Numerical and experimental study of the aerodynamic characteristics around two-dimensional terrain with different slope angles

doi:10.1007/s11707-019-0790-8

Front. Earth Sci.

2019, Vol. 13

Issue (4) : 705-720 https://doi.org/10.1007/s11707-019-0790-8

RESEARCH ARTICLE

Numerical and experimental study of the aerodynamic characteristics around two-dimensional terrain with different slope angles

Pingzhi FANG¹(

), Deqian ZHENG², Liang LI², Wenyong MA³, Shengming TANG¹

¹. Shanghai Typhoon Institute of China Meteorological Administration, Shanghai 200030, China
². School of Civil Engineering and Architecture, Henan University of Technology, Zhengzhou 450001, China
³. Wind Engineering Research Center, Shijiazhuang Tiedao University, Shijiazhuang 050043, China

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Abstract

Complicated terrain was considered and simplified as two-dimensional (2D) terrain in a dynamical downscaling model and a parametric wind field model for typhoons developed by the Shanghai Typhoon Institute. The 2D terrain was further modeled as uphill and downhill segments with various slope angles relative to the incoming flow. The wind speed ratios and pressure characteristics around the 2D terrain were numerically and experimentally investigated in this study. Aerodynamic characteristics of the 2D terrain with a limited-length upper surface were first investigated in the wind tunnel with sheared incoming flow. The corresponding numerical investigation was also conducted by using the commercial computational fluid dynamics code FLUENT with the realizable k-ε turbulence model. Special efforts were made to maintain the inflow boundary conditions throughout the computational domain. Aerodynamic characteristics were then investigated for the ideal 2D terrain with an unlimited-length upper surface by using a numerical method with uniform incoming flow. Comparisons of the different terrain models and incoming flows from the above studies show that the wind pressure coefficients and the wind speed ratios are both affected by the slope angle. A negative peak value of the wind pressure coefficients exists at the escarpment point, where flow separation occurs, for the uphill and downhill terrain models with slope angles of 40° and 30°, respectively. Correspondingly, the streamwise wind speed ratios at the points above the escarpment point for the uphill terrain model increase with increasing slope angle, reach their peak values at the slope angle of α = 40° and decrease when the slope angle increases further. For the downhill terrain model, similar trends exist at the points above the escarpment point with the exception that the critical slope angle is α = 30°.

Keywords numerical simulation wind tunnel test aerodynamic characteristics critical slope angle

Corresponding Author(s): Pingzhi FANG

Just Accepted Date: 18 September 2019 Online First Date: 12 November 2019 Issue Date: 30 December 2019

Cite this article:

Pingzhi FANG,Deqian ZHENG,Liang LI, et al. Numerical and experimental study of the aerodynamic characteristics around two-dimensional terrain with different slope angles[J]. Front. Earth Sci., 2019, 13(4): 705-720.

URL:

https://academic.hep.com.cn/fesci/EN/10.1007/s11707-019-0790-8
https://academic.hep.com.cn/fesci/EN/Y2019/V13/I4/705

Fig.1 (a) Sketches of the simplified 2D uphill terrain model with a limited length-upper surface of 7L. Aerodynamic characteristics at 5 locations along the slope surface and 11 points over each location along the slope surface were measured; and (b) the corresponding physical model in the wind tunnel with the Cobra Probes.

Fig.2 (a) Comparisons of the mean wind profiles among the wind tunnel test, fitted logarithmic law, the prescribed inlet flow at the inlet boundary (x = -10L) and the approaching flow before the uphill terrain model (x = -5L); and (b) comparisons near the land surface.

Fig.3 (a) Overview of the CFD domain and mesh scheme; and (b) close view of the mesh scheme around the terrain model with limited-length upper surface.

Wind field			Model constants
u/(m·s⁻¹)	z₀/m	$z ′ 0$ /m	C₂	s_e	s_k
0.3752	1.5538 × 10⁻⁴	9.7 × 10⁻⁵	1.9	1.2	0.4

Tab.1 Model constants for the wind field with the realizable k-ε turbulence model

Boundary	BC	Mathematical implication
Inlet	Velocity-Inlet	U	$U u * = 1 κ ln (z + z 0 z 0)$
		k	$k = 1.5 × (U g I u g) 2 = 0.28 m 2 / s 2$
		ε	$ε = C μ 1 / 2 k ∂ U ∂ z$ , $C μ = 0.09$
Outlet	Pressure-Outlet	k, ε: the same as those at the inlet boundary
Top	Symmetry	$∂ (U, P, k, ε) / ∂ z = 0$
Side	Symmetry	$∂ (U, P, k, ε) / ∂ y = 0$
Terrain surface	Wall	Standard wall function: $K s = 0$
Land surface	Wall	User defined wall function with $δ B = 7.0$ and $K s = 10.0 z 0$

Tab.2 BCs for the wind field with the realizable k-ε turbulence model

Fig.4 Comparisons of the mean wind pressure distribution from the terrain model with limited-length upper surface: (a) uphill model with α = 15°; (b) uphill model with α = 30°; (c) downhill model with α = 15°; and (d) downhill model with α = 30°.

Fig.5 Comparisons of the wind speed ratios from the uphill terrain model with limited-length upper surface: (a) streamwise wind speed ratios for slope angle α = 15°; (b) streamwise wind speed ratios for slope angle α = 30°; (c) vertical wind speed ratios for slope angle α = 15°; and (d) vertical wind speed ratios for slope angle α = 30°.

Fig.6 Comparisons of the wind speed ratios from the downhill terrain model with limited-length upper surface: (a) streamwise wind speed ratios for slope angle α = 15°; (b) streamwise wind speed ratios for slope angle α = 30°; (c) vertical wind speed ratios for slope angle α = 15°; and (d) vertical wind speed ratios for slope angle α = 30°.

Fig.7 Comparisons of the topographic multiplier from the uphill terrain model with limited-length upper surface among the available results: (a) comparisons for the slope angle α = 15° and (b) comparisons for the slope angle α = 30°.

Fig.8 (a) Overview of the CFD domain and mesh scheme and (b) close view of the mesh scheme around the terrain model with unlimited-length upper surface.

Fig.9 Variations in the mean wind pressure coefficients at locations along the slope surface with different slope angles for the ideal 2D terrain model with uniform incoming flow: (a) uphill terrain model and (b) downhill terrain model.

Fig.10 Variations in the streamwise wind speed ratios with the different slope angles for the 2D ideal uphill terrain model with uniform incoming flow.

Fig.11 Variations in the vertical wind speed ratios with the different slope angles for the ideal 2D uphill terrain model with uniform incoming flow.

Fig.12 Variations in the streamwise wind speed ratios with the different slope angles for the ideal 2D downhill terrain model with uniform incoming flow.

Fig.13 Variations in the vertical wind speed ratios with the different slope angles for the ideal 2D downhill terrain model with uniform incoming flow.

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