Power Cycles_ Diesel Cycle
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Power Cycles – The Carnot cycle (totally reversible, int. and ext.) is the ideal cycle for heat engines – The Otto cycle is the ideal cycle for spark ignition automobile engines – The Diesel cycle is the ideal cycle for compression ignition engines – The Brayton cycle is the ideal cycle for gas turbine engines – The Rankine cycle is the ideal cycle for vapor power plants
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Diesel Cycle – The ideal cycle for compression-ignition engines – Diesel cycles are designed to operate at higher compression ratios, typically between 12~24 • The 4 cycles of the Diesel engine are: (1--------2) Isentropic compression (2--------3) P=constant heat addition (combustion process) (3--------4) Isentropic expansion (4--------1) Constant volume heat rejection WMM
Gasoline Vs. Diesel engines fuel
Spark Plug
Fuel spray
Sparks
Air-fuel mixture
v
Gasoline Engine
Air
v
Diesel Engine
In Diesel engines, the spark plug and carburetor is replaced by a fuel injector and only air is compressed during the compression process WMM
Diesel Cycle •
The ideal Diesel cycle consists of four internally reversible processes (1------2) Isentropic compression (2------3) P=constant heat addition “combustion process” (3------4) Isentropic expansion
Team exercise: draw the P-v diagram for the Diesel cycle:
(4------1) Constant volume heat rejection T-s diagram
P
P2=P3
T
(3)
qin
(2) (4) (4)
qout
(1)
v1=v4
qout
(1)
v v4=v1
s2=s1
s3=s4
s
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Diesel Cycle •
The ideal Diesel cycle consists of four internally reversible processes (1------2) Isentropic compression (2------3) P=constant heat addition “combustion process” (3------4) Isentropic expansion (4------1) Constant volume heat rejection
P
T-s diagram
qin
P-v diagram
p2=p3
P2=P3
T
(3)
(3)
qin
(2) (2)
s3=s4
(4) (4)
s1=s2
qout
(1)
v1=v4
qout
(1)
v v4=v1
s2=s1
s3=s4
s
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Diesel Cycle P
qin
p2=p3
T-s diagram
P-v diagram P2=P3
T
(3) (2)
s3=s4
(3)
qin
(2) (4) (4)
qout
s1=s2
(1)
v1=v4
qout
(1)
v v4=v1
qin = h3 − h2 q
in
,
= h3 − h2 = c p (T 3 − T 2)
s2=s1
s3=s4
s
q out = u 4 − u1 q
out
= u 4 − u1 = cv (T 4 − T 1) WMM
Diesel Cycle •
Cutoff ratio rc » Is defined as the ratio of the cylinder volumes before and after the combustion process: Combustion process
Cutoff ratio
V r = V
3
c
2
v = v
P2 = P3
3 2
vmin
vmax=v4=v1
(1------2) Isentropic compression (2------3) P=constant heat addition
Team exercise: write below the compression ratio for the Diesel cycle:
(3------4) Isentropic expansion (4------1) Constant volume heat rejection WMM
Diesel Cycle •
Cutoff ratio rc » Is defined as the ratio of the cylinder volumes before and after the combustion process: Combustion process
Cutoff ratio
V r = V
3
c
2
v = v
P2 = P3
3 2
vmin
vmax=v4=v1
(1------2) Isentropic compression (2------3) P=constant heat addition (3------4) Isentropic expansion, (4------1) Constant volume heat rejection
