Nonlinear dynamics analysis of a low-temperature-differential kinematic Stirling heat engine

TL;DR

This paper models a low-temperature-differential Stirling engine as a nonlinear driven pendulum, analyzing how temperature differences influence its stable rotational motion through bifurcation analysis.

Contribution

It introduces a minimal nonlinear dynamic model of the LTD Stirling engine and identifies the bifurcation mechanism behind the loss of stable rotation.

Findings

Stable limit cycle exists at sufficient temperature difference.

Disappearance of the limit cycle occurs via homoclinic bifurcation.

Rotational motion depends critically on temperature difference.

Abstract

The low-temperature-differential (LTD) Stirling heat engine technology constitutes one of the important sustainable energy technologies. The basic question of how the rotational motion of the LTD Stirling heat engine is maintained or lost based on the temperature difference is thus a practically and physically important problem that needs to be clearly understood. Here, we approach this problem by proposing and investigating a minimal nonlinear dynamic model of an LTD kinematic Stirling heat engine. Our model is described as a driven nonlinear pendulum where the motive force is the temperature difference. The rotational state and the stationary state of the engine are described as a stable limit cycle and a stable fixed point of the dynamical equations, respectively. These two states coexist under a sufficient temperature difference, whereas the stable limit cycle does not exist under a temperature difference that is too small. Using a nonlinear bifurcation analysis, we show that the disappearance of the stable limit cycle occurs via a homoclinic bifurcation, with the temperature difference being the bifurcation parameter.