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Speed Torque (Starting) Characteristics for High Nss Pump - Acceleration Head Effects

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Slagathor

Mechanical
Jan 6, 2002
129
First of all, lets consider a High Nss pump...in the 9000+ range. So it has a steep H-C curve, and more importantly for the purposes of this issue, a high shut off HP. Shut-Off head HP is 2.4 x HP at BEP! Like the right most curve here:

fig2-51_rzfjwz.png


(If this image does not come though, you can view it here: See figure 2 about half way through the article. )

The key characteristic is the pump has high shut off HP. This means you can not just draw the speed torque curve as a parabola.

Why? Because of the affinity laws and the high SO HP. A normal pump (4500 Ns and lower) has peak HP at BEP, or right of BEP. When you start a pump up, you are by definition starting at zero speed. If you have any lift, you are essentially dead heading your pump. Even if you have NO lift, you are still dead heading your pump, because ACCELERATION head creates head above and beyond friction. This pushes you LEFT on any curve at a given speed. But for a normal pump, you don't care, because left on the curve reduces HP. As such, speed torque curves for most "normal" centrifugal pumps are just parabolas, and at full speed, the torque value coincides with the peak HP the pump will run at at full speed (based on a pump and system head curve intersection).

But with a high Nss pump, pushing left on the curve INCREASES HP dramatically. This means your speed torque curve has this S-Curve shape, which is not truly dependent just on speed. It is dependent on speed AND acceleration. The S-T curve is now made up of two parts. One is the paraolic part, as normal. The other is a function of speed AND acceleration. The faster you accelerate the pump, the more the acceleration of the fluid in the pipeline downstream resists, creating a transient acceleration head. This results in the pump seeing higher pressures during acceleration, and thus high loads because the high Ns pump sees HP rise when operated left. The more fluid mass you have to accelerate, the worse the effect. The faster you try to get the pump up to speed, the worse the effect.

As you increase the acceleration time (such as on a VFD), the S-T curve converges to the parabolic case, assuming you are not running the pump against a closed valve, and the system-pump intersection is in a good spot (at or right of the point used to the size the motor)

I have been tasked with creating a mathematical representation of this S-T characteristic due to a field problem where the pump is not starting properly on a reduced voltage starter. If we look at the parabolic case, the pump should start fine based on the motor S-T curve and the reduced voltage sequence being utilized. But we know from field experience, that the pump S-T curve is "worse" than the parabolic case. We just do not know how much worse.

Such a math model would have to take into account the following:
1. The base parabolic speed torque characteristic (T=cN^2...easy)
2. The pump curve and HP curve for any given speed (At a given speed, you need to know the load for a given head)
3. The mass of fluid that needs to be accelerated. This changes over time...which can make things worse. For instance...the worst case would be to start a pump slowly...then try to accelerate from 70% speed to 100% speed almost instantly. This would create a huge load spike. If the mass of the fluid is known, you can calculated the acceleration head for a given rate of acceleration.

Has anyone ever seen any technical guideance (text books, papers, etc) on such an task?
 
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seems a long involved posting for something that is probably fully explained on the internet - somewhere. Up to you to research it - not EngTips.

It is a capital mistake to theorise before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts. (Sherlock Holmes - A Scandal in Bohemia.)
 
Artisi,

Uh...no...it is not. The fact that you made such a comment reveals you did not come close to understanding the question. No pump engineering text addresses this (even Gulich, which is very thorough), and the only reference I can find relating to acceleration head effects are for PD pumps, and a generic comment that "centrifugal pumps can experience higher than expected power draw during start up due to acceleration head". There is no technical discussion of the phenomenon that I can find, which is why I asked here. I was hoping to find someone other than a smart ass.
 
Slagathor,

You've been around ET long enough to know that whatever you think of the reply, you really shouldn't make derogatory comments to a long term poster. I suggest you have a cup of something and then edit your post.

Anyway, the bit I still don't understand is this section.

"The faster you accelerate the pump, the more the acceleration of the fluid in the pipeline downstream resists, creating a transient acceleration head. This results in the pump seeing higher pressures during acceleration, and thus high loads because the high Ns pump sees HP rise when operated left. The more fluid mass you have to accelerate, the worse the effect. The faster you try to get the pump up to speed, the worse the effect. "

If your pump fluid is accelerating, this implies you're trying to fill an empty pipe and hence in fact your pump is operating on the far right of the pump curve because the flow is actually very high. Accceleration head as I understand it is limited to these very transient effect if you start up a centrifugal pump with no back pressure. In PD pumps this is an effect seen on inlet lines where the inrush of liquid caused by the piston accelerating downwards causes an increase in friction losses. Normally this effect is so small everyone ignores it, but in inlet lines even a few extra feet can make a difference. You seem to be describing a different effect.

Either way I still can't understand what the start sequence / pressures / flow is.

It sounds more like someone is trying to start a pump against a closed valve or a high pressure and hence at reduced voltage, the pump can't speed up.

