UNIVERSAL RELATIONSHIP BETWEEN COLLECTION EFFICIENCY AND THE CORONA POWER OF THE ELECTROSTATIC PRECIPITATOR

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1 Australia 006 Paper 5B UNIVERSAL RELATIONSHIP BETWEEN COLLECTION EFFICIENCY AND THE CORONA POWER OF THE ELECTROSTATIC PRECIPITATOR YAKOV S. KHODORKOVSKY & MICHAEL R. BELTRAN Beltran, In., U.S.A. ABSTRACT The basi priniples of aerosol and partile olletion using the eletrostati preipitation proess are well understood as the result of extensive laboratory and field testing arried out over almost a entury. Thanks to these tests the phenomena of ionization by orona disharge, partile harging and olletion, the influene of gas veloity distribution and gas flow turbulene, and so on, are now reasonably lear. The numerial predition of the main design parameters of the ESP is less advaned due to the very omplex flow phenomena whih are the result of the interation between a high-strength eletri field, a turbulent gas flow field, and the motion of partiulates. Therefore, to date the widely used ESP design approah is based on the systemati aumulation of performane data from existing devies. On the basis of these performane data one an evaluate the olletion effiieny, eletrial power and main design parameters of new ESP installations. Designs based on existing devies require experiene, talent and engineering intuition. The importane of these qualities annot be denied, nevertheless the design of an effetive and optimal industrial ESP has to be based on basi priniples and fundamental universal relationships that are still missing. In this paper we will disuss one of suh theoretially derived approahes whih desribes the relationship between olletion effiieny and the orona power of the Eletrostati Preipitator.

2 INTRODUCTION The use of eletrostati fores to remove dust from air by speial devies, so-alled eletrostati preipitators (ESP) has been known for many years as one of the most effiient tehnologies. The advantage of eletrostati preipitation is that energy is applied diretly the partiles to be harged and olleted, rather than to the gas stream, suh as happens in ylones and srubbers. The energy to aelerate the gas and partiles through a ylone or srubber is onsiderably higher than is required for eletrostati separation. Removal effiieny of the partiulates in an eletrostati preipitator is diretly proportional to the eletri power whih is supplied to the orona eletrodes to reate effetive ionization in the preipitation zone. The eletrial power onsumption determines mainly the operational ost of the gas leaning. Beause the initial and desired partile loading in the industrial air are known, the olletion effiieny of the ESP to be designed is therefore known at the first stage of designing. Hene, the relationship between olletion effiieny and orona power of the ESP allows an estimation to be made of the operational ost of the ESP at the first stage of the design. In the sixties of the last entury Harry J. White [] obtained an analytial relationship between preipitator partile loss p (penetration) and orona power: P = p exp K () Q where and P is the orona power in watts Q is the gas flow rate in ubi feet per seond K = 6.5 is a parameter H.J. White proves this relationship on the basis of performane data for a group of nine representative fly ash olletors installed in different plants of the United States, ranging from the Midwest to the Eastern and New England areas. It should be noted that the parameter K in Equation () is dimensional, beause the ratio P /Q is dimensional. The numerial value of the parameter K is obtained on the basis of performane data of very old ESP's and has to be proved useful for modern ESP designs developed more than half a entury later. In order to develop a new relationship between ESP olletion effiieny and the orona power we will disuss in this paper a new onept based on the theory of dimensional analysis and on a large number of laboratory tests [, 3]. This onept has allowed us to obtain a universal relationship between olletion effiieny and a new ESP nondimensional number, based on orona power, whih satisfies the onditions of similarity. APPLICATION OF THE THEORY OF SIMILARITY TO THE ESP PERFORMANCE Aording to the theory of dimensional analysis and similarity we will desribe the ESP performane using the following most important dimensional variables:

3 . Eletrial power supplied to the orona eletrodes of length unit kg m 3 P [ ] 3 L MT s m. Gas veloity U [ LT ] s kg 3. Gas visosity µ m s ML T 4. Cross-setional dimension of the olletor tube a (m) [L] 5. Distane from the olleting wall to the sharp edge of the orona eletrode d(m) [L] where L is the length sale T is the time sale M is the mass sale whih an be alled the primary or fundamental dimensions. From these five dimensional variables we seleted the following three variables with independent dimensions: power, gas veloity and side size. Aording to the Pi Theorem using five dimensional variables and three primary dimensions, we obtain two nondimensional parameters, so alled similarity numbers that an be used to desribe the ESP performane: P N p = () µ U a a a = (3) d On the basis of the law of similarity we an affirm that the olletion effiieny for two ESP's with onstant length and with different orona power, gas veloity, ross-setional dimension of the olletion tube, et., is equal to: when η = η (4) and P µ au = P µ au a d a = (5) (6) To verify the importane of these similarity numbers for ESP performane we use the experimental data obtained in Beltran's ESP test laboratory, varying, among others, the orona power, gas veloity, shape of tube ross setion (round, square and hexagonal), rosssetional dimension of the tube, the distane from the olleting wall to the sharp edge of the orona eletrodes and the number of energization edges. The tube length was l = m (4 feet). 3

4 As a result we obtained the universal relationship between olletion effiieny η and orona power similarity number N p at onstant numbers of a = a / d in the range from a =.3 to a =.7. A further useful orrelation is derived by plotting ESP olletion effiieny data versus ombined similarity number a N p. In Figure the experimental data of penetration values p% = 0-η% in perentages have been plotted against P µ au a at onstant length of the tube l = m. It an be seen that all the experimental data are in very good orrelation with the similarity number obtained on the basis of the theory of dimensional analysis and similarity. The obtained unique relationship an be desribed by the following mathematial expressions: P a 5 < p% 0 : log p% = exp 0.94log (7) µ au P p 5%:log p% = 9.7 log µ au a (8) CONCLUSION Numerous tests with laboratory ESP were performed, varying the orona power, gas veloity, shape of tube ross setion (round, square and hexagonal), ross-setional dimension, the distane from the olleting wall to the sharp edge of the orona eletrodes and the number of energization edges. On the basis of these experimental data and the theory of dimensional analysis and similarity, a universal relationship between olletion effiieny and the orona power of the ESP was obtained. This analytial formula allows an estimation to be made of the operational ost of the ESP by given leaning effiieny at the first stage of the design. REFERENCES. H.J. White, Industrial Eletrostati Preipitation, Pergamon Press, 963, 376 pp.. Y.S. Khodorkovsky and M.R. Beltran, "Drift veloity of Partiulates in an Eletrostati Preipitator: Comparison of Modeling with Experiments," Pro. of the th International Conf. of Air Pollution 00, Segovia, Spain, -3 July, Y.S. Khodorkovsky and M.R. Beltran, "Fundamental Priniples of Similarity with Referene to the Colletion Effiieny of an Eletrostati Preipitator (ESP)," Pro. of the 7th International Conf. on Eletrostati Preipitation, Sept. 998, Kyangju, Korea, p

5 Figure. Partile penetration p% versus the ESP similarity number P a µ au. 5