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Final Control Elements - Control Valves - Page 4

Article Index
Final Control Elements - Control Valves
Dampers and Louvres
Valve Packing
Valve Positioners
Control Valve Sizing, continued
Control Valve Problems

Valve positioners

Springs work quite nicely to convert mechanical force into mechanical motion (Hooke’s Law – F = kx) for valve actuators if and only if the sole forces involved are the diaphragm or piston force against the spring’s resistance force. If any other force acts upon the system, the relationship between actuating fluid pressure and valve stem travel will not necessarily be proportional.

Unfortunately, there typically are other forces acting on a valve stem besides the actuating fluid pressure’s force and the spring’s reaction force. Friction from the stem packing is one force, and reaction force at the valve plug caused by differential pressure across the plug’s area is another14.

These forces conspire to re-position the valve stem so stem travel does not precisely correlate to actuating fluid pressure.

A common solution to this dilemma is to add a positioner to the control valve assembly. A positioner is a motion-control device designed to actively compare stem position against the control signal, adjusting pressure to the actuator diaphragm or piston until the correct stem position is reached:

 

 

Positioners essentially act as control systems within themselves15: the valve’s stem position is the process variable (PV), the command signal to the positioner is the setpoint (SP), and the positioner’s signal to the valve actuator is the manipulated variable (MV) or output. Thus, when a process controller sends a command signal to a valve equipped with a positioner, the positioned receives that command signal and does its best to ensure the valve stem position follows along.

The following photograph shows a Fisher model 3582 pneumatic positioner mounted to a control valve. The positioner is the grey-colored box with three pressure gauges on the right-hand side:

 

 

A more modern positioner appears in the next photograph, the Fisher DVC6000 (again, the grey-colored box with pressure gauges on the right-hand side):

 

 

Positioners such as the DVC6000 are considered “smart” devices, containing digital electronic microprocessors to monitor and control valve stem position in accordance with the control signal, and also store data relevant to diagnostics16.

Control valve positioners are typically constructed in such a way to source and vent high air flow rates, such that the positioner also fulfills the functionality of a volume booster. Thus, a positioned not only ensures more precise valve stem positioning, but also faster stem velocity (and shorter time delays) than if the valve actuator were directly “powered” by an I/P transducer.

While beneficial on spring-equipped valve actuators, positioners are absolutely essential for positioners lacking springs such as double-acting pneumatic piston actuators. Some form of positioning mechanism is also required on electric motor actuators intended for throttling service, because an electric motor is not “aware” of its own shaft position in order that it may precisely move a control valve. Thus, a positioner circuit using a potentiometer or LVDT/RVDT sensor to detect valve stem position and a set of transistor outputs to drive the motor is necessary to make an electric actuator responsive to an analog control signal.

A simple force-balance pneumatic valve positioner design appears in the following illustration:

 


 

The control signal for this valve is a 3 to 15 PSI pneumatic signal, coming from either an I/P transducer or a pneumatic controller (neither one shown in the illustration). This control signal pressure applies an upward force on the force beam, such that the baffle tries to approach the nozzle. Increasing backpressure in the nozzle causes the pneumatic amplifying relay to output a greater air pressure to the valve actuator, which in turn lifts the valve stem up (opening up the valve). As the valve stem lifts up, the spring connecting the force beam to the valve stem becomes further stretched, applying additional force to the right-hand side of the force beam. When this additional force balances the bellows’ force, the system stabilizes at a new equilibrium.

Like all force-balance systems, the force beam motion is greatly constrained by the balancing forces, such that its motion is negligible for all practical purposes. In the end, equilibrium is achieved by one force balancing another, like two teams of people pulling oppositely on a length of rope: so long as the two teams’ forces remain equal in magnitude and opposite in direction, the rope will not deviate from its original position.

