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Control Valve Sizing

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1991, ALL RIGHTS RESERVED

BULLETIN NO. SM-8

1.‘94

TABLE OF CONTENTS

Valve Sizing ................................................. Page 2 Valve Sizing Equations ................................. Page 3 Viscosity Correction ..................................... Page 4 Small Flow Valve Sizing .............................. Page 4 Cv Table Series 24000 Lfttle Scatty ............. Page 5 Cv Table Series 24000s Stainless Steel......Pag e 6 Cv Table Series 21000 Elastomer Lined.. .. ..Pag e 7 Cv Table Series 25000 LO-T Rotary.. ......... .Page 7 Cv Series 26000 Corrosion Resistant .......... Page 7 Cv Series 86000 Corrosion Resistant.. ........ Page 7 CV Series 41000 Rotoglobe ......................... Page 8 Incipient Cavitation ....................................... Page 8 Damage Cavitation ................................... ..Pag e 8 Avoidance of Cavitation ............................... Page 9 Aerodynamic Noise Estrmate ..................... Page 10 Graphical Method .................................... Page 11

UMANN ASSOC, LTD. 35 Mirona Road

Portsmouth, NM. 03801 Phone: (603) 436-2044

Fax: (603) 436-4901

VALVE SIZING

Selecting the right size control valve is very important. For example, a valve that is too small might waste pump horsepower. On the other hand, a valve too large may not be able to handle reduced flows. %d

Most valve manufacturers publish a so-called rated C, Factor for each size and type of control valve. This simply indicates the maximum flow in gallons per minute of water which would pass through the valve at a pressure drop of 1 psi. To select the proper size valve. however, requires full knowledge of actual flowing conditions and method of calculating the required C,.

Valve sizing equations as standardized by the ISA (Standard S75.01) have vastly improved in accuracy primarily through the addition of a Pressure Recovery Factor F, and a Piping Geometry Factor F,. both of which were originated by Hans D. Baumann of our company in 1962 and 1968. respectively (formerly known as C, and R).

The following equations have been adapted from the ISA S75.01 Standard to allow for practical every- day use without significant sacrifice in accuracy. For more comprehensive sizing use our computer software “VS3”.

Proceed by calculating the required valve C, from given flow data, having prior determined whether the flow is critical or sub-critical.

Next, select a valve size (or trim size) from the capacity tables shown on pages 5. 6. and 7. Note, tf a Lo-T valve is installed between reducers, multiply rated C, by F,. The other valve types, having relatively lower capacity, do not require this correction. However, if the required maximum C, is more than 80% of the rated C,, or C, x F,, for a given valve size, then choose a next larger valve or trim. For example, for a given flow rate of 5670 Ibs/hr sat. steam at 250 psia inlet and 150 psia outlet, a C, WV

of 13.5 is calculated. A l-1 14’ Little Scatty with V-port trim has a maximum C, of 15. However, 13.5 is more than 80% of 15. therefore, a l-l /2’ size valve with a rated C, of 23 is recommended. Also. do not select a conventional globe valve or metal seated butterfly valve if the minimum required C, falls at less than 5% of valve travel (see C, Tables).

If no pressure drop is preselected. use 5 psi or 5% to 10% of maximum pump discharge pressure for sizing purposes.

For additional information refer to ‘Controol Valve Primer-4 User’s Guide” by Dr. Hans D. Baumann, a book published by the Instrument Society of America.

VALVE CHARACTERISTIC

The purpose of a valve flow characteristic is to linearize the installed relationship between actuator signal change and change of flow rate through the valve as much as possible. This ideally assures a constant gain of the control valve.

A Unear Characteristic does this only if the pressure drop across the valve is fairly constant,

The Equal Percentage or Modified Equal Percentage Characteristic, on the other hand, does compensate for varialrons in pressure drop with flow rate and should therefore be preferred if the AP vanes morefhan 2:l between min. and max. Row. Another reason why this characteristic is preferred, is the fact that such a plug is still substantially off the seat with small flow rates. For example. a 2’ V- port plug at only 1.7% of max. C, is still at 10% of rated travel.

