6
Liquid pressure recovery factors for various valve types
at rated travel and at lower valve travel are shown in
product bulletins. These values are determined by
laboratory test in accordance with prevailing ISA and
IEC standards.
Cavitation in Control Valves
Combined Liquid Pressure Recovery Factor F
LP
The liquid pressure recovery factor is a dimensionless
expression of the pressure recovery ratio in a control
valve. Mathematically, it is defined as follows:
In this expression, p
vc
is the pressure at the vena contracta
in the valve.
When a valve is installed with reducers, the liquid pressure
recovery of the valve reducer combination is not the
same as that for the valve alone. For calculations involving
choked flow, it is convenient to treat the piping geometry
factor F
p
and the F
L
factor for the valve reducer combination
as a single factor F
LP
. The value of F
L
for the combination
is then F
LP
/F
p
where :
Liquid Pressure Recovery Factor F
L
The following equation may be used to determine F
LP
.
where K
i
= K
1
+ K
B1
(inlet loss and Bernoulli coefficients)
Cavitation, a detrimental process long associated with
pumps, gains importance in control valves due to higher
pressure drops for liquids and increased employment of
high pressure recovery valves (e.g. butterfly and ball valves).
Cavitation, briefly, is the transformation of a portion of
liquid into the vapor phase during rapid acceleration of the
fluid in the valve orifice, and the subsequent collapse of
vapor bubbles downstream. The collapse of vapor
bubbles can produce localized pressure up to 100,000 psi
(7000 bar) and are singly most responsible for the rapid
erosion of valve trim under high pressure drop conditions.
It is, therefore, necessary to understand and to prevent
this phenomenon, particularly when high pressure drop
conditions are encountered.
Cavitation in a control valve handling a pure liquid may
occur if the static pressure of the flowing liquid tends to
decrease to a value less than the fluid vapor pressure. At
this point, continuity of flow is broken by the formation of
vapor bubbles. Since all control valves exhibit some pres-
sure recovery, the final downstream pressure is generally
higher than the orifice throat static pressure. When down-
stream pressure is higher than vapor pressure of the fluid,
the vapor bubbles revert back to liquid. This two-stage
transformation is defined as cavitation.
The pressure recovery in a valve is a function of its partic-
ular internal geometry. In general, the more streamlined
a valve is, the more pressure recovery is experienced.
This increases the possibility of cavitation.
The pressure recovery factor, F
L
, is useful for valve sizing
purposes to predict limiting choked flow rate under fully
cavitating conditions. However, the use of F
L
can be
misleading to predict limiting pressure drop at which
damaging cavitation will result.
An enhanced cavitation prediction method is described in
the ISA Recommended Practice ISA-RP75.23-1995
“Considerations for Evaluating Control Valve Cavitation”.
The recommended practice is based on the “Sigma”
method, where sigma is defined as:
The determination of sigma is based on cavitation energy
levels, not on choked flow. Laboratory testing using high-
frequency vibration data establishes sigma values. These
sigma values then define different operational regimes for
a specific product as illustrated below.