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EN
Elliptical bearing is characterized by low induced temperature and high stability at higher speed in comparison with the cylindrical journal bearing. The performance of such bearings can be affected by the type of oil used and its surface properties. The main goal of this work is to study the surface micro protrusion effect on the steady state operation of elliptical journal bearing lubricated with couple stress lubricant. The modified Reynolds’ equation to take into account the effects of couple stress lubricant and micro protrusions of the bearing surfaces is solved using finite difference method. The governing equations were solved using a prepared FORTRAN computer program. Pressure distribution, load carrying capacity and coefficient of friction have been studied for a bearing in laminar flow regime. The mathematical model was validated by comparing pressure results for the elliptical bearing of the present work with that obtained by Hussain et al.(1996). The obtained results demonstrate that the lubricant pressure and the load carried by the bearing decrease for the bearing with higher ellipticity factor while the load carried by the bearing increases for the bearing with higher protrusions or when using a couple stress fluid with higher couple stress variable.
EN
In this paper, the characteristics of the flow and forced heat transfer of power law non-Newtonian fluids that flow around a quadrilateral and rectangular cylinder that are located in a 2D channel are investigated by use of the finite volume method (FVM) in a steady state flow regime. To this accomplishment, in the constant temperature, the effects of a different obstruction ratio, aspect ratio and Reynolds number are investigated. The Reynolds number in the range 5 ≤ Re ≤ 40, the power index in the range 0.5 ≤ n ≤ 1.4, the aspect ratio in the range 0.5 ≤ a ≤ 2, and the obstruction ratio in the range 0.125 ≤ b ≤ 0.5 were selected. By surveying the drag coefficient profiles, it’s concluded that as the obstruction ratio increases, the drag coefficient is increased, while an increase in the Reynolds number causes the lower drag coefficient. In addition, the drag coefficient is strongly increased by aspect ratio enhancements.
3
PL
Przedstawiono wyniki badań eksperymentalnych nad przepływem wodnych roztworów polimerów oraz rozcieńczonych emulsji przez złoża porowate i siatkę o rozmiarze oczek 0,2 mm zamocowaną w aparacie typu SEM. Zaobserwowany gwałtowny wzrost strat ciśnienia podczas przepływu wodnych roztworów poli(tlenku etylenu) powiązano z ich dużą lepkością wzdłużną. Podczas przepływu emulsji przez złoże cząstek kulistych oraz siatki dochodzi do ich homogenizacji.
EN
A rapid increase in pressure loss was obsd. during the flow of polyethylene oxide solns. through the bed of spherical particles. Similarity was found between the course of the extensional viscosity curve obtained with the opposed nozzle devices, and the curve of effective viscosity detd. from the pressure drop during the flow through the porous bed. During the flow of dild. emulsions through the bed of glass microspheres with the size 100–150 μm, the droplets with diams. higher than 30 μm disappeared. A more than two-fold decreases in Sauter diam. and De Brouckere diam. were obsd. as well as a two-fold decrease in the polydispersity index. Usability of the sieve emulsification mixer for prepn. of oil/water emulsions was demonstrated.
EN
Customized patient drug delivery overcomes classic medicine setbacks such as side effects, improper drug absorption or slow action. Nanorobots can be successfully used for targeted patient-specific drug administration, but they must be reliable in the entire circulatory system environment. This paper analyzes the possibility of fractional order control applied to the nanomedicine field. The parameters of a fractional order proportional integral controller are determined with the purpose of controlling the velocity of the nanorobot in non-Newtonian fluids envisioning the blood flow in the circulatory system.
EN
The article describes the problem of mixing process analysis of non-Newtonian fluids supported by CFD numerical simulation. To introduce the analysis method of the mixing process a series of numerical experiments was carried out exemplified by vessel equipped with two types of agitator with rotary coil. There was shown velocity magnitude distribution in two perpendicular cutting planes and velocity profiles for both constructional agitator solutions. Moreover, it was provided comparative analysis, which showed impact of viscosity and rotation velocity of agitator on nature of the mixing process.
