1. UNIVERSITÁ DEGLI STUDI DI SALERNO
Bachelor Degree in Chemical Engineering
Course: Process Instrumentation and Control
(Strumentazione e Controllo dei Processi Chimici)
CONTROL VALVE SIZING
FLOW COEFFICIENT AND INHERENT CHARACTERISTIC
Rev. 2 – April 6, 2019

2. CONTROL VALVES: Terminology
NOMINAL PIPE SIZE (NPS): it is the identification value of the interface dimension of a valve and of the other piping elements. Elements having the same NPS and NP (nominal pressure) can be coupled.
PORT: fixed opening or orifice in the body which determines the crossing of the flow (for globe valves)
CLOSURE MEMBER: it is a properly shaped movable element. Its position determines the section area through which the flow crosses the valve. The closure member can assume every position between two limit positions: closed position, at which corresponds ZERO or the minimum flowrate, and the full-open position, at which corresponds the maximum flowrate.
TRIM: The assembly of the inside components of a valve, which are in contact directly with the fluid. The seat, plug, stem, and ball are all trim components. With their shapes they determine the flow characteristic of the valve.
Full close: a valve is defined full close when the flowrate is zero as the closure member is in closure.
TRAVEL or STROKE or LIFT or OPENING: it is the displacement of the closure member from the closed position. Usually it is from ½” to 1½“ in a globe valve.
NOMINAL TRAVEL or RATED TRAVEL: it is the travel corresponding to the full-open position.
RELATIVE TRAVEL: it is the ratio between the travel and the nominal travel. It is indicated with h. In closure position is h=0; in full open position is h=1.
See also:
23/09/2019
Process Instrumentation and Control - Prof. M. Miccio

3. Process Instrumentation and Control - Prof. M. Miccio
VALVES: COMPONENTS
COMPRESSED AIR
taken from:
Magnani, Ferretti e Rocco (2007)
ACTUATOR
ACTUATOR
MEMBRANE
SPRING
STEM
schematic drawing
BODY
CLOSURE MEMBER
SEAT
INGOING FLUID
OUTGOING FLUID
JOINTS
23/09/2019
Process Instrumentation and Control - Prof. M. Miccio

4. CONTROL VALVES: fluid properties
The flow rate of the fluid crossing the valve can be expressed as either volumetric or mass.
It depends on valve characteristics and on the state and properties of the fluid, such as:
Inlet pressure, P1;
Inlet temperature, T1;
Outlet pressure, P2;
Pressure drop, ΔP = P1 - P2;
Vapor pressure of the liquid, Pv, calculated at the inlet temperature, when considering negligible the temperature change inside the valve;
Specific gravity of the fluid, Gf = ρ/ρ0, where ρ is the density of the fluid at the inlet conditions and ρ0= 1000 kg/m3 (T=4°C) is the density of water at ambient conditions.
23/09/2019
Process Instrumentation and Control - Prof. M. Miccio

5. CONTROL VALVES: Flow coefficient Cv (for liquids)
To highlight the flow rate characteristics of the valve, it is necessary to express the flow rate passing through the valve for a fluid, and its physical reference state. The parameter, of Anglo-Saxon origin, which is used to define the flow characteristics of a valve is, traditionally, the flow coefficient Cv .
In particular, the Cv of a valve is the volumetric flow rate of water in US gal min-1 (one United States gallon is equal to liters) crossing the valve at a temperature between 5÷40°C (Gf=1) for a specified (partially or full open) valve opening with a static pressure drop ΔP = 1 psi [=] 6895 Pa.
Cv [=] US gal (H2O) min -1 psi-1/2
23/09/2019
Process Instrumentation and Control - Prof. M. Miccio

6. CONTROL VALVES: Terminology
The flow coefficient Cv is a monotonically non-decreasing function of the travel h of the closure member.
Therefore, Cv assumes values between the smallest flow coefficient Cvmin and the largest flow coefficient Cvmax when the closure member moves from the close position (h=0) to the full opening position (h=1).
To understand the relationship between Cv and h the following definitions have to be provided:
Nominal (or Rated) flow coefficient Cvn: value of Cv at the nominal travel (Cvn=Cvmax);
Relative flow coefficient Φ=Cv/Cvn; it is expressed as a non-dimensional ratio  [0,1]; Opening: value of Φ expressed as a percentage  [0,100];
Rangeability r = Cvmax/Cvmin: it is the ratio between the largest and the smallest flow coefficient; r   for Cvmin = 0 The higher the number, the better. The rangeability is 5:1 on typical small globe valves (1/2"), 75:1 on a large valve (2"), 100:1 on rotating valves, 6:1 practically on butterfly valves.
Inherent characteristic Φ(h): the relationship between the relative flow coefficient Φ and the closure member travel h with constant pressure drop ΔP across the valve. The inherent characteristic depends on the conformation of the trim, of which the shaping of the shutter is also part (in the cage valves, from the shape and dimensions of the holes of the cage).
23/09/2019
Process Instrumentation and Control - Prof. M. Miccio