The following photograph shows a PMV model 1500 force-balance positioner used to position a rotary valve actuator, with the cover on (left) and removed (right):

 

 

The 3-15 PSI pneumatic control signal enters into the bellows, which pushes downward on the horizontal force beam. A pneumatic pilot valve assembly at the left-hand side of the force beam detects any motion, increasing air pressure to the valve actuating diaphragm if any downward motion is detected and releasing air pressure from the actuator if any upward motion is detected:

 

 

As compressed air is admitted to the valve actuator by this pilot valve assembly, the rotary valve will begin to rotate open. The shaft’s rotary motion is converted into a linear motion inside the positioner by means of a cam: a disk with an irregular radius designed to produce linear displacement from angular displacement:

 

A roller-tipped follower at the end of another beam rides along the cam’s circumference. Beam motion caused by the cam is translated into linear force by the compression of a coil spring directly against the force of the pneumatic bellows on the force beam. When the cam moves far enough to compress the spring enough to balance the additional force generated by the bellows, the force beam will come to an equilibrium position and the valve will stop moving.

Motion-balance pneumatic valve positioner designs also exist, whereby the motion of the valve stem counteracts motion (not force) from another element. The following illustration shows how a simple motion-balance positioner would work:

 

 

In this mechanism, an increasing signal pressure causes the beam to advance toward the nozzle, generating increased nozzle backpressure which then causes the pneumatic amplifying relay to send more air pressure to the valve actuator. As the valve stem lifts up, the upward motion imparted to the right-hand end of the beam counters the beam’s previous advance toward the nozzle. When equilibrium is reached, the beam will be in an angled position with the bellows’ motion balanced by valve stem motion.

The following photograph shows a close view of a Fisher model 3582 pneumatic motion-balance positioner’s mechanism:

 

 

At the heart of this mechanism is a D-shaped metal ring translating bellows motion and valve stem motion into flapper (baffle) motion. As the bellows (located underneath the upper-right corner of the D-ring) expands with increasing pneumatic signal pressure, it rocks the beam along its vertical axis. With the positioner set for direct-acting operation, this rocking motion drives the flapper closer to the nozzle, increasing backpressure and sending more compressed air to the valve actuator:

 

 

 As the valve stem moves, a feedback lever rotates a cam underneath the bottom-most portion of the D-ring. A roller follower riding on that cam translates the valve stem’s motion to another rocking motion on the beam, this time along the horizontal axis. Depending on how the cam has been fixed to the feedback shaft, this motion may rock the flapper away from the nozzle or further toward the nozzle. This selection of cam orientation must match the action of the actuator: either direct (air to extend the stem) or reverse (air to retract the stem).

The D-ring mechanism is rather ingenious, as it allows convenient adjustment of span by angling the flapper (baffle) assembly at different points along the ring’s circumference. If the flapper assembly is set close to horizontal, it will be maximally sensitive to bellows motion and minimally sensitive to valve stem motion, forcing the valve to move further to balance small motions of the bellows (long stroke length). Conversely, if the flapper assembly is set close to vertical, it will be maximally sensitive to valve stem motion and minimally sensitive to bellows motion, resulting in little valve stroke (i.e. the bellows needs to expand greatly in order to balance a small amount of stem motion).

Electronic valve positioners, such as the Fisher model DVC6000, use an electronic sensor to detect valve stem position, compare that sensed position against the control signal by subtraction (error = position signal), then send an appropriate pneumatic pressure to the valve actuator to minimize that error. A photograph of the potentiometer from a Fisher DVC6000 positioner appears here:

 

 

The DVC6000 positioner also contains air pressure sensors to monitor actuator air pressure as the valve moves. Being able to measure both stem position and actuator air pressure in real time allows the positioner to correlate one variable to the other in the form of a graph. Such a graph contains much useful diagnostic information for troubleshooting valve problems such as excessive packing friction, bent valve stems, and valve trim damage.

“Smart” positioners used on electric actuators have the capability to provide similar diagnostic data, correlating stem position with actuator torque (measured either indirectly by motor current or directly by a torque sensor in the gear train). Such data is quite valuable in predictive maintenance programs, used to identify when valve packing friction becomes excessive, or if valve trim components become damaged and no longer seat together properly. These diagnostic tools apply even to open/close motor-operated valves not used for throttling service, and are especially useful on gate, plug, and ball-type shut-off valves where seat engagement is substantial for tight shut-off.

