Solution Analysis

For solution analysis, Simcenter STAR-CCM+ In-cylinder calculates the apparent heat release rate, the net indicated mean effective pressure (IMEP), and specific emissions as follows:
Apparent Heat Release Rate

The apparent heat release rate is calculated from the cylinder volume at any crank angle along with the pressure data as:

Figure 1. EQUATION_DISPLAY
d q a d t = 1 γ 1 V d p d t + γ γ 1 p d V d t
(648)

with:

Figure 2. EQUATION_DISPLAY
q a = q c + q w + q s
(649)
Figure 3. EQUATION_DISPLAY
γ = C p C v
(650)

where:

  • q a is the apparent heat release.
  • q c is the heat transfer due to combustion.
  • q w is the wall heat transfer.
  • q s is the heat transfer due to spray.
  • γ is the specific heat ratio.
  • C p is the specific heat at constant pressure.
  • C v is the specific heat at constant volume.
  • t is the time.
  • p is the pressure.
  • V is the cylinder volume.
IMEP
The indicated mean effective pressure is calculated as:
Figure 4. EQUATION_DISPLAY
I M E P = W N D
(651)

where the net indicated work/cycle (work done on the piston) is calculated as:

Figure 5. EQUATION_DISPLAY
W N = c y l i n d e r p d V
(652)

and D is the cylinder displacement given by Eqn. (585).

Specific Emission
The specific CO emission and the specific NOx emission are calculated as:
Figure 6. EQUATION_DISPLAY
E s p e c i f i c = { c y l i n d e r ρ Y C O / N O x d V I M E P D 0 i f I M E P D > 0 i f I M E P D 0
(653)

where Y C O / N O x is the mass fraction of CO or NOx, respectively.