PL
W artykule przedstawiono problematykę analizy procesu mieszania cieczy nienewtonowskich z wykorzystaniem symulacji numerycznej CFD. Celem prezentacji sposobu analizy zjawisk towarzyszących mieszaniu przeprowadzono serię eksperymentów numerycznych na przykładzie zbiornika wyposażonego w dwa warianty mieszadła wężownicowego. Przedstawiono mapy prędkości chwilowych mieszanej cieczy w wybranych płaszczyznach oraz profile prędkości dla obu rozwiązań konstrukcyjnych mieszadeł. Ponadto, dokonano analizy porównawczej obrazującej wpływ lepkości cieczy oraz prędkości obrotowej zespołu mieszającego na charakter procesu mieszania.
PL
W pracy przedstawiono stanowisko badawcze, za pomocą którego może być realizowany cykl badań operacji mieszania nieniutonowskich płynów spożywczych. Stanowisko wyposażone jest w aparaturę pomiarową w postaci obrotomierza i czujnika momentu obrotowego oraz w oprogramowanie umożliwiające rejestrację i przetwarzanie danych. Uzyskane parametry operacji mieszania oraz parametry reologiczne posłużą do budowy modeli mieszania strukturalnych płynów spożywczych z uwzględnieniem zmian ich charakterystyk reologicznych w czasie.
EN
The paper presents a research stand for studies of mixing of non-Newtonian food fluids. The stand is equipped with a tachometer and torque sensor and software enable recording and processing the measurements’ data. The resulting parameters of the mixing process and the rheological parameters can be used to develop models for the mixing of non-Newtonian fluids, including their changes in rheological characteristics in time.
EN
A similarity analysis of non-Newtonian fluid flow past an accelerated vertical infinite plate in the presence of free convection current is carried out. A group theoretic generalized dimensional analysis is employed to achieve the governing non-linear ordinary differential equations in the most general form. Numerical solutions of these equations are given with the plot of their velocity profiles with the effects of Pr-Prandtl number and Gr-Grashof number.
PL
Do analizy hydrodynamicznego smarowania łożysk ślizgowych olejami nienewtonowskimi o właściwościach lepkosprężystych często stosuje się równanie konstytutywne typu Rivlina-Ericksena. Podczas analizy oleju o modelu Rivlina-Ericksena niezbędna jest znajomość współczynnika lepkości η oraz współczynników pseudolepkości α, β, γ. W niniejszej pracy przedstawiono wyniki badań współczynnika lepkości dynamicznej i współczynników pseudolepkości dla kilku olejów silnikowych. Współczynniki pseudolepkości oszacowano metodą prezentowaną przez prof. K. Wierzcholskiego w publikacjach naukowych. Metoda ta polega na wyznaczeniu eksperymentalnym krzywych lepkości w szerokim zakresie prędkości ścinania. Kolejnym etapem jest opisanie tych krzywych formułą matematyczną i obliczenie pomocniczych współczynników. Ostatnim etapem jest wyznaczenie współczynników pseudolepkości z wykorzystaniem formuł podanych w literaturze przy znajomości wcześniej wyznaczonych współczynników i lepkości dynamicznej dla bardzo małych i bardzo dużych prędkości deformacji.
EN
During the operation of the internal combustion engines, lubricating oils wear out. The following has a significant impact on that process wear of engine parts and contact of wearing elements with working oil, the destruction of bonds in the polymer chains of oil and oil additives, contaminants from the environment, and combustion products. This causes the lubricant to become a non-Newtonian viscoelastic fluid. A Rivlin-Ericksen constitutive relation can by used in the analysis of slide bearings hydrodynamic lubrication by non-Newtonian viscoelastic oils. In a specific case that relation becomes a Newtonian model. The analysis makes it necessary to know the values of the viscosity coefficient η and also the values of pseudo-viscosity coefficients α, β, γ. The obtained values of viscosity and pseudo-viscosity coefficients will be used in further studies and analytical and numerical calculations of slide bearings hydrodynamic lubrication by non-Newtonian viscoelastic oils. Determining the viscosity and pseudo-viscosity coefficients is based on a method suggested by Prof. K. Wierzcholski and involves measuring a viscosity values in wide range of shear rates. The next step in that method is to describe the obtained curves by a mathematical formulae and calculate some required parameters. Finally, taking into account measured values of viscosity for low and high shear rates, pseudo-viscosity coefficients can be calculated.