 

14One way to minimize dynamic forces on a globe valve plug is to use a double-ported plug design, or to use a balanced plug on a cage-guided globe valve. A disadvantage to both these valve plug designs, though, is greater difficulty achieving tight shut-off.

15The technical term for this type of control system is cascade, where one controller’s output becomes the setpoint for a different controller. In the case of a valve positioner, the positioner receives a valve stem position setpoint from the main process controller.

16Examples of diagnostic data recorded by smart positioners includes error (command signal actual valve position), pressure versus motion relationships (used to measure valve packing friction), supply air pressure, and ambient temperature. Smart positioners even have the ability to totalize valve stem travel over long periods of time, enabling predictive maintenance alerts for wearing components such as packing and piston sealing rings.

 


Split-ranging

There are many process control applications in industry where it is desirable to have multiple control valves respond to the output of a common controller. Control valves configured to follow the command of the same controller are said to be split-ranged, or sequenced.

 Split-ranged control valves may take different forms of sequencing. A few different modes of control valve sequencing are commonly seen in industry: complementary, exclusive, and progressive17.

 

Complementary valve sequencing

The first is a mode where two valves serve to proportion a mixture of two fluid streams, such as this example where base and pigment liquids are mixed together to form colored paint:

 


 

Both base and pigment valves operate from the same 3 to 15 PSI pneumatic signal output by the I/P transducer (AY), but one of the valves is Air-To-Open while the other is Air-To-Close. The following table shows the relationship between valve opening for each control valve and the controller’s output:

 

  Controller output (%)     I/P output (PSI)     Pigment valve (stem position)     Base valve (stem position)  
0 % 3 PSI fully shut fully open
25 % 6 PSI 25% open 75% open
50 % 9 PSI half-open half-open
75 % 12 PSI 75% open 25% open
100 % 15 PSI fully open fully shut

 

An alternative expression for this split-range valve behavior is a graph showing each valve opening as a colored stripe of varying width (wider representing further open). For this particular mode of split-ranging, the graph would look like this:

 

With this form of split-ranging, there is never a condition in the controller’s output range where both valves are fully open or fully shut. Rather, each valve complements the other’s position18.

 

Exclusive valve sequencing

Other applications for split-ranged control valves call for a form of valve sequencing where both valves are fully closed at a 50% controller output signal, with one valve opening fully as the controller output drives toward 100% and the other valve opening fully as the controller output goes to 0%. The nature of this valve sequencing is to have an “either-or” throttled path for process fluid. That is, either process fluid flows through one valve or through the other, but never through both at the same time.

A practical example of this form of split-ranging is in reagent feed to a pH neutralization process, where the pH value of process liquid is brought closer to neutral by the addition of either acid or caustic:


Here, a pH analyzer monitors the pH value of the mixture and a single pH controller commands two reagent valves to open when needed. If the process pH begins to increase, the controller output signal increases as well (direct action) to open up the acid valve. The addition of acid to the mixture will have the effect of lowering the mixture’s pH value. Conversely, if the process pH begins to decrease, the controller output signal will decrease as well, closing the acid valve and opening the caustic valve. The addition of caustic to the mixture will have the effect of raising the mixture’s pH value.

Both reagent control valves operate from the same 3 to 15 PSI pneumatic signal output by the I/P transducer (AY), but the two valves’ calibrated ranges are not the same. The Air-To-Open acid valve has an operating range of 9 to 15 PSI, while the Air-To-Close caustic valve has an operating range of 9 to 3 PSI. The following table shows the relationship between valve opening for each control valve and the controller’s output:

 

  Controller output (%)     I/P output (PSI) 
  Acid valve (stem position)     Caustic valve (stem position) 
0 % 3 PSI fully shut fully open
25 % 6 PSI fully shut half-open
50 % 9 PSI fully shut fully shut
75 % 12 PSI half-open fully shut
100 % 15 PSI fully open fully shut

 

Again, we may express the two valves’ exclusive relationship in the form of a graph, with colored stripes representing valve opening:

 

Exclusive-sequenced control valves are used in applications where it would be undesirable to have both valves open simultaneously. In the example given of a pH neutralization process, the goal here is for the controller to be able to call forth either acid reagent or caustic reagent to “push” the pH value either direction as needed. However, simultaneously adding both acid and caustic to the process would be wasteful, as one reagent would simply neutralize the other with no benefit to the process liquid itself.

