Pipeline Generators

https://www.sciencedirect.com/topics/engineering/francis-turbines#:~:text=Francis%20turbine%20is%20basically%20a,a%20mixed%2Dflow%20Francis%20machine.

Probably cheaper to just use one turbine....

..."In contrast to the Pelton turbine, the Francis turbine operates at its best completely filled with water at all times. The turbine and the outlet channel may be placed lower than the lake or sea level outside, reducing the tendency for cavitation.

In addition to electrical production, they may also be used for pumped storage, where a reservoir is filled by the turbine (acting as a pump) driven by the generator acting as a large electrical motor during periods of low power demand, and then reversed and used to generate power during peak demand. These pump storage reservoirs act as large energy storage sources to store "excess" electrical energy in the form of water in elevated reservoirs. This is one of a few methods that allow temporary excess electrical capacity to be stored for later utilization."...

https://en.wikipedia.org/wiki/Francis_turbine

..."A Francis turbine model efficiency hill chart can be used to show the characteristics of a Francis turbine, including the formation of hydraulic phenomena and the relationship between water head, power, and discharge. The chart can be plotted using n11 as the ordinate and Q11 as the abscissa. "...

https://www.researchgate.net/figure/Design-specification-of-the-100-MW-class-Francis-turbine_tbl1_345724151

What is the question here?

Has anyone used pipeline generators like this?

A water turbine at the bottom of a gravity powered water transfer pipe... turbine spins a generator...

I believe this scheme is in use at the Glen Canyon dam. May be some other examples elsewhere... OP mentions Hoover dam.

No, I haven't... But having multiple turbines is probably not a good idea. Each turbine will reduce the ∆P available to the others, thereby reducing the power generated. A single properly sized turbine at the bottom of the slope is the standard mode of operation, AFAIK.

There's one here, for example.

The biggest one on the planet is this one, though.

This is the way nearly all hydro-electric power stations work, by definition.

Pipe diameter is a function of flow, power generation is a function of pressure drop and flow. Someone is not going to be happy when you reduce their pressure.

...or their flow.

Multiple turbines in a single closed pipe is not a good idea. Flow through all must be equal (incompressible water) and unless exactly balanced at all flow, velocity and pipe string friction combinations would encounter cavitation on at least one unit, probably the first in the string.

We have investigated having cascade in-line generators to recover energy from high water level reservoirs into water treatment plants and even for a two-unit system, the flow/pressure curves only intersected at one hypothetical point and that was not an intended operating point for the treatment plant.

These were at kW scale.

Yes we've considered it. No we didn't do it.

Thank you for your response. Our pipeline design is a 150 mile pipeline with an elevation drop of 5000 feet with water flowing downhill in the pipeline. Installing one generator every 500 foot drop in elevation, dropping head pressure to zero at each water turbine, next generator at the next 500 foot drop will have the full head pressure from the next 500 foot drop in elevation. Final output will be controlled to keep pipeline 100% full of water.

I'm by no means an expert at this type of thing, but I suspect you will need some sort of throttling valve at each turbine or means of throttling the water by virtue of the load on the generator to match the flow from penstock to penstock otherwise you will starve the following stage or over-flow your vent pipe at the output of the turbine. Care will need to be taken with the control system to prevent oscillations in a cascaded system such as this.

At the end of the day: the design and build of one large generator will cost less than ten "off the shelf" generators.

Hello,

With this proposal, you have introduced another pair of concerns as follows.

The first is that your average pipe length will be 15 miles. You pipeline friction loss will be significant, or you will need larger diameter pipes at much greater cost.

The second is that with 15 mile long pipe strings, you have substantial water hammer challenges, with valve operation times in the tens of minutes, maybe even an hour.

You might be better set to have a 145 mile long pipeline to a header reservoir and then a 5 mile discharge to a single generator. One electrical installation for the whole project, one switchyard, one turbine hall, one maintenance site.

On the other hand, neglecting friction losses, 500 feet of ∆ elevation will produce a static pressure around 250 PSI, which is quite manageable. 4,500 feed of ∆ elevation would produce a static pressure of roughly 2,250 PSI. Obviously the dynamic pressures will be lower, but any required shutdown would have to be done at the top or at multiple valves, with means of allowing air entry to prevent vacuum collapse.

I've been led to believe that someone tried this in northern Chile around the middle of the last century, and the pressure blew the pipes apart. They did have around twice the ∆ elevation...

We prefer to allow water entry rather than air for pipeline shutdown. We have "balance tank" around 2ML (500,000Gal) for a 35km pipeline at 600mm diameter with slightly under 2m/sec flow. If use air, then still need to refill the pipeline.

Anyhow, I hope that the OP has gathered some insight for their project.