Methodology to develop off-design models of heat exchangers with non-ideal fluids

Supercritical CO₂ (sCO₂) closed Brayton cycles are promising heat engines for next-generation thermal power plants since they are efficient, highly scalable, and compatible with a variety of heat sources. A potential application for these cycles is load-following concentrating solar power plants with thermal storage, which will frequently operate at off-design conditions. Accurate and computationally efficient models of the cycle's heat exchangers and turbomachinery are required to assess and optimise its off-design performance. The printed circuit heat exchangers (PCHEs) used in the sCO₂ closed Brayton cycle are challenging to model since they exhibit non-ideal-gas effects and typically use zigzag channels, for which flow patterns and heat transfer mechanisms are not completely understood. Moreover, heat transfer correlations that capture all effects relevant to a given geometry and flow conditions are often unavailable. We present a methodology to develop accurate and computationally efficient on- and off-design models of heat exchangers that exhibit complex nonlinear behaviours. This methodology involves fitting a 1D discretised heat exchanger model to experimental data using nonlinear least-squares optimisation. Unknown internal heat exchanger geometric parameters are used as fitting parameters. We demonstrate the proposed methodology by developing numerical models for two PCHEs: (1) an sCO₂–sCO₂ PCHE operating far from CO₂'s critical point and (2) an oil–sCO₂ PCHE operating close to CO₂'s critical point, where non-ideal fluid property variations are significant. Test data spans heat loads from 6–48% and 15–39% of name-plate duty for heat exchangers (1) and (2) respectively. Across these operating ranges, the maximum and mean heat transfer prediction residuals are 0.91% and 0.36% for heat exchanger (1) and 3.04% and 1.24% for heat exchanger (2). Additionally, we show that good accuracy can be obtained when using only the channel hydraulic diameter as a fitting parameter. Due to their low computational cost and high accuracy, models developed using the proposed methodology are eminently suitable for off-design modelling and optimisation of the sCO₂ closed Brayton cycle and other power cycles or industrial processes where heat exchangers exhibit complex nonlinear behaviour.