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EN
In the paper the effect of both bearing surfaces and the porosity of one bearing surface on the pressure distribution and load-carrying capacity of a squeeze film bearing is discussed. The equations of motion of a Bingham fluid in a bearing clearance and in a porous layer are presented. Using the Morgan-Cameron approximation and Christensen theory of rough lubrication the modified Reynolds equation is obtained. The analytical solutions of this equation for a squeeze film bearing are presented. As a result one obtains the formulae expressing pressure distribution and load-carrying capacity. A thrust radial bearing is considered as a numerical example.
PL
Rozpatrywano przepływ płynu opisanego równaniem Herschela-Bulkleya, reprezentującego własności reologiczne stopionej czekolady, w szczelinie między płaskim dnem aparatu a toczącym się po nim walcem. Wyprowadzono równania opisujące rozkład prędkości, naprężenia stycznego i gradientu ciśnienia w szczelinie oraz zapotrzebowanie mocy. Zaproponowano algorytm obliczeń powyższych wielkości.
EN
Flow of visco-plastic fluid described by the Herschel-Bulkley equation, representing rheological properties of molten chocolate, in a gap between the apparatus flat bottom and the cylinder rolling on it was considered. Equations describing velocity, shear stress, pressure gradient distribution and power consumption were derived. The algorithm for calculation of above mentioned properties was proposed.
3
Content available remote Separacja pęcherzy gazowych z substancji plastycznolepkich za pomocą wirówki
PL
Dokonano analizy zachowania pęcherza gazowego w płynie plastycz-nolepkim podczas odwirowania w wirówce oraz warunków niezbędnych, aby pęcherz mógł się poruszać i mógł zostać usunięty z płynu. Przedstawiono metodę obliczenia parametrów procesu separacji - rozmiaru najmniejszych pęcherzy możliwych do usunięcia w danych warunkach lub minimalnej szybkości obrotowej potrzebnej do usunięcia pęcherza o danych rozmiarach.
EN
The analysis of gas bubble behaviour in viscoplastic fluid during its centrifugation in the centrifuge and conditions necessary for a bubble to move inside and be removed from fluid was performed. A method for the calculation of separation process parameters, i.e. a minimal size of bubbles possible to be removed in given conditions or the minimal rotational frequency necessary for the removal of a bubble of certain sizes is presented.
EN
Flow of molten polymer in conical channels is considered in the paper. To describe the problem a model of viscoplastic fluid is used but the final results are illustrated by Bingham fluid flow. The dimensionless formulae for pressure distributions in conical annular channels with inertia effects are presented.
EN
Flow of molten polymer in conical channels is considered in the paper. To describe the problem a model of viscoplastic fluid is used and the results obtained are illustrated by Ostwald - de Waele fluid flow. The dimensionless formulae for pressure distributions in conical annular channels with inertia effects are presented.
EN
Technologies applied in polymers processing are permanently improved due to updating the knowledge on material proprieties, processes and phenomena during the processing. To determine the pressure distribution, one should define the geometrical shape of a channel, in the flow will be held the flow. The aim of calculations carried out is to determine the possibility of mathematical modelling of polymer flows between conical parallel surfaces. In this work, the flow of a polymer in conical channels was considered. To describe a melted polymer the model of a viscoplastic fluid was used but final results were illustrated by a flow of the Bingham fluid. The Bingham fluid chosen to modelling the flow of a polymer may by considered as legitimate, because its use will allow us to illustrate analytical methods of calculations. For the flow configuration and model under consideration the geometrical sizes of the channel and material coefficients of the fluid will be chosen on the basis of experimental data contained in literature. In the article, the on defining dimensionless pressure distribution for the flow in a conical channel as well as in a conical annular channel with the influence of inertia were presented. The results of calculations were introduced in tabular forms as well as in graphic forms.
EN
Technologies applied in polymer processing require permanent improvement by better recognition of material properties of polymer, mechanisms of process and physical phenomena arising in processing. In the work a polymer flow in an annular die modelled as narrow clearance between two fixed surfaces of revolution is considered. The problem is described by boundary layer equations. Using the method of averaged inertia one obtains the formulae expressing the pressure distribution. Generally, the flow of polymer given by the nonlinear model of Shulman is considered. The molten polymer modelled by a Herschel-Bulkley model flowing through an annular spherical channel is discussed in detail.
EN
Theoretical analysis was conducted of the hydrodynamic characteristics of the two-dimensional flow of electrorheological fluid between parallel plates by using the mechanical dynamic model proposed herein. The model includes the Voigt model and a slider. It can present four types of relations between shear stress and shear rate. The theoretical results were compared with the experimental data. The theoretical analysis explains the experimental results qualitatively. The qualitative tendency is the same for the four types of relations between shear rate and shear stress. Based on the theoretical results, velocity distribution of flow in four types of relations is not influenced by shear stress and shear rate. This finding differs from that for rotational flow around a rotating disk. The pressure difference depends on apparent viscosity. The local Reynolds number depends on the local velocity at a low given flow velocity and on the local kinematic viscosity at a high given flow velocity.
EN
An equation of Rabinowitsch-Mooney type together with the corresponding relations for consistency variables has been adopted for an approximate calculation of pressure drop in flow of viscoplastic fluids through straight ducts. The suitability of the suggested procedure of calculation of pressure drop is demonstrated by the comparison of calculation results with the published analytical solution of flow of Robertson-Stiff fluid through an annulus and with numerical solution of flow of Bingham fluid through ducts of rectangular cross section.
EN
The influence of inertia effect on the pressure distribution in a curvilinear thrust bearing with a viscoplastic squeeze film is considered. To solve this problem the boundary layer equations are used. The method of integral approaches is applied and the formulae expressing the pressure distribution are obtained. This distribution for Ostwald - de Waele, Bingham and Herschel - Bulkley fluids in the clearance between two disks is discussed in detail. It is found that the pressure increases with an increase of inertia effects and decreases with a decrease of the flow behaviour index N.
EN
The aim of this contribution is to present an additive method enabling a direct determination of axial flowrate for viscous (of power-law model) and viscoplastic (of Robertson-Stiff model) fluids in concentric annuli. This is based on addition of axial flowrates through individual partial concentric annuli forming the actual concentric annulus. The resulting relations for axial flowrate is possible to express in analytical forms without necessity of otherwise complicated derivations. The only numerical calculation consists in a determination of location of a zero shear stress for the original whole concentric annulus.
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