Linear and nonlinear instabilities in highly shear thinning fluid flow through a pipe
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866916912545398784 |
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| author | He, Xuerao Deguchi, Kengo Song, Runjie Blackburn, Hugh M. |
| author_facet | He, Xuerao Deguchi, Kengo Song, Runjie Blackburn, Hugh M. |
| contents | Shear-thinning fluids flowing through pipes are crucial in many practical applications, yet many unresolved problems remain regarding their turbulent transition. Using highly robust numerical tools for the Carreau-Yasuda model, we discovered that linear instability can arise when the power-law index falls below 0.35. This inelastic non-axisymmetric instability can universally arise in generalised Newtonian fluids that extend the power-law model. The viscosity ratio from infinite to zero shear rate can significantly impact instability, even if it is small. Two branches of finite-amplitude travelling wave solutions bifurcate subcritically from the linear critical point. The solutions exhibit sublaminar drag reduction, a phenomenon not possible in the Newtonian case. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_10037 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Linear and nonlinear instabilities in highly shear thinning fluid flow through a pipe He, Xuerao Deguchi, Kengo Song, Runjie Blackburn, Hugh M. Fluid Dynamics Shear-thinning fluids flowing through pipes are crucial in many practical applications, yet many unresolved problems remain regarding their turbulent transition. Using highly robust numerical tools for the Carreau-Yasuda model, we discovered that linear instability can arise when the power-law index falls below 0.35. This inelastic non-axisymmetric instability can universally arise in generalised Newtonian fluids that extend the power-law model. The viscosity ratio from infinite to zero shear rate can significantly impact instability, even if it is small. Two branches of finite-amplitude travelling wave solutions bifurcate subcritically from the linear critical point. The solutions exhibit sublaminar drag reduction, a phenomenon not possible in the Newtonian case. |
| title | Linear and nonlinear instabilities in highly shear thinning fluid flow through a pipe |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2412.10037 |