Flow instability in triangular lid-driven cavities with wall motion away from a rectangular corner

Manzoor, Ahmed; Kuhlmann, Hendrik C.

doi:10.1088/0169-5983/44/2/025501

Cited by 13 publications

(8 citation statements)

References 33 publications

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“…Gonzalez et al. (2011) and Ahmed & Kuhlmann (2012) have shown both experimentally and numerically that, as for LDSC flow, the first instability in lid-driven right-angled triangular cavities of various length-to-depth aspect ratios with the moving wall adjacent to the rectangular corner is also three-dimensional. For an aspect ratio such that the cavity is an isosceles triangle with the lid moving towards the rectangular corner, the leading mode is complex (oscillatory) and becomes unstable at ( according to experiments) with spanwise wavenumber ( ) and angular frequency ( ), values that are fully consistent with those of a rectangular cavity of aspect ratio 0.5, for which (Albensoeder et al.…”

Section: Introductionmentioning

confidence: 99%

The lid-driven right-angled isosceles triangular cavity flow

Bergadà

Mellibovsky

2019

J. Fluid Mech.

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We employ lattice Boltzmann simulation to numerically investigate the two-dimensional incompressible flow inside a right-angled isosceles triangular enclosure driven by the tangential motion of its hypotenuse. While the base flow, directly evolved from creeping flow at vanishing Reynolds number, remains stationary and stable for flow regimes beyond $Re\gtrsim 13\,400$, chaotic motion is nevertheless observed from as low as $Re\simeq 10\,600$. Chaotic dynamics is shown to arise from the destabilisation, following a variant of the classic Ruelle–Takens route, of a secondary solution branch that emerges at a relatively low $Re\simeq 4908$ and appears to bear no connection to the base state. We analyse the bifurcation sequence that takes the flow from steady to periodic and then quasi-periodic and show that the invariant torus is finally destroyed in a period-doubling cascade of a phase-locked limit cycle. As a result, a strange attractor arises that induces chaotic dynamics.

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Section: Introductionmentioning

confidence: 99%

The lid-driven right-angled isosceles triangular cavity flow

Bergadà

Mellibovsky

2019

J. Fluid Mech.

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“…Numerous extended cases are applicable to the lid-driven cavity flow. One case concerns the number of moving cavity walls, another case regards shape variation of the cavity, such as a trapezoidal cavity, 16 triangular cavity, 17,18 semi-circular cavity, 19 and cavities with different aspect ratios. 10,20,21 In addition, many investigators have conducted research to find out the effect of Mixed convection flow inside the cavity, like when it is filled with a porous medium and it is reported by Khanafer and Chamkha 22 also when it is inclined and filled with a nanofluid and it is shown by Abu-Nada and Chamkha.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of three‐sided lid‐driven square cavity

Kamel

Haraz

Hanna

2020

Engineering Reports

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In this article, an incompressible, two-dimensional (2D), time-dependent Newtonian fluid flow in a square cavity is simulated using finite difference method and alternating direction implicit technique. Navier-Stokes equations are solved numerically in stream function-vorticity formulation. In order to verify the numerical solver, the one-sided lid-driven cavity is studied and the results are compared with relevant data in the literature. They were in a very good agreement. Furthermore, two distinguished unexplored cases of the three-sided lid-driven cavity have been investigated. In case (1), the upper and lower walls are translated to the right, while the left wall is translated upward and the right wall remains stationary. Moreover, in case (2), the upper wall is translated to the right but the lower wall is translated to the left, while the left wall is translated downward and the right wall remains stationary. However, stream function and vorticity values in addition to the location of primary and secondary vortices' centers inside the square cavity have been revealed at low and intermediate Reynolds numbers (Re), typically (Re = 100 to 2000). Moreover, the higher the Re, the more main primary vortex approaches the cavity center and the bigger the secondary vortices. K E Y W O R D Sfinite difference method, incompressible flow, lid-driven cavity, Navier-Stokes equations, stream function-vorticity formulation 1 This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

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“…Several numerical methods are examined by studying the 2D and 3D lid-driven cavity with different shapes and aspect ratios at low and very high Reynolds number (Re). The following articles are used by a plethora of researchers to verify their results (Ghia et al [1], Gupta and Kalita [2], Ghadimi et al [3], Zhang et al [4], Ahmed and Kuhlmann [5], Abu-Nada and Chamkha [6], Botella and Peyret [7], Pinarbasi et al [8], Wahba [9], and Kuhlmann and Romanò [10]). However, Romanò and Kuhlmann [11] studied the motion of suspended solid particles in a fluid for an extensive range of geometry and flow factors for many well-known problems using the smoothed-profile technique that was combined with high-order spatial discretization.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of channel flow over a skewed equilateral cavity

Kamel¹,

Haraz²,

Hanna³

2020

J. Appl. Math. Comput. Mech.

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In this paper, an incompressible, two-dimensional (2D), time-dependent, Newtonian, laminar, and internal channel fluid flow over a skewed equilateral cavity is simulated using the finite difference method (FDM) and alternating direction implicit (ADI) technique. Navier-Stokes equations are solved numerically in stream function-vorticity formulation. The goal of tackling this problem depends on its academic significance by studying the difference between lid-driven and shear-driven cavity flows in terms of the formation of Moffatt eddies at the sharp corner, also to obtain the length and intensity ratios of these counter-rotating vortices. The value of velocity components along the centerlines of the skewed cavity was revealed at low and intermediate Reynolds numbers (Re), typically (Re = 200 and 2000) at two different skew angles of mainly 30° and 45°. Likewise, the blocked-off regions' method is used to deal with the geometry of the skewed cavity especially the sharp corners. Furthermore, as Re increases, the main vortex approaches the skewed cavity center and the counter-rotating vortices get bigger in size and intensity, and their number increases.

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Flow instability in triangular lid-driven cavities with wall motion away from a rectangular corner

Cited by 13 publications

References 33 publications

The lid-driven right-angled isosceles triangular cavity flow

The lid-driven right-angled isosceles triangular cavity flow

Numerical simulation of three‐sided lid‐driven square cavity

Numerical simulation of channel flow over a skewed equilateral cavity

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