Airfoil Noise Numerical Simulations with Direct Noise Computation and Hybrid Methods Using Inflow Synthetic Turbulence

Abstract

The interaction of inflow turbulence with an airfoil is significant for low Reynolds number applications, as it generates leading edge noise, but also strongly modifies the airfoil boundary layer properties and thus the produced noise. Inflow turbulence impact still demands to be better understood and is also a numerical challenge. Large Eddy Simulations are here carried out with both incompressible and compressible solvers. The Synthetic Eddy Method and the Random Fourier Modes method, used to generate synthetic turbulence, are studied in this work. In order to eventually perform airfoil simulations, the second method is modified to take into account spanwise periodic boundary conditions, to reduce spurious noise level in compressible simulations. First, properties of the methods are studied with a spatially decaying turbulence academic case. Even if the decay is not well represented, the methods show satisfactory properties in terms of isotropy, homogeneity and one-dimensional spectra. Furthermore, spurious noise levels are reduced thanks to the modified method. Preliminary airfoil simulations are then carried out with inflow turbulence for flow validation in presence of a laminar separation bubble. The drag coefficient is in very good agreement with experimental results. However, there are some discrepancies between simulations and experiments on the lift coefficient, which is extremely sensitive to perturbations. These discrepancies are attributed to a lack of experimental turbulence characteristic information, such as isotropy or integral length scale and to too short simulations at high angles of attack. * The Einstein convention is used : subscript repetition implies summation, subscript between brackets avoids it.

Low-Noise Synthetic Turbulence Tailored to Lateral Periodic Boundary Conditions

“…= 0.37. Additionally, the same small energy decay was already observed in a previous study [46] using the same numerical tools but with a larger domain length L x = 250Λ f . As a consequence, the convection time was comparable to the large-scale decaying time.…”

“…This could be due to the small domain length L z = 2Λ f , that may not be sufficient to introduce the largest scales. Indeed, using the same turbulence parameters, it was observed in [46] that the energy was correctly computed at the lowest wavenumber when the domain length along z was more than twice the present one. A different behavior is observed at intermediate wavenumbers (30 m −1 ≤ k y ≤ 60 m −1 ).…”

“…This explain why the resolved turbulent kinetic energy takes different values on x = 0 depending on the simulation. Additionally, this issue is present because the span is very small (only 2Λ f , 11 computational points), that means that all the points of the domain are affected by the periodicity condition, contrary to the study [46], where the span was 5Λ f and the turbulent kinetic energy of every simulation started from the same value. However, the high-amplitude spurious noise problem was present even in this configuration.…”