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

Abstract

Abstract: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 ks is the primary factor on which d and z0 depend. In different step height, step width, discharge and intake Froude number, the relations d/ks = 0.22-0.27, z0/ks = 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. OPEN ACCESSWater 2014, 6 3889 Keywords: displacement height; surface roughness length; stepped spillway; boundary layer development; numerical simulations; logarithmic law; inception of air entrainment

Effect of Height and Geometry of Stepped Spillway on Inception Point Location

“…It was suggested that the energy dissipation rate in the different types of pooled weirs followed the order, two-sided and central pool, full pool and central pool, full pool and two-sided pools, and full pool. Cheng et al [40] measured the logarithmic velocity profile in a stepped spillway using numerical simulation and compared it with experiments. According to their researches, the air inception location over stepped spillways exits until the boundary layer thickness is between the range of 0.72 and 0.79.…”

Simulação Numérica De Escoamentos Com Superfícies Livres Empregando O Método Weakly Compressible Smoothed Particle Hydrodynamics (Wcsph) E O Processamento Em Paralelo Com Unidades De Processamento Gráfico E a Api Cuda

“…Para a verificação do simulador numérico desenvolvido, na versão bidimensional, a geometria do problema foi a mesma que a descrita em Chanson e Toombes (2002) e Cheng et al (2014) (Fig. 3).…”

Stepped Spillways and Energy Dissipation: A Non-Uniform Step Length Approach

“…In addition to these experimental studies, flow on stepped spillways have been modeled numerically with a high degree of accuracy using computational fluid dynamics (CFD). In numerical studies of stepped spillways, the flow over the stepped spillway is investigated by the volume of fluid (VOF) method, with turbulence closures of the k-ε family [26][27][28][29][30][31][32][33][34][35]. For instance, Wan et al [36] have used VOF and the realizable k-ε model to determine the inception point of air entrainment in various stepped spillways, including flat steps, pooled steps, and round steps.…”