Nils Reidar Bøe Olsen

3D numerical modelling of open-channel flow with submerged vegetation

Velocity distributions in channels partially covered with vegetation have been computed using a three dimensional model. The Navier-Stokes equations were solved, using the SIMPLE method and the k-ε turbulence model. The vegetation was modeled as vertical cylinders. A formula for the drag force on the vegetation was included as a sink term in the Navier-Stokes equations. The advantage with this method compared with using large roughness is that effects of the vegetation over the whole water depth can be taken into account, instead of only affecting the velocity near the bed. The numerical model was tested against three laboratory experiments from straight flumes with uniform flow, where vegetation partially covered the cross-section. The velocity and vegetation density varied in both vertical and horizontal directions in the different cases. The experiments also included varying crosssectional shapes. All tests gave fairly good correspondence between computed and measured velocity profiles.

Three-dimensional numerical flow modeling for estimation of maximum local scour depth

Water flow is modeled numerically in three dimensions around a circular cylinder placed vertically in a flume. The numerical model solves the Navier-Stokes equations with the k-z turbulence model. This gives the shear stress on the bed. A formula for concentration at the bed as a function of the shear stress is used. The bed concentrations are used to solve the convection-diffusion equation for the sediments. Continuity for the cells close to the bed gives the bed changes. The water flow field is solved simultaneously with the sediment calculation. The models include time-dependency with transient terms, and calculation of the free surface is also done. An adaptive grid is used, which follows the changes in bed and water surface elevations. The model gives the development of the three-dimensional scour hole around the cylinder. The resulting scour hole has a maximum depth which compares well with empirical formulas for local scour.

Three-dimensional numerical modelling of water flow in a river with large bed roughness

A numerical model for three-dimensional simulation of water flow in rivers with large roughness elements is developed. The bed roughness elements are large stones and rocks in the rivers. The model uses a finite volume method to solve the Navier-Stokes equations for three dimensions on a general non-orthogonal grid. The k-e turbulence model is used to solve the Reynolds-stress term. A porosity model is developed to model the bed roughness elements. The porosity model is used in combination with the solution of the Navier-Stokes equations to calculate interactions between porous and non-porous areas. To test the model, a reach of the Norwegian river Sokna is modelled. Velocity measurements from the river are taken at a number of locations and at several discharges. The measured velocities compare well with the results from the numerical model.

Two-dimensional numerical modelling of flushing processes in water reservoirs

This study describes a two-dimensional numerical model simulating flushing of sediments from water reservoirs. The numerical model solves the depth-averaged Navier-Stokes equations on a two-dimensional grid. A zeroequation turbulence model is used. The resulting flow field is extrapolated to three dimensions, and the convectiondiffusion equation for the sediment concentration is solved. A formula for the bed concentration is used as boundary condition, resulting in a calculation of bed material load. Continuity for the cells closest to the bed is used to find the bed changes. The pressure field is used to calculate the location of the water surface. The grid is adaptive in the vertical direction, and changes according to the calculated water and bed levels. A porosity model is used to simulate the process when the water surface drops under the bed level at some locations of the geometry. The results from the numerical model were compared with data from physical model studies. The main features of the eros...

Three-dimensional numerical modeling of water and sediment flow in a sand trap

The flow of water in a three-dimensional sand trap is calculated by a numerical model, using a finite volume method to solve the Navier-Stokes equations for three dimensions on a general non-orthogonal grid. The k-∊ turbulence model is used to solve the Reynolds- stress term. The diffusion/convection equation for the sediment concentration is solved giving the sediment concentration in the sand trap. A physical model study carried out to verify the results shows the recirculation zone to be shorter than the numerical model result, but modifications in the turbulence model give better agreement. The sediment concentration calculations compare well with the experimental procedures. The concentration calculated by using the flow field from the original k-∊ model gives 87.1 % trap efficiency, whereas calculation with the more correct flow field gives 88.3 %.

