1

Is there a formula, which would allow to estimate water turbine rotor mass based on head and water flow, or based on the final energy output provided by the turbine? I am interested in rough estimate, not a precise formula.

The range of parameters I am interested in is head from 0 m to 500 m, and flow from $0\;\mathrm{m}^3/\mathrm{s}$ to $1000\;\mathrm{m}^3/\mathrm{s}$. I do not know if there is very significant difference in rotor mass between the Kaplan and the Francis turbine, but ideally I am interested in rotor mass of both.

Edit: I am interested in scaling of the turbine size in general. (How big would be the turbine of 10 kW power planet? And how big for 100 MW power plant?) Turbine mass is as good parameter to get idea about the scaling as rotor diameter or other turbine size-related parameter that is used in praxis.

Irigi
  • 119
  • 4
  • Thank you for the answer and for the comment. I am interested in connection between the power output and turbine mass to get an idea how does the size and mass of a turbine scale with the required head and flow. I would like to get a rough estimate how big and heavy would turbine for a small 10 kW power plant would be, or how heavy it would be for a 100 MW power plant. I am not an engineer and I am not building power plant for any specific purpose. What I would like is to get an rough estimate of how does the size and mass of the turbine scale with power plant size. – Irigi Nov 29 '15 at 21:38
  • My motivation comes from worldbuilding. I am trying to make very rough technical specification of space colony on different planet for a science-fiction novel. The question is: given fixed payload, how much power could I expect to get from a turbine of given mass and compare it with other available energy sources. (And do rough optimization between mass and power.) For this purpose, I do not need very precise answer, but I need to know the mass and power scaling over quite large parameter space to get an idea what is plausible and what is not. – Irigi Nov 29 '15 at 22:25
  • This (original) motivation aside, I am also asking just to know more about typical size of water power plants of different power inputs. From the engineering perspective, my interest is quite theoretical. (I hope this explanation helps, sorry if my motivation seems a little strange. :-) ) – Irigi Nov 29 '15 at 22:25
  • Ah, I see, so this isn't an actual engineering problem that you face, and that's why you can't clarify any further. – 410 gone Nov 29 '15 at 22:31
  • @Irigi look at descriptions of existing hydroplants, look at catalogues for small scale hydro to get an idea and visit a plant. – mart Nov 30 '15 at 07:13
  • I'm voting to close this question as off-topic because it is a Worldbuilding exercise and not an actual question about engineering. –  Nov 30 '15 at 18:55
  • @GlenH7 I do not understand why the motivation why I am asking the question is relevant for whether the question is off-topic, or not. I am asking here and not on worldbuilding or physics because I figured that engineers are the best people to ask when it comes to water power plants. I tried to get the information from power plant information centers, but it is quite difficult to get. Is there a way how the question should be reformulated to become on-topic? Thanks. – Irigi Nov 30 '15 at 19:54
  • Irigi - re-read EnergyNumbers' comment: "Ah, I see, so this isn't an actual engineering problem that you face, and that's why you can't clarify any further." And also look at the openings of the answers: "For world building purposes, quick interpolation would be sufficient." and "I am not sure why you would want rotor mass as it much more material dependent than design or power dependent." Your question is attempting to create a correlation that may be nice for building a story but has little to no meaning from an engineering perspective. –  Nov 30 '15 at 22:22
  • @Irigi, In the comment on my post you mentioned "...I can deduce its approximate size from it.". This is what you are actually after, not the mass. Please rephrase your question to be something like "Approximate hydro turbine diameter vs rated power?" or "What is the rotor diameter of a 10kw kaplan hydro turbine?" – ericnutsch Dec 01 '15 at 00:04

2 Answers2

2

I am not sure why you would want rotor mass as it much more material dependent than design or power dependent. I have seen kaplan turbines built from both plastic, brass, and steel. Obviously the mass would differ greatly.

Unless you are making one out of gold, I imagine that the mass is not end goal. What are you trying to do with this mass value? It is likely going to differ turbine for turbine because mass is something that does not need optimized in this design process. If you do indeed need the mass, the best approach would be to contact manufactures of turbines for the flow range your are interested in and ask for the shipping weight of a replacement rotor.

ericnutsch
  • 8,146
  • 1
  • 11
  • 29
  • Thank you for your answer and I apologize for replying late. I would like to get a rough estimate of how big and heavy would a turbine of 10 kW, or 100 MW power plant would look like. I understand that the turbine mass is heavily dependent on the material used, and I can account for it simply by knowing the material density. However, what I do not know is, how big the turbine needs to be to generate required power. Perhaps my question is confusing, because I am asking about mass, while I should be asking about typical size or some other size-related parameter. – Irigi Nov 29 '15 at 21:54
  • I was asking about mass, because (provided the turbine is from steel), I can deduce its approximate size from it. If there is a formula relating some key turbine size parameter to power plant output or flow through the turbine, it would basically answer my question as well. I am interested in scaling of turbine sizes from small power plants to big ones. – Irigi Nov 29 '15 at 21:54
2

For world building purposes, quick interpolation would be sufficient. Fortunately, I have a textbook with some data points.

A 125 MW (HP/LP) two stage turbine has 26" long blades, with a 14' x 14' exhaust piping while it's 400 MW cousin has 33.5" long blades, with an 18' x 20' exhaust piping. A 1000 MW (HP/LP/LP) three stage turbine has 43" long blades - exhaust piping is not given.

All of these are sub-critical (not super-critical), so the head can be expected to be well under the 3,200 psi range - 2,400 psi is a typical value for most sub-critical systems.

Of course, without a condenser, a turbine is useless - unless you are talking gas turbines. For the 125MW, expect a 36'-6" x 24'-4" x 23'-7" condenser with 48" water inlet piping. 400MW is 43'-6" x 38'-0" x 34'-3", with 78" inlet water piping. I'd imagine 2 - 500 MW condensers would be used on a 1000 MW turbine, which are 44'-6", x 41'-0" x 36'-1" each and have 84" piping, with 18'-0" x 20'-0" exhaust openings.

While these don't give you mass, these do give you dimensions as you were looking for. Hopefully this helps.

Mark
  • 5,343
  • 14
  • 47