A simple Rankine cycle with R-22 as the working fluid is to be used as a bottomi

Question

A simple Rankine cycle with R-22 as the working fluid is to be used as a bottoming cycle for an electrical generating facility driven by the exhaust gas from a Diesel engine as the high temperature energy source in the R-22 boiler. Diesel inlet conditions are 100 kPa, 20°C, the compression ratio is 20, and the maximum temperature in the cycle is 2800°C. Saturated vapor R-22 leaves the bottoming cycle boiler at 110°C, and the condenser temperature is 30°C. The power output of the Diesel engine is 1 MW. Assuming ideal cycles throughout, determine
a. The flow rate required in the diesel engine.
b. The power output of the bottoming cycle, assuming that the diesel exhaust is cooled to 200°C in the R-22 boiler

Explanation / Answer

Diesel cycle information given means: Inlet state: P1 = 100 kPa, T1 = 20 oC, Compression ratio: v1/v2 = 20, High temperature: T3 = 2800oC, Power output: W.DIESEL = 1.0 MW Rankine cycle information given means: Boiler exit state: T7 = 110 oC, x7 = 1.0 Condenser temperature: T5 = T8 = 30oC a) Consider the Diesel cycle T2 = T1(v1/v2)k-1 = 293.2(20)0.4 = 971.8 K P2 = P1(v1/v2)k = 100(20)1.4 = 6629 kPa qH = CP0(T3 - T2) = 1.004(3073.2 - 971.8) = 2109.8 kJ/kg v1 = 0.287 × 293.2100 = 0.8415, v2 = 0.841520 = 0.04208 v3 = v2(T3/T2) = 0.04208(3073.2/971.8) = 0.13307 T4 = T3? ? ? ???v3v4k-1 = 3073.2??? ???0.133 070.84150.4 = 1469.6 K qL = 0.717(293.2 - 1469.6) = -843.5 kJ/kg wNET = 2109.8 - 843.5 = 1266.3 kJ/kg m.AIR = W.NET/wNET = 1000/1266.3 = 0.79 kg/s b) Consider the Rankine cycle s8 = s7 = 0.60758 = 0.2399 + x8 × 0.4454, x8 = 0.8255 h8 = 64.59 + 0.8255 × 135.03 = 176.1 kJ/kg wT = h7 - h8 = 198.0 - 176.1 = 21.9 kJ/kg -wP = v5(P6 - P5) = 0.000774(3978.5 - 744.9) = 2.50 h6 = h5 - wP = 64.6 + 2.5 = 67.1 kJ/kg qH = h7 - h6 = 198.0 - 67.1 = 130.9 kJ/kg Connecting the two cycles. Q.H available from Diesel exhaust cooled to 200 oC: Q.H = 0.79 × 0.717(1469.6 - 473.2) = 564 kW ? m.R-12 = Q.H/qH = 564/130.9 = 4.309 kg/s W.R-12 = 4.309(21.9 - 2.5) = 83.6 kW

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