Shock Dynamics due to Downstream Pressure Perturbations: Idealization of Transonic Unstarted Cascade Flutter

Abstract

Shock wave unsteadiness is an important phenomenon in high-speed aerodynamics. This phenomenon is observed in many locations of high-speed vehicles, such as supersonic inlets, ramjet engines, transonic airfoils, high-speed fans, and compressors. In supersonic inlets and ramjet engines, unsteady shock motions can lead to large undesirable local fluctuations in properties such as pressure and heat transfer rate, besides overall thrust fluctuations. Shock unsteadiness in transonic airfoils can induce structural vibrations known as buffeting, while in gas turbine fans/compressors, shock oscillations can lead to blade vibrations known as flutter. Motivated by the above problems, the purpose of the present experimental study is to understand the response of a normal shock subjected to downstream pressure perturbations. Although several studies pertaining to shock dynamics due to downstream pressure perturbations have been reported in the literature, only a few of them have concentrated on the effect of downstream perturbation to the normal shock behavior in a constant area duct, with detailed flow field measurements that can help to understand the flow physics that drive these shock oscillations. With this in mind, in the present work, a detailed experimental study of shock dynamics due to downstream pressure perturbations within a constant area duct have been done in two different configurations. The first configuration is one in which the downstream pressure perturbations are generated in the far field region by rotating a triangular cross-sectional shaft, this being an idealization of inlet shock dynamics in ramjets caused by downstream combustion chamber pressure fluctuations. The second configuration is one in which the downstream pressure perturbations are generated in the near field region by heaving an airfoil, and this may be considered as an idealization of the unstarted cascade flutter of high-speed compressors. In both cases, the normal shock is induced and stabilized at low Mach numbers (M∞ ∼ 1.3) within a supersonic/transonic tunnel, and the shock dynamics in response to the downstream pressure perturbations are visualized using high-speed shadowgraphy. In addition to the high-speed shadowgraphy, high-speed wall pressure measurements have been carried out in the first configuration, and in the second configuration, unsteady force measurements have been carried out to understand the influence of shock oscillations on airfoil flutter. In the far field pressure perturbation case, pressure perturbations are generated by rotating a triangular cross-sectional shaft which is 580 mm downstream from the normal shock. The normal shock is induced and stabilized in the constant area section of a supersonic wind tunnel which is operated at M∞ = 1.4. The main parameter varied in this case is the perturbation frequency ( f ), which is varied from low frequencies to 60 Hz in steps of 10 Hz. High-speed shadowgraphy visualizations indicate that the shock oscillates in response to the exciter perturbation frequency, with a phase difference between exciter motion and the shock displacement. The shock shows large streamwise motions (up to 60 mm), with distinct differences in the shock structure and velocity during its upstream and downstream motions. It is also observed that the amplitude of shock motion decreases with increase in perturbation frequency, while the shock velocity is almost independent of the perturbation frequency. The results from-high speed pressure measurements indicate that the downstream pressure fluctuations are nearly 3-5% of the mean static pressure at the exciter region. In the near field pressure perturbation case, pressure perturbations are generated by heaving an airfoil (at frequency f ) with its leading edge being 0.1 chord length downstream from the normal shock. The normal shock is induced and stabilized in the constant area section of a transonic wind tunnel which is operated at M∞ = 1.3. The parameter varied in this case is the reduced frequency (k = π f c/U), which is varied from low values up to 0.264. Flutter characteristics of the airfoil are deduced in terms of the energy transfer to the heaving airfoil from the measured unsteady loads, and it indicates that there are two excitation regions, one corresponding to lower reduced frequency and other corresponding to higher reduced frequency, which is similar to the case of unstarted cascade flutter observed by Jutur (2018). High-speed shadowgraphy visualizations have been carried out at different airfoil heave frequencies, and the results indicate that the shock oscillates in response to the airfoil heave motions, with the phase between the shock motion and the airfoil motion being dependent on the reduced frequency. The correlation between the shock motion and airfoil position indicate a negative correlation value at k = 0.049, and for all cases with k ≥ 0.117, it is positively correlated. In summary, measurements from both configurations indicate that the shock oscillates in response to the exciter perturbation frequency, with a phase difference between shock motion and exciter motion. This phase difference observed between the shock displacement and the exciter for variation in perturbation frequency in the first configuration may be attributed to shock wave boundary layer interactions, while in the second configuration it is the phase of the unsteady shock motions with respect to the airfoil motion that is important in deciding the flutter characteristics of the downstream airfoil. Further, in both the configurations, the amplitude of shock motion is found to be decreasing with increase in perturbation frequency