Thermodynamics Steam Turbine Specific Entropy

[ConnorM]

Homework Statement

The mass flow rate through a steam turbine operating under steady conditions is 100 kg/s. Steam enters the turbine at 12 MPa and 400^oC. A mixture of vapour and liquid water exits the turbine at 10 kPa. At the exit state 93% of the mass of the water is in vapour form. The turbine loses heat to the surroundings at the rate
of 3 MW. Kinetic and potential energy effects can be ignored.

a) Draw a schematic of the system and clearly indicate the system boundary
using a dashed line. Indicate and label the mass flow inlets and outlets. Using
arrows, illustrate the energy transfers between the system and surroundings
by heat transfer and by work.

b) Write a 1st law energy balance for the system that agrees with your schematic. Cancel all unnecessary terms, providing justification for why these terms can be cancelled.

c) Draw the process on a T-s diagram, clearly indicating the state points and the isobars corresponding to the state points.

d) Calculate the power generated by the turbine in MW.

e) Calculate the change in specific entropy from inlet to exit in kJ/KgK.

Homework Equations

Question 2

s₁=s_f + x[ s_g - s_f ]
Also since there is one inlet and one exit,
m=m₁=m₂

I am pretty sure this equation will be useful as well,
0= Q - W + m[ (h₁ - h₂) + ((v₁² - v₂²)/2) + g(z₁ + z₂) ]

but since kinetic and potential energy is negligible I think I can cancel out ((v₁² - v₂²)/2) + g(z₁ + z₂)]
That would leave me with,

0= Q - W + m[ (h₁ - h₂) ]

The Attempt at a Solution

For the second question I'm not really sure what to do, I think that what I would have to do is find s_g from using 12 MPa, 400_oC and looking at the steam table for water.
I'm not sure what I could do next because I would have 2 unknowns for the equation,
s₁=s_f + x[ s_g - s_f ]

 

[SteamKing]

PF Rules generally ask that posters provide only one problem per thread. This policy is for the benefit of the users and the members since you are not mixing up answering different questions within a single thread.

 

[SteamKing]

Homework Statement

2) The mass flow rate through a steam turbine operating under steady conditions is 100 kg/s. Steam enters the turbine at 12 MPa and 400^oC. A mixture of vapour and liquid water exits the turbine at 10 kPa. At the exit state 93% of the mass of the water is in vapour form. The turbine loses heat to the surroundings at the rate
of 3 MW. Kinetic and potential energy effects can be ignored.

a) Draw a schematic of the system and clearly indicate the system boundary
using a dashed line. Indicate and label the mass flow inlets and outlets. Using
arrows, illustrate the energy transfers between the system and surroundings
by heat transfer and by work.

b) Write a 1st law energy balance for the system that agrees with your schematic. Cancel all unnecessary terms, providing justification for why these terms can be cancelled.

c) Draw the process on a T-s diagram, clearly indicating the state points and the isobars corresponding to the state points.

d) Calculate the power generated by the turbine in MW.

e) Calculate the change in specific entropy from inlet to exit in kJ/KgK.

Homework Equations

[/B]
Question 2
For the second question I think this equation may be useful since we are given the quality,
s₁=s_f + x[ s_g - s_f ]
Also since there is one inlet and one exit,
m=m₁=m₂

I am pretty sure this equation will be useful as well,
0= Q - W + m[ (h₁ - h₂) + ((v₁² - v₂²)/2) + g(z₁ + z₂) ]

but since kinetic and potential energy is negligible I think I can cancel out ((v₁² - v₂²)/2) + g(z₁ + z₂)]
That would leave me with,

0= Q - W + m[ (h₁ - h₂) ]

The Attempt at a Solution

For the second question I'm not really sure what to do, I think that what I would have to do is find s_g from using 12 MPa, 400^oC and looking at the steam table for water.

Maybe not water. At the inlet, you generally use superheated steam for turbines.

I'm not sure what I could do next because I would have 2 unknowns for the equation,
s₁=s_f + x[ s_g - s_f ]

You are given the exit pressure (10 kPa) and the vapor quality of the mixture (93%). What you have to do is supply the saturated properties of the liquid and vapor phases from the steam tables at this exit pressure to determine the specific entropy of the mixture (and the enthalpy).

 

[ConnorM]

Ok sorry about that! I changed this so it is now only one of the questions. So I should use the pressure table for propane to find s_g and s_f? Then I would use those values to find the specific entropy once it exits?
Using,

s =s_f + x[ s_g - s_f ]

 

[ConnorM]

Hey so I used 12 MPa and 400 C to get s₁ on the superheated table for water, which was 6.0747 kJ/kgK. Then I used the pressure table for water and the values of entropy at 0.10 bar to get s₂. I used the equation s=sf + x[ sg - sf ] and found that s₂=7.625 kJ/kgK.

How is that so far?

edit: Just remembered to get the enthalpy's. For h₁ I used the superheated table and got 3051.3 kJ/kg. Next I used my pressure table at 0.10 bar and found my h_f and h_g, from here I used,

h₂ = xh_g + (1-x)h_f

and found h₂ = 2417.1991 kJ/kg

 

[ConnorM]

Hey I got it right! Thanks for the tip =)

 

[SteamKing]

Hey so I used 12 MPa and 400 C to get s₁ on the superheated table for water, which was 6.0747 kJ/kgK. Then I used the pressure table for water and the values of entropy at 0.10 bar to get s₂. I used the equation s=sf + x[ sg - sf ] and found that s₂=7.625 kJ/kgK.

How is that so far?

edit: Just remembered to get the enthalpy's. For h₁ I used the superheated table and got 3051.3 kJ/kg. Next I used my pressure table at 0.10 bar and found my h_f and h_g, from here I used,

h₂ = xh_g + (1-x)h_f

and found h₂ = 2417.1991 kJ/kg

The thermo properties look OK. Now you can finish the steam turbine problem.