# Dual cycle-Diesel Engine question

• santeria13
In summary, a diesel engine works on the dual combustion cycle with a compression ratio of 20/1. The temperature at the beginning of the compression process is 22°C and heat is added at constant volume until the pressure increases by 50%. The remaining steps involve adding heat at constant pressure for 7% of the swept volume. The cutoff ratio, which is the ratio of the volume of air when fuel is added to the volume of air after the fuel and air mixture stops burning, can be calculated by using the relationship between the clearance volume and swept volume given by the compression ratio. This can then be used to find the remaining temperature points in the cycle.
santeria13

## Homework Statement

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)

## Homework 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)

## The Attempt at a Solution

Calculated all figures up until T4 at which the cutoff ratio is required.

Last edited:
santeria13 said:
I am working though a question which states that the compression ratio of a diesel engine is 20/1 . This allows me to find the first 3 temperatures until the constant pressure stage. I do this using the formula :
T2 = T1 * (Compression ratio)^1-k where k is 1.4 .

However, after T3, the cutoff ratio must be used instead of the compression ratio in a similar formula which writes as follows:

T4 = T3 * (cutoff ratio)^1-k where k is again 1.4 .

The cutoff ratio is the ratio of the volume of air when fuel is added over the volume of air once the fuel and air mixture has stopped burning.

The question states that the piston moves 7% of the swept volume during that time (between fuel being added to end of burning).

To get a better idea, the compression ratio is defined as
clearence volume + swept volume / clearance volume

so I assumed the cuttoff ratio would be 0.07 x 19 = 1.33 but I am not sure this is the right way to go.
The reason I did this is because compression ratios are generally given as a number and not a fraction.

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.

## What is the Dual Cycle-Diesel Engine?

The Dual Cycle-Diesel Engine is a type of internal combustion engine that combines the principles of both the Otto cycle and the Diesel cycle. It uses a combination of spark ignition and compression ignition to power the engine.

## How does the Dual Cycle-Diesel Engine work?

The Dual Cycle-Diesel Engine works by using two different cycles to generate power. The Otto cycle, also known as the spark ignition cycle, uses a spark plug to ignite a fuel-air mixture in the engine's combustion chamber. The Diesel cycle, also known as the compression ignition cycle, uses high compression and heat to ignite fuel injected into the combustion chamber.

## What are the advantages of the Dual Cycle-Diesel Engine?

One of the main advantages of the Dual Cycle-Diesel Engine is its efficiency. By combining the two cycles, it can achieve higher compression ratios and more complete combustion, resulting in better fuel efficiency. It also has lower emissions compared to traditional diesel engines.

## What are the applications of the Dual Cycle-Diesel Engine?

The Dual Cycle-Diesel Engine is commonly used in heavy-duty vehicles such as trucks and buses, as well as in marine and industrial applications. It is also being explored as a potential alternative to traditional gasoline and diesel engines in passenger cars.

## What are the challenges of implementing the Dual Cycle-Diesel Engine?

One of the main challenges of implementing the Dual Cycle-Diesel Engine is the complexity of the technology. It requires precise control of both spark ignition and compression ignition, as well as advanced engine management systems. Additionally, the cost of development and production may be higher compared to traditional engines.

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