The Use of the k- ω SST Turbulence Model for Mathematical Modeling of Jet Fire

Aim: The purpose of this study is to verify the usability of the k-ω SST turbulence model for the description of the combustion process during a vertical propane jet fire. Simulating a jet fire using computational fluid mechanics involves an appropriate selection of a mathematical model to describe the turbulent flow. It is important as the variables from this model also describe the rate of the combustion reaction. As a result, they have an impact on the size and shape of the flame. The selection of an appropriate model should be preceded by preliminary simulations. Project and methods: For this purpose, a vertical jet fire in no wind conditions was selected for simulation. Consequently, it was possible to develop a two-dimensional axisymmetric geometry. A good numerical mesh can be applied to such axisymmetric geometry. Selected process conditions allowed to create an axisymmetric numerical grid. Its values, proving the quality, are shown in a chart demonstrating the distribution of the parameter quality depending on the number of elements from which the numerical grid was built. In the work, a two-stage model of the combustion reaction was selected in order to verify whether the area in which the mole fraction of carbon monoxide will have significant values is so large that the selected kinetic reaction model will have an impact on the flame length. Results: Three simulations of jet fire taking place in the direction opposite to the force of gravity were performed. The simulations performed allowed for setting the basic L f parameter, which determines the flame length. Additionally, the length of the mixing path s lift-off , needed to initiate the combustion reaction, was determined. The simulations performed allowed for comparing significant parameters characterizing the flame with the parameters calcu lated using correlations included in the literature on the subject. Due to this comparison, it was possible to define an interesting scope of research work, because the length of the gas mixing path determined from the CFD simulation differed significantly from the values calculated from the correlation. Conclusions: Interestingly, such large differences between CFD results and correlations were not observed for the L f parameter. The correlations based on the Froude number give slightly higher values of the flame length than the results of the CFD simulation. On the other hand, the correlation based on the Reynolds number gives slightly lower values of the L f parameter than the values obtained from the CFD calculations. This may indicate that the effects related to the inertia forces ( Re number) better describe the simulation process conditions than the correlations based on the influence of inertia forces and gravity forces ( Fr number).

Typically, one of the two k-ε or k-ω turbulence models is used.
Both of these mathematical models allow for the correct descrip-

Mathematical description of jet fire
Pure propane gas was selected to simulate the jet fire. The propane combustion reactions were described by means of a two-step reaction: The transport of momentum, heat and mass in the considered process can be described by the following differential equations: 1. Continuity equation: (3)
Balance equations for k-th component: The turbulent Schmidt number is expressed by the relationship: In the equation (14) the reaction term R k describing the course of the reaction in turbulent flow is described by the relationship given by Magnussen and Hjertager [3].
Energy balance: The value of the effective thermal conductivity coefficient λ eff is expressed by the relationship: The enthalpy of the mixture is calculated by the formula: where N is the total number of the components in the gas mixture.

Geometric model of the simulated problem
The case of a vertical jet fire taking place in windless conditions was selected for the simulation. Therefore, the considered problem can be simplified to the case of a two-dimensional axisymmetric space. Figure    Opracowano siatkę numeryczną składająca się z 88 000 prostokątnych elementów. Parametr oznaczający jakość ortogonalną (ang. orthogonal quality) we wszystkich elementach wynosił 1. Na rycinie 2 przedstawiono wartości parametru określającego jakość numeryczną siatki w zależności od liczby elementów.
A numerical grid consisting of 88.000 rectangular elements has been developed. The parameter indicating the orthogonal quality in all elements was 1. Figure 2 shows the values of the parameter describing the numerical quality of the mesh depending on the number of the elements.

Number of the elements [thousands]
Reynolds and Froude numbers can be described by the relationships: SFT VOL. 59 ISSUE 1, 2022, PP. 28-40 The physicochemical parameters of all the ingredients were taken from the Fluent database. The exception was the dynamic viscosity of propane, the values of which were approximated by the Sutherland equation using the data included in [11].      The following figures show (see Figure 6-8) the distributions of the mole fractions of oxygen, carbon dioxide and carbon monoxide in the jet2 simulation. As it can be seen from these figures, the model of the two-stage reaction of propane combustion is justified because the zone in which carbon monoxide occurs is quite large (see Figure 8).
Despite the large Reynolds Rein (see Table 2) numbers of propane at the inlet to the system, turbulent vortices have some noticeable effect on the reaction of incomplete combustion of propane.      Table 3.
As can be seen from the data in Table 4