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FORMULAS FOR SIZING CONTROL VALVES

FOR LIQUID SERVICE

Subcritical Flow Critical Flow when AP is less than when AP is more than F,’ CAP,) or equal to F,’ (AP,)

Volumetric Flow

G f I

c,=Q - FL J APs

Flow by Weiqht

C” = W c, = W 5OOpp

/ 500FL,&hP,

FOR GAS AND STEAM SERVICE

Subcritical Flow Critical Flow when AP is less when AP is more than F: (P42) than FL2 (PJ2)

Volumetric Flow

G= &4X G= e

Flow by Weight

c, = W * c,= W 3.22,f&P(P,+p;IG, 2*0F,P,&

For Saturated Steam

C” = W c, = W 2.1JdP(P14P,) 1.83F,P,

For Suuerheated Steam

C" = W( 1 + 0.0007 T*J

c,= w~1+o.ooo7T,h)

2.1JAP(P,+P,) 1.83F,.P,

NOTE: When rotary valves are installed between reducers use C,F, instead of C, (in capacity tables).

Where: C, = Valve coefficient

C,, = Rated Cv of Valve Selected

d = Valve diameter (inch)

Fd = Valve Style Modifier

F, = Pressure Recovery Factor

F, = Reducer Correction Factor

F, = Viscosity Correction Factor

G = Gas specific gravity (air =l .O)

G, = Specific gravity @ flowing temperature’

PI = Upstream pressure, psia

P* = Downstream pressure, psia

AP = Pressure drop P,-P2, psi

PC = Pressure at thermodynamic critical point, psia (water = 3206 psia)

P, = Vapor pressure of liquid at flowing temperature, psia

AP, = Maximum AP for sizing

Use: P,-P, when outlet pressure is higher than vapor pressure.

I -\

use: P+.96-0.2E++"

when outlet pressure is equal to or lower than vapor pressure.

0 = Gas flow rate at 14.7 psia and O’F., scfh

9 = Liquid flow rate, U.S. gpm

T = Flowing temp., “R.(460+‘F)

T ,h = Steam superheat, OF

W = Flow rate, pounds per hour

‘Water =1 @ 60°F

OTHER METHODS: c, = & ; c, x -%; XT= .84F,* ; FL = m; FL = C,/.QO r

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VISCOSITY CORRECTION

Where highly viscous fluids (usually above 40 cSt) or small flow conditions are encountered, it will be necessary to correct the calculated C, turbulent, by dividing C, turbulent by F,, to ensure sufficient capacity of the selected valve.

C ~..,hrlsit -WV c fk “rOr,-d R

For small flow valve trim where C, r~ 0.1, this has to be done, regardless of viscosity, even if the flow medium is a gas.

FOR UQUIDS FOR GASES

Then determine F,. using the lower of F, or Fd:

Laminar Flow Gm > O-5)

F, = 0.776 JRey/ (c,/dZ) Laminar Flow (C, s 0.5) Fn = 0.026&

Transitional Flow’ (AlI GA F,' =

‘Do not use this equation for Re, values below 10.

Where Re, (Valve Reynolds Number):

Use Cv, at least 2 times the calculated Cv turbulent. This may have to be in- creased later if calculations show se- lected CvR is too small.

Where n = 1 +(89Od%&*) + log (Re,) n = 2 + log (Re,) for small flow

valves (C,,, < 0.5). NOTE: Minimum n = 2

FOR LIQUIDS FOR GASES

Rev= 17300 Fd q

VpT-Ci

v - Kinematic Viscosity (centistokes), if vfscosity is in Centipoise (u), divide u by G, to obtain v. For gases use Y at atmospheric conditions. For other definitions, see page 3.

