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Numerical Simulation of Non-Newtonian Power-Law Fluid Flow in a Lid-Driven Skewed Cavity

  • Sharaban Thohura
  • Md. Mamun MollaEmail author
  • Md. Manirul Alam Sarker
Original Paper
  • 35 Downloads

Abstract

Non-Newtonian laminar fluid flow in a lid-driven skewed cavity has been studied numerically using power-law viscosity model. The governing two-dimensional unsteady incompressible Navier–Stokes equations were initially non-dimensionalized using appropriate transformation, and then the dimensionless form is transformed to generalized curvilinear coordinates to simulate complex geometry. The transformed equations are discretized using finite volume method with the collocated grid arrangement. The code is first validated against the existing benchmark results for two-dimensional lid-driven square cavity problem considering both Newtonian and non-Newtonian fluids. The validation has also been carried out for a lid-driven skewed cavity in the case of a Newtonian fluid. Then the code is applied to the skewed cavity problem involving non-Newtonian fluid flow which can be described by the power-law viscosity model. Moreover, grid independence test has been performed for a skewed cavity for different values of power-law index. In the present case, the skewness of the geometry has been changed by changing the skew angle for both shear-thinning and shear-thickening fluids. The consequent numerical results are presented in terms of the velocity as well as streamlines for the different values of the power-law index \(n=0.5\), 1 and 1.5, Reynolds number \(Re = 100, 200, 300\) and 500 as well as for the different angles of the skewed cavity (\(\alpha =15^{\circ }\) to \(165^{\circ }\)).

Keywords

Curvilinear coordinates Non-orthogonal grid Non-Newtonian fluid flow Skewed cavity Power-law model Finite volume method 

List of Symbols

\(A_{ij}\)

Cofactors of the Jacobian matrix

D

Non-dimensional fluid viscosity

J

Jacobian matrix

H

Height of the cavity

\({\bar{p}}\)

Dimensional pressure of the fluid

p

Non-dimensional pressure

n

Power-law index

Re

Reynolds number

\({\bar{t}}\)

Dimensional time

t

Non-dimensional time

\({\bar{u}}\)

Velocity component in the x-direction

\({\bar{v}}\)

Velocity component in the y-direction

\(u_0\)

Reference velocity

u

Non-dimensional velocity component in the x-direction

v

Non-dimensional velocity component in the y-direction

x

Horizontal coordinate

y

Vertical coordinate

Greek Symbols

\(\alpha \)

Skew angle of the cavity

\({\dot{\gamma }}\)

Second invariant of the rate-of-strain tensor

\(\gamma _1,\gamma _2\)

Threshold shear-rate

\(\xi _1, \xi _2\)

Curvilinear coordinates

\(\eta \)

Normal direction to the wall

\(\mu _0\)

Reference molecular viscosity

\(\mu \)

Molecular viscosity

\(\nu \)

Kinematic viscosity

\(\nu _0\)

Reference kinematic viscosity

\(\rho \)

Fluid density

Notes

Acknowledgements

The first author gratefully acknowledges the People’s Republic of Bangladesh Government for providing the financial support for completing her Ph.D. during 2017–2019. She also grateful to NSU for using the computational resources. The second author would like to thank the PGI group for providing the University developer license of “PGI Accelerator Fortran/C/C++ compiler for a Workstation in Linux.”

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Copyright information

© Springer Nature India Private Limited 2019

Authors and Affiliations

  1. 1.Department of MathematicsJagannath UniversityDhakaBangladesh
  2. 2.Department of Mathematics and PhysicsNorth South UniversityDhakaBangladesh
  3. 3.Center for Scientific ComputingNorth South UniversityDhakaBangladesh
  4. 4.Department of MathematicsBangladesh University of Engineering and TechnologyDhakaBangladesh

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