## 5 Discussion
### Flow Characteristics of a 7.4 m/s Jet Impinging into a Plunge Pool with a Pool Depth of 0.8 m
Performing simulations with the DES K-OmegaSST model using the D24 mesh can lead to some pressure fluctuations, but the simulation time increases by 2.75 times, which is a need of 1.5 days to perform one second of simulation. A simulation with some seconds was needed to obtain statistical moments from the pressure signal. In practical engineering cases, a way to have numerical results for so long is incompatible with the deadlines of design phases. A significant limitation of using this type of method is the impossibility of using a curser mesh to start new simulations. This leads to the initial time of simulation, which must be used to stabilize the flow conditions before obtaining the pressure signal. Due to this, the simulation time will increase significantly. By applying the relation between the velocity fluctuations and the mean pressure coefficient proposed by [PERSON] et al. [3], Equation (11) produced a good agreement between the two data sets. Numerical results fit well the pressure fluctuation coefficient at the zone near the jet stagnation point, far from this region; \(r/D_{i}>0.69\), the numerical fluctuations are higher than the experimental ones. Then, at distances far from the jet centerline (\(r/D_{i}>2.80\)), the obtained experimental and numerical values are very close. [PERSON] [10] relates the pressure fluctuation at this region to the air concentration at the plunge pool bottom. The air concentration values at the bottom of the plunge pool are directly related to the jet air concentration at the impinging section of the plunge pool and the additional volume of air that locally enters that location. It must be pointed out when comparing experimental and numerical results that the experimental approach for measuring the pressure fluctuations involves several uncertain sources, particularly due to the inherent errors associated with the measurement chain, starting on the fact that the transducers, although very small, have physical dimensions. The numerical model also involves mesh-induced errors, boundary condition limitations and empirically estimated parameters. Despite the efforts to minimize these aspects, they are among the causes of observed differences between experimental and numerical results. The jet velocity profile obtained in the numerical simulations reveals a core persisted for \(5.0D_{i}\) when a turbulent intensity of 7% is used at the jet's initial section. For reference, [PERSON] and [PERSON] [4] observed core lengths of \(4.0D_{i}\) for circular plunging water jets with Reynolds numbers of \(10^{5}\) to \(10^{6}\). [PERSON] et al. [46] and [PERSON] and [PERSON] [47] reported core lengths between 6.2 to \(6.8D_{i}\) for air jets with Reynolds numbers exceeding 1500, while [PERSON] [12] proposed a maximum core length of \(7.8D_{i}\) for high-velocity flows. Despite these differences, the established flow zone showed a consistent velocity decrease slope when compared with [PERSON] et al. [44]. The analysis of the initial turbulent conditions confirms that the jet's initial state significantly affects the pressure and velocity fields. Consequently, direct comparisons with experimental data from other studies are challenging, as the initial turbulence conditions are not explicitly presented in those studies. Further research is needed to enhance solver capabilities, particularly in (i) expanding the range of jet velocities and pool depths by simulating additional scenarios that can be directly compared with experimental data, (ii) improving the simulation of jet diffusion under shear flow dominating conditions, (iii) enhancing the accuracy of pressure fluctuations predictions, and (iv) applying twoPhaseEulerFoam to other hydraulic structures for broader validation.