ENGINEERING RESEARCH INSTITUTE UNIVERSITY OF MICHIGAN ANN ARBOR INTERIM TECHNICAL REPORT THE PREDICTION OF DUST REMOVAL IN AN OIL-BATH AIR CLEANER SEYMOUR CALVERT Project 2233-4-T DETROIT ARSENAL, DEPARTMENT OF THE ARMY CONTRACT NO. DA-20-089-ORD-36962 July, 195

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ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN THE PREDICTION OF DUST REMOVAL IN AN OIL-BATH AIR CLEANER In order to evaluate the applicability of our present knowledge of particle dynamics to the problem of predicting the performance of an air cleaner, several calculations have been made. These calculations predict the efficiency of dust removal as a function of particle size in a Donaldson TrayType Cleaner operated at full capacity (model No. A 1411.at 600 cfm). While the computational methods are somewhat approximate they have been applied to various aerosol collection problems in the past with fair accuracy and are sufficiently reliable to serve as a guide for experimental design. MECHANSM OF DUST REMOVAL The mechanism of collection, which is the basis of the methods of prediction, is impaction due to the inertia of the particles. The physical situation consists of a moving dust-carrying air stream striking an obstacle and then changing direction to move around the obstacle. The dust particles tend to continue to move toward the obstacle because of their inertia, but the drag force exerted on them by the turning air stream tends to move them around the obstacle. If a particle has sufficient inertia and the drag force is insufficient to move it around the obstacle, it will strike the obstacle and presumably stick to it. Thus large particles are more easily removed from the air stream than small ones. It will be seen later that for any dust-removal system there is a narrow band of particle diameters above which all particles are removed and below which no particles are removed. Since this study is primarily concerned with oil-bath air cleaners, the Donaldson cleaner was chosen for the subject of the predictions as it is representative of the class. The method of analysis used here is applicable to all cleaners of this type. It should be noted that the function of the oil is assumed to be merely that of cleaning the impingement surfaces and is assumed not to affect the dust-removal process. It has also been assumed that dust concentration does. not affect the mechanism of removal. These points remain to be evaluated by experiment. * 1 ~ -— ~ - ~-~- - - - - - I

\ \J^\ ^ THE PREDICTION OF DUST REMOVAL.... ^ ' ^(IP Report No. B-f) X7. July, 1954 Computational methods are developed to predict the efficiency of dust G" removal in the impngement zone of a Donaldson Tray-Type Cleaner operated at full capacity. A These computational methods ' with those of OtanrxaHamgxx~m W. E. Ranz- and J.. W.ong, "Impaction of Dust and SrSoke Particles on Surface and 3Bodr Co11cotors", Inddstrial and Engineering Chemis-... " ".... - ~. ~ ~~it try, kh 1371 (1952). Although both methods are somewhat approximated, Ix is concluded that each is suitable for the prediction of trends and a the effect of changes in design. The basis Ior the computational methods' of prediction Fombf is derived from the mechanismr 'of collection from which it can be assummed: that if a particle in a moving dust;-carrying air stream has sufficient inertia and the drag force ~xic X is insufficient to move it around'an obstacle, the particle will strike the obstacle and presumably stick to it. As it is representative of the: class, the Donaldson cleaner was chosen for the subject of predictionsB, NeitheVPQil:no' 3ust concentra^en were assummed to affect-the mechanism of.removal, JiTd;Since the oil-bath cleaner is arbitrarily divided into two zones, impingement and packed, the performance of each is predicted separately. The impingement zone is that in which the entering air impinges upon and is turned by a baffle plate. Assuming the premise that the trajectory of a particle in a turning air stream may be approximated as an angular rather than a curved turn, calculations were made of the distance the particle would travel before being stopped by the air resistance. If this distance was at least equal to the particle's distance.from the collector baffle, the particle

