MODIFIED CALORIC EQUATIONS OF STATE BASED ON THE THERMAL TAMMANN EQUATION - Rusanov, А.V.; Rusanov, R.A.; Chugay, M.O.; Tretiak, S.P. (Municipal economy of cities. Series: «Economy science», 2025)
A new version of the caloric equations of state based on the thermal Tammann equation of state (modified Tammann equation of state), in which the specific heat capacities depend on temperature, has been developed. The modified equation of state was developed using the improved Helmholtz energy equation. The modified Tammann equation of state, unlike the original equation, makes it possible to find such local constants that ensure full compliance of thermodynamic (temperature, density, pressure) and caloric (enthalpy, entropy, internal energy) values with the values of a real media at isentropy at the beginning and end of a gas-dynamic process. This correspondence is achieved by introducing an additional term of the temperature function into the Helmholtz energy equation. The modified Tammann equation was tested in the calculation of the 3D flow of a low-pressure steam turbine and ORC microturbines with HFE7100 and R227ea low-boiling working medias. Comparison of the obtained results showed that the modified Tammann equation provides much better agreement with the Experimental and the results obtained using more complex equations of state such as IAPWS-95 and mBWR32. If the isentropic thermal drop in the gas-dynamic process will be relatively small, calculations with all the considered equations of state provide satisfactory results. This ensured that the difference in isentropic thermal drop between all variants of the equations of state did not exceed 3%. At the same time, the computational cost of calculations with the modified Tammann equation is almost the same as with the conventional Tammann equation, but several times less compared to the complex equations of state IAPWS-95 and mBWR32. The developed variant of the caloric equations of state based on the thermal equation of state of Tammann makes it possible to describe more accurately the thermodynamic properties of working medias and provide a given isentropic enthalpy drop. That’s why it is advisable to use such approach when developing or modernizing the turbine flow parts.