Die r�umliche Staupunktstr�mung f�r ein viskoelastisches Fluid

Teipel, I.

doi:10.1007/bf01332126

Cited by 23 publications

(8 citation statements)

References 4 publications

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“…In this micro-bearing lubrication problem for the visco-elastic properties of the oil the presented solutions are described by means of Rivlin-Ericksen constitutive relations with the two pseudo-viscosity constant coefficients and in Pas 2 [2,4]. Here is considered the unsteady liquid flow with full viscoelastic properties for enough large Deborah numbers inside thin boundary layer.…”

Section: Fig 1 the Geometry Of Hdd Microbearing: A) View Of Hdd B)mentioning

confidence: 99%

3d Hydrodynamic Pressure in Gap Height Direction for Cylindrical Bearing Viscoelastic Lubrication

Wierzcholski¹

2013

Journal of KONES. Powertrain and Transport

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In this paper we show the new method of solving the lubrication problem for visco-elastic oils occurring in cylindrical micro-bearing gap. In this method are taking into account all viscoelastic terms without simplifications. In the method presented in this paper for lubricants with non-Newtonian visco-elastic properties are questioning the hitherto prevailing assumptions using in hydrodynamic theory of lubrication such as for example constant value of the hydrodynamic pressure in gap height direction. The objective of the research under the paper topic is an analytical, unified formulation and a new view of general a non-classical solution of hydrodynamic problem of microbearing lubrication using algorithm to determine oil viscoelastic properties of the lubricant and the 3D hydrodynamic pressure distribution taking into account pressure changes in gap height direction.Up to now the complete influences of non-Newtonian visco-elastic oil features on the 3D hydrodynamic pressure distribution in cylindrical microbearing gap were not considered in analytical way. We assume viscous and complete visco-elastic non-Newtonian lubricant directly near the cooperating surfaces. Viscoelastic oil properties are described by means of total form of Rivlin-Ericksen constitutive relations without simplifications.During the solution process the oil velocity components and hydro dynamic pressure are derived. The equation of motion are considered in cylindrical coordinates. Present paper elaborates the analytical method of oil velocity, pressure and friction forces determination for cylindrical slide micro-bearing. In this paper are derived the analytical formulae for velocity components, pressure distributions, in cylindrical micro-bearings.

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Section: Fig 1 the Geometry Of Hdd Microbearing: A) View Of Hdd B)mentioning

confidence: 99%

3d Hydrodynamic Pressure in Gap Height Direction for Cylindrical Bearing Viscoelastic Lubrication

Wierzcholski¹

2013

Journal of KONES. Powertrain and Transport

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“…Indeed this is fundamental in obtaining the proper solutions of the BVP (4) and (5). It was used by both the authors [8,9] separately in getting their solutions started from y = 0. Without this condition, it is easy to see that f"(0) becomes unbounded, implying that the resulting solutions would be in error near q = 0.…”

Section: Equations Of Motionmentioning

confidence: 99%

“…Note that the eigenvalue problem at hand has the same typical feature as that of the original steady stite problem, namely, that the order of the system of differential equations exceeds the number of available boundary conditions. We can, therefore, solve it using the method of either TEIPEL [8] or ARIEL [9]. In the present paper we have chosen the latter approach.…”

Section: Numerical Solution Of Eigenvalue Problemmentioning

confidence: 99%

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On Dual Solutions of Stagnation Point Flow of a Viscoelastic Fluid

Ariel

Teipel

1994

Z Angew Math Mech

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Es wird die laminare zweidimensionale Strömung eines inkompressiblen viskoelastischen Fluids in der Nähe eines Staupunktes betrachtet. Eine Näherungslösung, die die orthogonale Kollokationspunktmethode mit Laguerreschen Polynomen benutzt, wird entwickelt. Sie unterstreicht die Nichtexistenz von Lösungen über den kritischen Wert des viskoelastischen Fluidparameters hinaus und die Existenz dualer Lösungen für den Parameterwert kleiner als dieser kritische Wert. Eine lineare Stabilitätsbetrachtung der zwei Lösungen wird vorgestellt. Die Lösung, die zum kleineren Wert der Schubspannungen gehört, ergibt sich als stabile Lösung, während die andere Lösung sich als instabil erweist.

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“…Numerical work in this area has been rather slow as seen by subsequent work by Davies (1966), Ng (1981) and Serth (1974). The most recent of these can be traced to Teipel (1986), Ariel (1992). Ariel (1993) introduced a numerical algorithm for computing the stagnation point flow of a second grade fluid with/without suction when the fluid is extracted from the plane at a uniform rate.…”

Section: Introductionmentioning

confidence: 99%

A Combined Analytic and Numerical Procedure for Stagnation-Point Flow

Onyejekwe¹

2017

ACM

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Abstract:The two dimensional vector form of the Navier-Stokes equation is reduced to a fourth-order equation for the streamfunction. Boundary conditions arise from considerations of the no-slip constraint at the surface as well the interaction of viscous flow with potential-flow at the edge of the boundary layer. By employing a separation of variables technique and introducing certain dimensionless variables, the stream function equation is converted into its dimensionless analog with appropriate boundary conditions. The resulting quasi-linear third-order ordinary differential equation facilitates the numerical computation of the velocity and the pressure terms. This is achieved by solving the nonlinear two-point boundary-value problem with a time-marching method involving a Crank-Nicolson and Newton-linearization schemes until steady-state solution is obtained. The velocity, stream-function and pressure profiles are discussed with reference to various computation parameters and are found to be in good agreement with the physics of the problem. It was also found that there is no penalty in accuracy for a broad range of CFL numbers. However as the CFL number exceeds a certain threshold, the approach to convergence becomes erratic as indicated by the spurious results produced by the solution residuals.

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Die r�umliche Staupunktstr�mung f�r ein viskoelastisches Fluid

Cited by 23 publications

References 4 publications

3d Hydrodynamic Pressure in Gap Height Direction for Cylindrical Bearing Viscoelastic Lubrication

3d Hydrodynamic Pressure in Gap Height Direction for Cylindrical Bearing Viscoelastic Lubrication

On Dual Solutions of Stagnation Point Flow of a Viscoelastic Fluid

A Combined Analytic and Numerical Procedure for Stagnation-Point Flow

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