Question

Question 3 Steam expands through a well-insulated turbine from inlet conditions 300°C and 4 MPa with negligible velocity to exit conditions 40 m/s and 0.075 MPa. The turbine is operating at steady state and has an exit diameter of 0.6 m. Select two (2) different values of exit quality in the range of 0.2 to 0.5 and subsequently plot the power generated by the turbine in kW. (10 MARKS]

Answer 1

m The problem. Since steam expands through insulated twbine, it may be assumed as an adiabatic expansion As per the conditions Inlet 0 given Power oſp=W Turbinel Inlet Condition: T-300C, P,=4 MPa velocityCu) zoNegligible) © outlet ExH condition: P=0.075 MPa , Velocity (us)=40 m/s Exit area (A)= I (02)2=Ix(0-6)? - A2=0.2827m2 P=4MPa B=0.075 MPa T A :: Dischangele) = A2Uz=11. 303 mily S From steamtable: At Ti=300°C & Pi= 4MPa (Inlet) Specific enthalpy ch=29617 KJ/kg 77=0-05877. nogle

have quality T (P = 4 MPa From steam table: P2=0-075MPa, he= =384.44 king & hfg=2277.g kol kas (Exit) Vf=0-00103 molig & Hšg= 2:2159 milkg As mentioned in the problem, the exit do steam may X=0.2 to 0.5 We know that, specific enthalpy ha=hftX txth- Specific volume (V2) =Vf t C Ufg Now, the power output of turbineci) w=mx Chi-hz) = Chi -ha) ; , hi&he depends on quality at state-2 is given by P2=0.075 MB hfg, ufg T2 he 2 (X) &f s is given by,

vf hf hfg h1 384.44 2277.9 2961.7 kJ/kg kJ/kg kJ/kg vfg Q 0.00103 2.2159 11.308 m3/kg m3/kg m3/s -For quality (x) = 0.2 - 0.5 , the value of power developed by turbine is calculated as shown in table. The graph of Power output vs. quality cx) is shown in the graph quality(x) 0.2 h2 0.25 0.3 0.35 Specific volume at exit Mass flow rate(m) h1 v2 =Q/v2 2961.7 840.02 0.44421 25.45642827 2961.7 953.915 0.555005 20.37459122 2961.7 1067.81 0.6658 16.9840793 2961.7| 1181.705 0.776595 14.56100026 2961.7 1295.6 0.88739 12.74298786 2961.7 1409.495 0.998185 11.32856134 Power o/p =m(h1-h2) kilo Watt 54010.39472 40907.79865 32165.97799 25918.50766 21231.09208 17584.24955 0.4 Power O/p(kW) vs Quality (x) 0.45 60000 50000 40000 30000 20000 10000 0 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5