Diesel Cycle

 

Diesel cycle is a gas power cycle invented by Rudolph Diesel in the year 1897. It is widely used in diesel engines.
Diesel cycle is similar to Otto cycle except in the fact that it has one constant pressure process instead of a constant volume process (in Otto cycle).
Diesel cycle can be understood well if you refer its p-V and T-s diagrams.

p-V and T-s Diagrams of Diesel Cycle:

p-V Diagram	T-s Diagram

Processes in Diesel Cycle:

Diesel cycle has four processes. They are:

1. Process 1-2: Isentropic (Reversible adiabatic) Compression
2. Process 2-3: Constant Pressure (Isobaric) Heat Addition
3. Process 3-4: Isentropic Expansion
4. Process 4-1: Constant Volume (Isochoric) Heat Rejection

Process 1-2: Isentropic Compression

In this process, the piston moves from Bottom Dead Centre (BDC) to Top Dead Centre (TDC) position. Air is compressed isentropically inside the cylinder. Pressure of air increases from p₁ to p₂, temperature increases from T₁ to T₂, and volume decreases from V₁ to V₂. Entropy remains constant (i.e., s₁ = s₂). Work is done on the system in this process (denoted by W_in in the diagrams above).

Process 2-3: Constant Pressure Heat Addition

In this process, heat is added at constant pressure from an external heat source. Volume increases from V₂ to V₃, temperature increases from T₂ to T₃ and entropy increases from s₂ to s₃.
Heat added in process 2-3 is given by
Q_in = mC_p(T₃ − T₂) kJ ………… (i)
where,
m → Mass of air in kg
C_p → Specific heat at constant pressure in kJ/kgK
T₂ → Temperature at point 2 in K
T₃ → Temperature at point 3 in K

Process 3-4: Isentropic Expansion

Here the compressed and heated air is expanded isentropically inside the cylinder. The piston is forced from TDC to BDC in the cylinder. Pressure of air decreases from p₃ to p₄, temperature decreases from T₃ to T₄, and volume increases from V₃ to V₄. Entropy remains constant (i.e., s₃ = s₄). Work is done by the system in this process (denoted by W_out in the p-V and T-s diagrams above).

Process 4-1: Constant Volume Heat Rejection

In this process, heat is rejected at constant volume (V₄ = V₁). Pressure decreases from P₄ to P₁, temperature decreases from T₄ to T₁ and entropy decreases from s₄ to s₁.
Heat rejected in process 4-1 is given by
Q_out = mC_v(T₄ − T₁) kJ ………… (ii)
where,
m → Mass of air in kg
C_v → Specific heat at constant volume in kJ/kgK
T₂ → Temperature at point 2 in K
T₃ → Temperature at point 3 in K
For a good understanding of every process, refer the p-V and T-s diagrams above

Air-standard Efficiency of Diesel Cycle:

Air-standard efficiency (or thermal efficiency) of diesel cycle is given by:

ηTh=ηDiesel=HeatAdded−HeatRejectedHeatAdded×100%

 ηDiesel=Qin−QoutQin×100%

From equations (i) and (ii)

ηDiesel=mCp(T3–T2)–mCV(T4–T1)mCp(T3–T2)×100%

ηDiesel=(1−mCV(T4−T1)mCp(T3−T2))×100%

ηDiesel=(1−CV(T4−T1)Cp(T3−T2))×100%

ηDiesel=(1−1γ(T4−T1)(T3−T2))×100%(Since,CpCV=γ⇒CVCp=1γ)