### Advanced Turbulence Closures for a Scalable Parallel Implicit Unstructured Grid Algorithm

*A Dissertation Presented for the Doctor of Philosophy in Computational Engineering, The
University of Tennessee at Chattanooga*

#### Muhanad K. Hajjawi, August 2007

Abstract:

The primary objective of this study is to assess advanced turbulence models and implement
them into an existing scalable, parallel, unstructured flow solver. Starting with
the linear eddy-viscosity models(EVMs), the k−e two-equation model is chosen because
it is one of the most widely used Reynolds-averaged Navier-Stokes (RANS) approaches
for turbulent flow computations. Despite its robustness and reasonable accuracy, well
recognized deficiencies are associated with this model when treating flows with large
streamline curvature and separation. On the other hand, the second-moment closure
models (SCMs) are known to possess a more accurate representation of the turbulent
production and have the capability to predict complex flows better than the EVMs.
The Launder-Shima (LS) Reynolds stress model is chosen for implementation since it
is one of the most promising SCM models for industrial computations. Unfortunately,
one major problem associated with these models is the numerical stiffness and instability
arising from coupling the stress equations with the mean flow momentum equations.
After investigating and testing of the LS model, the complexity of the dissipation
equation of this model appeared to add more stiffness and instability characteristics
to the equation system, particularly when integrating to the wall with sub-layer resolution.
In the present work, the dissipation equation from the LS model is replaced by the
well known k−e model dissipation equation to produce a more robust and stable Reynolds
stress model. This model will be referred to with LSe. Finally, a hybrid LES/RANS
filter based model is implemented and assessed in an effort to improve the predictive
capability of the current RANS-based engineering turbulence closures for highly separated
flows. These hybrid models are currently believed to become the future industrial
and environmental standard computational models.

Computations for a turbulent flat plate, square cylinder, backward facing step, surface

mounted cube, and DARPA SUBOFF body are compared to experimental data for all models.
The modified model shows a significant improvement in stability and robustness over
the Launder-Shima model, while keeping the same flow prediction accuracy. Additionally,
in comparison to the k−e model, the filtered-based LES/RANS model is shown to improve
the predictive capability considerably for time dependent separated flows.