5 Must-Have Features in a Electro hydraulic control valve

Author: Heather

Feb. 24, 2025

Understanding Electrohydraulic Valve Types - Power & Motion

Electrohydraulic valves are often classified as either servo or proportional, a distinction that gives an indication of expected performance. However, this classification tends to generalize and blur the true differences between the various types of electrohydraulic valves available in the market.

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Understanding the different types of electrohydraulic valves available and how each can help to control pressure or flow ensures the right valve is selected for a given application.

Traditionally, the term servo valve describes valves that use closed-loop control. They monitor and feed back the main-stage spool position to a pilot stage or driver either mechanically or electronically. Proportional valves, on the other hand, move the main-stage spool in direct proportion to a command signal, but they usually do not have any means of automatic error correction (feedback) within the valve.

Confusion often arises when a valve's construction resembles a proportional valve, but the presence of a spool position feedback sensor (usually an LVDT [linear variable differential transformer]) boosts its performance to that rivalling a servo valve. This reinforces the concept that designers and suppliers should use common terminology and focus on the performance requirements of the particular application at hand.

Typically, proportional valves use one or two proportional solenoids to move the spool by driving it against a set of balanced springs. The resultant spool displacement is proportional to the current driving the solenoids. The springs also center the main stage spool. Repeatability of the main-stage spool position is a function of the springs' symmetry and ability of the design to minimize nonlinear effects of spring hysteresis, friction, and machining tolerance variations.

An Explainer on Servo Valves

The term servo valve traditionally leads engineers to think of mechanical feedback valves, where a spring element (feedback wire) connects a torque motor to the main-stage spool. Spool displacement causes the wire to impart a torque onto the pilot-stage motor. The spool will hold position when torque from the feedback wire's deflection equals the torque from an electromagnetic field induced by the current through the motor coil. These two-stage valves contain a pilot stage or torque motor, and a main or second stage. Sometimes the main stage is referred to as the power stage. These valves can be separated primarily into two types, nozzle flapper and jet pipe, as seen in Figure 1 below.

The electromagnetic circuit of a nozzle flapper or jet pipe torque motor is essentially the same. The differences between the two lie in the hydraulic bridge design. A hydraulic bridge controls the pilot flow which, in turn, controls the main-stage spool movement. In a nozzle flapper, the torque produced on the armature by the magnetic field moves the flapper toward either nozzle depending on command-signal polarity. Flapper displacement induces a pressure imbalance on the spool ends which moves the spool. In a jet pipe, the armature movement deflects the jet pipe and asymmetrically imparts fluid between the spool ends through the jet receiver. This pressure imbalance remains until the feedback wire returns the jet pipe or flapper to neutral.

Historically, jet pipe and nozzle flapper servo valves have competed for similar applications that require high dynamics. Typically, better first-stage dynamics gives the nozzle flapper better overall response, whereas improved pressure recovery of the jet/receiver bridge design gives the jet pipe motors higher spool driving forces (chip-shearing capability).

Both valves require low command currents and therefore offer a large mechanical advantage. Motor current for these style valves is typically less than 50.0 mA. Note that these servo valves are also proportional valves, because spool displacement and flow are directly proportional to the input command.

READ MORE: Getting the Most out of Electrohydraulic Valves

Direct-Driven Electrohydraulic Valves

Direct-driven valves, unlike hydraulically piloted two-stage valves, displace the spool by physically linking it to the motor armature. These valves usually come in two basic varieties, those driven by linear force motors (LFM) and those actuated by proportional solenoids. Within these two general classifications, the valves can be separated into proportional and servoproportional. The distinction is based on the use of a position transducer to provide spool position feedback. Servoproportional valves must incorporate closed-loop spool position feedback to increase repeatability and accuracy necessary for high-control applications. Typically, servoproportional, direct-driven valves have an overall lower dynamic response than hydraulically piloted two-stage valves with the same flow characteristics. This is usually due to the large armature mass of the LFM or solenoid and the large time constant associated with the coil, which is a function of the induction and resistance of the coil.

Unlike hydraulically piloted servos, direct-driven valve performance does not vary with changes in supply pressure. This makes them ideal for applications where pilot flow for first-stage operation is not available. Direct-driven valves also tend to be viscosity insensitive devices, whereas nozzle flapper and jet pipe valves work best with oil viscosity below 6,000 SUS. However, most direct-driven valves cannot generate the high spool driving forces of their hydraulically piloted counterparts.

