M. Freitag

Assessment measures for URANS/DES/LES: an overview with applications

A survey of quality assessment methods is presented covering a range of possible errors in applications of CFD. Beside modeling and numerical errors further uncertainties in unsteady flow simulations are related to inlet conditions and statistical averaging. The main focus is on measures that can be applied to unsteady Reynolds averaged Navier–Stokes (URANS) solvers, hybrid large eddy simulations (HLES), detached eddy simulations (DES), and mostly LES applications. The quantification of uncertainty in LES (large eddy simulations) is difficult for two reasons: (i) substantial grid refinement is too expensive and time consuming; (ii) the modeling errors and discretization errors are convoluted in such a nonlinear manner that it is difficult to segregate one from the other. In hybrid URANS/LES this task is even more difficult because the transitional regions cannot be identified a priori. A brief review of attempts to quantify the accuracy of LES focusing on Richardson extrapolation (RE) is presented. Selected measures are applied to URANS, DES and LES cases from the literature. An attempt is made to separate the modeling contribution from the numerical errors in LES. The methods proposed for the quantification of LES and DES accuracy are still in their infancy stage. Early results are however, promising.

An improved method to assess the quality of large eddy simulations in the context of implicit filtering

Large eddy simulation (LES) quality assessment is very important in view of predictive LES applications, but it is more complex than the verification of solutions from the Reynolds averaged Navier–Stokes equations. One reason is that the numerical discretization error and the subgrid scale model contribution depend on the grid resolution and that both terms interact. Recently, a method has been proposed to evaluate these error contributions by a systematic grid and model variation, assuming that the numerical error and the modeling error scale like a power of the grid spacing resp. filter width. A second-order dissipation error has been assumed in that work. However, theoretical arguments suggest that the true subgrid stresses scale like Δ2/3. The determination of the suitability and generality of this assumption is part of the present work. It will be shown that smaller values of the scaling exponent for the modeling error, i.e. m≈ 2/3, seem to be more appropriate. Furthermore, a more conservative measure for estimating the uncertainty is proposed. Besides a wall bounded flow (channel flow) and a shear flow (plane jet) the new procedure will be applied to a third important flow category, swirling flows.

Modeling of noise sources in combustion processes via Large-Eddy Simulation

The focus of this chapter is the definition and development of the interface between CFD and CAA appproaches. Hybrid approaches for the investigation of noise resulting from flow phenomena are widely used and well accepted in aeroacoustics. Especially at low Mach number flows, the fluid dynamic and acoustic length scales are separated by more than an order of magnitude.

Time Resolved Combustion Noise Investigation Based on a Wave Equation Approach

A transient simulation technique is proposed and applied to an open turbulent non-premixed jet flame in order to investigate its acoustic near field. The hybrid approach consists of a three dimensional large eddy simulation (LES) with a low Mach number formulation and a two dimensional wave equation approach to solve for the acoustic propagation. In this manner, the disparity of scales between the incompressible flow field and the acoustics is exploited. The fluid properties, as well as the required acoustic sources are computed for every time step and updated in the acoustic solver. Since the LES is utilized as a tool, only a brief validation of the LES results is provided. The structure of the acoustic near field in the vicinity of the flame is of a monopole type, in agreement with the literature. A thorough spectral comparison of noise intensity levels to measurements reveals an acceptable agreement for the current approach. A further comparison to other hybrid approaches reported in the literature indicates, that this agreement is in a range that can be expected for a two dimensional acoustic technique. Two separate, well established solvers are combined in this contribution to an efficient simulation tool for transient combustion noise investigations.