Superheated Steam Turbine - on a question please

[Christy001]

1. Superheated Steam enters a turbine with a pressure of 10 bar and a temp of 300 degrees celcius, and exits with a pressure of 0.046 bar. As the steam flows through the turbine it undergoes adiabatic expansion according to the law pv to the power 1.131 = constant
From Steam tables I have to calculate :
a) specific volume of steam at the turbine input and output (I assume that's just v straight from the Superheated tables at the relevant pressures ?)
b) Saturated vapour specific volume for the steam output pressure and state the steam condition ?
c) dryness fraction of the steam at the turbine exit ?
d) theoretical specific work output of the turbine ?Can anyone help me on the above please as I've scoured the internet for a solution and got part of the way in understanding but then can't follow how the things are found on the steam tables and what equations are used - any help would be greatly appreciated

 

[SteamKing]

1. Superheated Steam enters a turbine with a pressure of 10 bar and a temp of 300 degrees celcius, and exits with a pressure of 0.046 bar. As the steam flows through the turbine it undergoes adiabatic expansion according to the law pv to the power 1.131 = constant
From Steam tables I have to calculate :
a) specific volume of steam at the turbine input and output (I assume that's just v straight from the Superheated tables at the relevant pressures ?)
b) Saturated vapour specific volume for the steam output pressure and state the steam condition ?
c) dryness fraction of the steam at the turbine exit ?
d) theoretical specific work output of the turbine ?Can anyone help me on the above please as I've scoured the internet for a solution and got part of the way in understanding but then can't follow how the things are found on the steam tables and what equations are used - any help would be greatly appreciated

Since this is a homework question, you should have filled out the HW Template. Those are the Rules.

In order to receive help, you must also show some attempt at solving these questions.

For a) You have sufficient info for the inlet conditions to find spec. volume.

The same is not true for the exit, as seen by questions b), c), and d), where you must determine how the steam changes condition as it flows thru the turbine.
As stated in the problem, PV^γ = Constant, where γ = 1.131

Here is more information on adiabatic processes:

http://en.wikipedia.org/wiki/Adiabatic_process

This should be enough information for you to work thru questions b), c), and d).

If you get stuck, repost to this thread with the details and we'll see if these blocks can't be overcome.

 

[Christy001]

Hi - this is what I have worked out so far :
a) specific volume of steam at the turbine input and output :
At state 1 call the values S1, H1 and at state 2 call the values S2, H2,
From the Superheated steam tables I've looked up 300 degrees C and 1000 Kpa to give S1 (Sg) 7.125KJ/KG-K and H1 (Hg) = 3,052.15 KJ/KG
I know that as the process is Adiabatic then S1 = S2 therefore I think the answer to part (a) is 7.125 Kj/Kg-K for both answers.
(b) I know for this part I need to use the formula : S2 = Sf + x times Sfg - where x=dryness factor (but I don't know what Sf and Sfg are so I can solve for x so I need a pointer here please .
(c) x is is dryness fraction so I have found this out in part (b) I believe
(d) to find the work done I know that for an adiabatic process this is the change in H, so it's H2 - H1 - I know H1 from above. I know I need to use the formula :
H2= Hf + x times Hfg (at 0.046 bar) = I have worked out x - so do I just get Hf and Hfg from the Superheated Steam tables ?
thanks.

 

[BvU]

You want to reconsider the meaning of "adiabatic". The case $\Delta S=0$ is goes under the name "Isentropic".
The given expression for $pv$ should help you further to find the exit temperature.

 

[SteamKing]

Hi - this is what I have worked out so far :
a) specific volume of steam at the turbine input and output :
At state 1 call the values S1, H1 and at state 2 call the values S2, H2,
From the Superheated steam tables I've looked up 300 degrees C and 1000 Kpa to give S1 (Sg) 7.125KJ/KG-K and H1 (Hg) = 3,052.15 KJ/KG
I know that as the process is Adiabatic then S1 = S2 therefore I think the answer to part (a) is 7.125 Kj/Kg-K for both answers.

S generally denotes the entropy of a substance, not specific volume, which is usually denoted by v. Also, the units of specific volume are m³/kg.
The steam tables also use g to denote the property in the vapor phase and f in the fluid phase; hence Sg is the entropy of the steam in the vapor phase.

You must pay attention to the units listed for each property.

(b) I know for this part I need to use the formula : S2 = Sf + x times Sfg - where x=dryness factor (but I don't know what Sf and Sfg are so I can solve for x so I need a pointer here please .

You must correct your work on part a) first.

(c) x is is dryness fraction so I have found this out in part (b) I believe

Not according to what you wrote in the previous section.

(d) to find the work done I know that for an adiabatic process this is the change in H, so it's H2 - H1 - I know H1 from above. I know I need to use the formula :
H2= Hf + x times Hfg (at 0.046 bar) = I have worked out x - so do I just get Hf and Hfg from the Superheated Steam tables ?
thanks.

If you've worked out the quality of the exhaust steam x, you haven't shared it with us yet.

The steam tables will list the enthalpy, entropy, and specific volume for the vapor and fluid phases of water/steam.

 

[Chestermiller]

You know the exit pressure, and you know that the exit stream is a combination of liquid water and water vapor. What does that tell you about whether it is saturated or not? If it's saturated, what is the entropy of the saturated liquid, and what is the entropy of the saturated vapor? What is the temperature? What is the enthalpy of the saturated liquid and the saturated vapor. What is the enthalpy of the stream?

Chet

 

[Christy001]

You know the exit pressure, and you know that the exit stream is a combination of liquid water and water vapor. What does that tell you about whether it is saturated or not? If it's saturated, what is the entropy of the saturated liquid, and what is the entropy of the saturated vapor? What is the temperature? What is the enthalpy of the saturated liquid and the saturated vapor. What is the enthalpy of the stream?

Chet

Hi. Thanks for the reply. This is where I get stuck as I can understand that when the steam enters at 450 it is superheated but at exit do I need to go back to the Saturated tables to obtain the temperature ?

 

[SteamKing]

Hi. Thanks for the reply. This is where I get stuck as I can understand that when the steam enters at 450 it is superheated but at exit do I need to go back to the Saturated tables to obtain the temperature ?

By nature, superheated steam has a vapor quality of 100%, so yes, for the turbine exhaust, you'll have to go to the saturated vapor tables and use the vapor quality to calculate the properties of the exhaust steam.

http://en.wikipedia.org/wiki/Vapor_quality