Like the torque motor used in the nozzle flapper/jet pipe servos, the LFM allows for bidirectional movement by adding permanent magnets to the design and therefore making the armature motion sensitive to command polarity. In the outstroke, the LFM must overcome spring force plus external flow and friction forces. During the backstroke to center position, however, the spring provides additional spool-driving force which makes the valve less contamination sensitive. Magnetic-field forces are balanced by a bidirectional spring that lets the spool remain centered without expending any power.

Unlike the LFM, the proportional solenoid is a unidirectional device. Two solenoids oppose each other to achieve a centered, no power, fail-safe position. When a single solenoid is used, holding the spool at midstroke requires a continuous current to balance the load generated by the return spring. This makes the design less energy efficient than its LFM or a dual-solenoids counterpart. During a power loss, the LFM and dual proportional solenoid designs fail to a neutral position and block flow to the load, that is the piston. When a single solenoid design loses power, the spool must move through an open position that tends to cause uncontrolled load movements.

Creation of Multistage Valves 

All of the aforementioned designs can be used to create a multistage hydraulic valve. The approach for each design is specific to the application requirements. Usually, most designs do not exceed three stages. Mounting a nozzle flapper, jet pipe, or direct-driven valve onto a larger main stage satisfies most requirements for dynamics and flow.

Sometimes, the jet pipe valve is used in a multistage configuration where the mechanical feedback of a traditional jet pipe is replaced with electronic feedback. This servojet style has pilot characteristics of a typical jet pipe. Depending on the required control, many multistage valves can close a position loop about the main stage using a linear variable differential transducer. This device monitors the spool position. In case of hydraulic power loss, springs on opposite sides of the main stage spool return it to a neutral position.

A Closer Look at Servo Valve Designs

Viewing the principal internal parts of a flapper-nozzle servo valve, as shown in Figure 3 below, it should be clear that torque applied from a torque motor to the flapper arm, say in the clockwise direction, moves the flapper closer to nozzle A and tends to close it.

Concurrently, the flapper moves away from nozzle B to allow more flow through it, so the net result is a rise in pressure Pa and a drop in pressure Pb. The pressure difference, Pa - Pb is felt across the two ends of the main valve spool, driving it to the right and creating communication from port P to port B, and from port A to port T.

Incoming current creates a second set of magnetic fluxes that unbalance the force bridge and results in net torque. The torque causes angular rotation until the flux-induced torque equals the counter-torque of the flexing spring plus any external load. An important characteristic of the torque motor is that the direction of rotation is affected by the direction of current through the coil. The electromagnetic field caused by the current is compared to the field of the permanent magnet in the magnetic bridge circuit and rotation ensues in a commensurate direction.

In the final valve assembly, the torque-motor armature is connected to a flapper sitting between two opposed nozzles, a jet pipe, or a swinging wand or blade. These last two steer a fluid stream, shown below in Figure 6, branch B. Basic operating principles and conceptual construction of flapper-nozzle and jet pipe servo valves are indicated in Figures 7 and 8 below, respectively. Torque motors almost exclusively pilot servo valves, and usually require less than 1W of power to fully operate although that is not a hard-and-fast rule.

The single-nozzle version has a hole laterally bored and centrally located in the wand such that the single fluid stream issuing from the single nozzle must pass through the hole. When the wand is centered, equal pressures are collected in the two receiving ports. A current into the coil causes the wand to shift and the fluid stream is deflected off the inside edge of the central hole resulting in different pressures being collected in the two receivers. The resulting differential pressure between the two receiving ports shifts the main spool.

This swinging-wand design has a supply pressure limitation in that the pilot head must be sized for a particular supply-pressure range. If flow issuing from the nozzle(s) is excessive, fluid momentum force acting on the wand can pin it against the receiver side, locking it there. Installing an orifice ' matched with the supply pressure and the needs of the pilot stage ' in series with the nozzle side, remedies this problem. An approximately 2:1 change in supply pressure is possible with a single orifice.

Force motors are the linear equivalent of torque motors in that they also have permanent magnets inside. Therefore, the direction of motion depends upon the direction of input current, as shown in Figure 12 below. There is only one manufacturer of force motors in the U. S.: Fema Corp., Portage, MI. The two permanent magnets each create attractive forces, each urging the armature toward it, but nominally offsetting one another when centered. Additionally, a stiff centering spring prevents either of the natural regenerative attractive forces from pulling the armature either way.

