constant flow variable speed pump for heat exchanger 1

[gaalfred]

Hello guys, I have searched high and low for clues to my problem and can't seem to get help. I have a centrifugal pump controlled by a VFD. The pump transfers milk from one tank to another through a milk-to-water and milk-to-glycol heat exchanger. The liquid levels in the two tanks are constantly changing. The source tank fills and empties and the destination tank fills, then is changed to an empty tank. I can monitor the levels of both tanks and use them in my PLC networks. I would like to arrive at an equation for my PID loop that varies the speed of the pump to keep the flow rate constant while the head pressure is changing. The number I want to arrive at is, how much do I need to change the speed of the pump for each change in total head to keep the flow constant. I have tried substituting the affinity equations in each other but I find myself running in circles. If anyone has done anything like this or knows how to approach it, I would appreciate hearing from you.

 

[georgeverghese]

It will be impossible to enable a constant flow in this system without an automatically set control valve some where in this line that will absorb the variable pressure drop in this system, which is the sum of the static head differential plus the friction pressure drop at the required flow. An inline FE and flow transmitter will be also most likely be required.

 

[LittleInch]

Shouldn't be that hard, but you will need the pump curves at different speeds from the vendor.

An approximate guess though is this.

Total head loss across the pump = Hp + Hd -Hs
where Hp is head loss in the piping (static for the same flowrate), Hd is height of delivery tank, Hs is height of source tank

Now depending on the ratio of Hp to (Hd-Hs) the system will work or not. If Hp is quite big compared to the max head difference ( i.e. >70%) the you should be ok.

I would just start with pump speed is proportional to head^2. It won't get you the same flow but then you can add a bit.

SO using some basic numbers, if your head loss is 100 and you're at 100% speed

then at head loss of 70, you're at about 83% speed, but you're not at the same flow, so add a bit to say 86%. A bit of trial and error as nothing is exact and you won't be more than 10% out once you establish a set of points or a simplified line. As said much easier with a set of pump curves for different speeds.

Of course it would be a lot easier to just add a flow meter (mag flow or UT) and control on that using your PLC??

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[Artisi]

An indication of flow rates and heads involved wouldn't hurt, people could then see if they are wasting time on answers completely unsuited for the application.

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.)

 

[SandCounter]

Not sure if it is an option, but a positive displacement pump is better suited for constant flow, no programming required.

I used to count sand. Now I don't count at all.

 

[davefitz]

as per the pump laws ( or fan laws) the volumetric flow varies with the rpm while the develop head varies with the RPM^2. If the required head varies then it would be necessary to run thepump at the RPM needed for the max developed head and then throttle the discharge pressure as the need for a lower flow is met.

"...when logic, and proportion, have fallen, sloppy dead..." Grace Slick

 

[LittleInch]

I disagree. what happens is that you will move further along the curve for the same flow but lower head. You need to remember here that the OPs system curve keeps changing as the tanks fill and empty.

Hence the speed reduction is proportional to SQR of flow, but a bit more speed is need to match up the flow.

Speed variation on a VFD is similar to changing impellor size.

Hence in the picture below, which is a little extreme, if you want to maintain say 200 GPM, then you can do that if your system curve changes ( which it does for the OP) so that at say 200 GPM his head across the pump could be 18 ft to 90 ft corresponding to 900rpm to 1800 rpm.

I think that range is a bit large myself so I would be more inclined to go for 300 gpm at min diff head of 40ft vs max diff head of 90 ft

VFDs run on flow control all the time to maintain a set flow.

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

 

[SandCounter]

There are also purely mechanical flow control fittings you could use on the discharge of the pump. Have a Tee after the discharge, one side with the flow control, the other as a re-circ line.

I used to count sand. Now I don't count at all.

 

[gaalfred]

Thanks to everyone, especially LittleInch, for answering. I think I see what to do, but want to post a response to you all to see if I understand what you have been saying. First, a little more clarification as to my installation. I left out some details earlier because I did not think they would be relevant to your answers, but I see that they may be interesting nonetheless. We are controlling the speed of the pump via a VFD where the process variable is the temperature of the milk leaving the heat exchanger. The PID loop response needs to be fairly sluggish to compensate for the reaction time of the temperature sensor and the 6 compressors that are chilling the glycol. If we respond too quickly, we speed up our pump and flowrate long before the chillers can start and take a couple degrees out of the glycol. Because of that, the perturbations from the rapid head changes make the system inherently unstable. For instance, the dairy will run 40 cows into the parlor, connect the milking units to them in about a minute, and they will start producing an average flow of about 16 lbs/min of milk. That flow, along with the residual flow from the other side of the parlor where the cows are finishing up, hits our tank at instantaneous rates reaching 80 gpm. Our supply tank is a circular, 275 gallon tank that stands about 7 feet tall with its bottom 1.5 feet off the floor. The 2 hp milk pump is connected right to the bottom of the tank, pumps the milk through about 20 feet of 2" pipe and a heat exchanger, then into a 7000 gallon truck whose bottom is about 4 feet high and whose top is about 10 feet high. You can see that our suction head (Hs) v aries between 0 and 5.5 feet and our discharge head (Hd) varies between 4 and 10 feet. Chiller capacity limits our flow rate to about 18 gpm, which can vary as they lose charge, blow fuses, overheat, etc. We want to correct our PID output to include the information about the changing static head to enable the PID loop to respond more rapidly and yet remain stable.

