Equations of Average Isobaric Heat Capacity of Air and Combustion Gases With Influence of Pressure and Effect of Thermal Dissociation

Abstract

All properties of thermomechanical systems working substance are two-parameter that is determined by two parameters, the most often they are temperature and pressure which are easily measured by experiment. Representing the isobaric heat capacity as a function of temperature cp = f(T) become a thing of the past. Analytical and tabular ways are used to represent dependencies as a function of temperature and pressure. The tabular method is convenient for single calculations, but the analytical one is more convenient for a series of calculations. The advantages of an analytical description in comparison with a tabular one are obvious, namely, compactness of information storage without reference to node points, the ability to integrate and differentiate, dependencies can be embedded directly in the program body and don’t require special subroutines to access to the tables. Developers of the programs for calculating thermophysical properties, as a rule, use functional dependencies which may have a different appearance for temperature and pressure intervals of the same substance. This is explained by the fact that in the region close to the saturation curve, there is a steep change in all the thermophysical properties of substances including the isobaric heat capacity. In thermogasdynamic calculations of heat machines, the main physical parameter of the working fluid is its heat capacity, both true and average. The article presents the analytical dependencies of the average specific isobaric heat capacities of the main components of air and combustion products of hydrocarbon fuels which are united throughout the specified range of pressures and temperatures (nitrogen: p = 1 ... 200 bar, T = 150 ... 2870 K, oxygen: p = 1 ... 200 bar, T = 210 ... 2870 K, argon: p = 1 ... 200 bar, T = 190 ... 1300 K, the water vapor: p = 0,1 ... 200 bar, T = 700 ... 2600 K, carbon dioxide: p = 1 ... 200 bar, T = 390 ... 2600 K). The analytical dependencies were derived on the basis of previously obtained analytical expressions for the specific isobaric heat capacities of these gases. The average specific isobaric heat capacities of gases are also functions of temperature and pressure cp = f(T, P) and take into account the effect of thermal dissociation. Formulas for average specific isobaric heat capacities are obtained by integrating expressions for specific isobaric heat capacities. Verification of the obtained dependencies for different temperature ranges was done.

Working process model development of the gas turbine engine combustor fueling on methanol

“…A limitation of the developed model is the existence of a working range for the specific heat capacity с раа (upper range of pressure p = 200 bar and temperature T = 2,600 K) [16]. If pressures and temperatures exceed these ope rational ranges, extrapolation is actually used, which may lead to calculation error accumulation.…”

“…To account for the influence of pressure and thermal dissociation, two approaches can be employed: solving a system of chemical kinetics equations with a large number of equations [6,7], or utilizing experimental values of enthalpies or specific isobaric heat capacity с р as functions of temperature Т and pressure p [8]. Additionally, by adopting the second approach to determine the enthalpy of combustion products, we obtain a correctly formulated equivalent chemical reaction path.…”

Development of a method to improve the calculation accuracy of specific fuel consumption for performance modeling of air-breathing engines

“…The model developed for calculating q f based on h(Т, р, q f ) was verified by comparing q f with the known experimental data of the combustion chamber of a General Electric CF6-80A engine [26,27] and by comparing the obtained values of c R =f(H, M h ) with the experimental data of the D436-148B engine [28].…”

“…Estimation of the calculation accuracy of c R was carried out by comparing the calculation results with the experimental data presented in the technical description of the D436 -148B turbofan engine [28].…”

“…The hourly fuel consumption G f was calculated using the obtained values of c R and R for comparison with the data presented in [28].…”