When a current is applied in the direction shown in Figure 12, the resulting electromagnetic fields act to strengthen the magnetic fields by increased flux density in air-gaps B and D while at the same time weakening the fields in air-gaps A and C. The resulting force moves the armature and poppet to the left. State-of-the-art force-motor design produces a maximum of about 5 lbs. of stall force, about 0.02-in. of travel (no load) at about 5W of power.

Comparing Solenoid and Motor Devices

Some differences between proportional solenoids and force/torque motors are apparent in the specifications while others are not. Torque/force motors require lower current levels. Proportional solenoids:

  • require much higher electrical input power than their motor counterparts,
  • produce substantially greater mechanical travel than motors,
  • produce higher levels of force,
  • produce higher levels of stiction,
  • operate with greater hysteresis, and
  • generate force in a direction independent of current direction.

Therefore, to make a 4-way directional valve operate requires two proportional solenoids but only one force/torque motor.

All of these factors make proportional-solenoid drive electronics more complex than that necessary for force/torque motors. Proportional-solenoid power requirements have caused manufacturers of proportional-valve drive electronics to adopt pulse width modulation (PWM) as the power-output method of choice. The major reason for the use of PWM is to handle the high-output power required of the solenoid without overburdening the power-output transistors.

There is a second benefit of using PWM: if the PWM frequency is sufficiently low, it automatically provides a mechanical dither that helps minimize stiction-induced hysteresis. In some valves the effects of dither can only be described as dramatic when looking at the reduction in hysteresis. The correct dither frequency must be determined after the valve is designed. Furthermore, the frequency selected must be a compromise between propagating the dither pulsations imperceptibly into the hydraulic circuit and yet achieving sufficient reduction in stiction. A low frequency helps the stiction problem but if too low, the user of the hydraulic system can feel the pulsations.

U.S. industry uses PWM frequencies from about 33 to about 400 Hz. At least one European manufacturer uses 40 kHz and receives no dither effects whatsoever. Their amplifier supplies dither with a separate on-board dither generator. There is an advantage to this method: dither power remains constant throughout the modulation range, whereas when relying on the PWM frequency for dithering, the dither power varies with the amount of modulation. There is none at the 0 and 100% modulation points, but maximum at 50% modulation.

READ MORE: Solenoid Valve Quality in Arctic Can Impact Oil and Gas Applications

A Summary of Pilot-Operated Valves

Figure 13 below shows a family tree of all electrically modulated, continuously variable pilot-operated valves. It is a peculiarity of the U.S. hydraulic valve manufacturing industry that each terminus of the tree also tends to define a specific manufacturer's product. For example, the A/C/E/I/N/V path rather accurately describes the servo valve built by Danfoss' Controls Div. in Minneapolis (note that its mate, U, has no supplier).

In contrast, though, the A/C/E/J/O path is well populated. That is where the products of Moog, Bosch Rexroth, Parker Hannifin's Dynamic Valve and others have congregated.

How to Choose the Right Electrohydraulic Valve 

To choose the proper electrohydraulic valve for a specific application, designers must consider specific application and system configurations. Supply pressure, fluid type, system force requirements, valve dynamic response, and load resonant frequency are examples of the various factors affecting system operation.

Hydraulically piloted valves are sensitive to supply pressure disturbances, whereas direct-driven valves are unaffected by supply pressure variation. Fluid type is important when considering seal compatibility and viscosity effects on performance over the system's operating temperature range.

Total force requirements must include all static and dynamic forces acting on the system. Load forces can aid or resist, depending on load orientation and direction. Forces required to overcome inertia can be large in high-speed applications and are critical to valve sizing.

The load resonance frequency is a function of the overall travel stiffness, which is the combination of the hydraulic and structural stiffness. For optimum dynamic performance, a valve's 90° phase point should exceed the load resonant frequency by a factor of three or more.

The valve's dynamic response is defined as the frequency where phase lag between input current and output flow is 90°. This 90° phase lag point varies with input signal amplitude, supply pressure, and fluid temperature so comparisons must use consistent conditions.

Control Valve Characteristics | Spirax Sarco

Examples of these and their inherent characteristics are shown in Figures 6.5.1 and 6.5.2.

