Troels Dyhr Pedersen.indd - Solid Mechanics

dQ
dt
= h ⋅ A ⋅
- 32 - -
( T − T )
Where h is the convective heat transfer coefficient with units W/m 2 K. Woschni
developed an expression for this coefficient, based on the empirical correlations for flow.
With HCCI combustion this expression was in need of a revision to account for the
difference with lean combustion. Junseok et al [20] made an extensive experimental study
on the instantaneous heat transfer in HCCI combustion and proposed a modified
expression for the heat transfer coefficient:
gas
sur
−0.
73
−0.
2 0.
8
h = α ⋅ L ⋅ p ⋅Tgas
⋅ v
Here, is a scaling factor which is adjusted to satisfy the total energy balance. The rest of
the left hand terms are instantaneous values. L is the characteristic length, which is
changed from being the cylinder bore in the original expression, to the instantaneous
chamber height. p and T are the pressure and temperature, respectively. v is the gas
velocity, which is divided into two separate terms, with the first being a mean gas
velocity and the second a combustion induced velocity:
C2
VdT
r
v = C S p + ( p − p
6 p V
1 mot
r r
Sp is the average piston speed and Vd is the displacement volume. Tr, pr and Vr are values
of temperature, pressure and volume at a reference location, such as intake valve closing.
p is the pressure and pmot is the motored pressure at the same reference location. The
modification to this expression is that C2 is divided by 6, since the combustion induced
velocity is much lower with HCCI combustion than with SI combustion.
The constants C1 and C2 are engine specific, but may be approximated by the
expressions:
πBw
p
C1
= 2. 28 + 3.
08 ; C2
= 0.
00324
S
Where wp is the swirl factor, which must be estimated if not provided by the engine
manufacturer.
p
)