An ideal diesel cycle has a volumetric compression ratio of 18 and a cut-off rat

Question

An ideal diesel cycle has a volumetric compression ratio of 18 and a cut-off ratio of 1.50. At the beginning of the compression stroke, the gas temperature and pressure arc 95 kPa and 17DegreeC (290.2 K). The working fluid is air (R = 287 J/kg-K; C, = 1.005 kJ/kg-J; Cv - 0.718 kJ/kg-K; and k - 1.400), which may be treated as a calorically pcrfect gas. The net work output per unit mass for the cycle is 300 kJ/kg. Determine: (a) the thermal efficiency for the cycle; (b) the energy added as heat per unit mass during the combustion process {kJ/kg} and (c) the air temperature at the end of the combustion process {K}.

Explanation / Answer

a)   T2   = T1*(V1/V2)^k-1    = 290*18^0.4   = 921.524 K

      T3 =   V3 * T2 / V2   = 1.5 * 921.524 = 1382.287 K

      T4 = T3 * (V3 / V1)^0.4   = 1382.287 * (1/12)^0.4   = 511.594 K

      thermal efficiency = 1 - (T1(T4/T1 - 1))/(T2(T3/T2 - 1))

                                  = 1 - (290(511.594/290-1)) / (1.4*921.524(1382.287/921.524 - 1))

                                 = 1 - 221.594 / ((1.4*921.524(1382.287/921.524 - 1))

                                 = 65.648 %

b) Heat added   = 1.005 * (1382.287 - 921.524)   = 463.066 kJ/kg

c) T4 = T3 * (V3 / V1)^0.4   = 1382.287 * (1/12)^0.4   = 511.594 K

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