Some sort of flow diagram or actual data would help us.

Maybe you just really need to introduce a start up bypass sloop to allow the pump to speed up and flow on the RHS of the curve from the beginning??

I don't think "acceleration head" has anything to do with your issue, but maybe I just can't follow your logic.



Remember - More details = better answers
Also: If you get a response it's polite to respond to it.
 
Little Inch, I've been abused and insulted by experts on many occasions, this particular post doesn't even rate. However you are somewhere near the mark, a long post without much substance, the first point missing as it's axial flow, is it starting against a fully charged delivery line or an empty one and a description of the application /installation would / could tell heaps.

It is a capital mistake to theorise before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts. (Sherlock Holmes - A Scandal in Bohemia.)
 
Little Inch,

Thank you for the response, and putting some thought into it.
*This is an open discharge system. No closed valves.
*The acceleration phase is pretty fast. The motor is designed for maximum 6-7 second acceleration when started across the line. At reduced voltage, it would be longer due to the voltage ramp up phases, etc.
*More recently, we are focusing on evaluating the worst case scenario which is a 6 second acceleration from 0 to 100% speed.
*Most of the piping system is vertical. It lifts water up, then make a 90 to discharge into a channel.
*When the discharge pipe is mostly full, the (transient/starting) loads are HIGHER. This is the opposite of what would be expected under steady state pump and system equilibrium analysis. Normally when the fluid is higher (wetwell level higher), the static head is lower, and the system head curve is lower. This would result in pump and system intersection, and operation far right on the curve where head and HP is lower on a pump of this type. But is not what happens. When starting, the loads are HIGHER when the water level is higher.

Please note the statement you made:
"If your pump fluid is accelerating, this implies you're trying to fill an empty pipe and hence in fact your pump is operating on the far right of the pump curve because the flow is actually very high."

This is exactly the opposite of what happens here. You state that "the flow is high". The key is...NOT YET. You have to accelerate to get to that point on the curve. With more fluid in the column, there is more mass to accelerate, and this creates a "transient shut off head" condition, which result in the pump effectively behaving like it is dead headed at lower speeds. The more rapidly you accelerate the pump, the worse this gets.
 
The formula would be some type of polynomial with several terms. There are statistical methods to fit a polynomial curve onto actual data points with a high R^2 value. However, the mathematical model would be very specific to the application.

On an hourly basis, the bypass loop is a much cheaper option than the time taken to generate an approximate curve. It would depend on your project budget.
 
Ok,

From what I understand you either have a situation where your pump has an empty pipe which is vertical of unknown height up to some sort of open end into a channel or this vertical pipe is full of water and hence has a static head which the pump is seeing as soon as it starts to move.

Neither of these situations is really "acceleration head", but more one of momemtum and where the pump is sitting on the curve as it tries to start.

This should have been allowed for in the design, so I'm not sure what the problem is you're trying to fix? Do you have issues in power supply that stop you applying full voltage?
Can you install a start up bypass valve which closes after say 10 seconds and allows the pump to start against a very low head on recycle?
Has it always operated this way or has something changed?

As is often the case, the pump is not the issue, it's the system design which is at fault.

I think there are too many variables and rapidly changing criteria to come up with any sort of speed torque curve.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.
 
Little Inch,

I think I have finally wrapped my head around it. It only took a week or so thinking about it on and off....

Basically you need to fit algebraic functions to your pump curves. You are describing a surface, since it is a function of two variables (speed and flow are the independent variables), but using the affinity laws, these are pretty simple surfaces to derive once you fit a function to the head capacity curve and hp capacity curves at full speed. So, once you have these surfaces fit, mathematically, you can then do a simple numerical time step analysis.

The initial approach it to assume a linear acceleration from 0 to full speed over a given period of time. The key is to understand that even after you get to full speed, the pump is going to be ahead of the system. At any discrete time step, you are going to have more head than the system draws. Flip the acceleration head concept around, and assume whatever "extra" head you have, will go towards accelerating the system. You have to re-calc the system at every time step, because everything is changing. For every acceleration time assumed, you will develop a unique speed torque curve.

This approach passes the smell test if you consider the following scenario. Imagine running a pump against a closed valve at full speed. Imagine you instantaneously open the valve. You now have an open system. Does the pump "know" at that instant that the valve is open? No...because the mass of water is sitting still. There is no friction head. There is no velocity head. If there is no static head, then ALL the head the pump develops will go towards acceleration.... So you calc the acceleration. Look at the system...see how much flow increases for a time step....repeat over and over. What will actually happen is that even after you get to full speed, the system will still not be stable. Flow will still be increasing till the "extra head" vanishes. This is just like you see in the real world.

So you were right on the money when you said "I think there are too many variables and rapidly changing criteria to come up with any sort of speed torque curve.", except for the part about it not being possible. I think it is if you do a time step, numerical analysis approach. Solving it analytically...I agree...impossible.

If I can solve this, I will post the approach and results.....it will likely be a long excel spreadsheet.
 
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