text:
6th Edition
Published by
Jari Kirmanen
Ismo Niemel
Jouni Pytsi
Markku Simula
Markus Hauhia
Jari Riihilahti
Vesa Lempinen
Jussi Koukkuluoma
Petri Kanerva
1.1 General ......................................................................................................8
1.1.1 Turbulent and laminar flow in pipes ...........................................................8
1.1.2 Velocity distributions ..................................................................................9
1.1.3 Flow separation .......................................................................................10
1.1.4 Pulsation in flow.......................................................................................12
1.2 Throttling process for incompressible flow...............................................13
1.3 Defining pressure.....................................................................................14
1.4 Pressure loss behaviour of piping components .......................................16
1.5 Valve dynamic torque ..............................................................................17
3.1 General ....................................................................................................39
3.2 Sizing equations for liquid flow ................................................................43
- Factors FF, FR, FP, and FLP ..................................................................44
3.3 Cavitation and flashing ............................................................................47
3.3.1 Cavitation phenomenon...........................................................................47
3.3.2 Investigating the existence of cavitation ..................................................50
- Cavitation and noise .............................................................................50
3.3.3 Flashing of liquids ....................................................................................53
3.4 Cavitation and hydrodynamic noise abatement .......................................55
- Velocity control .....................................................................................56
- Acoustic noise and bubble size control ................................................57
- Location control ....................................................................................57
- Flat baffle plates ...................................................................................57
- Orifice plates.........................................................................................58
- Sizing baffle and orifice plates ..............................................................59
- Example of noise and cavitation abatement .........................................61
3.5 Hydrodynamic noise prediction for valves ...............................................62
3.6 Hydrodynamic noise prediction for baffle and orifice plates ....................64
3.7 Recommended flow velocities for liquids.................................................65
A Sizing examples.....................................................................................109
- Liquid flow sizing example..................................................................109
- Water flow sizing example .................................................................. 111
- Gas flow sizing example..................................................................... 113
- Steam flow sizing example ................................................................. 116
- Two phase flow of liquid and gas sizing example............................... 118
- Pulp flow sizing example ....................................................................121
This manual is intended to give an overview of the role of control valves in the
behaviour of a process control loop. This overview consists the information on fluid
behaviour and valve installed performance as well as the theory and practices of
control valve sizing.
Computer based simulation, design and sizing programs have been developing fast
during past years and these are well in used by advanced control valve manufacturers
to provide and maximize the benefits of process controlling.
Control valve is a critical element in achieving the desired accuracy in process control.
A full understanding of the interaction between the control valves and the process is in
a key role in further development of the control performance.
This is the area we believe this manual can provide valuable information and help the
plant instrumentation, maintenance and process engineers.
We hope this manual provides valuable aid and we appreciate any comments and
suggestions for further improvement.
1.1 General
This section presents several complicated flow problems in very simple form: firstly,
flow behaviour in common fluid systems; and secondly pressure behaviour in different
piping components and flow induced dynamic torque.
The flow in conventional control valve installations is almost always turbulent. Laminar
flow can occur with very viscous fluids such as lube oil and with very small flow velocities.
If the velocity is increased above a certain limit the laminar flow field is disturbed and
fluid particles start to move in erratic paths. When this happens, the flow becomes tur-
bulent. Transition from laminar to turbulent flow can be predicted by a single parameter,
the Reynolds number (Re), as defined in equation (1).
Introduction to pipeline flow 9
Re = V --- (1)
Above a critical value of the Reynolds number the flow goes through a transition to
become turbulent. The critical value of Reynolds number is around 3000 for flow in a
straight pipe. When the flow is turbulent, part of the flow energy is used to create
eddies, which cause increasing pressure losses. Turbulent flow can be described as
irregular secondary motion of fluid particles. Secondary motion does not correspond to
the principal direction of the flow. The flow path of a single flow particle is irregular.
With a smoothly shaped outlet from tank to pipe, the velocity profile is a function of dis-
tance. The fully developed profile is constant, if it is not disturbed. In a pipe elbow, the
fully developed velocity profile is disturbed by inertia forces in the fluid (figure 3).
A more drastic change in velocity profile can be caused by an orifice or a valve that cre-
ate a high velocity jet into a flow stream. On the downstream side of an orifice there are
strong vortices which cause flow pressure losses. High velocity jets are also accompa-
nied by the noise, especially in the case of compressible flow. The velocity profile after
the valve is dependent on the valve type and design, and on valve travel. A fully open
ball valve behaves as an extension to the pipe and thus does not disturb the velocity
profile in the way that, for instance, butterfly and globe valves do.
10 Introduction to pipeline flow
After an abrupt increase in flow area, static pressure at the pipe wall may increase in
the direction of flow. This creates a situation in which the forces in the fluid are imbal-
anced. If this imbalance continues over a sufficient distance, the inner layer of the flow
may come to rest and even start to flow backwards. At the point where there is no for-
ward flow the velocity gradient near the wall becomes zero. This point is called the sep-
aration point because just beyond it the flow is reversed and the free flow streamlines
are diverted from the boundary (figure 4). Large energy losses are associated with sep-
arated flow.
Introduction to pipeline flow 11
In throttling control, the pressure differences are created through losses caused by
separation. In pumps, piping and piping bends flow separation creates unnecessary
pressure losses. Improperly designed or installed flange connections, pipe expanders
and bends require oversizing the pumps.
The idea of a control valve is to control the flow rate by controlling pressure losses
across the valve. Flow separation is in practice the physical phenomenon which causes
differential pressure across the valve. In future stricter requirements for energy con-
sumption change the design requirements for fluid transport pipelines. This means that
permitted pressure losses in systems are going to decrease. Stricter limits on permitted
pressure losses will require significant research efforts by engineering companies and
valve manufacturers.
12 Introduction to pipeline flow
Separated flow can produce a large-scale vortex pattern downstream of the valve ori-
fice. The periodic large-scale vortex frequency (f) after a valve plug can be calculated
from the equation (2).
f = ----------- (2)
The Strouhal number is relatively constant for different Reynolds numbers, and its
value depends on the geometry of the obstacle in the flow. Common values for the
Strouhal number (S) are from 0.1 to 0.3.
The large-scale vortex shedding forming in certain valve types is illustrated in figure 7.
It should be noted that vortex separation can cause disturbances in valve capacity, par-
ticularly with certain large-diameter valves in liquid flows.
Figure 7. Periodic vortex pattern after a butterfly and a flow-to-close globe valve.
Introduction to pipeline flow 13
The disturbances caused by large-scale vortices due to flow separation can be elimi-
nated or significantly reduced by increasing micro turbulence, or by shaping the flow
path. Figure 8 shows examples of valve designs where these principles are used.
Figure 8. Examples of flow path modification used in rotary type control valves.
Pipe flows involving valves for throttling control can be studied using simple one-
dimensional flow dynamics theory. Incompressible flow through an orifice is taken as a
basic example for flow velocity and static pressure behaviour in a valve. Compressible
flow can be studied similarly if gas expansion is taken into account.
Bernoulli's equation (4) gives the relation between mean velocity and static pressure.
The continuity equation (3), and Bernoulli's equation (4) are all that is required to
understand flow through a throttling device.
v1 A1 = v2 A2
1 2 1 2
--- 1 v 1 + 1 g H 1 + p 1 = --- 2 v 2 + 2 g H 2 + p 2 + p h (4)
2 2
The continuity equation (3) demonstrates the balance between flow area and mean
velocity. As the flow area decreases the mean velocity increases and vice versa. The
velocity reaches the highest value at the vena contracta point of an orifice. Vena con-
tracta is the point where the actual flow area reaches its minimum value. Because of
contraction caused by fluid dynamics, the area of vena contracta is usually smaller than
the physical area of the orifice.
Bernoulli's equation (4) demonstrates the balance between dynamic, hydrostatic and
static pressure. The hydrostatic pressure (*g*H) can be assumed constant in the flow
through a control valve. As the velocity increases towards the vena contracta point, the
static pressure decreases. After the vena contracta, the fluid velocity decreases and
static pressure increases. This phenomenon is called pressure recovery. Due to the
pressure losses caused by flow separation and vortices, the level of static pressure is
decreased across the orifice.
In Bernoulli's equation (4) there are three different forms of pressure; static, hydrostatic,
and dynamic pressure. Static pressure can be demonstrated with a small cylinder full of
fluid and a piston on top of the cylinder, as shown in figure 10. If the piston is pressed
downwards with force (F), pressure is exerted onto the cylinder. The value of the pres-
sure equals to force (F) divided by piston area (A). The fluid in the cylinder exerts equal
pressure on the walls of the cylinder.
Introduction to pipeline flow 15
Dynamic pressure is related to relative speed of the pressure gauge and the fluid. It
makes no difference whether the gauge is moving or the fluid is moving. The dynamic
pressure is proportional to the square of the fluid velocity. Static and hydrostatic pres-
sures can be used to measure dynamic pressure and velocity. The measurement can
be done within a relatively small range and takes into account only local velocity. To
measure the pipe velocity profile or the mean velocity, many measurement points
across the fluid cross section are required.
16 Introduction to pipeline flow
Pipe components including pumps, control valves, shut-off valves, elbows, joints and
the pipe itself have their own typical pressure loss versus flow rate behaviour.
The pump pressure head is typically strongly dependent on the flow rate so that the
pressure head decreases when the flow rate increases. Pump manufacturers usually
give this dependence in their manuals. In fluid transport systems, the pump is normally
sized to operate at maximum efficiency in normal flow conditions. In minimum flow con-
ditions the pump pressure head is higher, and in maximum flow conditions the pressure
head is lower than the optimum. This variation is seen in an increase in the pressure at
control valve inlet as the flow rate decreases.
In a straight pipe pressure losses are the result of pipe-wall roughness. Pressure loss
is proportional to the square of the velocity, as indicated in equation (5), which means
that it is also proportional to the flow rate squared if the pipe diameter is constant.
p h = --- --- v
2 d (5)
Piping loss increases rapidly as the flow rate increases. Almost all pipe components
exhibit a strong dependence of pressure loss on the square of the velocity. For tank
inlets and exits, elbows, shut-off valves, orifices etc. pressure loss characteristics can
be expressed in the form of equation (6)
p h = --- --- v
2 d (6)
In fluid transport systems, the differential pressure across a flow control valve is
strongly dependent on the flow rate. Under normal flow conditions the control valve typ-
ically accounts roughly one third of the total pressure loss of the system. In the future,
due to energy saving requirements, this will change so that control valves take smaller
portion of the total pressure drop.
Valve dynamic torque, which tends to close or open the valve depending on the type of
valve, is caused by asymmetric pressure distribution on the surface of the throttling ele-
ment. Theoretical determination of the dynamic torque requires that the pressure distri-
bution on the throttling element surface is known. Figure 14 shows a principle drawing
of a pressure distribution that results in dynamic torque in a ball valve. In practice,
dynamic torque (Md) is usually calculated from experimentally defined equation (7).
18 Introduction to pipeline flow
Figure 14. Ball valve dynamic torque is formed by asymmetric pressure distribution
on the inner ball surface.
M d = C d(h) D N p (7)
2.1 General
This chapter introduces a process pipeline model and calculation procedure that make
it possible to predict control valve installed performance accurately and quickly using a
valve sizing and selection software. Choked flow conditions are taken into account for
all calculated points, a factor that was listed as a limitation in previously presented
models. The results and their utilization are discussed in detail, with practical guidelines
on how to correct nonlinear installed flow characteristics using a digital controller signal
modification block.
It is also important to note that control valve installed accuracy is the method that
should be used to judge control valve accuracy, not just the mechanical accuracy. The
installed gain multiplied by the mechanical accuracy gives the installed flow accuracy.
Successful control valve sizing and selection depend on knowing the actual process
conditions in the system in which the valve is to be installed. It is known that distinct
information on operating conditions very seldom exists. The more assumptions one
has to make on flow conditions, the less accurate the control valve sizing is going to be.
Fortunately, when a few flow conditions are known accurately, an algorithm can be
found that can model the behaviour of a given control valve for the whole flow range.
The selection of a control valve is divided into two parts. First, the mechanical selection
in which suitable valve style, materials and pressure rating are picked to guarantee
safe and reliable performance according to good engineering practices, local laws and
regulations etc. This selection should be made using bulletins and technical information
specific for each valve type. Secondly, the sizing of a selected valve, in which the size
of the given valve type is determined, while trying to prevent unwanted phenomena like
excessive noise or liquid cavitation. After the valve size has been determined, the
installed performance of the valve to phase out poor control performance like hunting,
excessive slow or fast response and poor accuracy is further predicted.
KPL2 Page 20 Monday, January 2, 2012 12:11 PM
This control valve selection here concentrates on sizing and installed performance con-
siderations. It should be noted that these calculations do not, by themselves, guarantee
the selection of a correct valve. Therefore, careful mechanical and material evaluations
should always precede sizing calculations.
In the past, selection of control valves has been based largely on approximate estimation
methods and practical experience. Modern sizing and selection software enables faster
and more accurate calculation methods to select a control valve with optimum controlla-
bility and accuracy for each individual process application. The method is based on mod-
elling or predicting the actual flow characteristic and gain of the installed valve.
Selection of the optimum size and type of control valve starts with the valve's inherent
flow characteristic. For this reason, all control valve types must be laboratory tested to
determine their exact inherent flow characteristics.
Valve inherent flow characteristic are defined so that the pressure differential across
the valve (p) is kept constant. As the differential pressure (p) is constant, the flow
rate (q) through the valve is proportional to the valve flow coefficient (Cv), as expressed
in the simplified equation (8).
q = C v p (8)
Because the valve flow coefficient (Cv) reflects the effective flow crosssection of the
valve, the valve inherent flow characteristic shows how the effective flow crosssection
changes as a function of relative travel (h).
KPL2 Page 21 Monday, January 2, 2012 12:11 PM
Figure 16 shows the most common valve inherent flow characteristics. The relative
flow coefficient () is determined as shown in equation (9).
C v(h)
(h) = ------------------- (9)
C v(1.0)
The inherent flow characteristic is the shape of a flow curve through the valve with a
constant pressure drop across the valve. Note that in any case where process piping is
attached to the valve, the piping pressure loss, a function of flow rate, will cause the
valve pressure drop to vary as a function of flow rate, even if the pressures at the
source and receiver are constant.
KPL2 Page 22 Monday, January 2, 2012 12:11 PM
Under operating conditions a control valve is part of a process pipeline. The differential
pressure across a valve is seldom constant in the valve travel range because dynamic
pressure losses in the flow cause the valve inlet pressure to fall and the outlet pressure
to rise as the flow rate increases. For an installed valve, the dependence of the flow
rate (q) on the travel (h), i.e. the shape of the installed flow characteristic curve, is
therefore a function of the process pipeline and of the inherent flow characteristic of the
valve. The changes in differential pressure that take place across a control valve
installed in a process pipeline are illustrated in figure 17.
KPL2 Page 23 Monday, January 2, 2012 12:11 PM
Figure 17. Change in effective differential pressure across the valve due to a change
in the flow rate.
The character of a process pipeline is described by the process pressure ratio factors
DPf or DPm. The subscripts refer to situations in which the valve is fully open
(subscript f) or opened to allow the maximum flow rate (subscript m) required by the
process. The process pressure ratio factor DPm is the differential pressure across the
valve at the process maximum flow rate divided by the differential pressure across the
valve when the valve is closed, as expressed in equation (10).
p m
DP m = ----------- (10)
p 0
The character of the process pipeline can be determined with a sizing and selection
software when at least two different flow conditions in the process are known, or if the
process pressure ratio factor DPm, which describes the character of the pipeline, and
the maximum flow conditions are known.
