Thermal and inertia effects in externally pressurized conical thrust oil bearings

This paper presents theoretical and experimental investigations of thermal and inertia effects on the performance of externally pressurized conical thrust bearings. The analysis, as well as the experimental results, revealed that the increase in oil temperature due to pad rotation has a detrimental effect on the load carrying capacity, while it increases the flow rate. Increasing the speed of rotation, will increase or decrease the bearing load carrying capacity depending on the recess dimensions.Nomenclature c lubricant specific heat - F frictional torque - h film thickness - L load carrying capacity - P pressure - P pressure ratio (P/P ₁) - P ₁ inlet pressure - Q volume flow rate - r radius measured on cone surface - r radius ratio (R/R ₃) - R ₁ supply hole radius - R ₂ recess radius - R ₃ outside radius of bearing - S inertia parameter (0.15 ² R ₃ ² /P ₁) - T temperature - u, v, w velocity components (see Fig. 2) - z coordinate normal to cone surface - lubricant density - lubricant viscosity - 2 cone apex angle - rotational speed - recess depth     

On the Development of Negative Pressure in Oil Film and the Characteristics of Journal Bearing

The stability and vibration characteristics of turbo-rotors running in journal bearings depend strongly on the characteristics of journal bearing determined by the oil film pressure and negative pressure developed in journal bearings. This paper is concerned with clarifying the development of this negative pressure and its influences by taking into account air bubbles in oil film, especially the surface dilatational viscosity, which decelerates the compression and expansion of air bubbles. Deceleration of the bubble expansion under negative pressure helps the bubbles to withstand greater negative pressure. When the negative pressure is developed in the oil film, the locus of center of journal running in bearing deviates from the well-known semi-circle like shape, and the journal center is pushed outwards and horizontally under vertical static load. This means that the stability of a turbo-rotor will be reduced when negative pressure is developed.     

Effect of radial and rotational lubricant inertia on the pressure distribution in externally pressurised thrust bearings

Expressions are obtained for the pressure distribution in an externally pressurised thrust bearing for the condition when one bearing surface is rotated. The influence of centripetal acceleration and the combined effect of rotational and radial inertia terms are included in the analysis. Rotation of the bearing causes the lubricant to have a velocity component in an axial direction towards the rotating surface as it spirals radially outwards between the bearing surfaces. This results in an increase in the pumping losses and a decrease in the load capacity of the bearing. A further loss in the performance of the bearing is found when the radial inertia term, in addition to the rotational inertia term is included in the analysis.Nomenclature r, z, cylindrical co-ordinates - V _r, V , V _z velocity components in the r, and z directions respectively - U, X, W representative velocities - coefficient of viscosity - p static pressure at radius r - p mean static pressure at radius r - Q volume flow per unit time - 2h lubricant film thickness - density of the lubricant - r ₂ outside radius of bearing = D/2 - angular velocity of bearing - R dimensionless radius = r/h - P dimensionless pressure = h ³ p/Q - Re channel Reynolds number = Q/h     

Motion of large gas bubbles ascending in a liquid

An equation is derived for the ascent velocity of large gas bubbles in a liquid. This velocity is assumed to be governed by the propagation of a wavelike perturbation caused by the bubble in the liquid.Notation w bubble (or drop) velocity - specific gravity - dynamic viscosity - kinematic viscosity - r bubble (or drop) radius - surface tension - coefficient of friction - g gravitational acceleration - D bubble (or drop) diameter - p pressure - c propagation velocity of the wavelike perturbation - wavelength     

