Assessment on Partial Derivatives for Thermal-Physical Properties of Carbon Dioxide

To adapt to a requirement of improving the accuracy and efficiency of calculation, a full or partial implicit scheme is usually employed in solving the conservative equations of the supercritical carbon dioxide (S-CO2) Brayton cycle, and partial derivatives of thermal properties such as (∂h/∂ρ)p and (∂h/∂p)ρ are needed in numerical solver. In this paper, the most representative state equations of carbon dioxide are investigated and evaluated by experimental data. The Span-Wagner (SW) equation has a minimal error in all state equations, so the SW equation is chosen as the fundamental equation of thermal properties for partial derivatives. Based on that, the equations of partial derivatives such as (∂h/∂ρ)p and (∂h/∂p)ρ are presented by the Maxwell equation. The paper also evaluates the closure of partial derivatives equations. The deviations of (∂h/∂ρ)p and (∂h/∂p)ρ are within ±0.01% for most points. The maximum closure error of (∂h/∂ρ)p is 0.373%, and the maximum one of (∂h/∂p)ρ is −0.798%. Therefore, the partial derivatives equations obtained in this paper can play a significant role in the safety analysis code.