KPL2 Page 24 Monday, January 2, 2012 12:11 PM
The process pressure losses are relative to the square of the flow velocity, which corre-
sponds to the square of the flow rate. This basic assumption facilitates the creation of a
model for pressure variations at the valve inlet and outlet.
Figure 18 shows an installed flow characteristic curve calculated using a sizing and
selection software for an eccentric rotary plug control valve in a process application.
Figure 18. Installed flow characteristic of an eccentric rotary plug control valve.
The quality of the installed flow characteristic curve with respect to valve controllability
and accuracy can be examined by means of a valve gain curve. The valve gain curve
describes the changes that take place in the slope of the installed flow characteristic
curve for different amounts of valve travel. The gain of an installed valve is the change
in relative flow rate (dQp = d(q/qm)) divided by the change in relative travel (dh), as
expressed in equation (11).
dQ p
The installed gain gives the rate of change in flow as a function of the change in signal.
A gain of 1 means that a 1 % change in valve opening causes the flow to change by
1 % of the maximum flow. A gain of 2 means that a 1 % change in the signal causes a
2 % change in the relative flow rate (dQp), and so forth.
KPL2 Page 25 Monday, January 2, 2012 12:11 PM
dQp = G dh (12)
In other words, the change in flow rate (dQp) is the gain (G) multiplied by the change in
valve travel (dh).
From equation (12) it can be seen that variation of the gain (G) in the required flow
range causes different relative flow changes (dQp) for the same relative signal change.
This is usually undesirable for process controllability.
The installed valve gain is the starting point for selecting an optimum control valve size
and an inherent flow characteristic for a certain process application. For the standard
PID controllers in most control loops the best possible inherent flow characteristic is the
one that gives closest to constant installed gain for the required flow range. In this case
the controller's parameter tuning can be kept optimal and unchanged in spite of varia-
tions in the load in the process operating range. In applying the above rules it must,
however, be noted that only a full dynamic analysis of the control loop is sufficient to
include all the nonlinearities of the process and equipment and to absolutely guarantee
the choice of an optimum control valve. This kind of analysis is feasible for a control
valve simulation program.
The rule of thumb for permissible limits for the installed gain is that a change in gain
larger than 2 (equation (13)), or a relative gain smaller than 0.5 (equation (14)) should
be avoided in the process operating range.
G max
-------------- < 2 (13)
G min
If the gain is too low or too high, or if it changes considerably in the process operating
range, process control will generally become very difficult. Moreover, too high a gain
also means problems for the control accuracy of the control valve because the relative
flow rate error (Q) for a control valve is the gain (G) multiplied by the relative travel
error (h) of the control valve.
KPL2 Page 26 Monday, January 2, 2012 12:11 PM
Figures 19 and 20 illustrate the importance of selecting the proper size control valve for
each application. An oversized control valve causes high gain with small flows resulting
in poor control accuracy and possible hunting, as shown in figure 19. Selecting a
smaller valve will lower the gain, resulting in high accuracy and stable control, as
shown in figure 20.
Figure 21 shows a sample installed gain curve for a new type of eccentric rotary plug
control valve. The figure demonstrates that an almost constant gain is achieved on the
inherent flow characteristics of the eccentric rotary plug control valve. This is often the
optimum gain in the process operating range. Furthermore, a smooth gain results in
excellent control accuracy.
With a sizing and selection software it is possible to predict the installed control valve
flow characteristic and gain curves, if at least two separate sets of flow conditions or if
the process maximum flow and DPm factor are known.
The program accurately predicts installed control valve performance, if the following
conditions are true:
Condition 1: The process is such that a specific flow corresponds to a specific pressure
drop across the valve.
Condition 2: Pressure drop changes across the control valve are dependent on pres-
sure losses in the piping system such that the sum of those pressure
losses is proportional to the square of flow velocity.
The program uses following procedures to calculate the installed flow characteristic
and gain:
KPL2 Page 28 Monday, January 2, 2012 12:11 PM
Using given flow data the program generates a process model for the pressures,
and checks whether conditions 1 and 2 above are fulfilled. The process model
for the valve inlet and outlet pressures is created using 'the sum of least squares'
method such that the derivative equals zero at the origin of the pressure curves.
The program predicts the flow through a fully open control valve (qf) using the
process model to determine pressure drop across the fully open control valve.
Possible choked liquid flow, determined by pressure recovery factor (FL), or criti-
cal gas flow, determined by pressure drop ratio factor (xT), are taken into
account when determining flow through a fully open control valve (qf).
The valve pressure drop, opening and predicted noise level for the whole flow
range are calculated at intervals of 5 % of the maximum flow (qf). At each of the
calculation points possible choked flow is taken into account in the calculations.
The installed flow characteristic displayed on the screen is the relative flow rate
(q/qf), which is the actual flow rate divided by the flow in a fully open valve, given
as a function of relative travel (h).
The installed control valve gain is the slope of the installed flow characteristic
curve defined using finite difference method. It is important to note that the
installed gain curve is calculated and drawn as a function of the maximum pro-
cess flow (q/qm) and not as a function of the flow with the valve fully open (q/qf).
This is important, as it allows different valve types and sizes to be compared
based on process requirements, and not just from the valve viewpoint. It is worth
mentioning, that this method increases the gain as compared with the gain pre-
sented as a function of flow in a fully open valve.
The pressure behaviour of the process can be estimated accurately enough for practi-
cal purposes, when the pressure conditions (upstream pressure, pressure drop across
valve) and flow rates are known for at least two flow conditions, such as the maximum
and minimum flows. If only the maximum flow for the process (qm) and the correspond-
ing pressure drop (pm) are known, the process model can be found by using the pro-
cess pressure ratio DPm, as in figure 22.
KPL2 Page 29 Monday, January 2, 2012 12:11 PM
DPm is the valve pressure loss portion of the total dynamic pressure loss of the system
with maximum process flow. The DPm information should thus be easily available from
system pressure loss calculations.
The program is able to calculate the pressure process model using two or more given
flow conditions, if these flow conditions comply with conditions 1 and 2 of the proce-
dure. Figure 23 gives examples of defined process models the program can handle,
and that of undefined process models that it cannot.
The process pressure ratio DPm is affected by the dynamic pressure loss in the piping.
The piping pressure loss is generated by the length of the pipe, the diameter, surface
roughness, and individual resistances of piping components. Additionally, the pressure
drop across a control valve depends on the flow velocity and piping boundary condi-
tions, e.g. if the fluid is a liquid, the pump curve needs to be taken into account when
evaluating the change in pressure drop across the valve.
DPm ratio gives the program user a chance to evaluate and optimize piping structure
options and the effect different valves have on overall process total function. The DPm
ratio can be optimized such that a minimum amount of energy is used in the control
valve, leading to significant saving in the energy cost of pumping. The following A and
B give examples of the selection of DPm ratios for liquids and gases.
A. Liquid flow
In practice most process piping systems are now designed such that the control valve
pressure loss at maximum designed flow is roughly one third of the total dynamic pres-
sure loss in the piping. In that case, DPm ratio as a rule of thumb for liquid piping is as
presented in equation (15).
DP m = 0.30 (15)
As mentioned before, piping designers are an invaluable asset in calculation the real
DPm factor, particularly for new piping systems. Old systems can be evaluated using
common sense to determine a DPm ratio accurate enough for present purposes. Figure
24 presents an estimation of DPm ratio in two different kinds of process piping.
B. Gas flow
For compressible flows, such as those of gases and steam, the pressure drop changes
across a control valve are usually smaller than those for liquid flows. The difficulties
involved in presenting 'rules of thumb' for gas and steam flows are firstly, that there is
huge variation in different process and piping systems and, secondly, that fluid com-
pressibility, particularly at large flow velocities, has a big effect on the pressure drop
across a control valve. Equation (16) gives 'a rule of thumb', which can be used when
no accurate information is available.
DP m = 0.50 (16)
Trying out several possible DPm ratios to view the effect this has on the installed flow
characteristic and gain is suggested in such cases. Some example estimates for DPm
ratios for gas or steam flows in different process piping systems are given in figure 25.
Figure 25. Evaluation of DPm ratio for gas and steam flows.
A control valve in a control loop determines much of the quality of the overall control
loop function. Specific attention should thus be paid to control valve selection in order
to get the full benefits of the extensive product development that has occurred in other
components of the control loop, such as measuring devices and DCS process control
KPL2 Page 32 Monday, January 2, 2012 12:11 PM
A control valve is the final control element, a mechanical device that effects the
changes in flow or pressure deemed necessary by the rest of the system. Therefore,
the control valve accuracy is a main element in defining the accuracy of the whole con-
trol loop.
The relative flow error of a control valve (Q) is the valve gain (G) multiplied by the rel-
ative valve travel error (h), as expressed in equation (17).
Q = G h (17)
The relative flow error of a control valve (Q) can also be expressed as in the following
equation (18).
The installed gain (G) in the equation (17) is the control valve installed gain, which can
be calculated by a sizing and selection software.
The accuracy of the flow controlled by a control valve is the mechanical error of the
control valve assembly multiplied by the installed flow gain. A figure for the mechanical
error alone does not indicate the accuracy of the flow being controlled.
The inherent flow characteristic of a control valve is traditionally chosen so that in the
process operating range the controller tuning can be kept constant in spite of load
changes. If the process being controlled is nonlinear, the control valve flow characteris-
tic should be inversely nonlinear. Thus the control valve flow characteristic will compen-
sate for a nonlinear process.
KPL2 Page 33 Monday, January 2, 2012 12:11 PM
The rapid development of process control systems has, however, made it possible to
apply highly developed control strategies and algorithms. In this case, there is a ten-
dency to select various subsections of the control loop to be as linear as possible in the
process operating range. For control valves this can be done by selecting a valve type
and size that give a linear installed flow characteristic and constant gain in the given
process flow range.
Most control systems assume that the installed flow characteristic of the control valve is
linear. Therefore, for optimal performance of the control valve measures should be
taken to ensure installed flow characteristic to be as close to linear as possible by
selecting the valve style and type accordingly.
The controller characterization curve in figure 27 can be plotted using a sizing software,
when the installed flow characteristic graph relative flow rate (Q) is replaced by the
input signal (I) for the linearization block, and relative travel (h) is replaced by the out-
put of the linearization block (Imod):
h Imod
The linearization curve derived this way can be fed into the controller point by point, as
presented in figure 27.
Modern process controllers are capable of linearizing the control valve installed charac-
teristic by signal modification. This method, which is applied by using a graph, like the
one shown in figure 27, provides accurate linearization for the particular application.
Positioner cam modification simply distorts the valve inherent flow characteristic with-
out taking into account the actual requirements of the specific system being consid-
Control valve function can be divided into subsections, as in the block diagram in figure
28. The function of each block of the control valve can be described in terms of its indi-
vidual gain (G), the ratio of the change in output to input. The figure 29 shows the posi-
tion control block diagram in which GPV is pilot valve gain, GAC is actuator gain and
GFB is feedback loop gain. In figure 29, a linear feedback cam is used. A linear feed-
back cam gives the constant feedback gain GFB=1.
The behaviour of a feedback system can be studied through its transfer function. Fig-
ure 29 illustrates the equation (19) for the position closed loop gain.
h G PV G AC
As shown in equation (19), the gain in position control depends on the gains in the indi-
vidual blocks of the system.
The problem with positioner cam modification is that the correction is made in the
mechanical feedback loop of the positioner. Thus, the correction is made after the point
where it was required. Cam modification is thus only suitable for very slow control
loops. Moreover, it has the following disadvantages:
The control valve operates very rapidly in one flow range and very slowly in
another flow range, due to the feedback gain (GFB) change with different valve
openings (h); in other words, the control loop time constant changes depending
on the valve position.
Control valve position control can become unstable in a certain opening range,
due to the stability criterium given in equation (20).
KPL2 Page 37 Monday, January 2, 2012 12:11 PM
If GFB changes, there can be an opening for which equation (20) equals 0 and thus the
position control gain approaches infinity: GPC .
The transfer function for control valve characterization using the controller output signal
can now be found from figure 32.
Equation (21) shows that with the nonlinear characterization block (GOUT 1) of a con-
troller output and linear feedback cam (GFB 1) there is a small chance for the position
control to become unstable (GPC ).
h G PV G AC
The installed characteristic modification is done on the signal level very rapidly
compared with changes on the pneumatic and mechanical level.
The error in positioner is constant, and does not change according to the
The chance for position control instability is small.
Liquid flow 39
The flow of incompressible fluids through control valves has been well defined by uni-
versal, standardized sizing equations (ISA/IEC). A description of these equations and
the basic fluid mechanics of incompressible flows forms the first half of this chapter. In
the second half, there is explained the phenomenon, and the prevention of cavitation in
a fresh way, providing new insight into theories that are well-known in the industry.
Determination of levels of damaging cavitation from the predicted noise level is a start-
ing point for making recommendations on when cavitation prevention techniques are
required. Methods of abating cavitation using both valve trim variation and external
means like back-pressure baffles are explained further on in the text.The chapter ends
with hydrodynamic noise prediction, which is presented in the form of the equations
used. Guidance on maximum flow velocities for liquid flow valves is given in the last
3.1 General
Liquid flow is an incompressible type of flow. A typical process installation for a liquid
flow control valve is illustrated in figure 33.
The following part of this manual concentrates on the throttling process between
upstream pressure p1 and downstream pressure p2, as shown in figure 33, where
upstream pressure p1 is the pressure measured by a tap located two pipe diameters
upstream of the upstream valve flange, and downstream pressure p2 is the pressure
measured by a tap located six pipe diameters downstream of the valve downstream
flange (per std. IEC 60534/ISA S75).
To displaying the general behaviour of flow through a control valve itself, the valve is
simplified to an orifice in a pipeline, as shown in figure 34. Naturally, continuity equation
(3) and Bernoulli's equation (4) are also valid in this context.
Figure 34 shows the change in the cross-section area of the actual flow when the flow
goes through a control valve. In a control valve the flow is forced through the control
valve orifice, or a series of orifices, by the pressure difference across the valve. The
actual flow area is smallest at the point called the vena contracta (AVC), the location of
which is typically a little downstream the valve orifice, but can be extended even into
the downstream piping, depending on pressure conditions across the valve, and on the
valve type and size.
Due to the reduction in flow area a significant increase in flow velocity has to occur to
give equal amounts of flow through the valve inlet area (AID) and vena contracta area
(AVC). The energy for this velocity change is taken from the valve inlet pressure, which
gives a typical pressure profile inside the valve (figure 35).
The pressure inside the valve drops as the effective flow area is reduced, up to the
vena contracta point, which is the smallest flow area available to the flow inside the
valve. After reaching the vena contracta point the velocity of the flow is reduced due to
the fact that more flow area becomes available to the flow. Thus some of the pressure
lost up to the vena contracta point is recovered.
Liquid flow 41
Figure 35. Pressure profile inside the valve in the valve trim.
The pressure recovery after the vena contracta point depends on the valve style, and is
represented by valve pressure recovery factor (FL), as given in equation (22). The
closer the valve pressure recovery factor (FL) is to 1.0, the less the pressure recovery
p1 p2
p 1 p vc
When upstream pressure (p1) is constant, the interrelation between the pressure differ-
ential (p) across the control valve at a constant opening and the resulting flow rate (q)
can be expressed by figure 36.
Figure 36. Interrelation between flow rate and square root of pressure drop across a
control valve.
42 Liquid flow
Up to a certain pressure drop value the flow through a control valve follows the square
root of the pressure drop applied across the valve in a direct line equation, where the
slope of the line is expressed as the valve flow coefficient (Cv).