9
Content available remote Generalised Herschel model applied to blood flow modelling
EN
This paper introduces a new rheological model of blood as a certain generalization of the standard Herschel-Bulkley model (Herschel W H and Bulkley R 1926 Kolloid-Zeitschnft 39 (4) 291). This model is a rheological constitutive equation and belongs to the group of the so-called generalised Newtonian fluids. Experimental data (Yeleswarapu K K et al. 1998 Mech. Res. Comm. 25 (3) 257) is compared with the results obtained from the new model, to demonstrate that it allows obtaining the best agreement together with the Luo-Kuang model (Luo X and Kuang Z B 1992 J. Biomechanics 25 (8) 929; Easthope P L and Brooks D E 1980 Biorheology 17 235). The new model may be easily implemented into commercial CFD codes, which is not that obvious for more complicated models such as differential, integral and rate type fluids (Astarita G and Marrucci G 1974 Principles of non-Newtonian Fluid Mechanics London, McGraw-Hill; Tesch K 2012 Selected Topics of Blood Flows and Microclimate Modelling in Protective Suits Gdansk. Gdansk University of Technology Press). What is more, it allows modelling of such phenomena as shear thinning, yield stress and constant viscosity values at high shear rates.
EN
The problem of a steady two-dimensional flow of a conducting power-law fluid past a flat plate in the presence of a transverse magnetic field under the influence of a pressure gradient by considering viscous dissipation effects is studied. The resulting governing partial differential equations are transformed into a set of non linear ordinary differential equations using appropriate transformation. The set of non linear ordinary differential equations is first linearized by using the Quasi-linearization technique and then solved numerically by using an implicit finite difference scheme. The system of algebraic equations is solved by using the Gauss-Seidal iterative method. The energy equation for a special case for which a similarity solution exist is also considered. The effects of the power-law index, magnetic parameter, viscous dissipation and generalized Prandtl number on the velocity and temperature profiles are of special interest. Numerical results are tabulated for the skin friction co-efficient. Velocity and temperature profiles are drawn for different controlling parameters which reveal the tendency of the solution.
EN
Various silica suspensions were synthesized. Presented studies revealed that the silica fumed dispersed in ethylene glycol does not demonstrate shear thickening properties; it is rather a shear thinning liquid. In the case of the biogenic amorphous silica (BAS) dispersed in dipropylene glycol (DPG) the effect is discontinuous while the silica LUDOX suspended in ethylene glycol (EG) indicate continuous viscosity value under critical shear rate. However, the BAS silica demonstrates 100 times higher viscosity values (26000 mPas) than those presented by the LUDOX suspended in EG(260 mPas), but the maximum properties appear at the 5 times smaller shear rate. The shear thickening fluids are developed in the light of their application in smart body armour.
PL
Przeprowadzono syntezę zawiesin na bazie krzemionek. Prezentowane badania wykazały, że krzemionka zdyspergowana w glikolu etylenowym wykazuje właściwości rozrzedzania ścinaniem (rys. 2). W przypadku krzemionki BAS zdyspergowanej w DPG uzyskano efekt zagęszczania ścinaniem, nie jest on jednak ciągły (rys. 3). Natomiast krzemionka LUDOX zawieszona w EG wykazuje ciągły wzrost lepkości po przekroczeniu krytycznej szybkości ścinania, jednak wartość lepkości jest 100 razy mniejsza (260 mPas), niż ta uzyskana w przypadku krzemionki BAS zawieszonej w DPG (26000 mPas) (rys. 4). Krzemionka LUDOX zdyspergowana w EG wykazuje maksymalne właściwości przy 5 razy większych szybkościach ścinania, niż krzemionka BAS zdyspergowana w DPG. Ciecze zagęszczane ścinaniem są opracowywane z myślą o zastosowaniu ich przy budowie inteligentnych pancerzy pasywnych.
EN
This note is devoted to a mathematical study of a phenomenon of dead core which appears in a magnetohydrodynamic Couette flow. For this purpose, let us start by giving some considerations on the notion of Newtonian fluids.
EN
The present analysis investigates the non-Darcian free convection of a non-Newtonian fluid from a vertical sinusoidal wavy plate embedded in a homogenous porous medium with constant wall temperature. After a suitable coordinate transformation to reduce the complexity of the goveming boundary-layer equations, the resulting nonlinear, coupled differential equations were solved with the Runge-Kutta integration scheme. The Darcy-Rayleigh number is considered to be very large. The power-law model is used for non-Newtonian fluids with exponent n < 1 for pseudoplastic fluids; n= 1 for Newtonian fluids and n > 1 for dilatant fluids. The effects of the Grashof number Gr * , the wavy geometry, and the non-Newtonian nature of the fluids on the local and global rates of heat transfer are discussed. An increase in the power-law index leads to a greater fluctuation of the local Nusselt number and increasses the global rate of heat transfer. An increase in the Grashof num ber leads to a smaller fluctuation of the local heat transfer and increasing the boundary layer thickness, hence decreasing the global rate ofheat transfer.
