Steam turbines, spreadsheets, and a few observations.

[Nerd1000]

As a result of ongoing discussions, I've been working on a steam turbine design spreadsheet. This is the latest (probably final, for now) model.

New features compared to the Mk II version posted on the tesla turbine thread:
Condensation within the turbine is now considered, and a target exit steam quality can be set. Generally this would be in the range 0.9 to 1.
Calculation of convergent-divergent nozzle throat sizes.
A method for estimating the partial admission losses on the first stage, this can be used to set the losses parameter to an appropriate value.

Funky issues:
The convergent-divergent nozzle throat calculations can't handle partially condensed steam, and will sometimes specify a throat larger than the outlet if there is condensation in the nozzle. I don't even know what should actually happen when steam is condensing in the gas stream as it exits a supersonic nozzle. Perhaps it would be best to only use subsonic nozzles in condensing stages.

So, some general observations.
Model sized turbines have a big problem: If you want a practical size of turbine, you must use partial admission (not all of the turbine rotor is in front of nozzles). This rules out using reaction turbines, and causes big problems for impulse turbines too because partial admission can dramatically reduce the turbine efficiency. In fact in small turbines it tends to be by far the largest source of losses. The issue is generally worse when the system is operating at higher pressure because the steam is denser. Multiple pressure stages tend to amplify the issue because the losses apply for every stage! Velocity staging can be a bit of a workaround if only because using it tends to result in larger nozzle areas per pressure stage, but generally the efficiency is poor. This issue starts getting much more manageable above a few kW rated output... but that's a lot for a model!

So for anyone hypothetically wanting to power their house with a little steam turbine, not good news. I think the best operating condition for a small scale steam turbine would be as the second stage after a reciprocating expander. Then it can work in low density pre-expanded steam and have a much higher degree of admission- still not full admission, but enough that the efficiency isn't reduced too much. The other thing that helps a lot is strong condenser vacuum, as it allows everything to work at lower pressure and density.

 

[Toymaker]

As a result of ongoing discussions, I've been working on a steam turbine design spreadsheet. This is the latest (probably final, for now) model.

New features compared to the Mk II version posted on the tesla turbine thread:
Condensation within the turbine is now considered, and a target exit steam quality can be set. Generally this would be in the range 0.9 to 1.
Calculation of convergent-divergent nozzle throat sizes.
A method for estimating the partial admission losses on the first stage, this can be used to set the losses parameter to an appropriate value.

Funky issues:
The convergent-divergent nozzle throat calculations can't handle partially condensed steam, and will sometimes specify a throat larger than the outlet if there is condensation in the nozzle. I don't even know what should actually happen when steam is condensing in the gas stream as it exits a supersonic nozzle. Perhaps it would be best to only use subsonic nozzles in condensing stages.

So, some general observations.
Model sized turbines have a big problem: If you want a practical size of turbine, you must use partial admission (not all of the turbine rotor is in front of nozzles). This rules out using reaction turbines, and causes big problems for impulse turbines too because partial admission can dramatically reduce the turbine efficiency. In fact in small turbines it tends to be by far the largest source of losses. The issue is generally worse when the system is operating at higher pressure because the steam is denser. Multiple pressure stages tend to amplify the issue because the losses apply for every stage! Velocity staging can be a bit of a workaround if only because using it tends to result in larger nozzle areas per pressure stage, but generally the efficiency is poor. This issue starts getting much more manageable above a few kW rated output... but that's a lot for a model!

So for anyone hypothetically wanting to power their house with a little steam turbine, not good news. I think the best operating condition for a small scale steam turbine would be as the second stage after a reciprocating expander. Then it can work in low density pre-expanded steam and have a much higher degree of admission- still not full admission, but enough that the efficiency isn't reduced too much. The other thing that helps a lot is strong condenser vacuum, as it allows everything to work at lower pressure and density.

You've clearly put in a great deal of work into your spreadsheet,...are you planning to build a 4 stage axial flow turbine ?

 

[Nerd1000]

You've clearly put in a great deal of work into your spreadsheet,...are you planning to build a 4 stage axial flow turbine ?

Heh no. I just get obsessed with something technical and have to understand it sometimes.

 

[Toymaker]

Model sized turbines have a big problem: If you want a practical size of turbine, you must use partial admission (not all of the turbine rotor is in front of nozzles).

Why must partial admission be used?? The tiny gas turbines made for model airplanes , the few that use axial flow blades in the hot section, use full admission. Why is steam flow different ?

 

[Jasonb]

Long thread on ME about model turbines with plenty of practical examples.

https://www.model-engineer.co.uk/forums/topic/model-turbines/

 

[Nerd1000]

Why must partial admission be used?? The tiny gas turbines made for model airplanes , the few that use axial flow blades in the hot section, use full admission. Why is steam flow different ?

gas turbines develop far more shaft power than steam turbines for a given net output, it would not be unusual for 60% of the power developed by the turbine stages to be used driving the compressor. Also the working fluid is less dense, in large part due to lower pressure ratios. So the volume flow through the turbine is much greater. This is further increased by the fact that they pump lots of extra air just to limit the turbine inlet temperature to something the turbine can withstand. Finally they actually develop quite a bit of power! This 64mm unit develops 2.5 kW at the output: https://www.kingtechturbinesaustralia.com.au/product-page/k30tpg4

I'd guess it's developing at least 3 kW on the gas generator turbine.

