horizontally Homogeneous Canopy

Canopy edge flow: A momentum balance analysis

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