Design optimization of supercritical CO2 Brayton cycle with adjoint method

An adjoint sensitivity based optimization methodology for S-CO2 cycle optimization is developed in this paper. The adjoint sensitivity method is a method to analyze sensitivity quickly and accurately. For optimization, Levenberg-Marquardt algorithm is adopted after obtaining the sensitivities of the variables. The S-CO2 recompression Brayton Cycle is used as an example. For thermodynamic analysis of the S-CO2 recompression Brayton Cycle, total 24 functions are expressed mathematically. The developed adjoint method can analyze the 1st order sensitivity (Gradient) and the 2nd order sensitivity (Hessian) quickly and accurately. The time consumption of the proposed adjoint based optimization method is known to be independent from the number of variables considered and this is confirmed. Validation for finding the optimal point is also performed by using a response surface analysis and iteration path way check. For the given test case, the developed algorithm shows the ability to make the design parameters converge with a precision of 10^-6 by total less than 15 times of iteration. In contrast, this would be physically impossible to carry out the optimization process with the same precision if one uses a brute force algorithm or a probability-based optimization algorithm.