Your company is considering the installation of a steam turbine to generate powe

Question

Your company is considering the installation of a steam turbine to generate power for a part of the plant where you work. Being the lead process engineer for this section of the plant you are involved in the decision making process. The peak desired power rating for this turbine would be 1.0 MW. House steam is available to drive the turbine with a pressure of 4 MPa, a temperature of 500°C, and a maximum supply rate of 1.2 kg/s. The plant requires that the return steam be no less than 200 kPa with a minimum quality of 0.95 at the outlet of the turbine. The inlet and outlet areas of the turbine currently being considered are both 0.010 m2. Based on these requirements, i.e., without considering cost, would you recommend this turbine for the proposed upgrade? Support your answer.

Explanation / Answer

From steam properties at P1 = 4 MPa and T1 = 500 deg C, we get h1 = 3450 kJ/kg and v1 = 0.0864 m^3/kg

From steam properties at P2 = 200 kPa and quality x2 = 0.95, we get h2 = 2600 kJ/kg and v2 = 0.841 m^3/kg

Mass conservation: m = A1*V1/v1 = A2*V2/v2

1.2 = 0.01*V1 / 0.0864 = 0.01*V2 / 0.841

Solving this, V1 = 10.368 m/s

V2 = 100.9 m/s

Steady flow energy equation: h1 + V1^2 /2 = h2 + V2^2 /2 + w

3450*10^3 + 10.368^2 /2 = 2600*10^3 + 100.9^2 /2 + w

w = 844961 J/kg = 845 kJ/kg

From 1.2 kg/s of steam flow, power delivered W = 1.2*845 = 1014 kW = 1.014 MW

Since turbine power is more than desired 1.0 MW, we can recommend it.

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