Numerical modelling of shallow jet flows

Abstract

Shallow jet flows are often coupled to high flow velocities and complex flow patterns. To properly ensure the stability of the barrier between both water bodies surrounding the jet, a scour analysis is often a necessity. Such analyses are inevitably coupled to the hydrodynamic processes occurring in jet flows, either in the form of loads on potential bed protections or equilibrium scour hole depths. Numerical models could assist in the design of bed protections by supplying accurate hydrodynamic input parameters for the design formulae or by predicting the hydrodynamic processes at play. Due to the limited computational power available, simplifications must be made within the numerical model to ensure reasonable computational costs. One of these simplifications is to resolve the flow in depth-averaged sense to create a 2DH model. To allow this simplification to be made, the performance of a 2DH model compared to a fully 3D model needs to be researched. By comparing simulations of a controlled environment and of a prototype scenario, insight in the predictive capabilities of the numerical models for possible other projects can be gained. This work aims to research the performance of 2DH and 3D numerical models regarding the reproduction of the hydrodynamic processes in shallow jets. First, it was investigated which hydrodynamic processes thrive at a prototype shallow jet by analysing measurement data available at Waterdunen. Afterwards, we systematically determine the performance of both a 2DH and 3D numerical model by setting up FINEL models both for a laboratory experiment of a shallow jet and for the shallow jet at Waterdunen. Insight in the predictive capabilities of 2DH and 3D numerical models for shallow jets can contribute to future design problems surrounding shallow jets. Information regarding the shallow jet at the seaside of the culvert at Waterdunen was obtained by Svasek Hydraulics, commissioned by the public government Waterschap Scheldestromen and the province of Zeeland, during a measurement campaign split into six individual measurement scenarios. Immediately at outflow from the culvert, the jet is subject to a 1:6 slope in streamwise direction. The geometry of the seaside channel is asymmetric, with 1:4 lateral slopes at either side of the channel. Furthermore, morphological changes as a result of the jet flow introduce an asymmetric topography in the channel. Visual observations during the measurement campaign indicated the flow can be characterized by an horizontal contraction over the longitudinal slope and an asymmetric flow profile depending on which casings were active within the culvert. The analysis of the measurement data shows the jet concentrates on the eastern side of the channel during all six scenarios. As a result, the recirculation zones on either side of the jet can be characterized as a small, non-dominant recirculation zone on the east side of the jet and a large, dominant recirculation zone on the west side of the jet. The streamlines show a continuous horizontal contraction until the flow hits the eastern side of the channel. Over the longitudinal slope, the flow seems to remain attached to the bottom rather than separating. However, due to a relatively large clearance of the ADCP measurements with respect to the bottom, this cannot be proven directly. It was decided to simulate the shallow jet of experiment 2.4.1 of van de Zande (2018) to investigate the performance of a 2DH and 3D numerical model for a laboratory simulation. In this experiment, the behaviour of an asymmetric shallow jet over a longitudinal slope at the point of the horizontal expansion was investigated. It was shown that both the 2DH and 3D numerical model were capable of reproducing the most dominant hydrodynamic processes within the jet. However, the accuracy with which the processes were reproduced differed significantly. The 2DH model reproduced too much curvature of the flow towards the lower wall of the flume compared to both the 3D model and the measurement data. As a result, the high flow velocities in the jet center were located further down in the channel. The flow velocities in the jet center were modelled with a maximum error of 12.4% in the 2DH model and 3.02% in the 3D model. The lower accuracy of the 2DH model is caused by the comparison between depth-averaged velocities and surface PIV velocities. Due to the additional curvature the recirculating velocities in the non-dominant recirculation zone were modelled too high by the 2DH model, with an error of up to 56.6% relative to the jet center velocity. In the 3D model, this error decreased to 18.9%. However, it was remarked the recirculating flow velocities in the PIV data were subject to clumping of tracer particles. The horizontal streamline contraction was simulated in the 2DH model, but can only be directly related to the changes in water depth. In both the 3D model and the measurements, this horizontal streamline contraction was shown to continue further downstream of the slope. It was concluded the horizontal streamline contraction is directly related to the vertical velocity profile, which was observed to differ from the standard log-profile both on the slope and downstream thereof. The 3D model was capable of reproducing the vertical velocity profile with a maximum relative error of 10%. In the numerical simulations at Waterdunen, both the 2DH and 3D models were shown to behave similarly. Both the 2DH and 3D numerical models were capable of reproducing the eastern concentration of the flow. However, the curvature of the jet further downstream was modelled more accurate in the 3D model. The better reproduction of the flow curvature in the 2DH model compared to the laboratory simulations is the result of the asymmetric inflow boundary, which allows the 2DH model to more easily resolve the flow curvature. Both models underestimate the flow velocities throughout the entire DOI. It was concluded this was caused by errors in the model input. Similar to the laboratory simulations, the 2DH model reproduced the horizontal streamline contraction over the slope but failed to reproduce the contraction further downstream. The 3D model was capable of reproducing the continuing streamline contraction. Furthermore, the 3D model reproduced vertical flow attachment over the slope, which complies well with the measurement data. It was concluded that a 3D numerical model can better reproduce the flow curvature in case of asymmetrical flows. Furthermore, the recirculating flow is better reproduced by a 3D model compared to a 2DH model. Finally, a 3D model is capable of accurately reproducing the vertical velocity profile, which supplies additional information of accurate flow velocities at the bed. However, on a prototype scale the differences between a 2DH and 3D numerical model are small. In channels with symmetrical boundaries, it is suggested to use a 3D numerical model in case the flow is subject to the Coanda-like effect. However, if the inflow into the channel is already asymmetrical, a 2DH numerical model can be considered to save computational effort. Nevertheless, when employing a 2DH model one should be wary of geometric and topographic asymmetries, as the effect of both factors on the flow symmetry is still unclear.