Steady viscous flow in a trapezoidal cavity

McQuain, William D.; Ribbens, Calvin J.; Wang, Chang Y.; Watson, Layne T.

doi:10.1016/0045-7930(94)90055-8

Cited by 42 publications

(42 citation statements)

References 13 publications

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“…Ribbens et al (1991) described the flow in an elliptic región with a moving boundary, while Darr & Vanka (1991) have studied two-dimensional flow in a trapezoidal cavity, permitting lid motion of either of the unequal trapezium sides and documenting the respective steady flow patterns in the Reynolds number range Re e [100,1000]. Motivated by the aforementioned prediction of Batchelor (1956), the same trapezoidal lid-driven cavity flow, as well as flow in an equilateral triangular cavity, was solved by McQuain et al (1994) in the range Re e [1, 500], while addressed the equilateral triangular lid-driven cavity flow in the same Reynolds number range. Several lid-driven cavity geometries of complex two-dimensional crosssectional profile may be built by superposition of rectangular domains.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional flow instability in a lid-driven isosceles triangular cavity

et al. 2011

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Linear three-dimensional modal instability of steady laminar two-dimensional states developing in a lid-driven cavity of isósceles triangular cross-section is investigated theoretically and experimentally for the case in which the equal sides form a rectangular córner. An asymmetric steady two-dimensional motion is driven by the steady motion of one of the equal sides. If the side moves away from the rectangular córner, a stationary three-dimensional instability is found. If the motion is directed towards the córner, the instability is oscillatory. The respective critical Reynolds numbers are identified both theoretically and experimentally. The neutral curves pertinent to the two configurations and the properties of the respective leading eigenmodes are documented and analogies to instabilities in rectangular lid-driven cavities are discussed.

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Section: Introductionmentioning

confidence: 99%

Three-dimensional flow instability in a lid-driven isosceles triangular cavity

et al. 2011

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“…Besides, the slopes play a major role in the reduction of the size of the primary eddies (Mcquain et al, 1994). The presense of slopes also result in increase in the wind speed (Figure 2).…”

Section: Slopes and Benchesmentioning

confidence: 99%

Particle Dispersion Within a Deep Open Cast Coal Mine

Chinthala¹,

Khare²

2011

Air Quality-Models and Applications

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“…Using (20), for the two vertical walls, computational boundary conditions for the vorticity are obtained as follows…”

Section: Square Cavitymentioning

confidence: 99%

“…In early numerical studies, e.g. [18,20], finite differences were constructed on a transformed geometry and the flows were considered for Re ≤ 500 only. Later on, solutions for higher Re numbers were achieved by means of, for example, the so-called computational boundary method in which the computational region under consideration is one-grid inside the physical domain [21] and the flow-condition-based interpolation [19].…”

Section: Triangular Cavitymentioning

confidence: 99%

A high‐order upwind control‐volume method based on integrated RBFs for fluid‐flow problems

Mai‐Duy

Tran-Cong

2010

Numerical Methods in Fluids

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1Summary This paper is concerned with the development of a high-order upwind conservative discretisation method for the simulation of flows of a Newtonian fluid in two dimensions. The fluid-flow domain is discretised using a Cartesian grid from which nonoverlapping rectangular control-volumes are formed. Line integrals arising from the integration of the diffusion and convection terms over control volumes are evaluated using the middle-point rule. One-dimensional integrated radial basis function schemes using the multiquadric basis function are employed to represent the variations of the field variables along the grid lines. The convection term is effectively treated using an upwind scheme with the deferred-correction strategy. Several highly-nonlinear test problems governed by the Burgers and the Navier-Stokes equations are simulated, which show that the proposed technique is stable, accurate and converges well.

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Steady viscous flow in a trapezoidal cavity

Cited by 42 publications

References 13 publications

Three-dimensional flow instability in a lid-driven isosceles triangular cavity

Three-dimensional flow instability in a lid-driven isosceles triangular cavity

Particle Dispersion Within a Deep Open Cast Coal Mine

A high‐order upwind control‐volume method based on integrated RBFs for fluid‐flow problems

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