Wednesday, May 10, 2006

HW #9, P#6 - Ideal Brayton Cycle with Reheating and Multistage Compression - 8 pts

Consider an ideal Brayton cycle with two stages of compression and two stages of expansion. The pressure ratio across each stage of the compressor and turbine is 3. The air enters each stage of the compressor at 300 K and each stage of the turbine at 1200 K. Determine the back work ratio and the thermal efficiency of the cycle. Use variable specific heats. Solve this problem assuming...
a.) no regenerator is used
b.) a regenerator with 75% effectiveness is used

13 comments:

Anonymous said...

Ok uhm, I tried to use thermo CD to find the "back work ratio" which isn't covered anywhere in the notebook, but I cant get ThermoCD to work, surprise surprise. Any chance you can post that equation on here, Dr. B?

Anonymous said...

Yeah, ive been having trouble With this too.
On ThermoCd it says BWR is
(-Wcomp/mdot)/(Wturb/mdot)

I cant get any answers right on this problem even though i have all the H values filled in my table. im going to office hours tomorrow...

Anonymous said...

I'm not getting the correct thermo efficency for #1. I determined all of the temperatures that weren't given by using reduced pressures. Once I figured out the temperature at all points I used the shomate equation to determine Q(hex1) and Q(hex2). Then assuming Q(hex1)=Qh and Q(hex2)=Qc I got values of Qh=25278 J/mol and Qc=18890 J/mol. These values gave me the wrong thermo effenciency. Do you know what I'm doing wrong?

Anonymous said...

Is the Back Work Ratio the same for part a and b...because the temperature inputs for the compressors are the same in part a as in part b, as well as the temp. input for the turbines, AND the pressure ratios across each turbine and compressor does not change in part b from part a?

Anonymous said...

I am really confused about how to work this problem. Do we use ideal H values from the Ideal Gas table, or is there something more that goes into this? I don't even know where to start...

Dr. B said...

Anon 3:20 PM
This is the first problem I have heard about with Thermo-CD in a few weeks.
BWR = -(Wc1+Wc2)/(Wt1+Wt2)

Dr. B said...

AdamAnt 4:07 PM
Your eqn for BWR is correct.
The only other point that I can see might give you some trouble on this problem is the regenerator in part (b).
Effectivness = Qact/Qmax = [mdot(H9-H10)]/[mdot(H9-H4)] =
[mdot(H4-H5)]/[mdot(H9-H4)]
And the mdot's cancel.

Dr. B said...

GreenPepper7 8:28 PM
OK, the relative pressure method will work here because the compressors and turbines are isentropic (and the heat capacities are not constant).
I am not sure which device is Qhex1, but I suggest you look up H's in the IG Property Table for Air instead of using Shomate. There is less chance of making a mistake.
You put heat into the system in TWO places...the combustor and the reheater, so QH is the sum of these two heats.
If you want to use efficiency = 1 - Qc/Qh, then Qc must include all THREE units where heat leaves the system !
I have numbers in kJ/kg because I used the IG Prop tables.

Dr. B said...

Yoda 11:12 PM
Yes. You spoiled the surprise :)

Dr. B said...

Anon 12:33 AM
Yes, I suggest you use the IG Property Table for air.
The compressors and turbines are isentropic, so use either Snought or Pr to determine the H's of the streams leaving each of them.
Build a table and fill in allthe H values. Then calculate the answers to the questions in the problem statement.
You may find some help in the comments I have posted here.

Dr. B said...

Graham 1:47 PM
I did not use Shomate directly, I used the IG Prop Table for air instead.
Thermal Efficiency = Wcycle / Qinput. There are multiple W's and QH's in this problem. Calculate each of them and add them up. Use the result to calculate the thermal efficiency.
If you try to use Eta = 1 - Qc / Qh, then Qh is all the heat input and Qc is all the heat rejected.
You don't need to know Mdot at all. It is in every W and Q term, so when you take the ratio, it cancels.

Anonymous said...

This may seem really obvious, but are the effluent streams coming out of the two compressors the same? (at the same H and S).

Anonymous said...

claire,
h2=h4 but s2 does not equal to s4.