Equation of state based analytical formulation for optimization of sCO2 Brayton cycle

Real gas thermodynamic cycles employ state-of-the-art property routines to compute the state properties as ideal gas relations are inaccurate. Multiparameter equation of state (EOS), though accurate, is computationally time consuming due to iterative solutions needed for complex cycles. Alternatively, look-up tables alleviate the computational time but compromise the accuracy due to interpolation and extrapolation schemes. This paper proposes a novel analytical formulation to overcome the tradeoff between accuracy and computation cost. Helmholtz energy-based EOS in combination with Jacobian transformations and real gas thermodynamics is used to arrive at a single equation linking the state points of a thermodynamic cycle. The efficacy of the formulation is demonstrated to deduce the optimum pressure ratio while maximizing specific work or efficiency of a simple recuperated supercritical CO2 Brayton cycle. The difference in optimum pressure ratio predicted by the analytical formulation and conventional property-routine is inconsequential compared to an order of gain in the computational time.