On the Length Scales of Turbulence for Aeroacoustic Applications

Abstract

Accurate evaluation of the turbulence integral correlation length scales is important for a large group of numerical flow-induced noise prediction methods. Due to the complex mathematical interrelationships of the two-point space-time velocity statistics, a direct evaluation of the integral length scale is a challenging task from the standard CFD methods. The present paper focuses on the theoretical and experimental investigations of five different integral length scales evaluation methodologies, namely i) two-point space correlation based method, ii) single point power-spectrum based approach, iii) wavenumber of the most energy containing eddy dependent method, iv) auto correlation via Taylor’s hypothesis and, v) correlation function curve fitting method. All these methods are analyzed based on the previously performed two-point turbulent boundary-layer (BL) correlation measurement data. A detail comparison study has been performed with discussions on the limitations and drawbacks of each method. Other length scales found in turbulence theory such as pseudo length scale, dissipation length scale, Prandtl mixing length, Taylor microscale and Kolmogorov scale have been also discussed elaborately. A theoretical relationship for the derivation of integral length scales based on standard RANS simulation is derived by employing Kolmogorov local isotropy hypothesis. The enhanced method allows modelling of the isotropic length scale and dissipation from the anisotropic experimental spectral data. This outcome is applied further for the RANS turbulence model validation purpose in the framework of a turbulent boundary-layer trailingedge interaction (TBL-TE) noise prediction model. Results are extensively validated with the wind tunnel measurement of high Reynolds number airfoil BL flows.