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Oscillatory Carreau flows in straight channels.
S Tabakova1, N Kutev2, St Radev1
1Institute of Mechanics, Bulgarian Academy of Sciences, Sofia, Bulgaria.
Royal Society Open Science
|June 16, 2020
Summary
This study analyzes Carreau fluid flow in a channel, revealing how Womersley and Carreau numbers influence velocity. The Carreau number modifies flow behavior, making it resemble Newtonian fluids under varying shear conditions.
Area of Science:
- Fluid dynamics
- Non-Newtonian fluid mechanics
- Rheology
Background:
- Understanding non-Newtonian fluid behavior is crucial in various industrial applications.
- Carreau fluids exhibit complex flow properties that differ from Newtonian fluids.
- Channel flow dynamics are fundamental in fluid mechanics research.
Purpose of the Study:
- To investigate the oscillatory flow of Carreau fluid within a channel.
- To analyze the impact of varying Womersley and Carreau numbers on fluid velocity.
- To develop theoretical bounds and asymptotic expansions for flow solutions.
Main Methods:
- Asymptotic expansions were employed for high and low Womersley numbers.
- Theoretical bounds for velocity and its gradient were proven for intermediate Womersley numbers.
- Numerical simulations were conducted to illustrate velocity profiles.
Main Results:
- The Carreau number was shown to alter flow velocity, mimicking Newtonian fluids at low/high shear or exhibiting transitional characteristics.
- Asymptotic expansions provided analytical solutions for specific Womersley number regimes.
- Explicit theoretical bounds were established for velocity and its gradient.
Conclusions:
- The study provides a comprehensive analysis of Carreau fluid flow under different flow conditions.
- The findings offer insights into the rheological behavior of Carreau fluids in channel flow.
- The developed methods and results can be applied to optimize processes involving non-Newtonian fluids.
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