Friday, January 18, 2013

Turbine Speed, Torque, Flow, Pressure, and Efficiency Relationships

Here is some information you may find helpful in evaluating speed torque flow and power relationships in rotating machines. The graph showing these relationships works for most any rotating machine once you recognize that Volts, (the pressure pushing electrons) is analogous to water pressure, and current (Amps, the flow of electrons) is analogous to flow of water. And just like head Pressure x Flow= Watts so too Volts x Amps = Watts. Consistent units of measure have to be used to have this work out to the same numerical values.
In most well designed turbines, the runaway, or no load speed is ~1.8 to 2 x rated load speed. This means that under no load conditions the water slides by the impeller surface, without transferring any energy because they are moving at nearly the same speed. Another feature of the runaway speed is that the turbine output shaft torque is zero, (nothing loading it) no matter how much water flows through the machine.

The mechanical power is therefore null (about twice the rated speed multiplied by zero torque). The torque will rise by applying an external braking torque (the electric generator and its electrical load does that), while the speed will decrease, and that means you will start harvesting power (the water slips partially by the impeller, partially "pushing" it = energy transfer). You are moving (left on the speed axis) towards the best operating area where you will have rated torque, speed, and power.

Note that water consumption or flow also decreases so you are getting more power for less water and better efficiency. For simplicity the torque and flow plots are shown as straight lines whereas in most cases these curve, particularly near the ends.

Compared to this best operating point, if you apply even higher braking torque ( or electrical loading), the turbine speed will go down, while the torque will go up. You will ultimately reach the standstill point (turbine stalling), where the impeller is standing still, the water hits them with the greatest force (torque around 2 x T normal). Again, the power is null (zero speed multiplied by twice the rated torque). Basically, while you go from zero to runaway speed, the torque decreases with the speed, from 2x Tn at zero speed, to zero torque at 2 x rated speed. If you multiply this torque characteristics with the speed, you will have the power vs. speed curve, which is the yellow hill shaped graph, having it's maximum around midway between the speed extremes, 0 rpm and No Load rpm.

Note that for best efficiency, you will want to increase the turbine loading a bit, by reducing turbine speed (with a slightly larger pulley on the turbine, while maintaining synchronous speed on the generator). If you are just looking for maximum power (as when water pressure and volume are free and plentiful) run at a higher speed where the (yellow) power output peaks.

Here is a slightly different explanation (not mine) from the point of view of a pumping application:

Centrifugal pumps are bound by the Laws of Affinity. With respect to the speed of the pump, here are some facts. There is only one way to increase or decrease the head (pressure) that a centrifugal pump will produce. That is to vary the "tip speed" of the impeller. If, for instance you have an impeller with a 5" diameter, and it is spinning at 1750 RPM, the tip speed would be 20.825 fps. There are two ways to increase the tip speed you can 1) - Speed up the driver (say from 1750 RPM to 2000 RPM) 2) - increase the diameter of the impeller thus increasing the travel of the tip of the impeller in each revolution. Now the Laws of Affinity say that the Head changes in proportion to the square of the speed. That is how you can predict the head you can get from the impeller. These laws also say that the flow changes in direct proportion to the tip speed. As you can see, these predictions are based on the CHANGES in the tip speed. The flow, for instance, is relative to the height and type of the impeller. A wider, thicker if you will, impeller delivers more flow than a lower, more narrow impeller. So you see where i am going with this. The element that is missing is satisfied by - testing. You test the impeller and adjust as necessary with predictable calculations. 
"The Commoner"

Happy Hydro