Effect of lubricant inertia in bearings with a non-Newtonian lubricant

Summary The inertia effects in externally pressurized and squeeze film bearings with lubricants obeying a power law are considered. It is found that the inertia forces decrease the load capacity of the externally pressurized bearing with a given flow rate and the inertia effect increases with the flow behaviour index. At a given feeding pressure, on the other hand, the inertia increases or decreases the load capacity when the flow behaviour index is smaller than or greater than 3, respectively. For squeeze films between circular plates and rectangular plates, the rate of squeeze is slowed down by the inertia and the inertia effect is larger in dilatant lubricants than in pseudoplastic lubricants.Nomenclature 2a diameter of the bearing, width of rectangular plates - 2b diameter of the recess - 2h film thickness - 2h ₀ initial thickness of squeeze films - l length of the rectangular plates - m consistency index - n flow behaviour index - p pressure - p _e external pressure - p _i feeding pressure - q flow rate - r radial distance - t time - u velocity of the lubricant - v squeeze velocity - w load capacity - W dimensionless load capacity - axial distance - viscosity of the lubricant - density of the lubricant     

Rheodynamic lubrication of a journal bearing

Summary The problem of a journal bearing lubricated by a Bingham material has been solved. It has been found that the load capacity, and the moment of friction of the bearing are larger than in a journal bearing, lubricated with a Newtonian material.Nomenclature r radius of the journal - c radial clearance - r + c radius of the bearing - e eccentricity - w angular velocity of the journal - h thickness of the lubricant film at any point - thickness of the core - ø angular distance of a point, from the point, where film thickness is maximum - eccentricity ratio (e/c) - x distance along the bearing surface - y distance normal to the bearing surface - T shear stress in the lubricant - T ₀ yield value of a Bingham solid - viscosity of a Newtonian fluid - plastic viscosity of a Bingham solid - p fluid pressure in the lubricant film - Q volume flow of the lubricant - W ₀ load capacity of the bearing for ordinary lubricants - W load capacity of the bearing - M moment of friction - F coefficient of friction - ₁ maximum thickness of the inlet core - ₂ maximum thickness of the outlet core - ₁ circumferential extent of the inlet core in the journal bearing - ₂ circumferential extent of the outlet core in the journal bearing - h ₀ minimum hieght of core formation in the slider bearing - h _p maximum height of core formation in the slider bearing - u velocity of the fluid in the direction of x in the slider bearing - V velocity in the y direction - h ₁ height of the inlet core at the circumferential extent ₁ - h ₂ height of the outlet core at the circumferential extent ₂ - h ₃ height of the outlet core in the region ₂ - q Q/(cwr) - q ₀ value of q for Newtonian lubricants - p ₀ pressure at =0 - H h/c - H ₁ h ₁/c - H ₂ h ₂/c - B T ₀ C/wr = Bingham number     

Neutrally buoyant bubbles used as flow tracers in air

Research has been performed to determine the accuracy of neutrally buoyant and near-neutrally-buoyant bubbles used as flow tracers in an incompressible potential flowfield. Experimental and computational results are presented to evaluate the quantitative accuracy of neutrally buoyant bubbles using a commercially available helium bubble generation system. A two-dimensional experiment was conducted to determine actual bubble trajectories in the stagnation region of a NACA 0012 airfoil at 0° angle of attack. A computational scheme evaluating the equation of motion for a single bubble was also used to determine the factors which affect a bubble's trajectory. The theoretical and computational analysis have shown that neutrally buoyant bubbles will trace complex flow patterns faithfully in the flowfield of interest. Experimental analysis revealed that the use of bubbles generated by the commercially available system to trace flow patterns should be limited to qualitative measurements unless care is taken to ensure neutral buoyancy.Nomenclature a _c centripetal acceleration - c model chord - c _D bubble drag coefficient - D bubble diameter - g acceleration due to gravity - g _v acceleration due to gravity vector - h trajectory deviation normalization parameter - K nondimensional inertia parameter, - m _f mass of fluid - m _p mass of bubble - p static pressure - r radial distance, bubble radius - R gas constant - Re free-stream Reynolds number, - Re _p bubble slip Reynolds number, - S cross-sectional area of sphere - T temperature - t time - u streamwise velocity component - U free-stream velocity - v _f fluid velocity vector - V _p bubble velocity vector - x _p bubble position vector - y _b bubble trajectory y/c - y _s streamline y/c - model angle of attack - bubble solution surface tension - potential vortex strength - _bfs bubble solution density - fluid density - bubble density - bubble wall thickness - fluid viscosity     

