# Influence of Burner Nozzle Parameters Analysis on the Aluminium Melting Process
## 2 Experimental Research
### CFD Modeling  
Numerical simulation of the combustion process was computed in ANSYS CFX v 17.2. ANSYS CFX computes discrete values of time-dependent Navier-Stokes equations, which are conservation equations of momentum in \(x\), \(y\)-, and \(z\)-directions, and the conservation equation of mass. Time-dependent details of turbulent eddies are removed from the Navier-Stokes equations with Reynolds averaging and the effect of turbulent motion on transport of momentum in the averaged flow is assumed by means of the Boussinesq hypothesis, which defines turbulent viscosity. Turbulent viscosity increases the basic molecular viscosity of the fluid. Computation of turbulent viscosity requires additional equations, which are based on the k-epsilon RNG model. The combustion process was defined using a combination of finite rate chemistry and eddy dissipation models. The basis for the calculation of combustion was the global reaction scheme of methane combustion, methane air water-gas shift (WGS) [18], defined by the following relationships [16; 18; 19]:  
\[CH_{4}+0.5O_{2}\to CO+2H_{2}O, \tag{3}\]  
\[H_{2}+0.5O_{2}\to H_{2}O, \tag{4}\]  
\[CO+0.5O_{2}\to CO_{2}, \tag{5}\]  
\[CO+H_{2}O\to CO_{2}+H_{2}. \tag{6}\]  
The Equations (3) to (6) were defined for the combustion of methane and air. However, the flame temperature and the course of chemical reactions at oxy-combustion and air-combustion differ. The higher combustion temperatures lead to a greater dissociation of the flue gas components. Therefore, these changes have to be incorporated into the mathematical model. The course of chemical reactions in the mathematical model can be influenced by the change of mathematical dependences of the chemical reaction on temperature, which is expressed by the Arrhenius equation (7). In their work, [PERSON] [19], [PERSON] [20], and [PERSON] [21] optimised kinetic parameters of the chemical reactions in order to make them suitable for mathematical modelling of oxy-combustion (8; 9; 10; 11). \[k=A.e^{\frac{-E_{a}}{kT}}, \tag{7}\]  
where \(k\) is the rate constant, \(E_{a}\) is the activation energy (J mol\({}^{-1}\)), \(R\) is the universal gas constant 8.314 J K\({}^{-1}\) mol\({}^{-1}\), and \(T\) is the absolute temperature (K). Figure 3: (**a**) Schematic presentation of the gas and oxidizer flow; (**b**) Formation of the combustion mixture. The optimized rate constant for the Equations (3) to (6) is given as follows [19; 20; 21]:  
\[k_{1}=1.5910^{13}.e^{\frac{-47800}{KT}}[CH_{4}]^{0.7}[O_{2}]^{0.8}, \tag{8}\]  
\[k_{2}=5.010^{20}.e^{\frac{-3000}{KT}}[H_{2}]^{0.25}[O_{2}]^{1.5}, \tag{9}\]  
\[k_{3}=3.9810^{8}.e^{\frac{-1000}{KT}}[CO][O_{2}]^{0.25}[H_{2}O]^{0.5}, \tag{10}\]  
\[k_{4}=2.7510^{12}.e^{\frac{-20000}{KT}}[CO][H_{2}O]. \tag{11}\]  
Boundary conditions for the gas and oxidizer inlet were defined by the mass flow, pursuant to \[H_{2}+0.5O_{2}\to H_{2}O, \tag{4}\]0 The radiation heat transfer was modelled using the P1 model based on the expansion of the radiation intensity into an orthogonal series of spherical harmonics. The DesignModeler software was used to create a model of a furnace with the incorporated combustion chamber of the physical model and the charge. The mathematical model of the physical module was discretized for the computing network. The combustion chamber was created using tetrahedral mesh and it was concentrated more in the area of the walls and burner, where larger gradients were assumed due to the hexahedral layer, which ensured the correctness of the velocity field creation. The mesh adjacent to the walls in the region of the boundary layer has perpendicular geometric spacing, with a multiple of 1.15 between the heights of consecutive layers of volumes, and the first layer of volume has a height of 0.035 mm. The worst value of y+ was 15 and it was observed in the stack area. In other areas, it ranged from 0 to 1.5.