Deutsch equation

Several investigators have attempted to modify the basic Deutsch equation so that it would more nearly describe precipitator performance. Cooperman ( A NewTheoiy of Precipitator Efficiency, Pap. 69-4, APCA meeting, New York, 1969) introduced correction fac tors for diffusional forces arising from variations in particle concentration along the precipitator length and also perpendiciilar to the collecting surface. Robinson [Atmos. Environ. 1(31 193 (1967)] derived an equation for collec tion efficiency in which two erosion or reentrainment terms are introduced. 

This equation, which is called the Deutsch equation, has been shown to be a useful tool for estimating the performance of electrostatic precipitators. An interesting detail in the Deutsch equation is the exponent, which is equal to the collection efficiency of a laminar flow system. The equations based on laminar flow and turbulent flow can be assumed to be the extreme conditions, and the true situation is somewhere in between these two cases (see Fig. 13.1,5). 

A relatively simple modification of the Deutsch equation is obtained by assuming that the particle concentration near the collection surface is linearly... 

The collection efficiency of the wire-plate-type of electrostatic precipitator can be estimated by the widely used Deutsch theory [Deutsch, 1922]. To obtain the Deutsch equation, the following assumptions are made (1) because of the turbulent mixing effect, particle concentration at any cross section of the precipitator is uniformly distributed ... 

Example 7.2 Consider a dust-laden gas passing through an electrostatic precipitator. Assume that all particles have the same charge-to-mass ratio, q/m, and the electric field is uniform. Use the Deutsch equation to estimate the overall collection efficiency if the particle size distribution based on weight percentage (wt%) can be expressed by the mass density function, /M, as... 

Use the Deutsch-Anderson equation to calculate the efficiency of the precipitator. Also, use the modified Deutsch equation with a range of exponents varying from 0.4 to 0.7 (in increments of 0.05) to calculate the efficiency of the electrostatic precipitator. 

The second exponent (in this, the so-called modified Deutsch equation) provides a more accurate prediction of performance at high-efficiency levels but can become too pessimistic in certain situations. Typical values of m range between 0.4 and 0.7, with 0.5 as the norm. This and the previous equation are employed in the solution that follows. 

The quantity ( BpL/AcVfl) in the Deutsch equation carries additional significance. It is essentially the ratio of the collecting electrode surface area over the gas flow rate. Thus, for identical values of Upy, similar particle collection efficiencies will be obtained in two different size precipitators if the value of (BpL/AcVz) is identical. This provides a basis for precipitator scaleup. A survey of the volumes of electrostatic precipitators needed for required gas flow rates is given in Figure 7.3.9 (Soo and Rodgers, 1971). 

The Deutsch equation is based on a highly simplified situation where particle capture is dependent on its entering the wall region in a probabilistic sense. It does... 

We consider now briefly one of the effects not considered in the derivation of the Deutsch equation (7.3.42), namely the presence of a particle size distribution. Let J rp) be the particle size density function and let f tp) be the corresponding distribution function of the dust cloud entering the precipitator. Then... 

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