Non-uniform pressure distribution

Turbomaehinery bearing systems are normally designed for radial loads eorresponding to the weight of the rotor. Non-uniform pressure distribution around the wheel(s) of a turbomaehine may also eontri-bute to the magnitude of gas dynamie radial load, oeeasionally ealled side load. The sourees of gas dynamie radial loads on the eom-pressor wheel are different from those at the expander wheel. 

On the expander side, the expander wheel is surrounded by the nozzle vanes. The nozzle vanes, in turn, reeeive gas from a toroidal spaee that is eonneeted to tlie expander inlet piping. Any non-uniformity in the torus spaee and/or in the nozzle vane design may result in a non-uniform pressure distribution around the expander wheel. Non-uniform gas pressure around the expander wheel will result in a non-uniform load and, henee, produee a gas dynamie radial load on the bearing. In the expander ease, however, the nozzle throat flow resistanee is mueh larger than the easing peripheral pressure nonuniformity. The latter aets as a buffer making the expander wheel eireumferential pressure variations smaller than those of the eompressor side. This smaller pressure variation produees mueh less radial load when eompared to that of the eompressor side. 

If the relative velocity is sufficiently low, the fluid streamlines can follow the contour of the body almost completely all the way around (this is called creeping flow). For this case, the microscopic momentum balance equations in spherical coordinates for the two-dimensional flow [vr(r, 0), v0(r, 0)] of a Newtonian fluid were solved by Stokes for the distribution of pressure and the local stress components. These equations can then be integrated over the surface of the sphere to determine the total drag acting on the sphere, two-thirds of which results from viscous drag and one-third from the non-uniform pressure distribution (refered to as form drag). The result can be expressed in dimensionless form as a theoretical expression for the drag coefficient ... 

Non-uniform pressure distribution in compact limits aspect ratio of parts. Can be improved by pressing from top and bottom, rather than from one direction only. Tooling cost relatively high but powder pressing often more economical than other methods. 

Compact density and its distribution is also strongly influenced by interactions between the solid particles and of the particulate mass with equipment features (e.g. die walls, punch surfaces, roller press pockets, etc.). If a perfectly lubricated particulate solid (i.e. featuring no interparticle friction) were compacted in a cylindrical die with frictionless walls, it could be expected that the force exerted by the smooth, flat punch is transmitted through the entire volume of material resulting in uniform pressure and, therefore, uniform density throughout the compact. In reality, the presence of frictional and shear forces leads to a non-uniform pressure distribution and irregular particle movement (displacement) causing variations in compact density. 

Another possible cause of lateral deflection of the screw is non-uniform pressure distribution around the circumference of the screw. Figure 8.8 shows a possible pressure distribution that will result in a considerable lateral force on the screw. 

A problem known as the core shift is closely related to the mold deformation problem. A core is the part of a mold that shapes the inside of a molded product. Core shift is the spatial deviation of the position of the core caused by non-uniform pressure distribution over the surface of the core during the filling and packing stages. Prediction of the core shift in injection molding has been attempted by some researchers, e.g., Bakharev et al. (2004). 

Apart from the flow-induced drag force, moving particles experience an additional transverse lift force due to the non-uniform relative velocity between shear-layers and particles [29]. The resulting non-uniform pressure distribution around the resolved particle surface leads to a lift force which acts towards the direction of higher slip velocity. Figure 6 illustrates this behaviour by means of the horizontal offset between the initial and final positions of the upper particles shown in Fig. 6a-f. 

Biancone, F., A. Campanile, G. Galimi, and M. Goffi, 1965, Forced Convection Burnout and Hydrodynamic Instability. Experiments for Water at High Pressure. I. Presentation of Data for Round Tubes with Uniform and Non-Uniform Power Distribution, Italian Rep. EUR-2490 e, European Atomic Energy Community, Brussels, Belgium. (5)... 

This discussion assumes uniform pressure distribution over the whole apparent area of contact. In the case of elastic contact between non-conformal surfaces, the contact pressure varies over the apparent contact area in accordance with a Herzian pressure distribution. For an elastic contact between a spherical surface and a flat surface the relationship becomes ... 

The reactions were carried out in a TEOM reactor where the weight of the catalyst bed is continuously recorded. The setup is similar to that described previously [8]. The methanol flow was controlled by a liquid flow controller while DME and propene were fed using gas flow controller. The MTO and DTO reactions were carried out at 425°C, WHSV=417h" and a methanol or DME partial pressure of 8 kPa, with helium as diluent. One DTO experiment was also performed at WHSV=600 h" to keep the residence time identical to those from the MTC) experiments. Such high space velocity and low partial pressure were used to avoid non-uniform coke distribution through the catalyst bed, and to keep the conversion well below 100% to minimize secondary reactions of olefins. 

Single cells produce less than 1 V of electricity, which is far from enough to power a vehicle. In order to produce a useful voltage, multiple cells must be assembled into a fuel cell stack. This can be achieved in a parallel and/or a series mode to supply feed gas to the stacks. In a parallel gas supply fuel cell stack, all cells are fed in parallel from a common hydrogen/air inlet. In the serial configuration the gas from the outlet of the first cell is fed to the inlet of the second cell and so on until the last cell, which helps prevent non-uniform gas distribution. To avoid a large pressure drop this arrangement can be used only for stacks with a small number of fuel cells [7]. 

This is an empirical equation of the mean-field type, based on the assumption that should be proportional to the local density of monomers. The magnitude of the excluded volume interactions is described by the volume-like parameter Ve, with typical values in the order of 0.01-1 nm. The factor kT is explicitly included, not only for dimensional reasons, but also in order to stress that excluded volume energies, like hard core interactions in general, are of entropic nature (entropic forces are always proportional to T, as is exemplified by the pressure exerted by an ideal gas, or the restoring force in an ideal rubber, to be discussed in a later chapter). If the local potential experienced by a monomer is given by Eq. (2.78), then forces arise for all non-uniform density distributions. For the coil under discussion, forces in radial direction result since everywhere, with the exception of the center at x = 0, we have dcm/d x < 0. The obvious consequence is an expansion of the chain. 

FIGURE 7.101 Pressure distribution doe to wind effect o) uniform wind velocity profile (6) non-uniform wind velocity profile. 

L5. Lee, D. H., and Obertelli, J. D., An experimental investigation of forced convection burn-out in high pressure water. 2. Preliminary results for round tubes with non-uniform axial heat flux distribution, AEEW-R309 (1963). 

Lee, D. H., and J. D. Obertelli, 1963, An Experimental Investigation of Forced Convection Burnout in High Pressure Water, Part 2. Preliminary Results for Round Tubes with Non-Uniform Axial Heat Flux Distribution, UK Rep. AEEW-R-309, UK AEEW, Winfrith, England. (5)... 

While adsorption equiUbrium considerations do justify the possibility to regenerate an adsorbent bed completely and to uniform levels, this is rarely achieved in practice in either thermal swing adsorption and is almost never the case in pressure swing adsorption. Some residual sorbate is always left on the sorbent and in general, except for TSA with only one or two sorbates, the residual loadings are almost always found as a non-uniformly distributed profile across the length of the bed. 

In conventional rocket engines, propellant distribution tends to be non-uniform across the injector face. Furthermore, relatively large changes in flow velocity may be associated with small fluctuations in supply pressures (4). Improved distribution of fuel and oxidizer across the injector face may be achieved by using orifice designs in which fully turbulent flow is attained reproducibly (4, 18). 

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