# 4.8. Atkinson Cycle

```Gas Power Cycles
Prof. U.S.P. Shet , Prof. T. Sundararajan and Prof. J.M . Mallikarjuna
4.8. Atkinson Cycle:
Atkinson cycle is an ideal cycle for Otto engine exhausting to a gas turbine. In this cycle
the isentropic expansion (3-4) of an Otto cycle (1-2-3-4) is further allowed to proceed to
the lowest cycle pressure so as to increase the work output. With this modification the
cycle is known as Atkinson cycle. The cycle is shown on p-v and T-s diagrams in
Fig.4.8. Processes involved are:
Process 1-2: Reversible adiabatic compression (v1 to v2).
Process 2-3: Constant volume heat addition.
Process 3-4: Reversible adiabatic expansion (v3 to v4).
Process 4-1: Constant pressure heat rejection.
3
2
4'
1
Volume
(a)
4
Gas Power Cycles
Prof. U.S.P. Shet , Prof. T. Sundararajan and Prof. J.M . Mallikarjuna
3
4'
2
4
1
Entropy
(b)
Fig.4.8. Atkinson cycle on p-v and T-s diagrams
Thermal Efficiency:
Heat supplied = C v ( T3 - T2 )
Heat rejected = Cp ( T4 - T1 )
Net workdone = C v ( T3 - T2 ) - Cp ( T4 - T1 )
ηth =
C v ( T3 - T2 ) - Cp ( T4 - T1 )
C v ( T3 - T2 )
= 1-
γ ( T4 - T1 )
Let, r =
( T3 - T2 )
v1
= CR
v2
T2 = T1 r γ - 1
T3
P
= 3 = rp = Pressure ratio
T2
P2
Gas Power Cycles
Prof. U.S.P. Shet , Prof. T. Sundararajan and Prof. J.M . Mallikarjuna
T3 = T2 rp = T1 r γ - 1 rp
⎛P ⎞
T3
=⎜ 3⎟
T4
⎝ P4 ⎠
γ -1
γ
⎛P ⎞
= ⎜ 3⎟
⎝ P1 ⎠
γ -1
γ
⎛P P ⎞
= ⎜ 3. 2⎟
⎝ P2 P1 ⎠
γ -1
γ
⎛ P ⎞
= ⎜ rp . 2 ⎟
⎝ P1 ⎠
since,
γ
⎛v ⎞
P2
= ⎜ 1 ⎟ = rγ
P1
⎝ v2 ⎠
and
T4 =
T3
γ -1
rp γ
ηth
T1 rp r γ - 1
=
γ -1
rp γ
rγ - 1
=
rγ - 1
1
⎡
⎤
⎢ rγ - 1 ⎥
p
⎥
=1-γ ⎢
⎢ rp - 1 r γ - 1 ⎥
⎢
⎥
⎣
⎦
(
)
1
T1 rpγ
γ -1
γ
=
γ -1
rp γ . r γ−1
```