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Mean pressure coefficient distributions over hyperbolic paraboloid roof and canopy structures with different shape parameters in a uniform flow with very small turbulence

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Abstract
The hyperbolic paraboloid with two high and low corners is the most basic anticlastic double curved shape of tensile surface structures. However, this shape is currently not considered in the existing wind load standards and only very few investigations are documented in literature. Therefore, this study aims to map the mean aerodynamics over hyperbolic paraboloid roofs and extremely thin canopies to help engineers understand the general aerodynamics of these structures. In this study, scaled wind tunnel testing is performed on rigid models of a roof with enclosing walls and a canopy without enclosing walls to draft mean Cp-distributions and standard deviations for various wind orientations. These mean Cp-distributions are validated with the limited studies in literature and used to calibrate and benchmark a numerical wind tunnel, using CFD RANS simulations, that allows to further reduce the thickness of the canopy compared to the wind tunnel models. The numerical wind tunnel is used to study the mean wind load distributions for hyperbolic paraboloid roofs and canopies with different surface curvature for the most important wind orientations. The results in this paper show good agreement between wind tunnel experiments and CFD simulations, with similar variations as established by different studies of the Silsoe cube. First mean Cp-distributions obtained with scaled wind tunnel testing are presented for hyperbolic paraboloid canopies of only 5 mm thick, with similar mean net Cp and only slightly larger suction over the upper and lower face compared to the numerical results for a zero-thickness canopy. The numerical study of different surface curvatures indicates different geometrical patterns in the mean Cp-distributions when the flow starts to separate for highly curved hypars. In general, suction and pressure increase for higher surface curvature, with similar geometrical patterns in the mean Cp-distributions, as long as the flow remains attached. If the flow separates for highly curved hypars, the geometrical pattern differs and the mean Cp drops due to the different behavior of the flow. Finally, the presented mean Cp-distributions give insight in the aerodynamics of hypar roofs and canopies with different surface curvature and could form a basis for future analysis towards peak loads for the design of these structures.
Keywords
Canopy, CFD, Doubly curved, Hypar, Roof, Pressure coefficients, Wind analysis, Wind tunnel

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MLA
Colliers, Jimmy, et al. “Mean Pressure Coefficient Distributions over Hyperbolic Paraboloid Roof and Canopy Structures with Different Shape Parameters in a Uniform Flow with Very Small Turbulence.” ENGINEERING STRUCTURES, vol. 205, 2020.
APA
Colliers, J., Degroote, J., Mollaert, M., & De Laet, L. (2020). Mean pressure coefficient distributions over hyperbolic paraboloid roof and canopy structures with different shape parameters in a uniform flow with very small turbulence. ENGINEERING STRUCTURES, 205.
Chicago author-date
Colliers, Jimmy, Joris Degroote, Marijke Mollaert, and Lars De Laet. 2020. “Mean Pressure Coefficient Distributions over Hyperbolic Paraboloid Roof and Canopy Structures with Different Shape Parameters in a Uniform Flow with Very Small Turbulence.” ENGINEERING STRUCTURES 205.
Chicago author-date (all authors)
Colliers, Jimmy, Joris Degroote, Marijke Mollaert, and Lars De Laet. 2020. “Mean Pressure Coefficient Distributions over Hyperbolic Paraboloid Roof and Canopy Structures with Different Shape Parameters in a Uniform Flow with Very Small Turbulence.” ENGINEERING STRUCTURES 205.
Vancouver
1.
Colliers J, Degroote J, Mollaert M, De Laet L. Mean pressure coefficient distributions over hyperbolic paraboloid roof and canopy structures with different shape parameters in a uniform flow with very small turbulence. ENGINEERING STRUCTURES. 2020;205.
IEEE
[1]
J. Colliers, J. Degroote, M. Mollaert, and L. De Laet, “Mean pressure coefficient distributions over hyperbolic paraboloid roof and canopy structures with different shape parameters in a uniform flow with very small turbulence,” ENGINEERING STRUCTURES, vol. 205, 2020.
@article{8639968,
  abstract     = {{The hyperbolic paraboloid with two high and low corners is the most basic anticlastic double curved shape of tensile surface structures. However, this shape is currently not considered in the existing wind load standards and only very few investigations are documented in literature. Therefore, this study aims to map the mean aerodynamics over hyperbolic paraboloid roofs and extremely thin canopies to help engineers understand the general aerodynamics of these structures. In this study, scaled wind tunnel testing is performed on rigid models of a roof with enclosing walls and a canopy without enclosing walls to draft mean Cp-distributions and standard deviations for various wind orientations. These mean Cp-distributions are validated with the limited studies in literature and used to calibrate and benchmark a numerical wind tunnel, using CFD RANS simulations, that allows to further reduce the thickness of the canopy compared to the wind tunnel models. The numerical wind tunnel is used to study the mean wind load distributions for hyperbolic paraboloid roofs and canopies with different surface curvature for the most important wind orientations. The results in this paper show good agreement between wind tunnel experiments and CFD simulations, with similar variations as established by different studies of the Silsoe cube. First mean Cp-distributions obtained with scaled wind tunnel testing are presented for hyperbolic paraboloid canopies of only 5 mm thick, with similar mean net Cp and only slightly larger suction over the upper and lower face compared to the numerical results for a zero-thickness canopy. The numerical study of different surface curvatures indicates different geometrical patterns in the mean Cp-distributions when the flow starts to separate for highly curved hypars. In general, suction and pressure increase for higher surface curvature, with similar geometrical patterns in the mean Cp-distributions, as long as the flow remains attached. If the flow separates for highly curved hypars, the geometrical pattern differs and the mean Cp drops due to the different behavior of the flow. Finally, the presented mean Cp-distributions give insight in the aerodynamics of hypar roofs and canopies with different surface curvature and could form a basis for future analysis towards peak loads for the design of these structures.}},
  articleno    = {{110043}},
  author       = {{Colliers, Jimmy and Degroote, Joris and Mollaert, Marijke and De Laet, Lars}},
  issn         = {{0141-0296}},
  journal      = {{ENGINEERING STRUCTURES}},
  keywords     = {{Canopy,CFD,Doubly curved,Hypar,Roof,Pressure coefficients,Wind analysis,Wind tunnel}},
  language     = {{eng}},
  pages        = {{25}},
  title        = {{Mean pressure coefficient distributions over hyperbolic paraboloid roof and canopy structures with different shape parameters in a uniform flow with very small turbulence}},
  url          = {{http://dx.doi.org/10.1016/j.engstruct.2019.110043}},
  volume       = {{205}},
  year         = {{2020}},
}

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