Steam enters the high-pressure turbine of a steam power plant that operates on the ideal reheat Rankine cycle at 800 psia and 900°F and leaves as saturated vapor. Steam is then reheated to 800°F before it expands to a pressure of 1psia. Heat is transferred to the steam in the boiler at a rate of 6 104 Btu/s. Steam is cooled in the condenser by the cooling water from a nearby river, which enters the condenser at 45°F. Show the cycle on a TS diagram with respect to saturation lines, and determine...
a.) The pressure at which reheating takes place
b.) The net power output and thermal efficiency
c.) The minimum mass flow rate of the cooling water required
23 comments:
I started using step 1 as the step between the condenser and the pump. I found Wpump,in, but I don't know what to do next...
Some ideas on how to approach the problem would be great.
Thanks Dr. B.
Tyler 12:45 PM
Use the flow diagram and TS Diagram on page 234. Look at Example 9C-1.
NOTICE
There was a typo in this problem statement that I correct at 3:45 PM on Th 5/25.
The problem should have said:
Qboiler = 6x10^4 Btu/s.
for the last question about the min mdot of cooling water, do we need to look up Cp for water or do we assume that the exit temp = temp of working fluid at the entrance to the compressor??
AdamAnt 3:56 PM
Cp = 1 Btu/lbm-degF
The minimum cooling water flow rate results in the cooling water being heated all the way up to the saturation temperature of the water/steam in the condenser.
Graham 2:41 PM
Your value of Mdot does not agree with mine.
Your procedure for determining the efficiency is fine. The problem is your Mdot is low by about 50%.
It might be faster to use
Nth = 1-Qc/Qh
than to calculate all 3 W's. Just a thought.
Dr. B, Can we assume the at state 5 the quality is one? This is based on the TS diagram..
Okay so I am just slightly confused. On stream 4 I have a temp of 800F and I know that stream 5 is a saturated vap (when dealing with ideal rankine) with a P= 1 psia. The problem I am having is that I look at the tables and find a S(hat) of 1.9776 at 1 psia for water at stream 5 and that should be the same for stream 4, but when I solve for the P in the superheated for #4 I don't get the right answer and the only way I have been able to get a P of 62 at stream 4 is by having a S of 1.89938 at stream 5 which equals stream 4. What am I missing? If 5 does have a quality how do I find this?
Belle 5:13 PM
No, the quality is not 1.0 at state 5 (out of the LP turbine). But, because the turbine is isentropic, you know P5 and S5 so you can evaluate the quality. It turns out to be about 96%.
Anon 5:27 PM
T2 = 900 degF, not 800 degF.
There is no saturated vapor stream in this problem.
IDEAL means the pump and turbines are isentropic. It does NOT mean that the turbine outlet is saturated vapor.
Basic Rankine really means the condenser effluent is saturated liquid and the boiler effluent is saturated vapor. In practice, the boiler effluent is almost always superheated vapor. So, Rankine really only means that the condenser effluent is saturated liquid.
I hope this helps !
I read the blog about the last question of the m(dot), but I still don't understand how to get it unfortunately. I got QH and W cycle and then I can find Qc through taking Qh-Qc=Wcycle. I also know I ant to find the m(dot) in Qc = m* delta H and I thought I could find delta H based on Cp * delta T with the T of 5 and the temperature that the water came in 45. none of this is working though so I know I am doing something wrong. Thank You for your help.
Anon 8:50 AM
OK, the key here is that the minimum cooling water (CW) flow rate is the rate just barely able to remove Qc from the condenser. This corresponds to a slow trickle of water through a HUGE heat exchanger. In this case, the CW heats all the way up to the temperature of the condensing steam Tsat at 1 psia.
So, Qc = Mdot * deltaHcw
But deltaHcw = Cp,cw * deltaTcw
Cp,cw = 1.0 Btu/lbm-degF
I'm really stuck here. How do I find the mass flow rate of steam in the system, it seems critical to finding Qc or W and thus Nth. Using Qh into the boiler and the deltaH changes for both heating stages combined doesn't yield the right answer. To find Qc I use Mdot(H6-H5) which is delta H across the condenser, but this requires Mdot again.
I'm trying to fill in all the information on a chart...I'm having difficulty calculating H1 (into boiler). I'm using the Q equation for a boiler, but H1 comes out very negative and I know that's not right.
This entire homework has me pretty lost.
has anybody figured this problem out? i swear there is a typo. i even have the most recent version. is Q12 = 6e4 Btu/s??? Please help! I have a million equations but no mdot. I figured out the W cycle to be 644.9 Btu/lbm which is not a power amount. I assumed that all the turbines and pumps are isentropic and adiabatic.
I'm so angry at this problem... How do you find Qc without knowning Mdot?!?!
So I used the same procedure as graham intially. I found Wdot through summing all the works seperatly and got a mdot of 46.05 lbm/s and Wdot as 29700Btu/s. I used Wdot,cycle=Qh-Qc to find Qc. This gave me a nth of 50% and an mdot,cw of 534lbm/s. I think something is wrong with my work term. so I tried using the nth=1-Qc/Qh method instead using Qc=mdotCp(H6-H5). That gave me an answer that was also worng. Is it a problem with my ethalpies in the table? Thanks.
Washburn 4:49 PM
You can determine Mdot from Qh. Qh is the heat transer rate into both the boiler and reheater. Your approach is correct. If this did not yield the right answer for you, give me some of your H values for comparison and I may be able to help you find the problem.
You are correct, you need to apply the 1st Law to the condenser to determine Qc.
You don't really need Mdot to determine the efficiency because the mass flow rate cancels out.
Carina 9:22 PM
I do not see how you could apply the 1st Law to the boiler to get H1 because the given value of Q is for BOTH the boiler and the reheater. So...
You have 2 choices about how to determine H1.
1- Assume the pump is isentropic and use NIST, P1 and S1 = S6 to determine H1.
2- Assume the liquid is incompressible so Wpump = INT{Vhat dP}=Vhat deltaP and use Vhat = Vhat of the saturated liquid. The Vhat of the saturated liquid should be at the same temperature, but you can use Vhat sat liq at 1 psia here if you want to. Anyway, once you have Wpump, apply the 1st Law to the (assumed adiabatic) pump and solve for H1.
Anon 12:05 AM
I think I have this one OK now.
Q12 + Q34 = 6x10^4 Btu/s
You can use this info and apply the 1st Law to the boiler and reheater to determine Mdot, but you can determine efficiency without determining Mdot by working the problem on a specific or per lbm basis.
Your answer for Wcycle is correct. Yes, you should multiply by Mdot to get power units.
Yes, the pump and turbines are isentropic & adiabatic.
Shooter 12:48 AM
I am sorry this problem has made you angry.
See my comment to Anon to see how to get Mdot.
You can use Qc^ and Qh^ to calculate the efficiency without knowing Mdot.
Swidder 7:36 AM
I cannot tell what is wrong for sure, but I think the problem may be that you assumed Q12 = 6x10^4 Btu/s. This is not correct. The correct use for this value is:
Q12 + Q34 = 6x10^4 Btu/s
This gives Mdot ~ 36 lbm/s and Wcycle ~ 24000 Btu/s
I hope this helps.
Graham,
Your H3 is a little bit off.
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