chosen WAS assummed to have struck the baffle. Two arbitrarily/loci of points were Etas mmused to represent the places from which particles were thrown ina flow of streamlines and ir 1 sx-t a particle trajectories with a vena contracta as occurs in flow'through an orifice. The equation of motion of a particle thrown into still air was obtained by equating the forces on a particle to its mass times acceleration. Since its effect was small, the force of gravity was neglected a2m3 Evaluations of drag coefficient for turbulent flow, air density, particle density, and poise were w'W introduced into the. -':.... - were equation. By rearrangment and integration, equations xs derived by which the values of velocity and penetration distance versus time e. could be computed. By using these and an evaluation of maximum penetration time at 0.005 seconds, total penetration and fraction of stream impinging were computed. A plot of percent removal of dust versus particle size yielded the conclusion that all particles larger than 15 microns are removed and no particles smaller than about two' i'irons aTe-.removeed. By applying this data- to the removal of AC Test Duit, _.x'"i x xkkX'x the efficiency of removal was predicted at 4i-:percet for AC Fine Dust and 79.3 percent for AC Coarse Dust. These figures compared favorably with the prediction of impingement-zone efficiency by use of the Ranz and Wong method in which the impingement section is considered as a cylindrical jet fIllowed by a rectangular jet. The calculation: of~;paokedzone.eperformano. was carried out to indicate the difference between the packed zone and the impingement zone. By employing the data of Ranz and Wong on cylindrical collector efficiency, it was predicted that the packing would remove approximately 90 percent of AC Fine Dust and 96.5 percent of AC Coarse Dust. The results showed.that the impingement zone will take out the relatively large particles and no' reat increase in efficiency should be expected; and that the packed zone is capable of removing the small particles and can be modified to attain increased efficiency.

F - Intruents up to 300 PSIG Designs Purchase Piping Total esignatian Location Inastallati1c X... | e Coat Tuinig Direct Co, TI Direct 20 10 30 P Direct 20 10. 35 TI Board 20 10 20 50 PI Board 20 20 50 I 'Board 80 0O 20 1l0 LI Direct 225 100 50 375 TR | EBoard 175 90 35 400 PR Board 250 125 60 35 TR Boad 150 75 75 300 LLIR Board 275 150 80 505 TRC | Board 750 325 12 1200 PRO Board 525 250 150 925 PRC Board 1 6 32 150 1125 LLIRC Board 725 300 150 1175

-12 -6. Ppingts 1. Carrbo steel Cost of talues Purchase cost of ppe valves & fittig o6I Purchase cost Istld direct cost *40. 2. SS & ally. Cost of alves Purchase cost of pipe valve & fitting Pmrchase cost - TIstaled cost diret H8. tactural Costs 1. Sbstructures Net Excavation - Machine * 15o0/u yd Hand 6.00/cr yd ackfill 1.80/cu yd Bo rof'l i.OO/cu yd. 2. Fromdation Colun pedestals & footers 75.00/cu yd Walls & footers 95*00/cu yd 3; Superstructure concrete Uifirilshed floor labs.75/8q ft 10" - 00' PS ft Xnfirnished floor slap 45/q ft 6" - 200 PS ft Misc concrete. 10000/c yd

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN The oil-bath air cleaner is arbitrarily divided into two zoneso One zone is that in which the entering air impinges upon and is turned by a baffle plate. The other zone is that in which the air passes through layers of smallsize packing. The impingement zone will be considered first and its performance will be predicted by two different methods: one derived by us and the other by Ranz and Wongl. Next, the packed zone will be considered and its performance predicted from the data of Ranz and Wong. IMPINGEMENT ZONE The first method of prediction of dust-collection efficiency is derived from the premise that the trajectory of a particle in a turning air stream may be approximated as that which it would follow if the air made an angular rather than a curved turn. The particle is assumed to be thrown into still air at a given velocity and the distance it would then travel before being stopped by the air resistance is calculated. If this distance is at least equal to the particle distance from the collector baffle, the particle will strike the baffle. Figure 1 is a sketch of the impingement section and illustrates the streamlines and particle trajectories which are being considered. While the actual path of a particle might be like the curved dashed line from point 1 to point 5, we will assume that it is thrown abruptly from points 1 and 3 and that the distances 1-2 and 3-4 are equal to the particle's penetration into still air if thrown at the same velocity as at 1 or 3. It will be noted that the air streamlines are drawn (free hand) with a vena contracta as occurs in flow through an orifice. This has been observed in a cutaway model demonstrated for us by the Donaldson Company. Lines A-C and B-C are arbitrarily chosen as the loci of points from which the particles are thrown. In outline, the following are the steps inthismethod of calculation (which will be described in detail below): 1. Calculate the distance of penetration for particles thrown into still air with initial velocities equal to that at the end of the vertical tube and that at the vertical plane passing through the vena contracta (a perpendicular passing through point C). 2. Compute the penetration distance for particles of various diameters going around the first bend (A-C). -2 -

FRACTION OF FLOW ENCLOSED BY STREAM LINE 0 01 _12 466.A, A B Fig. I Air and Dust Flow in the Impingement Section of an Air Cleaner

