This report presents the development of turbulence models for shear flows using a double expansion technique. The approach builds upon the renormalization group (RNG) method of Yakhot and Orszag, incorporating scale expansions for Reynolds stress and dissipation production. A new two-equation model and Reynolds stress transport model are developed for turbulent shear flows. The models are tested for homogeneous shear flow and flow over a backward-facing step, showing excellent agreement with experimental data. The key idea is the introduction of an expansion parameter, η, defined as the ratio of turbulent to mean strain time scales. While low-order expansions provide adequate descriptions for Reynolds stress, higher-order terms are necessary for dissipation production. The models are validated against experimental data, demonstrating their effectiveness in predicting turbulence behavior. The report discusses the theoretical foundations of turbulence modeling, including the Kolmogorov theory of turbulence, the role of effective viscosity, and the importance of dimensionless constants in turbulence theory. It also addresses the challenges of modeling turbulence in flows with large strain values, where traditional models may not perform well. The study introduces a generalized K-ε model that incorporates a relaxation time approximation and accounts for the effects of strain on turbulence production. This model is tested in homogeneous shear flow and turbulent flow over a backward-facing step, showing excellent agreement with experimental results. The report concludes that the new turbulence models, based on the RNG method and double expansion technique, provide accurate predictions for turbulent flows. The models are particularly effective in capturing the behavior of turbulence in flows with large strain values, where traditional models may fail. The results demonstrate the importance of considering the effects of strain on turbulence production and the need for more accurate models that account for these effects. The study highlights the potential of the RNG method and double expansion technique in developing more accurate turbulence models for engineering applications.This report presents the development of turbulence models for shear flows using a double expansion technique. The approach builds upon the renormalization group (RNG) method of Yakhot and Orszag, incorporating scale expansions for Reynolds stress and dissipation production. A new two-equation model and Reynolds stress transport model are developed for turbulent shear flows. The models are tested for homogeneous shear flow and flow over a backward-facing step, showing excellent agreement with experimental data. The key idea is the introduction of an expansion parameter, η, defined as the ratio of turbulent to mean strain time scales. While low-order expansions provide adequate descriptions for Reynolds stress, higher-order terms are necessary for dissipation production. The models are validated against experimental data, demonstrating their effectiveness in predicting turbulence behavior. The report discusses the theoretical foundations of turbulence modeling, including the Kolmogorov theory of turbulence, the role of effective viscosity, and the importance of dimensionless constants in turbulence theory. It also addresses the challenges of modeling turbulence in flows with large strain values, where traditional models may not perform well. The study introduces a generalized K-ε model that incorporates a relaxation time approximation and accounts for the effects of strain on turbulence production. This model is tested in homogeneous shear flow and turbulent flow over a backward-facing step, showing excellent agreement with experimental results. The report concludes that the new turbulence models, based on the RNG method and double expansion technique, provide accurate predictions for turbulent flows. The models are particularly effective in capturing the behavior of turbulence in flows with large strain values, where traditional models may fail. The results demonstrate the importance of considering the effects of strain on turbulence production and the need for more accurate models that account for these effects. The study highlights the potential of the RNG method and double expansion technique in developing more accurate turbulence models for engineering applications.