Theoretical Analysis of the Incompressible Laminar Flow in a Macro-Roughness Cell

Arghir, Mihaï; Roucou, Nicolas; Helene, Mathieu; Frêne, Jean

doi:10.1115/1.1506328

Cited by 137 publications

(100 citation statements)

References 11 publications

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“…According to the no-slip conditions (7), (8), the variations δu and δv of the velocity field have to vanish at the boundary. For the pressure p, however, allowing for free variation at the boundary leads, according to Anthony [27], to the additional Neumann-type boundary…”

Section: Semi-analytical Approach (Stokes Flow)mentioning

confidence: 99%

“…Hence, the kinematic boundary conditions along the upper and the lower plates, which are the normal components of (7,8), feature automatically in the variational formulation, whereas the respective tangential components at these two boundaries have to be prescribed explicitly and depend on the choice of test functions.…”

Section: Semi-analytical Approach (Stokes Flow)mentioning

confidence: 99%

“…The presence of eddies is of both practical and scientific interest since the onset of recirculating flow can enhance load carrying capacity significantly and reduce frictional drag in, for example, lubricated contacts [8,9], as well as affecting wear characteristics by trapping loose, sub-micron particles [6]. Related examples of where exploration of the effects of local flow structure within laminar shear flow has proved extremely informative include the role played by eddies in industrial roll coaters [10,11,12], eddy formation and the effect of localised disturbances on stagnation lines [13,14], and eddy motions and flow patterns [15,16,17].…”

Section: Introductionmentioning

confidence: 99%

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Eddy genesis and manipulation in plane laminar shear flow

et al. 2009

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Eddy formation and presence in a plane laminar shear flow configuration consisting of two infinitely long plates orientated parallel to each other is investigated theoretically. The upper plate, which is planar, drives the flow; the lower one has a sinusoidal profile and is fixed. The governing equations are solved via a full finite element formulation for the general case and semi-analytically at the Stokes flow limit. The effects of varying geometry (involving changes in the mean plate separation or the amplitude and wavelength of the lower plate) and inertia are explored separately. For Stokes flow and varying geometry, excellent agreement between the two methods of solution is found. Of particular interest with regard to the flow structure is the importance of the clearance that exists between the upper plate and the tops of the corrugations forming the lower one. When the clearance is large, an eddy is only present at sufficiently large amplitudes or small wavelengths. 1However, as the plate clearance is reduced, a critical value is found which triggers the formation of an eddy in an otherwise fully attached flow for any finite amplitude and arbitrarily large wavelength. This is a precursor to the primary eddy to be expected in the lid-driven cavity flow which is formed in the limit of zero clearance between the plates.The influence of the flow driving mechanism is assessed by comparison with corresponding solutions for the case of gravity-driven fluid films flowing over an undulating substrate.When inertia is present, the flow generally becomes asymmetrical. However, it is found that for large mean plate separations the flow local to the lower plate becomes effectively decoupled from the inertia dominated overlying flow if the wavelength of the lower plate is sufficiently small. In such cases the local flow retains its symmetry. A local Reynolds number based on the wavelength is shown to be useful in characterising these large-gap flows. As the mean plate separation is reduced, the form of the asymmetry caused by inertia changes, and becomes strongly dependent on the plate separation. For lower plate wavelengths which do not exhibit a kinematically induced secondary eddy, an inertially induced secondary eddy can be created if the mean plate separation is sufficiently small and the global Reynolds number sufficiently large.

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Section: Semi-analytical Approach (Stokes Flow)mentioning

confidence: 99%

Section: Semi-analytical Approach (Stokes Flow)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Eddy genesis and manipulation in plane laminar shear flow

et al. 2009

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“…Studies which compare solutions to Reynolds, Stokes and Navier-Stokes equations for textured surfaces have been conducted by a number of researchers [10][11][12][13][14][15]. For more details see Gao and Hewson [16].…”

Section: Introductionmentioning

confidence: 99%

Two-scale EHL: Three-dimensional topography in tilted-pad bearings

Boer

Hewson

Thompson

et al. 2014

Tribology International

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Derived from the Heterogeneous Multiscale Methods (HMM), a two-scale method is developed for the analysis of Elastohydrodynamic Lubrication (EHL) and micro-EHL in tilted-pad bearings with threedimensional topography. A relationship linking the pressure gradient to mass flow rate is derived and represented in the bearing domain through homogenisation of near-periodic simulations describing the Fluid Structure Interaction (FSI) of topographical features. For the parameters investigated the influence of compressibility and piezoviscosity was found to be more significant than that of non-Newtonian (shear-thinning) behaviour on textured bearing performance. As the size of topography increased twoscale solutions demonstrated that at constant load the coefficient of friction increased and the minimum film thickness decreased over a range of pad lengths and tilt angles.

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“…The main objective of this paper is to develop less complicated as well as more effective labyrinth seal configurations. Earlier works illustrate the need for creating stronger vortex velocities (Asok et al, 2007;Villasmil, Chen and Childs, 2005) and stable mean flow recirculation zone within each cavity (Arghir, Roucou and Frene, 2002) for achieving higher pressure drops. Since a triangular geometry could favorably fulfill these requirements, the present paper focuses on labyrinth seals having triangular cavities machined in a circular fashion (circular-grooved) as seen in Fig.…”

Section: Introductionmentioning

confidence: 99%

Pressure Drop Characteristics of Water Flow Through Static Annular and Triangular Cavity Labyrinth Seals

Asok¹,

Sankaranarayanasamy

Sundararajan

et al. 2008

Engineering Applications of Computational Fluid Mechanics

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Non-contacting static seals are intended to provide high pressure drop at different leakage flow rates for better sealing. In special applications such as cryogenic engines and nuclear reactors which have high sealing requirements, conventional annular seals and circular-grooved square cavity labyrinth seals often do not meet the demand. This paper investigates newer configurations like circular-grooved triangular cavity labyrinth seals and sinusoidal-grooved triangular cavity labyrinth seals which can provide improved sealing than conventional seals. For these seals, pressure drop data over a wide range of water flow rates has been obtained using computational simulations and experiments. The pressure drops for the triangular seals are observed to be marginally more than those for square labyrinth seals and markedly higher than those for annular seals. The numerical results are also in good agreement with experimental and available analytical results. In order to highlight the effects of cavity shape and seal configuration, optimisation of a circular-grooved triangular labyrinth seal has been carried out using Artificial Neural Network (ANN), in association with a semi-theoretical model. The pressure drop for the identified optimal triangular labyrinth seal is 16% higher than that of the optimal square labyrinth seal. Among the seals tested, the sinusoidal-grooved triangular labyrinth seal exhibits the highest pressure drop, exceeding that of the optimal circular-grooved triangular labyrinth seal by 57%, at the rated flow rate.

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Theoretical Analysis of the Incompressible Laminar Flow in a Macro-Roughness Cell

Cited by 137 publications

References 11 publications

Eddy genesis and manipulation in plane laminar shear flow

Eddy genesis and manipulation in plane laminar shear flow

Two-scale EHL: Three-dimensional topography in tilted-pad bearings

Pressure Drop Characteristics of Water Flow Through Static Annular and Triangular Cavity Labyrinth Seals

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