Mar 262013
 

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
Diesel Cycle p-V Diagram Diesel Cycle 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 Win 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

Qin = mCp(T3 − T2) kJ ………… (i)

where,

m → Mass of air in kg

Cp → 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 Wout 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

Qout = mCv(T4 − T1) kJ ………… (ii)

where,

m → Mass of air in kg

Cv → 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:

\(\mathrm{\large{\eta\,_{Th}=\eta\,_{Diesel}=}\Large{\frac{Heat\; Added\; -\; Heat\; Rejected}{Heat\; Added}} \large{ \; \times \; 100 \; \%}}\)

\(\mathrm{\large{\eta\, _{Diesel}=}\Large{\frac{Q_{in}\; -\; Q_{out}}{Q_{in}}}\large{ \; \times \; 100 \; \%}}\)

From equations (i) and (ii)

\({\mathrm{\large{\eta\, _{Diesel}=}\Large{\frac{mC_{p}\;(T_{3} \; – \; T_{2})\; – \;mC_{V}\;(T_{4}\; – \; T_{1})}{mC_{p}\;(T_{3} \; – \;T_{2})}}}  \large {\; \times \; 100 \; \%}}\)

\(\mathrm{\large{\eta\, _{Diesel}=}\LARGE{(}\large{ 1\; -\;} \Large{\frac{mC_{V}\;(T_{4}\;- \;T_{1})}{mC_{p}\;(T_{3}\; -\; T_{2})}}\LARGE{)} \large {\; \times \; 100 \; \%}}\)

\(\mathrm{\large{\eta\, _{Diesel}=}\LARGE{(}\large{ 1\; -\;} \Large{\frac{C_{V}\;(T_{4}\;- \;T_{1})}{C_{p}\;(T_{3}\; -\; T_{2})}}\LARGE{)} \large {\; \times \; 100 \; \%}}\)

\(\mathrm{\large{\eta\, _{Diesel}=}\LARGE{(}\large{ 1\; -\;}\Large{\frac{1}{\gamma}}\Large{\frac{(T_{4}\;- \;T_{1})}{ (T_{3}\;- \;T_{2})}}\LARGE{)} \large{ \; \times \; 100 \; \% \; \; \; \; \; ( Since,} \Large{\frac{C_{p}}{C_{V}}}=\large{\gamma }\large{\;\Rightarrow\;} \Large{\frac{C_{V}}{C_{p}}=\frac{1}{\gamma}})}\)

If you have any ideas or suggestions regarding diesel cycle, you can comment on this article :)

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I am a mechanical engineer with a passion for technical stuff. I am the founder and former editor-in-chief of Mechteacher.com.

  • sampath

    I get more information in your site.thank you.

    • http://mechteacher.com/ Surjeet S

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  • kunu

    what is exhaust temperature??

  • Joydip Bhowmick

    What is Expansion ratio and cut-off ratio ?

    • deesha

      expansion ratio: v1:v2
      cutt-of ratio: v1:v3

      • aravindhan Chandru

        what is the exhaust temperature
        t1 or t2

        • eric mcghee

          t4

          t1 is intake temp, and t2 is the compressesd temp before ignition

  • Kinc Voodoodoll Eagle

    when they say “the temperature before constant pressure heat addition is 761.2K” which temperature are they referring to? please advise for a diesel cycle.

    • http://mechteacher.com/ Surjeet Sankararaj

      For an ideal diesel cycle (explained in this article), they should be referring to Temperature T2.

  • karthick

    where is the mean effective pressure in diesel cycle derivation?

  • Mohamed

    Thanks for summarizing otto and diesel cycles