The conveyance of fluids from one terminal to another incurs considerable expenses primarily due to the significant costs associated with addressing pressure losses arising from shear stresses and friction along the inner surface during the pumping operations within pipelines. This study was conducted with the objective of simulating turbulent flow in pipes containing drag-reducing fluids. This was achieved through the utilization of both RKE and RNG versions of a non-Newtonian model for low Reynolds numbers, based on the k-ε model, along with a non-Newtonian damping function. The outcomes were subsequently compared to simulations carried out by Pinho and experimental data sourced from the existing literature. To simulate the flow in pipelines, computational fluid dynamics (CFD) software was employed, which incorporated non-linear molecular viscosity and a damping function to accurately account for near-wall effects. In addition, this research entailed the optimization of C and C0 parameters in the damping function and the stress term, which quantifies the cross-correlation between fluctuating viscosity and the fluctuating rate of strain. Furthermore, non-Newtonian terms were incorporated into the equations for turbulent kinetic energy (k), dissipation rate (ε), and momentum transfer. The study involved a comprehensive comparison of model predictions with experimental data across various flow parameters, including friction factor, axial velocity, turbulent kinetic energy, and Reynolds shear stresses. The results revealed a significant enhancement in the model's ability to predict critical flow parameters, such as friction factor, mean axial velocity, and Reynolds stress profiles. Nevertheless, the model displayed some limitations in predicting turbulent kinetic energy. Notably, the average error in calculating the friction factor for the fluids under investigation was found to be 5.45%, marking a substantial improvement compared to the Pinho model, which exhibited an average error of 32.49%.