7. INHERENT CHARACTERISTICS
The inherent flow characteristics of a valve are defined and provided by the manufacturer considering:
a reference fluid (i.e., water)
a reference temperature
a reference pressure drop
They allow to characterize the dependence of the flow rate on the valve's own characteristics and to compare the ability to pass a flow rate in different valves.
They are defined from the flow coefficient CV (or AV or KV)
NOTE:
The ON/OFF valves generally allow, by varying the degree of opening, an intermediate position of the closure member and, hence, a partial flow rate. However, there is no unique correspondence between closure member position and flowrate. Therefore, they cannot be used for control and regulation purposes.
23/09/2019
Process Instrumentation and Control - Prof. M. Miccio

8. THE MOST COMMON INHERENT CHARACTERISTICS
Hypothesis:
ΔP = cost.
Nominal travel h
Inherent characteristics:
linear
equal percentage
quadratic
quick opening
butterfly valve or V-Port globe (green)
23/09/2019
Process Instrumentation and Control - Prof. M. Miccio

9. THE MOST COMMON INHERENT CHARACTERISTICS
Following the IEC norm, the manufacturer must provide the inherent characteristic of a control valve as table or diagram. In this latter case, the Cv at 5%, 10% up to 100% of the relative travel at 10% intervals has to be provided.
Linear characteristic:
= 0 +  h
0, : constant
Curve a in figure of previous slide, for r = 20, is an example of linear characteristic.
Equal percentage characteristic:
 = 0 eh
0 , : constant.
An equal percentage valve does not allow a full-closed position.
Curve b in previous slide, for r = 20, is an example of equal percentage characteristic.
In this case, we have:
the relative increase of the flow coefficient is proportional to the travel increase. Therefore, equal increase of the travel h produces equal percentage increase of the flow coefficient.
Quadratic (or parabolic) characteristic:
 = 0 + h2
0 ,  : constant.
Curve c in figure of previous slide, for r = 20, is an example of quadratic characteristic.
Quick opening characteristic:
It is characterized by a curve with decreasing derivative (curve d in figure).  = h(1/δ) with δ>1 
23/09/2019
Process Instrumentation and Control - Prof. M. Miccio

10. THE MOST COMMON INHERENT CHARACTERISTICS
Constants of previous equations can be related to the rangeability of the valve,
for which:
for h = 0
for h = 1
We obtain the following equations:
for the linear characteristic :
for the equal percentage characteristic:
for the quadratic characteristic:
for h = 1 1 = 0 e
r = e
 = (1/r) rh 
23/09/2019
Process Instrumentation and Control - Prof. M. Miccio

11. INHERENT CHARACTERISTIC and CLOSURE MEMBER
INHERENT CHARACTERISTIC and CLOSURE MEMBER
The proper shape of the closure member corresponds to a specified inherent characteristic.
TAPERED PLUG
In this case for a constant increase of the trim travel we have an equal percentage increase of the flow rate, for the same pressure drop. Considering an increase of 10% of the opening, the flow rate increases about 50% of the initial flow rate. It follows that the most increase of flow rate of the valve occurs in the last part of the travel of the closure member.
The equal percentage closure members are used when most of the pressure drop is localized in the plant and only the lower part occurs crossing the valve. They are also suggested when the flow rate and the operating pressure drop are subjected to significant changes during the process.
PARABOLOID
In this case a linear relation occurs between the opening of the valve and the flow rate.
Closure members with a linear characteristic are used when the operating pressure drop or flow rate do not change significantly with the time during the process.
DISK
The increase of the flow rate occurs almost exclusively in the first part of the opening, after which further increase of flow rate are almost negligible. For this reason, the disk closure member is also formerly known as quick opening.
It is commonly used for on/off or isolating function.
23/09/2019
Process Instrumentation and Control - Prof. M. Miccio