# Dual cycle-Diesel Engine question

1. Dec 26, 2015

### santeria13

1. The problem statement, all variables and given/known data
A diesel engine works on the dual combustion cycle and has a compression ratio of 20/1. At the beginning of the compression process the pressure and temperature are 1.0 bar and 22°C respectively. In the cycle, heat is added at constant volume until the pressure has increased by 50% and then at constant pressure for 7% of the swept volume. For air assume k= 1.4; cv = 0.718 kJ/kg K; cp = 1.005 kJ/kg K.

Calculate for the cycle: a) The temperature at the remaining state points in the cycle; (5 marks)

2. Relevant equations
V3/V4 = cutoff ratio (rc) V2/V1 = compression ratio (r) = 20/1 P3/P2 = pressure ratio(rp)
T2 = T1 * (r)^k-1
T3 = T1 * (r)^k-1 * rp
T4 = T1 * (r)^k-1 * rp *rc ----------------- confused on how to calculate the cutoff ratio(rc)

3. The attempt at a solution
Calculated all figures up until T4 at which the cutoff ratio is required.

Last edited: Dec 26, 2015
2. Dec 26, 2015

### SteamKing

Staff Emeritus
There's a definite relationship between a ratio and a fraction. For example, a ratio of 2:1 implies that something is 1/2 as big as something else.

A CR of 20:1 means that the volume inside the cylinder just before the injection of the fuel is 1/20 = 0.05 = 5% of the total volume when the piston is at bottom dead center.

In other words, total volume = swept volume + clearance volume

and $CR = \frac{CV}{SV + CV} = \frac{V_1}{V_2}$ as shown in the Wiki article on the Diesel cycle below

where SV = swept volume and CV = clearance volume, which means V1 = CV and V2 = SV + CV

https://en.wikipedia.org/wiki/Compression_ratio

The cutoff ratio is defined:

$α = \frac{V_3}{V_2}$, where V2 is defined as above and V3 = CV + 0.07 * SV, in this case

https://en.wikipedia.org/wiki/Diesel_cycle

You can calculate the cutoff ratio knowing the relationship between the CV and the SV given by the CR.