F,, (Valve Style Modifier) and F, (Pressure Recovery Factor) For Standard Valves:

84000/86000 F, = 0.35 F, = .80 V-Port & Splined Trim Fd = 0.7 F, = .98 Globe Valves Fd = 0.46 F, = .90 Mikroseal C, 2 0.3 Fd = 0.2 F, = .85 Butterfty Valves, F, = 0.30 F, = .70

70' (Open) Tapered P?gz Ffi. 102) 2 1 i:ic : f 1:: See Cv Tables For Others

Example: Bunker C Oil @ 1 loOF, P, = 100 psig, P, = 75 psig, G, = 0.99. q = 70 gpm, v = 1100 centistokes

Re = 17300 x .45 x70 = 101 " 1100 J.9 x28

So, salact l-112” Globe valveve, parabolic F~ = 0.776 ,fitii/(28/1.5=)=0.63

pfug,rated C, = 28, FL =0.9, Fd = 0.46 C = 13 = 22.1

"a- 0.63 (O.K. 79% of Rated CJ

d-

Cv Table SERIES 24000 BRONZE LllTLE SCOlTY CONTROL VALVE

’ 1 20 30 40 , j 80 50_-,www60 i 1

Cv Table SERIES 24000s STAINLESS STEEL CONTROL VALVE

ERCENTAGE OF PLUG_TRAVEL+- 5 1~ 10 ! 20 30 40 -70~609 70 1 80 1 00 j TM.,, ~66~~6 VALVE

ALVE MODEL ., P

SIZE NO.

IIN.)

‘ORT

DIA.

IIN.) -

I

11

‘LUG hECOVERY SlYLE

RAVEL RATED CV (FLOW TO OPEN) FACTOR MODIFIER

IIN.) 1 (FL) (Fd

1246775: 375

i-- -iG?x 375

1’ pas j 813

I 2458% 150

i

c c c

0:

