CONTROL VALVE PRESSURE DROP AND SIZING

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CONTENT

Chapter Description Page

I Purpose of Control Valve 2

II Type and Main Components of Control Valve 3

III Power 5

IV. Pressure Drop Across Control Valve 7

V. Symbols and Units 10

VI. Unit Conversion 11

Table 1. Typical Flow Factors for single ported C.V. 12 Table 2. Typical flow factor for rotary type C.V. 13

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2 I. PURPOSE OF CONTROL VALVE

Control valve is required to control capacity or pressure of fluid where is flowing in piping system. Pressure control is included liquid level such as in level control. Control valve is also used as an instrument to control temperature where capacity of mixing fluid in an equipment or piping is handled by control valve. Figure 1 shows typical application of control valve.

Temperature control Level control

Flow controller

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3

Typical pressure controller

Figure 1. (continue) Typical application of control valve

II. TYPE AND MAIN COMPONENTS OF CONTROL VALVE

Figure 2 shows main components of control valve and figure 3 shows several type of control valves.

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Figure 3. Types of control valve when divided into number of port, plug & seat type, number of connection and valve types

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Figure 3. (continue) Types of control valve

III. POWER

Control valves are powered by manual, pneumatic system or electric motor. Instrument air is commonly used for pneumatic power. Figure 4 shows typical of control valve power system.

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6

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7

2 2

.

363 .

1 Cv

Q

SG

2 2 2 7 2

.

10 .

.

3136

.

2 Po

Cv

Y

Qn

Z

To

MW

IV. PRESSURE DROP ACROSS CONTROL VALVE

The following figure is schematic illustration to show fluid flow at around port and plug of control valve.

Figure 5. Illustration of fluid flow inside the control valve

Pressure drop of fluid where flows across control valve can be determined as the following equations. For liquid, PLOSS = kg/cm2 (1) For gas P/Po = (2) Or by other method, P/Po = 2 5 . 0

.

333 .

.

483 .

2 sin

64 .

59

1 To

SG

Po

Cg

Qn

arc

C

(2A)

Where Cv is flow coefficient of valve or valve sizing coefficient given by manufacturers. Q is volume flow in m3/hr, Qn is volume flow at normal condition in Nm3/hr, Po and To is fluid pressure and temperature in kg/cm2A and K, MW is fluid and SG is specific gravity. Y is expansion coefficient, C1 universal flow coefficient, Cg is gas flow coefficient also given by manufacturers. Typical Y is,

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8

2 2 2

.

364 .

1 Cvm

Y

Q

SG

Y = T

X

k

Po

P

.

3 )

/

(

4 .

1

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k is gas adiabatic exponent, XT is pressure ratio factor when valve is installed without fitting (elbows or reducers very close to valve). XT is given by manufacturers.

When control valve is installed with fittings, replace XT by XTP,

X

TP = 1 2 2 4 4 2 2 2

1

47 .

207

1

V V V T P T

d

Cv

Do

d

Do

d

X

F

X

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And equation (3) become, Y = TP

X

k

Po

P

.

3 )

/

(

4 .

1

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FP is piping construction factor and dV is nominal valve size in mm (it is not port diameter, d but casing connection size) are given by manufacturers. Do is pipe diameter upstream fitting in mm. If control valve constructed between identical reducers,

FP = 5 . 0 2 2 2 2 2

1

93 .

700

1

V V

d

Cv

Do

d

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If all fittings pressure drop installed in the piping system has been calculated such as in article “Fluid flow in pipe” in this blog, it will more simple to use equation (3) without XTP and FP factor.

For liquid-gas mixture

PLOSS = kg/cm2 (7)

Cvm = (Cv+Cg)(1+Fm) (8)

Fm = RQ for RQ < 0.6 and Fm=1.334 RQ – 0.201 for 0.6< RQ <0.9 (9) RQ = Qg / (QLIQ + Qg)

Qg is gas volume flow, QLIQ is liquid volume flow and RQ is gas-liquid volume ratio.

Limitation and correction Viscosity correction

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CVR = Cv.Fv (10)

Fv is viscosity correction for Cv. For pressure drop calculation, Fv is given as the following equations.

If Re < 35, Fv = 18.12 Re-0.517235_{. If 35<Re< 3000, Fv = 2.5422 – 0.001843 Re + 4.5572 Re}2_.10-5 If 3000<Re<60,000, Fv = 1.4683 Re-0.0349125

_{. If Re > 60,000, Fv = 1}

₍₁₁₎

Choked Flow and Cavitation

High velocity of liquid at vena contracta will reduce static pressure. If static pressure at the vena contracta is lower than vapor pressure of liquid, vaporation will accour (flashing) and than cavitation will also accour at downstream of vena contracta or surrounding valve plug and other parts nearby where vapor bubbles are become liquid again when static pressure is back to higher than vapor pressure. If bubbles due to flashing occurrence are so much, these bubbles will crowd space at downstream of valve port and limit liquid to flow. This occurrence is called choked flow.