 

Progressive valve sequencing

A third form of control valve sequencing is used to expand the operating range of flow control for some fluid beyond that which a single control valve could muster. Once again pH control provides a suitable example to illustrate an application of this form of sequencing.

pH is an especially challenging application of process control because the dynamic range of the process is enormous. Each unit of pH value change represents a ten-fold change in hydrogen ion concentration within the process liquid. This means the difference in ion concentration between a process liquid having a value of 10 pH and a process liquid having a value of 7 pH is a factor of one thousand! Consequently, the flow rate of reagent necessary to neutralize a process liquid stream may vary widely. It is quite possible that a control valve sized to handle minimum flow will simply be too small to meet the demands of high flow when needed. Yet, a control valve sized large enough to meet the maximum flow rate may be too large to precisely “turn down” when just a trickle of reagent is needed.

This general control problem was encountered by automotive engineers in the days when carburetors were used to mix gasoline with air prior to combustion in an engine. A carburetor is a mechanical air flow control device using a “butterfly” valve element to throttle air flow into the engine, and a venturi element producing vacuum to aspirate fuel droplets into the air stream to create an air-fuel mixture. A carburetor with a butterfly valve and flow tube sized to idle well and respond to the needs of in-town driving would not flow enough air to provide high-end performance. Conversely, a large carburetor suitable for performance driving would be almost uncontrollable for low-speed and idling operation. Their solution to this problem was the progressive carburetor, having two butterfly valves to throttle the flow of air into the engine. One butterfly valve handled low amounts of air flow only, while a larger butterfly valve opened up only when the accelerator pedal was nearly at its maximum position. The combination of two differently-sized butterfly valves – progressively opened – gave drivers the best of both worlds. Now, an automobile engine could perform well both at low power levels and at high power levels.

On a fundamental level, the problem faced in pH control as well as by early automotive engineers is the same thing: insufficient rangeability. Some processes demand a greater range of control than any single valve can deliver, and it is within these processes that a pair of progressively-sequenced control valves is a valid solution.

Applying this solution to a pH control process where the incoming liquid always has a high pH value, and must be neutralized with acid:

 

 

Proper sequencing of the small and large acid control valves is shown in the table and the graph:



  Controller output (%)     I/P output (PSI)     Small acid valve (stem position)     Large acid valve (stem position)  
0 % 3 PSI fully shut fully shut
25 % 6 PSI half-open fully shut
50 % 9 PSI fully open fully shut
75 % 12 PSI fully open half-open
100 % 15 PSI fully open fully open


 

With the two acid control valves sequenced progressively, the control system will have sufficient rangeability to handle widely varying process conditions.

 

Valve sequencing methods

In all previous control valve sequencing examples shown, both control valves received the same pneumatic signal from a common I/P (current-to-pressure) converter. Sequencing between the two valves was a matter of proper bench-set pressure ranges.

Several alternative methods exist for control valve sequencing, as shown in the following illustration:

 

 
 
 

The common pneumatic signal approach (one controller, one I/P transducer) is simple but suffers from the disadvantage of slow response, since one I/P transducer must drive two pneumatic actuators. Response time may be improved by adding a pneumatic volume booster between the I/P and the valve actuators, or by adding a positioner to at least one of the valves. Either of these solutions works by the same principle: reducing the air volume demand on the one I/P transducer.

