Onset of unsteadiness in the flow past a blade cascade

Abstract

There has been little research on the system stability of the flow past a blade when the domain is finite in the transverse direction. In this study, we first explore the influence of the domain size and periodic boundary conditions in the transverse direction on the stability of the flow past a single blade in a finite domain. As the transverse width decreases, the base flow and instability characteristics change. Furthermore, the stability of the flow past a cascade including n blades is analyzed. There exist n perturbation modes corresponding to different temporal growth rates and frequencies with various staggered spatial distributions of the dominant region, embodied as the inter-blade phase angle in the frequency domain. The critical value and leading mode are related to the blade number. Therefore, when analyzing the stability of the flow past a cascade, it is important to extend the domain to the real blade number. The influence of the geometric cascade parameters on system stability is also studied. Finally, when the circumferential periodic flow is broken in a cascade including n blades, there exists only one eigenvalue near the stability boundary. The system stability deteriorates, and the critical Reynolds value drops sharply, even when several blades are restaggered to have a smaller angle of attack. From the distribution of the leading mode, the initial location of unsteadiness is associated with the region of maximum deficit in the velocity profile of the wake flow.