To prevent from above condition, design of pressure drop of liquid across control valve shall be limited at the following equations.

For globe type valve,

P

LOSS-MAX-GLOBE

=F

L2

(Po – r

C

.Pv )

kg/cm2 (12) Km (Po – rC.Pv)

FL is valve recovery coefficient given by manufacturers. Po is upstream pressure and Pv vapor pressure of liquid in kg/cm2A. rC is critical pressure ratio

r

C

= 0.96 – 0.28 (Pv/Pc)

0.5 (13)

where Pc is thermodynamic critical pressure of liquid.

If valve installed with fittings (reducers or elbows), equation (12) become,

P

LOSS-MAX-GLOBE

= F

L2

(Po – r

C

.Pv )/F

p2 kg/cm2 (14)

For ball and butterfly (ROTARY) type valve,

P

LOSS-MAX-ROTARY

= F

L2

(Po – r

C

.Pv )

or =

F

L2

(Po – r

C

.Pv )/F

p2 kg/cm2 (15) FL2 can also be replaced by Km. Ball and butterfly valve is more tend to cavitation. Use following equation to prevent cavitation.

P

LOSS-MAX-ROTARY

= Kc(Po – Pv )

(16) Fc is approximately = 0.67 FL2 or see table.

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Choked condition will also accour for gas, steam and vapor if velocity at vena contracta reach the sound velocity. Port pressure drop of gas or steam at 0.8 x sound velocity is,

P

sonic

= 0.4 Po.k

kg/cm2 (17) Cg MIN = 0.16585.Qn.(SG To)0.5/Po (18)

V. SYMBOLS AND UNITS

Unless otherwise noted, the following symbols and units are used in this manual.

Symbol Description Unit

Cv Flow coefficient

Cvm Flow coefficient for liquid-gas mixture Cg Gas sizing coefficient

Cs Steam sizing coefficient

D or Do Inside pipe diameter mm dV, d Nominal control valve size, port dia. mm Fm Liquid-gas mixture factor

Fp Installation factor

Fv Viscosity correction factor

g Gravity 9.81 m/s2

FL Valve recovery coefficient

L Pipe length m

Viscosity cP (centipoise)

Po Upstream pipe pressure kg/cm2_A

Pv Vapor pressure kg/cm2_A

Pc Thermodynamic critical pressure kg/cm2_A P or PLOSS Differential pressure/pressure drop kg/cm2

Q Volume flow (see note) m3/hr

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RQ Gas-liquid volume ratio

Fluid density kg/m3

Re Reynold Number rC Critical pressure ratio SG Specific gravity

T Absolute temperature 0_K

V Fluid velocity m/s

Y Gas net expansion factor

VI. UNIT CONVERSION

Designation Unit to be converted Factor Unit to be used

Length ft 304.8 mm inch 25.4 mm Pressure psi 0.07031 kg/cm2 bar 1.0194 kg/cm2 atm. 1.0326 kg/cm2 Pa (Pascal) 1.0194 x 10-5 _kg/cm2 Temperature F (Fahrenheit) (tF -32) x (5/9) C R (Rankin) (5/9) K C (Celcius) tC + 273 K Velocity ft/s 0.3048 m/s ft/min (fpm) 0.00508 m/s

Volume flow GPM (US) 0.227 m3/hr

CFM 1.699 m3/hr

Mass lb 0.4536 kg

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Head ft 0.3048 m

Enthalpy kcal/kg 4.1868 kJ/kg

BTU/lb 2.326 kJ/kg

Gas constant kcal/kg.K 4.1868 kJ/kg.K Specific heat BTU/lb.R 4.1868 kJ/kg.K

Density lb/ft3 16.0185 kg/m3

Specific volume ft3 /lb 0.06243 m3/kg

Viscosity N.s/m2 1000 cP

lbf.s/ft2 47880.3 cP

Kinematic to absolute viscosity, = SG . in cSt (centistokes), in cP

Note :

American Standard State condition is condition where pressure at 1.013 bar A and

temperature at 15.5 C. In volume, is common written as SCF.Normal condition is at 1.0132

bar A and 0 C. In volume, is common written as Nm3_{(Symbol for flow in this article is Qn)}

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Table 2. Typical Cv, FL and XT for rotary shaft valve

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Table 3. Properties of some fluids

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