A steam engine avoids the large compressor power demand by condensing the steam into water, because this reduces its volume by a huge amount the pump work is greatly reduced and almost all of the power from the engine drives the load. Unfortunately there are no free lunches, so the tradeoff is that all the latent heat used turning water into steam is for the most part unable to be used by the expander. This is why superheating is so great, you basically get to use all of the heat added in the superheater to do work, vs only a fraction of the heat added in the boiler itself.

 

[Toymaker]

it would not be unusual for 60% of the power developed by the turbine stages to be used driving the compressor.

Agreed. In fact, most modern aviation turbines today are twin-spool designs, with a few 3-spool designs. The primary tasks of the core turbine, (often referred to as the gas generator) in a twin-spool engine, is to turn the compressor for the core section and supply enough exhaust gasses to turn the outer spool, which turns the fan and provides most of the thrust.

Also the working fluid is less dense, in large part due to lower pressure ratios. So the volume flow through the turbine is much greater. This is further increased by the fact that they pump lots of extra air just to limit the turbine inlet temperature to something the turbine can withstand. Finally they actually develop quite a bit of power! This 64mm unit develops 2.5 kW at the output: https://www.kingtechturbinesaustralia.com.au/product-page/k30tpg4

I'd guess it's developing at least 3 kW on the gas generator turbine.

A steam engine avoids the large compressor power demand by condensing the steam into water, because this reduces its volume by a huge amount the pump work is greatly reduced and almost all of the power from the engine drives the load. Unfortunately there are no free lunches, so the tradeoff is that all the latent heat used turning water into steam is for the most part unable to be used by the expander. This is why superheating is so great, you basically get to use all of the heat added in the superheater to do work, vs only a fraction of the heat added in the boiler itself.

So, can you link any of your statements above to explain why partial admission must be used?

I ask because the only reason I can think of to use partial admission in small steam turbines is, "to be able to actually machine an ideal CD nozzle configuration"; all full admission nozzles are a compromise between what can be machined in an annular configuration and the ideal CD shape.

 

[Toymaker]

I'll try to better explain my previous post using several pictures.

The drawing below shows a typical De Laval turbine with 4 perfectly shaped CD (Convergent-Divergent) nozzles, which taken together, direct steam flow through only part of the turbine wheel.

The below pic shows parts of a full admission CD nozzle and turbine blades of a radial inflow turbine. It appears that not all of the nozzle parts are in place in the photo.

The below pic shows a computer generated representation of steam flow through the CD nozzles. Although the opening produced by the flat metal parts create a Convergent-Divergent shape, it's only in two dimensions; it's not the perfectly shaped conical nozzle in the first drawing.

This final drawing shows the high pressure section of a typical axial flow steam turbine, notice the CD nozzles on the far left side allow for full admission. No matter how small this design is scaled down, full admission from the nozzles is maintained. However,.... at some point of shrinking the model to ever smaller dimensions, the size of the opening at the nozzle's narrowest point will become impossible for a hobbyist to machine.

 

[HMEL]

As a result of ongoing discussions, I've been working on a steam turbine design spreadsheet. This is the latest (probably final, for now) model.

New features compared to the Mk II version posted on the tesla turbine thread:
Condensation within the turbine is now considered, and a target exit steam quality can be set. Generally this would be in the range 0.9 to 1.
Calculation of convergent-divergent nozzle throat sizes.
A method for estimating the partial admission losses on the first stage, this can be used to set the losses parameter to an appropriate value.

Funky issues:
The convergent-divergent nozzle throat calculations can't handle partially condensed steam, and will sometimes specify a throat larger than the outlet if there is condensation in the nozzle. I don't even know what should actually happen when steam is condensing in the gas stream as it exits a supersonic nozzle. Perhaps it would be best to only use subsonic nozzles in condensing stages.

So, some general observations.
Model sized turbines have a big problem: If you want a practical size of turbine, you must use partial admission (not all of the turbine rotor is in front of nozzles). This rules out using reaction turbines, and causes big problems for impulse turbines too because partial admission can dramatically reduce the turbine efficiency. In fact in small turbines it tends to be by far the largest source of losses. The issue is generally worse when the system is operating at higher pressure because the steam is denser. Multiple pressure stages tend to amplify the issue because the losses apply for every stage! Velocity staging can be a bit of a workaround if only because using it tends to result in larger nozzle areas per pressure stage, but generally the efficiency is poor. This issue starts getting much more manageable above a few kW rated output... but that's a lot for a model!

So for anyone hypothetically wanting to power their house with a little steam turbine, not good news. I think the best operating condition for a small scale steam turbine would be as the second stage after a reciprocating expander. Then it can work in low density pre-expanded steam and have a much higher degree of admission- still not full admission, but enough that the efficiency isn't reduced too much. The other thing that helps a lot is strong condenser vacuum, as it allows everything to work at lower pressure and density.

