Minimization and Quantification of Errors and Uncertainties in RANS Modeling

Tobias Schmidt, Charles Mockett, and Frank Thiele

1 Introduction

Owing to their affordable computational cost relative to higher-fidelity approaches such as large-eddy simulation (LES), statistical turbulence models are currently the principle workhorse for the simulation of turbulent flows in industrial aerodynamics. However, significant problems arise from the inherent empricism of such Reynolds – averaged Navier-Stokes (RANS) approaches. First and foremost, the current state of the art is that no universally-applicable model is available. Instead, a very large number of different RANS models exist, with varying degrees of mathematical com­plexity and with calibration valid for limited classes of flows. This state of affairs is further compounded by the experience that more complex formulations do not necessarily deliver better results. For these reasons, the choice of turbulence model for an engineering simulation has a strong impact on the quality of the results ob­tained. In addition to this, simulation results using a fixed RANS model show a strong sensitivity to other aspects of the simulation setup, most notably the grid. For external aerodynamics applications, the spatial resolution of the thin boundary layer regions is seen to be particularly important. All these factors lead to a very high dependency on the decisions made by the engineer in setting up the simulation, and strong reliance is placed on a combination of best practice guidelines (BPG) and user experience.

The motivation of this work is therefore the development of a series of extensions to the TAU flow solver, intended to reduce this user burden and to improve the quality of simulation results in an industrial environment. The approach taken is the development of a range of sensors to check important grid design parameters

Tobias Schmidt • Charles Mockett • Frank Thiele TU Berlin, Muller-Breslau-Str. 8, D-10623 Berlin

e-mail: {tobias. schmidt, charles. mockett}@cfd. tu-berlin. de, frank. thiele@cfd. tu-berlin. de

B. Eisfeld et al. (Eds.): Management & Minimisation of Uncert. & Errors, NNFM 122, pp. 77-100. DOI: 10.1007/978-3-642-36185-2_4 © Springer-Verlag Berlin Heidelberg 2013

and to detect the occurrence of flow phenomena known to be correlated with high model-dependency. For the grid error sensors, this amounts to the incorporation of BPG within the software itself. With these sensors in place, the next step is to attempt to quantify the error introduced. For this, the feasibility of an empirical approach is assessed, whereby the solution sensitivity to various error mechanisms is established on simple datum test cases and extrapolated to more complex flows. The implemented module provides the engineer with enhanced textual and graphical feedback, drawing attention to possible problems and suggesting appropriate steps to improve results and minimise such errors.