Prediction of Tonal Acoustic Radiation Due to Feedback-Loop Resonant Interactions in Transitional Airfoils

The objective to this work is to employ the surface integral methods to study the far-field noise propagation from the flow acoustic resonant interactions of the transitional airfoil. The Potential-Theoretic Method (PTM) as an advancement to traditional Kirchhoff methods is presented. The PTM eliminated the need to calculate the normal derivatives of pressure and an arbitrary Kirchhoff surface can be employed. The numerical procedure to implement the PTM is fairly simple. The formulation and physical assumptions of the approach is reviewed, and the numerical procedure is implemented. Furthermore, the two dimensional formulation of the Ffowcs Williams - Hawkings (FW-H) equation in frequency, domain is reviewed and then the method is implemented to be used for extending the numerical simulations to far-field evaluations. In order to verify the implemented methods, monopole source verification problems has been studied and the accuracy of the methods is validated. Then, PTM and FW-H methods are used in the transitional airfoil application. The noise generation process of the problem in the near-field is highly nonlinear. This, high accuracy 2D simulations based on an Implicit Large Eddy Simulation (ILES) code are conducted for a NACA-0012 airfoil for the Reynolds of 140,000 and zero angle of attack as the baseline case, to obtain the time-dependent flow variables in the near-field. Then the near-field data is passed to the developed PTM and FW-H codes to evaluate the far-field noise acoustics. The predicted acoustic sound pressure level and the directivities are compared with direct CFD simulation in the mid region where toe CFD results are still reliable. Comparing the results, it is deduced that the FW-H is more robust in regards to the choice of control surface. Some remarks about signal processing and properties of the methods are suggested. The acoustic predictions are also evaluated for a far-field microphone probe, to compare them with experimental results. The effects of variations of angle of attack on the tonal noise regime has been studied