4.5 Air Standard Diesel Cycle: - nptel - Indian Institute of Technology ...

Gas Power Cycles Prof. U.S.P. Shet , Prof. T. Sundararajan and Prof. J.M . Mallikarjuna
4.5 Air Standard Diesel Cycle:
Air standard diesel cycle is a idealized cycle for diesel engines. It is as shown on P-v
and T-s diagrams. The processes in the cycle are as follows:
Indian Institute of Technology Madras
2
2
1
3
Volume
Entropy
Fig.4.5. Air standard diesel cycle on p-v and T-s diagrams.
1
3
4
4

Gas Power Cycles Prof. U.S.P. Shet , Prof. T. Sundararajan and Prof. J.M . Mallikarjuna
Process 1-2: Reversible adiabatic Compression.
Process 2-3: Constant pressure heat addition.
Process 3-5: Reversible adiabatic Compression.
Process 4-1: Constant volume heat rejection.
Consider ‘m’ kg of working fluid. Since the compression and expansion processes are
reversible adiabatic processes, we can write,
Now, we can write, thermal efficiency as,
Indian Institute of Technology Madras
( ) ( )
Heat sup plied = m C T - T = h - h
p 3 2 3 2
( ) ( )
Heat rejected = m C T - T = u - u
v 4 1 4 1
Workdone = m Cp ( T 3 - T 2) - m Cv( T 4 - T1)
η =
th
( ) ( )
m C ( T - T )
m C T - T - m C T - T
p 3 2 v 4 1
p 3 2
1 ⎛T - T ⎞
= 1 - ⎜ ⎟
4 1
γ ⎝ T3 - T2
⎠
v v
T 2 = T 1 r ; r = =
v v
2 2
γ-1
1 4
2 2
T3 v3
= = r c = cutoff ratio
T v
T r T r T r γ
= =
3 c 2 c 1
γ-1
⎛ v3 ⎞ v4
4 3⎜ ⎟ 3
v4 v3
⎛ ⎞
T = T = T ⎜ ⎟
⎝ ⎠ ⎝ ⎠
-1
γ-1

Gas Power Cycles Prof. U.S.P. Shet , Prof. T. Sundararajan and Prof. J.M . Mallikarjuna
Hence,
Indian Institute of Technology Madras
1-γ
⎛v4 v2
⎞
3
⎝v2 v3
⎠
= T ⎜ . ⎟
= r c T 1 r ⎜ ⎟
r
⎛ r ⎞
= T3 ⎜ ⎟
⎝rc⎠ 1-γ
1-γ
γ-1 ⎛ r ⎞
γ
; T 4 = r c T1
⎝ c ⎠
1 ⎧ γ
⎪ r c T1- T ⎫
1 ⎪
η th = 1 - ⎨ γ-1 γ-1
⎬
γ
⎩⎪r c r T 1 - r T1⎭⎪
⎧ γ
1-γ ⎪ rc-1 ⎫⎪
= 1 - r ⎨ ⎬
⎪⎩ γ ( rc-1) ⎭⎪
From the above equation, it is observed that, the thermal efficiency of the diesel engine
can be increased by increasing the compression ratio, r, by decreasing the cut-off ratio,
α2, or by using a gas with large value of γ. Since the quantity (r γ -1)/γ(rp-1) in above
equation is always greater than unity, the efficiency of a Diesel cycle is always lower
than that of an Otto cycle having the same compression ratio. However, practical Diesel
engines uses higher compression ratios compared to petrol engines.
Mean effective Pressure:
=
Net workdone
mep =
Displacement volume
( ) ( )
m C T - T - m C T - T
p 3 2 v 4 1
v - v
1 2
⎛ v2 ⎞ ⎛ 1 ⎞
v1 - v 2 = v1⎜1 - ⎟ = v1⎜1 - ⎟
⎝ v1⎠ ⎝ r⎠
⎛r - 1⎞
⎝ r ⎠
= m R T1
⎜ ⎟
( )
m Cv γ -1 T1 ⎛r - 1⎞
= ⎜ ⎟
P ⎝ r ⎠
1

Gas Power Cycles Prof. U.S.P. Shet , Prof. T. Sundararajan and Prof. J.M . Mallikarjuna
Indian Institute of Technology Madras
mep
=
( ) ( )
m C T - T - m C T -T
p 3 2 v 4 1
⎛γ- 1⎞⎛r - 1⎞
m C T ⎜ ⎟⎜ ⎟
P ⎝ r ⎠
v 1
⎝ 1 ⎠
⎛ P 1 r ⎞⎛ 1 ⎞⎧⎪⎛T
3 - T2
⎞ ⎛T 4 - T1
⎞⎫⎪
= ⎜ -
r - 1
⎟⎜ ⎟⎨γ⎜
⎟ ⎜ ⎟⎬
⎝ ⎠⎝γ- 1⎠⎪⎩ ⎝ T1 ⎠ ⎝ T1
⎠⎭⎪
( c ) ( c )
⎧ γ-1 γ ⎫
⎪
γ r r - 1 - r - 1
⎪
= P 1 r⎨
⎬
⎪ ( r - 1 )( γ - 1)
⎩ ⎭
⎪
Difference between Actual Diesel and the Otto Engines:
Otto Engine
1. Homogenous mixture of fuel and air
formed in the carburetor is supplied
to engine cylinder.
2. Ignition is initiated by means of an
electric spark plug.
3. Power output is controlled by varying
the mass of fuel-air mixture by
means of a throttle valve in the
carburetor.
Diesel Engine
1. No carburetor is used. Air alone is
supplied to the engine cylinder. Fuel is
injected directly into the engine
cylinder at the end of compression
stroke by means of a fuel injector.
Fuel-air mixture is heterogeneous.
2. No spark plug is used. Compression
ratio is high and the high temperature
of air ignites fuel.
3. No throttle value is used. Power output
is controlled only by means of the
mass of fuel injected by the fuel
injector.