Reynolds and Mach Number Effects on Propulsive Performance for a Pitching Airfoil

In this work, numerical simulations are conducted to investigate the effects of Reynolds ([Formula: see text]) and Mach ([Formula: see text]) numbers on thrust characteristics for a pitching airfoil. The results show that as [Formula: see text] increases, the thrust performance is improved. The inverse square root of Reynolds number is demonstrated to be a universal scaling law for both thrust coefficients and drag-to-thrust crossovers across [Formula: see text] and [Formula: see text]. In contrast, as [Formula: see text] increases above 0.1, the thrust performance is significantly reduced, especially when [Formula: see text] approaches 0.3. The thrust coefficients follow the square law of the Mach number, which also exhibits universality. Furthermore, the incompressible vortex projection method and the compressible vortex projection method are employed for thrust decomposition. Before this, the full expression of the compressible vortex projection method is derived. It is revealed that as [Formula: see text] increases, the improvement of thrust performance is primarily attributed to the reduced flow viscous effect and, meanwhile, benefits from the formation of more intense boundary layers and vortex structures in near wake. As [Formula: see text] increases, the enhancement of local flow compressibility ultimately leads to the divergence of added mass drag and thereby reduces the thrust performance.