Heat Pump Optimization—Comparative Study of Different Optimization Algorithms and Heat Exchanger Area Approximations

More energy efficient heat pumps can be designed if the industry is able to identify reliable optimization schemes able to predict how a fixed amount of money is best spent on the different individual components. For example, how to optimally design and size the different heat exchangers (HEs) in a heat pump with respect to cost and performance. In this work, different optimization algorithms and HE area integral approximations are compared for heat pumps with two and three HEs, with or without ejectors. Since the main goal is to identify optimal numerical schemes, not optimal designs, heat transfer is simplified, assuming a constant U-value for all HEs, which reduces the computational work significantly. Results show that high-order HE area approximations are 10−400 times faster than conventional trapezoidal and adaptive integral methods. High-order schemes with 45 grid points (N) obtained 80−100% optimization success rates. For subcritical processes, the LMTD method produced accurate results with N≤5, but such schemes are unreliable and difficult to extend to real HE models with non-constant U. Results also show that constrained gradient-based optimizations are 10 times faster than particle swarm, and that conventional GA optimizations are extremely inefficient. This study therefore recommends applying high-order HE area approximations and gradient-based optimizations methods developing accurate optimization schemes for the industry, which include realistic heat transfer coefficients.