Wiring two I/P transducers in series so they share the exact same current is another way to split-range two control valves. This approach does not suffer from slow response, since each valve has its own dedicated I/P transducer to supply it with actuating air. We now have a choice where we implement the split ranges: we can do it in each of the I/P transducers (with non-standard I/P calibrations) or in the valve bench-set ranges as before. Since it is generally easier to re-range an I/P than it is to rebuild a control valve with a different spring (to give it a different actuating pressure range), this approach has the advantage of convenient configuration. A disadvantage of this approach is the extra demand placed on the controller’s output signal circuitry: one must be careful to ensure the two series-connected I/P converters do not drop too much voltage at full current, or else the controller may have difficulty driving both in series. Another (potential) disadvantage of series-connected valve devices in one current loop is the inability to install “smart” instruments communicating with the HART protocol, since multiple devices on the same loop will experience address conflicts19.

A very common way to implement split-ranging is to use a controller with multiple 4-20 mA outputs. This is very easy to do if the controller is part of a large system (e.g. a DCS or a PLC with multiple output channels). Now, each valve has its own dedicated wire pair for control. A further advantage of dual controller outputs is the ability to perform the split-range sequencing within the controller itself, which is often easier than re-ranging an I/P or calibrating a valve positioner.

Dual controllers are an option only for specialized applications requiring different degrees of responsiveness for each valve, usually for exclusive or progressive split-ranging applications only. Care must be taken to ensure the controllers’ output signals do not wander outside of their intended ranges, or that the controllers do not begin to “fight” each other in trying to control the same process variable20.

An important consideration – and one that is easily overlooked – in split-range valve systems is fail-safe mode. The basis of fail-safe control system design is that the control valve(s) must be chosen to fail in the mode that is safest for the process in the event of actuating power loss or control signal loss. The actions of all other instruments in the loop should then be selected to complement the valves’ natural operating mode.

In control systems where valves are split-ranged in either complementary or exclusive fashion, one control valve will be fully closed and the other will be fully open at each extreme end of the signal range (e.g. at 4 mA and at 20 mA). If the control valves are driven by the same controller signal, the failure modes of the two valves must likewise be opposite each other: one will fail open while the other fails closed if the signal goes dead or if air pressure is lost. However, if it is deemed safer for the process to have the two valves fail in the same state – for example, to both fail closed in the event of air pressure or signal loss – it is still possible to sequence them for complementary or exclusive control action by driving the two valves with different output signals. In other words, split-ranging two control valves so they normally behave in opposite fashion does not necessarily mean the two valves must fail in opposite states.


As an example, consider the following temperature control system supplying either hot water or chilled water to a “jacket” surrounding a chemical reactor vessel. The purpose of this system is to control temperature within the reactor to a constant setpoint value, regardless of the chemical reaction’s thermal properties. If the reaction inside the vessel is exothermic (releasing heat), the control system will respond by sending chilled water to the jacket to remove that heat. If the reaction inside the vessel is endothermic (absorbing heat), the control system will respond with hot water to the jacket to add heat. Chemical piping in and out of the reactor vessel has been omitted from this P&ID for simplicity, so we can focus just on the reactor’s temperature control system:


 Here, the controller has been configured for dual-output operation, where the output value drives two identical 4-20 mA signals to the control valve positioners, which directly input the current signals from the controller without the need for I/P transducers in between. The hot water valve (TV-37a) is fail-closed (FC) while the cold water valve (TV-37b) is fail-open (FO). Half-range positioned calibrations provide the exclusive sequencing necessary to ensure the two valves are never open simultaneously – TV-37b operates on the lower half of the 4-20 mA signal range (4-12 mA), while  TV-37a operates on the upper half (12-20 mA).

Consider the effects from the controller (TIC-37) losing power. Both 4-20 mA signals will go dead, driving both valves to their fail-safe modes: hot water valve TV-37a will fully close, while cold water valve TV-37b will fully open. Now consider the effects of air pressure loss to both valves. With no air pressure to operate, the actuators will spring-return to their fail-safe modes: once again hot water valve TV-37a will fully close, while cold water valve TV-37b will fully open. In both failure events, the two control valves assume consistent states, ensuring the reactor will cool down rather than heat up.

