NUMERICAL COMPUTATION OF PARTICLE TRANSPORT IN TURBULENT FLOW FIELD IN ELECTROSTATIC PRECIPITATOR

Transcription

1 NUMERICAL COMPUTATION OF PARTICLE TRANSPORT IN TURBULENT FLOW FIELD IN ELECTROSTATIC PRECIPITATOR Jenő SUDA, István BERTA, Gergel KRISTÓF +, Tamás LAJOS # Ph.D. Student, + Assistant, # Professor, Department of Fluid Mechanics Technical Universit of Budapest, Hungar, H- Budapest, Bertalan L. u Tel.: (+36-1) , Fa: (+36-1) , suda@simba.ara.bme.hu Professor, Department of High Voltage Engineering and Equipment Technical Universit of Budapest, Hungar, H- Budapest, Egr J. u. 18. Tel.: (+36-1) , Fa: (+36-1) , berta@ntb.bme.hu Summar The paper proposes a numerical model for computing the particle transport in turbulent boundar laer flow in a model-scale electrostatic precipitator (ESP). The numerical model can be used for calculation of 2D turbulent flow field, the streamlines of the dust phase, the dust concentration distribution and the grade efficienc in the ESP channel. The results of calculations with variable parameters (e.g. dust particle size, inlet gas velocit and electric field strength due to space-charges) demonstrate both the effect of the turbulent diffusion and the effect of inhomogeneous electric field on the particle motion. 1 INTRODUCTION Electrostatic precipitators (ESPs) are etensivel used for decontaminating of industrial gases and for air cleaning, since this dust separation method ensures high dust collection efficiencies. This precipitation technolog is based on the effect of electrostatic forces acting on the suspended dust particles in a gas stream. B investigating the turbulent transport of dust phase suspended in gas the precipitation process can be better understood. Describing and computing the dust particle motion in the turbulent flow field of an ESP channel needs several considerations in electrostatics and in fluid dnamics. The precipitation process can be separated into three main phases: particle charging, transport, and collection. The dust particles entering the precipitator channel reach their saturation charge ver quickl charging b the phenomenon of corona discharge. The Coulomb- or separation forces increase proportionall with particle charge. The charged dust particles move across the channel due to electric field between the electrodes. The inhomogeneous electric field of corona wires eerts great influence on the particle motion. Besides the electrostatic field of corona wires and collecting electrodes two additional electric fields eist due to the charged ionic clouds and to the charged dust phase moving in the precipitator channel. This comple electric field acts on the charged dust particles moving in the turbulent gas stream. This paper is focused particularl on the numerical modelling of turbulent rediffusion of dust particles toward the central plane of the channel. Limited numbers of theoretical models are available in the literature for following the turbulent transport of the suspended dust. One possibilit is the computation the particle trajectories. This method is often called as particle tracking model (PTM). Application of PTM with a turbulent transport model requires an appropriate setting of the time-dependent turbulent velocit field. Such model is proposed b RIEHLE [6], in which the flow field is defined as a sum of the main field and a randoml fluctuating turbulent field. Application of

2 k-ε model in a two-dimensional fluid dnamic simulation program is another possibilit of determination of turbulent transport process (see GALLIMBERTI [9] and MEDLIN et al [5]). In the case of a high Renolds-number flow the streamwise diffusion is neglectable and a parabolic approimation of the governing equations can be applied. In this paper the flow field is described through parabolic tpe boundar laer equations. This approimation has the advantages of particularl quick computation and low memor requirements. Structure of dust phase flow is usuall measured with the help of optical methods because the presence of high voltage electric field causes severe difficulties in the placement an kind of test probes in the ESP channel. Eperimental data are available b WHITE [1], RIEHLE [4], [7] and b SCHMIED et al [8] showing the spatial distribution of the suspended dust. We used the parameters of an eisting model precipitator for definition of problem geometr in our simulation model, proposing further eperimental validation of the computer code. Horizontal cross-section of the model precipitator is outlined in Fig.1. 4 mm 2s IN OUT CE DE L IN 2c L CE L Diffuser =37 mm L=6 mm L Confuser Fig.A. Model-scale ESP unit cross-section. Channel half width s= mm; precipitator length L CE =3 mm; corona wire radius r DE =.5 mm; wire distance 2c=5 mm The tpical wire-smooth plate tpe model ESP used for lab-scale eperiments has seven discharge (corona) electrodes (DE) in one ESP channel. The grounded collecting electrodes (CE) are parallel smooth plates. 2 ELECTRIC FIELD The particle collection in electrostatic precipitators is largel influenced b the characteristics of electric field (Fig.2.) in the interelectrodic space, which influences almost all the phsical processes that occur in electrostatic precipitation. The electric field determines the characteristics of corona discharges, and therefore the ionic charge flu and the strength of local electric field influences the particle charging and their saturation charge.

