Quantifying damping coefficients in a rhombic-drive β-type Stirling engine based on a novel CFD-mechanism dynamic model and experimental data

Effectively exploiting renewable thermal energy sources and reducing the operating costs of renewable thermal systems remain challenging. Stirling engines, which serve as the heart of some renewable thermal systems, significantly impact both the maintenance and overall efficiency of these systems. However, the lack of information on friction behaviors in Stirling engines hinders the achievement of these goals. Therefore, this study clarifies the behaviors of damping coefficients in a rhombic-drive β-type Stirling engine. A novel CFD-mechanism dynamic model is developed to compute numerical values of cyclic-averaged engine speed corresponding to various loading torques. By employing the steepest descent method, the unknown values of the damping coefficients are adjusted to ensure the best match between numerical and experimental variations of loading torque with cyclic-averaged engine speed. Consequently, the study sheds light on the variation of damping coefficients with the instantaneous engine speed. The damping coefficient between the cylinder and piston is consistently lower than that between the displacer and cylinder. Additionally, the damping coefficient between the cylinder and piston ranges from 15.8 to 63.4 N s/m, while the coefficient between the cylinder and displacer increases from 50.0 to 195.5 N s/m as the instantaneous engine speed decreases from 1650 to 450 rpm.