Investigation on behavior of non-Newtonian fluid flow inside an annulus based on different turbulence theories: a numerical study

Abstract The importance of drilling in the development and exploitation of oil and gas reservoirs is very vital and is one of the most costly tasks in the extraction of underground resources. For drilling, a drilling fluid is needed that can perform tasks such as cleaning the drill tip, cooling the drilling site, and transporting the cut rocks from inside the well to the outside. Since the fluids used in this field are non-Newtonian fluids, the drilling mud flow inside the well can be simulated as a non-Newtonian turbulent flow in order to study the hydrodynamics of the drilling fluid flow and to investigate the conditions for improving drilling performance. In this research, a numerical study of the turbulent flow of the non-Newtonian fluid water and carboxymethyl cellulose around a rotating cylinder was conducted. The purpose of this project is to investigate the fluid velocity field calculated by different turbulence models under these conditions. The main turbulence model considered for this study will be the $$k- \varepsilon \text{RNG}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>-</mml:mo> <mml:mi>ε</mml:mi> <mml:mtext>RNG</mml:mtext> </mml:mrow> </mml:math> model, which is one of the most commonly used models for turbulent flow, and the results obtained from this model will be compared with other turbulence models including $$k-\omega \text{SST}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>-</mml:mo> <mml:mi>ω</mml:mi> <mml:mtext>SST</mml:mtext> </mml:mrow> </mml:math> , large-eddy simulation, Spalart–Allmaras, Reynolds stress turbulence model, and SST transition. For this purpose, computational fluid dynamics (CFD) software will be used to calculate and obtain the desired responses. The results obtained using the method used in this study show a good agreement with the experimental results. It was also observed that the different turbulence methods provided responses close to each other. This research provides a new criterion for evaluating the accuracy of turbulence models in non-Newtonian fluid flow conditions and helps to better understand the interaction between viscoelastic effects and turbulence. In addition, the results are useful as a guide to selecting the most optimal turbulence model based on the required accuracy and computational constraints in industries such as food, pharmaceutical, and petrochemical.