Mathematics (Jan 2024)
Numerical Simulation of the Stability of Low Viscosity Ratio Viscoelastic Lid-Driven Cavity Flow Based on the Log-Conformation Representation (LCR) Algorithm
Abstract
Log-Conformation Representation (LCR) method effectively enhances the stability of viscoelastic fluid flow driven by a cavity at high Wi numbers. However, its stability is relatively poor under low viscosity ratio conditions. In this study, three momentum equation stabilization algorithms (Both-Sides-Diffusion, Discrete Elastic Viscous Split Stress-Vorticity, and velocity–stress coupling) were tested and compared in OpenFOAM to assess their stabilizing effects on the LCR method under low viscosity ratio conditions. The evaluation was based on changes in average kinetic energy and the maximum critical time step. The results indicate that the different momentum equation stabilization algorithms improve the numerical oscillations observed in the numerical simulation of low viscosity ratio cavity-driven flow to varying extents. This enables a reduction in the viscosity ratio that can be stably simulated by 0.03 to 0.15. Furthermore, these cases using the momentum equation stabilization algorithms require time steps that are 33% to 100% shorter than those of the original cases. This demonstrates the promoting effect of the additional diffusion term in the momentum equation on stability under low viscosity ratio conditions. The combination of LCR and velocity–stress coupling was used to analyze the impact of viscosity ratios on velocity, logarithmic conformation tensor, and average kinetic energy. As the viscosity ratio decreases, the contribution of fluid elasticity increases, resulting in more pronounced variations in velocity and stress. However, the viscosity ratio has little effect on the stress boundary layer at the top cover and corners. Under conditions with the same Wi number, the average kinetic energy decreases as the viscosity ratio decreases until stability is achieved.
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