Publication: Sensitivity-Based Analysis of the k-ε Model for the Turbulent Flow Between Two Plates
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Sensitivity-Based Analysis of the k-ε Model for the Turbulent Flow Between Two Plates

- Article in a journal -
 

Area
Computational Fluid Dynamics, Optimization

Author(s)
A. Bardow , C. H. Bischof , H. M. Bücker , G. Dietze , R. Kneer , A. Leefken , W. Marquardt , U. Renz , E. Slusanschi

Published in
Chemical Engineering Science

Year
2008

Abstract
Eddy viscosity models (EVM) constitute the most successful 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. Interestingly, the choice of turbulence parameters on the basis of the purely formal a priori analysis agrees quite well with physical understanding of the k-ε model.

AD Tools
ADIFOR

BibTeX
@ARTICLE{
         Bardow2008SBA,
       author = "A. Bardow and C. H. Bischof and H. M. B{\"u}cker and G. Dietze and R. Kneer
         and A. Leefken and W. Marquardt and U. Renz and E. Slusanschi",
       title = "Sensitivity-Based Analysis of the $k$-$\varepsilon$ Model for the Turbulent Flow
         Between Two Plates",
       journal = "Chemical Engineering Science",
       pages = "4763--4775",
       doi = "10.1016/j.ces.2007.12.029",
       abstract = "Eddy viscosity models (EVM) constitute the most successful 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 $k$-$\epsilon$ 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 $k$-$\epsilon$ model may easily fail
         due to over-parameterization of the underlying model or insufficient data. Therefore, an
         \emph{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 \emph{a~priori} methods for model assessment and calibration. Interestingly, the
         choice of turbulence parameters on the basis of the purely formal a priori analysis agrees quite
         well with physical understanding of the $k$-$\epsilon$ model.",
       year = "2008",
       volume = "63",
       number = "19",
       ad_area = "Computational Fluid Dynamics, Optimization",
       ad_tools = "ADIFOR"
}


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