Calculation of the Capacity, Power and Specific Energy of a Rotary Drum Scrubber
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In this paper, it is given the general equation, expressing the capacity (flow of the apparent volume) of cylindrical drum scrubbers, as a function of the key variables (% filling factor, drum diameter, drum length and the material residence or cleaning time) determining the axial flow of the material through the drum.From the respective values of the key variables (derived from the literature) by applying regression (least squares), it was derived the equation that gives the motor power of the cylindrical drum scrubber. Further, combining the above two equations, it was resulted the equation giving the specific energy of the scrubbing equipment.Finally, it is proposed a graphical method to compare the capacity, calculated by the simplified equation (as a function of the drum diameter), with the maximum and the minimum capacity of the cylindrical drum scrubbers given by “Telsmith” scrubber manufacturer.Στην εργασία αυτή δίνεται η γενική εξίσωση που εκφράζει τη δυναμικότητα (παροχή φαινόμενού όγκου υλικού) κυλινδρικούυδροαυτοκαθαριστή συναρτήσει των βασικών μεταβλητών που καθορίζουντην αξονική ροή του υλικού μέσα στο τύμπανο (συντελεστήςπλήρωσης, διάμετρος, μήκος τυμπάνου και χρόνος καθαρισμού).Απο δεδομένες στη βιβλιογραφία τιμές των βασικών μεταβλητών διαμορφώνεται, με εφαρμογή παλινδρόμησης (ελαχίστων τετραγώνων), η εξίσωση που δίνει την ισχύ του κινητήpn κυλινδρικού υδροαυτοκαθαριστή. Από τις παραπάνω δύο εξισώσεις προκύπτει η εξίσωση που δίνει την ειδική ενέργεια καθαρισμού του υλικού.
Transcript of Calculation of the Capacity, Power and Specific Energy of a Rotary Drum Scrubber
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( ) ~ ~ ~, ( ~), pn
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. ~ ( 1, 2, 3 4 min). (~)
, , ~ ~ "Telsmith.
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1.
( 1 ). (l)
() () : Q ( D)
t .
:
Q = /t = f( / 4)D 2 /t ( 1) f . = fD 2 /4. (1)
() Q :
Q = 60f(/4)2 /t = 47124 fo 2 /t ( 2 ) Q = 47124 fD 3/t = /D ( 3 ) : D m t m;n f .
= 18( 3 )( 4 ) f = 2(l), 3 :
D m t min ( 4) ( ) 4 (Q D): (438 152) (75 1 83) (1188, 2 , 13} (150 244) "elsmith"( 3 ), :
Q. = 1184 D- 1375 ( 5)
: Q. m 3 / D m. r = 997.
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2
( Q. : Q : = QMEr./2) u
elsmith'' - D 1, 4 t: 1,5 , 2,0
4 min.
2. .
() (/min) , , D.
( ) (N,D)( 3):(30, 1,52), (27, 1,83), (25, 2,13) (23, 2,44), :
= 37,86 D-0, 556 /min, D m ( 6 ) , , :
= 36,5//fi /min, D m ( 7)
D 2.
7 : Nc = 42,3/10 /min, D m, (Telsmith) , , () :
fc = N/Nc = (36,5//D)/(42,3//D) = 0,86 86%. fc (86 %) ( }
.
= 36,5/15 ( 7) 2, , :
31 . m ( 8)
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3
3.
( .. u) (piio shaft}. . , : (), ( )
.
( p) : p (), f, , ,
( ) .
, , f, , :
= CpfNO P/pfN = = con ( 9 )
C , a : , , f,
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( ) (= P/pfN, D}( 4 }: ( 1,06, 1,52), (1,69, 1,83) (2,39, 2,13) (2,97, 2,44), ( 0}:
= I f = C = , 43 2 ' 2
= 0,43 f 2 2 (r = 0,996) (10)
kw ( 11}
: ( k w } (. ( s 1 i - r i g mo to r) , (;m3 ), f (), p-
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4
(/min), D (p) L (p).
p (high-torque squirrel cage motor) C = 0,431,28 = 0,55.
11 = LID = 1,8, f = 0,2 = 36,5//0 :
= 5,65 pD 2 ' 7 kw ( 1 2 ) : p m3 D m. p, , : 5,65 1,28 = 7,23.
, 12, 1 D
p .
4.
2 11, , :
( 1 3)
: (kwh/m3) , p m 3 , m i n , D m t min.
p w :
kwhl ( 1 4)
, , , 13 14, : 9,12 1- 3 1,28 = 11,67 1- 3 . = 36,5/10 13 14 :
= 0,333 - 0 ' 3 t kwh/m 3 ( 1 5) = 333 o- 0 , 3 t kwhl w '
( 1 6 )
: D m t min.
