Labyrinth and Carbon Ring Seal Leakage Calculations

AppendixD

Labyrinthand CarbonRingSeal Leakage Calculations Straight Labyrinth Seal W = 5.76 K

h P1 ~ (1 - (x) 1/2 (RT1) 1/2 ~

where W = weight flow, lb/sec A = annular area, in. 2

586

Appendix DmLabyrinth and Carbon Ring Seal Leakage Calculations

587

Pa = upstream labyrinth pressure, psia R = specific gas constant = 1,545/MW T1 - upstream labyrinth temperature, ~

13 = pressure factor =

IN 1+ ~Inr 2_ .]1/2 1/rJ

(see Figures D-1 and D-2) r - labyrinth pressure ratio = P2/P1 P2 = downstream labyrinth pressure, psia N = n u m b e r of restrictions 8.52 et -- residual energy factor = (~-~) + 7.23 (see Figure D-4) s I c K

--

axial distance b e t w e e n restrictions, in. tip width of restriction, in. radial clearance, in. flow coefficient (see Figure D-3)

Re--- Reynolds n u m b e r =

24W arDgix

Note: Values of g tx m a y be substituted directly from Figure D-6. Units are correct. D = labyrinth diameter, in. Ix = absolute viscosity, lb-sec/ft 2 g = gravitational constant, ft/sec 2

Staggered Labyrinth Seal W -- 5.76AK

Pl (RT1)1/2 [3'

This formula differs from that of the straight seal in that the residual energy t e r m v ~ omitted and [3' is a function of the equivalent n u m b e r of restrictions N'.

ct is

N' = ( N / 2 ) y where N ~ - equivalent n u m b e r of restrictions N - actual n u m b e r of restrictions y -- a function of s/c (See Figure D-5) It should be noted that for values of s/c greater than 15, the reduction in leakage attained by using a staggered labyrinth is very small. The reduction in flow varies from 10% at s / c - - 15 to 8% at s/c = 50.

Carbon Ring Seal W=

1070 ct D hPo

(RTon) 1/2

Compressors:Selection and Sizing

588 where W D h Po To R n oL

= leakage, lb/min. = shaft d i a m e t e r , in. --- radial clearance, in. -- high side pressure, psia = temperature, ~ = specific gas constant -- n u m b e r of rings in series -- p a r a m e t e r , function of Ix & Po (see Figure D-7)

where Ix = Pn/Po Po = .02(s/h)

Pn -- low side pressure, psia s -- seal ring width, in.

E q u a t i o n s and charts: C o u r t e s y of A - C C o m p r e s s o r C o r p o r a t i o n .

Appendix DmLabyrinth and Carbon Ring Seal Leakage Calculations

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Figure D-4. Residual energy factors for straight labyrinths. (Reprintedby permission and

courtesy of GE Energy.)

Appendix D--Labyrinth and Carbon Ring Seal Leakage Calculations

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Compressors: Selection and Sizing

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Appendix D--Labyrinth and Carbon Ring Seal Leakage Calculations

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courtesy of GE Energy.)