Now imagine someone reconfigures the system, using identical control valves (signal-to-open, fail-closed) for both hot and cold water supply, and a different program in the controller to exclusively sequence two different 4-20 mA current signals:

 


 

Consider the effects from the controller (TIC-37) losing power. Both 4-20 mA signals will go dead, driving both valves to their fail-safe modes: fully closed. Now consider the effects of air pressure loss to both valves. With no air pressure to operate, the actuators will spring-return to their fail-safe modes: once again both control valves fully close. In both failure events, the two control valves assume consistent states where the reactor is neither heated nor cooled, but rather left to assume its own temperature. The failure modes of both valves are still consistent regardless of the nature of the fault, but note how this scheme allows both valves to fail in the same mode if that is what we deem safest for the process.

As with all fail-safe system designs, we begin by choosing the proper fail-safe mode for each control valve as determined by the nature of the process, not by what we would consider the simplest or easiest-to-understand instrument configurations. Only after we have chosen each valve’s failure mode do we design the rest of the system to behave they way we wish. This includes split-range sequencing: where and how we sequence the valve operation is a decision to be made only after the valves’ natural fail-safe states are chosen based on the needs of process safety.

 

17I have searched in vain for standardized names to categorize different forms of control valve sequencing. The names “complementary,” “exclusive,” and “progressive” are my own invention. If I have missed someone else’s categorization of split-ranging in my research, I sincerely apologize.

18In mathematics, a “complement” is a value whose sum with another quantity always results in a fixed total. Complementary angles, for instance, always add to 90o (a right angle).

19Although the HART standard does support “multidrop” mode where multiple devices exist on the same current loop, this mode is digital-only with no analog signal support. Not only do many host systems not support HART multidrop mode, but the relatively slow data communication rate of HART makes this choice unwise for most process control applications. If analog control of multiple HART valve positioner devices from the same 4-20 mA signal is desired, the address conflict problem may be resolved through the use of one or more isolator devices, allowing all devices to share the same analog current signal but isolating each other from HART signals.

20Both controllers should be equipped with provisions for reset windup control (or have no integral action at all), such that the output signal values are predictable enough that they behave as a synchronized pair rather than as two separate controllers.

 


Control valve sizing

When control valves operate between fully open and fully shut, they serve much the same purpose in process systems as resistors do in electric circuits: to dissipate energy. Like resistors, the form that this dissipated energy takes is mostly heat, although some of the dissipated energy manifests in the form of vibration and noise21.

In most control valves, the dominant mechanism of energy dissipation comes as a result of turbulence introduced to the fluid as it travels through constrictive portions of the valve trim. The following illustration shows these constrictive points within two different control valve types (shown by arrows):

 

 

The act of choosing an appropriate control valve for the expected energy dissipation is called valve sizing.

 

Physics of energy dissipation in a turbulent fluid stream

As one might expect, control valves are rated in their ability to throttle fluid flow, much as resistors are rated in their ability to throttle the flow of electrons in a circuit. For resistors, the unit of measurement for electron flow restriction is the ohm: 1 ohm of resistance results in a voltage drop of 1 volt across that resistance given a current through the resistance equal to 1 ampere:

 

The mathematical relationship between current, voltage, and resistance for any resistor is Ohm’s Law:

 

 

Where,

  R = Electrical resistance in ohms

  V = Electrical voltage drop in volts

  I = Electrical current in amperes

 

Ohm’s Law is a simple, linear relationship, expressing the “friction” encountered by electric charge carriers as they slowly drift through a solid object.