With larger relative pressure drops across the valve, the gain in flow decreases, and
ultimately becomes zero. The cavitation begins where the flow starts to deviate from
the straight line, as illustrated in figure 36. In other words, when upstream pressure (p1)
is constant, an increase in pressure drop does not produce any increase in the flow
rate through the valve. The cause of this phenomenon is choking. When the valve vena
contracta pressure drops below the vapour pressure of the flowing liquid (figure 37), it
causes formation of vapour bubbles in the control valve orifice, thereby restricting the
liquid flow through the orifice.
Figure 37. Pressure behaviour in a control valve in cavitating and flashing application.
The flow is considered to be choked when the valve actual pressure drop is above the
terminal pressure drop (pT), sometimes called the allowed pressure drop, derived as
the corner point of the lines expressingnon-choked and choked flows in figure 36.
In choked flow cases where valve downstream pressure recovers above the liquid
vapour pressure is produced a phenomenon called cavitation. If the valve downstream
pressure remains below the liquid vapour pressure, the phenomenon is called flashing.
Liquid flow 43
p1 p2 (23)
q = N 1 F P F R C v ------------------
where q = liquid volumetric flow rate (SI units: [m3/h]; US units: [gpm])
N1 = 0.865 (SI units: [m3/h],[barA])
= 1.0 (US units: [gpm],[psiA])
FP = piping geometry factor
FR = Reynold's number factor
Cv = valve flow coefficient
p1 = upstream pressure (SI units: [barA]; US units: [psiA])
p2 = downstream pressure (SI units: [barA]; US units: [psiA])
Gf = specific gravity (Gf = /0 = 1 for water at 15.6C or at 60F)
= fluid density (SI units: [kg/m3]; US units: [lb/ft3]
p0 = density of water at 15.6C or at 60F
= 999 (SI units: [kg/m3])
= 62.36 (US units: [lb/ft3]
With an increasing pressure drop (p1-p2), the vena contracta pressure in the valve
drops below the vapour pressure of the liquid, and the vapour cavities begin to form in
the liquid. At a certain point, when sufficient vapour has formed, the flow becomes com-
pletely choked, and the flow rate does not increase with increasing pressure drop, if
upstream pressure is constant. The corresponding pressure drop is called the terminal
pressure drop (pT).
p T = --------- ( p 1 F F p v )
Consequently, the maximum flow rate (qmax) under choked conditions is reached when
(p1-p2) pT
p1 FF pv
q max = N 1 F LP F R C v ----------------------------- (25)
When a valve is operated in such a way that the pressure drop is close to the terminal
pressure drop (pT), the rate of flow may be less than that predicted by equations (23)
or (25) because the real behaviour of the flow rate is approximated using straight lines,
as shown in figure 36. However, the error is insignificant.
Factor FR, which is the Reynolds number factor, usually has a value of 1.0. The Reyn-
olds number factor has an effect in non-turbulent flow, which usually occurs with high
viscosity fluids, such as oil, and with low flow velocities and small valve sizes. Reynolds
number factor (FR) can be defined using the valve Reynolds number and figure 38. The
valve Reynolds number is derived from the following equation (27).
2 ---
N4 Fd q ( Fp FL Cv ) 4
Re v = ---------------------------------------- -----------------------------------
Fp FL Cv N2 d
After calculating the Reynolds number for the valve (Rev), the Reynold's number factor
(FR) can be determined from the diagram in figure 38.
The piping geometry factor (Fp) can be calculated as shown in equation (28).
F p = ------------------------------------------
K C v (28)
1 + ------- ------2
N2 d
where K = K1+K2+KB1-KB2
K1 = upstream resistance coefficient
K2 = downstream resistance coefficient
KB1 = inlet Bernoulli coefficient
KB2 = outlet B ernoulli coefficient
N2 = 0.00214 (SI units: [mm])
= 890 (US units: [in])
When the inlet and outlet fittings are identical, KB1 = KB2, and they cancel out at the
equation. If the pipe diameters approaching and leaving the control valve are different,
the KB coefficients are calculated as in equation (29).
d 4
where d = valve inlet diameter for KB1 and outlet diameter for KB2
(SI units: [mm]; US units: [in])
D = pipe inlet diameter for KB1 and outlet diameter for KB2
(SI units: [mm]; US units: [in])
For standard concentric reducers, the upstream and downstream resistance coeffi-
cients (K1) and (K2) can be approximated as shown in equations (30) and (31).
d 2 2
d 2 2
Liquid flow 47
Factor FLP is the product of the liquid pressure recovery factor of a valve with attached
fittings and the piping geometry factor (FP). It is calculated using the given valve pres-
sure recovery factor (FL) and piping geometry factor (FP) as shown in equation (32).
F L C v 2 (32)
1 + --------- ------2 K i
N2 d
Figure 39. A simplified model of pressure and velocity changes in control valves in
cavitating and flashing conditions.
48 Liquid flow
A reduction in the area available for the flow leads to a large increase in fluid velocity,
which in turn causes a drop in the fluid pressure due to the conservation of energy. The
pressure is at its lowest level at the vena contracta point, which is located a little down-
stream of the physical valve orifice. When the pressure at the valve vena contracta
point is lower than the liquid vapour pressure (pv) and the downstream pressure of the
valve (p2) is higher than the liquid vapour pressure (pv), cavitation takes place.
Cavitation occurs in two stages. Firstly, as the pressure of the liquid is reduced below
the liquid vapour pressure, vapour bubbles form in the liquid. The formation of vapour
bubbles starts from boundary layers of the nuclei, minuscule solid particles or gas bub-
bles that are carried by the fluid. Secondly, recovery of pressure after the vena con-
tracta raises the pressure above the liquid vapour pressure, causing collapse of the
vapour bubbles. The collapsing vapour bubbles cause large pressure shocks, due to
either a liquid microjet or a spherical shock wave as shown in figure 40.
If the vapour bubble is very close to or in contact with a solid wall, the microjet gener-
ated can hit the wall with a pressure shock of the order of 104 MPa (1.5 * 106 psi).
Spherical pressure shock waves are generated when the bubbles collapse further
away from solid walls, in the body of the liquid. The pressure shock in this case is of the
order 103 MPa (1.5 * 105 psi) and the effect of the microjet does not reach a solid wall.
If bubbles collapse close to a solid wall, the microjet or shock wave can cause yield or
surface cracks on the material. Cavitation-damaged surfaces are rough and spongy.
Figure 39 right side shows a situation in which the valve outlet pressure is lower than
the liquid vapour pressure. In this case vapour bubbles cannot collapse and the fluid
exits the valve as a two-phase mixture. The fluid is not cavitating, as the second phase
(collapse of the bubbles) does not occur. This phenomenon is called flashing, and it is
not nearly as damaging as cavitation. Selecting all stainless steel valve body and trim
Liquid flow 49
materials and limiting the flow velocity at the valve inlet and outlet typically gives satis-
factory control valve life.
Mechanical damages to cavitating valves has been shown to correlate very closely with
the noise level produced. The maximum noise level is usually reached before the valve
chokes. When choking and any flashing takes place, the bubble collapse location and,
thus, the source of noise, moves further downstream. Cavitation damage also corre-
lates with the materials and coatings used in the valve and downstream piping.
= k Vn (33)
In applications where cavitation exists, close attention should thus be paid to selecting
the correct trim style and materials to avoid erosion related to cavitation corrosion.
Equation (33) suggests the following:
Reduce the flow velocity inside the valve by using multistage pressure drop trim
to minimize valve trim velocities.
Reduce the wear by using stainless and hardened materials.
One way to estimate the level of cavitation is to use the pressure recovery factor (FL).
The FL factor is determined according to the Cv measurement. The definition for the FL
factor is shown in equation (22). On the basis of that equation, the terminal pressure
drop for the valve can be calculated. When the terminal pressure drop is reached, the
flow is fully choked.
Some manufacturers publish a cavitation index (KC) for their valves. This number is
the ratio (p1-p2) / (p1-pV). The value for the cavitation index is based on Cv measure-
ment with water. The point where the valve is considered to cavitate is the point where
the curve in Figure 36 diverges 2 % from a straight line. The value of the cavitation
index varies with valve opening. The deviation is caused by cavitation, i.e. the valve is
cavitating to some extent even before the limit set by the cavitation index is reached.
The intensity of the cavitation depends on the valve type and pressure level, so it is not
easy to give an absolute limit for non-cavitating flow. For this reason, Metso has
decided to use both noise level and terminal pressure drop to predict cavitation level.
On the other hand, Figure 42 shows that cavitation starts before the terminal pressure
drop is reached. The curve shows how the sound pressure level (SPL) of a valve devel-
ops as a function of the ratio (p1-p2) / (p1-pV). It can be seen from next picture that the
region of laminar flow is practically negligible, and noise levels are low. Following the
laminar region, the curve is characterized by turbulence of the liquid flow and a moder-
ate increase in the sound pressure level. From a certain value of the valve pressure dif-
ferential, p = z(p1-pV) onwards, the noise level curve starts to rise rapidly. The valve-
specific characteristic pressure drop ratio (z), for incipient cavitation, is determined by
the manufacturer's laboratory measurement of hydrodynamic noise. These values are
typically shown in the valve manufacturer's sizing coefficient documents. The reason
for this increase in sound pressure level is cavitation. It can be seen from laboratory
tests that the sound pressure levels start to rise even before actual steam bubbles can
be observed visually.
Lam. Turbulent flow
z DpT / (p1-pV)
(p1-p2) / (p1-pV)
When the p across the valve is close to the terminal pressure drop (pT), the sound
pressure level reaches its maximum. Further increase in pressure ratio (p1-p2)/(p1-pV)
will, as a rule, cause the noise pressure level curve to level off again, as can seen from
figure. This is predicted by the standard VDMA 24422 (1979) which, like most other
standards, predicts the noise level one metre downstream from the valve. When the
valve is cavitating heavily the implosion of the cavitation bubbles occurs further away
from the valve in the downstream piping. That is the reason for the reduction in sound
52 Liquid flow
pressure levels predicted by VDMA 24422 (1979). The noise does not disappear, but
simply moves to another place (downstream piping). Also, the length of the area where
the implosions occur increases, so the intensity of the noise declines, even though the
number of bubbles increases. On the other hand, the nature of the flow approaches
more closely that of a gas/liquid mixture when the pressure differential increases.
Typically, a valve which is noisy in liquid service is cavitating. Cavitation bubble implo-
sions are the main source of disturbing noise, and noise level is directly related to cavi-
tation intensity. In the early stages of cavitation (incipient cavitation) the noise can
sound like sand going through the valve . When the pressure difference across the
valve is increased, the intensity of the cavitation rises and severe cavitation and rough
noise occurs. Cavitation noise can also be predicted accurately. Therefore, the pre-
dicted noise level is a good indicator of mechanical cavitation damage.
The pressure drop needed to mechanically damage valves or piping depends on the
valve type, size and material. Various studies suggest that the lower the recovery of the
valve, the closer the terminal pressure drop (pT) can be approached without cavitation
damage. Terminal pressure drop (pT) occurs at a much higher level with a low reco-
very valve. It is not always true that when p>pT there will be damage. If the pressure
differential is very small and the time that the valve is exposed to the cavitation is short,
there may not be a problem. Corrosion is also a factor, which depends on the material
and the medium used.
the pressure drop across the valve may not exceed the terminal pressure drop (pT)
(If p is small, pT may be exceeded, but then the material selection is critical)
the noise level of the valve may not exceed the values given in Table 1
Noise limits for preventing cavitation damage in valves for non-insulated schedule 40
piping are given in Table 1. It is important to note that even if the sound pressure level
is below the limits given in Table 1, the valve might be cavitating heavily if the pressure
difference over the valve is greater than the terminal pressure drop.
Liquid flow 53
When the downstream pressure of a control valve is less than the liquid vapour pres-
sure, part of the liquid is vapourized and remains as vapour downstream of the valve.
Flow downstream of valve is part liquid and part vapour. The flow is choked and there-
fore a decrease in downstream pressure does not increase the flow rate. Flashing flow
sizing is done according to liquid choked flow equations. In some cases where
upstream pressure is very close to vapour pressure, flow may occur in two phases
upstream of the valve, and sizing is not as accurate. Two-phase flow sizing can be
used in such cases.
Flashing flow may cause mechanical difficulties, like erosion and vibration, but unlike
cavitation, the reason is the high velocity of the two-phase flow stream. High velocity is
due to the larger vapour volume compared with liquid. High velocity can be very erosive
and it is recommended that more resistant materials be used in such cases. Valve
downstream velocity can be approximated according to the following calculations.
The amount of vapour in the flow stream is expressed as a fraction of flash, so that one
hundred percent of flash is totally vapourized. The fraction of flash (xv) can be calcu-
lated from the enthalpy changes in the vapourizing process, as given in equation (34).
h f1 h f2
x v = --------------------- (34)
h fg2
The density of the vapour in downstream conditions (g2), equation (35), is needed to
calculate downstream velocity. Vapour density given for upstream conditions may be
significantly different from the density in downstream conditions because of vapour
2 p M (35)
g2 = N 12 --------------
The outlet velocity of the liquid and vapour mixture (vfg2) can be calculated from equa-
tion (36).
N 13 1 xv xv (36)
- w -------------- + ---------
v fg2 = --------
2 f2 g2
The recommended maximum flow velocity (vmax) at the valve exit port is given in terms
of sonic velocity (vs) as follows.
v s = N 14 -----------
where vs = sonic velocity (SI units [m/s]; US units [ft/s])
k = ratio of specific heats
M = molecular weight
N14 = 91 for SI units
= 223 for US units
There is currently no noise prediction method for flashing control valves. However, the
noise level of control valves in flashing conditions generally stays below 85 db(A).
The most significant source of control valve noise in liquid applications is cavitation.
The abatement of noise and cavitation are therefore dealt together here. The basic divi-
sion between methods of noise and cavitation abatement in liquid valves is between
'source' treatment, i.e. modification of the valve and its trim so that the cavitation inten-
sity is reduced or the existence of cavitation is prevented, and 'path' treatment, i.e.
dampening of the noise generated. The source treatment of hydrodynamic noise and
cavitation abatement can be performed using at least four different methods, as indi-
cated in figure 43.
Source treatment, whenever possible and feasible, is the preferred way of dampening
liquid cavitation and the associated hydrodynamic noise, because only then can exces-
sive generation of cavitation bubbles be avoided across a wide flow range. Path treat-
ment reduces the noise radiated by the piping system, but it does not eliminate
cavitation inside the valve and adjacent piping.
56 Liquid flow
Velocity control
Controlling the fluid velocity, which is equivalent to controlling the pressure in the valve
trim, is an effective mean avoiding cavitation. The aim of this is to get the lowest pres-
sure in the valve trim above the vapour pressure for the liquid in question. This is done
by dividing the valve pressure drop into several stages. There are two basic methods
for pressure drop staging:
Identical pressure drop across each stage
Identical minimum pressure in each stage
The first principle requires a constant flow area trim. Due to the equal area, the flow velocity
in each stage is constant and the pressure drop is equal in each step. The second principle
involves an expanding area trim, in which the pressure drop in the first stages is very high,
but a higher minimum pressure is maintained in the last stages, thereby better avoiding
cavitation within the valve trim. Figure 44 shows the two principles.
Throttle points
Location control
Location control is a principle of flow path design to over come that bubble implosions
can be directed far away from solid boundaries.
If the valve outlet pressure is increased with a baffle plate, the pressure drop ratio
across the control valve can be brought back to the most effective valve operating
range. The baffle plate is thereby used to create the required back-pressure for the
Figure 45. Typical installation of a noise attenuating valve with a flat baffle plate.
