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Understanding Water Hammer

2010-11-30

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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