Sensitivity-based analysis of the k – ε model for the turbulent flow between two plates

Eddy viscosity models (EVM) constitute a powerful approach for turbulence modeling in engineering applications. However, the correct formulation of EVM models is still subject to discussion, in particular the impact of model parameters on the practical relevance of models in different classes of application scenarios is not fully understood. A systematic approach for assessing parameter impact involves optimization methods for computational fluid dynamics that allow for quantitative model analysis by rigorous comparison with experimental data. In order to illustrate this systematic approach, the k – ε turbulence model is analyzed on the basis of laser Doppler velocimetry measurements for the flow between two plates. It is shown that ad hoc approaches for adapting parameter values for the k – ε model may easily fail due to over-parameterization of the underlying model or insufficient data. Therefore, an a priori method for the identification of potential problems is important which is based on the sensitivity coefficients of the measurements with respect to the model parameters. The commercial software package FLUENT employed in our application is augmented using the automatic differentiation system ADIFOR for efficient sensitivity computation. Taken together, this results in reliable a priori methods for model assessment and calibration. Noteworthy, the choice of turbulence parameters on the basis of the formal a priori analysis agrees well with the physical understanding of the k – ε model.