Water is the working fluid in a vapor power cycle with superheat and reheat. Sup

Question

Water is the working fluid in a vapor power cycle with superheat and reheat. Superheated vapor enters the first turbine stage at 8 MPa, 480 degrees C, and expands to .7 MPa. Then, it is reheated to 480 degrees C befor entering the second turbine stage, where it expands to the condenser pressure of 8 kPa. The mass flow rate of steam entering the first turbine stage is 2.63*(10^5) kg/h. Each turbine stage operates with an isentropic efficiency of 88%. The pump operates with an efficiency of 80%. Determine for the cycle:

a. the net power developed, in kW

b. the thermal efficiency

c. the rate of heat transfer to cooling water passing through the condenser, in kW

Explanation / Answer

From steam properties,

At P1 = 8 MPa and T1 = 480 deg C, we get h1 = 3350 kJ/kg, and s1 = 6.66 kJ/kg-K

At P2_is = 0.7 MPa and s2_is = s1 = 6.66 kJ/kg-K, we get h2_is = 2740 kJ/kg

Turb eff = (h1 - h2) / (h1 - h2_is)

0.88 = (3350 - h2) / (3350 - 2740)

h2 = 2813.2 kJ/kg

At P3 = 0.7 MPa and T3 = 480 deg C, we get h3 = 3440 kJ/kg and s3 = 7.88 kJ/kg-K

At P4 = 8 kPa and s4_is = s3 = 7.88 kJ/kg-K, we get h4_is = 2470 kJ/kg-K

Turb eff = (h3 - h4) / (h3 - h4_is)

0.88 = (3440 - h4) / (3440 - 2470)

h4 = 2586.4 kJ/kg

At P5 = 8 kPa and quality = 0, we get h5 = 174 kJ/kg, and s5 = 0.592 kJ/kg-K

At P6 = 8 MPa and s6_is = s5 = 0.592 kJ/kg-K, we get h6_is = 182 kJ/kg

Pump eff = (h6_is - h5) / (h6 - h5)

0.8 = (182 - 174) / (h6 - 174)

h6 = 184 kJ/kg

Mass flow m = 2.63*10^5 kg/h = 2.63*10^5 / (60*60) kg/s = 73.055 kg/s

a)

Turb1 power = m*(h1 - h2) = 73.055*(3350 - 2813.2) = 39215.9 kW

Turb2 power = m*(h3 - h4) = 73.055*(3440 - 2586.4) = 62359.7 kW

Pump power = m*(h6 - h5) = 73.055*(184 - 174) = 730.55 kW

Net power = 39215.9 + 62359.7 - 730.55 = 100845.1 kW

b)

Heat input = m*(h1 - h6) + m*(h3 - h2)

= 73.055*(3350 - 184 + 3440 - 2813.2)

= 277083 kW

Thermal eff = 100845.1 / 277083 = 0.3639 or 36.39 %

c)

Rate of heat transfer to cooling water = m*(h4 - h5)

= 73.055*(2586.4 - 174)

= 176237.9 kW

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