An ideal Rankine cycle with water as the working fluid operates a boiler at 15,0

Question

An ideal Rankine cycle with water as the working fluid operates a boiler at 15,000 kPa and the condenser at 100 kPa. The temperature at the turbine entrance is 450C and there is a mass flow rate of 1.74 kg/s through the cycle. To increase the effciency of the system, a reheater and a second turbine is added to the cycle. If the reheater is kept at 2000 kPa, the low-pressure turbine inlet temperature is also 450c, and all other parameters remain the same, calculate:

required power for pumps (kW)
power produced by the cycle (kW)
thermal efficiency

Explanation / Answer

Pressure

(kPa)

Temperature

(C)

Enthalpy

(kJ/kg)

Entropy

(kJ/kgK)

Power required for pump is

W_p = m_dot * (h2 - h1) = 1.74 * (432.4 - 417.4) = 26 kW

Power produced by the cycle is

W_t = m_dot * [ (h3 - h4) + (h5 - h6) ] = 1.74 * [ (3156.6 - 2702.3) + (3357.5 - 2647.4) ] = 2026 kW

Heat input in boiler and reheater

Q_in = m_dot * [ (h3 - h2) + (h5 - h4) ]= 1.74 * [ (3156.6 - 432.3) + (3357.5 - 2702.3) = 5880.33 kW

Thermal efficiency

Eff_th = [ W_t - W_p ] / Q_b = [ 2026 - 26 ] / 5880.33 = 0.34 or 34%

State point Description

Pressure

(kPa)

Temperature

(C)

Enthalpy

(kJ/kg)

Entropy

(kJ/kgK)

Details 1 Pump inlet (condensor exit) 100 417.4 1.302 Pump inlet and condensor were at same pressure. Usually water here is saturated liquid (x=0) 2 Pump exit (boiler inlet) 15000 417.4+14.9=432.3 pump work = v*(p_2-p_1)=0.001*(15000-100)=14.9 3 Turbine-1 inlet (Boiler exit) 15000 450 3156.6 6.141 superheated steam 4 Turbine-1 exit (Reheater inlet) 2000 2702.3 6.141 constant entropy in turbine-1 (s3 = s4) 5 Turbine-2 inlet (Reheater exit) 2000 450 3357.5 7.285 superheated steam 6 Turbine-2 exit (Condensor inlet) 100 2647.4 7.285 constant entropy in turbine-2 (s5 = s6)

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