Understanding Water Hammer
I've been doing some reading on water hammer and trying to 'really' understand it.
I've
been asked to look at a relatively simple problem of a pump station
pump water up a relatively constant slope. Initially this was to be done
by others, but I was keen (stupid) to learn.
Details:
Flow: 50 MLD
Head: ~250 m (~200m static)
Length: 10,000m
Diameter: ~1000mm
Pipe: Steel, ~10mm thick
I've
assumed the most likely cause of water hammer will be due to pump trip
as; pump isolation valves are manual, there is a control valve near
discharge, but this is relatively 'slow' (over 60s open/close). At this
stage I've assumed pump will take less than 5s before it's head drops
below static head, hence flow 'stops'.
I've assumed time for
'valve closure' (in this case pump stop) is 5s, therefore given celerity
is in the order of 1100 m/s, this disturbance is rapid (5s < 2L/a
< 20). Therefore elastic theory should used.
Elastic theory indicates that I'll get a pressure rise of about 100m.
I have two question:
1.
Does a pressure rise of 100m seem to be accurate based on my simple
analysis? When the pump stops, the water column continues to move,
causing a low pressure at the pump discharge. This low pressure wave
travels up the water column. The low pressure cause the water column to
stop, then it will 'pull' the water back, at which point it will collide
with the check valve and cause a pressure spike. Should I assume that
if the spike is 100m, the low pressure will be -100m (if static head
200m, then 100m)?
2. It has been suggested that a fast acting non
return valve can reduce the pressure spike. Is this true and if so how?
Or does it just protect the pump?
I'm not sure that your analogy of the pump stopping as being equivalent
to a slow closing valve is necessarily correct. In the water hammer
case where we look at a closing valve, the upstream pressure remains
constant and we have a certain amount of momentum in the fluid that
wants to keep moving but can not. In the case of a pump trip, there is
nothing to stop the fluid momentum from carrying it forward but we
gradually lose the upstream pressure and so the "high" downstream
pressure starts to want to drive fluid back the other direction. If the
fluid is allowed to reverse direction and then is subsequently stopped
(perhaps by a slow closing check valve), we can have water hammer. If
on the other hand we are able to stop the fluid from reversing
direction, or we can catch it before it builds appreciable reverse
momentum, we will avoid water hammer.
A fast acting check valve
will minimize the chance for reverse flow to occur and will minimize the
potential for water hammer. Consequently, the potential for water
hammer in a pump trip scenario should I think be dependent on the
characteristics of the check valve and I'm not sure that looking at the
pump as a "valve closure" fits the situation.
An old valve catalogue I have says the following:
"forward
flow continues for a while after the pump is switched off, but the
downstream pressure decelerates the flow more rapidly and then reverses
its direction. Without a check valve, the reverse flow would increase
and stabilize at some value, unless the downstream pressure declined. An
"ideal" check valve would allow no reverse flow and would close exactly
at the time the velocity curve passes through zero; there would be no
water hammer. A "real" check valve starts closing while the flow is
still forward, but it lags the velocity curve. Still, with fast
response, it closes before a high reverse velocity develops and thus
minimizes the water hammer surge."
This particular catalogue
recommended tilting disc check valves in pump discharge applications
because of their rapid response relative to other designs but I don't
think they are all that commonly used anymore. I know one end user with a
strong preference for Durabla check valves in pump discharge
applications.
Anyway, I'm sure many of the reputable check valve manufacturers can provide all sorts of information on this.
"If it is a perfect check valve there will be no pressure surge. Is this correct?"
Not
correct. The check valve (if it survives) will stop the surge from
continuing back to the pump. There may be sufficient volume between the
check and pump impeller to attempt to reverse spin the pump for a
fraction of a second, or at least slow it down considerably. Its common
petroleum pipeline design practice to consider the cases where the pump
trips and also where a check or other control valve, or an automatic
shutdown valve fails.
"When the check valve closes, the local
pressure around the check valve should be less than the static pressure
(due to moment of water)."
When the check valve closes, the flow
has stopped AT THE CHECK VALVE, but the flow farther downstream is still
moving along so you will not yet have anything like a static pressure
situation at the check valve. When the check valve closes all you can
say is that the pressure upstream is less than the pressure downstream
at that instant
in time. When the moving fluid column impacts a closed valve, say at
the end of the pipeline, (or just runs out on an uphill section) the
algebraic sum of the velocity head converted to pressure plus original
operating pressure there will then attempt to accelarate the column from
that end back to the pump station. That reversed pressure wave will
not reach the check valve until a time equal to the pipeline
length/sonic_velocity has expired.
Caution: Should lowest
pressure go below the vapour pressure of water, the fluid column will
part at that point creating a vapour space filling with water vapour as
the downstream portion of the column continues to move along. The
reverse pressure wave will probably be sufficient to collapse that
vapour space on its return and may increase pressures well above that
predicted by elastic theory, as the two segments of the fluid column
impact each other.
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