Three-dimensional numerical flow modelling for estimation of spillway capacity

Water flow over a spillway was modelled numerically in two and three dimensions for various geometries. The model solved the Navier-Stokes equations with the k-t turbulence model on a structured non-orthogonal grid. A method based on water continuity was used to calculate the movement of the water surface. Using an adaptive grid in the vertical direction, the location of the water surface was recalculated from an initially horizontal profile. After several iterations a steady solution emerged. The location of the water surface was used to calculate the capacity and the coefficient of discharge for the spillway. Physical model studies were carried out to determine the accuracy of the numerical model. The coefficient of discharge was also compared with empirical formulas. The deviation of the calculated coefficient of discharge was 1% for the two-dimensional cases, and 0.5 % for the three-dimensional case. Reasonable agreement was also found for the pressure at the spillway bed, which was measured in one of...

Numerical Modeling of Flow Over Trapezoidal Broad-Crested Weir

Abstract Two computational fluid dynamics (CFD) codes, Flow-3D and SSIIM 2, have been used to calculate the water flow over a trapezoidal broad-crested weir. The two programs apply different algorithms for making the grid and computing the free water surface. Flow-3D uses the Volume of Fluid (VOF) method with a fixed grid, while SSIIM 2 uses an algorithm based on the continuity equation and the Marker-and-Cell method, together with an adaptive grid for the water surface. The results have been compared with measurements from a physical model study, using different discharges. The deviation between the computed and measured upstream water level was between 1.0 and 3.5%. The difference between the results from the two CFD models was in the range of 1–1.5%. The accuracy of the algorithms depends on the grid size. The computational time on one core of a CPU (Intel Q9650 3.00 GHz) was between 435 and 15,500 seconds, using between 6,350 and 10,000 cells.

Coupling remote sensing with computational fluid dynamics modelling to estimate lake chlorophyll-a concentration

A remotely sensed image of Loch Leven, a shallow meso-eutrophic lake in Central East Scotland, UK, revealed a strong gradient in chlorophyll-a (chl-a) concentration. As a means of interpreting the spatial distribution of chl-a in this image, a combined three-dimensional computational fluid dynamics (CFD) and ecological model was run using estimates of the environmental and planktonic conditions concurrent with and preceding the time of image acquisition. The post facto modelling of the dynamics of the lake produced spatial distributions of surface chl-a that were consistent with that evident in the remotely sensed image. It is proposed that CFD modelling benefits the interpretation of remotely sensed images of water bodies in that it may be used to infer the causes of the spatial distributions evident in the remotely sensed imagery. This is because modelling extends the analysis into the temporal and vertical domains. However, the value of combining CFD with remote sensing is limited by the quality and quantity of data available through surface observation and remote sensing, and the implications of this to the integration of CFD with remote sensing are discussed.

Three-dimensional numerical modelling of bed changes in a sand trap

Water and sediment flow was modelled numerically in three dimensions in a tunnel-type sand trap. The numerical model solved the transient Navier-Stokes equations with the k-∊ turbulence model. Simu...

Three-dimensional numerical modelling of reservoir flushing in a prototype scale

A fully three-dimensional numerical model for reservoir flushing has been tested against field measurements for the Angostura reservoir in Costa Rica. The numerical program solves the Reynolds-averaged Navier–Stokes (RANS) equations in three-dimensions and uses for discretization the finite-volume method together with a second-order upwind scheme. The used grid is unstructured and non-orthogonal, made of a mixture of hexahedral and tetrahedral cells. In addition to the bathymetry data of the prototype, the model uses grain size distributions of the bed, discharge rates and water levels during the flushing. Simulated bed level changes during the flushing are presented in this study as well as the computed amount of eroded sediments. Where the amount of flushed out sediments show reasonable agreement, differences in the developed flushing channel simulated by the model and compared to the prototype were observed. However, the presented study shows that due to the increasing development of three-dimensional RANS models, the simulation of a reservoir flushing in a prototype becomes feasible.