UC Santa Barbara

This work proposes a new Stirling engine design which we refer to as an actuated Stirling engine. The thermodynamic cycle which drives the engine is controlled by the motion of the displacer piston. In traditional designs this motion is a result the design parameters of the engine. In the Beta engine design the motion of the displacer is determined by the design of the flywheel, while in a free piston design the motion is determined by the restorative force applied to the displacer (be that from a gas spring used in some designs or a mechanical spring used in others). This work proposes a new design wherein the displacer motion is directly controlled via an actuator. This allows for more direct control over the thermodynamic process which drives the engine. To answer the question of how well this engine design compares to a more traditional engine, the best possible design of both engines are compared to one another. This requires optimizing not only the proposed design, but the more traditional design as well.

The traditional Beta engine design is chosen as the benchmark with which the actuated design is compared to. Optimizing the design of the Beta engine is a standard parameter optimization problem, as the motion of the pistons is determined by the flywheel parameters. Optimizing the actuated engine is more difficult as it requires finding the optimal trajectory of the displacer, which is an optimal control problem.

This work is divided into two sections. In the first section the problem of optimally designing both the actuated and Beta engine designs is solved using a very simple of the Stirling engine, the isothermal (or Schmidt) model. In the second section the same design problem is solved but with a much higher fidelity engine model. The large state dimension of the high fidelity model makes it ill suited for use in an optimization algorithm. To resolve this, a method of model reduction is proposed and applied to the high fidelity model to yield a reduced model more suitable for use in an optimization algorithm. For both the simple isothermal and high fidelity models it is shown that the actuated design has the potential to significantly outperform the more traditional Beta engine design.