What I take from your answers is that I need to use the Affinity Law regarding the relationship between head and pump speed to arrive at my answer. This law states: dp1 / dp2 = (n1 / n2)2 where dp = head and n = rpm. Manipulating this equation, I get that n2 = n1 / sqrt(dp1/dp2). For example, if my head increases by 10% during my 'scan time' of 10 seconds since I last checked, then dp2 = 1.1 * dp1, so dp1/dp2 = 0.91 and sqrt(dp1/dp2)=0.95 and n2 = n1/0.95. Following this, I should expect that if my temperature sensor has not changed its reading, I should expect my new speed for my pump should be 105% of what it was before the head changed. If my head increases by 20%, I expect my speed should increase to 109.5% of what it was. If 100%, 141% and so on.

After talking about it with my boss, because our Hp changes very slowly, due to a filter plugging and a large tank filling, we may need to monitor only the head changes in the supply tank for the above formula. The supply head changes at least 5 times faster than our system's ability to respond, but the discharge head changes 50 times slower and is not an issue in our installations.

Thanks again. If your head is spinning, don't feel bad, so is mine.

 

[BigInch]

You could run the discharge to the top of the last tank, pump at constant speed & constant flow against constant elevation head and throw the VFD away.

Technology is stealing American jobs. Stop H1-Bs for robots.

 

[LittleInch]

The factor that is missing from your equations is that as the speed decreases so does the flow when following the same system curve.

Therefore to increase head, but not increase flow you need an increase in speed, but maybe not quite as much as you calculate above as flow ratio = speed ratio.

BI - his issue as described is that it is his inlet static head which changes a lot, not his discharge head.

however if you really want to do it (strict flow control) this way as another poster said, swap out your centrifugal pump for some sort of PD pump ( screw maybe) and then speed of motor = flow virtually regardless of inlet and outlet head. Or fit a flow meter and control on that and not level.

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

 

[Artisi]

Seems all too complicated and expensive for a 2 hp pump, think BigInch had given you the solution to your problem.


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.)

 

[BigInch]

I think so. He's trying to fix something that isn't broke.

Kind of rediculous to run a pump at constant flow (basically constant speed) using a VFD. You might get really fine flow control, but I seriously doubt you need it that fine and you're having a hard time working out how you're going to control it. I also refuse to believe it won't work with a slightly variable inlet head. NPSH is critical with milk?

Technology is stealing American jobs. Stop H1-Bs for robots.

 

[LittleInch]

I had a look at a 2hp (1.5kW pump) and at 18 gpm you could have a huge differential head ( 75m+) There must be some large pressure drop in the HX or the pump is operating so slowly it's struggling to work properly and maybe that's more of the problem here.

Gaalfred - can you please give us some real number to work with here for head or discharge pressure of the pump please and also confirm your steady flow is 18 GPM / 4100 litres/hour.

what frequency / percent of speed is it operating at?

At 18 GPM it's going to take you 6 1/2 hours to fill your 7000 gallon truck. That sounds like an awfully long tome to me...

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

 

[gaalfred]

I need to respond to a couple of your comments, guys:

So...Artisi, would you say that accurate control of a morphine pump in a hospital is "too complicated and expensive" because it is a 1/400th horsepower pump? What does the size of the pump have to do with the accuracy or value of the process?

BigInch...How far are you from Pipestone, MN? You could come out and see it for yourself. You could visit the National Monument while you are at it. I need accurate control of the milk exiting the heat exchanger, not accurate control of the flow. The milk needs to be 38 degrees, not 35, not 42, and not wildly varying between 38 and 42. When the suction head goes up by 4 feet, the temperature of the milk goes up by 4 degrees until the VFD can reduce the speed of the pump to get the temperature back down. The response time needs to be slow because the system response time is slow. Like I said in my long post yesterday, the suction head changes at least 5 times faster than the system can respond and causes a properly quick response time to overshoot and the milk temperature to oscillate. Believe me, I am not trying to fix something that is not broken. I asked for help with the formula, not criticism of my project. Using a VFD to run this pump is not ridiculous. The pump needs to run at full speed or greater for the wash process, and it needs to run at just the right speed for cooling and transferring the milk. If a chiller compressor stops for some reason, I can't be standing there to slow down the pump, it needs to do that itself based on the milk temperature. No one wants to dump $10,000 worth of milk down the drain one morning because a compressor failed and someone thought a VFD was ridiculous.

