Finite element surface model for flow around vertical wall abutments

Abstract A two-dimensional finite element surface model is developed to determine velocities, depths, and turning angles around vertical wall abutments. The model solves the Reynolds-averaged turbulent flow equations along a horizontal plane passing through the average water surface. This approach is an improvement over the depth-averaged flow models where dispersion terms reflecting vertical effects are neglected. In the model, vertical gradient effects are accounted for through the use of power law for the vertical distribution of the longitudinal velocity; a similar treatment is applied to lateral turbulent shear stresses. The model is capable of computing the dynamic pressure distribution, which in turn is converted to water elevation values. The model, being two dimensional, is computationally efficient and practical to use. The numerical model was successfully verified using experimental data from vertical wall abutments and groins with protrusion ratios (ratio of protrusion length perpendicular to direction of flow to total channel width) of 0·1, 0·2 and 0·3. The results show the occurrence of a high intensity velocity zone close to the upstream abutment nose similar to those observed experimentally. The effects of roughness, depth, and energy slope on the intensity of flow field is investigated and an analytical expression is developed. Numerical experiments indicate that grain roughness affects flow field around the abutment nose by controlling the magnitude of the lateral velocity component and by controlling the lateral extent of the affected zone. Velocity amplification at the abutment nose is found to be mainly related to the protrusion ratio and to the friction factor, and can be up to 1·75 times the approach velocities for protrusion ratios of 0·3. For a protrusion ratio of 0·3, for a typical range of roughness values the increase in nose velocities due to friction factor alone was found to be up to 20 percent.