Rotor series

As a first example the states of any pure rotor series should all have maximum probability for r, = r2 and 0l2 = n, and the probability densities for members of a given rotor series should have very similar spatial distributions in their internal coordinate system (called the intrinsic coordinate system in the context of nuclear physics). The total wavefunctions of different rotor states in any series should differ primarily only in the parts that describe the rotation of the figure axis in space these parts do not affect the distributions in their internal coordinate systems. At a higher level of approximation, the distributions for the states of a given series may be expected to differ a little because of centrifugal distortion such differences, of course, are apparent in the internal coordinate system. 

The left-hand column of Fig. 2 shows just such spatial distributions of probability density for the rotor series of He with nt = n2 = 2. In the traditional independent-particle representation, these would be designated 2s2 lSe, 2s2p 3P°, and 2p2 lDe for convenience, we shall sometimes refer to them in this way, but with quotation marks. The three distributions in the column, all drawn for the most probable value of rl5 are similar but differ in the increasing angular spread, as the angular momentum increases. 

Within this "rigid rotor" model, the absorption speetrum of a rigid diatomie moleeule should display a series of peaks, eaeh of whieh eorresponds to a speeifie J ==> J + 1 transition. The energies at whieh these peaks oeeur should grow linearally with J. An example of sueh a progression of rotational lines is shown in the figure below. 

Examples of prolate near-symmetric rotors are the s-trans and s-cis isomers of crotonic acid, shown in Figure 5.8, the a axis straddling a chain of the heavier atoms in both species. The rotational term values for both isomers are given approximately by Equation (5.37) but, because A and B are different for each of them, their rotational transitions are not quite coincident. Figure 5.9 shows a part of a low-resolution microwave spectmm of crotonic acid in which the weaker series of lines is due to the less abundant s-cis isomer and the stronger series is due to the more abundant s-trans isomer. 

The American version of the dynamic filter, known as the Artisan continuous filter (Fig. 30), uses such nonfiltering rotors in the form of turbine-type elements. The cylindrical vessel is divided into a series of disk-type compartments, each housing one rotor, and the stationary surfaces are covered with filter cloth. The feed is pumped in at one end of the vessel, forced to pass through the compartments in series, and discharged as a thick paste at the other end. At low rotor speeds the cake thickness is controlled by the clearance between the scraper and the filter medium on the stationary plate, while at higher speeds part of the cake is swept away and only a thin layer remains and acts as the actual medium. 

Straight-Lobe Type This type is illustrated in Fig. 10-79. Such units are available for pressure differentials up to about 83 kPa (12 Ibf/in ) and capacities up to 2.549 X lO mvh (15,000 ftVmin). Sometimes multipfe units are operated in series to produce higher pressures individual-stage pressure differentials are limited by the shaft deflection, which must necessarily be kept small to maintain rotor and casing clearance. 

The pressurized process stream is guided radially into the rotor by the primary nozzles, which are a series of vanes forming nozzles jetting the gas tangentially and inwardly into the rotor (see Fig. 29-47). These... 

Variable nozzles produce a series of jets of gas entering the rotor, and these impulses add up to form a frequency equal to the blade-passing frequency the number of revolutions per second multiplied by the number of nozzle vanes, which is of the order of thousands of cycles per second. Frequently the rotor will resonate at this frequency, and if it does, it will be fatigued and crack and break up thus these frequencies must be avoided, and the manufac turer should be asked to supply information to the customer on this subject. 

If a large induction motor is switched on such a system it is possible that its rotor may lock up at the sub-synchronous speed and keep running at higher slips. This situation is also undesirable, as it would cause higher slip losses in addition to higher stator current and overvoltage across the series capacitors. 

The sliding vane compressor consists of a single rotor mounted eccentrically in a cylinder slightly larger than the rotor. The rotor has a series of radial slots that hold a set of vanes. The vanes are free to move radially within the rotor slots. They maintain contact with the cylinder wall by centrifugal force generated as the rotor turns. 

Axial compressor blades are usually forged and milled. Precision casting has been used on occasion. The most common material used is a 12 chrome steel, in the AISI 400 series, and is also known as 400 series stainless steel. While the stator blades are occasionally shrouded, the rotor blades are free-standing. Lashing wires have been used on rotor blades, but are generally used to solve a blade vibrational stress problem. 

End view showing male and female rotors and slide valve on an 85-ton intermediate compressor. The robust design of the Series R compressor can ingest amounts of liquid refrigerant that would severely damage reciprocating compressor valves, piston rods, and cylinders. (Used by permission Cat. RLC-DS-2, Aug. 1995. The Trane Company.)... 

Starting Capacitance for a Capacitor Motor. The starting capacitance for a capacitor motor is the total effective capacitance in series with the starting winding under locked-rotor conditions. 

The rotor of the Moineau-type positive displacement motor has a helical design. The axial wave number of the rotor is one less than the axial wave number for the stator for a given chamber. This allows the formation of a series of fluid cavities as the rotor rotates. The number of stator wave lengths n and the number of rotor wave lengths n per chamber are related by [79,86]... 

With this technique the motor has a wound rotor brought out to slip rings and an external resistance is connected into the rotor circuit. This resistance usually consists of a series of resistor banks, which are switched out progressively in a number of steps as the motor accelerates. The number and rating of each step is chosen so that starting current and motor torque are within requirements. 

Turbine rotors are comprised of a series of vanes or blades mounted on individual wheels. Each of the wheel units, which is referred to as a stage of compression, has a different number of blades. Narrowbands should be established to monitor the blade-pass frequency of each wheel. Loss of a blade or flexing of blades or wheels is detected by these narrowbands. 

The rotor of the vane pump is mounted off centre in a cylindrical casing (Figure 8.9). It carries rectangular vanes in a series of slots arranged at intervals round the curved surface of the rotor. The vanes are thrown outwards by centrifugal action and the fluid is carried in the spaces bounded by adjacent vanes, the rotor, and the casing. Most of the wear is on the vanes and these can readily be replaced. 

MultiPREP rotors (Fig. 3.7) For high-throughput synthesis, Milestone offers a series of different parallel rotors for 36, 50 or 80 glass or Teflon-PFA vessels (35/50 mL) to perform reactions at atmospheric pressure up to 230 °C. 

A volume of gas is enclosed in the space bounded by the rotor, the stator and the two vanes (see Fig. 1.6). The pump removes the gas by compressing it to a pressure slightly higher than the atmospheric pressure. This overpressure opens the spring-loaded outlet valve, and the gas escapes to the atmosphere. A thin film of oil makes the final seal therefore the ultimate pressure depends also on the oil vapour pressure. With one stage, the lowest attainable pressure is about 10 2torr and with two stages in series 10-3 torr. 

The Alfa-Laval contactor shown in Figure 13.41, has a vertical spindle and the rotor is fitted with concentric cylindrical inserts with helical wings forming a series of spiral... 

Sparks, T. G., Brown, D. E. and Green, A. Assessing rotor/stator mixers for rapid chemical reactions using overall power characteristics (BHR conference series. Publication 18. Mechanical Engineering Publications Ltd. London, 1995). 

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