# Overall combined cycle efficiency calculation

Discussion in 'Homework Help' started by KevinEamon, Jan 15, 2018.

1. ### KevinEamon Thread Starter Member

Apr 9, 2017
228
9
Hey guys

So just trying to find a few good topics to study for the exam. If I remember correctly this was a fairly easy problem to solve.

So there's questions in the past papers, that give examples like this one above, or simply, ask to recall the formula and explain each element. I seem to remember this being very straightforward, if I could find my dang notes on it! which btw I can't

So obviously the eta η here is the efficiency. That appears frequently throughout this section of the module. The subscripts are all fine: combined cycle... gas turbine... steam cycle.

Also the C thing at the end, I think this was the HRSG. I also remember it being set to 1 in some circumstances, though I could be wrong.

Any extra info would be very much appreciated.

Last edited: Jan 15, 2018
2. ### WBahn Moderator

Mar 31, 2012
23,391
7,099
This is what would make sense to me, but keep in mind that I know nothing about combined cycle stuff.

So my guess is that first you use some energy to run a gas turbine to produce electricity and the efficiency of that is ηTG. Now you are trying to improve that by using the waste heat to run a steam generator. Since your starting point is what is left after running the gas turbine, your input begins at (1-ηTG). But you don't get all of that since some of it is lost in the exhaust, so that's ζ. Next, you need to convert that to heat for your steam plant and that's where the r comes in, which is essentially the efficiency at which the recoverable waste heat from the exhaust can be turned into a heat source for the steam plant. After that, you have the efficiency of the steam plant in producing electricity given by ηSC.

3. ### KevinEamon Thread Starter Member

Apr 9, 2017
228
9
Yes yes looks great... yes....hmm I wonder if the lecturer said, if that r was a value close to 1...? perhaps a ratio!
I shall dig a lil deeper. Thanks once again my friend. You are perhaps the most intelligent person that I know.

4. ### WBahn Moderator

Mar 31, 2012
23,391
7,099
Terms in something like this are almost always ratios and usually (not always) constrained to lie between 0 and 1.

Notice that we are adding efficiency terms and that should always red flags about the possibility of getting a result that is over-unity. Can you see and explain why the this expression is guaranteed to not exceed 100%.

It's kind of you to say that, but I can pretty much guarantee that it's not the case without even known anyone that you know.

5. ### KevinEamon Thread Starter Member

Apr 9, 2017
228
9
Haha then you definitely don't know the people that I know. Collection of reprobates and degenerates if I ever met em... Lul joking...

Kk so I've done a lil digging the r is the Hrsg. Which seems to be always set to 1.
C was the losses.

In response to the unity question. I'm guessing you use the ratio version of the percentages.
So for 60% it's 0.60 and not 60....
The 1 inside the brackets is going to insure that the value remains below 1. Resulting in a negative value. So why does it give a positive value for the overall result... hmmm? Strange...

I wonder why r, is always 1 as well? Even though the HRSG gives a value of 85% in the question....

6. ### WBahn Moderator

Mar 31, 2012
23,391
7,099
I'm guessing that HRSG means something like heat-recovery steam generator and that, as mentioned earlier, the fraction of exhaust heat that makes it into the unit makes it to the input of the steam generator. It might commonly be used set to 1 if a better value isn't available; but as you noted, here you HAVE a value that is specified.

You are on the right track as far as why the end result is always less than one.

Think of the energy coming into the system (in terms of the energy in the fuel for the gas turbine). The fraction ηGT is the amount of it that is converted to electrical energy, leaving (1-ηGT) that wasn't. So even if there are no other losses from any source the total combined efficiency can't exceed 1. If the ζ term weren't there, then it would be mathematically impossible for it to go negative, either (since all the values are between 0 and 1). But, at least mathematically, if ζ is large (even though it's still less than 1), the overall could go negative. But in practice it can never be greater than (1-ηGT) precisely because you can't lose as heat in your exhaust energy that was converted to electricity by the gas turbine.

7. ### KevinEamon Thread Starter Member

Apr 9, 2017
228
9
Haha I was looking for a mathematical reason, but that makes perfect sense. Thank you as always Wbahn. Gentleman...

Back to the grind here, I go. Soon it will be over for a lil break... sweet