π
<-

## FLOW CURVE

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### Description

UNIVERSITÀ DEGLI STUDI DI SALERNO

Bachelor Degree in Chemical Engineering

Course:
Process Instrumentation and Control
(Strumentazione e Controllo dei Processi Chimici)

CONTROL VALVE SIZING

FLOW CURVE

Rev. 2.3 of April 6, 2021
SUDDEN CONTRACTION

From
• Continuity equation
• Mechanical energy balance (Bernoulli’s principle)
• simplified conditions (see Appendix)
• liquid flow

general flow equation across a contraction for an incompressible fluid

15/09/2021 Process Instrumentation and Control - Prof M. Miccio 2
SUDDEN CONTRACTION
General flow equation across a contraction
for an incompressible fluid

V  S2
P1  P2  (3)

where:

Vሶ = Volumetric FLOW RATE [m3/s]
2
 = FLOW COEFFICIENT OF A CONTRACTION  4
 D2 
1   
D2/D1 = CONTRACTION RATIO  D1 

15/09/2021 Process Instrumentation and Control - Prof M. Miccio 3
FLOW EQUATION
across a CONTRACTION (for liquid)
1st HYPOTHESIS: contraction with the same pressure drop (P1 – P2) and the same sectional area S
for:
Generic liquid Water
 P1  P2
Vf  S (1)   S P1  P2
V (2)
f w
w
Dividing the respective members of eqs. (1) and (2):

Vf 1 1  
V
   Vf  w
(3)

V w
f Gf Gf
w

2nd HYPOTHESIS: The control valve in “nominal” condition is considered as an ideal contraction:

V
C vn  w
(4)
Cvn [=] US gpm(H2O)/psi1/2 P1  P2
 C
We have: Vw vn P1  P2 (5)

 P1  P2
Replacing eq. (5) in (3): Vf  C vn (6)
Gf

15/09/2021 Process Instrumentation and Control - Prof M. Miccio 4
FLOW EQUATION for a CONTROL VALVE
(liquid flow)
For NON nominal conditions eq. (6) becomes:

 P1  P2
Vf ( h )  C v ( h ) (7)
Gf

where:

Cv(h) = Cvn ɸ(h) [=] US gal(H2O) / (min psi ½)

ɸ(h) is the intrinsic characteristic of the control valve

(Ρ1 – P2) = ΔP [=] psi

Gf = specific gravity [=] -

Volumetric flow rate [=] US gal/min

15/09/2021 Process Instrumentation and Control - Prof M. Miccio 5
FLOW EQUATION for a CONTROL VALVE (2)
(liquid flow)

The previous Eq. (7) can be expressed in SI units for mass flow rate:

m ( h )  N 1 C v h  ( P1  P2 ) G f eq. (5.7)

where:

N1= 0.0007598 [(kg/s)/(gpm(Pa/psi)1/2)]

Cv(h) = Cvn ɸ(h) [=] US gal(H2O) / (min psi ½)

(Ρ1 – P2) = ΔP [=] Pa

Gf = specific gravity [ =] –

Mass flow rate [=] kg/s

15/09/2021 Process Instrumentation and Control - Prof M. Miccio 6
GLOBE CONTROL VALVE

P1 P2

ΔP = P1 – P2

MAXIMUM TRAVEL
MINIMUM TRAVEL (nominal condition)
h=0 Φ=Φ0
h=1 Φ=1

Φ=Φ0=0 Φ=Φ0 #0 e >0 Φ = (Cvn/Cvmax) = 1
ΔPmin ΔPn
Cvmin = 0 Cvmin # 0 Cvmax
The valve has also Vሶ min # 0 Vሶ n
an isolating function
15/09/2021 Process Instrumentation and Control - Prof M. Miccio 8
FLOW curve
Now we analyze the effect of the pressure drop on the valve flowrate.
A qualitative representation is showed in figure.
The continuous line represents the common trend of the mass flowrate of a liquid across a valve vs. the
square root of the pressure drop P
HYPOTHESES:
• liquid flow
• ρ=constant
• P1=constant
• Newtonian fluid
• Re > 2100 Slope ≈ Cv (h)
• h = constant
• P2 decreasing ↓

From the diagram in figure, we can distinguish three operating zones:
• Normal flow, where the flow rate is proportional to P1/2;
• Semi-critical flow, where the flow rate increases less than proportional to P;
• Choked flow, for which flow rate does not depend on P and is equal to wmax.

15/09/2021 Process Instrumentation and Control - Prof M. Miccio 9
CAVITATION and FLASHING VENA
CONTRACTA

HYPOTHESES:
• LIQUID FLOW
• valve represented as a contraction (convergent followed by divergent)
• Horizontal flow
• Equal inlet and outlet cross sectional area: S1 = S2

PRESSURE DROP ΔP = P1 - P2

1. The inlet pressure of the valve P1, for liquid, at the beginning of the convergent, is always higher than the
outlet pressure P2 (pressure drop).
2. The qualitative trends of pressure and velocity of fluid inside the valve are reported in figure with a
continuous and a plotted line, respectively.
3. Along the converging section, following the Bernoulli’s equation, the velocity increases and the pressure
decreases as the cross-sectional area decrease. The opposite occurs in the diverging section.
4. The minimum cross−sectional area of the flow stream occurs just downstream of the actual physical
restriction at a point called the vena contracta, because the fluid vein continues to contract, as shown in
figure.
5. In this point, the pressure (Pvc, vena contracta pressure) is minimum while the fluid velocity is maximum.
6. If the vena contracta pressure Pvc becomes lower than the vapor pressure Pv, vapor bubbles form inside
the valve and cavitation or flashing occur depending on the value of the outlet pressure P2.

15/09/2021 Process Instrumentation and Control - Prof M. Miccio 10
CAVITATION, FLASHING and NOISE

HYPOTHESIS : Pvc ≤ Pv
• If P2 > Pv, cavitation occurs:
vapor bubbles collapses when the fluid pressure reaches values higher than Pv. Collapsing
of the vapor bubbles releases energy and produces a noise similar to what one would
expect if small stones were flowing through the valve.
• If P2 Pv, flashing occurs:
vapor bubbles remain in the outlet fluid, where there may be a mixture of liquid and vapor
or just vapor. Also flashing produces loud noise.
Both phenomena damage and wear the metallic surface in contact with the fluid. Special
valves are commercially available with anti-cavitation trim able to reduce noise and damaging
effects of cavitation and flashing.
For the preservation of the valve, cavitation has to be avoided. On the other hand, flashing can
not always be avoided since it depends on the inlet fluid as concerns vapor pressure (Pv) and
on outlet pressure.
The negative effects of flashing (noise and damage) increase as the velocity increases.
In order to keep down it, harder trims are used and a maximum fluid velocity about 3.5 m/s is
considered when sizing the valve properly.

15/09/2021 Process Instrumentation and Control - Prof M. Miccio...

### Archive contentsContenu de l'archive

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3.65 Ko KB lisezmoi.txt
1.09 Ko KB FLOW_CUR.hpprgm
2.38 Mo MB FLOW_CUR 01_20.hpappdir.zip
444.58 Ko KB FLOW_CUR 21_24.hpappdir.zip
167 octets bytes appslist.txt

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