Compression ratio
r = V max = V 1 =
V
min
V
2
v v
1 2
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h Vs. u Diesel Cycle Noting that the Diesel cycle is executed in a piston-cylinder (closed system) the amount of heat transferred to the working fluid at P=constant and and rejected from it at V=constant can be expressed as: P2 = P3
Process (2-------3)
E in − E out = ∆ system
q −w
∴
q
in
−
b , out
in
3
2
2
wb , out = ∫ p2 dv = p2 ∫ dv = p2 (v3 − v2 )
= u3 − u 2
vmin
p (v 3−v 2) = u − u 3
2
3
q
2
= h2
= h3
qin = u 3 + p3 v3 − (u 2 + p 2 v 2 ) Or in terms of temperatures
∴
f (T )
qin
q
in
using
vmax
p2= p3
in
= u3 − u 2 +
∴
p (v 3−v 2) 2
q = h −h 3
in
cp =
2
∂h ⇒ ∆h = c p * ∆T ∂T
= h3 − h2 = c p (T 3 − T 2)
D-1 WMM
Diesel Cycle
h Vs. u
Employing process (4-------1) P2 = P3
The heat X-fer out is given by:
−q
out
= u1 − u 4
q
out
= u 4 − u1 vmin
Or in terms of temperatures
∴
f (T )
qin
q
out
using
cv =
= u 4 − u1 = cv (T 4 − T 1)
vmax
∂u ⇒ ∆u = c v * ∆T ∂T
D-2
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Diesel Cycle The thermal efficiency of the ideal Diesel cycle under the cold-air-standard assumptions becomes: = 4 − 1 = v ( 4 − 1) D-2
η
=w q
net
Th , Diesel
=
q
in
−q
q
in
out
in
q = 1− q
q u u c T T q = h − h = c (T − T ) out
out in
k=
∴
η
(T − T ) c = 1− c (T − T ) v
Th , Diesel
p
⎛T 4 ⎞ T ⎜ −1⎟ ⎝ T1 ⎠ = 1− ⎛T3 ⎞ k T 2⎜ −1⎟ ⎝T 2 ⎠
Th , Diesel
c c
p
2
D-1
(specific heat ratio)
η
(T − T ) = 1− k (T − T ) 1
4
Th , Diesel
3
2
3
3
p
v
1
4
2
2
Utilizing the cutoff ratio rc and the isentropic Ideal gas relations for processes 1----2 and 3----4 the above expression simplifies to eq D-3
1
η
3
in
D-3
k ⎡ −1 ⎤ 1 r c η Th, Diesel = 1 − k −1 ⎢⎢ k ( − 1) ⎥⎥ r ⎣ rc ⎦
T1 ⎛ v 2 ⎞ = ⎜⎜ ⎟⎟ T2 ⎝ v1 ⎠
k −1
⎛v = ⎜⎜ 3 ⎝ v4
⎞ ⎟⎟ ⎠
k −1
=
T4 T3
Solve for T4/T1 and T3/T2 and substitute into equation D-3 to obtain the efficiency
c k= c
p v
V v r = = Cutoff ratio V v r = V max = V 1 = v1 Compression ratio WMM V min V 2 v2
Specific heat ratio
3
3
2
2
c
Diesel Cycle k ⎡ −1 ⎤ 1 r c η Th, Diesel = 1 − k −1 ⎢⎢ k ( − 1) ⎥⎥ r ⎣ rc ⎦
Cutoff ratio
Compression ratio
r
c
=V3 =
V
2
v v
3 2
r = V max = V 1 =
V
min
V
2
v v
1 2
K = 1.4
Plotted
•Thermal efficiency of the ideal Diesel cycle as function of compression ratio and cutoff ratios of 1, 2, 3, and 4. • At rc = 1 implies that all the heat (combustion process) would take place at constant volume WMM
Diesel Cycle
η •
•
Th , otto
= 1−
1
r
k −1
k 1 ⎡ rc − 1 ⎤ η Th, Diesel = 1 − k −1 ⎢⎢ k ( − 1) ⎥⎥ r ⎣ rc ⎦
By comparing the efficiencies of the Diesel and Otto cycles the efficiency of the Diesel cycle differs from the efficiency of an Otto cycle by the quantity in the brackets The quantity present in the brackets for the Diesel cycle is always greater than 1. therefore,
η th ,Otto > η th , Diesel If only if both cycles are operating on the same compression ratio WMM
