Question

In a Rankine cycle, the steam at inlet to turbine is saturated at a pressure of 35 bar and the exhaust pressure is 0.2 bar. Determine : 

(i) The pump work, 

(ii) The turbine work, 

(iii) The Rankine efficiency, 

(iv) The condenser heat flow, 

(v) The dryness at the end of expansion. Assume flow rate of 9.5 kg/s

Answer 1

Pressure and condition of steam, at inlet to the turbine,

p₁ = 35 bar, x = 1

Exhaust pressure, p₂ = 0.2 bar

Flow rate, m = 9.5 kg/s

From steam tables : 

At 35 bar : 

h₁ = h_g1 = 2802 kJ/kg, 

s_g1 = 6.1228 kJ/kg K 

At 0.26 bar : 

h_f = 251.5 kJ/kg, 

h_fg = 2358.4 kJ/kg, 

v_f = 0.001017 m³/kg, 

s_f = 0.8321 kJ/kg K, 

s_fg = 7.0773 kJ/kg K. 

(i) The pump work : 

Pump work = (p₄ – p₃) 

v_f = (35 – 0.2) × 10⁵ × 0.001017 J or 3.54 kJ/kg

Now power required to drive the pump 

= 9.5 × 3.54 kJ/s or 33.63 kW.

(ii) The turbine work : 

s₁ = s₂ = s_f2 + x₂ × s_fg2 

6.1228 = 0.8321 + x₂ × 7.0773

h₂ = h_f2 + x₂ h_fg2 = 251.5 + 0.747 × 2358.4 = 2013 kJ/kg

Turbine work = m (h₁ – h₂) = 9.5 (2802 – 2013) = 7495.5 kW

It may be noted that pump work (33.63 kW) is very small as compared to the turbine work (7495.5 kW). 

(iii) The Rankine efficiency :

(iv) The condenser heat flow :

The condenser heat flow = m (h₂ – h_f3 ) = 9.5 (2013 – 251.5) = 16734.25 kW. 

(v) The dryness at the end of expansion, x₂ :

The dryness at the end of expansion,

 x₂ = 0.747 or 74.7%.