Input power

The effect of increasing gas holdup on the gas-liquid interfacial area (a) is often ambiguous. This is a special situation for the STR because the power input determines the bubble diameter and hydrodynamics (Bouaifi et al., 2001 Nocentini et al., 1993), while the gas flow rate has a driving influence on bubble dynamics in other reactor designs (to be discussed in other chapters). In other words, gas holdup information does not necessarily contain any (quantitative or qualitative) information about bubble diameter and interfacial surface area for STRs such that an increase in gas holdup does not necessarily increase a (Moilanen et al., 2008). However, gas holdup is still reported as an indicator of hydrodynamic performance, gas distribution (Boden et al., 2008), and gas-liquid contacting (Garcia-Ochoa and Gomez, 2004). 

Gas-liquid mass transfer correlations, however, typically fail to reflect STR hydrodynamics and predict an increase in mass transfer with an increase in the superficial gas velocity. If these correlations are used improperly, such as during scale-up or outside their representative size and operating conditions, inaccurate estimates will result. In other words, the correlation form is simply incapable of representing the hydrodynamic situation and fails to decouple events occurring due to the superficial gas velocity and those occurring due to the power concentration. The current state-of-the-art ki a correlations with respect to STR conditions will be described in detail in Section 6.9, but it is important to realize that a correlation that is capable of communicating a more complete hydrodynamic picture still remains elusive. 

The power dissipation influence on the liquid-phase mass transfer coefficient (/cl) is highly debated in STRs, especially at higher power densities. The slip velocity model and eddy turbulence model have been used to explain mass transfer, but they come to different conclusions with respect to power. The slip velocity model predicts a decrease in mass transfer with increasing power dissipation while the eddy turbulence model predicts an increase. Linek et al. (2004) postulate that the main reason for the confusion stems from the miscalculation of They investigated different measurement methods and models used by others and concluded that the slip velocity models were underestimating and, hence, 

Superficial gas velocity does not necessarily control the interfacial area or liquid-phase mass transfer in STRs directly, but influences the gas dispersion efficiency and power dissipation rate. It is very difficult to disconnect the superficial gas velocity from the power concentration in STRs, even under experimental settings. Thus, most ki a correlations include the power concentration and superficial gas velocity as variables with the power concentration having a larger role than the superficial gas velocity this will be discussed in more detail in Section 6.9. 

For example, with regard to the hot-spot theory outlined above, it would clearly be useful to understand the effects of changing the solvent, or the ambient temperature and at which the reaction was carried out. Furthermore, the design of ultrasonic probe systems allows for ready variation of the power input and occasionally variation of the frequency of the output. Hence, there are a number of factors that must be bom in mind when setting up a viable system. For this reason, the following section is devoted to a discussion of the effects of extrinsic variables on the sonochemical process. 

The credibility of the hot spot theory is reinforced by its ability to account for the effects of extrinsic variables on the sonochemical process. Nevertheless, the frequency of ultrasound applied is surprisingly irrelevant to the course of the reaction. Cleaning baths produce a range of frequencies which often vary from day to day, or even during the course of a reaction, and yet this has no discemable effect on the sonochemistry observed. 

Experiments have shown that aqueous sonochemistry is unchanged over the frequency range in which cavitation occurs i.e. 10 Hz to 10 MHz [22]. Since there is no direct coupling of the sound field with species on a molecular level, changing the frequency of the sound input simply alters the resonant size of the cavitation bubble. The effect of this over the range of interest is negligible. It should, however, be noted that although there is both an upper and a lower limit to the frequencies at which cavitation will occur, the band of frequencies used for sonochemistry lies well within these limits. 

It has also been shown that ten times more power is required to make water cavitate at 400 kHz than at 10 kHz. This effect is due to the increased power losses which occur as the rate of molecular motion within the liquid increases. Hence, there is no advantage to be gained from using frequencies higher than those which can be obtained using a simple cleaning bath. 

Conversely, changing the power input to the transducer alters the volume of liquid which can be forced to cavitate and dramatically affects the observed sonochemical rate. Hence, a number of reactions which give low or erratic yields in cleaning baths, produce high yields when a probe transducer is used, as a result of the ability to control the acoustic intensity input. There is a school of thought that an optimal value for the energy input exists. However, Luche has reported that the rate of the Barbier reaction between an alkyllithium and an aldehyde increases continuously as the voltage input to the transducer is increased from 60 to 160 V (Fig. 5) [23]. 

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The emitted beam of coherent radiation is narrow and can be focused into a very small area. This means that the density of radiation that can be delivered for any one pulse over a small area is very high, much higher than can be delivered by conventional light sources operating with similar power inputs. 

Eigure 6 enables a comparison to be made of kj a values in stirred bioreactors and bubble columns (51). It can be seen that bubble columns are at least as energy-efficient as stirred bioreactors in coalescing systems and considerably more so when coalescence is repressed at low specific power inputs (gas velocities). 

From equation 23, it can be seen that the higher the power input per unit volume, the lower the oxygen transfer efficiency. Therefore, devices should be compared at equal transfer rates. AH devices become less energy efficient as rates of transfer increase (3). 

P = power input P = electrical loss P = induced power and P = thermal loss. 

Wetox uses a single-reactor vessel that is baffled to simulate multiple stages. The design allows for higher destmction efficiency at lower power input and reduced temperature. Its commercial use has been limited to one faciHty in Canada for treatment of a complex industrial waste stream. Kenox Corp. (North York, Ontario, Canada) has developed a wet oxidation reactor design (28). The system operates at 4.1—4.7 MPa (600 to 680 psi) with air, using a static mixer to achieve good dispersion of Hquid and air bubbles. 

In practice, triple alloy is added to a clay graphite cmcible in a refractory-lined vacuum-tight chamber (Fig. 14). Power input is controlled by adjusting the appHed voltage until the charge is melted. A refractory cover is placed over the cmcible and sealed with sand. The furnace cover contains an opening which mates with a port connecting to a condenser. 

Performance is described in a variety of ways depending on the desired appHcation of the LED. The power efficiency, P, of a LED is the ratio of the output power to the power input to the device, and can be expressed as... 

Pumping, Velocity Head, and Power. Mechanical mixers can be compared with pumps (1) because they produce circulating capacity and velocity head H. The analogy between a pump and mixer can be appreciated by comparing a pumping loop with a mixing tank (Fig. 2). Power input P to a pump is represented by... 

Eig. 11. Power saving for variable speed drives. Power input for variable speed adjusts with flow to naturally match the frictional losses. FIC = flow... 

The heated-thermocouple anemometer measures gas velocity from the cooling effect of the gas stream flowing across the hot junctions of a thermopile supplied with constant electrical power input. Alternate junctions are maintained at ambient temperature, thus compensatiug for the effect of ambient temperature. For details see Bunker, Proc. Instrum. Soc. Am., 9, pap. 54-43-2 (1954). 

The power input to a pump is greater than the power output because of internal losses resulting from friction, leakage, etc. The efficiency of a pump is therefore defined as... 

Pump efficiency = (power output)/(power input) (10-53)... 

When making a selection, the stall-out condition, which develops when the fan cannot produce any more air regardless of power input, should be considerecL... 

FIG. 11-82 Typical capacity and power-input curves for reciprocating compressor. 

Subsequently, Calvert (R-19, p. 228) has combined mathematical modehng with performance tests on a variety of industrial scrubbers and has obtained a refinement of the power-input/cut-size relationship as shown in Fig. 14-130. He considers these relationships sufficiently reliable to use this data as a tool for selection of scrubber type and performance prediction. The power input for this figure is based solely on gas pressure drop across the device. 

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