Fast opening characteristic

The fast opening characteristic valve plug will give a large change in flowrate for a small valve lift from the closed position. For example, a valve lift of 50% may result in an orifice pass area and flowrate up to 90% of its maximum potential.

A valve using this type of plug is sometimes referred to as having an 'on/off' characteristic.

Unlike linear and equal percentage characteristics, the exact shape of the fast opening curve is not defined in standards. Therefore, two valves, one giving a 80% flow for 50% lift, the other 90% flow for 60% lift, may both be regarded as having a fast opening characteristic.

Fast opening valves tend to be electrically or pneumatically actuated and used for 'on/off' control.

The self-acting type of control valve tends to have a plug shape similar to the fast opening plug in Figure 6.5.1. The plug position responds to changes in liquid or vapour pressure in the control system. The movement of this type of valve plug can be extremely small relative to small changes in the controlled condition, and consequently the valve has an inherently high rangeability. The valve plug is therefore able to reproduce small changes in flowrate, and should not be regarded as a fast opening control valve.

Linear characteristic

The linear characteristic valve plug is shaped so that the flowrate is directly proportional to the valve lift (H), at a constant differential pressure. A linear valve achieves this by having a linear relationship between the valve lift and the orifice pass area (see Figure 6.5.3).

For example, at 40% valve lift, a 40% orifice size allows 40% of the full flow to pass.

Equal percentage characteristic (or logarithmic characteristic)

These valves have a valve plug shaped so that each increment in valve lift increases the flowrate by a certain percentage of the previous flow. The relationship between valve lift and orifice size (and therefore flowrate) is not linear but logarithmic, and is expressed mathematically in Equation 6.5.1:

Example 6.5.1

The maximum flowrate through a control valve with an equal percentage characteristic is 10 m³/h. If the valve has a turndown of 50:1, and is subjected to a constant differential pressure, by using Equation 6.5.1 what quantity will pass through the valve with lifts of 40%, 50%, and 60% respectively?

The increase in volumetric flowrate through this type of control valve increases by an equal percentage per equal increment of valve movement:

  • When the valve is 50% open, it will pass 1.414 m³/h, an increase of 48% over the flow of 0.956 m³/h when the valve is 40% open.
  • When the valve is 60% open, it will pass 2.091 m³/h, an increase of 48% over the flow of 1.414 m³/h when the valve is 50% open.

It can be seen that (with a constant differential pressure) for any 10% increase in valve lift, there is a 48% increase in flowrate through the control valve. This will always be the case for an equal percentage valve with rangeability of 50. For interest, if a valve has a rangeability of 100, the incremental increase in flowrate for a 10% change in valve lift is 58%.

Table 6.5.1 shows how the change in flowrate alters across the range of valve lift for the equal percentage valve in Example 6.5.1 with a rangeability of 50 and with a constant differential pressure.

A few other inherent valve characteristics are sometimes used, such as parabolic, modified linear or hyperbolic, but the most common types in manufacture are fast opening, linear, and equal percentage.

Matching the valve characteristic to the installation characteristic

Each application will have a unique installation characteristic that relates fluid flow to heat demand. The pressure differential across the valve controlling the flow of the heating fluid may also vary:

  • In water systems, the pump characteristic curve means that as flow is reduced, the upstream valve pressure is increased (refer to Example 6.5.2, and Module 6.3).
  • In steam temperature control systems, the pressure drop over the control valve is deliberately varied to satisfy the required heat load.

The characteristic of the control valve chosen for an application should result in a direct relationship between valve opening and flow, over as much of the travel of the valve as possible.

This section will consider the various options of valve characteristics for controlling water and steam systems. In general, linear valves are used for water systems whilst steam systems tend to operate better with equal percentage valves.

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1. A water circulating heating system with three-port valve

In water systems where a constant flowrate of water is mixed or diverted by a three-port valve into a balanced circuit, the pressure loss over the valve is kept as stable as possible to maintain balance in the system.

Conclusion 
- The best choice in these applications is usually a valve with a linear characteristic. Because of this, the installed and inherent characteristics are always similar and linear, and there will be limited gain in the control loop.

