## 2 Materials and Methods
### CFD-FVM Model (Step 2.1)  
After the first experimental phase, a computational phase started, making use of the data corresponding to the first operative point P\({}_{0}\). In this phase, a list of different cases was simulated (simulations plan) to progressively align the output of an initial CFD-FVM model of the exhaust pipe with reality. Firstly, a complete 3D model of the exhaust line (Figure 5a), including the exhaust pipe used in the experimental layout (obtained from the drawings used to manufacture the exhaust duct) and part of the exhaust manifold in the engine head (developed from the technical drawings of the engine), was created through the CAD-CAE software suite SolidWorks 2020 SP2.0 (by Dassault Systemes, Velizy-Villacoublay, France). It is worth noting that, since the goal of such a CFD-FVM model was having the correct path (in terms of length and bends) of the exhaust duct, even in the part inside the engine head, to have the correct flow motion of the exhaust gas, the engine head was carefully modeled only in the exhaust duct starting from some cross-sections found in the technical documentation of the engine. On the contrary, the head was externally modeled with very simple, parallelepiped volumes useful to contain the duct (hence only a \"simulacrum\" of the engine head was created for this simulation). Therefore, the actual mass and shape, outer surfaces, gaskets and inner cavities of the engine head (including the presence of engine fluids and possible sludge in it) were deliberately not taken into account to have, in the simulation, an element as simple as possible. Subsequently, the CAD drawings of this system were imported into the computational package \"Flow Simulation\" (developed by Mentor Graphics Corporation, part of Siemens group), included in the same software suite SolidWorks, to perform some computational fluid dynamics simulations [55]. This CFD-FVM package is an agile software program sufficiently accurate for industrial applications (hence very widespread in an industrial context), and it was deliberately chosen over other software because of some specific advantages it has for the purposes of this work, not finalized at performing a detailed study on the fluid dynamics of the used exhaust pipe but rather using the CFD-FVM simulation as a tool of a more general procedure. Indeed, \"Flow Simulation\" has a direct interface with the CAD package, making the model-import operations very quick, simple and error-proof, and setting a simulation is very fast. Notwithstanding some limitations with respect to other more famous CFD-FVM programs, SolidWorks Flow Simulation proved to be more than suitable for the aims of this study, whose novelty is the joint use of some numerical tools, included but not exclusively, a CFD-FVM software. Specifically, the imported geometry was used to bound the spatial domain for the subsequent CFD calculations. In this regard, the geometry of the engine head, far enough from TCs (in particular, TC1) not to influence the results, was properly simplified, not to increase the simulation time uselessly. The spatial domain was then discretized (\"meshed\") into small control volumes to perform the calculations (Figures 5b and 6). The numerical method used to solve the fluid dynamics equations is based on the cell-centered finite volume method (FVM) with the \"two-scales wall functions model\" [55; 56; 57], using two different approaches depending on the mesh refinement level. The resulting mesh (hexcore-type mesh) is composed of a total of 258 398 parallelepiped-shaped elements (hexahedrons) for the fluid, having the sides parallel to the three references planes constituting the base trihedron (this is a peculiarity of this software program), and 140 900 elements at the fluid-solid interfaces, composed by elements divided geometrically by the solid wall surface (locally approximated by portions of plane), coupling two different calculation domains.