Dependence of the stability criterion of nucleate boiling on the compressibility of the vapor

The article gives the results of a study of the motion of bubbles and their deformation near the heating surface at different pressures. It was observed that, during the time of their growth, the gaseous medium in the bubbles is in a compressed state.Nomenclature R) radius of bubble - R_h) maximul radius of a deformed bubble in the horizontal plane - R_v) maximal radius of a deformed bubble in the vertical plane - ) specific weight - B) universal gas constant - ) surface-tension coefficient - p) pressure - ) edge wetting angle - g) acceleration due to gravity - V) volume - ) molecular weight - C_T) isothermal velocity of sound Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 77–81, July–August, 1971.     

Bouncing and Coalescence of Bubble Pairs Rising at High Reynolds Number in Pure Water or Aqueous Surfactant Solutions

The encounter of bubble pairs of O(1 mm) in both pure water and aqueous surfactant solutions was studied experimentally. In pure water, two equally sized bubbles were found to coalesce if the Weber number, W = V² R/, based on the velocity of approach, V, was below a critical value, W_cr = 0.18, where and are the density and surface tension of the liquid respectively and R the equivalent radius of the bubbles. After coalescence bubbles perform volume and shape oscillations.When W_cr is exceeded, bubbles bounce. After bouncing, bubbles can either coalesce or separate without coalescing. This was found to depend on the Weber number, based on the rise velocity U, We = U² R/. If this number was below a critical value, bubbles coalesced after bouncing. The relative motion of the bubbles was found to be damped out by acoustic damping due to surface oscillations rather then by viscosity.If We was above a critical value, which was close to that for path instability of a single bubble (We = 3.3), the bubbles separated after bouncing. This is probably caused by shedding of vortices which dominate the relative motion of the bubbles. This mechanism may cause bubbles in bubbly flows not aggregating in horizontal planes, as was found in calculations based on potential flow theory. For modelling bubbly flows it will therefore be essential to incorporate the influence of vorticity.When surfactants are added to the water it was found that bubbles are prevented to coalesce above a critical concentration, which is nearly identical to that of single rising bubbles. Above this critical concentration, bubbles behave as rigid spheres and trajectories cannot be predicted by potential flow theory.     

The problem of a gas bubble in plane ideal fluid flow

We study the problem of two-dimensional fluid flow past a gas bubble adjacent to an infinite rectilinear solid wall.Two-dimensional ideal fluid flow past a gas bubble on whose boundary surface-tension forces act (or a gas bubble bounded by an elastic film) has been studied by several authors. Zhukovskii, who first studied jet flows with consideration of the capillary forces, constructed an exact solution of the problem of symmetric flow past a gas bubble in a rectilinear channel [1]. However, Zhukovskii's solution is not the general solution of the problem; in particular, we cannot obtain the flow past an isolated bubble from his solution. Slezkin [2] reduced the problem of symmetric flow of an infinite fluid stream past a bubble to the study of a nonlinear integral equation. The numerical solution of this problem has recently been found by Petrova [3]. McLeod [4] obtained an exact solution under the assumption that the gas pressure p₁ in the bubble equals the flow stagnation pressure p₀. Beyer [5] proved the existence of a solution to the problem of flow of a stream having a given velocity circulation provided p₁p₀.We examine the problem of two-dimensional ideal fluid flow past a gas bubble adjacent to an infinite rectilinear solid wall. The solution depends on the value of the contact angle . The existence of a solution is proved in some range of variation of the parameters, and a technique for finding this solution is given. The situation in which =1/2 is studied in detail.     