2. A boiler water level control system ' a water system with a two-port valve

In systems of this type (an example is shown in Figure 6.5.6), where a two-port feedwater control valve varies the flowrate of water, the pressure drop across the control valve will vary with flow. This variation is caused by:

  • The pump characteristic. As flowrate is decreased, the differential pressure between the pump and boiler is increased (this phenomenon is discussed in further detail in Module 6.3).
  • The frictional resistance of the pipework changes with flowrate. The head lost to friction is proportional to the square of the velocity. (This phenomenon is discussed in further detail in Module 6.3).
  • The pressure within the boiler will vary as a function of the steam load, the type of burner control system and its mode of control.

Example 6.5.2 Select and size the feedwater valve in Figure 6.5.6

In a simplified example (which assumes a constant boiler pressure and constant friction loss in the pipework), a boiler is rated to produce 10 tonnes of steam per hour. The boiler feedpump performance characteristic is tabulated in Table 6.5.2, along with the resulting differential pressure (ΔP) across the feedwater valve at various flowrates at, and below, the maximum flow requirement of 10 m³/h of feedwater.

Note: The valve ΔP is the difference between the pump discharge pressure and a constant boiler pressure of 10 bar g. Note that the pump discharge pressure will fall as the feedwater flow increases. This means that the water pressure before the feedwater valve also falls with increased flowrate, which will affect the relationship between the pressure drop and the flowrate through the valve.

It can be determined from Table 6.5.2 that the fall in the pump discharge pressure is about 26% from no-load to full-load, but the fall in differential pressure across the feedwater valve is a lot greater at 72%. If the falling differential pressure across the valve is not taken into consideration when sizing the valve, the valve could be undersized.

As discussed in Modules 6.2 and 6.3, valve capacities are generally measured in terms of Kv. More specifically, Kvs relates to the pass area of the valve when fully open, whilst Kvr relates to the pass area of the valve as required by the application. 

Consider if the pass area of a fully open valve with a Kvs of 10 is 100%. If the valve closes so the pass area is 60% of the full-open pass area, the Kvr is also 60% of 10 = 6. This applies regardless of the inherent valve characteristic. The flowrate through the valve at each opening will depend upon the differential pressure at the time. 

Using the data in Table 6.5.2, the required valve capacity, Kvr, can be calculated for each incremental flowrate and valve differential pressure, by using Equation 6.5.2, which is derived from Equation 6.3.2.The Kvr can be thought of as being the actual valve capacity required by the installation and, if plotted against the required flowrate, the resulting graph can be referred to as the 'installation curve'.

At the full-load condition, from Table 6.5.2:

Required flow through the valve = 10 m³/ h

ΔP across the valve = 1.54 bar

From Equation 6.5.2:

Taking the valve flowrate and valve ΔP from Table 6.5.2, a Kvr for each increment can be determined from Equation 6.5.2; and these are tabulated in Table 6.5.3.

Constructing the installation curve

The Kvr of 8.06 satisfies the maximum flow condition of 10 m3/h for this example.

The installation curve could be constructed by comparing flowrate to Kvr, but it is usually more convenient to view the installation curve in percentage terms. This simply means the percentage of Kvr to Kvs, or in other words, the percentage of actual pass area relative to the full open pass area.

For this example: The installation curve is constructed, by taking the ratio of Kvr at any load relative to the Kvs of 8.06. A valve with a Kvs of 8.06 would be 'perfectly sized', and would describe the installation curve, as tabulated in Table 6.5.4, and drawn in Figure 6.5.7. This installation curve can be thought of as the valve capacity of a perfectly sized valve for this example.

It can be seen that, as the valve is 'perfectly sized' for this installation, the maximum flowrate is satisfied when the valve is fully open.

However, it is unlikely and undesirable to select a perfectly sized valve. In practice, the selected valve would usually be at least one size larger, and therefore have a Kvs larger than the installation Kvr.

As a valve with a Kvs of 8.06 is not commercially available, the next larger standard valve would have a Kvs of 10 with nominal DN25 connections.

It is interesting to compare linear and equal percentage valves having a Kvs of 10 against the installation curve for this example.

Consider a valve with a linear inherent characteristic

A valve with a linear characteristic means that the relationship between valve lift and orifice pass area is linear. Therefore, both the pass area and valve lift at any flow condition is simply the Kvr expressed as a proportion of the valve Kvs. For example:

It can be seen from Table 6.5.4, that at the maximum flowrate of 10 m³/h, the Kvr is 8.06. If the linear valve has a Kvs of 10, for the valve to satisfy the required maximum flowrate, the valve will lift:

Using the same routine, the orifice size and valve lift required at various flowrates may be determined for the linear valve, as shown in Table 6.5.5.

