1 Fluid Mechanics, Department of Mechanical Engineering, Technical University of Denmark2 Department of Mechanical Engineering, Technical University of Denmark3 Department of Wind Energy, Technical University of Denmark
A high-order finite difference method to predict flow-generated noise is introduced in this thesis. The technique consists of solving the viscous incompressible flow equations and inviscid acoustic equations using an incompressible/acoustic splitting technique. The incompressible flow equations are solved using the in-house flow solver EllipSys2D/3D which is a second-order finite volume code. The acoustic equations are solved using high-order finite difference schemes. The incompressible flow equations and the acoustic equations are solved at the same time levels where the pressure and the velocities obtained from the incompressible equations form the input to the acoustic equations. To achieve low dissipation and dispersion errors, either Dispersion-Relation-Preserving (DRP) schemes or optimized compact finite difference schemes are used for spatial discretizations of the acoustic equations. The acoustic solver consists of numerical schemes from fourth-order up to tenth-order accuracy, the use of different schemes are case dependent. In practice, at high Reynolds numbers when flow becomes turbulent, schemes with the highest order of accuracy are always used to resolve the small waves. For time integration, the classical 4-stage Runge-Kutta scheme is applied. Non-centered high-order schemes at numerical boundaries and high-order filter schemes are also discussed due to their importance. The method was validated against a few test cases and further applied for flows around a cylinder and an airfoil both for laminar and turbulent flows. Results have shown that sound generation is due to the unsteadiness of the flow field and the spectrum of sound has a strong relation with fluctuating forces on the solid body. Flow and acoustic simulation were also carried out for a wind turbine where general trends of sound generation from blades was found.