Three-Dimensional Turbulent Simulation of Bivariate Normal Distribution Protection Device

Abstract

In response to the deficiencies in existing bridge pier scour protection technologies, this paper introduces a novel protective device, namely a normal distribution-shaped surface (BND) protection devices formed by rotating a concave normal curve. A three-dimensional turbulent SST k−ω model is constructed, and physical model experiments of conical surfaces are conducted to validate the mathematical model. The simulation analyzes longitudinal water flow, downflow, vorticity intensity, and shear stress within normal and conical surfaces. The results show that the downflow distribution in front of the pier spans a relative water depth of (−0.45, 0.67), with a peak velocity approximately 70% of the longitudinal flow velocity. Circulation forms within the surfaces, with the main vortex flux inside the BND being 33% lower than that inside the conical surface. The maximum shear stress coefficient inside the BND can reach 9, and the protective surface isolates the bed from the flow to prevent scouring by high shear stress. The velocity gradient at the edge of the surface is small, and the edge shear stress of the 3D normal distribution-shaped surface (BND) protection device is only one-third of that of the conical surface, preventing edge scouring. The large shear stress and its distribution area decrease monotonically with the increase in surface width. When the surface width is four times the diameter, the distribution range of the shear stress coefficient greater than 1 is very small. The study of three-Dimensional turbulence within the BND provides a numerical basis for an anti-scour design.