### Solved Problem 6.1 - A Supercritical Steam Power Plant for Athens, Ohio

Consider the supercritical steam power plant with reheat for Athens, Ohio, which we evaluated in Solved Problem 4.1. The system diagram is repeated here for convenience: In this exercise we wish to evaluate the high pressure (HP) and low pressure (LP) turbines of this system (circled in red), both of which are assumed to be adiabatic.

• 1) Plot the two turbine processes (Stations (1)-(2) and (3)-(4)) on the enthalpy-entropy h-s "Mollier" diagram. Plot also the equivalent isentropic turbine processes on the diagram, and indicate the actual turbine specific work as well as the isentropic turbine specific work for both turbines on the h-s diagram.

• 2) Using steam tables, determine the turbine adiabatic efficiency ηT of both turbines.

• 3) Discuss your results as well as the feasibility of the turbine set.

Justify all values used and derive all equations used starting from the basic energy equation for a flow system, the basic definition of turbine adiabatic efficiency ηT.
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Solution Approach:

• 1) Plot the two turbine processes (Stations (1)-(2) and (3)-(4)) on the enthalpy-entropy h-s "Mollier" diagram below. Plot also the equivalent isentropic turbine processes on the diagram, and indicate the actual turbine specific work as well as the isentropic turbine specific work for both turbines on the h-s diagram. [refer h-s diagram below] • 2) Using steam tables, determine the turbine adiabatic efficiency ηT of both turbines. [enthalpy and entropy data derived from steam tables shown in red on schematic diagram below. State (2s) required linear interpolation of the superheat table values and both states (4a) and (4s) required the saturation properties (pressure) table and use of the quality relation X indicated below. These values were then indicated on the above h-s diagram plot in order to validate their feasibility.] • 3) Discuss your results as well as the feasibility of the turbine set. [Both adiabatic efficiencies seem to be feasible and do not violate the second law. We need to question why the LP turbine efficiency (90%) is so much higher than the HP turbine efficiency (77%) - it may be due to the ability of higher relative accuracy in the manufacture of a much larger turbine however this large difference is suspect and needs more investigation.]

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