Application of adjoint sensitivity analysis method to supercritical CO₂ power cycle optimization

Adjoint sensitivity based optimization methodology for a supercritical CO₂ (S-CO₂) cycle is developed in this paper. The adjoint sensitivity analysis method (adjoint method) is a way to analyze sensitivity very quickly. By using the developed methodology, the optimal state variation due to the change of cycle parameters is analyzed. The S-CO₂ recompression Brayton cycle is used for an example case for the demonstration of the proposed method. The independence of time consumption for the developed adjoint sensitivity analysis method to the number of optimized variables is demonstrated. For the test case, the developed algorithm shows the ability to make the design parameters converge with a precision of 10⁻⁶ by more than ten times faster for calculating the sensitivity than conventional optimization methods. Validation of the obtained optimal point is also included in the paper. For the validation, a response surface analysis is performed to visualize the pathway during the iteration for optimization. It is very challenging to carry out the optimization having the same precision using a brute force algorithm or a probability-based optimization algorithm since the number of variables to be optimized is substantial for this type of a problem. The smoothness of an optimal cycle efficiency variation is observed in every case.