58 Liquid flow
A flat baffle is a flow restrictor with a custom-made constant flow area and multiple
holes for a particular flow condition. The pressure drop across a baffle plate is propor-
tional to the flow squared. If it is assumed that the inlet pressure (p1) falls and the outlet
pressure (p2) increases in proportion to the flow squared (cf. installed flow characteris-
tics), the division of the total pressure drop (p1 - p2) between the valve and baffle plate
described is in figure 46.
Figure 46. Typical pressure drop division between valve and baffle plate.
It has to be remembered that a baffle plate is a fixed restrictor, which produces the
desired pressure drop only at one given flow, that used for sizing the baffle. The baffle
plates are typically sized for the valve maximum flow. As the flow is reduced the pres-
sure drop across the baffle decreases and the pressure drop across the valve
increases. Thus, the baffle plate loses its effect at low flow rates.
Orifice plates
An orifice plate is a constant flow resistance. Unlike a baffle plate, there is only one
large hole in an orifice plate, rather than multiple small holes.
An orifice plate can be used for producing linear valve installed flow characteristic, and
in limited cases, also for cavitation abatement. An orifice plate can be installed both
upstream and downstream of a control valve. Sizing an orifice plate is basically similar
to sizing a baffle plate.
Liquid flow 59
Choose a value for valve back pressure (pi) under maximum flow conditions. The
capacity of the plate (Cv) is then calculated using a pressure drop (pi - p2) as in equa-
tion (38).
pi p2
q = N 1 C v ---------------- (38)
where q = liquid volumetric flow rate (SI units: [m3/h]; US units: [gpm])
Cv = flow coefficient of the baffle plate
pi - p2 = pressure drop across the baffle plate (SI units: [bar];
US units: [psi])
Gf = specific gravity (Gf=/0 = 1 for water at 15.6C or at 60F)
= fluid density (SI units: [kg/m3]; US units: [lb/ft3]
0 = density of water at 15.6C or at 60F
= 999 (SI units: [kg/m3])
= 62.36 (US units: [lb/ft3]
N1 = 0.865 (SI units: [m3/h], [barA])
= 1.0 (US units: [gpm],[psiA])
The back pressure chosen must ensure that the actual pressure drop across the plate
does not exceed the terminal pressure drop of the plate, given by the equation (39).
The calculation procedure may require iteration.
pi p2 FL ( pi FF pv )
where L = liquid pressure recovery factor of a baffle plate (see figure 47)
FF = critical pressure drop ratio factor for liquids (see equation (26))
pv = liquid vapour pressure (SI units: [barA]; US units: [psiA])
60 Liquid flow
Figure 47. The pressure recovery factor FL for orifice and for baffle plates as a func-
tion of Cv/d2 (note that the nominal size (d) of the plate is in inches).
When the capacity of the plate is determined, the pressure drop across it at flows other
than maximum flow can be calculated using liquid flow sizing equations. In non-choked
flow conditions liquid flow can be simplified as in equation (40).
q 2
p 1 p 2 = ( p 1 p 2 ) max -------------
q max (40)
For nonchoked flow the required flow cross-section area for the plate can be calcu-
lated using equation (41).
2 (41)
N 11 p q 2
- + ------2
FL Gf Ap
The maximum ratio of AB/AP for mechanical integrity of the baffle is ap proximately 0.4.
Single orifices can have a larger area ratio.
Liquid flow 61
In equation (42), it is shown how a single hole orifice plate, when used upstream of the
valve, is to be sized to ensure that there is no cavitation.
p1 pi z ( pi pv ) (42)
Incipient cavitation coefficient (z) can be determined from figure 48. Higher cavitation
coefficient (z) value for orifice plates compared to value for baffle plate is due to greater
hole diameter ratio to hole length.
Figure 48. Incipient cavitation coefficient z for orifice and for baffle plates as a function
of Cv/d2 (note that the nominal size (d) of the plate is in inches).
Noise generated by liquid flow is called hydrodynamic noise. At low pressure ratios,
xF = p/(p1 - pv), with laminar or turbulent flow, the noise level is normally low. At a cer-
tain pressure ratio (xF=z) the noise level increases sharply. The reason for this sharp
increase is cavitation. The value of cavitation coefficient (z) depends on the valve type
and opening angle.
There are two well known noise prediction methods used in the valve market. One is
based on the German VDMA 24422 recommended practise which origins to 1979 (see
appendix K). The second method is an international standard for hydrodynamic noise
prediction generated by a control valve, IEC 60534-8-4.
According to the VDMA 24422 (1979) the noise level in dB(A) can be calculated using
the following equations (equation (43) for SI units and equation (44) for US units) when
the flow is turbulent but cavitation has no effect on the noise level; (xT < z). In equations
(43) and (44) LF = 0
xF (43)
L A = 10 log ( C v ) + 18 log ( p 1 p v ) 5 log ( ) + 18 log ------ + 39 + L F + L P
xF (44)
L A = 10 log ( C v ) + 18 log ( p 1 p v ) 5 log ( ) + 18 log ------ + 12.1 + L F + L P
When cavitation (xF>z) has an effect, the noise level LA in dB(A) can be calculated
using the following equations (equation (45) for SI units and equation (46) for US units)
L A = 10 log ( C v ) + 18 log ( p 1 p v ) 5 log ( )
+ 292 ( x F z ) (46)
( 268 + 38 z ) ( x F z )
For each valve, the z and LF values for equations (45) and (46) are usually presented
in the manufacturers Cv-tables and noise prediction graphs.
Liquid flow 63
Correction coefficient Lp is the correction for pipe attenuation, and is given by the fol-
lowing graph (figure 49) and table 2.
The hydrodynamic noise prediction according to the IEC 60534-8-4 is more laborious
than noise prediction according to VDMA 24422 (1979). The noise prediction is based
on a method where mechanical stream power as well as acoustical efficiency factors
are calculated in different flow regimes i.e. turbulent and cavitation conditions. The
sound pressure level inside the pipe is estimated and the pipe external noise is attained
from inner sound pressure level by reducing the transmission loss of the piping.
64 Liquid flow
In short the IEC hydrodynamic noise prediction can be presented in the five following
1. The noise source is the mechanical energy dissipated in the valve orifice.
The mechanical stream power is calculated at vena contracta of the valve.
2. Small part of mechanical power is transferred to acoustical energy. The
portion of the mechanical power converted to (acoustical) sound power is
defined by using acoustical efficiency factors. Different flow regimes (tur-
bulent and cavitation) have different acoustical efficiency factors.
3. The sound power is converted to internal sound pressure level at the
downstream of the valve. The peak frequency of the generated noise is
also estimated.
4. The transmission losses of the piping are defined. The transmission loss
is dependent of the piping, the peak frequency and the fluid properties.
Step 4 also covers the part where the pipe external sound power level is
5. Define the A-weighted sound pressure level at the observation point at a
distance of 1 m from the pipe wall.
The total noise LpTOT is calculated by adding the noise levels from different sources
logarithmically as in the following equation (47).
Limitation of liquid flow velocity in pipelines and control valves is mainly used to prevent
excessive erosion. Other reasons include piping pressure losses (proportional to veloc-
ity squared), and corrosion (wearing away of protective film from metal surface). In the
case of butterfly valves, high inlet velocities can also lead to instability of the valve trim.
The following are recommended inlet velocities for liquid service control valves:
1 Segment, ball, globe, eccentric rotary plug, and Q-trimTM valves:
Inlet velocity 10m/s (32 ft/s) for continuous duty
Inlet velocity 12 m/s (39 ft/s) for infrequent duty
2 Butterfly valves:
Inlet velocity 7 m/s (23 ft/s) for continuous duty
Inlet velocity 8.5 m/s (27 ft/s) for infrequent duty
Typical piping design velocities range from 2 to 3 m/s (6 to 10 ft/s) for liquids.
The above values are for relatively pure liquids. As well as cavitation and flashing,
impurities in the flow may reduce the allowed maximum flow velocities.
66 Gas and steam flow
The flow of gas and steam through control valves has been well defined by universal,
standardized sizing equations (ISA/IEC). In the first half of this chapter, a description of
these equations and the basic fluid mechanics involved in gas or steam flow through
control valves is given much emphasis.
In the second half of this chapter, a great deal of attention is placed on techniques of
aerodynamic noise generation, prediction and abatement. This is done for two reasons:
firstly, noise is again, after some years of relatively low emphasis, becoming a major
environmental issue; and secondly, there is no good, easily understandable literature
on the actual generation and abatement mechanics of noise in control valves. The
details of aerodynamic noise generation and abatement given here should help to
explain the reasons for aerodynamic noise generation in control valves and the differ-
ent means that are available for dampening aerodynamic noise.
4.1 General
The main difference of gas or steam flow compared with liquid flow, is that the interrela-
tion of flow and pressure is typically much weaker. A typical pressure source is a mani-
fold with a relatively constant pressure unless the particular process pipe takes a major
share of the gas or steam led into it. A typical process installation model for a com-
pressible-flow such as a gas or steam flow control valve is shown in figure 52.
In figure 52, the upstream pressure (p1) is located two pipe diameters upstream of
valve inlet flange and downstream pressure (p2) is located six pipe diameters down-
stream of the valve downstream flange (per std. IEC 60534/ISA S75). This chapter
concentrates on the throttling process between upstream pressure (p1) and down-
stream pressure (p2) of figure 52.
The most important difference between liquid and gas flow is compressibility: when the
pressure is increased the volume of the gas decreases and vice versa. For the flow
there is used constant flow units like mass flow or standard volumetric flow units. The
pressure drop ratio x = p/p1 is used instead of pressure drop alone because gas
expansion is related to this ratio. The speed of sound is a significant measure of the
effects of compressibility compared with the velocity of flow. This introduces a dimen-
sionless parameter which is called the Mach number. The calculation for the Mach
number (Ma) is given in equation (48).
v (48)
Ma = -----
Figure 53 shows the interrelation of flow through a control valve at a constant opening
and constant upstream pressure (p1). It shows the flow through a gas or steam valve
starting to deviate from a straight line at fairly low pressure drop due to gas compress-
ibility. Accordingly, the valve inlet pressure is higher and the volume smaller than at the
outlet, where lower pressure causes higher volume. This expansion becomes a signifi-
cant factor at higher pressure drop ratios (p/p1).
68 Gas and steam flow
Figure 53. Interrelation of flow and pressure drop ratio in gas or steam valves.
The phenomenon of choking, i.e. a situation in which an increase in pressure drop (p)
across the valve does not produce an increase in flow, also occurs in gas and steam
flows, but here the reason is different. Whenever the fluid reaches sonic flow velocity at
the vena contracta , the smallest actual flow area location, a further increase in pres-
sure drop (p) at constant inlet pressure will not increase the flow velocity at the vena
contracta, although supersonic velocities may exist downstream of the vena contracta.
The flow can still be increased as a result of vena contracta enlargement. When the
pressure drop is further increased beyond the sonic velocity at the vena contracta, the
vena contracta moves upstream towards the valve orifice and the area of the vena con-
tracta gets larger, therefore increasing the flow. When the vena contracta reaches the
physical valve orifice the flow becomes fully choked, and an increase in the pressure
drop will not increase the flow. The terminal pressure drop at which this happens can
be calculated using the pressure drop ratio factor of valve (xT) as in equation (50).
p T = p 1 F k x T
The gas or vapour flow through the valve can be calculated using any of these forms of
basic equations (51) to (54).
w = N6 F p Cv Y x p1 1 (51)
q = N 7 F p C v p 1 Y --------------------------
Gg T1 Z
Gas and steam flow 69
w = N 8 F p C v p 1 Y --------------
q = N 9 F p C v p 1 Y ------------------------
x (55)
3 Fk xT
G g = -----------
M air
p1 p2 (57)
x = ------------------
k (58)
F k = -----------
If x Fk * xT, then the flow becomes critical and Y = 0.667 and Fk* xT must be use d
instead of x in equations (51) to (54).
For dry saturated steam, a simplified equation (59) can be used where x may not
exceed xT.
x (59)
w = N 10 F P C 1 p 1 3 ------ x
x T
If x xT, then pressure drop ratio factor (xT) must be used instead of pressure drop
ratio (x). For a valve with attached fittings pressure drop ratio factor (xT) has to be
replaced by pressure drop ratio factor (xTP).
xT x T K i C v 2 1
- 1 + --------------- ------2
2 N5 d
Factor Z is the compressibility factor, and for perfect gas has a value of 1.0. In many
flows, the fluid behaves as a perfect gas and the compressibility factor (Z) will be 1.
Compressibility factor (Z) can determined from the graph in appendix G as a function of
reduced pressure (pr) and reduced temperature (Tr).
Reduced pressure (pr) is defined as the ratio of the actual inlet absolute pressure to the
absolute thermodynamic critical pressure, as in equation (61). The reduced tempera-
ture Tr is defined similarly, as in equation (62).
p1 (61)
p r = ------
T r = ------
Gas and steam flow 71
The noise created by throttling gas or steam is called aerodynamic noise. Aerodynamic
noise at subsonic velocities is generated by three forms of aerodynamic sources:
monopole, dipole and quadropole. Aerodynamic monopole noise can be described as
a pulsating sphere causing the acoustic pressure waves. This type of noise is typical of
pulse jets, sirens and propellers. Monopole sources can also be caused by flow insta-
bility. The intensity of noise in this case is proportional to the fourth power of the flow
Control valve aerodynamic noise is mainly caused by dipole sources when the flow
velocity is subsonic. An aerodynamic dipole consists of two monopoles pulsing 180out
of phase near a solid boundary. In this case the acoustic intensity is given by the follow-
ing proportionality equation (63).
6 2
2 v Dj
- (63)
A very important implication in equation (63) is that the noise intensity is proportional to
the velocity to the sixth power.
72 Gas and steam flow
8 2
2 v Dj
- (64)
The noise intensity here is proportional to the eight power of the velocity. This applies
to a free jet.
In choked flows, where the flow velocity reaches sonic velocity, the flow becomes criti-
cal, and the main sources of noise are the shock waves and turbulence interactions.
Shock waves and turbulence interactions have been found to create a 'screech' from
acoustic feedback. Figure 54 describes the change in noise intensity as a function of
fluid velocity.
Shock waves which are perpendicular to the free jet stream are called normal shocks
or direct shocks. A normal shock is illustrated in figure 55.
The shock wave can also be oblique, if the flow passes a wedge or sharp object or if
supersonic flow is forced to change direction by a solid boundary. Figure 56 shows an
attached and a detached shock wave.
Gas and steam flow 73
Shock waves can be reflected from solid boundaries and can penetrate each other. A
control valve outlet flow stream can create an oscillating chain of compression shock
waves with declining cycles and intensity, as shown in figure 57. This is a very powerful
noise source.
At low pressure ratios (p1/p2), the cause of aerodynamic noise is turbulence. At high
pressure ratios, the flow becomes critical and the turbulent interactions of the shock
waves become the major source of noise.
p1 (65)
+ 20 log log ------ + 51 + L G + L p + L p2
p 2
Gas and steam flow 75
The aerodynamic noise prediction according to the IEC 60534-8-3 is very similar to IEC
hydrodynamic noise prediction. The noise prediction is based on similar method where
mechanical stream power as well as acoustical efficiency factors are calculated in five
different flow regimes. Standard defines regimes as function of the pressure drop ratio
(x). Then the sound pressure level inside the pipe is estimated and the pipe external
noise is attained from inner sound pressure level by reducing the transmission loss of
the piping.
Acoustical efficiency factors, the peak frequency and the mechanical stream power cal-
culations are depending on the flow regime but otherwise the IEC aerodynamic noise
prediction has similar steps than in hydrodynamic noise (see steps in chapter 3.5).
