Numerical Simulation of Shear-Thinning Fluid Flow: Finite Element Method

• Published in: CFD letters Vol. 17; no. 10; pp. 106 - 119
• Main Authors: Ghanim, Ahmed Jameel, Al-Muslimawi, Alaa Hasan, Al-Bahrani, Bashaer Kadhim
• Format: Journal Article
• Language: English
• Published: 01.10.2025
• ISSN: 2180-1363; 2180-1363
• DOI: 10.37934/cfdl.17.10.106119

In the current investigation, the simulation of shear-thinning inelastic fluid flow is considered through the axisymmetric rectangular channel. To describe the fluid motion, the mass conservation and conservation of momentum partial differential equations are usually used. These equations are presented in this study in the cylindrical coordinate system. The key point here is that viscosity needs to be defined as a variable, which requires introducing an additional equation constitutive. Accordingly, a shear-thinning inelastic model, SI-Fit-I, is presented for treating the viscosity condition. In this model, a viscosity dependent on shear-rate is employed through the second invariant but does not include full viscoelastic effects. Numerically, the Galerkin finite element approach based on the artificial compression method (AC-method) is performed in this study, which is considered a continuation of our previous study conducted on the power-law inelastic. To satisfy the analysis of the algorithm used in this study, a circular channel is utilized as an application problem. In such a problem, the proposed algorithm is employed with isothermal Poiseuille flow by taking a circular section of the channel. The influence of many parameters such as the consistency parameter and power index of the model, artificial compressibility parameter (β_ac) and Reynolds number (Re) was discussed. The results show that the velocity temporal convergence-rate is greatly affected by the inelastic parameters, in contrast, a simple change in the level of pressure convergence has appeared. Moreover, as the values of the artificial compressibility parameter are decreased the level of convergence is raised.