Time-domain inflow boundary condition for turbulence–airfoil interaction noise prediction using synthetic turbulence modeling

Abstract

The present paper deals with development of the synthetic turbulence inflow boundary condition (STIBC) to predict inflow broadband noise generated by interaction between turbulence and an airfoil/a cascade of airfoils in the time-domain. The STIBC is derived by combining inflow boundary conditions that have been successfully applied in external and internal computational aeroacoustics (CAA) simulations with a synthetic turbulence model. The random particle mesh (RPM) method based on a digital filter is used as the synthetic turbulence model. Gaussian and Liepmann spectra are used to define the filters for turbulence energy spectra. The linearized Euler equations are used as governing equations to evaluate the suitability of the STIBC in time-domain CAA simulations. First, the velocity correlations and energy spectra of the synthesized turbulent velocities are compared with analytic ones. The comparison results reveal that the STIBC can reproduce a turbulent velocity field satisfying the required statistical characteristics of turbulence. Particularly, the Liepmann filter representing a non-Gaussian filter is shown to be effectively described by superposing the Gaussian filters. Each Gaussian filter has a different turbulent kinetic energy and integral length scale. Second, two inflow noise problems are numerically solved using the STIBC: the turbulence–airfoil interaction and the turbulence-a cascade of airfoils interaction problems. The power spectrum of noise due to an isolated flat plate airfoil interacting with incident turbulence is predicted, and its result is successfully validated against Amiet׳s analytic model (Amiet, 1975) [4]. The prediction results of the upstream and downstream acoustic power spectra from a cascade of flat plates are then compared with Cheong׳s analytic model (Cheong et al., 2006) [30]. These comparisons are also in excellent agreement. On the basis of these illustrative computation results, the STIBC is expected to be applied to investigate more complicated inflow noise problems including the effects of non-uniform mean flow, nonlinear interaction, and real airfoil shapes.