Date of Award


Degree Name

MS in Aerospace Engineering


Aerospace Engineering


David D. Marshall


The use of Computational Fluid Dynamics (CFD) tools throughout the engineering industry has become standard. Simulations are used during nearly all steps throughout the life cycle of products including design, production, and testing. Due to their wide range of use, industrial CFD codes are becoming more flexible and easier to use. These commercial codes require robustness, reliability, and efficiency. Consequently, linear eddy viscosity models (LEVM) are used to model turbulence for an increasing number of flow types. LEVM such as k-ε and k-ω provide modeling with little loss of computational efficiency and have proven to be robust. The LEVM that are most common in CFD tools, however, are not adequate for accurate prediction of complex flows. This includes flows with high streamline curvature, strong rotation and separation regions. Unfortunately, due to their ease of use in the commercial CFD tools, the models are used frequently for complex flows. Modifications have been made to LEVM such as k-ε in order to improve modeling, but generally, the modifications have only improved modeling of less complex flows. More advanced LEVM models have been developed using elliptic relaxation equations to help resolve these issues.

The ν2-f model was developed to better capture flow physics for complex flows while being applicable to general flows. It is generally considered one of the most accurate LEVMs. It does, however, have issues with stability and robustness. Several improvements have been proposed. One of the most notable is its reformulation into the ζ-f model which offers several improvements while maintaining accurate flow prediction. The model improvement is still limited by being a LEVM. While models, such as differential Reynolds stress models, do exist which are able to capture relevant flow physics in complex flows, modeling difficulties make them impractical for use in a commercial CFD code.

Algebraic Reynolds stress models have attempted to bridge this gap with varying levels of success. The models express the Reynolds stress tensor as a function of different higher level tensors. This is the same process used to derive non-linear eddy-viscosity models which add extra high-order terms to the Boussinesq approximation. According to Kassinos and Reynolds, however, this technique is fundamentally flawed. These models fail to capture all relevant information about the turbulence structure. The Reynolds stresses capture information regarding the turbulent componentiality, i.e. velocity components of turbulence. The dimensionality, which carries information regarding the direction of turbulent eddies, is not modeled, however. Kassinos and Reynolds constructed a structure-based model which attempts to capture turbulent componentiality and dimensionality by expressing the Reynolds stress tensor as a function of one-point turbulence structure tensors. Their original model introduced hypothetical turbulence eddies which could be averaged and then used to relate the eddy-axis transport equation to the proper structure tensors. The ideas behind this model were adapted into several different models including the R-D model and the Q-model. These formulations were able to accurately capture the flow physics for many complex flow types especially those with mean rotation. These resulting models, however, were overly complicated for application in commercial CFD codes. These structure-based models later resulted in the development of the algebraic structure based model (ASBM).

The ASBM was developed in order to ensure computational efficiency while capturing relevant turbulence physics. The ASBM uses an algebraic model for the eddy statistics which is constructed from the local mean deformation and two turbulent scales. The original turbulent scales used were the turbulent kinetic energy and the large scale vorticity. Although the model was calibrated specifically for use with the turbulent kinetic energy and large scale vorticity transport equations, the algebraic model can be used in conjunction with any scalar transport equations as long as the field distribution of turbulent kinetic energy and turbulence time scale can be obtained. Based on its formulation, the ASBM, used in combination with any scalar transport equations, should be applicable to most commercial CFD codes.

The objective of this work was to implement the ζ-f model and ASBM, coupled with k-ε and v2-f, in the commercial CFD solver FLUENT and validate its performance for canonical turbulent flows including a subsonic turbulent flat-plate, S3H4 2D hill, and backward-facing step. Each turbulent flow was evaluated using various turbulence models including Spalart-Allmaras, k-ε, k-ω, k-ω-SST, v2-f, ζ-f and two ASBM formulations and compared against experimental results. The ζ-f model produced improved results for both the flat plate and backward facing step as compared to all two-equation or less turbulence models and showed similar predictive capabilities to the v2-f model. It had difficulties predicting attached flow past the S3H4 2D hill just as the v2-f model. This, however, was expected due to its basis on the v2-f model. The model was also more stable than the v2-f model during calculation of the turbulent flat plate but showed no improvement in robustness for the more complex backward facing step. The semicoupled (linear eddy viscosity model based) v2-f-ASBM’s predictive capabilities were comparable to the two equation models for the turbulent flat plate case. It performed surprisingly well for the backward facing step and matched the experimental data within experimental uncertainty. The model did, however, have problems predicting the S3H4 2D hill just as the with the v2-f model.