A new method for measuring static pressure fluctuations with application to wind-wave interaction

A new technique for in stream static pressure fluctuations sensing is presented. The higher capability of the method with regard the classical one, particularly over laboratory wind wave, is proved. First measurements have been done in a turbulent boundary layer above the air-water interface during the wave generation stage. The results show that, for pure laboratory wind waves at short fetches, a strong coupling exists between air and water motions and that the energy transfer from wind to the waves seems mainly due to the work done by the wave induced pressure fluctuations.List of symbols C wave phase celerity - C _g wave group celerity - Coh coherency function - C _ps pressure coefficient for a static pressure sensing head - C _pt pressure coefficient for a total pressure sensing head - g gravitational acceleration - n frequency - p instantaneous static pressure - p _m measured instantaneous static pressure - p _t instantaneous total pressure - p _tm measured instantaneous total pressure - p (t) static pressure fluctuation - Q _pn quadspectrum between static pressure fluctuations and water level deflections - S _p static pressure fluctuations spectrum - S _pt total pressure fluctuations spectrum - S _n wave spectrum - u instantaneous air velocity vector - U air velocity outside the boundary layer - X fetch - instantaneous incidence angle of the air velocity - instantaneous water level - phase shift - wave energy amplification ratio - ^p non dimensional energy transfer ratio by pressure work - _M non dimensional energy transfer ratio predicted by Miles theory - _a air density - _w water density A version of this paper was presented at the 10th Symposium on Turbulence, University of Missouri-Rolla, September 22–24, 1986     

A three-dimensional variational problem in the gasdynamic theory of a lubricant

In [1–3] optimal forms of the gap were found for one-dimensional aerodynamic sliding bearings. The coefficient of the bearing capacity is optimized under the condition that the one-dimensional Reynolds equation of a gas lubricant is used to determine the pressure in the bearing. In the present article the three-dimensional problem of finding the optimal profile of an aerodynamic sliding bearing in the case of small compressibility numbers is considered. The problem is solved by the methods of variational calculation. A qualitative investigation is made of the form of the optimal profile, the results of which are confirmed by a numerical solution of a system of Euler-Lagrange equations. The results of the calculations are given for different elongations of the bearing. On the basis of the profiles obtained, optimal profiles with a rectangular pocket, which are more practical to fabricate, are found.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 34–39, September–October, 1975.     

Studies on the drag and shape of gas bubbles rising through a stagnant liquid

In connection with our investigations on the motion of gas bubbles rising through a stagnant liquid, experiments were conducted to determine the drag and shape of air bubbles rising freely in water. — A new experimental technique which consists of phototubes, light beams and an electronic circuit has been used to measure the velocity of rise, and the drag coefficient has been determined by equating the buoyancy with the drag. — The size and the deformation of the bubble were determined by a photographic technique. — The results show that, for bubbles rising with a rectilinear motion, theoretical solutions for the drag must be compared with the drag coefficient calculated with the maximum rise velocity, and the results are in good agreement with theory. — There is no wall effect on the rise velocity of the bubble if the ratio of the medium diameter to the equivalent bubble diameter is greater than 18. — Weber number determined according to the maximum velocity is a significant parameter involved in the determination of the shape of air bnbbles. The critical Weber number above which bubbles are not spherical is 0.62, and the bubble surface oscillations begin at the Weber number of 3.70.

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Zusammenfassung In Verbindung mit unseren Untersuchungen über die Bewegung von Gasblasen, die in einer ruhenden Flüssigkeit aufsteigen, wurden auch Versuche zur Bestimmung des Widerstandes und der Form von frei in Wasser aufsteigenden Luftblasen angestellt. — Zur Messung der Aufstiegsgeschwindigkeit wurde eine neuartige Versuchsanordnung benutzt, bestehend aus Photozellen, Lichtstrahlen und einem elektronischen Schaltkreis. Der Widerstandskoeffizient wurde aus dem Vergleich des Auftriebs mit dem Widerstand ermittelt. Größe und Verformung der Blasen wurden photographisch bestimmt. — Die Versuche zeigen, daß für Blasen mit gradliniger Bahn die theoretische Lösung für den Widerstand mit dem Widerstandskoeffizienten verglichen werden muß, der aus der maximalen Aufstiegsgeschwindigkeit berechnet wird. Die Übereinstimmung zwischen Theorie und Versuch ist gut. — Ein Einfluß der Gefäßwand auf die Aufstiegsgeschwindigkeit ist nicht vorhanden, wenn der Gefäßdurchmesser mehr als 18mal so groß ist wie der äquivalente Blasendurchmesser. — Die Weber-Zahl, gebildet mit der größten Aufstiegsgeschwindigkeit, ist maßgebend für die Blasenform. Die kritische Weber-Zahl, oberhalb deren die Blasen nicht mehr kugelig sind, beträgt 0,62, und bei einer Weber-Zahl von 3,70 beginnt die Blasenwand zu schwingen.

