Fluid transport in human physiology, either air exchange in the pulmonary system or blood flowing through heart chambers, relies on the proper functioning of biological valves that provide passive flow control over the transport procedure. During actuation, valve leaflets can undergo self-excited oscillations due to the fluid-induced instability, which in turn can lead to a dysfunctional fluid transport. Although extensive investigations have been proposed in the realm of fluttering motion, the onset of a limit-cycle oscillation in a valve-like configuration remains not well understood. To the end, this work aims at covering this scientific gap, specifically correlating the onset of self sustained oscillations with operating parameters in a general-purpose configuration by means of high-fidelity simulations. The investigation is carried out with an extensively validated software which employs a partitioned framework to handle Fluid-Structure Interaction (FSI) problems. The fluid field is solved by a finite-difference fractional step scheme over a staggered mesh, whereas the discretization of structural domain relies on a NURBS based Isogeometric method which has proven to be efficient and accurate in capturing large strain gradients with minimal degrees of freedom. Concerning the interface, we adopted an immersed boundary forcing whose interpolation/spreading kernel is built by a moving-least-squares (MLS) approach. Our preliminary results support the existence of critical reduced velocity actuating the flapping motion of valve leaflets which is jointly regulated by the geometric parameters, the structural property and the flow condition.