An equal percentage valve will require exactly the same pass area to satisfy the same maximum flowrate, but its lift will be different to that of the linear valve.

Consider a valve with an equal percentage inherent characteristic
Given a valve rangeability of 50:1, τ  = 50, the lift (H) may be determined using Equation 6.5.1:

Percentage valve lift is denoted by Equation 6.5.3.

As the volumetric flowrate through any valve is proportional to the orifice pass area, Equation 6.5.3 can be modified to give the equal percentage valve lift in terms of pass area and therefore Kv.

This is shown by Equation 6.5.4.

As already calculated, the Kvr at the maximum flowrate of 10 m³/h is 8.06, and the Kvs of the DN25 valve is 10. By using Equation 6.5.4 the required valve lift at full-load is therefore: therefore:

Using the same routine, the valve lift required at various flowrates can be determined from Equation 6.5.4 and is shown in Table 6.5.6.

Comparing the linear and equal percentage valves for this application

The resulting application curve and valve curves for the application in Example 6.5.2 for both the linear and equal percentage inherent valve characteristics are shown in Figure 6.5.8.

Note that the equal percentage valve has a significantly higher lift than the linear valve to achieve the same flowrate. It is also interesting to see that, although each of these valves has a Kvs larger than a 'perfectly sized valve' (which would produce the installation curve), the equal percentage valve gives a significantly higher lift than the installation curve. In comparison, the linear valve always has a lower lift than the installation curve.

The rounded nature of the curve for the linear valve is due to the differential pressure falling across the valve as the flow increases. If the pump pressure had remained constant across the whole range of flowrates, the installation curve and the curve for the linear valve would both have been straight lines.

By observing the curve for the equal percentage valve, it can be seen that, although a linear relationship is not achieved throughout its whole travel, it is above 50% of the flowrate.

The equal percentage valve offers an advantage over the linear valve at low flowrates. Consider, at a 10% flowrate of 1 m³/h, the linear valve only lifts roughly 4%, whereas the equal percentage valve lifts roughly 20%. Although the orifice pass area of both valves will be exactly the same, the shape of the equal percentage valve plug means that it operates further away from its seat, reducing the risk of impact damage between the valve plug and seat due to quick reductions in load at low flowrates.

An oversized equal percentage valve will still give good control over its full range, whereas an oversized linear valve might perform less effectively by causing fast changes in flowrate for small changes in lift.

Conclusion - In most applications, an equal percentage valve will provide good results, and is very tolerant of over-sizing. It will offer a more constant gain as the load changes, helping to provide a more stable control loop at all times. However, it can be observed from Figure 6.5.8, that if the linear valve is properly sized, it will perform perfectly well in this type of water application.

3. Temperature control of a steam application with a two-port valve

In heat exchangers, which use steam as the primary heating agent, temperature control is achieved by varying the flow of steam through a two-port control valve to match the rate at which steam condenses on the heating surfaces. This varying steam flow varies the pressure (and hence temperature) of the steam in the heat exchanger and thus the rate of heat transfer.

Example 6.5.3

In a particular steam-to-water heat exchange process, it is proposed that:

  • Water is heated from 10°C to a constant 60°C.
  • The water flowrate varies between 0 and 10 L/s (kg/s).
  • At full-load, steam is required at 4 bar a in the heat exchanger coils.
  • The overall heat transfer coefficient (U) is 1 500 W/m2°C at full-load, and reduces by 4% for every 10% drop in secondary water flowrate.

Using this data, and by applying the correct equations, the following properties can be determined:

  • The heat transfer area to satisfy the maximum load. Not until this is established can the following be found:
  • The steam temperature at various heat loads.
  • The steam pressure at various heat loads.

At maximum load:

  • Find the heat load.

Heat load is determined from Equation 2.6.5:

  • Find the heat transfer area required to satisfy the maximum load.

The heat transfer area (A) can be determined from Equation 2.5.3:

 At this stage, ΔTLM is unknown, but can be calculated from the primary steam and secondary water temperatures, using Equation 2.5.5.

  • Find the log mean temperature difference.

ΔTLM may be determined from Equation 2.5.5:

Find the conditions at other heat loads at a 10% reduced water flowrate:

  • Find the heat load.