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Nomenclature C _D Drag coefficient - Drag coefficient determined forv _{z max} - Drag coefficient determined forv _{z ave} - D Drag - Re Reynolds number determined in terms of the equivalent bubble diameter (Re=vd _e/ _l) - We Weber number determined in terms of the equivalent bubble diameter (We=d _{e l} v ²/) - a Major axis of the ellipse - b Minor axis of the ellipse - d _e Equivalent bubble diameter - g Acceleration of gravity - h Helix pitch - m Mass - y Acceleration - _l Dynamic viscosity of the liquid - _g Dynamic viscosity of the gas - _l Kinematic viscosity of the liquid - _l Density of the liquid - _g Density of the gas - Helix slope defined by tg=h/(D _h) - Surface tension - x Bubble deformation (x=a/b) This research is sponsored by the Turkish Scientific and Technical Research Council.     

Simulations of bubble growth and interaction in high viscous fluids using the lattice Boltzmann method

Phenomena of growth, coalescence and breakdown of bubbles within high viscous fluids are of great interest in the fluid dynamics of multiphase fluids because of their industrial relevance, e.g. in polymer, metal alloy and food processing fields. The dynamics of multiple bubble growth in hot viscous fluids is a complex issue governed by pressure forces, vapour diffusion, surface tension and viscous forces. Effects of water evaporation from the mixture surface are responsible for phenomena like glass transition, viscous increase and dough solidification. This article presents Lattice Boltzmann simulations of nucleating bubbles with large density ratio, that grow and interact in a hot high-viscous fluid. The work focuses on the first phases of the bubble expansion, neglecting the effects of evaporation. The simulations are performed using the Lattice Boltzmann Method (LBM). The Free Surface method is used to reduce a liquid/gas two-phase flow to a single-phase flow. The interface layer between gas and fluid is tracked using the volume of fluid (VOF) method. To avoid numerical instabilities due to the high viscosity ($\eta =100Pas$), the problem is scaled from physical to LB-units through non-dimensional quantities. The bubbles are initially punched randomly into the domain with a dimension comparable with the dimension of nucleation and are allowed to grow under an internal over-pressure. The simulated final structure of the bubbles is compared with images of a pure starch fluid, extruded under same conditions. It is shown as the final bubble distribution, matrix dimension and bubble diameters in the simulation are in good agreement with the real final conformation.     

Magneto-hydrodynamically lubricated externally pressurised bearing with variable film thickness

Summary This paper studies theoretically the use of a conducting lubricant in an externally pressurised bearing with variable film-thickness in the presence of an axial magnetic field. The flow and other characteristics are determined and it is shown that the pressure and load capacity can be increased by increasing the strength of the applied magnetic field at a given flow rate. But at a given feeding pressure the load capacity and pressure do not depend upon the magnetic field. The load capacity of this bearing is greater than that of a bearing having a constant film-thickness. It is also pointed out that the frictional drag on the rotor can be minimised by supplying electrical energy to the system.Nomenclature angle which the rotor surface makes with the stator (see fig. 1) - angular velocity of the rotor - _t terminal voltage between the electrodes - _t.o.c. open circuit voltage - viscosity of the lubricant - conductivity of the lubricant - B ₀ strength of the applied magnetic field - E _r radial component of the electric field - h variable film-thickness - h ₀ minimum film-thickness - I total current - I _s.c. short circuit current - L depth of the recess - M Hartmann number - p pressure - p _e exit pressure - p _i inlet pressure - Q rate of volume flow - r radial coordinate - R ₀ radius of the recess - R outer radius of the stator - R _i internal resistance - T frictional drag - u radial velocity - v tangential velocity - W load capacity - normalised load capacity - z axial coordinate     

