Velocity distribution in open channel flow with spatially distributed roughness

Abstract

A numerical procedure is proposed to estimate the velocity distribution in open channel flow, for engineering applications. A method based on the mixing length model and subdivision of the wetted surface, is modified to easily integrate a lateral distribution of roughness. Several friction models for vegetated or rough flows can be added, two of which have been tested. The numerical procedure was developed with a commercial software (Matlab) to ensure fast computation and possible coupling with 1D hydraulic models. The validation of the computation has been done with rectangular and compound channels with spatially distributed roughness. The usefulness of the method for ecohydraulics is demonstrated with two applications: box culvert design for fish passes and 1D modelling of mountain river flows for which experimental results from a laboratory scale-model is compared to predictions. The interest of a friction law calibrated with a real grain roughness size is put forward.

An Enhanced Treatment of Boundary Conditions for 2D RANS Streamwise Velocity Models in Open Channel Flow

“…Against this background, the estimation of bed shear stress using this method has three main issues: (i) small errors in the velocity distribution affect isovelocity curves and could have a great effect when calculating bed shear stress since the geometry of the rays defines the control volume; (ii) it requires analyzing velocity distribution over the full section to compute bed shear stress at any point along the wetted perimeter, where the relation among velocity and shear stress is mainly local; and (iii) the shear stress along the water-air interface is not considered in the momentum balance. Additionally, the eddy viscosity in the model by Cassan et al [18] increases up to free surface without setting a maximum value, contrary to what is observed in reality.…”

“…Additionally, Kean and Smith [11] found that the eddy viscosity increases along each ray until it reaches a maximum value to be calibrated. However, in Cassan et al [18], the eddy viscosity increases as it approaches the free surface without reaching a maximum value. For simplicity reasons and avoiding the use of adjustment parameters, a shear stress-independent function similar to Equation ( 5) is considered hereinafter for the eddy viscosity distribution along the rays, increasing until it reaches its maximum value of ν t,max = κu * h/4 at d = h/2, and then remaining constant from that point to the end of the ray, at the point where maximum velocity is located.…”

“…Later, Kean et al [17] validated the previous model against a high-resolution laboratory dataset of velocity and boundary shear stress measurements for a trapezoidal channel. More recently, Cassan et al [18] presented a simplified method based on previously mentioned works to estimate the streamwise velocity distribution in rectangular and compound channels with spatially varying roughness, imposing as boundary condition the velocity at a certain fixed distance to the wall given by the logarithmic law for smooth and rough boundaries. This method incorporates a fully predictive mixing length model and a sub-division of the wetted surface to calculate bed shear stress along the perimeter applying the momentum balance over each portion between adjacent rays, but it neglects the influence of the free surface boundary layer.…”

“…The downstream component of the momentum in each portion is compensated only by the local bed shear stress acting along its corresponding length of the rigid contour, which heavily depends on the computed streamwise velocity distribution. Both methods [17,18] require an iterative procedure to alternatively solve the momentum equation for velocity and the equation for shear stress and eddy viscosity until convergence. Against this background, the estimation of bed shear stress using this method has three main issues: (i) small errors in the velocity distribution affect isovelocity curves and could have a great effect when calculating bed shear stress since the geometry of the rays defines the control volume; (ii) it requires analyzing velocity distribution over the full section to compute bed shear stress at any point along the wetted perimeter, where the relation among velocity and shear stress is mainly local; and (iii) the shear stress along the water-air interface is not considered in the momentum balance.…”

Environmental fluid mechanics in hydraulic engineering

“…Both d-type and k-type roughness boundary conditions are discussed, including the secondary flow motion. Cassan et al [8] analyse the effect of spatial roughness distribution along fixed boundaries. Based upon a simplified solution of the Navier-Stokes equations, the boundary shear stress distribution may be derived along the wetted perimeter.…”