Application of Displacement Height and Surface Roughness Length to Determination Boundary Layer Development Length over Stepped Spillway

Water

Xiangju Cheng¹  John S. Gulliver²  Dantong Zhu¹ 

[1] School of Civil Engineering and Transportation, South China University of Technology, Guangzhou 510640, China; E-Mail:;St. Anthony Falls Laboratory, Department of Civil Engineering, University of Minnesota, Minneapolis, MN 55112, USA; E-Mail:

关键词: displacement height;    surface roughness length;    stepped spillway;    boundary layer development;    numerical simulations;    logarithmic law;    inception of air entrainment;   

DOI  :  10.3390/w6123888

来源: mdpi

【 摘 要 】

One of the most uncertain parameters in stepped spillway design is the length (from the crest) of boundary layer development. The normal velocity profiles responding to the steps as bed roughness are investigated in the developing non-aerated flow region. A detailed analysis of the logarithmic vertical velocity profiles on stepped spillways is conducted through experimental data to verify the computational code and numerical experiments to expand the data available. To determine development length, the hydraulic roughness and displacement thickness, along with the shear velocity, are needed. This includes determining displacement height d and surface roughness length z₀ and the relationship of d and z₀ to the step geometry. The results show that the hydraulic roughness height k_s is the primary factor on which d and z₀ depend. In different step height, step width, discharge and intake Froude number, the relations d/k_s = 0.22–0.27, z₀/k_s = 0.06–0.1 and d/z₀ = 2.2–4 result in a good estimate. Using the computational code and numerical experiments, air inception will occur over stepped spillway flow as long as the Bauer-defined boundary layer thickness is between 0.72 and 0.79.

【 授权许可】

CC BY   
© 2014 by the authors; licensee MDPI, Basel, Switzerland.