# How to calculate the speed of a steam turbine?

1. Dec 8, 2013

### Webbd050

For a uni project one of my concepts is to use the exhaust heat of a formula student car to boil water and use the steam to either spin a turbocharger or an electric generator to produce electricity. How would i calculate how fast i could get the turbine to spin? What equations do i use? And what parameters do i need to know? Just not sure how to get started calculating it.
Thanks

2. Dec 9, 2013

### Baluncore

You will need to know the volume and pressure of steam available.
Given gas flow volume and turbine section, the angle of the turbine blades will determine the maximum RPM. The most efficient power extraction RPM will be when the turbine blades have an optimum angle of attack.

Where are you going to get the water that you boil. Are you going to condense the exhaust steam and re-inject it back into the boiler? Your condenser will need a large radiator.

3. Dec 9, 2013

### SteamKing

Staff Emeritus
If you want to convert the waste heat of the engine exhaust into generating electrical energy, the whole process of generating steam should be avoided. Use your turbine to turn the gen. directly and avoid all the plumbing hassles of trying to build a steam plant for your generator.

4. Dec 9, 2013

### Staff: Mentor

Steamking, the problem with that is that you aren't gaining any efficiency that way. Yes, it is more of a hassle, but it really is better from an efficiency standpoint to use a steam turbine.

Anyway, "how fast" is really the wrong question as it doesn't tell you anything about how much energy you are recovering, which is really what you want to know. You can drive the turbine as fast or slow as you want (within limits) - what you really want to find is the optimal speed to drive your generator.

5. Dec 9, 2013

### SteamKing

Staff Emeritus
I don't think so. Using the waste heat to boil the water into steam, run the steam thru a turbine, and re-condense it for a closed system necessarily introduces additional inefficiencies into the process of turning waste heat into electrical energy. (Unless you have a magic turbine which no one knows about) Then, as well, you have another sub-system (the steam plant) to carry around and maintain on your vehicle.

6. Dec 9, 2013

### AlephZero

The overall efficiency depends on the thermodynamics as much as on "inefficiency" in individual components of the system.

You are starting with exhaust gas that is hot, with some kinetic energy (i.e. its flow velocity) and some pressure above atmospheric. The first "efficiency" question is, how much of that energy into mechanical work with a turbine (given the limitations of Carnot's theorem) compared with how much heat energy can you extract in a steam boiler?

If the IC engine was "efficient," the exhaust gas pressure will be low, so it's not obvious how you could make an efficient turbine to get the heat energy from the exhaust. The gas needs to expand and cool down as it goes through the turbine, to get the heat energy out of it. On the other hand, a counter-current heat exchanger would certainly be able to cool the exhaust gas down to (almost) atmospheric temperature.

Of course the next question is how efficiently you can use the steam once you have made it.

YOu could make you turbine more efficient by increasing the exhaust back pressure of the IC engine, but of course that would reduce the efficiency of the IC engine, unless you used the turbine to drive a compressor and increase the IC engine inlet pressure. But I don't think that's what the OP wants to do.

Last edited: Dec 9, 2013
7. Dec 9, 2013

### SteamKing

Staff Emeritus
It's like when aircraft were powered by reciprocating engines. At altitude, performance took a big hit, until somebody figured out that if the engines could be supercharged, a lot of the performance loss could be avoided. To avoid making the engines more complex, GE figured out how to drive the superchargers using the exhaust from the reciprocating engine. To make a long story short, the plumbing for the turbo-superchargers got so complex that power growth for reciprocating engines hit a hard limit, until someone figured out that the problems would go away by eliminating the reciprocating engine entirely and just use the turbine, first in the form of a turboprop, and then a turbojet.

8. Dec 9, 2013

### cjl

This isn't really correct - a turbocharged engine (which is running a turbine off of the exhaust) is indeed more efficient than a naturally aspirated engine of the same power output. It's possible that the steam method would allow for even greater efficiency, but there are tradeoffs with efficiency vs complexity if this is the case.

9. Dec 9, 2013

Of course we are talking about a Formula car here, which necessarily must be quite light, and carrying around a bunch of water and a bulky radiator and condenser likely will more than negate any benefit you see from creating such a system. At the very least it will take up weight that would be much better used for additional fuel.

Is there a reason you are set on a steam plant? Why not use the waste heat to drive a series of thermopiles?

10. Dec 9, 2013

### Baluncore

As an academic exercise in efficiency, economics and thermodynamics it should be possible to analyse the existing system and evaluate ways to improve it. The proof that a concept cannot give an advantage is better than a forlorn search for an unattainable goal.

11. Dec 9, 2013

I don't necessarily disagree, but if you are going to prove something won't work, you are better off proving it with something that is a best-case scenario, and I can't imagine that to be a steam plant. Then again, if this is a thermodynamics class for which this is a project, I can see why a stream plant may be the preferred method.

12. Dec 9, 2013

### Staff: Mentor

[can of worms]
Hmm... Researching, it looks like this was an issue of theory meeting practice and in theory I was wrong....
I'm not saying the added steam plant is 100% efficient. What I'm saying is that the added steam plant does not ever harm the efficiency of the ICE you connect it to and if anything will improve the efficiency due to the lower exhaust manifold pressure it creates - in addition to recovering some of the waste heat.

A turbocharger, on the other hand, obstructs the flow of the exhaust and can harm the [fuel] efficiency of the engine. Because there are several different possible cases for comparing, there isn't a single answer on fuel efficiency...
That's a little tricky due to the several ways to generate the same power output:

Case 1: Smaller displacement engine of the same peak power as a larger displacement engine. This will generally be more efficient. But that isn't the scenario being discussed:

Case 2 (OP Scenario): Retrofit an existing engine for a turbo. Efficiency will be improved in some of the operating range, but not all of it - particularly not in the lower end or at idle.

Case 3 (OP alternate): Turbo running a generator. It may hold an advantage in total system efficiency due to the higher efficiency of the electric generator vs the car engine.

Some examples:
I drive a Kia Optima, which has the following engines/fuel economies:
2.4L, 200hp -- 28 mpg combined
2.0L Turbo, 274hp -- 26 mph combined

I drive the turbo. The combined fuel economy I get is even worse due to very bad city fuel economy. Seems at idle it still uses a lot of fuel to keep the turbo spinning.

Conversely, here's an article about a VW, with a 2.0 and 2.0 turbo: http://www.autospeed.com/cms/A_109931/article.html
The turbo is slightly more efficient.

It is likely true that the smaller the engine, the more benefit and less penalty you get from a turbo since the smaller engine will tend to be running at a higher fraction of full power.

My view of the steamer concept for heat recovery is that it probably has more potential for efficiency increases because it isn't at all parasitic at idle, unlike the turbo.