Reynolds Stress Model for Viscoelastic Drag-Reducing Flow Induced by Polymer Solution

Area of Science:

• Fluid Dynamics
• Rheology
• Computational Science

Background:

• Viscoelastic polymer solutions reduce pipe flow pumping energy.
• Direct numerical simulation (DNS) provides accurate data but is computationally expensive.
• Turbulent models offer speed but often lack precision.

Purpose of the Study:

• To develop a high-precision turbulent model for viscoelastic drag-reducing flow.
• To leverage DNS data for accurate turbulent model construction.
• To improve the computational efficiency of simulating these flows.

Main Methods:

• Established a Reynolds stress model (RSM) for viscoelastic polymer drag-reducing flow.
• Utilized the Giesekus constitutive equation to describe rheological behavior.
• Validated the model against DNS data for mean velocity, conformation tensor, drag reduction, and stresses.

Main Results:

• The RSM accurately predicted key flow parameters at low Reynolds and Weissenberg numbers.
• Model accuracy decreased as Reynolds and Weissenberg numbers increased.
• The RSM achieved a computational time 1/120,960th of DNS, demonstrating significant speed advantage.

Conclusions:

• The developed Reynolds stress model offers a computationally efficient alternative to DNS for viscoelastic drag-reducing flows.
• The model shows promise for engineering applications requiring accurate predictions of drag reduction.
• Further refinement is needed for high Reynolds and Weissenberg number regimes.