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN 3. Compute the penetration distance for particles going around the second bend (B-C). 4. Add the penetration on the second bend to R times the penetration on the first bend. R is the ratio of the average distance between streamlines downstream of the second bend to the average distance between streamlines downstream of the first bend. In the example shown in Fig. 1, R is approximately 1/2. 5. Compute the fraction removed for each particle diameter. This is the ratio of total penetration distance to the width of the stream downstream of the second bend. In other words, if particles of a particular diameter will move half the width of the air stream half the original number will strike the baffle while-the other half will not go far enough to do so. Derivation of Equations for Penetration Distance The equation of motion of a particle thrown into still air is obtained, by equating the forces acting on a particle to its mass times acceleration. F = ma = iDP2Cpu2 Fg (1) 8 where: F = force m = mass (g) a = acceleration (cm/sec2) DI = particle diameter (cm) C = drag coefficient p = air density (g/cm3) u = velocity (cm/sec) Fg = force of gravity The force of gravity can be neglected since its effect is small, and the drag coefficient for turbulent flow evaluated as:2 18.5 C = 1O8 (for 2 < Re < 1000), (2') Re DpUP where: Re = Reynolds number -= ~-, =u = air viscosity (poise). 4, ~~.

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN Then, Then: - 18p2 18.5 p()6 u2 du =F. = -~m~~ ---- (3) 8 (Dup ). dt m = particle mass = Dp, (4) where: pp = particle density. Substitutions into Eq. (3) and evaluation of p =.069 gm/cc, I 0.00018 poise and pp = 2.6 gm/cc yields du dt (DP)l'( where: D = particle diameter in microns. A rearrangment of Eq. (5) gives: du- 5.07 x 103 dt (6) (DP ( )1. J and integration of Eq. (6) gives: uo4 4 2 x= 2 103] ta] (7) L (D)i.8 I To find the displacent (penetration), Eq. (7) must be integrated and is first put in the form of an indefinite integral. -0.4 f2^ x 1+ C( (Dp) at t =, u = u, and C1 = uo- 0.4 0o 4. (D) = At +C1, (9) ~ - --

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN where: x = distance (cm), A 2.03 x 103 (D )1'6 u = original velocity (cm/sec). Then: dr = (At + C1)-f (10) and dt Adx = (At + C1) - Adt. (11) Integration of Eq. (11) gives: / x 1I -.4 -0.4 -1.5 [2.03x10] [1t- (U ),( p -1.5 1=5 which is identical with 0.8 0.6 2.03 x 103 U - L(J - 5 -(1 3) The equation of motion for laminar flow is developed similarly with the difference being that F = 3xTuDp = ma =.d (14) 6 dtThe end results are: u [1.24 6 x 1051 uO L Dp.J (15) and 1,26 x 10.26 o 1 [1246 x 105] 140 Uo~~~~. (16) By using, Eqs. (8) and (12) (or (13)) for Reynolds numbers greater than 2 and Eqs. (15) and (16) for Reynolds numbers smaller than 2, one can compute values of u and x versus t. Figure 2 is a plot of the results of such computations for an initial velocity of 100 feet per second. Figure 3 is a plot of u and x versus time for uo = 75 feet per second and Fig. 4 is a plot of x versus time for Uo = 50 feet per second. ^~ ~ ~ ~ ~ ~~~~~~- 6 -~....

100 ~~~~~~100.^~~~~~~~~~~~~~~~~~~~~~R..n2 5~~~ 40p DISTANCE VS. TIME — I0d 1.0 1. 0.11 o.i _________ L _____________________________________________ o.i 0.001.01.02.03.04.05.06 TIME (SEC) Fig. 2 Velocity and Penetration Distance Versus Time for Particles With an Initial Velocity * IO0/sec

1001 100 I K~ 10 10.005.0 U) 1 TIME {SEC) Fig. 3 Velocity and Penetration Distance Versus Time for Particles with an Initial Velocity - 75~sec Time for Particles with an initial Velocity 75Ysec

10 15p u 1, 'O I 0.001.002.003.004.005.01 TIME (SEC).Fiq. 4 Penetration Distance Versus Time for Particles With an Initial Velocity = 50'/sec

