Compressible fluid transfer line compression/pumping losses

[garycvv]

Hello everyone,
I've been asked to investigage a cryogenic transfer line that is carrying supercritical helium. This isn't my area of expertise and I'm struggling to find help, our previous Cryogenic engineer left in a hurry and I can't find anything in the literature although I'm probably looking in the wrong place.

My questions relate to compression/pumping losses. For hypothetical example we have a tranferline of 100m in length through which x g/s of helium flows, there is a uniform heat load of y W/m along the length. I've created a small routine that has split the transfer line into discrete sections and can use this to calculate the pressure drop etc. through the pipe taking into account the changing properties.
If I ignore the heating to begin with I've calculated the compression/pumping losses by calculating the fluid power at the inlet (volume flow x pressure) and subtracting fluid power at the outlet. Without the heating this gives reasonable believeable results.

When I start heating the fluid it changed. Initially I'd forgotten about the heat so when I subtracted the outlet power from the inlet I got a negative number which isn't physcially possible. It then got me to thinking I should calculate the power in the fluid at the inlet add on the heating power and then subtract the outlet power. Is this the correct approach? I get different numbers to those our Cryogenic engineer calculated but have found we've made a number of different assumptions.

 

[LittleInch]

So super critical is <2K and below 25 bar?

Why subtract the "power" at the outlet?

Head loss is just that - If your density is changing a lot then you need to consider pressure as well, but head is a much better thing to look at surely?

I'm not really following your thoughts here so perhaps some numbers might help to see what it is you're doing.

Also what exactly are you trying to find / calculate. "Power" is a bit odd, but fluids will only flow from an area of higher pressure to l=one of lower pressure, but "power" can increase, e.g. a cold water line heated to steam has more "power", but must flow from high pressure to low pressure.

what sort of temperature and density range are you working with here?

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

 

[Snickster]

I am not familiar with supercritical flow. Is it like a compressible gas or more like a imcompressible fluid? However, I am a little confused about your explanation. You speak about inlet and outlet. It appears the inlet is the inlet to the discharge pipe and the outlet is the outlet of the discharge piping downstream, and you are adding heat along the discharge piping.

If you are doing a calculation on sizing a pump or compressor you would do a pressure drop calculation at flow to determine the discharge conditions and subtract from the suction conditions to get the energy/power required. Any energy due to heat you add downstream does not contribute or deduct from the power required of the pump/compressor. If you are just adding heat downstream then you are just increasing the enthalpy and possibly the specific volume of the fluid but still it is developing more pressure drop as it travels down the pipe and building up more pressure at the pump/compressor discharge which has to be provided by a pump/compressor. There are equations for flow that consider heat input to piping with friction I think its called the Rayleigh equations.

 

[garycvv]

Hello, thank you for the comments received and I apologise for the delay in responding. Supercritical helium is a compressible fluid.


To give an example I've chosen some arbritrary values. I've selected a 10mm diameter transfer line that is 50m long. Through this flows 10g/s of helium with an inlet temperture of 8K and an inlet pressure of 5 bar absolute.
For the first case I've not applied any additional heating. For this case I calculate a pressure drop of .3bar and an outlet temperature of 7.9K. I've calculated the compression/pumping losses by calculating the fluid power at the inlet (volume flow x pressure) and subtracting fluid power at the outlet. This gives:

Inlet pressure = 500000 (Pa), Outlet pressure = 470060 Pa => delta P = -29940 Pa
Inlet temperature = 8K, Outlet temperature out 7.9 K =>delta T = -0.1K
Inlet Density = 41.47768409 kg/m3, Outlet Density = 39.27469663 kg/m3 => delta D = 2.20298746 kg/m3
Inlet volume flow = 0.00024109 m3/s, Outlet volume flow = 0.00025462 m3/s

Although there is a change in density for the unheated example this is small so can be ignored and the pumping power can be calculated by pressure drop x volume flow. This gives 7.2W to 7.6W.


So if I add 2W/m which is fairly bad for a cryogenic transfer line but is plausible. This would give a total of 100W.
Inlet pressure = 500000 (Pa), Outlet pressure = 464783 Pa => delta P = -35217 Pa
Inlet temperature = 8K, Outlet temperature out 9.23 K =>delta T = 1.23K
Inlet Density = 41.47768409 kg/m3, Outlet Density = 29.12010523 kg/m3 => delta D = 12.35757886 kg/m3
Inlet volume flow = 0.00024109 m3/s, Outlet volume flow = 0.00034341 m3/s

Now to calculate the pumping power, if I take pressure drop x outlet volume flow it gives 12W. But as I said before I the power in the fluid is pressure x volume flow, so for a compressible fluid if I take the inlet power (inlet volume flow x inlet pressure) and subtract the outlet power (outlet volume flow x outlet pressure). I get a figure of -39W pumping power which isn't possible, but I had forgotten about the power I've added to the system by way of heat which was 100W. So adding this back in I calculate the pumping power as 61W.

 

[Jacc]

This sub forum is for fluid power as in Hydraulics and Pneumatics.



I think you will have better luck in any of these sub forums:

Pipelines, Piping and Fluid Mechanics engineering

https://www.eng-tips.com/threadminder.cfm?pid=378

Gas compression engineering

https://www.eng-tips.com/threadminder.cfm?pid=1036

Pump engineering

https://www.eng-tips.com/threadminder.cfm?pid=407

 

[PNachtwey]

way back I did a simulation for the department of energy. It was about fuel injection for a diesel. Some of the fuels they were experimenting with would compress a lot. These light fuels would enter a diaphragm pump at 150 PSI and be injected at 40,000+ psi into the fuel header for the diesel. While increasing the pressure from 150 ps to 40K+ PSI the fuel volume compressed about 30%. That was a lot. The original designers of this fuel injection system didn't account for any of that. The designer was strictly a flow makes it go designer that had little true knowledge of the physics of fluids.

So yes, fluids will compress in long pipes. One needs to know the bulk modulus of the fluid being compressed. Normally, in my hydraulic simulations I assume the bulk modulus is constant but in the fuel injection simulation I had to change the bulk modulus from a constant to a function of pressure.


Peter Nachtwey
Delta Computer Systems

http://www.deltamotion.com

http://forum.deltamotion.com/

IFPS Hall of Fame Member