Aerodynamic noise generation in boundary layer flows

• Applicant: Professor Dr.-Ing. Martin Oberlack
• Subject Area: Fluid Mechanics
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 456793479

Noise has long been known the cause of a wide range of health problems. At the same time, high-precision noise prediction is still only possible to a limited extent, but this would be necessary to drastically reduce noise emissions. This is precisely where the present proposal comes in. Specifically, the applicant has developed a new theory of noise generation in boundary layer flows, which describes all acoustic modes, eigenfunctions and a large number of derived quantities with high precision. The central goal is to further develop the new theory and, since it is a linear theory, to simultaneously follow the acoustic modes far into the non-linear regime by means of highly accurate simulations. In view of a physical application and the subsequent numerical simulations, the first step is to extend the previously solved temporal problem to the spatial eigenvalue problem. In the second step, and in extension of the above-mentioned theory, besides the acoustic instabilities also reflections and refractions of acoustic waves at the boundary layer shall be analyzed. This is to be performed on the basis of the analytically given eigenfunctions under changes of the boundary conditions. Depending on the angle of incidence and the flow parameters, the reflection and refraction can be calculated exactly, and a corresponding reflection-refraction map will be created. In the third step, the above theory is to be extended to non-isothermal boundary layers. This is of central importance especially for high Mach numbers which show strong wall normal temperature gradients due to dissipation effects. Internal preliminary work shows that the eigenfunctions can be expressed in the general Heun functions. The mode spectrum is thus extended by the 1st Mack mode. For the goal of an optimal noise reduction the impedance can be introduced explicitly into the above eigenvalue problem very easily in the fourth step. The eigenvalue, i.e. in the spatial case the complex wave number, depends on the impedance in addition to the frequency and Mach number. Based on this, an extreme value algorithm is to be applied, which calculates an optimal impedance for each parameter combination, so that the growth of disturbances is significantly reduced, or even attenuation occurs. Thus, an optimal noise damping curve for boundary layer flows is obtained. In the final numerical simulations, the above theoretical results are to be recalculated for selected parameters using the discontinuous Galerkin method. In particular, the linear solutions for selected parameters will be followed deep into the non-linear range. Central questions here are further destabilization or a saturation by nonlinear effects, the generation of nonlinear acoustic induced structures or even turbulence and the associated generation of higher modes.

• DFG Programme: Research Grants