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN Computation of Penetration Distance The data of Figs, 3 and 4 were used for predicting the performance of an air cleaner with the following dimensions: (1) Diameter of central tube = 5 in. (2) Distance from bottom of tube to horizontal portion of baffle = 2 in. (3) Height of baffle cup = 3 in. (4) Diameter of baffle cup at bottom = 7 in. (5) Diameter of baffle cup at 2 in. elevation = 9 in. Figure 1 is drawn to scale for these dimensions, which are approximately those of a Donaldson Model No. A-1411 Tray Type Cleaner, At the maximum rated capacity of 600 cfm, the velocity through the central tube is about 75 ft/sec and the velocity through the vena contracta at the second bend is about 50 ft/sec. The width of the air stream after the second bend is estimated at 2.5 cm. A calculation of the time it takes a particle to move along any streamline shows that there is sufficient time for all particles to reach their maximum penetration. Thus the data presented in Table I may be obtained from Figs. 3 and 4 by evaluating maximum penetration at 0.005 seconds, which is about the minimum time for a particle going around the bend. TABLE I Dp Xmax 1 (cm) Xmax 2 (cm) XT (cm) Fraction Particle Penetration Penetration Total Of Stream Diameter After First After Second Penetration Impinging (microns) Bend Bend (xM + ) X = 225 15 2.25 (.9) (1-7) 2.66 1.0 14 2.1 (.9) (1.5) 2.4 0.96 10 1.2 (.9) (.9) 1.4 0.56 8.8 (.9) (.62) 0.95 0.38 5 0.33 (.9) (.25) 0.39 0.155 3 0.13 (.9) (.11) 0.165 0.066 ~Note: Maximum penetration is multiplied by 0.9 to compensate for the slope baffle cup. 10

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN The data of Table I were used in drawing Fig. 5, a plot of percent removal of dust versus particle size. It can be seen that all particles larger than 15 microns are removed and no particles smaller than about 2 microns are removed. These data may now be used to predict the efficiency of the impingement section for removing AC Test Dust. The size analysis for AC dust was plotted and then broken down into cumulative weight percent for small fractions. These data were used in Table II which presents the prediction of removal efficiency. The total removal efficiency for AC Fine dust is 48.6 percent, and for AC Coarse dust it is 79.3 percent TABLE II Weight Weight Weight Weight Percent D Fraction Percent Percent of AC Percent of AC Removed in AC (microns) in AC Fine Fine Removed Co Coarse Removed 0-2 0.0 20.0 0. 5.0 0 2-3 0.03 8.0 0.24 2.0 0.06 5-55 0.11 11o 0 1.21 5.0 0.55 5-8 0. 27 12. 0 3.24 7.0 l 9 8-10 0.47 6,0 2.82 5.0 2.35 10-12 0o 65 4.0 2.6 3 0 1.95 12-15 0.9 5.0 4.5 5. 0' 4,5 15 1.0 34.0 34. 8. 68.0 68 Total 48.6 % 79.31 1 Prediction of Impingement-Zone Efficiency with the Data of Ranz and Wong Ranz and Wong have presented experimentally determined data on efficiency of impaction for cylindrical and rectangular aerosol jets impinging on plates, and for cylindrical and spherical collectors in an aerosol stream, Their data are reproduced here in Fig. 6, a plot of efficiency versus the dimensionless inertial parameter 4, for aerosol jets impinging on infinite flat plates, and Fig. 7, a plot of efficiency versus 4 for variously shaped collectors in an aerosol stream. The predicted curves shown in these figures were calculated on the basis that potential flow exists, Ranz and Wong assumed simplified boundary conditions for their solution of the differential equations of particle ~1~~~~ II -~11~

100 90 80 ~~~..~ 70 60 r 50 40 O 30 20 ~..~~ i0 0 5 10 15 20 PARTICLE DIAMETER (microns) Fig. 5 Dust Removal Versus Particle Diameter Predicted for the Impingement Section

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN motion while Langmuir and Blodgett performed the solutions of their equations on a differential analyser. The basic mechanism behind these calculations is the same as that described in the preceding section. The drag force acting upon a particle is related to its acceleration to define its motion. The methods differ only in the degree of accuracy with which the velocity pattern and its effect on drag are defined. The efficiency data can be applied to the problem at hand by considering the impingement section to consist of a cylindrical jet followed by a rectangular jet. The dimensions of the rectangular jet are given by the width of the air stream at the vena contracta after the first bend and the circumference of the circle passing through the same position. In accordance with the above described assumptions we have a system consisting of a cylindrical jet 5 inches in diameter followed by a "rectangulaer jet 1.6 inches wide and 15.7 inches long: These dimensions are for the same air cleaner as for the previous calculation of efficiency. The inertial parameter is defined as: = -' v, (17) 18 g DC where: vo = average jet velocity, D = width or diameter of jet, C = drag coefficient = 1.0 for particles larger than 1 micron. If vo is 75 ft/sec = 2,280 cm/sec, and D is in microns, = 144 x 10-3 (p)2, (18), = 0.038 (D). (19) For the rectangular jet, vo = 50 ft/sec; = 0.0585 (Dp) Values of efficiency of collection are taken from Fig. 6 for values of '.4 corresponding to a range of particle diameters. It is found that both the rectangular and the cylindrical jet should take out all particles larger than 15 microns and none smaller than5 microns. Thus the effect of the rectangular jet is to give greater efficiency only in the range of particle sizes between 5 and 15 microns. This can be seen in Table III which presents the predicted efficiency of removal for each stage and the total of botho \~1~ ^ ~i,~~~13

