Reynolds bearing

Rothfus, Monrad, Sikchi, and Heideger [Ind. Eng. Chem., 47, 913 (1955)] report that the friction factor/g for the outer wall bears the same relation to the Reynolds number for the outer portion of the anniilar stream 2(r9 — A, )Vp/r9 l as the fricBon factor for circular tubes does to the Reynolds number for circular tubes, where / is the radius of the outer tube and is the position of maximum velocity in... 

A turbine flowmeter consists of a straight flow tube containing a turbine which is free to rotate on a shaft supported by one or more bearings and located on the centerline of the tube. Means are provided for magnetic detection of the rotational speed, which is proportional to the volumetric flow rate. Its use is generally restric ted to clean, noncorrosive fluids. Additional information on construction, operation, range, and accuracy can be obtained from Holzbock (Instruments for Measurement and Control, 2d ed., Reinhold, New York, 1962, pp. 155-162). For performance characteristics of these meters with liquids, see Shafer,y. Basic Eng., 84,471-485 (December 1962) or May, Chem. Eng., 78(5), 105-108 (1971) and for the effect of density and Reynolds number when used in gas flowmetering, see Lee and Evans, y. Basic Eng., 82, 1043-1057 (December 1965). 

Turboexpanders eurrently in operation range in size from about 1 hp to above 10,000 hp. In the small sizes, the problems are miniaturization, Reynolds Number effeets, heat transfer, seal, and meehanieal problems, and often inelude bearing and eritieal speed eoneerns. In intermediate sizes, these problems beeome less signifieant, but bearing rubbing speeds and vibration beeome inereasingly important. 

There are two causes for oscillations of the heat flux, with 7 = const. (1) fluctuations of the heat transfer coefficient due to velocity fluctuations, and (2) fluctuations of the fluid temperature. At small enough Reynolds numbers the heat transfer coefficient is constant (Bejan 1993), whereas at moderate Re (Re 10 ) it is a weak function of velocity (Peng and Peterson 1995 Incropera 1999 Sobhan and Garimella 2001). Bearing this in mind, it is possible to neglect the influence of velocity fluctuations on the heat transfer coefficient and assume that heat flux flucmations are expressed as follows ... 

Singh, C., and Suiha, P., The Three-Dimensional Reynolds Equation for Micropolar-Fluid Lubricated Bearings, Wear, Vol. 76, No. 2,1982,pp. 199-209. 

Reynolds (Rl, R2) was one of the earlier investigators to appreciate the random nature of turbulence. The dimensionless parameter bearing his name is widely used as a measure of the physical characteristics of steady, uniform flow. Such a measure is essentially macroscopic and does not describe the local or transient behavior at a point in the stream. In recent years much effort has been devoted to understanding the basic mechanism of momentum transport by turbulence. The early work of Prandtl (P6), Taylor (Tl), Karmdn (Kl), and Howarth (K4) laid a basis for the statistical theory of turbulence which is apparently in reasonable agreement with experiment. More recently Onsager (03), Corrsin (C6), and Kolmogoroff (K10) extended the statistical theory of turbulence to describe the available experimental data in terms of kinetic-energy... 

Pioneering work by Osborne Reynolds in the late 19th century added considerably to the understanding of fluid flow in relation to surfaces, and established concepts on which subsequent theoretical, empirical, and practical work could be based. The principal finding was in connection with fluid flow in pipes, visually demonstrating the difference between laminar and turbulent flow. Reynolds discovered that the dimensionless number that now bears his name, the Reynolds number Re), defined the flow condition in a tube. 

Equation 1 is an integrated Reynolds equation for the hydrodynamic lubrication of a bearing (for steady state one-dimensional relative motion flow with negligible side leakage (transverse flow) where p is fluid pressure, x the one-dimensional distance into the bearing, h the film thickness and hm at maximum pressure). 

Equation 2-15 is the Reynolds equation in two dimensions for the pressure p developed by hydrodynamic action in a film of incompressible fluid lubricant with no side leakage. The other variables are h, the film thickness, and x, the distance along the length of the bearing. For example, in Fig. 2-1 x is the distance along the circumference from the inlet to the outlet. 

The application of the Reynolds equation to a simple problem in lubrication is illustrated by an examination of the plane slider bearing, which is basically a combination of two plane surfaces, one of which is inclined relative to the other. Figure 2-4 is a diagrammatic cross-... 

Application of the Reynolds Equation to the Full Journal Bearing... 

In applying the Reynolds equation to a real bearing, the film thickness h is expressed as a function of position in the bearing. In the journal bearing this is done as follows. Let a be the radius of the shaft and let us define the radial clearance c between the shaft and the... 

To use the Reynolds equation for a journal bearing we change from... 

Equation 2-39 cannot be readily solved as it is written. Osborne Reynolds obtained a solution for it in the form of a Fourier series which converges for eccentricity ratios less than 0.5 and is therefore useful only for lightly loaded bearings. The exact solution of A. Sommerfeld, details of which can be found in most of the standard texts on hydrodynamic lubrication of bearings, yields the following expression ... 

The application of the Reynolds equation, even in its simplified two-dimensional version, to specific bearing problems generally requires detailed, laborious computational treatments to arrive at usable solutions. The foregoing presentation in this chapter is intended to give the uninitiated reader an idea of the basic concepts of hydrodynamic lubrication. The limited space allotted to the subject does not permit an extensive exposition. A large array of books and periodical literature is available to the student who wishes to develop skill in the fluid film aspect of lubrication engineering. A few of the texts and monographs which treat hydrodynamic lubrication and related problems in detail are listed below. 

Conformal bearing geometry is associated with the support of large loads by relatively thick lubricant films at relatively low maximum film pressures. Counterformal geometry, on the other hand, is associated with concentrated loading. The Reynolds equation has been solved for... 

The term /R Tot is proportional to the speed of sound at the inlet stagnation conditions, and is a velocity term. Hence, bearing in mind the definition of the Reynolds number ... 

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