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Dual Cycle

The dual cycle is a model that more closely approximates the actual pressure-volume variation in a compression ignition engine compared to the air standard diesel cycle. In the dual cycle, heat is added to the air in two steps - partly at constant volume and partly at constant pressure. The efficiency of the dual cycle depends on the compression ratio, expansion ratio, and cutoff ratio and can be expressed as a function of these parameters.

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Rajesh Panda
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1K views2 pages

Dual Cycle

The dual cycle is a model that more closely approximates the actual pressure-volume variation in a compression ignition engine compared to the air standard diesel cycle. In the dual cycle, heat is added to the air in two steps - partly at constant volume and partly at constant pressure. The efficiency of the dual cycle depends on the compression ratio, expansion ratio, and cutoff ratio and can be expressed as a function of these parameters.

Uploaded by

Rajesh Panda
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as DOCX, PDF, TXT or read online on Scribd
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DUAL CYCLE

The air standard diesel cycle does not stimulate extactly the pressure volume variation in an actual
compression ignition engine, where the fuel injection is started before the end of compression stroke. A
closer approximation is the limited pressure cycle in which some part of heat is added to air at constant
volume and the remainder at constant pressure.

Heat is added reversible, partly at constant volume (2-3) and partly at constant pressure (3-4)
Heat supplied (Q1) = mcv(T3 – T2) + mcp(T4 – T3)
Heat rejected (Q2) = mev(T5 – T1)
Q
()  1  2
Q1
Efficiency
mc v (T5  T1 )
eff.  1 
mc v (T3  T2 )  mc p (T4  T3 )
Now
1
(rk ) 
2
Compression ratio
5
(re ) 
4
Expansion ratio
4
(rc ) 
3
Cut-off ratio
p3
(rp ) 
p2
Constant vol. pressure ratio
Now
  
rk  1  1  3
 2 3  4
 rc × re
rk
re 
rc
Process 3-4
 T T
rc  4  4  T3  4
 3 T3 rc
P V  mRT
V
T = const.
Process 2-3
T2 P2 r T
  T2  T3  1  T2  4
T3 P3 rp rprc
P V  mRT
P
T = const.
Process 1-2
 1
T1  v 2   1  T4
    T1  T2    T1   1
T2  v1  r
 k   1  rk rprc
PV  = const

PV = mRT PV
PV = T
Process 4-5
 1
T5   4  T4  r   1
   T5   1
 T4  c 
T4   5  re  rk   1 
T5  T1
eff.  1 
(T3  T2 )  (T4  T3 )
 r  1  T
T4  c  1    14
 k  k rprc
r r
1
 T4 T4   r  1
      c 
r
 c r r
p c   rc 
rp rc  1 rprc   1
 1
rk .rprc rk  1rp
1  1
r p  1  r  1
  c
(rp  1)  rp (rc  1)

rc rp  rc  rp
1 rprc   1
Dual  1   1 .
rk  rP  1  rP (rc  1)

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