Shock Waves in a Fluid with Bubbles Containing Evaporating Drops of a Liquefied Gas

The propagation and reflection of one-dimensional plane unsteady waves and pulses in a mixture of a fluid with two-phase bubbles containing evaporating drops is investigated. A significant effect of unsteady evaporation of the drops in the zone ahead of the shock wave on the wave propagation is demonstrated. The evaporation of the drops results in a pressure increase ahead of the wave and the shock wave as it were climbs to increasing pressure level. In contrast to bubbly fluids with single-phase bubbles, in a fluid with two-phase bubbles, at a fixed phase volume fraction, a decrease in bubble size results in an increase rather than a decrease of the oscillation amplitude. The wave reflection from a solid wall is essentially nonlinear and the maximum pressure attained at the wall is several times greater than the incident-wave intensity.     

The motion of gas bubbles rising through stagnant liquid

The scope of the present over-all investigation comprises the determination of rise velocity, path, shape and drag characteristics of gas bubbles rising freely in water in terms of bubble size.The material presented in this first report is limited to the measurement of the rise velocity of air bubbles of various sizes and the determination of their paths.A new experimental technique is introduced which consists essentially of measuring the time interval when the bubble traverses two light beams. An electronic system including two phototubes, a pulse amplifier and shaper, and an electronic timer has been used. Also a photographic technique has been used to determine the bubble's size, shape and path.The results show that the type of motion may be predicted from the value of the Reynolds number at which the motion takes place. Five types of motion were observed in the experiments: 1. Rectilinear motion, 2. motion on a helical path, 3. first plane then helical motion, 4. plane motion, 5. rectilinear motion with rocking.The rise velocity of the bubbles which move on those paths varies with the heightz. All the bubbles studied are accelerated to a maximum velocity in a few cm above the capillary tube. For the bubbles smaller than 4.2 mm, this maximum velocity decreased to an asymptotic value far from the capillary tube.

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Zusammenfassung Das Ziel dieser gesamten Untersuchungen ist die Bestimmung der Steiggeschwindigkeit sowie charakteristischer Daten der Bahn, der Form und des Widerstandes von frei in Wasser aufsteigenden Gasblasen in Abhängigkeit von der Blasengröße. Dieser erste Bericht handelt nur von der Messung der Aufstiegsgeschwindigkeit von Luftblasen verschiedener Größe und der Bahnbestimmung.Eine neue, hier angewandte Experimentiertechnik besteht im wesentlichen in der Messung des Zeitintervalls zwischen den Durchgängen der Blase durch zwei Lichtstrahlen. Es wurde ein elektronisches System benutzt, bestehend aus zwei Photozellen, Verstärker, Umformer und Zeitnehmer. Größe, Form und Bahn der Blasen wurde photographisch bestimmt.Die Ergebnisse zeigen, daß die Bewegungsform sich im wesentlichen aus dem Wert der Reynolds-Zahl voraussagen läßt. Fünf verschiedene Formen wurden beobachtet: 1. gradlinige Bewegung, 2. spiralige Bewegung, 3. anfangs ebene, später spiralige Bewegung, 4. ebene Bewegung, 5. gradlinige Schaukelbewegung.Die Aufstiegsgeschwindigkeit längs dieser Bahnen ändert sich mit der Höhe. Alle beobachteten Blasen werden innerhalb einiger Zentimeter oberhalb der Kapillare auf eine Maximalgeschwindigkeit beschleunigt. Für Blasen unter 4,2 mm Durchmesser sinkt diese Maximalgeschwindigkeit auf einen asymptotischen Wert ab, der in größerer Entfernung von der Kapillare erreicht wird.

