# Evaluation of Three-Dimensional Environmental Hydraulic Modeling in Scour Hole
## 3 Results and Discussion
### Turbulent Kinetic Energy  
Values of turbulent kinetic energy were calculated and presented in Figure 8. Mostly, at 2 cm from the scoured hole, the values were estimated as excessively increased due to the larger values of velocity gradients and flow circulation. According to previous studies [20; 21], high turbulence intensities are possible in decelerating turbulent flows, due  
Figure 7: Comparison of velocity profile results of laboratory experiment, OpenFOAM, and Ansys Fluent at different downstream distances.  
to the formation of layers with great velocity gradients in abrupt expansions of water depth. [PERSON] and [PERSON] [21] described turbulent mixing (or shear) layer in the scour hole with experimental data and numerical approaches. As they proposed, re-circulation (or reverse movement) of flow in the upstream scour slope occurs near the bed, and a mixing layer develops between the transient flow and the recirculating flow [20; 21].  
The non-dimensional turbulent kinetic energy profiles produced by the two numerical models at several cross-sections are plotted as in Figure 9 in comparison with the laboratory experimental data. For a turbulent flow, such as the flow of water running from a smooth bed through a sand bed channel in this study, the turbulent kinetic energy \(k\) is normally used to investigate the turbulence characteristic of that flow, since it is defined as the mean kinetic energy per unit mass associated with eddies in turbulent flow.  
As can be seen here, both OpenFOAM and Ansys Fluent well captured the happenings of the high turbulent region in the scour hole. The turbulent kinetic energy value increases dramatically from the layer close to the bed to reach the maximum in the center of the circulation flow, and then decreases in the free stream upper region, to finally reach a constant value, which is similar to the value of \(k\) at the transition point of \(x/h_{0\,\mathrm{Fig  
Figure 8: Distribution of turbulent kinetic energy in the scoured hole (modified from [18]).  
Figure 9: Comparison of turbulent kinetic energy profile results of laboratory experiment, OpenFOAM, and Ansys Fluent at downstream distances of \(x/h_{0}=0.0\), \(2.1\), and \(4.2\).  
This is due to the change in horizontal, vertical, and lateral velocity fluctuations in these regions. While velocities near the bed are relatively low due to the vertical flow separation, the circulation causes back-flow and induces the formation of small eddy scales in the scour hole that increase the velocity fluctuation, and therefore increases the turbulent kinetic energy of this zone. At the beginning of the scour hole and in the free stream region above the fixed bed level, the results of \(k\) from both models are almost identical for both model results. However, they show some difference inside the circulation zone. In this region, the predicted turbulent kinetic energy from Ansys Fluent model is smaller than that from OpenFOAM. Overall, the difference between these two results is RMSE = 2.5 \(\times\) 10\({}^{-4}\), but it reaches RMSE = 3.5 \(\times\) 10\({}^{-4}\) in the scour hole. Moreover, though both the OpenFOAM and Ansys Fluent models can capture the overall behavior of turbulent kinetic energy profile of the flow, they are still not so accurate when compared with the experimental data. In this study, the \(k-\omega SST\), which was developed to simulate both the low and high Reynolds number or close and far from the wall, was used in all simulations. However, overall, the value of differences compared to laboratory experiment case reached RMSE = 0.0058 and 0.0062 for OpenFOAM and Ansys Fluent, respectively.