Question

A diesel engine with CR= 20 has inlet at 520R, a maximum pressure of 920 psia and maximum temperature of 3200 R. With cold air properties find the cutoff ratio, the expansion ratio v4/v3, and the exhaust temperature.

Answer 1

Cut-off ratio
`(V_3)/(V_2)=6.15`

Cxpansion ratio
`(V_4)/(V_3)=3.25`

The exhaust temperature
`T_4=1997.5R`

Step-by-step explanation:

Compression ratio CR(r)=20

`(V_1)/(V_2)=20`

`P_2=P_3=920 psia`

`T_1=520 R ,T_(max)=T_3,T_3=3200 R`

We know that for air γ=1.4

If we assume that in diesel engine all process is adiabatic then

`(T_2)/(T_1)=r^(\gamma -1)`

`(T_2)/(520)=20^(1.4 -1)`

`T_2=1723.28R`

`(V_3)/(V_2)=(T_3)/(T_2)`

`(V_3)/(V_2)=(3200)/(520)`

So cut-off ratio
`(V_3)/(V_2)=6.15`

`(V_1)/(V_2)=(V_4)/(V_3)*(V_3)/(V_2)`

Now putting the values in above equation

`\frac20=(V_4)/(V_3)* 6.15`

`(V_4)/(V_3)=3.25`

So expansion ratio
`(V_4)/(V_3)=3.25`.

`(T_4)/(T_3)=(expansion\ ratio)^(\gamma -1)`

`(T_3)/(T_4)=(3.25)^(1.4 -1)`

`T_4=1997.5R`

So the exhaust temperature
`T_4=1997.5R`