The pressure and temperature at the beginning of compression

The pressure and temperature at the beginning of compression

The pressure and temperature at the beginning of compression of an air-standard Diesel cycle are 100 kPa and 300 K, respectively. At the end of the heat addition, the pressure is 5 MPa and the temperature is 2000 K. Determine the thermal efficiency of the cycle. (Do not interpolate and consider the closest values for this problem only)

Solution

Given,

P1 = 100 kPa

T1 = 300 K

P3 = 5 MPa = 5000 kPa

T3 = 2000 K

In diesel cycle, for combustion process, P2 = P3.

Hence, P2 = 5000 kPa

Also for compression process, P2 / P1 = (V1 / V2)^k

Taking k = 1.4 for air we get,

5000 / 100 = (V1 / V2)^1.4

V1 / V2 = 16.35

Hence, Compression ratio r_c = V1 / V2 = 16.35

Also, for compression process, T2 / T1 = (P2 / P1)^(k-1)/k

T2 / 300 = (5000 / 100)^{(1.4 - 1)/1.4}

T2 = 917.4 K

For combustion process, V2 / V3 = T2 / T3

V2 / V3 = 917.4 / 2000 = 0.45868

Now, expansion ratio re = V1 / V3 = (V1 / V2)*(V2 / V3)

= 16.35 * 0.45868

r_e = 7.5

Thermal Efficiency of diesel cycle = 1 - (1/k)(r_e^-k - r_c^-k) / (r_e^-1 - r_c^-1)

By putting values, we get efficiency = 0.6085 or 60.85%