If the water flowrate falls by 10% to 9 kg/s, the heat load reduces to:

Q̇ = 9 kg/s x (60 ' 10°C) x 4.19 kJ / kg °C = 1 885.5 kW

The initial 'U' value of 1 500 W/m2 °C is reduced by 4%, so the temperature required in the steam space may be calculated from Equation 2.5.3:

  • Find the steam temperature at this reduced load.

If ΔTLM = 100°C, and T1, T2 are already known, then Ts may be determined from Equation 2.5.5:

  • Find the steam flowrate.

The saturated steam pressure for 137°C is 3.32 bar a (from the Spirax Sarco steam tables).

At 3.32 bar a, hfg = 2 153.5 kJ/kg, consequently from Equation 2.8.1:

Using this routine, a set of values may be determined over the operating range of the heat exchanger, as shown in Table 6.5.7.

If the steam pressure supplying the control valve is given as 5.0 bar a, and using the steam pressure and steam flowrate information from Table 6.5.7; the Kvr can be calculated from Equation 6.5.6, which is derived from the steam flow formula, Equation 3.21.2.

Using this routine, the Kvr for each increment of flow can be determined, as shown in Table 6.5.8.

The installation curve can also be defined by considering the Kvr at all loads against the 'perfectly sized' Kvs of 69.2.

The Kvr of 69.2 satisfies the maximum secondary flow of 10 kg / s.

In the same way as in Example 6.5.2, the installation curve is described by taking the ratio of Kvr at any load relative to a Kvs of 69.2.

Such a valve would be 'perfectly sized' for the example, and would describe the installation curve, as tabulated in Table 6.5.8, and drawn in Figure 6.5.9.

The installation curve can be thought of as the valve capacity of a valve perfectly sized to match the application requirement.

It can be seen that, as the valve with a Kvs of 69.2 is 'perfectly sized' for this application, the maximum flowrate is satisfied when the valve is fully open.

However, as in the water valve sizing Example 6.5.2, it is undesirable to select a perfectly sized valve. In practice, it would always be the case that the selected valve would be at least one size larger than that required, and therefore have a Kvs larger than the application Kvr.

A valve with a Kvs of 69.2 is not commercially available, and the next larger standard valve has a Kvs of 100 with nominal DN80 connections.

It is interesting to compare linear and equal percentage valves having a Kvs of 100 against the installation curve for this example.

Consider a valve with a linear inherent characteristic

A valve with a linear characteristic means that the relationship between valve lift and orifice pass area is linear. Therefore, both the pass area and valve lift at any flow condition is simply the Kvr expressed as a proportion of the valve Kvs. For example.

At the maximum water flowrate of 10 kg/s, the steam valve Kvr is 69.2. The Kvs of the selected valve is 100, consequently the lift is:

Using the same procedure, the linear valve lifts can be determined for a range of flows, and are tabulated in Table 6.5.9.

* The installation curve is the percentage of Kvr at any load to the Kvr at maximum load

Consider a valve with an equal percentage inherent characteristic

An equal percentage valve will require exactly the same pass area to satisfy the same maximum flowrate, but its lift will be different to that of the linear valve.

Given that the valve turndown ratio, τ = 50, the lift (H) may be determined using Equation 6.5.4.

Using the same procedure, the percentage valve lift can be determined from Equation 6.5.4 for a range of flows for this installation.

The corresponding lifts for linear and equal percentage valves are shown in Table 6.5.9 along with the installation curve.

As in Example 6.5.2, the equal percentage valve requires a much higher lift than the linear valve to achieve the same flowrate. The results are graphed in Figure 6.5.10.

There is a sudden change in the shape of the graphs at roughly 90% of the load; this is due to the effect of critical pressure drop across the control valve which occurs at this point.

Above 86% load in this example, it can be shown that the steam pressure in the heat exchanger is above 2.9 bar a which, with 5 bar a feeding the control valve, is the critical pressure value. (For more information on critical pressure, refer to Module 6.4, Control valve sizing for steam).

It is generally agreed that control valves find it difficult to control below 10% of their range, and in practice, it is usual for them to operate between 20% and 80% of their range.

The graphs in Figure 6.5.10 refer to linear and equal percentage valves having a Kvs of 100, which are the next larger standard valves with suitable capacity above the application curve (the required Kvr of 69.2), and would normally be chosen for this particular example.

The effect of a control valve which is larger than necessary

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