What is the role of blade velocity in Pelton wheel turbines?

[hanson]

Hi all!
I am learning things about turbomachinery, starting with the Pelton Wheel.
The analysis of seems to be straighforward, but I still have some questions.

I refer to this website:
http://www.du.edu/~jcalvert/tech/fluids/turbine.htm

There is a blade velocity u. I would like to know if this is the initial starting speed of the wheel? That means even if there is no jet on the wheel, the Pelton wheel is rotating by its own (either by motor etc), is this true?

I don't see why we need to do so...It's apparent from the efficiency relation that when u=0, efficiency=0 too. But, physically, it is hard for me to imagine what's happening. When the wheel is not rotating initally and when there is a jet of water impacting on the wheel, isn't there should also be an energy transfer from the jet to the wheel and the wheel will then rotate? How come the efficiency being zero?

Second, actually I don't really know the objective of having the Pelton wheel turbine. Do we want to accelerate rotation of the wheel? or we just want the wheel to rotate at certain constant speed?

If the latter is true, that means when there is jet impacting on the wheel, it will still be rotating at u? So the power output is just used to overcome the frictional things? It seems strange...

If the former is true, that means the wheel will keep on accelerating? But the maximum speed is restricted by the velocity of the jet, v? It seems strange also.

I am really stucked here.

Please kindly help.

 

[Astronuc]

There is a blade velocity u. I would like to know if this is the initial starting speed of the wheel? That means even if there is no jet on the wheel, the Pelton wheel is rotating by its own (either by motor etc), is this true?

The Pelton wheel does not rotate unless it has energy/momentum transferred to it by the water jet. The explanation is somewhat confusing and could be better worded.

u is the steady-velocity of the bucket which is struck by the water jet traveling at velocity V. So the effective velocity of the jet with respect to the bucket control volume surface is V-u. Note that as the speed u increases, the transfer of energy/momentum would be less effective, as V-u decreases. The maximum theoretical velocity of u would be V, but that would not happen because there would be no energy transfer from jet to wheel (V-u = if u=V). So u < V, unless something else is turning the Pelton wheel, which would not make sense.

In the bucket the water jet reverses direction. The velocity (mass flowrate) is determined from the continuity equation (assume no loss of water from evaporation or splashing).

The any turbine is design to transform the mechanical energy/force of the water to torque, and the turbine could run a mill or pump mechanically, or it could be connected to a generator to produce electricity. The work done by the mill or pump or the electrical load provides resistance through the shaft to the Pelton wheel. With some losses (we don't get 100% efficiency), the process is simply energy conversion - converting the pressure head into useful energy/work.

For AC electrical it is desirable to have 60 Hz, which means that the shaft should be a multiple of 60 Hz or likely 1800 rpm. Think of turbines in a hydroelectic plant. http://en.wikipedia.org/wiki/Hydroelectric

Turbines have governors or other control systems to control the flow of energy (steam, water, or combustion gas) and hence the speed. Even windmills can be controlled by changing the pitch of the blades.

See also - http://en.wikipedia.org/wiki/Pelton_wheel

 

[hanson]

The Pelton wheel does not rotate unless it has energy/momentum transferred to it by the water jet. The explanation is somewhat confusing and could be better worded.
u is the steady-velocity of the bucket which is struck by the water jet traveling at velocity V. So the effective velocity of the jet with respect to the bucket control volume surface is V-u. Note that as the speed u increases, the transfer of energy/momentum would be less effective, as V-u decreases. The maximum theoretical velocity of u would be V, but that would not happen because there would be no energy transfer from jet to wheel (V-u = if u=V). So u < V, unless something else is turning the Pelton wheel, which would not make sense.
In the bucket the water jet reverses direction. The velocity (mass flowrate) is determined from the continuity equation (assume no loss of water from evaporation or splashing).
The any turbine is design to transform the mechanical energy/force of the water to torque, and the turbine could run a mill or pump mechanically, or it could be connected to a generator to produce electricity. The work done by the mill or pump or the electrical load provides resistance through the shaft to the Pelton wheel. With some losses (we don't get 100% efficiency), the process is simply energy conversion - converting the pressure head into useful energy/work.
For AC electrical it is desirable to have 60 Hz, which means that the shaft should be a multiple of 60 Hz or likely 1800 rpm. Think of turbines in a hydroelectic plant. http://en.wikipedia.org/wiki/Hydroelectric
Turbines have governors or other control systems to control the flow of energy (steam, water, or combustion gas) and hence the speed. Even windmills can be controlled by changing the pitch of the blades.
See also - http://en.wikipedia.org/wiki/Pelton_wheel

Hello!
Do you mean that there is a control system that will monitor the blade velocity so that the maximum efficiency is achieved? (If the blade speed is too fst, then reduce the speed, and vice versa? so that the blade will rotate approximately at a constant velocity?)

Actually I have also asked my lecturer about this question, and he answered:"We do need to have the wheel rotating by its own first, so that a higher efficiency can be obtained. If not, the energy you get will be just the energy of the reservior" What does he mean?

Also from the analysis, the Euler's head = Vb(V1-Vb)(1-kcosX)/g, whit Vb being the blade velocity, V1 being the jet velocity etc.
How would you interpret this equation?

The blade velocity here is the initial blade velocity?

Also, the Euler's head is a change in enthalpy of the jet, right? But I don't see what things are changed in the jet. Enhalpy=u+pv. So, after being repelled from the wheel, what exactly is changed in the jet? u? p? v?
I just can see that the direction of the velocity/ momentum is changed...

Please help.

 

[Astronuc]

Do you mean that there is a control system that will monitor the blade velocity so that the maximum efficiency is achieved? (If the blade speed is too fst, then reduce the speed, and vice versa? so that the blade will rotate approximately at a constant velocity?)

Yes, I mean that there is a control system that monitors the rotational speed of the turbine and controls the flow to optimize the energy transfer. Basic feedback and control theory.

I'll catch the other stuff later.