Due to the extent of the standard the reader is recommended to refer to the IEC 60534-
8-3 for details.
76 Gas and steam flow
Venting gas or steam to the atmosphere usually generates high noise levels around the
vent exit. In such cases, the jet noise inside the pipe released into the air and sound pres-
sure levels from 140 up to 170 dBA one meter from the vent exit may be generated.
Noise levels of this magnitude are hazardous to personnel and in many countries strict
noise abatement laws require action to reduce noise to acceptable levels near the manu-
facturing facilities.
As a result of high noise level in atmospheric venting, a control valve is normally equiped
with a low noise trim. Often a special vent diffuser or vent silencer is required to achieve
an acceptable noise level.
The observation point for vent noise is usually far from the vent exit, which can be consid-
ered a point noise source, and the sound pressure level decreases as a function of dis-
tance, as in equation (67).
r (67)
L d = 20 log ----
When the vent exits are high above ground level, for example, in gas-to-flare applica-
tions, the observation direction has a substantial effect on the noise. The directivity
effect attenuates most in opposite direction of the vent flow and least in the direction of
the vent flow. Attenuation can be as high as 15 dBA depending on the observation
Further away, in addition to the above reductions, more attenuation can be expected
owing to environmental and other conditions such as absorption in to the air, attenua-
tion by barriers, vegetation, and topography, or by wind and temperature gradients.
VDMA 24422 (version 1979) calculates noise only in a closed piping system and there
are no standard methods for predicting noise at an open pipe end. That is why noise
prediction for an atmospheric outlet uses an empirical method.
Gas and steam flow 77
Abatement of the noise produced in the throttling process can be done in several ways.
The basic division of these is between 'source' treatment, i.e. valve and trim modifica-
tion in a way that generation of excessive noise is prevented, and 'path' treatment, i.e.
dampening the generated noise.
Source treatment, whenever possible and feasible, is the preferred form of noise
abatement. This is because when source treatment is used the high mechanical vibra-
tion levels always associated with noise can be prevented, thus ensuring reliable oper-
ation of the process.
A combination of source and path treatment often provides the most economical sound
dampening system. Figure 59 shows the basic options for aerodynamic noise abate-
Source treatment of noise, i.e. preventing the generation of excessive noise levels, can
be performed by at least four different methods: velocity control, acoustic control, loca-
tion control and by using diffusers.
Velocity control
Controlling the maximum fluid velocity inside a control valve trim is a very effective way
of controlling noise at sub-sonic flow velocities in the trim, as the acoustic intensity of a
jet has been shown to be proportional to the sixth power of the flow velocity in a system
with solid boundaries like a valve trim or a pipe. The relation between sound pressure
level (SPL) and acoustic intensity is given in equation (69).
I vj
SPL ( dB ) = 10 log ----
The control valve trim velocity can be most effectively controlled using a multistage
pressure drop and by increasing the valve trim outlet area such that the flow velocity
and pressure at the valve outlet are the minimum and the gas volume is the maximum.
Figure 60 illustrates the basic principle of a staged pressure drop.
Gas and steam flow 79
When the pressure drop across a control valve is taken in multiple stages, as in figure
59, the total pressure drop (p1 - p3) is divided into several smaller successive pressure
drops (p1 - p2, p2 - p3). The successive stages are spaced in such a way that the gas
pressure is allowed to recover to an intermediate pressure (p2) and velocity (v2) before
the next throttling stage. This intermediate recovery of pressure and the resulting veloc-
ity reduction prevents the fluid from reaching the velocity it would have in a single-stage
pressure drop system. In other words, the smaller the pressure drop, the smaller the
recovery and fluid velocity increase downstream of the orifice. An infinite number of
stages would, therefore, produce a valve with no pressure recovery, in which the veloc-
ity at the vena contracta would equal the downstream velocity. However, economics
and mechanics limit the number of stages actually used in valves. Note that an expand-
ing flow area is used for each successive stage in gas processes to counter the expan-
sion of the gas as the pressure drops.
80 Gas and steam flow
Acoustic control
Acoustic control affects the noise level by means of acoustics. Two methods used in
control valves are described here: flow division into multiple streams and the modifica-
tion of acoustic field.
In theory, as given by equations (63) and (64), flow division into multiple streams is
effective because intensity of noise generated by a single orifice decreases rapidly
when hole diameter is decreased. Thus a number of small holes attenuates noise more
effectively than one big hole. A rule of thumb is that each doubling of the number of
holes reduces noise by 3 dB, as illustrated in figure 61.
In practice increasing the number of flow passages by making them smaller also affects
the noise frequency distribution. Equation (70) is an experimental equation showing the
noise reducing effect of smaller orifices.
SPL = 17 log ---------------
The smaller the passage, the higher the noise frequency. High-frequency noise is eas-
ily attenuated by the pipe wall, and does not contribute to the 'A'-weighted sound pres-
sure level scale (figure 62). High frequencies also extend beyond the capabilities of the
human ear.
Modification of the acoustic field directs the flow path in such a way that the peak noise
field is broken up in a more diffused space. Figure 63 gives the values for a dynamically
balanced butterfly valve as an example of acoustic field modification.
Gas and steam flow 81
Figure 63 shows a typical acoustic field for a conventional butterfly valve (top of the pic-
ture), and for a noise and cavitation attenuating equipped butterfly valve which diffuses
the checkered acoustic field.
Location control
Location control involves designing a valve trim in such a way that the location and the
shape of the jet streams in the valve trim, and especially leaving the valve trim, are
such that the minimum noise is produced.
The formation of turbulence in the mixing region between where the jet exits from an
orifice and the gas flow at the outlet region as well as attachment and interaction of
shock waves (generated during throttling if the flow reaches sonic velocity in the valve)
are major sources of noise that can be controlled to an extent by intelligent valve trim
design. One way to do this is to smooth the velocity profile of the jet by introducing a
lower velocity gas stream alongside the jet, as shown in figure 64.
Other methods include using orifice shapes and spacing orifices ensuring that the
shock wave interactions generate the minimum amount of total noise.
Dividing the pressure drop between a control valve and a downstream diffuser provides
an effective way of further increasing the noise attenuation in cases where there is a
constant, high pressure drop across the control valve and the flow rate is relatively con-
stant. Diffusers are fixed area flow resistances and are custom-made for a particular
flow condition.
Gas and steam flow 83
A high pressure drop over the valve generally causes noise and vibration problems in
the gas and steam flow. An inline diffuser is a constant area flow resistance used at the
valve outlet to increase valve downstream pressure.
The pressure differential (p1 - pi) is set for flows in which the highest capacity (Cv) is
needed for the valve. The capacity (Cv) of the diffuser is calculated under maximum
flow conditions using equations (51) to (54). Intermediate pressure (pi) and correspond-
ing density (i) are used as upstream pressure and density. The pressure drop ratio
factor (xT) is 0.5 for a single-stage and 0.7 for double-stage diffuser. The capacity (Cv)
of the diffuser remains constant, and this is used to calculate (p1 - pi) and the intermedi-
ate pressure (pi) for other flow conditions.
84 Gas and steam flow
In noise calculations, the noise from the valve and diffuser are first calculated sepa-
rately using standard VDMA 24422 noise prediction method. The intermediate pres-
sure (pi) is the valve downstream and diffuser upstream pressure. The noise level of
the total package is achieved by summing both noise levels logarithmically. A 6 dBA
insertion loss is subtracted from the valve noise level and the total noise level is then
given by equation (71).
The outer shell diameter of the diffuser is normally sized to match the downstream pip-
ing. However, the flow velocity in the annular area between the inlet tube and the outer
shell of the diffuser should not exceed 0.5 * vs if regenerated noise caused by high flow
velocity is to be prevented.
The minimum outer shell diameter to meet this requirement is given by equation (72).
2 w (72)
D out = D in + ------------------------------
N 15 v s 2
A smaller outlet shell than calculated from equation (72) can be used if, for example,
the outlet shell should be the same size as the downstream pipe. In these cases the
fact that flow velocity in the annular area will be greater than 0.5*vs resulting in limited
diffuser noise reduction capability for the diffuser must be taken into account.
When the outlet shell specified by equation (72) is bigger than the downstream piping,
the reduction of the downstream pipe can begin straight after the end of the diffuser
inlet tube.
Attenuator plates
Dividing the pressure drop between the valve and a downstream device provides an
effective methods noise attenuation in cases where the pressure drop is close to con-
stant across the valve. An attenuator plate is a fixed restriction installed downstream of
the valve, as shown in figure 70.
High pressure drop across a valve generally causes noise and vibration problems in
the gas and steam flow. An attenuator plate is a constant-area flow resistance, which is
used at the valve outlet to increase valve downstream pressure. Noise attenuation is
achieved by specific hole geometry. This hole geometry is a result of computational
and experimental studies. Figure 69 is a printout of a calculation of the flow through
one hole in an attenuator plate. The lines in figure 68 represent constant density
86 Gas and steam flow
Figure 69. Constant density regions of flow through a hole in an attenuator plate.
The attenuator plate capacity is fixed for each nominal size. If a higher capacity is
needed, the nominal size of the attenuator plate has to be increased. Normally the
nominal size must be selected between the valve and downstream pipe diameter.
Pressure and flow conditions with the selected plate are calculated using standard ISA/
IEC sizing equations.
The attenuator plate is mounted between flanges downstream of valve. Mounting can
be between the valve and pipe flanges or between piping flanges. For some valves an
attenuator plate are also available as an integrated unit inside the valve body.
Mounting the attenuator plate between the valve and pipe flanges is not allowed if the
valve is a butterfly valve, or flangless segment valve or if the attenuator plate is already
integrated into the valve body. In these cases at least one pipe diameter of pipe is
required between the valve and the attenuator plate.
The attenuator plate is usually effective for noise reduction when the pressure drop
ratio (p1-p2)/p1 is less than from 0.8 to 0.9, depending on the valve type and opening. A
diffuser is recommended for higher pressure drop ratios.
The pressure differential across the attenuator plate is calculated for each flow accord-
ing to basic gas sizing equations. The intermediate pressure (pi) is iterated from equa-
tions (51) to (54) replacing upstream pressure (p1) with intermediate pressure (pi).
Sizing is most easily done with a sizing and selection software. The critical pressure
drop ratio for an attenuator plate is 0.39. Cv is obtained by selecting the nominal size of
the attenuator.
Gas and steam flow 87
Noise calculations for valve and attenuator plate are first performed separately using
intermediate pressure (pi) as both the valve downstream and the attenuator plate
upstream pressure. The noise level of the total package is found by summing both
noise levels logarithmically. A 4 dBA insertion loss is subtracted from the valve noise
level. The total noise level is then as given in equation (73).
LpV 4 10 LpA 10
L PTOT = 10 log ( 10 + 10 )
Figure 70. A noise control trim provides a combination of effects for reducing noise
level in gas controlling applications; in right, an attenuator plate is installed
between valve and pipe flanges.
88 Gas and steam flow
These noise control trims use a combination of the effects listed in the following para-
The trim velocity is minimized using a multistage pressure drop. Trim outlet
velocity is minimized by opening up the downstream cheek of the trunnion
mounted ball valve or by using segment valves with no restriction at the trim out-
Division of the flow into multiple streams in attenuator holes attenuates the noise
following the principles of acoustic control.
The trim outlet is designed to provide a uniform acoustic field in the valve outlet
port, thus minimizing disturbances creating high-noise areas in the acoustic field.
The rotary motion of these valves has the additional benefits of allowing very large flow
ranges and the passing of impurities through the valve.
The path treatment of noise, i.e. suppressing the transmission of excessive noise lev-
els, can be performed by using least three different methods: silencers, insulation and
by heavier pipe schedule.
Silencers are mufflers used in-line or at an outlet to the atmosphere to dampen the
noise produced. Reactive silencers create frequency interactions to dampen noise,
whereas dissipative silencers use sound-absorbing materials like glass-fibre to
dampen the noise.
The main use for silencers is on atmospheric outlets for gas or steam. In such cases,
the jet noise inside the pipe is released to the open air and very high noise levels can
easily develop. Typically, a combination of reactive and dissipative methods are used in
atmospheric vent silencers.
Gas and steam flow 89
Pipe insulation may be used to dampen noise in gas and steam lines, particularly in
steam lines, where there is already thermal lagging. Thermal insulation can dampen
noise 1-2 dB(A) per 10 mm of insulation thickness (3 to 5 dB(A) per inch). The practical
maximum is about 12 dB(A) due to leaks and acoustic bridges. Special acoustic insula-
tion reduces noise up to 4 dB(A) per 10 mm of insulation thickness (10 dB(A) per inch).
The maximum attenuation for acoustic insulation is 20-25 dB(A).
Two things should be noted in using insulation for dampening noise: First, a noise level
greater than 100 dB(A) should primarily be handled by source treatment methods to
avoid hiding potential vibration damage by insulation. Second, the true cost of installing
acoustic insulation should be calculated before using it for long pipelines. This is
because noise is attenuated very slowly in piping filled with gas or vapour, and because
long pipe runs may have to be insulated in order to achieve acceptable noise reduction.
The flow velocity for gases or steam downstream of the valve can be calculated as in
equation (74).
qT (74)
v = N 16 ----------------2
p2 d
The recommended flow velocity at the valve exit port is given in terms of sonic velocity,
as in inequality equations (75) and (76).
Naturally, the above velocity limits are for relatively pure gases and steam. In the case
of impurities in the flow or wet steam, the flow velocities need to be lowered to prevent
erosion damage.
5.1 General
Control valve sizing theory for multiphase flow is not nearly so well developed as it is
for single-phase fluids. Sizing control valves for a pure liquid or gas flow can be done
using existing standard sizing equations based on flow dynamics and valve- specific
sizing coefficients. When a control valve is sized for a two-phase flow, which is usually
a mixture of liquid and gaseous fluid, no generally accepted standard method exists.
This is because in two-phase flow liquid and gas cannot be mathematically described
in a simple and exact way at the same time. Also, experimental research requires a lot
of tests with different kinds of mixtures and mass fractions using various valve types.
For this reason it is not possible to size valves for multi-phase flow with the same accu-
racy as for single component streams.
A large part of this section concentrates on sizing control valves for a particular multi-
phase fluid, i.e. pulpstock. Metso has done a lot of the basic research on determining
the behaviour of pulpstock flow through control valves. As a result of this research
there is now introduced a method for sizing control valves for pulpstock flows that
applies to all rotary control valve types.
The method presented here is based on a homogeneous flow theory which assumes
that liquid and gas move with the same velocity and are homogeneously intermixed.
The method can be applied in the following two cases of two-phase flow presented
Case 1 Single component, two-phase flow (e.g. steam and liquid water)
Case 2 Two component, two-phase flow (e.g. crude oil and natural gas)
92 Multi-phase flow
Sizing equations
Homogeneous flow theory is based on average properties such as the density and
velocity of a two-phase mixture. After necessary average properties have been deter-
mined, a valve can be sized using equations similar to the standard equations for sin-
gle-phase flow.
