## 1 Introduction  
Jet impingement is a very efficient solution for cooling hot components, since very high heat fluxes can be removed. In many industrial processes, this cooling technique is used for the cooling of gas turbine blades, of electronic components, and the cooling process of metallic and glassy materials. In the galvanizing lines, it is necessary to quickly cool the steel before it enters the molten zinc bath. The temperature decrease in the metal, during the passage through close cooling sections, lies between 250 and 280 \({}^{\circ}\)C, and must be carried out with a certain rate that correlates with the mechanical characteristic of the steel under production and with the speed of the production line (production rate). A thorough study of this section of the system is of some importance; by optimizing the system, the overall dimensions can be reduced, as well as the electricity consumption of the fans. The energetic optimization of industrial components in industrial plants with very high energy consumption, like steel or glass production systems, is of utmost importance to reduce both fuel consumption and pollutant emissions; a small percentage increase in efficiency can give relevant fuel and money savings. Even the tiniest effect in design improvement is therefore welcome. The use of CFD (Computational Fluid Dynamics) simulation can give a significant support to the development of industrial components where the heat transfer process is involved [1; 2; 3]. The effect of real gas flow can be also introduced [4] when severe expansion processes with a strong temperature gradient and heat transfer are involved, like in turbomachinery applications [5]. Over the years, several experimental and numerical studies have been conducted both on single jets and on multi-jet systems. In the available literature, dealing with both experimental and numerical analysis, the effect of different parameters on the flow field and on the heat exchange properties at the wall was tested; the main parameters considered were: Reynolds number, distance between jet and wall, spacing between the jets, and geometry of the nozzle. [PERSON] and [PERSON] [6] have reviewed the rich literature on the subject, reporting a number of empirical correlations developed by various authors for the prediction of the average Nusselt number on the surface to be cooled. [PERSON] and [PERSON] [7] experimentally investigated the effects of Reynolds number and of jet-wall distance on the heat exchange, for a single jet system, with a detailed study of the variation in the heat exchange coefficient along the radial distance from the jet axis. [PERSON] [8] has experimentally tested the interaction of flows from multi-jet systems. The multi-jet configuration primarily affects the flow field, increasing the production of turbulent kinetic energy that determines the spatial distribution of heat exchange. The above solution is of particular interest to the present application and different simulations are discussed in the following sections. On the numerical side, research applications ([PERSON] al. [9]) have mainly studied axisymmetric jet impingement models, analyzing the influence of operating parameters and checking the validity of turbulence models in predicting both flow and thermal fields. Taking into account other studies from [PERSON] et al. [10], [PERSON] [11], [PERSON] et al. [12], [PERSON] et al. [13], and [PERSON] et al. [14], it is clear that there is no single turbulence model that can be identified as the most effective for this physical phenomenon. In the present work, the attention is focused on the heat transfer from a single jet or from a jet cluster to set up a proper CFD model for the analysis of the actual industrial configuration. Different test cases have been considered in order to have a proper insight into the flow mechanisms and to validate the proposed CFD approach. Initial simulations were performed on 2D axisymmetric models, comparing the results with experimental data from the literature and from the ERCOFTAC database [15].