006 I 009 a 13 01s

08

1

046

0 08

0 12

019

uz-

9 52

046

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SERIES 21000E~A~_T_OMER LINED BUlTERFLY VAtyE - _ ~-

~~~~~~~~~~~,-~-~~~~~~:~~~“::~. ;I0

-~~~ . i 1 ’ / 3 . 05 + 2.5 1 8 : 19 39 64 ? 91 121 154 190 216 230 i .a65 79 025 I

4 12 6 16 28 56 97 132 180 232 292 I 354 j 435 .a5 77 0.74

1 6' - 25 T-125 35 69 139 229 327 441 566 707 1 836 975 85 77 j 0.22

-

6' i 15 32 a0 i 130 190 265 345 ____ 8 I 20 45 102 195 310 465 695

lo' T31 73 174 265 474 665 750

12 i 45 105 750 6a0 960 1080 - 16' : 65

I I 164 391

__!Xe t

570 1060 1500 ._ _

I

_ 16i5

(lbF~- Pressure recweqfactor (2\ KC - Coetf~cmt of inclptentcavdatm (3)Fp- Mult1plyva~erat~dC~byFp1pcompensatefor reducer losses

(D=lrnesire/d=valveslre)

-- SE~I~S~26O~O~CORRO~lON RESlSTANT”CONTROL-VALVE r~

PORT. j PLUG

.____ VALVE

,i%,

MODEL ;TRAVEL; PERCENTOFPLUGTRAVEL(flowloopen,

NUMaER / (%I, j (INCH) j 5 10 20 30 40 50 60 70 a0 90 IOO’FL i Fa

i 26OOl I .312 : .50 ;.OOOG'XQLl~~ 00013~ooO24,ooO36

50~0004 .OoOjS 0004 .OOOi ..0009

.00048~,00060; 0007 1 OOO8~lOO9I~l {

226005 / 312 :

; 26010~.312 ; 50 ;

XNl12 ;,0018.1.0025 ?.0033 ..004!00~;

00007 .00015 mo4 .(X)08 m13 t

,002 : / .007 T !

i

qoc&lo5 7- o09;mllm .'

i 76070 i 312 : SO I 0001 .0oa2~~06~~?008 .?017 0031 j .0048 Y ,007 1 ,010 j .013 j 02 1 1

iQ~O50 I 312 50 j 0003 .0005 .OOl ,002 004 ; .008 1 ,012 ,017 : ,023 ! .033 ! 05

1' j 26100 j ,312 50 j 008

VALVE, MODEL PERCENTOF~UAT~RTRAVEL

CAVITATION

Cavitation (Fig. 1 b) occurs with liquids only when high velocity reduces the static pressure inside a valve to below the pressure level at which the liquid starts to boil and produce vapor bubbles. These vapor bubbles collapse whenever the downstream pressure is higher than the so-called vapor pressure (PJ causing very high pressure waves. These “implosions” are responsible for a very high noise level and for great damage (under prolonged service) of the affected valve body or trim parts. Avoid the damage level of cavitation by not allowing the valve pressure drop to exceed K, x (P,-P,).

Use of the Lo-T rotary control valve is beneficial, since the teeth reduce the size of the vapor bubbles and deflect the implosions away from the vane. If the process permits, air injection can be applied with the Lo-T valve to greatly reduce cavitation noises.

Note, a process called “flashing” (Fig. 1~) will occur if the downstream pressure is equal to or less than the vapor pressure P,. This process is relatively harmless and there is no noise problem as long as high outlet velocities are avoided (connect outlet directly to flash tank or condenser) and as long as stainless steel or chrome moly body and trim are employed.

INCIPIENT CAVITATION

Cavitation in a valve is usually a gradual process beginning with only small portions of a plug or vane experiencing vapor bubbles. This so-called incipient cavitation, which is relatively harmless, will start to occur when the following pressure drop in a valve is exceeded:

*pm - Kc O’,-“A

Where: & = Coefficient of incipient cavitation vanes typically between 0.2 and 0.4. P, = Valve inlet pressure (psia) P, = Vapor Pressure of liquid at flowing temperature

(Water @ 70°F = 0.38 psia)

DAMAGE INDUCING CAVITATION

Pressure drops high enough to produce significant damage (and usually objectional noise levels) should be avoided, parficularly over prolonged time periods. While there is no exact scientifically established limit, the following rules may serve as a guide:

AP damage = K, (P, - P,)

Where: K,=K, x K,xFL3 P, = Inlet Pressure (psia) K, = (l/d).‘2s P, = Outlet Pressure (psia) 6 = (loo/p,).‘~ P, = Vapor Pressure (psia) d = Valve Size, Inches

MAX. INLET PRESSURE TO AVOID EXCEEDING 90 DBA CAVITATION NOISE OF LO-T VALVES

Medium: Cold Water at atmosoheric downstream oressure.

Valve Size: 2” 3” 4” 6” 8” ,O,’ 12” 16”

Max. P, (Psig) 150 105 65 45 42 32 25 20

NOTE: The above figures are based on the valve being approximately 2/3 open.

NO CAVITATION CAVITATION FLASHING 1 pt I Pl I P%

t-----

- --

---B-B*- -t-----y ------I -t----- \,_,; -

1 I I

FmJRF 18 FlGUAE lb FIGURE Ic

FULL CAVITATION

Full cavitation or choked flow will be reached if a critical pressure drop (AP,) is exceeded.

