Identification and Development of a Reliable Framework to Predict Passive Scalar Transport for Turbulent Bounded Shear Flows

Abstract

Heat transfer modeling plays an integral role in optimization and development of highly efficient modern thermal-fluid systems. However, currently available heat flux models suffer from fundamental shortcomings. For example, their development is based on the general notion that an accurate prediction of the flow field will guarantee an appropriate prediction of the thermal field, as the Reynolds Analogy does. Furthermore, literature about advanced models that aim to overcome this notion, does not provide reliable information about prediction capabilities. These advanced models can be separated into two distinct heat flux model categories, namely the implicit and explicit models. Both model categories differ fundamentally in their mathematical and physical formulation.

Hence, this dissertation presents a comprehensive assessment of the Reynolds Analogy regarding steady and unsteady calculations. It further analyses the entropy generation capability in detail and evaluates the prediction accuracy of implicit and explicit models when applied to turbulent shear flows of fluids with different Prandtl numbers. Moreover, the implicit and explicit models are modified such that important thermal second order statistics are included. This enables deeper insight into the mechanics of thermal dissipation and delivers a better understanding towards the sensitivity and reliability of predictions using heat flux models. Finally, to overcome the shortcomings of the Reynolds Analogy in unsteady calculations, an anisotropic extension is proposed.

This dissertation shows that even for first order statistics within steady state calculations, the Reynolds Analogy is only appropriate for fluids with Prandtl numbers around unity. For second order statistics within unsteady simulations, the Reynolds Analogy could provide acceptable results only if an appropriate grid design/resolution is provided that allows resolving essential dynamics of the thermal field. Concerning entropy generation, the Reynolds Analogy provides acceptable results only for mean entropy generation, while it fails to predict entropy generation at small/sub-grid scales. The anisotropic extension of the Reynolds Analogy is a promising approach to overcome these shortcomings.

Furthermore and concerning the implicit and explicit heat flux models, this work shows that only the explicit framework is potentially capable of dealing with complex turbulent thermal fields and to address longstanding shortcomings of currently available models, if the flow field is predicted accurately. Moreover, it has been shown that thermal time scale plays an integral role to predict thermal phenomena, particularly those of fluids with low/high Pr numbers.