I have read your comments and would kindly ask for what you consider the definition of partial admission. Most of my experience does not deal with that term and converging diverging nozzles are delt with in terms of Mach numbers with consideration of choke flow. In general flow through turbines is generally handled with enthalpy pressure diagrams to ensure state properties do not reach low quality steam conditions. Curious as to the terms you use. Thanks

 

[Nerd1000]

Agreed. In fact, most modern aviation turbines today are twin-spool designs, with a few 3-spool designs. The primary tasks of the core turbine, (often referred to as the gas generator) in a twin-spool engine, is to turn the compressor for the core section and supply enough exhaust gasses to turn the outer spool, which turns the fan and provides most of the thrust.



So, can you link any of your statements above to explain why partial admission must be used?

I ask because the only reason I can think of to use partial admission in small steam turbines is, "to be able to actually machine an ideal CD nozzle configuration"; all full admission nozzles are a compromise between what can be machined in an annular configuration and the ideal CD shape.

If the blade height is too low there will be high boundary layer drag losses (by necessity) and it also becomes very difficult to avoid high leakage losses.

 

[Nerd1000]

I have read your comments and would kindly ask for what you consider the definition of partial admission. Most of my experience does not deal with that term and converging diverging nozzles are delt with in terms of Mach numbers with consideration of choke flow. In general flow through turbines is generally handled with enthalpy pressure diagrams to ensure state properties do not reach low quality steam conditions. Curious as to the terms you use. Thanks

Partial admission means that only a portion of the turbine wheel is impinged upon by the gas. Only used for impulse turbines, it allows a 'oversized' wheel to operate at lower mass flow rates than it should. Also popular for controlling power output in early stages of larger machines.

 

[Toymaker]

I have read your comments and would kindly ask for what you consider the definition of partial admission. Most of my experience does not deal with that term and converging diverging nozzles are delt with in terms of Mach numbers with consideration of choke flow. In general flow through turbines is generally handled with enthalpy pressure diagrams to ensure state properties do not reach low quality steam conditions. Curious as to the terms you use. Thanks

The first diagram in post #8 shows an example of partial admission. Only a small part of the turbine wheel is being pushed by the steam from a nozzle.

 

[Toymaker]

If the blade height is too low there will be high boundary layer drag losses (by necessity) and it also becomes very difficult to avoid high leakage losses.

So what you're saying is that the increased efficiency and power output seen by turbines using full admission as compared to those using partial admission will be offset by some amount due to boundary layer drag when blade height becomes sufficiently small. I agree,...but how short? And how bad are boundary layer losses?
Given that boundary layer thickness is governed by the viscosity of a fluid (steam, in our case), and that viscosity becomes lower as steam temperature increases,...how thick is the boundary layer of steam at 100 C? 200 C?
The distance needed between two Tesla turbine blades provides a clue; max gap distance is usually 1 mm with 0.5mm being better. It's seems likely that a 1mm height blade would be operating completely within the boundary layer.

But, how inefficient is a turbine blade operating within a boundary layer? I don't have sufficient fluidics knowledge to provide a math based answer. Nerd, does your spreadsheet take into account boundary layer thickness as it varies with temperature and pressure?

 

[HMEL]

The first diagram in post #8 shows an example of partial admission. Only a small part of the turbine wheel is being pushed by the steam from a nozzle.

Ok, that definition makes sense but I have operated turbines where the throttle valves were split into as many as four sections so that the wheel actually saw a fairly high proportion of nozzles to the blades on the wheel. Never thought about the percentage. These valves worked together. You could by reading the pressure in the throttle bay determine fairly accurately the flow through the turbine. The valves fed a chamber which contained the nozzle blocks. Not sure how small you could go with such a design but if not built for commercial use I suspect it could be done to increase the power on a small unit that is if the steam is available.

 

[Nerd1000]

So what you're saying is that the increased efficiency and power output seen by turbines using full admission as compared to those using partial admission will be offset by some amount due to boundary layer drag when blade height becomes sufficiently small. I agree,...but how short? And how bad are boundary layer losses?
Given that boundary layer thickness is governed by the viscosity of a fluid (steam, in our case), and that viscosity becomes lower as steam temperature increases,...how thick is the boundary layer of steam at 100 C? 200 C?
The distance needed between two Tesla turbine blades provides a clue; max gap distance is usually 1 mm with 0.5mm being better. It's seems likely that a 1mm height blade would be operating completely within the boundary layer.

But, how inefficient is a turbine blade operating within a boundary layer? I don't have sufficient fluidics knowledge to provide an a math based answer. Nerd, does your spreadsheet take into account boundary layer thickness as it varies with temperature and pressure?

It doesn't account for boundary layer losses, that's a complex fluid dynamics problem that I think would be hard to handle in a spreadsheet, especially because we are often discussing supersonic flows! Perhaps some CFD could be used once an initial set of parameters was obtained.