Two-phase thermofluidic engines for low-grade heat recovery : system analysis and supporting algorithms

This thesis considers a two-phase thermofluidic oscillator known as the non-inertive thermofluidic engine (NIFTE), that is capable of utilizing heat supplied at a steady temperature to induce persistent thermal-fluid oscillations. The NIFTE is appealing for its simplicity and ability to operate across small temperature differences, as low as 30 °C on current prototypes. But it is also expected for these prototypes to exhibit low efficiencies relative to conventional heat recovery technologies that target higher-grade heat conversion. The first part of this work involves a system analysis based on a nonlinear model of the NIFTE, which we extend to encompass irreversible thermal losses. The NIFTE is predicted to exhibit multiple cyclic steady states (CSS) for certain design configurations, either stable or unstable, a behavior that had never been hypothesized. A parametric analysis of the main design parameters of the NIFTE is conducted using local optimization techniques based on randomized multistart. The results confirm that failure to include the irreversible thermal losses in the NIFTE model can grossly overpredict its performance, especially over extended parameter domains. The optimization potential of this technology is also assessed by conducting a multi-objective optimization. Our results reveal that most of the optimization potential is achievable via targeted modifications of three design parameters only. The Pareto frontier between exergetic efficiency and power output is also found to be highly sensitive to these optimized parameters. Rigorous analysis and optimization of the NIFTE calls for the implementation of global optimization due to the presence of multiple cyclic steady state and other uncertainties, and this is notoriously difficult. The second part of the work focuses on improving ODE bounding methods that form an essential step in global dynamic optimization. Unlike most available bounding methods, we follow a discretization approach to convert the differential equations to sparse algebraic equation systems; and we take advantage of their block structure. A simple block diagonal decomposition strategy is shown to result in significant overestimation due to the wrapping effect. Therefore, we develop a recursive block decomposition strategy, which fully retains the inter-dependency between the blocks. Numerical case studies reveal that the2 proposed discretization approach can potentially outperform the state-of-the-art set-propagation methods for nonlinear dynamic ODE bounding, both in terms of bounds tightness and CPU time. However, for larger systems with more complex dynamics, such as the NIFTE, our method may end up being more computationally demanding than the set-propagation method due to the much larger number of operations involved. Moreover, all of these methods are prone to fail when either a large uncertainty set or a long time horizon is considered. To circumvent the numerical challenges associated with solving nonlinear ODEs, a switched-linear version of the NIFTE model is developed and validated. This model has three distinct modes for its dynamics, between which the NIFTE switches continuously. The conventional approach of bounding such linear hybrid automata using set-propagation methods proves useful for small-scale problems, but not for the NIFTE. Instead, we develop a new optimization-based approach in the final chapter of this thesis. The switched-linear dynamical system is first discretized. The resulting algebraic system is then reformulated using mixed-integer linear constraints, which can be solved using state-of-the-art MILP solvers. This proposed optimization-based approach is shown to generate tight state enclosures, especially in the presence of large uncertainties where set-propagation ODE bounding methods fail. However, the run-time complexity grows exponentially with the length of the time horizon. All the numerical methods developed in this thesis are implemented in the in-house toolkit CRONOS, which is publicly available.