PL
W artykule przedstawiono: - opis zjawisk reologicznych, - modele matematyczne krzywej płynięcia.
EN
In article there is description: - phenomenon of rheology, - mathematical models of flow curve.
15
Content available remote Non-Newtonian squeeze films with slip boundary conditions
EN
The paper describes the squeeze film of the non-Newtonian fluids between two circular plates with slip boundary conditions, having as final result the pressure distribution and the load capacity.
PL
W artykule opisano wyciskaną warstwę cieczy nie-Newtonowskiej pomiędzy dwoma kolistymi dyskami, z uwzględnieniem warunków brzegowych ujmujących poślizg. Efektem rozważań jest opis rozkładu ciśnienia oraz nośności.
16
Content available remote Analysis of tilting pads thrust bearings behavior lubricated by power law fluid
EN
The numerical modeling of non-Newtonian lubricant flows in titling pads thrust bearing is developed to predict some interesting factors in industrial view point. It means parameters such as load, friction and power loss whose evaluation contributes strongly to improve the design and performances of the titling pads thrust bearing. The non-Newtonian rheological model chosen is the power law because of its large domain of use. The dynamic field is described through the resolution of the generalized Reynolds equation and the thermal effects, due to the lubricant shearing, is taken into account through a global thermal balance. The discretisation of equations is made by the finite differences scheme.
EN
An approach to the calculation of drag and fall or rise velocity of a solid and Newtonian fluid spheres in viscoplastic fluids and to the calculation of pressure drop in viscoplastic fluid flow through random fixed beds of particles is suggested. It is based on the application of the modified Rabinowitsch-Mooney equations together with corresponding relations for consistency variables and on the application of the relationship of Hadamard-Rybczynski valid for both the fluid and solid spheres. The solution is concretized for Bingham, Casson and Robertson-Stiff flow models, and in the case of fixed beds also for Herschel-Bulkley flow model.
PL
W pracy przedstawiono wyniki weryfikacji doświadczalnej oryginalnej metody wielokrotnej transformacji, opisującej laminarny i turbulentny przepływ reostabilnych cieczy nienewtonowskich w prostoosiowych i zakrzywionych przewodach o przekroju eliptycznym. Przepływ roztworów polimerowych w prostoosiowych przewodach o przekroju eliptycznym można uogólnić na przepływ pseudonewtonowski, w którym liczby kryterialne cf i De stanowią newtonowskie analogony tych liczb dla rzeczywistego przepływu cieczy nienewtonowskiej. Metodę można następnie uogólnić na przepływ cieczy nienewtonowskich w przewodach zakrzywionych o przekroju eliptycznym.
EN
In the paper an experimental verification of the original, multi-stage transformation method describing laminar and turbulent flow of purely viscous, non-Newtonian fluids in straight and curved pipes of elliptic cross-section has been shown. The flow of polymer solutions in straight pipes of elliptic cross-section can be generalised on the pseudo-Newtonian flow where the dimensionless numbers cf and De are analogues to those describing real Newtonian fluid flow. The method can be generalised on the non-Newtonian flow in curved pipes of elliptic cross-section.
EN
The problem of mixed convection in power-law type non-Newtonian fluids along a non-isothermal vertical plate with surface mass transfer is investigated. The transformed conservation laws are solved numerically for the case of variable wall temperature conditions. Numerical results are presented for the details of the velocity and temperature fields. A discussion is provided for the effect of suction and injection as well as the viscosity index on the surface heat transfer rate.
EN
Nonsimilarity solutions for mixed convection in power-law type non-Newtonian fluids from a vertical flat plate embedded in a porous medium are reported for a variable wall temperature of the power law form. The governing equations, including internal heat generation, are first transformed into a dimensionless form by the nonsimilar transformation and then solved by a finite-difference scheme. Numerical results are presented for the fluid velocity and temperature fields.
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