The effect of non-Newtonian viscosity on the stability of the Blasius boundary layer

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The effect of non-Newtonian viscosity on the stability of the Blasius boundary layer. / Gallagher, Meurig; Griffiths, Paul; Stephen, Sharon.

In: Physics of Fluids, Vol. 28, No. 7, 31.07.2016.

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@article{537ccfb219904d3490632fdbdbcbbdf7,
title = "The effect of non-Newtonian viscosity on the stability of the Blasius boundary layer",
abstract = "We consider, for the first time, the stability of the non-Newtonian boundary layer flow over a flat plate. Shear-thinning and shear-thickening flows are modelled using a Carreau constitutive viscosity relationship. The boundary layer equations are solved in a self-similar fashion. A linear asymptotic stability analysis, that concerns the lower-branch structure of the neutral curve, is presented in the limit of large Reynolds number. It is shown that the lower-branch mode is destabilised and stabilised for shear-thinning and shear-thickening fluids, respectively. Favourable agreement is obtained between these asymptotic predictions and numerical results owing from an equivalent Orr-Sommerfeld type analysis. Our results indicate that an increase in shear-thinning has the effect of significantly reducing the value of the critical Reynolds number, this suggests that the onset of instability will be significantly advanced in this case. This postulation that shear-thinning destabilises the boundary layer flow is further supported by our calculations regarding the development of the steamwise eigenfunctions and the relative magnitude of the temporal growth rates.",
keywords = "Boundary Layers, Stability, Flow Control, Non-Newtonian flows, instability",
author = "Meurig Gallagher and Paul Griffiths and Sharon Stephen",
year = "2016",
month = jul,
day = "31",
doi = "10.1063/1.4958970",
language = "English",
volume = "28",
journal = "Physics of Fluids",
issn = "1070-6631",
publisher = "American Institute of Physics",
number = "7",

}

RIS

TY - JOUR

T1 - The effect of non-Newtonian viscosity on the stability of the Blasius boundary layer

AU - Gallagher, Meurig

AU - Griffiths, Paul

AU - Stephen, Sharon

PY - 2016/7/31

Y1 - 2016/7/31

N2 - We consider, for the first time, the stability of the non-Newtonian boundary layer flow over a flat plate. Shear-thinning and shear-thickening flows are modelled using a Carreau constitutive viscosity relationship. The boundary layer equations are solved in a self-similar fashion. A linear asymptotic stability analysis, that concerns the lower-branch structure of the neutral curve, is presented in the limit of large Reynolds number. It is shown that the lower-branch mode is destabilised and stabilised for shear-thinning and shear-thickening fluids, respectively. Favourable agreement is obtained between these asymptotic predictions and numerical results owing from an equivalent Orr-Sommerfeld type analysis. Our results indicate that an increase in shear-thinning has the effect of significantly reducing the value of the critical Reynolds number, this suggests that the onset of instability will be significantly advanced in this case. This postulation that shear-thinning destabilises the boundary layer flow is further supported by our calculations regarding the development of the steamwise eigenfunctions and the relative magnitude of the temporal growth rates.

AB - We consider, for the first time, the stability of the non-Newtonian boundary layer flow over a flat plate. Shear-thinning and shear-thickening flows are modelled using a Carreau constitutive viscosity relationship. The boundary layer equations are solved in a self-similar fashion. A linear asymptotic stability analysis, that concerns the lower-branch structure of the neutral curve, is presented in the limit of large Reynolds number. It is shown that the lower-branch mode is destabilised and stabilised for shear-thinning and shear-thickening fluids, respectively. Favourable agreement is obtained between these asymptotic predictions and numerical results owing from an equivalent Orr-Sommerfeld type analysis. Our results indicate that an increase in shear-thinning has the effect of significantly reducing the value of the critical Reynolds number, this suggests that the onset of instability will be significantly advanced in this case. This postulation that shear-thinning destabilises the boundary layer flow is further supported by our calculations regarding the development of the steamwise eigenfunctions and the relative magnitude of the temporal growth rates.

KW - Boundary Layers

KW - Stability

KW - Flow Control

KW - Non-Newtonian flows

KW - instability

U2 - 10.1063/1.4958970

DO - 10.1063/1.4958970

M3 - Article

VL - 28

JO - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 7

ER -