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Nomenclature C _D Drag coefficient - D _h Helix diameter - R _h Helix radius - R Radius of curvature of the spherical cap - R _e Reynolds number determined in terms of the equivalent bubble diameter (=(vd _e)/ ₁) - d _e Equivalent bubble diameter - g Acceleration of gravity - h Helix pitch - m Mass - r Bubble radius - v Bubble velocity - v _z Bubble rise velocity - Acceleration - ₁ Dynamic viscosity of the liquid - _g Dynamic viscosity of the gas - ₁ Kinematic viscosity of the liquid - ₁ Density of the liquid - _g Density of the gas - Helix slope defined by tg =h/D _h     

Effect of angular inertia of lubricant in MHD hydrostatic thrust bearings

Summary Circumferential motion of a conducting lubricant in a hydrostatic thrust bearing is caused either by the angular motion of a rotating disk or by the interaction of a radial electric field and an axial magnetic field. Under the assumption that the fluid inertia due to radial motion is negligibly small in comparison with that due to angular motion, it is found analytically that the rotor causes an increase in flow rate and a decrease in load capacity, while both are increased by the application of an electric field in the presence of an axial magnetic field. The critical angular speed of the rotor at which the bearing can no longer support any load is obtained, and the possibility of flow separation in the lubricant is discussed.Nomenclature a recess radius - b outside disk radius - B ₀ magnetic induction of uniform axial magnetic field - E ₀ radial electric field at r=a - E _r radial electric field - h half of lubricant film thickness - M Hartmann number = (B ₀ ² h ²/)^1/2 - P pressure - P ₀ pressure at r=a - P _e pressure at r=b - Q volume flow rate of lubricant - Q ₀ flow rate of a nonrotating bearing without magnetic field - r radial coordinate - r _s position of flow separation on stationary disk - u, v fluid velocity components in radial and circumferential directions, respectively - W load carrying capacity of bearing - W ₀ load capacity of a nonrotating bearing without magnetic field - z axial coordinate - coefficient of viscosity - _e magnetic permeability - fluid density - electrical conductivity - electric potential - angular speed of rotating disk - _c critical rotor speed at which W=0     

The behavior of a spherical bubble near a solid wall in a compressible liquid

Summary The behavior of a spherical bubble near a solid wall is analysed by considering the liquid compressibility. The equation of motion of the bubble with first order correction for the effects of liquid compressibility and solid wall is derived. The equation obtained here coincides with the known result in case of L or C . Further experimental study is made on the motion of bubbles produced by a spark discharge in water. The theoretical results are in good agreement with the experiments.

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Das Verhalten einer kugelförmigen Blase in einer kompressiblen Flüssigkeit in der Nähe einer festen Wand

Übersicht Bei Berücksichtigung der Flüssigkeitskompressibilität wird das Verhalten einer kugelförmigen Blase in der Nähe einer festen Wand analysiert. Die Gleichung der Bewegung der Blase wird mit der Korrektur erster Ordnung für den Einfluß der Flüssigkeitskompressibilität und der festen Wand angegeben. Aus der erhaltenen Gleichung wird für L oder C das bekannte Ergebnis hergeleitet. Darüber hinaus wird eine experimentelle Untersuchung der Blasenbewegung durchgeführt. Die Blase wird mit Hilfe von Funkendurchschlägen zwischen Elektroden in Wasser erzeugt. Die theoretischen Ergebnisse stimmen gut mit den Experimenten überein.

     

The rheology of suspensions of vinylon fibers in polymer liquids. II. Suspensions in polymer solutions

Summary The rheological properties of vinylon fiber suspensions in polymer solutions were studied in steady shear flow. Shear viscosity, first normal-stress difference, yield stress, relative viscosity, and other properties were discussed. Three kinds of flexible vinylon fibers of uniform length and three kinds of polymer solutions as mediums which exhibited remarkable non-Newtonian behaviors were employed. The shear viscosity and relative viscosity ( _r ) increased with the fiber content and the aspect ratio, and depended upon the shear rate. Shear rate dependence of _r was found only in the low shear rate region. This result was different from that of vinylon fiber suspensions in Newtonian fluids. The first normal-stress difference increased at first slightly with increasing fiber content but rather decreased and showed lower values for high content suspensions than that of the medium. A yield stress could be determined by using a modified equation of Casson type. The flow properties of the fiber suspensions depended on the viscosity of the medium in the suspensions under consideration.With 16 figures and 1 table