The density of two-phase flow is calculated using separate densities for both phases on
the upstream side of a valve. In addition, gas expansion must be taken into account
when gas flows through the valve. The density of the mixture, the so called effective
density, can then be formulated as in equation (77).
g f 1
- + ----
g Y f (77)
where fg = wg/w ; the fraction of gas mass flow rate of the total mass
flow rate
ff = wf/w ; the fraction of liquid mass flow rate of the total mass
flow rate
f = density of the liquid-phase on the valve inlet side
(SI units: [kg/m3]; US units: [lb/ft3])
g = density of the gas-phase on the valve inlet side
(SI units: [kg/m3]; US units: [lb/ft3])
Y = gas expansion factor
w = N 6 F p C v p E
where w = wg + wf ; total mass flow rate of the mixture (SI units: [kg/h];
US units: [lb/h])
Fp = piping geometry factor
Cv = valve flow coefficient
E = effective density (SI units: [kg/m3]; US units: [lb/ft3])
p = pressure drop across the valve (SI units: [bar]; US units: [psi])
N6 = 27.3 for SI units
= 63.3 for US units
Multi-phase flow 93
Choked flow
Experimental studies of choked two-phase flow are too few to allow exact terminal
pressure drops to be determined. In control valve sizing, the terminal pressure drop
approximation is performed using a combination of the terminal pressure drop values
of pure gas and pure liquid. Pure gas flow chokes when the pressure drop reaches the
value given by equation (79).
p = p 1 F k x TP (79)
The corresponding pressure drop for a pure liquid flow is given by equation (80).
F Lp 2
p = --------- ( P 1 F F P v ) (80)
In a case where all the fluid is in the liquid-phase flow, choking will start when the pres-
sure drop in equation (80) is reached. When a small fraction of gas is added to the flow,
the choked flow pressure differential changes, but is still quite close to the value in
equation (80). An increased mass fraction of gas will further change the terminal pres-
sure drop that produces choking, but it is not clear how this happens in control valves.
Finally, when all the fluid is in the gas-phase, choking will start with a pressure drop as
in equation (79). Theoretical calculations and flow tests have been performed to deter-
mine the terminal pressure drop for ideal nozzles. These results show that the linear
relationship between the terminal pressure drop in the liquid and gas-phase as a func-
tion of gas mass fraction describes the terminal pressure drop in choked two-phase
flow accurately enough, and can be formulated as in equation (81).
F Lp 2
P T 2PH = ( P 1 F k x TP ) f g + --------- ( P 1 F F P v ) f f (81)
When the actual pressure drop exceeds the value of equation (81) the two-phase flow
is considered to be a choked flow, and the pressure drop in equation (81) is used in the
valve sizing equation (78), and to calculate the expansion factor Y. Note that the mini-
mum value for expansion factor Y is Ymin (= 0.667).
94 Multi-phase flow
Due to the nature of the two-phase flow of liquid and gas it is impossible to describe the
various possible forms of flow adequately with a single mathematical formula. The
method presented here is based on so called homogeneous flow theory, which
assumes that the velocities of liquid and gas are the same, and that they are com-
pletely intermixed. This is a fairly common flow type, so the method described can be
applied in many two-phase flow applications.
Accuracy of sizing decreases if the form of the flow deviates from the type described.
The following forms of flow are possible in a pipe:
bubble flow: gas-phase is divided into bubbles and liquid; the bubbles
have the velocity of the liquid
plug and slug flow: when the amount of gas increases, the bubbles unite,
forming-bullet shaped plugs and slugs
churn flow: when the amount of gas increases further, the plug and slug
shapes break, leading to a very unstable form of flow
annular flow: the liquid flows as a thin film along the pipe wall and the gas
flows at high speed in the middle
stratified flow: in a horizontal pipe the phases are completely separate from
each other due to gravity. When the speed of the gas increases,
waves form on the surface of the liquid.
mist flow: almost all the liquid is in drops which move together with
the gas
Phase changes in the liquid and gas, vapourization of the liquid or condensation of the
gas into liquid make the calculation of mass fractions and effective density difficult.
These factors in sizing accuracy are especially evident with single-component two-
phase flow. When the pressure decreases and the temperature is almost constant, the
liquid tends to evapourate whereby the mass fraction of vapour and the required valve
capacity increase. On the other hand, the so called metastability phenomenon tends to
'slow down' the phase change, which means that the liquid does not vapourize at once
in the vena contracta although the thermodynamic equilibrium of the substance would
indicate the case to be such, but vapourization occurs only after the vena contracta.
Multi-phase flow 95
The effect of mass fractions on sizing accuracy is especially visible with small mass
fractions of vapour. For example, a change in the mass fraction from 1 % to 2 % of a
saturated 7 barA water and steam mixture causes a 73 % change in the specific vol-
ume of the mixture. This means that the required capacity increases by about 30 %. On
the other hand, if the mass fraction of the flow changes from 98 % to 99 %, the specific
volume of the mixture changes by 1 %. If the mass fractions with single-component
two-phase flow are not known exactly, the sizing can be checked by assuming the
whole mass flow as vapour flow, which guarantees that the valve capacity is adequate
in all situations.
There are no methods for predicting noise in two-phase flow. In practice, estimation of
noise in two-phase flow is very difficult. It is known from experience that cavitation
noise in pure liquid flow is lower if, for instance, air is mixed with the liquid. Air bubbles
attenuate the pressure waves created by the collapse of cavitation bubbles.
5.3 Pulpstock
Paper and pulp mills use a large number of control valves to throttling the flow of pulp-
stock. The costs of both building and running the process are largely determined by
how the throttling control valves are sized and selected, as the selection process deter-
mines the pumping energy 'burnt' in the control valve and the piping. Correct selection
of the pulpstock control valves can determine the selection of the optimal size pumps
and piping. In the past, over-dimensioning of pumps and valves have been used for all
the uncertainties in the behaviour of the pulpstock flow. Rough correction coefficients
has been used to account for the greater capacity (Cv) requirement of pulpstock com-
pared with water. Now, new studies go a long way towards predicting exactly how pulp-
stock behaves in control valves, and towards improving the accuracy of sizing
Previous studies, mainly performed to evaluate consistency effects on pipe flow, it indi-
cate that pulpstock flow behaviour is highly dependent on flow velocity, as shown in
figure 70.
When the flow velocity of the pulpstock is very small, it flows in the pipe like a solid plug
and forms 'rolls', which spin between the plug and pipe wall. As the flow velocity is
increased, the flow changes into a plug flow, in which the fibers no longer touch the
pipe wall as there is a narrow boundary layer between the plug and the pipe wall. In this
area the pressure loss remains relatively constant in spite of flow velocity changes, and
can even have an inverse relation to the flow velocity increase (unstable area in
96 Multi-phase flow
figure 71). As the flow velocity is increased further, the thickness of the boundary layer
increases and turbulence starts appearing in the boundary layer and at the surfaces of
the pulp plug. The centre of the pulp plug remains pluglike. This is called mixed flow.
When the flow velocity is further increased, the pulp plug disappears and the whole
flow crosssection becomes turbulent.
Figure 71. The piping pressure loss in relation to flow velocity for pulpstock and water
describes the changes in piping pressure loss at different flow velocities in
pulpstock and water flows.
The three basic forms of pulpstock flow are illustrated in figure 72.
Note also that at high flow velocities, as in figure 71, the pressure loss of the pulpstock
can be lower than that of water.
There has been performed over 2000 measurements of pulpstock flow through control
valves. The tests were performed on three different types of quarterturn control valve in
three different sizes (50 mm/2", 100 mm/4" and 200 mm/8"). The pulp stocks used
were bleached kraft (sulphate pulp), thermo-mechanical pulp and recycled pulp. The
tests resulted an empirical correction coefficient (k), which is presented in appendix J.
The coefficient (k) is determined by equation (82).
q stock
k = ---------------- (82)
q water
Note that a correction of the flow rate is used instead of a correction in the required
Cvvalue. This is done so that valves would be sized using correct sizing parameters
pressure recovery factor (FL) and cavitation index (z), which relate to the real opening
of the control valve.
The differences in the results for different size control valves and different quarterturn
valve types were found to be insignificant, and thus to justify using a single set of cor-
rection curves for each type of pulpstock. The correction coefficients (k) are given in
appendix J for both SI units and US units.
There has been establish the following relationships in the pulpstock flow through con-
trol valves:
Control valve sizing for pulpstock applications is performed using an 'equivalent water
flow rate' and water sizing equations. The 'equivalent water flow rate' is derived from
equation (83).
q stock
q water = --------------- (83)
where qstock = pulp stock flow rate
k = correction coefficient (see appendix J)
After calculating an equivalent water flow rate, the sizing is done utilizing standard IEC/
ISA sizing equations for water, as presented in chapter 3.
Figure 72 shows that when the valve opening is already relatively large, the actual flow
decreases if the valve is opened further. This kind of situation has to be avoided in
order to maintain the fluid flow control of the process.
In the described case, the valve maximum opening should be set at about 55 % to
guarantee process controllability, and a valve with an expanded outlet should be used.
In the above case, when the valve maximum opening is set at 55 %, increasing the
valve opening, the capacity (Cv) increase produces a constantly larger flow.
100 Multi-phase flow
5.4 Slurries
A typical twophase flow of a liquid and solids is wet slurry. Wet slurry is a mixture of a
liquid and solid particles. Suspensions are slurries if the particle sizes are so small that
the mixture remains unseparated for a long time. Suspensions can be treated as non-
Newtonian fluids, where basic liquid equations can be applied to the calculated 'appar-
ent viscosity' for the suspension.
Settling slurries are suspensions in which particle size is bigger than 0.25 mm (0.01 in).
These can be calculated as liquids, as long as the two phases can be assumed to flow
through the control valve as a homogenous mixture; with the densities of different
phases close to each other, and viscosity small enough to guarantee effective mixing.
The density () in that case is taken as the effective density (E) weighted mass ratios
of liquid and solids.
A typical twophase flow of dry slurry, is a mixture of gas and solids. This kind of mixture
is rarely controlled by conventional valves due to mechanical problems like erosion and
plugging. If a control valve is to be sized for dry slurry, equation (78) gives the best
results, although it is slightly conservative. In this case, the density of the mixture is
taken as the effective density in equation (77), where the liquid is replaced by a solid.
Mathematical simulation of control valve behaviour 101
6.1 General
The use of computational science has resulted in a control valve simulation program
that can be used to describe the dynamic behaviour of control valves.
Before the delivery to a customer, the operation of a control valve packages can be
simulated in conditions that equal the real process conditions. Simulation makes it pos-
sible to study the operation of the whole control loop including the customer's process.
The simulation program can also be used to study various questions relating to the
safety of process plants.
In training of personnel about control valves, simulation can be used to illustrate the
operation of different control valve units in process pipelines. In addition, simulation
makes it possible to examine different control valve characteristics in the whole control
The starting point for the control valve simulation program is a comprehensive mathe-
matical model describing the operation of the control valve, right from the control signal
from the controller to the fluid flow through the valve.
The dynamics equation of a quarter-turn control valve can be found using the basic
equations (84) and (85).
d x
Fi = mred --------
Mi = J ---------
- (85)
Equations (84) and (85) can be used to produce the equations for the dynamics of an
installed quarter-turn control valve as in equation (86).
2 2
dx d d x d 2
- + m red ----------2- -------
m red ------- + J b ( , ) ---------
d 2 dt
dt d
dx d
+ f m -------
d v
+ f b ( , ) -------
+ sign -------
b ( , ) M v ( , , p )
+ b ( , ) M d ( , p ) F m ( P A P B ) = 0
The actuator coefficient (b) used in equation (86) is a function of the actuator turning
angle () and friction coefficient (). Figure 74 shows the actuator coefficient for one
manufacturer's actuator as a function of actuator relative travel (h) when the friction
coefficient () is assumed to be constant.
The non-linearity of the actuator coefficient (b) depends on the lever mechanism of the
actuator. In practice, actuator friction coefficients vary greatly as a function of velocity.
This means that the actuator coefficient is in reality less linear than indicated in figure 74.
Figure 75 shows the non-linearity of the derivatives in equation (86) for the actuator
examined, as a function of actuator relative travel (h). The first derivative in figure 74
describes the non-linearity between the actuator piston position (x) and the valve turn-
ing angle (). The non-linearity of the derivatives depends on the lever mechanism of
the actuator.
104 Mathematical simulation of control valve behaviour
As the control valve dynamic equation (86) includes pressures pA and pB, which affect
both sides of the actuator piston, they must be solved from the mathematical models
describing positioner dynamics and actuator thermodynamics.
In equation (86) the valve load has been divided into the load caused by friction (Mv)
and the load caused by dynamic torque (Md) since the dynamic torque usually tends to
close the valve. The valve load consists of the seat friction, gland packing friction, bear-
ing frictions and dynamic torque of the valve. A mathematical model is needed to solve
these torques as a function of valve travel (h) and the pressure difference (p) across
the valve throttling element. Because the pressure difference (p) over the throttling
element changes considerably in a control situation especially with large travel
changes, the mathematical model of the control valve must include a dynamic model of
pipe flow.
Unsteady pipe flow control is calculated using the continuity equation (87) and the
equation of motion, equation (88).
h h a v
2 (87)
------ + v ------ + ------ ------ = 0
t x g x
v v h v lvl (88)
------ + v ------ + g ------ + ------------- = 0
t x x 2d
A large decrease in the friction coefficient right after the valve starts to move is an
important factor in the dynamics of a control valve equipped with a pneumatic cylinder
actuator. This means that the correct modelling of friction behaviour is decisive for
proper functioning of the simulation program.
Lubrication mechanisms can be divided into contact lubrication and fluid lubrication. In
contact lubrication, the sliding bearing surfaces touch each other, although the lubricant
limits the contact area by penetrating between the contact points. In fluid lubrication the
pressure generated in the bearings prevents any contact between surfaces, and the
friction force is created only by the shear stress of the lubricant.
The starting point for the contact friction model used is the exponential friction model, in
which the friction force depends exponentially on relative slide velocity (vr). Applying
the model gives the equations (89) and (90) for the contact friction coefficients.
v r
d 1 = dmin + ( s dmin ) e
d 2 = dmin + ( 0s dmin ) e
v r (90)
By approximating the contact friction using the exponential friction coefficient and by
assuming that the fluid friction is directly proportional to velocity, the control valve fric-
tion model can be determined.
Figure 76. Step response calculated theoretically with the simulation program when
the value of the relative signal changes from 40 % to 45 %.
Mathematical simulation of control valve behaviour 107
Figure 77. The corresponding step response measured in the laboratory using an
The characteristic pressure difference ratio (DPf) describing the pipeline is determined
using equation (91).
P f (91)
DP f = ----------
The starting point for the case is a constant gain inherent flow characteristic valve
which performs the signal change from 100 % to 10 %. For the equal percentage open-
ing valve with a corresponding steady-state pressure difference and flow rate change,
the signal change is from 100 % to 12.0 %. For a linear valve the corresponding signal
change is from 100 % to 3.2 %.
Figure 78 shows that the water-hammer caused by a valve with a linear inherent flow
characteristic is very strong and sharp. With equal percentage and constant gain inher-
ent flow characteristics, water-hammers are considerably smaller. Note that in the con-
stant gain inherent flow characteristics the change in flow rate is almost linear as a
function of time.
Figure 78. Water-hammer caused by a valve with different inherent flow characteristics.
Appendix A Sizing examples 109
The sizing examples presented here are based on sizing coefficients of Metso control
valves. The sizing coefficients can be found from Metso sizing coefficient tables.
D series ball valve is controlling high pressure viscous oil flow. Valve size is 100
mm. What is required capacity Cv and opening of the valve with given flow data?
Flow data:
Fluid properties:
Piping configuration:
Cv = 320
= 51.8
h = 75 %
Appendix A Sizing examples 111
Top entry rotary control valve with Q-Trim is controlling cooling water flow. Valve size is
50 mm. What is required capacity Cv and opening of the valve with given flow data?
