On stochastic inlet boundary condition for unsteady simulations

Abstract

Abstract. The paper deals with the stochastic generation of synthesized turbulence, which may be used for a generating of an inlet boundary condition for unsteady simulations, e.g. Direct Numerical Simulation (DNS) or Large Eddy Simulation (LES). Assumptions for the generated turbulence are isotropy and homogeneity. The described method produces a stochastic turbulent velocity field using the synthesis of a finite sum of random Fourier modes. The calculation of individual Fourier modes is based on known energy spectrum of turbulent flow, and some turbulent quantities, e.g. turbulent kinetic energy and turbulent dissipation rate. A division of wave number range of the energy spectrum determines directly the number of Fourier modes, and has a direct impact on accuracy and speed of this calculation. Therefore, this work will examine the influence of the number of Fourier modes on a conservation of the first and second statistical moments of turbulent velocity components, which are prespecified. It is important to ensure a sufficient size of a computational domain, and a sufficient number of cells for meaningful comparative results. Dimensionless parameters characterizing the resolution and size of the computational domain according to a turbulent length scale will be introduced for this purpose. Subsequently, the sufficient values of this parameters will be shown for individual numbers of Fourier modes.

3D CAA methodology using synthetic turbulence to assess turbulence-cascade interaction noise emission and reduction from serrated airfoils

“…However, as shown in the present work, the latter approach is not directly expandable to 3D turbulence structures. Consequently, the framework used for homogeneous isotopic turbulence (HIT) generation and currently relying on the energy spectrum definition such as proposed in [14] and in [17] is considered. An equivalent mathematical formalism is originally proposed to still link the energy spectrum with wavenumber distribution over a spherical volume to the velocity autocorrelation spectra using a Cartesian writing over a rectangular volume.…”