Plume characteristic scales

It is very useful to minimize significant variables by expressing the equations in dimensionless terms. To do this we need a characteristic length to normalize z. If we had a finite source diameter, D, it would be a natural selection however, it does not exist in the point source problem. We can determine this natural length scale, zc, by exploring the equations dimensionally. We equate dimensions. From Equation (10.22), 

Incidentally, if we were examining a line source in which the source strength would need to be expressed as Q, i.e. energy release rate per unit length of the linear source, Equation (10.23) could be reexamined dimensionally as 

This is the characteristic length scale for a line plume. 

To complete the point source normalization, we determine, in general, a characteristic 

Solutions for a Gaussian profile, with Equation (10.1) for an axisymmetric point source, and for a line source 

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The sample data presented in this chapter were collected for fairly simple flow conditions. The flow was a unidirectional open-channel flow without large-scale flow meander, and the release condition was isokinetic in the direction of the bulk flow. Thus, chemical filaments were advected by the bulk flow in the stream-wise direction, while turbulent mixing acted to expand the plume size and dilute the chemical concentration. Changes in the flow and release conditions lead to significant variation in the plume characteristics and structure. 

For a new process plant, calculations can be carried out using the heat release and plume flow rate equations outlined in Table 13.16 from a paper by Bender. For the theory to he valid, the hood must he more than two source diameters (or widths for line sources) above the source, and the temperature difference must be less than 110 °C. Experimental results have also been obtained for the case of hood plume eccentricity. These results account for cross drafts which occur within most industrial buildings. The physical and chemical characteristics of the fume and the fume loadings are obtained from published or available data of similar installations or established through laboratory or pilot-plant scale tests. - If exhaust volume requirements must he established accurately, small scale modeling can he used to augment and calibrate the analytical approach. 

If a plume is photographed or measured by a device having an averaging time of the order of a fraction of a second, the appearance will have a sinuous form. The sinuosities appear to increase in amplitude and characteristic wavelength as one observes at greater distances from the source. Generally, eddies of aU scales can be expected to be present in the atmosphere but not necessarily to an equal degree. Near the source, the diffu-... 

In a third study, single unit recordings from the moth Heliothis virescens placed in a wind tunnel corroborated the previously described results by showing how well single neurons follow the fine-scale temporal characteristics of a natural odor plume (Vickers et al., 2001). Also in this study it was clear that the occurrence of a stimulus over time heavily influences the temporal structure of the response to a given stimulus. Both stimulus intensity and dynamics of the odor plume had an effect on the time course of the PN spike pattern. Furthermore, no wave-like periodicity in PN spiking could be observed and PN spike frequency did only rarely match the frequency range of local field potential oscillations that has been reported from moths (M. sexta Heinbockel et al., 1998). 

The response time of a chemical sensor should be appropriate for the application for which it is intended. For example, if the sensor is used to monitor acutely toxic (lethal) substances in the workplace, the response time should be faster than the biological/ toxicological re.sponse — perhaps only a few seconds. On the other hand, some applications, such as monitoring the spread of a chemical waste plume underground, have characteristic time scales of days to years, permitting utilization of sensors that respond more slowly. 

Many of the physical characteristics of the atmosphere, such as wind, temperature, cloud cover, humidity, and precipitation, are easily perceived. Sometimes, chemicals in the atmosphere also can be observed, as in smoke plumes and smog, and their physical transport tracked downwind just as downstream transport of substances in a river can be measured. Other atmospheric processes are less apparent to the unaided observer, however, occurring either on the microscopic scale of a chemical reaction, or on a global scale, or at high altitudes. Such processes may be detected only by instrumentation on satellites or some high-altitude aircraft. 

Figure 2.12 Characteristic dispersion mechanisms in canopies in the case of multiple buildings (see also Figure 2.3) On discrete/obstacle scale (for well-separated buildings, b/d 1) plume dimensions less than obstacle width.

Castello-Branco MASC, Schwerrtdfeger K (1994) Large-scale measurements of the physical characteristics of round vertical bubble plumes in liquids. Metall Mater Trans B 256 359-371... 

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