Thermo help

[RoseChm05E]

I just went back to graduate school and am lost on these problems.

If an 85% efficient adiabatic steam turbine's inlet is 4.00 MPa and the outlet is 0.01 MPa, how do you find the superheat required on the inlet, and the work produced by the turbine?

I have my Sv = 8.146 kJ/kg-K, T = 45.8C and H = 2583 kJ/kg for 0.01 MPa saturated steam and steam tables for 4.0 MPa in front of me...It's just that I'm lost about where to go next, it's been many years since I saw this in undergrad.

 

[insult2injury]

just look up the definition of turbine efficiency in your textbook.

I2I

 

[RoseChm05E]

Yes, I have that definition in front of me, too.

Am I supposed to match the 8.146 entropy with the same value by interpolating between 700 and 750 C on my 4.0 MPa value to get 739C superheated steam, then interpolate on enthalpies the same way and take the difference, then multiply that by 0.85?

 

[25362]

Find the superheated steam properties at 4.0 MPa and Sv=8.416 kJ/(kg.K) by use of tables or a Mollier diagram, and then apply the formula for machine efficiency.

 

[RoseChm05E]

"Find the superheated steam properties at 4.0 MPa and Sv=8.416 kJ/(kg.K) by use of tables or a Mollier diagram, and then apply the formula for machine efficiency"

Yeah, that's what I did, I was confused because the section included steam quality calculations, but for the superheated steam involved there isn't a liquid portion to worry about on either end.

Got 739 C as I said, and then (4480 - 2583) * 0.85 = 1612 kJ/kg.

 

[25362]

Now just convert kJ/kg into kWh/kg, knowing that 1 kJ=1 kW.s, to find the steam rate.

 

[RoseChm05E]

Thanks for the help...it only asks for the amount of work and not steam rate but that'd be simple enough if I had to get it.

 

[UmeshMathur]

I hope you're still looking for answers.

In this post, I assume you are using absolute pressures. Normally, you start with a supply steam P and T. This gives you the steam inlet entropy and enthalpy. The discharge entropy is simply the inlet entropy divided by the fractional turbine efficiency. Given the discharge entropy and pressure (may be either superheated or 2-phase, you don't know), you can find the discharge enthalpy and wetness by trial and error interpolation of the steam tables.

In the calculations below, I am using software based on the ASME steam tables with values converted by me to SI units. (Note that the ASME enthalpy and entroppy datum is not the same as that for the IAPWS).

You seem interested in finding the inlet temperature required to achieve an exhaust steam that is saturated vapor at 0.01 MPa. At 0.01 MPa absolute, the exhaust would be saturated vapor only if its entropy, Sout, is 8.1456 kJ/kg/K. Also, saturated steam Hout = 2583.055 kJ/kg at 0.01 MPa.

Therefore the inlet entropy, Sin is found using:

Sin = Sout*efficiency = 8.1456*0.85 = 6.9238 kJ/kg/K.

The inlet steam T required for Sin = 6.9238 kJ/kg/K at 4 Mpa is found from the steam table by trial and error interpolation. I used my program to do this automatically and came up with Tin = 719.9 K. At this condition, Hin = 3321.5 kJ/kg.

Therefore, work done is Hin - Hout = 3321.5 - 2583.1 = 738.4 kJ/kg steam.

Does this check your own calculations?

 

[djack77494]

Good job, Umesh. I think you nailed down the required calculational procedure. Of course, you have assumed saturated conditions at the turbine outlet, but I would contend that you needed to make that assumption. Otherwise, the problem is underspecified.
Doug

 

[UmeshMathur]

The following correction is based on a note to me from DickRussell:

"My understanding is that efficiency is work actually extracted (enthalpy) divided by what would be obtained under reversible (isentropic) conditions. Thus you would get the actual enthalpy change over the expansion by multiplying the isentropic enthalpy change by the adiabatic efficiency."

Dick is of course right and I apologize to both RoseChm05E and djack77494 for the error in defining the adiabatic efficiency in my computation of 18 Sep 2006. The corrected inlet temperature required to achieve a saturated discharge vapor at 0.01 MPa is about 923.0 K.

 

[RoseChm05E]

Hey, I got it along with a full answer key, thanks guys.