POWER June 2022 - 33

OPERATIONS & MAINTENANCE
Mechanism 1-Steam Discharging
1. The sequence of events is shown here
when steam is discharged into sub-cooled
water and a valve is closed to stop flow. A
pressure pulse is created when the water
column strikes the valve. Courtesy: Michael F.
Czyszczewski, PE
Water Slug Impact
When a water slug strikes something
in its path, a water hammer pressure
pulse is generated. Neglecting friction,
the impact velocity is calculated using
Equation 5:
VI = ∆V = √((( 288 gc
/ LS
))
where PU
sure (psi); PD
is the upstream steam presis
the downstream void
pressure (psi); LS
slug (ft); and LV
is the length of the
is the length of the vapor
space (ft).
The pressure pulse at impact (∆P) can
be found using Equation 3 with k = 1.0.
The slug impact force (FS
, lbf) is primarily
a function of the slug's momentum,
shown in Equation 6:
FS
= ( AP
( ρ VI
2 )) / gc
where AP is the pipe internal flow area
(ft2). To include the dynamic effects of impact,
a conservative dynamic load factor
(DLF) equal to 2X is frequently used for
design. This factor represents the ratio of
stress from a rapidly applied load to the
stress that would have occurred had the
load been applied slowly.
CIWH Mechanisms
Hydraulic transient events in power
plants were extensively studied by the
Electric Power Research Institute (EPRI)
in the 1970s through the 1990s. Much of
the material presented in this article is
based on EPRI's " Water Hammer Handbook
for Nuclear Plant Engineers and
Operators " TR-106438, which was published
in 1996 and can be downloaded
from EPRI's website at: www.epri.com.
The study identified and defined the following
four basic CIWH mechanisms.
June 2022 | POWER
( PU
- PD
)) / ρ ) ( LV
into Sub-Cooled Water. If a steam line
discharges under water and the steam
flow is stopped by closing an upstream
valve, a pocket of vapor will be trapped
in the pipe (Figure 1). The water at the
pipe exit will begin to cool, because it is
no longer being heated by the steam.
Contact with sub-cooled water will
cause the vapor pocket to rapidly condense.
The low-pressure zone created
by the implosion causes the water column
to be drawn up the pipe and slam
into the closed valve at high velocity. A
water hammer pressure pulse is emitted
at impact. It's not surprising that
this CIWH mechanism is referred to as
a water-cannon.
The differential head across the water
column (∆H, ft) is found using Equation
7:
∆H = Ha
+ x0 - HVP
where x0 is the pipe emersion depth (ft);
Ha
surface; and HVP
is the pressure head on the water
is the pressure in the
vapor pocket.
The water column velocity (VO
is found using Equation 8:
VO
= ∆V = √((2 gc
∆H ) / KTotal
)
where KTotal is the sum of the " DarcyWeisbach "
component loss coefficients
plus (f L) / D. Where, f is the pipe friction
factor, L is the distance from the valve
to the pipe outlet, and D is pipe inside
diameter.
The impact velocity (VI
) can be found
based on Equation 9, which is an empirical
curve fit to data in the EPRI handbook:
VI
=
VO
(( 0.0097 L / ∆H - 0.438 ) KTotal
( -0.161 L / ∆H + 1.18 ) KTotal
∆H + 1.056)
2 +
- 0.061 L /
The impact pressure pulse (∆P) can be
found using Equation 3 with k = 1.0.
To prevent Mechanism 1 transients:
■ Don't discharge steam under water.
■ Add a vacuum breaker below the
shut-off valve to inject air into the
vacuum space to relieve the vacuum
and cushion the water column
impact.
■ Close the steam shutoff valve slowly.
■ Increase the length of the discharge
pipe. The height that the water column
can climb is limited by the lowest
possible pressure in the void.
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, ft/sec)
2. The sequence of events is shown here
when stratified steam and water counter-flow
in a horizontal pipe. Pressure pulses are created
when the vapor pocket collapses and
when a water slug strikes the elbow. Courtesy:
Michael F. Czyszczewski, PE
Mechanism 2-Stratified Steam and
Water Counter-Flow in a Horizontal Pipe.
This CIWH mechanism occurs in horizontal
pipes containing two-phase flow.
Figure 2 shows an example where a
pipeline is used to supply a steam vessel
with sub-cooled water. Initially, the
pipe is full of steam. When the fill valve
opens, the pipeline starts to fill from the
bottom up with water. Vertical pipe sections
will run full of water; however, horizontal
pipe sections will have two-phase
flow with water resting on the bottom
surface of the pipe while steam occupies
the space above the water.
The steam in contact with the water
will condense, which will cause more
steam to be drawn into the pipe, increasing
the condensation and steam
flowrates. This initiates a counter-flow
pattern between the steam and water,
and a transition to slug flow conditions.
A large surface wave that fills the pipe
cross section will create a vapor pocket
on its downstream side. The wave is
pushed downstream by steam pressure.
The compressed vapor pocket collapses
as it comes in contact with sub-cooled
water. The implosion creates a water
hammer pressure pulse and a large pressure
differential across the wave accelerates
it down the pipeline as a water slug.
When the slug hits a change in direction
or a flow obstruction, the impact creates
another large pressure pulse.
A mechanism 2 transient can't occur if
the pipe runs full of water. The minimum
mass flowrate (m, lbm/sec) to run full of
33
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POWER June 2022

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