Flow data:
Fluid properties:
Piping configuration:
Pv 0.023
Pc 221.2
112 Appendix A Sizing examples
P T = --------- ( P 1 F F P v )
0.9 2
= -------- ( 10 0.957 0.023 )
= 8.08
C v = -------------------------------------------------
p T
= ---------------------------------------------------
0.865 1 1 -----------
= 16.3
h = 68 %
Appendix A Sizing examples 113
R-series segment valve with Q-Trim is controlling air flow to atmosphere. Valve size is
80 mm. What is required capacity Cv and opening of the valve with given flow data?
Flow data:
Fluid properties:
Piping configuration:
d 4 80 4
114 Appendix A Sizing examples
Sum of K coefficients:
= 0.06 + 0.51 + 0.59 0.92
= 0.24
xT x T ( K 1 + K B 1 ) C v 2 1
x TP = --------- 1 + --------------------------------------- ------2
2 N5 d
Flow is choked because x > Fk * xTP. Therefore Fk * xTP (= 0.69) is used instead of x
(= 0.745) in sizing.
C v = ----------------------------------------------------------------------
F k x TP
N 9 F p p 1 Y ------------------------
= -------------------------------------------------------------------------------------------------------- = 58.9
1.0 0.69
2250 0.99 2.7 0.667 ----------------------------------
28.9 293 1
h = 67 %
116 Appendix A Sizing examples
L-series butterfly valve is controlling saturated steam flow. Valve size is 100 mm. What
is required capacity Cv and opening of the valve with given flow data?
Flow data:
Fluid properties:
Piping configuration:
3 Fk x TP
= 1 -----------------------------------
3 0.93 0.41
= 0.91
C v = ------------------------------------------------------------
N6 Fp Y x p1 1
= -------------------------------------------------------------------------------------------
27.3 1 0.90 0.105 4.75 2.54
= 253
h = 70 %
118 Appendix A Sizing examples
Top entry rotary control valve with Q-Trim is controlling mixture of crude oil and natural
gas. Valve size is 150 mm. What is required capacity Cv and opening of the valve with
given flow data?
Flow data:
Fluid properties:
Piping configuration:
p T 2PH = ( p 1 F k x TP ) f g + --------- ( p 1 F F p v ) f f
= ( 82.7 0.943 0.75 ) 0.1755
0.91 2
+ ----------
- ( 82.7 0.934 0.37 ) 0.8245
= 66.5 bar
120 Appendix A Sizing examples
3 F k x TP
82.7 34.7
= 1 ---------------------------------------
3 0.943 0.75
= 0.726
g f f f 1
- + -----
g 1 Y 2 f
0.1755 0.8245
= ----------------------------2- + ------------------
62 0.726 800
= 156.2 kg/m
C v = ---------------------------------------------
N 6 F p p E
288 083
= ------------------------------------------------------
27.3 1 48 156.2
= 122
h = 70 %
Appendix A Sizing examples 121
R-series segment valve is controlling flow of mechanical stock. Valve size is 80 mm.
What is required capacity Cv and opening of the valve with given flow data?
Flow data:
Fluid properties:
Piping configuration:
q water
C v = ----------------------------------------------
= ------------------------------------------------
0.865 1 1 --------
= 93.3
h = 65 %
Appendix B Conversion tables 123
mm cm m km in ft yd ml
millimeters mm 1 0.1 0.001 0.000001 0.03937 0.003281 0.001094 6.21e07
centimeters cm 10 1 0.01 0.00001 0.393701 0.032808 0.010936 0.000006
meters m 1000 100 1 0.001 39.37008 3.28084 1.093613 0.000621
kilometers km 1000000 100000 1000 1 39370.08 3280.84 1093.613 0.621371
inches in 25.4 2.54 0.0254 0.000025 1 0.083333 0.027778 0.000016
feet ft 304.8 30.48 0.3048 0.000305 12 1 0.333333 0.000189
yards yd 914.4 91.44 0.9144 0.000914 36 3 1 0.000568
miles ml 1609344 160934.4 1609.344 1.609344 63360 5280 1760 1
mm2 cm2 m2 in2 ft2 yd2
square millimeters mm2 1 0.01 0.000001 0.00155 0.000011 0.000001
square centimeters cm2 100 1 0.0001 0.155 0.001076 0.00012
square meters m2 1000000 10000 1 1550.003 10.76391 1.19599
square inches in2 645.16 6.4516 0.000645 1 0.006944 0.000772
square feet ft2 92903 929.0304 0.092903 144 1 0.111111
square yards yd2 836127 8361.274 0.836127 1296 9 1
cm3 m3 ltr in3 ft3 US gal Imp.gal US brl
cubic centimeters cm3 1 0.000001 0.001 0.061024 0.000035 0.000264 0.00022 0.000006
cubic meters m3 1000000 1 1000 61024 35 264 220 6.29
liters ltr 1000 0.001 1 61.0 0.035 0.264201 0.22 0.00629
cubic inches in3 16.4 0.000016 0.016387 1 0.000579 0.004329 0.003605 0.000103
cubic feet ft3 28317 0.028317 28.31685 1728.0 1 7.481333 6.229712 0.178127
US gallon US gal 3785 0.003785 3.79 231 0.13 1 0.832701 0.02381
Imp gallon Imp.gal 4545 0.004545 4.55 277 0.16 1.20 1 0.028593
US barrel for oil US brl 158970 0.15897 159 9701 6 42 35.0 1
g kg tonne shton Lton lb oz
grams g 1 0.001 0.000001 0.000001 9.84e07 0.002205 0.035273
kilograms kg 1000 1 0.001 0.001102 0.000984 2.204586 35.27337
metric tons tonne 1000000 1000 1 1.102293 0.984252 2204.586 35273.37
short tons shton 907200 907.2 0.9072 1 0.892913 2000 32000
long tons Lton 1016000 1016 1.016 1.119929 1 2239.859 35837.74
pounds lb 453.6 0.4536 0.000454 0.0005 0.000446 1 16
ounces oz 28 0.02835 0.000028 0.000031 0.000028 0.0625 1
124 Appendix B Conversion tables
g/ml kg/m3 lb/ft3 lb/in3
gram per milliliter g/ml 1 1000 62.42197 0.036127
kilogram per cubic meter kg/m3 0.001 1 0.062422 0.000036
pound per cubic foot lb/ft3 0.01602 16.02 1 0.000579
pound per cubic inch lb/in3 27.68 27680 1727.84 1
m/s m/min km/h ft/s ft/min mi/h
meter per second m/s 1 59.988 3.599712 3.28084 196.8504 2.237136
meter per minute m/min 0.01667 1 0.060007 0.054692 3.281496 0.037293
kilometer per hour km/h 0.2778 16.66467 1 0.911417 54.68504 0.621477
feet per second ft/s 0.3048 18.28434 1.097192 1 60 0.681879
feet per minute ft/min 0.00508 0.304739 0.018287 0.016667 1 0.011365
miles per hour mi/h 0.447 26.81464 1.609071 1.466535 87.99213 1
Appendix B Conversion tables 125
bar psi kPa MPa kgf/cm2 mmHg atm
bar bar 1 14.50326 100 0.1 1.01968 750.0188 0.987167
pound per square inch psi 0.06895 1 6.895 0.006895 0.070307 51.71379 0.068065
kilo Pascal kPa 0.01 0.1450 1 0.001 0.01020 7.5002 0.00987
Mega Pascal MPa 10 145.03 1000 1 10.197 7500.2 9.8717
kilogram force per cm2 kgf/cm2 0.9807 14.22335 98.07 0.09807 1 735.5434 0.968115
millimeter of mercury mmHg,torr 0.001333 0.019337 0.13333 0.000133 0.00136 1 0.001316
Int.St.Atm. atm 1.013 14.69181 101.3 0.1013 1.032936 759.769 1
meter of water mH2O 0.09806 1.42219 9.806 0.00981 0.09999 73.54684 0.096802
foot of water ftH2O 0.02989 0.433503 2.989 0.00299 0.030478 22.41806 0.029506
centimeter of mercury cmHg 0.01333 0.193328 1.333 0.00133 0.013592 9.99775 0.013159
inch of mercury inHg 0.03386 0.49108 3.386 0.00339 0.034526 25.39563 0.033425
inch of water inH2O 0.002491 0.036128 0.2491 0.000249 0.00254 1.868297 0.002459
Pascal = N/m2 Pa 0.00001 0.000145 0.001 0.000001 0.00001 0.0075 0.00001
mmH2O, kp/m2 kp/m2 9.81e05 0.001422 0.009807 0.00001 0.00099 0.073552 0.000097
2116 lb/ft2
30 inch mercury STANDARD ATMOSPHERIC PRESSURE
34 feet water LOCAL ATMOSPHERIC PRESSURE
1 atmosphere
K = Kelvin
C = degrees in Celsius
F = degrees in Fahrenheit
R = degrees in Rankine
Nm kgfm ftlb inlb
Newton Meter Nm 1 0.101972 0.737561 8.850732
kilogram force meter kgfm 9.80665 1 7.233003 86.79603
foot pound ftlb 1.35582 0.138255 1 12
inch pound inlb 0.112985 0.011521 0.083333 1
Appendix B Conversion tables 129
100 373.15 1.01325 1.67351 0.59755 270 543.15 55.0581 0.03566 28.0454
105 378.15 1.20800 1.41980 0.70432 275 548.15 59.4960 0.03280 30.4923
110 383.15 1.43266 1.21046 0.82613 280 553.15 64.2018 0.03018 33.1362
115 388.15 1.69060 1.03681 0.96450 285 558.15 69.1863 0.02778 35.9946
120 393.15 1.98543 0.89203 1.12104 290 563.15 74.4607 0.02558 39.0874
125 398.15 2.32098 0.77072 1.29748 295 568.15 80.0369 0.02356 42.4372
130 403.15 2.70132 0.66861 1.49564 300 573.15 85.9269 0.02171 46.0694
135 408.15 3.13075 0.58226 1.71743 305 578.15 92.1435 0.01999 50.0130
140 413.15 3.61379 0.50894 1.96488 310 583.15 98.7001 0.01842 54.3017
145 418.15 4.15520 0.44640 2.24013 315 588.15 105.611 0.01696 58.9740
150 423.15 4.75997 0.39286 2.54541 320 593.15 112.891 0.01561 64.0754
155 428.15 5.43330 0.34685 2.88311 325 598.15 120.556 0.01436 69.6593
160 433.15 6.18065 0.30715 3.25573 330 603.15 128.625 0.01319 75.7892
165 438.15 7.00766 0.27278 3.66590 335 608.15 137.117 0.01212 82.5418
Appendix D Superheated steam 133
Specific volume (V) (unit: [m3/kg]) as a function of temperature (unit: [C]) and pressure
(unit: [barA]).
Gas phase
Gas with the molecular formula Molecular Weight of Specific Critical Critical Ratio of
weight std. cubic gravity Pressure temp. specific
M metre Gg pc tc heats
g/mol n [bar] [C] k *)
Acetylene C2H2 26.04 1.11 0.91 62.4 35.7 1.23
Air 28.98 1.23 1.00 37.7 -140.7 1.40
Ammonia NH3 17.08 0.73 0.60 113.0 132.4 1.32
Argon Ar 39.94 1.69 1.38 48.6 -122.4 1.67
Bentzene C6H6 78.11 3.30 2.70 48.5 288.5 1.10 (90C)
Butane (n) C4H10 58.12 2.59 2.09 36.5 153.2
Butane (i) C4H10 58.12 2.51 2.05 36.5 135.1 1.11 (15C)
Butylene C4H8 56.11 2.37 1.94 39.3 146.6
Carbon dioxide CO2 44.01 1.87 1.53 74.0 31.0 1.31
Carbon monoxide CO 28.01 1.18 0.97 35.0 -140.2 1.40
Chlorine Cl2 70.91 3.05 2.49 77.0 144 1.34
Chlorine dioxide ClO2 67.46 2.94 2.40
Cyanogen C2N2 52.04 2.23 1.78 60.8 128.3 1.26
Dichordi fluor CF2Cl2 120.92 4.82 3.93 40.1 111.5 1.14
Ethane C2H6 30.07 1.29 1.05 48.8 32.2 1.22
Ethylene C2H4 28.05 1.19 0.98 51.2 9.7 1.25
Fluorine F2 38.00 1.61 1.31 55.7 -128.7
Formaldehyde CH2O 30.03 1.32
Helium He 4.00 0.17 0.14 2.30 -267.9 1.66
Hydrogen H2 2.02 0.08 0.07 13.0 -239.9 1.41
Hydrogen bromide HBr 80.92 3.45 2.82 85.6 90.00 1.36
Hydrogen chloride HCl 36.47 1.55 1.27 84.1 51.40 1.41
Hydrogen iodide HJ 127.93 5.49 4.48 83.1 150.80 1.40
Hydrogen sulfide H2S 34.08 1.46 1.19 90.1 100.50 1.33
Methane, Natural gas CH4 16.04 0.68 0.55 46.3 82.50 1.30
Methyl chloride CH3Cl 50.49 2.19 1.78 66.8 143.10 1.28
Methyl ether C2H6O 46.07 1.98 1.62 53.3 126.90 1.11 (20C)
Methyl mercaptan CH4S 48.10 1.06 0.87 72.3 196.80
Neon Ne 20.18 0.85 0.70 27.2 -228.7 1.67
Nitric oxide NO 30.01 1.27 1.04 65.9 94.00 1.40
Nitrogen N2 28.02 1.18 0.97 33.9 -147.10 1.40
Nitrous oxide N2O 44.02 1.88 1.53 72.7 36.60 1.28
Oxygen O2 32.00 1.35 1.11 50.4 -118.8 1.40
Ozone O3 48.00 2.03 1.66 93.5 5.00 1.29
Propane (n) C3H8 44.09 1.90 1.56 42.6 96.80 1.14
Propylene C3H6 42.08 1.81 1.48 45.9 92.00 1.14
Sulphur dioxide SO2 64.06 2.77 2.26 78.8 157.30 1.29
Steam H2O 18.02 (0.76) (0.622) 220.4 374 1.3 (std. cond.)