3 E [kv/cm] 1 E [kv/cm] Eelectrostatic 44 Electrostatic field strength Espacecharges Electrostatic field strength space-charges including Fig.B. Influence of additional electric field strength due to the ionic and dust space-charges on the electric field strength distribution in the interelectrodic space of the first 2 corona wires. The calculated surface plots of electric field strength distribution E [kv/cm] in Fig.2. illustrate that the additional field strength caused b ions and dust particles plas an important role TURBULENT 2D FLOW FIELD The gas flow within the ESP channel can be described b means of continuit equation and momentum conservation law. The continuit equation for incompressible medium is: + = (1) B neglecting the electrostatic forces acting on the gas phase and the interaction with the dust phase a simple boundar laer equation can be applied for determining the velocit field: v v V dv v ν + = + t (2) d The turbulent viscosit ν t is evaluated on the bases of the miing length model (see SCHLICHTING [2] ). Disregarding the streamvise diffusion of the dust phase the concentration c can be computed with the help of a parabolic tpe transport equation: v c c ν t + v = Sc t ( ) c c WTH (3) where WTH refers to the theoretical migration velocit of Deutsch (theoretische Wanderungsgeschwindigkeit: w th in RIEHLE [4] and WHITE [1]). WTH = Qp Cu 3πµ d E p (4)

4 Q p is the saturation charge of spherical dust particle with a diameter d p, Cu is the Cunningham correction factor, Sc t turbulent Schmidt-number and E the component of electric field strength, perpendicular to the channel center line. Equation (1)-(3) can be solved b application of an straightforward method, so obtaining a laer b laer solution for v, v and c marching along the ais ( see e.g. FLETCHER [3] ). Since the suspended dust particles in gas are regarded as continuum, its flow can be characterized with stream function. Equation (3) can be written in the following alternative form: div r j tot = (5) where r j tot is the total flu vector of the dust phase: r j c v t tot = gradc + c ( WTH ) ν (6) Sc t On the bases of eq.(5) we can define the stream function as: r j tot r, j = tot = (7) Tangents of the streamlines of the dust phase were defined to be parallel with the j tot total flu vector, that is =const lines visualize the dust phase motion presented in Ch.4 below. 4 RESULTS A FORTRAN computer code have been developed for the numerical solution of the two-dimensional transport problem. The average CPU time required to solve the 3 node problem on a PC-486 is less then one hour V ESP channel length, C ESP channel length, ESP channel half width, ESP channel half width, V [m/s] =5 mm =1 mm = mm =2 mm =25 mm =3 mm Fig.3. Velocit field distribution, v [m/s] C [ g/m3 ] =5 mm =1 mm = mm =2 mm =25 mm =3 mm Fig.4. Concentration distribution, c [g/m³] Velocit profiles of a tpical boundar laer flow can be seen from the graphs of Fig.3. for the half width of the ESP channel. The concentration contour plots of Fig.4. show the migration of the dust phase toward the collecting plate.

