An investigation of a temperature calculation procedure from mole fractions of chemical species and enthalpy in incompressible thermo fluid dynamics simulation

This paper presents a procedure for calculation of temperature from mole fractions of chemical species and enthalpy, which are obtained from conservation equations of thermo fluid dynamics simulation. Fifteen chemical species that are often taken into account in gas and pulverized combustion simulation were investigated: N₂, O₂, CO, CO₂, H₂, H₂O, SO₂, H₂S, CH₄, C ₂H₂, C₂H₄, C₂H ₆, C₃H₄, C₃H₆ and C ₃H₈. When temperature is calculated from mole fractions of chemical species and enthalpy, a large error is involved if heat capacity is assumed to be constant. Thus, the equation expressing the relationship between enthalpy and temperature, derived by integrating the approximation of heat capacity with respect to temperature, should be used to obtain the temperature with high precision. When heat capacity is approximated by a quadratic or cubic polynomial with respect to temperature, the polynomial approximation expressing the relationship between enthalpy and temperature is cubic or a fourth degree polynomial approximation. A non-iterative solution such as the Cardano method or the Ferrari method is available for the solution of the cubic or fourth degree polynomial approximation in a temperature calculation procedure. When heat capacity is approximated by a fourth or higher degree polynomial approximation with respect to temperature, an iterative method such as the Newton method is necessary to solve temperature. The higher the degree of the polynomial approximation is, the higher the computational load becomes. The computational load of the non-iterative method is the same as that of the iterative method when the degree of the enthalpy as a function of temperature is the fourth.