*) k is in temperature 0 C unless otherwise specified
136 Appendix E Physical constants of various gases and liquids
Liquid phase
Liquid with the molecular formula Molecular Specific Critical Critical Vapour
weight Gravity Pressure Temp. Pressure
M Gf pc Tc Curve
g/mol [barA] [K] Page
Acetaldehyde C2H40 44.05 0.783 55.7 461 141
Acetic acid C2H4O2 60.05 1.049 57.9 594 143
Acetone C3H6O 58.08 0.792 47.0 508 145
Air 28.98 0.559 37.7 132 150
Ammonia NH3 17.08 0.639 113.0 406 141
Aniline C6H5NH2 93.12 1.022 53.1 426 142
Argon A 39.94 1.373 48.6 151 150
Benzene C6H6 78.11 0.879 48.5 562 145
Benzoic acid C7H6O2 122.12 1.075 45.6 752 142
Benzyl alcohol C7H8O 108.14 1.041 46.6 677 142
Boron trichloride BCl3 117.17 1.35 38.7 452 141
Bromine Br2 159.81 3.12 103.4 584 145
Bromobenzene C6H5Br 157.01 1.495 45.2 670 143
Butyl ether C8H18O 130.23 0.768 25.3 580 143
Carbon dioxide COS 44.01 0.777 74.0 304 150
Carbon disulfide CS2 76.13 1.263 74.0 546 145
Carbon monoxide CO 28.01 0.803 35.0 132 150
Carbon tetrachloride CCl4 153.82 1.594 45.6 556 145
Carbon tetrafluoride CF4 88.01 1.33 37.9 227 150
Carbonyl sulfide COS 60.07 1.274 64.3 378 141
Chlorine Cl2 70.91 1.563 77.0 417 141
Chlorobenzene C6H5Cl 112.56 1.107 45.2 632 143
Chloroform CHCl3 119.39 1.489 54.7 536 145
Cis-2-butene C4H8 56.11 0.621 42.0 435 141
Cis-2-hexene C6H12 84.16 0.687 32.8 518 145
Cis-2-pentene C5H10 70.14 0.656 36.5 476 141
Cis-3-hexene C6H12 84.16 0.68 32.8 517 145
Cyclohexane C6H12 84.16 0.779 40.3 553 145
Cyclohexanone C6H10O 98.15 0.951 38.5 629 143
Cyclohexene C6H10 82.15 0.816 43.5 560 145
Cyclopentane C5H10 70.14 0.745 45.1 512 145
Cyclopentanone C5H8O 84.12 0.95 53.7 626 143
Deuterium oxide D2O 20.03 1.105 219.5 644 145
Dichloromethane CH2Cl2 84.93 1.317 60.8 510 148
Diethyl amine C4H11N 73.14 0.707 37.1 497 145
Diethyl ketone C5H10O 86.13 0.814 37.4 561 146
Diethyl sulfide C4H10S 90.18 0.837 39.6 557 146
Diisopropyl ether C6H14O 102.18 0.724 28.8 500 146
Diphenyl C12H10 154.21 0.99 38.5 789 142
Dipropylamine C6H15N 101.19 0.738 31.4 550 143
Ethane C2H6 30.07 0.548 48.8 305 150
Ethanol C2H6O 46.07 0.79 63.9 516 146
Ethyl acetate CH3COOC2H5 88.10 0.9 38.3 523 146
Ethyl acrylate C5H8O2 100.12 0.921 37.5 552 146
Ethyl amine C2H7N 45.09 0.683 56.2 456 148
Ethyl benzoate C9H10O2 150.18 1.046 32.4 697 142
Ethyl bromide C2H5Br 108.97 1.451 62.3 504 148
Ethyl butyl ether C6H14O 102.18 0.749 30.4 531 146
Ethyl chloride C2H5Cl 64.52 0.896 52.7 460 148
Appendix E Physical constants of various gases and liquids 137
Liquid with the molecular formula Molecular Specific Critical Critical Vapour
weight Gravity Pressure Temp. Pressure
M Gf pc Tc Curve
g/mol [barA] [K] Page
Ethyl ether C4H10O 74.12 0.714 36.5 467 148
Ethyl formate C3H6O2 74.08 0.927 47.4 508 146
Ethyl propionate C5H10O2 102.13 0.895 33.6 546 146
Ethylbenzene C8H10 106.17 0.867 36.1 617 143
Ethylcyclopentane C7H14 98.19 0.771 33.9 570 143
Ethylene C2H4 28.05 0.577 51.2 282 150
Ethylene glycol C2H6O2 62.07 1.155 77.0 645 142
Ethylene oxide C2H4O 44.05 0.899 71.9 469 148
Fluorine F2 38.00 1.51 52.2 144 150
Fluorobenzene C6H5F 96.10 1.024 45.5 560 146
Formaldehyde CH2O 30.03 0.815 65.9 408 148
Formic acid CH2O2 46.03 1.226 85.1 580 146
Furan C4H4O 68.08 0.938 55.0 490 148
Heptane C7H16 100.20 0.684 27.2 540 146
Hexane C6H14 86.17 0.659 30.0 508 146
Hydrazine H4N2 32.05 1.008 146.9 653 143
Hydrogen bromide HBr 80.92 2.16 85.6 363 150
Hydrogen chloride HCl 36.47 1.193 84.1 325 150
Hydrogen fluoride HF 20.01 0.967 64.8 461 148
Hydrogen iodide HI 127.93 2.803 83.1 424 148
Hydrogen sulfide H2S 34.08 0.993 90.1 373 150
Iodide I2 253.81 3.74 116.5 819 142
Isobutane C4H10 58.12 0.557 36.5 408 148
Isobutanol C4H10O 74.12 0.802 43.0 548 146
Isobutyl acetate C6H12O 116.16 0.875 30.4 561 143
Isobutyric acid C4H8O2 88.11 0.968 40.5 609 143
Isopropyl amine C3H9N 59.11 0.688 50.7 476 148
Isopropyl chloride C3H7Cl 78.54 0.862 47.2 485 148
M-cresol C7H8O 108.14 1.034 45.6 706 142
M-xylene C8H10 106.17 0.864 35.5 617 144
Methanol CH4O 32.04 0.792 79.7 513 149
Methyl acetate C3H6O2 74.08 0.934 46.9 507 147
Methyl acrylate C4H6O2 86.09 0.956 42.6 536 147
Methylamine CH5N 31.06 0.703 74.6 430 149
Methyl bromide CH3Br 94.94 1.737 86.1 464 149
Methyl chloride CH3Cl 50.49 0.915 66.8 416 149
Methyl ethyl ether C3H8O 60.10 0.7 44.0 438 149
Methyl ethyl ketone C4H8O 72.11 0.805 41.5 536 147
Methylcyclohexane C7H14 98.19 0.774 34.8 572 147
Methylcyclopentane C6H12 84.16 0.754 37.9 533 147
Morpholine C4H9NO 87.12 1 54.7 618 144
N-butane C4H10 58.12 0.579 38.0 425 141
N-butanol C4H10O 74.12 0.81 44.2 563 144
N-butylaniline C10H15N 149.24 0.932 28.4 721 142
N-butyric acid C4H8O2 88.11 0.958 52.7 628 144
N-hexane C6H14 86.18 0.659 29.7 507 147
N-octane C8H18 114.23 0.703 24.8 569 144
Nitric oxide NO 30.01 1.28 65.9 180 151
Nitro methane CH3NO2 61.04 1.138 63.1 588 147
Nitrogen N2 28.02 0.804 33.9 126 151
138 Appendix E Physical constants of various gases and liquids
Liquid with the molecular formula Molecular Specific Critical Critical Vapour
weight Gravity Pressure Temp. Pressure
M Gf pc Tc Curve
g/mol [barA] [K] Page
Nitrogen dioxide NO2 46.01 1.447 101.3 431 141
Nitrous oxide N2 O 44.02 1.226 72.7 310 151
Octane C8H18 114.22 0.702 25.0 569 144
O-cresol C7H8O 108.14 1.028 50.1 698 142
O-xylene C8H10 106.17 0.88 37.3 630 144
Oxygen O2 32.00 1.149 50.4 155 151
Ozone O3 48.00 1.356 93.5 261 151
P-cresol C7H8O 108.14 1.019 51.5 705 142
P-xylene C8H10 106.17 0.861 35.2 616 144
Pentane C5H12 72.15 0.626 33.4 470 141
Perchloryl fluoride ClFO3 102.45 2.003 54.4 368 141
Phenol C6H6O 94.11 1.059 61.3 694 142
Phosgene CCl2O 98.92 1.381 57.5 455 141
Propane C3H8 44.09 0.582 42.6 370 141
Propionic acid C3H6O2 74.08 0.993 53.7 612 144
Propyl chloride C3H7Cl 78.54 0.891 45.8 503 147
Propylene C3H6 42.08 0.612 45.9 365 149
Propylene oxide C3H6O 58.08 0.829 49.2 482 149
Pyridine C5H5N 79.10 0.983 60.8 617 144
Styrene C8H8 104.15 0.906 39.9 647 144
Sulphur dioxide SO2 64.06 1.455 78.8 431 149
Toluene C7H8 92.13 0.866 42.2 594 144
Trans-2-butene C4H8 56.11 0.604 41.0 429 149
Trans-2-hexene C6H12 84.16 0.678 32.7 516 147
Trans-2-pentene C5H10 70.14 0.649 36.6 475 149
Trans-3-hexene C6H12 84.16 0.677 32.5 520 147
Trichloroethylene C2HCl3 131.39 1.462 49.2 571 147
Triethylamine C6H15N 101.19 0.728 30.4 535 144
Valeraldehyde C5H10O 86.13 0.81 35.5 554 147
Vinyl acetate C4H6O2 86.09 0.932 43.6 525 147
Vinyl chloride C2H3Cl 62.50 0.969 56.0 430 149
Water H2O 18.02 0.998 220.4 647 132-133
Appendix F Vapour pressure curves 139
Vapour pressure [barA]
-200 -180 -160 -140 -120 -100 -80 -60 -40 -20
Temperature [ C]
Vapour pressure [barA]
-200 -150 -100 -50 0 50
Temperature [ C]
Appendix F Vapour pressure curves 149
150 Appendix G Compressibility factor Z
Dimensions and weights of most common welded and seamless wrought steel pipe
based on ANSI/ASME B36.10M standard.
Nominal US UNITS IDENTIFICATION SI UNITS
size Outside Wall Plain end API Strength Schedule Outside Wall thick- Plain end
[in] diameter thickness weight Spec. standard *) number diameter ness weight
[in] [in] [lb/ft] [mm] [mm] [kg/m]
/2 0.840 0.188 1.31 ... ... 160 21.3 4.78 1.95
3/ 1.050 0.219 1.94 ... ... 160 26.7 5.56 2.90
*) STD = standard
XS = extra strong
XXS = double extra strong
154 Appendix I PRESSURE DROP IN STEEL PIPES
v q p v q p v q p v q p
[m/s] [m3/h] [bar] [m/s] [m3/h] [bar] [m/s] [m3/h] [bar] [m/s] [m3/h] [bar]
0.1 0.177 0.00060 0.1 0.452 0.00050 0.1 0.707 0.00040 0.1 1.810 0.00021
0.2 0.353 0.00304 0.2 0.905 0.00170 0.2 1.414 0.00128 0.2 3.619 0.00070
0.5 0.884 0.01500 0.5 2.262 0.00844 0.5 3.534 0.00625 0.5 9.048 0.00344
1 1.767 0.05000 1 4.524 0.02875 1 7.069 0.02200 1 18.096 0.01250
2 3.534 0.17600 2 9.048 0.10000 2 14.137 0.08000 2 36.191 0.04500
3 5.301 0.37800 3 13.572 0.22500 3 21.206 0.18000 3 54.287 0.10125
5 8.836 1.05000 5 22.619 0.59375 5 35.343 0.47500 5 90.478 0.26563
10 17.671 3.80000 10 45.239 2.31250 10 70.686 1.80000 10 180.96 1.03125
dead band The range through which an input signal can be varied
without response in output.
dead time The interval of time between input change and the
start of output response.
hysteresis plus dead band Maximum deviation between measured output with
increasing signal compared to output measured with
decreasing signal. Hysteresis can be achieved by sub-
tracting dead band from measured value.
Appendix L Control valve performance terminology 159
response time The time required for an output to change from an ini-
tial value to a specified percentage of the final value as
a result of input change.
Since every case is individual there are no universal rules for manifold design, but the
following pages contain some information about the subject. The designer should
always remember that control valve applications are usually designed individually,
using detailed data for each case.
x= 90 deg bent or an T-joint
O= two or more 90 deg bend in same plane
= two or more 90 deg bend in different plane
= straight distance after the apparat in question
= flow port area / pipe area
Figure 2. Straight pipeline needed with orifices to achieve fully formed velocity
Appendix M Manifold design guidelines for valves 161
Figure 3. Flow pattern in a 90 bend. Where the turbulence is heavy cavitation may
As can be seen from the examples above, it is important in pipeline design to try to
avoid an assembly that combines, for instance, a 90 bend just before a butterfly valve.
In the case of liquid flow there could be problems with cavitation in the bend, causing
noise and damage. Disturbances from a bend can also affect the performance of the
control valve. Usually the effect on the maximum capacity is insignificant, especially
when the control valve is installed with pipe reducing and expansion pieces as is usu-
ally the case. The cavitation features of the valve can also change.
Particular points that should be taken into account in manifold design for butterfly
Figure 7. If two butterfly valves are installed in series, their shafts should be at a 90
angle to each other.
Appendix M Manifold design guidelines for valves 163
To ensure optimum performance from the valve, the following guidelines should be fol-
lowed. This will ensure the valve behaves as predicted. In practice, however, millions of
valves have been installed in all kinds of piping configurations without any problems.
This is because, in most cases, the accuracy of the flow data actually contributes more
to the control valve sizing accuracy than any of the issues described above. Thus the
table below can be used as a guideline for building accurate laboratory equipment, but
for a typical flow loop in the mill, these instructions are not critical.
The affect of the reducing pieces just before and after the valve are taken into account
when the valve is sized with, for instance, the control valve sizing and selection pro-
gram 'Nelprof'.
Sooner or later, the designer faces a situation where he must compromise on manifold
design. It may not be possible to have enough straight pipeline. In such cases the
designer has to consider the complete installation. Are the velocities high or low, is the
pressure high or low? With high velocities and low pressure it is more important to try to
avoid complicated manifold designs. If the control valve is very close to cavitation point,
it is a natural solution to extend the straight pipeline downstream of the valve. It is
always worth investigating whether the valve could be relocated etc. If the capacity of
the control valve is at its upper limit, it is important to ensure a constant velocity profile
at the valve inlet. This can be achieved with sufficient length of straight pipe upstream
from the valve. These are the kind of things that the designer should consider before
the final layout is decided. As a rule of thumb, it can be said that the easier the case,
the greater the compromise that can be made with manifold design and still maintain
control valve performance at the desired level.
List of symbols 165
List of symbols
kinematic viscosity cSt
pressure head loss coefficient
loss of material
density (SI units: [kg/m3]; US units: [lb/ft3])
geometry factor
0.70 for baffle plates
0.00762 * (cv/d2) + 0.55 for orifice plates, when (Cv/d2) < 21
0.71 for orifice plates, when (Cv/d2) 21
valve turning angle
pipe friction factor
sliding materials constant
stick-slip parameter
(h) relative flow coefficient at relative opening h
0 density of water at 15.6 C or at 60 F
999 (SI units: [kg/m3])
62.36 (US units: [lb/ft3])
1 upstream density (SI units: [kg/m3]; US units: [lb/ft3])
2 downstream density (SI units: [kg/m3]; US units: [lb/ft3])
E effective density (SI units: [kg/m3]; US units: [lb/ft3])
f density of the liquid-phase on the valve inlet side (SI units: [kg/m3]; US units: [lb/ft3])
g density of the gas-phase on the valve inlet side (SI units: [kg/m3]; US units: [lb/ft3])
n gas density (SI units: [kg/m3]; US units: [lb/ft3]) at normal conditions; pressure of 1.013 barA at 15.6C or pressure of 14.7 psiA
at 60F
h relative valve travel error
i head loss coefficient for an inlet fitting = K1 + KB1
Ld change in sound pressure level [dBA]
LG valve-specific correction coefficient; usually presented in the manufacturer's noise prediction graphs along the Cv tables
p pressure drop (SI units: [bar]; US units: [psi])
p0 pressure difference across a closed valve
pf pressure difference across a fully open valve
ph pressure lost
pm differential pressure across the valve at the maximum designed flow rate
pT terminal pressure drop (SI units: [bar]; US units [psi])
Q relative flow rate error
q flow rate error
SPL difference in sound pressure level [db(A)]
friction coefficient
0 static friction coefficient for decelerating motion
d1 contact friction coefficient for accelerating motion
d2 contact friction coefficient for decelerating motion
dmin minimum value for dynamic friction coefficient
s static friction coefficient for accelerating motion
A flow area
a speed of pressure pulse
AB plate cross-section flow area (mm2 or in2)
AP pipe area at the plate (mm2 or in2)
b actuator coefficient
Cv flow coefficient of the valve/baffle plate
Cv(1.0) valve flow coefficient when valve is fully open
Cv(h) valve flow coefficient at relative opening h
Cvf maximum capacity coefficient of valve
d inlet diameter of a valve (SI units: [mm]; US units: [in])
166 List of symbols