Air-flow

It turns out that there is another branch of mathematics, closely related to tire calculus of variations, although historically the two fields grew up somewhat separately, known as optimal control theory (OCT). Although the boundary between these two fields is somewhat blurred, in practice one may view optimal control theory as the application of the calculus of variations to problems with differential equation constraints. OCT is used in chemical, electrical, and aeronautical engineering where the differential equation constraints may be chemical kinetic equations, electrical circuit equations, the Navier-Stokes equations for air flow, or Newton s equations. In our case, the differential equation constraint is the TDSE in the presence of the control, which is the electric field interacting with the dipole (pemianent or transition dipole moment) of the molecule [53, 54, 55 and 56]. From the point of view of control theory, this application presents many new features relative to conventional applications perhaps most interesting mathematically is the admission of a complex state variable and a complex control conceptually, the application of control teclmiques to steer the microscopic equations of motion is both a novel and potentially very important new direction. 

Drain Opener. This reaction MUST be performed in an area of adequate upward ventilation, or at feast with the air flowing away from you. 

Until recently most industrial scale, and even bench scale, bioreactors of this type were agitated by a set of Rushton turbines having about one-thind the diameter of the bioreactor (43) (Fig. 3). In this system, the air enters into the lower agitator and is dispersed from the back of the impeller blades by gas-fiUed or ventilated cavities (44). The presence of these cavities causes the power drawn by the agitator, ie, the power requited to drive it through the broth, to fall and this has important consequences for the performance of the bioreactor with respect to aeration (35). k a has been related to the power per unit volume, P/ U, in W/m and to the superficial air velocity, in m/s (20), where is the air flow rate per cross-sectional area of bioreactor. This relationship in water is... 

Cyclone Pressure Drop. Typical cyclone pressure drops range from 250 to 2000 Pa. Most data are reported for clean air flowing through the cyclone and these data are conservative for design purposes. Many investigators have unsuccessfully attempted to relate pressure drops to inlet and oudet dimension ratios. Manufacturers caUbration curves or experimental measurements on cyclones of similar dimension should be used where possible. If a rehable experimental measurement is available, however, the pressure drop at other conditions can be estimated by first evaluating the constant i in equation 17. 

Some empirical equations to predict cyclone pressure drop have been proposed (165,166). One (166) rehably predicts pressure drop under clean air flow for a cyclone having the API model dimensions. Somewhat surprisingly, pressure drop decreases with increasing dust loading. One reasonable explanation for this phenomenon is that dust particles approaching the cyclone wall break up the boundary layer film (much like spoiler knobs on an airplane wing) and reduce drag forces. 

For air-flow control, the system may contain a control valve or damper that automatically or manually modulates system pressure drop. The dotted curves in Figure 4a on each side of the system resistance curve might represent operating extremes of the system resistance as the control valve is varied from maximum to minimum opening. These curves also intersect the fan curve at desirable operating portions of its range both for efficiency and flow control. 

Axial fans are classified as propeller, tube-axial, and vane-axial (Fig. 9). The choice of fan requited is determined by the resistance (static pressure) the fan must work against as well as the volume flow requited. PtopeUet fans usually discharge iato a plenum or directly iato the atmosphere. Tube-axial fans are usually mounted ia ducts as ia an air conditioning system. Vane-axial fans are also mounted ia ducts but feature a stationary guide vane on the discharge side that straightens the air flow to improve efficiency. Tube-axial fans can work at static pressures up to 623 Pa (2.5 ia. H2O) vane-axial fans can work up to 2000 Pa (8 ia. H2O). 

Fig. 9. Types of axial-flow fans where the dashed arrows denote the direction of air flow (a) propeller fans (b) tube-axial fans (c) vane-axial fans (17).

Variable Air Flow Fans. Variable air flow fans are needed ia the process iadustry for steam or vapor condensing or other temperature critical duties. These also produce significant power saviags. Variable air flow is accompHshed by (/) variable speed motors (most commonly variable frequency drives (VFDs) (2) variable pitch fan hubs (J) two-speed motors (4) selectively turning off fans ia multiple fan iastaHations or (5) variable exit louvers or dampers. Of these methods, VFDs and variable pitch fans are the most efficient. Variable louvers, which throttle the airflow, are the least efficient. The various means of controlling air flow are summarized ia Table 3. 

Device Air flow control Initial Cost Operating Noise... 

Two-speed motors are typically used on noncondensing services where the process is not sensitive to temperature but mostly seasonal or variable throughput of fluids in the air cooler requires some degree of air flow control. This is a simple, rather inexpensive means to control air flow when volume air flow is not critical. Typical motor ratings are 1800/900 rpm, although 1800/1200 rpm types are available. 

Air control louvers or dampers, popular in the past for air flow control, are used primarily for only very low scale air flow control. Louvers are used in many winterized heat exchangers in extremely low ambient temperature locations to retain and recirculate warm air in completely enclosed heat exchangers, sometimes in very compHcated control schemes. The use of louvers on the discharge side of a fan to control air flow is inefficient and creates mechanical problems in the louvers because of the turbulence. A fan is a constant volume device, thus use of louvers to control flow is equivalent to... 

An axial fan is a constant volume device. That is, a fan at a certain pitch moves a constant volume of air or gas at a constant speed and resistance (static pressure). If the density changes, the static pressure and wattage change, but the volume remains constant, ie, if the density (temperature) decreases, the static pressure and kW go up, but air flow remains the same. 

The heated polymer solution emerges as filaments from the spinneret into a column of warm air. Instantaneous loss of solvent from the surface of the filament causes a soHd skin to form over the stiU-Hquid interior. As the filament is heated by the warm air, more solvent evaporates. More than 80% of the solvent can be removed during a brief residence time of less than 1 s in the hot air column. The air column or cabinet height is 2—8 m, depending on the extent of drying required and the extmsion speed. The air flow may be concurrent or countercurrent to the direction of fiber movement. The fiber properties are contingent on the solvent-removal rate, and precise air flow and temperature control are necessary. 

The air jet textured yam process is based on overfeeding a yam into a turbulent air jet so that the excess length forms into loops that are trapped in the yam stmcture. The air flow is unheated, turbulent, and asymmetrically impinges the yam. The process includes a heat stabilization zone. Key process variables include texturing speed, air pressure, percentage overfeed, filament linear density, air flow, spin finish, and fiber modulus (100). The loops create visual and tactile aesthetics similar to false twist textured and staple spun yams. 

The operating pressure is kept low to reduce air consumption. To obtain high capacities, the disks spin fairly fast (up to 2 or 3 rpm) and this leads to thin cakes which give Htde resistance to air flow the only way to keep this flow within economical limits is to reduce the air pressure in the vessel. 

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