5 d p =,5 [µm] ESP channel length, Collection efficienc, [%] Collection efficienc ESP channel length, V= [m/s], dp=.5 [micron] Fig.5. Dust streamlines, contour plot of Fig.6. Collection efficienc, η [%] 9.2 Fig.5. shows the contour plot of the stream function. These contour lines are the streamlines of the dust phase moving in the ESP channel from the inlet cross-section toward the outlet cross-section. Particles, in those streamtubes that reach the wall, were precipitated from the gas flow. Dust particles, indicated b the streamtubes passing through the outlet, are not deposited in the ESP. B neglecting the re-entrainment of particles from the wall the collection efficienc η can be calculated from the dust concentration distribution in each cross-section along the precipitator length as shown in Fig.6. Dependence of the precipitation process on various parameters was investigated with the help of the present numerical simulation. The results are shown in the Figs 7-8. The inlet dust concentration profile was constant c inlet =1 [g/m³]. Effect of the near-wall boundar laer on the transport of solid phase is clearl seen from the curvature of the streamlines. Turbulent rediffusion of the suspended dust toward the smmetr plane of the channel also can be seen from the contour plots of Figs 7-8. v =2 [m/s] d p =,5 [µm] ESP channel length, ESP channel length, v =[m/s] d p =1 [µm] ESP channel length, ESP channel length, v =1 [m/s] d p =5 [µm] Collecting ESP channel length, Collecting ESP channel length, Fig.7. Influence of inlet gas velocit (v ) on the dust streamlines (d p =1[µm], inhomogeneous electric field strength E ) Fig.8. Influence of dust particle diameter (d p ) on the dust streamlines (v inlet =[m/s], inhomogeneous electric field strength E )

6 As shown in Figs 7-8. the presented various parameters of inlet gas velocit and the dust particle diameter has a well pronounced influence on the collection efficienc. The precipitation of particles strongl depends on the development of the boundar laer. In the case of the highest velocit flow (2 [m/s]) the dust particles pass through the channel rapidl due to the increased convective transport. As can be seen in Fig.8. the collection efficienc increases with increasing particle size. Particles of diameter d p =5 [µm] are collected alread within the first third of the precipitator channel because of their relative high saturation charge. 5 CONCLUSIONS It has been shown, that the solution of the turbulent transport equation and turbulent boundar laer equation is a fast and effective method for 2D modelling of the electrostatic precipitation process. Influence of dust particle size and the gas velocit on the particle transport process were shown through the mapping of the streamlines of the dust phase. The comparison of eperimental and theoretical results needs further investigation. REFERENCES 1. White H.J. (1963), Industrial Electrostatic Precipitation Addison-Wesle Publishing Compan, Inc. 2. Schlichting H. (1968), Boundar-Laer Theor 6th Edition, McGRAW-HILL 3. Fletcher C.A.J. (1991), Computational Techniques For Fluid Dnamics 2nd Edition, Volumes I-II Springer-Verlag 4. Riehle C. (1992), Bewegung und Abscheidung von Partikeln im Elektrofilter Dr.-Ing. Thesis, Universit of Karlsruhe (TH) 5. Medlin A.J. et al (1996), An Efficient Pseudo-transient Solution Method for Monopolar Corona with Charge Advection and Diffusion in Proc. 6th International Conference on Electrostatic Precipitation (Budapest, Hungar) Riehle C. (1996), Precipitation Modelling b Calculating Particle Tracks in Simulated Flow Fields in Proc. 6th International Conference on Electrostatic Precipitation (Budapest, Hungar) Riehle C. (1996), Measuring and Modelling Mass Flues in ESP in Proc. 6th International Conference on Electrostatic Precipitation (Budapest, Hungar) Schmid H.J., Umhauer H. (1996), Investigations on Particle Dnamics in a Plate Tpe Electrostatic Precipitator using Double-Pulse Holograph in Proc. 6th International Conference on Electrostatic Precipitation (Budapest, Hungar) Gallimberti I. (1997), Recent Advancements in the Phsical Modelling of Electrostatic Precipitators in Proc. 8th International Conference on Electrostatics (Poitiers, France) 1-3.