.9 / /./.4' ~ jl~ t y ^^J^ROUND (PREDICTED) X\ f i^ GROUND (EXPERIMENTAL) /l~ / r -^ RECTANGULAR (PREDICTED) __________ _______l / -RECTANGULAR (EXPERIMENTAL) I I~,,,,', 1 1 1,1.1.2.3.4.5.6.7.8.9 Fig. 6 Predicted and Experimental knpaction Efficiencies for Aerosol Jets from: Rant and Wong I& EC 44, 1371

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN TABLE III D Partcle tC 'XR "IT Size Efficiency for Efficiency for Total (microns) Cylindrical Jets Rectangular Jets Efficiency 5 0 0 0 8 o.18 0.26 0o36 10 0 0.55 0o75 15 1.0 1.0 1.0 The efficiency of removal of AC dust was computed from the total efficiency and is given in Table IV. TABLE IV Dp Particle Total Wt. % in Wt. % of Wt. % in Wt. % of Size Efficiency Fraction A( Fine Fraction AC Coarse (m^icrons ) (Average for AC Fine Collected AC Coarse Collected Range of Dp) 0-5 0 39o.0 0 12 0 5-8.10 12.0 1.2 7 0.7 8-10.6 6.0 3.6 5 3.0 10-12.85 40 o 3. 4 255 12-15 95 50.o 4.75 5 4,75 15-80 1.0 34.0 34.0 68 68.0 Total 47.0% 79.0 The predicted total collection efficiency on AC Fine dust is 47 percent, which agrees with the prediction of 48.6 percent by the other method, and for AC Coarse dust both methods predict 79 percent removal. 15

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN PACKED ZONE The calculation of packed zone performance was carried out more to indicate the difference between the packed zone and the impingement zone than to evaluate the actual packing arrangement in a production air cleaner. The efficiency is predicted for a 1/2-inch-deep bed of 0.025-cm-diameter wires which form 20 layers in the 1/2-inch depth. The air velocity is taken as that which would occur in the annular space of a Donaldson No. A-1411 at 600 cfm or 11 ft/sec, By employing the data of Ranz and Wong on cylindrical collector efficiency we obtain the data presented in Table V. TABLE V D I P(T = (1-a)2 Efficiency Particle Efficiency = Total of Diameter of Penetration Penetration Removal (microns) Collection per Layer for 20 Layers (percent) 0.76 0 1.0 1,0 0 1..05.983.71 29. 2..27.91.15 85.0 3..42.86.05 95o0 4,.53.823.02 98.0 5. o 64 786.0082 99 2 6.,74 753.0034 99.7 8..82.726.0017 99 8 10..87 -71.0011 99.9 This packing would remove approximately 90 percent of AC Fine dust and 96.5 percent of AC Coarse dust according to the data of Table V. DISCUSSION OF RESULTS The most important thing shown by the calculations of efficiency is the relative functions of the two zones of the cleaner. The impingement zone will take out the relatively large particles and no great increase in 16

1.0.9 0.4.3 DISK (PREDICTED, R 8W) SPHERE (EXPERIMENTAL, R8W) RIBBON (PREDICTED, R&W).2 CYLINDER (LANGMUIR aBLODGETT PREDICTION) CYLINDER (EXPERIMENTAL, RANZ a WONG) 0.1.2.3.4.5 1.0 2.0 3.0 Fig. 7 Predicted and Experimental Impaction Efficiencies for Collectors of Various Shapes from: Ranz & Wong I l EC 44, 1371

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN its efficiency should be expected. The packed zone is capable of removing the small particles and can be modified in several ways to attain increased efficiency. While there are several simplifying assumptions in both methods used for prediction of impingment.- zone efficiency, these do not detract much from the accuracy since their major effect is to influence the efficiency within a narrow size band (5-1 microns in the cases shown) rather than to shift the limits of the band. The methods certainly are suitable for the prediction of trends and the effect of changes in design. REFERENCES 1. Ranz, W. E. and Wong, J. B., "Impaction of Dust and Smoke Particles on Surface and Body Collectors,' Industrial and Engineering Chemistry, 44, 1371 (1952). 2. Lapple, C. E., "Fluid and Particle Mechanics," University of Delaware (1951). 18

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