Degree Type


Date of Award


Degree Name

Doctor of Philosophy


Aerospace Engineering


Aerospace Engineering

First Advisor

Paul Durbin


The work presented in this dissertation extends upon the elliptic-blending lag parameter approach for linear eddy-viscosity model (LVM). The model aims at preserving the numerical simplicity of an LVM while incorporating important features of an underlying Reynolds Stress Model(RSM). One important phenomenon in a non-equilibrium turbulent flow that the proposed model attempts to represent is the stress-strain misalignment. To this end, the model includes an additional transport equation of a field variable φ ∗ (coined as a “lag” parameter) in addition to thconventional two equations (k & ω for the current formulation). φ∗ is then used to suitably scale the eddy viscosity which turns out to be critical for improved predictions of non-equilibrium, separated flows in particular. Similar to the precursor models of the lag family, the proposed model preserves capability to project the six equations of an RSM onto a single equation through the definition of

φ∗ as φ∗ =−a ij S ij/S ω/S.

A review of the family of lag models are first presented in the dissertation. In particular, derivation of the Lag k − ε model is discussed. The present formulation is a derivative of the underlying framework use for the Lag k − ε version. The derivation of the new model, Lag k − ω is then discussed in detail. Two new non-dimensional variables, namely φ ∗ and α provides the backbone for the proposed formulation. Purpose and behaviour of each of these for plane shear flows are then discussed.

Finally the lag models are compared for a number of flow problems, both 2D and 3D, complexity of which range from canonical to industrial in nature. The predictions are then compared to commonly used RANS models, namely Wilcox’s k − ω and Menter’s k − ω SST formulations. The advantages and shortcomings of the lag approaches compared to the other models are discussed in detail for each of the studied cases. One key benefit of introducing the lag parameter is a better scaling of the turbulent eddy viscosity particularly in the near-wall region. This is critical for improved predictions of separated flows.

Copyright Owner

Rajarshi Biswas



File Format


File Size

120 pages