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1

A Mean-Line Flow Model of Viscous Liquids in a Vortex Pump

Li Wenguang

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2022

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Vol. 26, No 2

1--18

EN

The axial, radial and tangential velocity profiles of six fluids were extracted from computational fluid dynamics simulation results at points in a pump chamber 1 mm distant from the blades in a vortex pump at the specific speed of 76. The critical radius was specified in the axial velocity radial profiles to determine the impeller inlet and outlet at six viscosities and part-load, design, and over-load points. A mean-line flow model and hydraulic loss model were built from the profiles. The incidence, incidence loss in the inlet, deviation angle, and slip factor in the outlet were calculated. The impeller theoretical head, pump hydraulic efficiency and volumetric efficiency were analyzed. It was shown that the axial, radial and tangential velocity profiles relate closely to the flow rate as usual, but also the viscosity, especially at low flow rates and in the inlet. The low flow rate and viscosity lead to near zero axial and radial velocities, a faster tangential velocity than the blade speed, negative incidence, and a small incidence loss coefficient in the inlet. The dimensionless critical radius ranged within 0.77–0.89 and reduces with the increasing flow rate and viscosity. The mean slip factor is between 0.11 and 0.20 and rises with the increasing flow rate and viscosity. The mean incidence loss coefficient is within 0.0020–0.15 and augments with the increasing flow rate but increases with the decreasing viscosity under part-load conditions. The theoretical head estimated by using the fluid tangential velocity between the outlet of the impeller and the inlet of the chamber is more reasonable.

2

Slip flow of a sphere in non-concentric spherical hypothetical cell

Krishna-Prasad Madasu

Journal of Applied Mathematics and Computational Mechanics

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2020

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Vol. 19, nr 3

59--70

EN

Slow axisymmetric flow of an incompressible viscous fluid caused by a slip sphere within a non-concentric spherical cell surface is investigated. The uniform velocity (Cunningham’s model) and tangential velocity reaches minimum along a radial direction are imposed conditions at the cell surface (Kvashnin’s model). The general solution of the problem is combined using superposition of the fundamental solution in the two spherical coordinate systems based on the centers of the slip sphere and spherical cell surface. Numerical results for the correction factor on the inner sphere are obtained with good convergence for various values of the relative distance between the centers of the sphere and spherical cell, the slip coefficient, and the volume fraction. The obtained results are in good agreement with the published results. The effect of concentration is more in the Cunningham’s model compared to the Kvashnin’s model. The wall correction factor on the no-slip sphere is more compared to that of a slip sphere. The correction factor on the slip sphere is more than that of a spherical gas bubble.

3

Mathematical study on the guidance of the tibiofemoral joint as theoretical background for total knee replacements

Fiedler Ch., Gezzi R., Frosch K.-H., Wachowski M. M., Kubein-Meesenburg D., Dörner J., Fanghänel J., Nägerl H.

Acta of Bioengineering and Biomechanics

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2011

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Vol. 13, no. 4

37-49

EN

The mathematical approach presented allows main features of kinematics and force transfer in the loaded natural tibiofemoral joint (TFJ) or in loaded knee endoprostheses with asymmetric condyles to be deduced from the spatial curvature morphology of the articulating surfaces. The mathematical considerations provide the theoretical background for the development of total knee replacements (TKR) which closely reproduce biomechanical features of the natural TFJ. The model demonstrates that in flexion/extension such kinematic features as centrodes or slip ratios can be implemented in distinct curvature designs of the contact trajectories in such a way that they conform to the kinematics of the natural TFJ in close approximation. Especially the natural roll back in the stance phase during gait can be reproduced. Any external compressive force system, applied to the TFJ or the TKR, produces two joint reaction forces which - when applying screw theory - represent a force wrench. It consists of a force featuring a distinct spatial location of its line and a torque parallel to it. The dependence of the geometrical configuration of the force wrench on flexion angle, lateral/medial distribution of the joint forces, and design of the slopes of the tuberculum intercondylare is calculated. The mathematical considerations give strong hints about TKR design and show how main biomechanical features of the natural TFJ can be reproduced.

4

Change in the properties of beds granulated in disc granulators

Heim A., Obraniak A., Gluba T.

Physicochemical Problems of Mineral Processing

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2010

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Vol. 44

53-62

EN

During tumbling of a powder bed wetted with liquid, material particles are agglomerated. Both the formation of granules and increase of the bed moisture content cause changes in bulk density and the coefficient of material friction against the granulator surface. They in turn determine energy transfer to the granulated material. In the present study, a change of the above mentioned parameters during batch granulation was investigated by comparing results obtained with a change in granulation degree and torque on the granulator shaft. Experiments were made in three disc granulators of diameters 0.5, 0.7 and 1 m, with rotational speeds equal to 0.2 of critical velocity. Variable parameters were the degree of disc filling and the angle of inclination of the disc axis to the level. The experimental material was bentonite with particles from 0 to 0.16 mm in diameter (dm = 0.056 mm), specific density 2420 kg/m3 and bulk density 790 kg/m3. The material was wetted drop-wise with water during the granulation at constant liquid flow rate Q = 0.7 ml/s. The angle of disc axis inclination in the applied range of its changes had no effect on the process and layer properties. In all cases, bulk density of the bed during granulation decreased. When observing change of the coefficient of friction between the bed and disc surface during granulation, three ranges of this parameter change were found. In the first, the coefficient was growing. In the second, short period, the coefficient decreased slightly. In the third, it increased again. Changing the in torque on the granulator shaft was also analysed. Three ranges could be distinguished here as well. In the first, unit moment increased to up to 50%. In the second, it dropped. In the third, it remained constant.

PL

Granulacja talerzowa to uniwersalna metoda aglomeracji pozwalająca prowadzić proces w sposób okresowy lub ciągły oraz sterować poprzez dobór parametrów procesowych rozmiarem i właściwościami uzyskanego produktu. Celem pracy było zbadanie wpływu parametrach aparaturowo-procesowych (średnicy talerza, stopnia jego wypełnienia oraz kąta pochylenia) na zmiany wartości średniego rozmiaru granul, gęstości nasypowej granulatu, oraz kąta tarcia złoża podczas procesu granulacji talerzowej. Proces prowadzono w sposób okresowy dla następujących zakresów zmian parametrów: kąt pochylenia osi talerza w stosunku do poziomu .𗅑-53% co 2 stopnie ; stopień wypełnienia aparatu materiałem k=3-7% co 1%; średnica talerza granulatora D=0.5, 0.7, 1m. Do badań jako materiał modelowy użyto drobnoziarnistego bentonitu odlewniczego o składzie granulometrycznym z zakresu 0-0.16mm. Badania granulacji przeprowadzono przy stałym natężeniu dopływu cieczy zwilżającej (woda) Q=0.7 g/s i ustalonej końcowej wilgotności granulowanego wsadu w=0.29. Uzyskane podczas trwania eksperymentów wartości badanych parametrów uzależniono od zmian wilgotności granulowanego złoża ziarnistego oraz czasu granulacji. Dokonano porównania szybkości zmian rozmiaru średniego oraz gęstości nasypowej dla szeregu granulatorów talerzowych różniących się średnicą talerza i kątem jego pochylenia, przy zmiennym stopniu wypełnienia surowcem.