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Fluid flow application for Pelton Turbine issue

Fluid flow application for Pelton Turbine issue

Fluid flow application for Pelton Turbine issue

(OP)
Hello,

I'm currently undergoing a MicroHydro project where I need to call on my learnings from fluid mechanics to optimise my system. I'm becoming very unsure of my working and so would like some feedback on my logic.

I need the minimum figures to produce 1kwh from a pelton wheel turbine - generator set up with the following parameters:

1. Open dam of water 7m above the turbine.
2. Water flowing through a 50mm inside diameter pipe
3. Pelton wheel has a pitch diameter of 500mm
4. Losses are negligible (until I'm confident with my initial workings)
5. The turbine runs at 80% efficiecny
6. The generator runs at 80% efficiency

The initial jet velocity, derived from Bernoullis principle:
Vi= √2gh= √(2*9.81*7) = 11.72 m/s

The optimal wheel speed:
u = Vi/2 = 11.72/2 = 5.86 m/s

The RPM of the wheel:
RPM=u/(π*Dpitch )*60= 5.86/(π*0.5)*60=223.82 RPM

Volumetric Flow Rate of the water:
Q=Anozzle*Vi=(〖0.025〗^2*π)*11.72= 0.023m^3/s or 23 l/s

Power from the turbine:
PTurbine=μ*p*g*h*Q=0.8*1*9.81*7*0.023=1263.53Watts

Power from the generator:
PGenerator=PTurbine*0.8=1263.52*0.8=1010.8224 Watts

∴ With a head of 7m,a pitch diameter of 500mm and a nozzle diameter of 50mm, the required output is satified.

NOTE: These workings are displayed in the attachments in an easier to understand form.


Now here are my questions:

1. In the derivation of bernoullis, the pressure/(density*gravity) is constant on both sides of the Steady Flow Energy Equation. This is because the dam at the top is open (so atmospheric pressure) and the water exiting the pipe at the bottom is exposed to the atmosphere (so atmospheric pressure). Therefore the two pressure constants can be removed from the SFEE? Is that correct?

2. The volumetric flow rate seems incredibly unrealistic to me, do you agree?

3. I feel there are errors in the logic somewhere but I'm unsure where, can you think of anything?

What I decided to do was create a spreadsheet based on my workings in the above example to show the differences of values with varying user input (shown in yellow).

http://i33.photobucket.com/albums/d52/Serene_being/peltontable.jpg


From the outlined information, can anyone see any obvious flaws in my logic. My knowledge of fluid dynamics is poor as it was not covered much in my degree.

Thanks for any info.

DFC101

 

RE: Fluid flow application for Pelton Turbine issue

My guess is that you've never been hit by a 7m wave.
The numbers appear correct, aside from a possible discharge coefficient loss at the dam to pipe entrance, and the 23 l/s is the theoretical maximum steady state velocity you could reach.  The other numbers appear reasonable, although I didn't check any of them.

BTW, we give extra points for posting the spreadsheet.  Saves us a lot of typing just to check someone else's numbers.



//virtualpipeline.spaces.live.com

RE: Fluid flow application for Pelton Turbine issue

(OP)
Thanks for the reply,

I understand what you mean, a 7m head of water is tremendous I guess when you look at it in the manner which you described.

I will being to incorporate losses into my system now that I feel more confident in my workings.

Attached here is the spreadhsheet I created

RE: Fluid flow application for Pelton Turbine issue

2 foot of head will push your car off the road.
I still very well remember a rogue wave that came over the top of the Galveston jetty that I was fishing off of and washed my A out into the channel.  That was only 3 m.

Thanks for the sheet.



//virtualpipeline.spaces.live.com

RE: Fluid flow application for Pelton Turbine issue

Think you should check the 23l/s thru 50mm ID pipe -  you haven't stipulated any length and I don't have my friction charts to hand.

RE: Fluid flow application for Pelton Turbine issue

Obviously you have neglected the friction in your pipe that brings the water to the Pelton turbine. This is important since you have relatively small diameter. Please take a look to this post and look for the examples that I've posted there.
http://www.eng-tips.com/viewthread.cfm?qid=283070

Please note that you are talking about a Pelton turbine. therefore the turbine is located in atmosphere and you have to calculated the turbine output based on the jet speed not the efficiency.RO.g.h.Q formula. Please take a look to some related academic books for turbine calculations.  

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