When a fluid moves turbulently through any restriction, energy is inevitably dissipated in that turbulence. The amount of energy dissipated is proportional to the kinetic energy of the turbulent motion, which is proportional to the square of velocity according to the classic kinetic energy equation for moving objects:


If we were to re-write this equation to express the amount of kinetic energy represented by a volume of moving fluid with velocity v, it would look like this:

 

We know that the amount of energy dissipated by turbulence in such a fluid stream will be some proportion (k) of the total kinetic energy, so:

 
Any energy lost in turbulence eventually manifests as a loss in fluid pressure. Thus, a control valve throttling a fluid flowstream will have a greater upstream pressure than downstream pressure (assuming all other factors such as pipe size and height above ground level being the same downstream as upstream):
 

This pressure drop (P1 P2, or _P) is equivalent to the voltage drop seen across any current carrying resistor, and may be substituted for dissipated energy per unit volume in the previous equation22. We may also substitute for velocity v because we know volumetric flow rate (Q) is the product of fluid velocity and pipe cross-section area (Q = Av) for incompressible fluids such as liquids:


Next, we will solve for a quotient with pressure drop (P1 P2) in the numerator and flow rate Q in the denominator so the equation bears a resemblance to Ohm’s Law ( ):

 

 

Either side of the last equation represents a sort of “Ohm’s Law” for turbulent liquid restrictions: the left-hand side expressing fluid “resistance” in the state variables of pressure drop and volumetric flow, and the right-hand term expressing fluid “resistance” as a function of fluid density and restriction geometry. We can see how pressure drop (P1 P2) and volumetric flow rate (Q) are not linearly related as voltage and current are for resistors, but that nevertheless we still have a quantity that acts like a “resistance” term:

 

 

Where,

  R = Fluid “resistance”

  P1 = Upstream fluid pressure

  P2 = Downstream fluid pressure

  Q = Volumetric fluid flow rate

  k = Turbulent energy dissipation factor

  ρ = Mass density of fluid

  A = Cross-sectional area of restriction

 

The fluid “resistance” of a restriction depends on several variables: the proportion of kinetic energy lost due to turbulence (k), the density of the fluid (ρ), and the cross-sectional area of the restriction (A). In a control valve throttling a liquid flow stream, only the first and last variables are subject to change with stem position, fluid density remaining relatively constant.

In a wide-open control valve, especially valves offering a nearly unrestricted path for moving fluid (e.g. ball valves, eccentric disk valves), the value of A will be at a maximum value essentially equal to the pipe’s area, and k will be nearly zero23. In a fully shut control valve, A is zero, creating a condition of infinite “resistance” to fluid flow.

It is customary in control valve engineering to express the “restrictiveness” of any valve in terms of how much flow it will pass given a certain pressure drop and fluid specific gravity (Gf ). This measure of valve performance is called flow capacity or flow coefficient, symbolized as Cv. A greater flow capacity value represents a less restrictive (less “resistive”) valve, able to pass greater rates of flow for the same pressure drop. This is analogous to expressing an electrical resistor’s rating in terms of conductance (G) rather than resistance (R): how many amperes of current it will pass with 1 volt of potential drop (I = GV instead of ).

If we return to one of our earlier equations expressing pressure drop in terms of flow rate, restriction area, dissipation factor, and density, we will be able to manipulate it into a form expressing flow rate (Q) in terms of pressure drop and density, collecting k and A into a third term which will become flow capacity (Cv):



First, we must substitute specific gravity (Gf ) for mass density (ρ) using the following definition of specific gravity:

 

 

Substituting and continuing with the algebraic manipulation:

 

 

The first square-rooted term in the equation,, is the valve capacity or Cv factor.

Substituting Cv for this term results in the simplest form of valve sizing equation (for incompressible fluids):


In the United States of America, Cv is defined as the number of gallons per minute of water that will flow through a valve with 1 PSI of pressure drop24. A similar valve capacity expression used elsewhere in the world rates valves in terms of how many cubic meters per hour of water will flow through a valve with a pressure drop of 1 bar. This latter flow capacity is symbolized as Kv.

For the best results predicting required Cv values for control valves in any service, it is recommended that you use valve sizing software provided by control valve manufacturers. Modern valve sizing software is easy to use, especially when referenced to specific models of control valve sold by that manufacturer, and is able to account for a diverse multitude of factors affecting proper sizing.

Control valve sizing is complex enough that some valve manufacturers used to give away “slide rule” calculator devices so customers could choose the Cv values they needed with relative ease. Photographs of a two-sided valve sizing slide rule are shown here for historical reference:

 

 
 

 



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