Diesel Cycle • The Diesel cycle is the ideal cycle for CI (internal combustion) engines • The CI engine, first proposed by Rudolph Diesel in the 1890s, is very similar to the SI (spark ignition engines) of the Otto cycle • The only thing that differs between the Otto and Diesel cycle is the method to ignite the combustion » In the Otto cycle (spark-ignition engines also known as gasoline engines) the air-fuel mixture is compressed to a temperature that is below the autoignition temperature of the fuel and the combustion process is initiated by firing a spark plug » In the Diesel cycle (also known as the internal combustion engine) the air is compressed to a temperature that is above the autoignition temperature of the fuel, and combustion starts on contact as the fuel is injected into the hot air
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Diesel Cycle • Remember that Diesel engines operate at much higher compression ratios than the spark-ignition engines • The Diesel engines also burn the fuel more completely since they usually operate lower resolutions per minute than sparkignition engines • Thermal efficiencies of large diesel engines range from about 35 to 40 percent • The higher efficiency and lower fuel costs of diesel engines make them the clear choice in application requiring a relatively large amount of power such as in: » » » » »
Locomotive engines Emergency power generation units Large ships and Heavy trucks As an example of how large a diesel engine can be, a 12-cylinder diesel engine built in 1964 by the Fiat Corp. of Italy had a normal power output of 25,200 hp (18.8 MW) at 122rpm, a cylinder of 90 cm, and a stroke of 91 cm.
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Diesel Cycle •
The ideal Diesel cycle consists of four internally reversible processes
T-s and P-v diagrams for the ideal Otto cycle
P-v diagram
T-s diagram
T-s and P-v diagrams for the ideal Diesel cycle
P-v diagram
T-s diagram WMM
Diesel Cycle Consider a Diesel cycle when the specific heats vary with temperature (Air-Standard Assumptions)
Similar to the OTTO cycle the air tables account explicitly for the variation of the specific heats with temperatures
Relative volumes
v r2
v2 = v r1 v1
v2 1 v r2 = v r2 = v r1 v1 r
r=
v1 v2
Compression ratio
Process 2-------3
P2V2 P3V3 = T2 T3
T3 =
V3 P 3 V3 T2 = rcT2 T 2 P2 = P3 T3 = V2 P2 V2
rc =
V3 cutoff ratio V2 WMM
Diesel Cycle Process 3-------4
V4 V4 V2 = V3 V2 V3
V4 = V1
V4 V1 V2 r = = V3 V2 V3 r c
(Air-Standard Assumptions)
η=
wcycle qin
qin − q out q out u 4 − u1 = = 1− = 1− qin qin h3 −h 2
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Diesel Cycle • Ideal Gas Isentropic Processes: Cold-Air-Standard Analysis (constant specific heats at room temperature). ⎞ ⎛V ⎞ ⎟⎟ = ⎜⎜ 1 ⎟⎟ ⎠ s =const ⎝ V2 ⎠
k −1
⎛ T4 ⎜⎜ ⎝ T3
⎞ ⎛V ⎞ ⎟⎟ = ⎜⎜ 3 ⎟⎟ ⎠ s =const ⎝ V4 ⎠
k −1
⎛ P2 ⎜⎜ ⎝ P1
⎞ ⎛V ⎞ ⎟⎟ = ⎜⎜ 1 ⎟⎟ ⎠ s =const ⎝ V2 ⎠
k
⎛ P4 ⎜⎜ ⎝ P3
⎞ ⎛V ⎞ ⎟⎟ = ⎜⎜ 3 ⎟⎟ ⎠ s =const ⎝ V4 ⎠
k
⎛ T2 ⎜⎜ ⎝ T1
Cutoff Ratio
V3 v3 = rc = V2 v 2
Compression Ratio
Vmax V1 v1 r = = = Vmin V2 v 2
k=
Cp Cv
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Diesel Cycle and assuming constant specific heats
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