Numerical analysis of aerodynamic damping in a transonic compressor

Abstract: Aeromechanics is one of the main limitations for more efficient, lighter, cheaper and reliable turbomachines, such as steam or gas turbines, as well as compressors and fans. In fact, aircraft engines designed in the last few years feature more slender, thinner and more highly loaded blades, but this trend gives rise to increased sensitivity for vibrations induced by the fluid and result in increasing challenges regarding structural integrity of the engine. Forced vibration as well as flutter failures need to be carefully avoided and an important parameter predicting instabilities in both cases is the aerodynamic damping. The aim of the present project is to numerically investigate aerodynamic damping in the first rotor of a transonic compressor (VINK6). The transonic flow field leads to a bow shock at each blade leading edge, which propagates to the suction side of the adjacent blade. This, along with the fact that the rotating blade row vibrates in different mode shapes and this induces unsteady pressure fluctuations, suggests to evaluate unsteady flow field solutions for different cases. In particular, the work focuses on the unsteady aerodynamic damping prediction for the first six mode shapes. The aerodynamic coupling between the blades of this rotor is estimated by employing a transient blade row model set in blade flutter case. The commercial CFD code used for these investigations is ANSYS CFX. Aerodynamic damping is evaluated on the basis of the Energy Method, which allows to calculate the logarithmic decrement employed as a stability parameter in this study. The least logarithmic decrement values for each mode shape are better investigated by finding the unsteady pressure distribution at different span locations, indication of the generalized force of the blade surface and the local work distribution, useful to get insights into the coupling between displacements and consequent generated unsteady pressure. Two different transient methods (Time Integration and Harmonic Balance) are employed showing the same trend of the quantities under consideration with similar computational effort. The first mode is the only one with a flutter risk, while the higher modes feature higher reduced frequencies, out from the critical range found in literature. Unsteady pressure for all the modes is quite comparable at higher span locations, where the largest displacements are prescribed, while at mid-span less comparable values are found due to different amplitude and direction of the mode shape. SST turbulence model is analyzed, which does not influence in significant manner the predictions in this case, with respect to the k-epsilon model employed for the whole work. Unsteady pressure predictions based on the Fourier transformation are validated with MATLAB codes making use of Fast Fourier Transform in order to ensure the goodness of CFX computations. Convergence level and discrepancy in aerodamping values are stated for each result and this allows to estimate the computational effort for every simulation and the permanent presence of numerical propagation errors.