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Numerical Solutions of Steady Flow in a Three-Sided Lid-Driven Square Cavity

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Abstract

This paper reports a numerical investigation of the steady two-dimensional incompressible flow in a three-sided lid-driven cavity of unit aspect ratios (Г = 1). The two opposite horizontal walls move in parallel and antiparallel motions, while the left vertical sidewall moves upwards and downwards. The right vertical sidewall is stationary. A detailed analysis of the fluid flow has been carried out with the finite volume method for a Reynolds number up to 5000 using a fine mesh resolution, whereas the coupled algorithm has been employed to handle the pressure–velocity coupling. The results are displayed in terms of stream-function contours, fluid properties, and velocity profiles and have indicated a good agreement with the set of literature. Among the three driving processes considered, a most complex topological flow pattern has been shown with the antiparallel-downwards case. This is embodied by a significant amount of robustness induced in three opposing directions leading to multiple changes of streamline patterns. This is accompanied by high rotation rates of secondary vortices in the near-wall regions.

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Data Availability

All data generated or analysed during this study are included in this published article.

Code Availability

Ansys Fluent.

Abbreviations

H :

Physical height of the cavity [m]

p :

Pressure [N m−2]

Re :

Reynolds number

u, v :

Velocity components [m s−1]

U, V :

Dimensionless velocity components

U 0 :

Initial velocity components

x, y :

Cartesian coordinates [m]

X, Y :

Dimensionless coordinates

α :

Under-relaxation factor

Г :

Cavity aspect ratio

μ :

Fluid dynamic viscosity [Pa s]

ρ :

Fluid density [kg/m3]

ψ :

Stream-function [m2/s]

Ψ :

Dimensionless stream-function

ω :

Vorticity [s−1]

BR:

Bottom right secondary vortex

BL:

Bottom left secondary vortex

CFL:

Flow courant number

PV:

Primary vortex

SV:

Secondary vortex

1-6:

Hierarchy of vortices’ appearance

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Acknowledgements

Our sincere thanks to the reviewers for the time and consecrated efforts. The authors wish also to acknowledge the helpful technical support of Professor Dellil Ahmed Zineddine from University of Mohamed Ben Ahmed Oran2 (IMSI).

Funding

The authors did not receive support from any organization for the submitted work.

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Authors and Affiliations

  1. Institute of Maintenance and Industrial Safety, University Mohamed Ben Ahmed Oran 2, Oran, Algeria

    El Amin Azzouz

  2. MSMPT Group, MNEPM Laboratory, University of Abdelhamid IbnBadis of Mostaganem, Mostaganem, Algeria

    Samir Houat

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  1. El Amin Azzouz
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  2. Samir Houat
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The authors conducted the numerical investigation which also concern the writing and editing of the paper. Professor Houat Samir gave the final approval for publication.

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Correspondence to El Amin Azzouz.

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Appendix

Appendix

See Tables 7, 8, 9, 10, 11 and 12.

Table 7 Results for U-velocity through the vertical centerline of the cavity
Full size table
Table 8 Results for V-velocity through the horizontal centerline of the cavity
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Table 9 Results for U-velocity through the vertical centerline of the cavity
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Table 10 Results for V-velocity through the horizontal centerline of the cavity
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Table 11 Results for U-velocity through the vertical centerline of the cavity
Full size table
Table 12 Results for V-velocity through the vertical centerline of the cavity
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Azzouz, E.A., Houat, S. Numerical Solutions of Steady Flow in a Three-Sided Lid-Driven Square Cavity. Int. J. Appl. Comput. Math 8, 118 (2022). https://doi.org/10.1007/s40819-022-01314-4

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