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5
, , 15 16 : 0,333 1,28 = = 0,43 .
( ) Q ( 4) ( 16) -
w , D t , 2 3.
4. pp
11, : ) f = 0,16 ( f: 0,156 , 0,155 , 0,154 0,160
p 3), ) (, grael,
= 40 %) p = 1,6 /m 3 . ', f pf = 1,6 0,16 = 0,256 /m3 = P/fNL = P/0,256NL
.
8, 15 16 p = 36,5//D ( 7) p Q ( 8), ( - ) p
t ( p V = L/ t). , 7 (: 8, 12, 15 16). , , 1,5- 4,0 min, ~ ( ) .
p 11 12 ( ). : , pp (
) . , p,
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6
1,28 ( ~ 3) .
5.
2, (): f, , t , (f = 0,2 = S/0 = 1 ,8), 4 ( ) ( 3)
( ) 11, : , f, , , (f = 0,2, = S/0 = 1,8 = 36,5J/D), 12 ( ).
() , , 14 : , t , = 36,5//D, 16 ( 3). Q
2 (Q oc 2 , : f, t) : f = 0,2 = S/ 0 = 1,8 ( 4) = 36,5//0 ( 8) . ()
~ 11 ( : 2 2 , , f, )
12 : f = 0,2 , = S/ 0 = 1,8 = 36,5//D. ,
( w) 13 ( oc 0 2 ,
2 : p , t ) 1 4 ( w oc D ' , : t) 15 16
: = 36,5//0.
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7
( ).
n = 2,2 ( 11)
(n = 3) oc 3 , ~ ( . . ) , L uv(S) a f,
(flow pattern) (
, - ). oc 0 2 oc
(torque-arm equation)( 6 ),( ),(B),( 9 ).
1. . ., . . , , -, 56, - 1984.
2. . . , , , , . . . / (
), 1990.
3. Telsmith Bulletin . 292. Equipment for Scrubbing, Washing, Classifying, Smith Engineering Works, Milwaukee Wisconsin, U.S . A
4 . Telsmith Bulletin . 2668. Equipment for Hines, Quarries and Grael Plants, Smith Engineering Works, Milwaukee Wisconsin, U.S.A.
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8
5. Harris C.C. and Arbiter tl., Grinding Mills Scale-up Problems, Mining Engineering, Vo l. 34, . 1, Jan. 1982 .
6. Arbi t er . and Harris C.C. Scale up and Dynamics of Large Gri nding Mi lls / A Study Case, Chapter 26, Design and instal-la t ion of comminution circuits, edi t ed by Mular A.L. and Jergensen G.V . , SHE of the , .., 1982.
7 . Nordberg (Process Machinery), Grinding Mills, Bulletin 463 . 8. Morgardshammar Grinding Mills, Bulletin 8978.
9 . Smid t h F.L. ( Industr i al Equipment Diision), Hining Mills, Bulletin 3-02-78.
1. ( 12) .
*
. , c/m3
1 '6 1 '8 2,0 2,2 2,4 ' /m 3
D 2,7 3,0 3,3 3,7 4,0 m
' kw ( 12) *
1,0 9 , 04 1 1 7 11 '3 12,43 13,56
1 '5 27,0 2 30,39 33,77 37,15 40,52
2,0 58,74 66,08 73,43 80,77 88,11
2,5 10 7,30 12 0 ,71 134. 13 147,54 160,95
3,0 175,55 197,49 219,43 2 41 '38 263,32
. 1 ,28.
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9
2 . ( 4 ) 16)
.
*
t, min 1 2 3 4
'
m Q' m 3 /w
1 ' 16,96 8 , 48 5,65 4,24
1,5 57,24 28,62 19,08 14,31
2,0 135,68 67,84 45,23 33,92
2,5 265,00 132,50 88 ,33 66,25
3, 0 454,92 228,96 15 2 ,64 114,48
m * w ' kwh /
1 ' 0,33 3 0,666 1 ,000 1, 333
1,5 0 , 295 0,590 0,885 1,180
2,0 0, 27 0 0,5 40 0 , 810 1, 080
2,5 0 , 253 0,506 0 ,7 59 1, 012
3,0 0 , 240 0,480 0, 720 0,960
. - 1,28.
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F \
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30
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= 37t86 - 0 5 56 (r=0 , 9995) ~ 36,5 / 10
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~ 2 . ~ ~~ ~ ~ (Telsmfth Bu l letfn . 292).
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