**3. CFD modeling approach of erosion in the HET**

The turbulence of the water flowing inside the HET sample hole is modeled using Fluent software. Fluent is a general-purpose CFD code that has been applied to various problems in the fields of fluid mechanics and heat transfer. The code has been validated in numerous studies. Fluent is, especially, appropriate for the complex physics involved in heat and mass transfer and considers mixtures by modeling each fluid phase independently or as a homogenized medium [9].

Flow taking place inside the hole is turbulent. To perform realistic simulation of turbulence, the exact instantaneous Navier-Stokes governing equations are habitually time-averaged or ensemble-averaged. The obtained averaged equations contain further unknown variables, and turbulence models are introduced in order to determine them in terms of known quantities. Various turbulence models have been proposed in the literature; however, there is no single turbulence model, which could be applied for all classes of problems [10]. The choice of a pertinent model for a given problem will depend on the actual physics of the flow, the degree of accuracy required, and the computational cost tolerated. Fieldview Reference Manual [9] gives a detailed discussion on how to perform at best the appropriate choice of a turbulence model. Among the various models, the standard *k* � *ε* model, which was proposed first by Launder and Spalding [11], has become the most popular one when dealing with practical engineering flow calculations. This model relies on phenomenological considerations and integrates empiricism to perform closure of turbulence equations.

Improvements of the standard *k* � *ε* model, such as the RNG *k* � *ε* model, have been made by [12]. This model was derived by using a rigorous statistical technique called renormalization group theory (RNG) [13].