LittleInch...You are exactly right, I could do better with a PD pump or a meter. A 3A sanitary pump costs about $5000, 5x a centrigugal one and a 3A meter costs about $5000. I don't know if you are at all familiar with daires, but they are extremely price-conscious and operate on the brink of bankruptcy most of the time. Just when they think they are getting ahead, some government decision screws them, like Canada's recent decision not to import milk from a certain supplier in WI. Now all the farmers that sell to that supplier suddenly have NO MARKET for their product since all the other creameries are running at capacity. I either provide them with an affordable solution or they don't do the project. Efficiently cooling milk to the optimum temperature saves them a LOT of money and is well worth the effort we put into these designs.
Also, why is it that you think my equations will not be accurate using flow ratio = speed ratio? Do those affinity laws not apply to all centrifugal pumps within their operating range? Or are they rules of thumb and not laws? Or can I not combine two of them like I did? It seems like I should be able to combine them since n1/n2 occurs in both. Thanks so much for your careful analysis and understanding of what I am trying to do.

 

[gaalfred]

Also...to LittleInch, you are correct that it takes 6 1/2 hours to fill the truck. The large dairies have dispensed with the bulk milk tank with cooling capability and have gone to direct-load into trucks. The trucking company backs the tanker up to a hole with a foam seal around it in the milk room. The pipe is connected to the tanker and the valves are opened and the milk begins to flow. The tractor part of the truck unhooks from the tanker, moves over to the next bay, connects to the full tanker that is waiting there, and heads down the road with it. There are usually at least 3 bays, one for an empty tanker, one for a full tanker, and one for the tanker that is connected to the pipe and being filled. The tankers are insulated so the milk stays cold. This is why we need to get the milk accurately to its desired temperature as it is going into the tanker. There is no provision for cooling it later.

 

[BigInch]

The milk needs to be 38 degrees, not 35, not 42,
Fine. Now we're getting somewhere. Then you need temperature control, NOT flow control. Let the output temperature control pump speed. Too cold, slow the flow down. Too hot, speed the flow up.

Technology is stealing American jobs. Stop H1-Bs for robots.

 

[btrueblood]

What Big said, but also - you should control the pump speed based on delta-T (diff. between entering warm milk and chilled milk temperatures) also, as flow rate and delta-T are directly proportional. Presumably, the milk tank temperature varies as the milking process runs, from whatever temp. the cows are at to some lower temperature as it sits and cools.

 

[LittleInch]

Gaalfred,
Understand your issues but if you can provide the information that would be good. I think one cheap way out of your problem may be to increase the fixed head loss so that the inlet head becomes less important. I think your pump is running very low speed and maybe something like 20m of 1" pipe after the pump but before the cooler might work. Or you might need 40m of pipe. I can't judge unless I can see what your pump discharge pressure range is.

It's difficult to get the same flow but different head by varying speed when also having a different system curve so an exact ratio doesn't work.


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

 

[georgeverghese]

A large source of dead time error ( which cause these dreaded oscillations in the final controlled temp) in your current process control loop setup would be in the final discharge milk temperature sensor. An RTD sitting in a thick thermowell is the root cause of this dead time. Solutions to reducing dead time errors are (a) use specially engineered thin wall thermowell to reduce the thermal inertia in the thermowell (b) use fins on the thermowell if the fluid is nonfouling to enable faster heat conduction into / out of the thermowell. A thermocouple also gives faster response in comparison to an RTD.

Your later posts give a more complete picture, and agree with others that in principal, a VFD may be part of the solution here. So your new proposal is to (a) monitor fast moving suction tank level and directly vary pump speed to get you constant flow (b) slower moving transients such as discharge tank head and suction tank temp can be handled by final milk temp TIC modulating coolant glycol flow into the milk to glycol HX.

A better estimate of the Q vs speed mathematical relationship is to draw a constant flow line on the flow map for the actual pump, derive the required polynomial expression for this and substract the constant friction drop on this at the desired flow ( friction piping press drop from suction tank exit to discharge tank inlet ) to get to the required differential level. Generalised affinity laws only work for small changes in flow / head / power / speed around any reference point, and are no use for larger deviations.