AP, = F,’ (P, - P,)

Where: F, is the Pressure Recovery Factor.

For globe valves, full area trim: V-Port plug = 0.98 Parabolic plug = 0.90

Lo-T = 0.7 @ 100% travel (see page 7)

AVOIDANCE OF CAVITATION

If possible, cavitation should be avoided by using valves having a higher F, factor, by reducing the pressure drop across the valve or by increasing the outlet pressure (elevation, etc.). Resistance plates’ are sometimes applied to absorb some or most of the valve pressure drop when placed downstream of the control valve. Another method is the application of two valves in series (separated by at least six pipe diameters). The overall Kc or FL of such a combination is the square root of each individual F, factor.

The F, required to avoid damage producing cavitation must be more than:

For example: One 8” Lo-T valve near wide open has an F, factor of 0.72. Two valves in series have a combined F, of m= .84. thereby increasing the allowable AP by about 58%! Note: It is important that both valves be identical. Assuming an inlet pressure of 115 psia. the two valve K,, = (118) ‘<’ x (1001115) “’ x 0.84j = 0.45 compared to a & of 0.28 for a single valve.

& While it may not be economical to avoid cavitation in all cases, care should be taken not to exceed the 90 dBA OSHA limit since noise and wear are interrelated. See table on page 8.

‘May be supplied by l-f. D. Baumann Assoc., Ltd., see Bulletin RP-3.

AERODYNAMIC VALVE NOISE PREDICTION

The calculation of the aerodynamic noise level for control valves is based on methods established by Hans D. Baumann’ which are concurrent with ISA Standard 75.17 (1989). They are further modified to suit the particular low noise characteristics of the Lo-T line. The method has been kd verified by air and steam tests on selective sizes and it is believed that the calculations yield typical accuracies of within + 3 dBA. However, the somewhat simplified equations shown below are accurate for globe valves only if the actual C, is less than 65% of maximum rated C, or less than 9 C, per valve diameter squared, and at valve outlet velocities of less than 0.1 Mach. For higher Mach numbers see correction below.

A pocket calculator solvable calculation method is shown below. A simplified graphical method for field use and quick estimating purposes for the Lo-T valve is shown on page 11.

SPL = 48 + 10 log(C, F, P, P,) + 5 log(D) - 20 log&,) - 20 log(D/d) + n,,, + 20 log(F,) + F. + L, in dBA @ 1 m from outer pipe wall.

Where: C, = Flow coefficient under actual conditions

FL = Pressure Recovery Coefficient

P, = Inlet pressure, psia

P2 = Outlet pressure, psia

D = External pipe diameter (inch)

d = Valve Size (inch)

t = Pipe wall thickness (inch)

Lo = Pipe wall thickness Schedule 40 pipe

F, = Valve style modifier (see Page 4)

For Lo-T Fd = 0.30 (2”), 0.25 (3”). 0.24 (4”) 0.22 (6”), 0.18 (8’ - 16”)

For globe valves F, = 0.33 @ 65% of Rated C,. Otherwise F,, = [(e/2.4) + 6 I 1001; 4 = % of max. rated C,.

% = For globe valves: 25 log (P,/P,-1) below PJP, = 2.5. and I .75 + 15 log(P,/P,-1) above 2.5.

%l = For Lo-T rotary valves: 12 log(P,/P, - 1.05)

F, = Gas property correction factor = 10 log [(C,)’ x (G,)T - 122. (C, = Speed of sound in gas (f/s). G, =Specific gravity of gas)

Saturated Steam -2 Superheated Steam Natural Gas 1; Air 0 Helium +1

Mach Number Correction: L, = 26 log O.O23P, C,F, 1 D2 P2 )I

‘8aumann, H.D. 1987, ‘A Method for Predictin Jet Noise Theories” ASME paper 87-WA/NC ‘h

Aerodynamic Valve Noise Based on Modified Free -7.

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Lo-l AERODYNAMlC NOISE PREDICTION (air.gas.steam)

PRESSURE RATIO P,/P2 [PSIA!

100

95

70

105: 1.2 1.5 2 3 4 5 6 7 a910

6” /’

/ / P,: 115 PSIA I

PRESSURE RATIO P,/P2 IPSIAI

Calculate ratio PI/P,, follow P,/P2 line to valve size and read SPL at intersection with valve size.

Above values based on 80% rated valve capacity (rated G). For flow at 40%, rated G. subtract 3 dBA.

SPL based on Sched. 40 pipe. For Sched. 80, subtract 5 d0A.

Note: If inlet pressure is half as shown, subtract 6 dBA. If inlet pressure is twice as shown, add 6 dBA.

110

a5

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