Page 223 - Air pollution and greenhouse gases from basic concepts to engineering applications for air emission control

7.2 Liquid Fuel Combustion 199

As a simplification, the term in {} can be assumed constant at quasi-steady state.
Then the droplet diameter over time can be determined by integration from the
initial droplet diameter r s ¼ r s0 at t = 0 and r s at any time t.

r Z s Z t k c p T 1 T s Þ
ð
r s dr s ¼ ln 1 þ dt ð7:12Þ
q c p h fg
l
r s0 0

tk c p T 1 T s Þ
ð
1 2 2
r r s ¼ ln 1 þ ð7:13Þ
s0
2 q c p h fg
l
Equation (7.13) can be used to estimatethe time for a liquid fuel droplet to complete
vaporization, or life time of the droplet. Substitute r s = 0 into Eq. (7.13), we have
r 2 s0
t e ¼ h i ð7:14Þ
ð
2k c p T 1 T s Þ
ln 1 þ
q l c p h fg
The lifetime of the droplets increases with their sizes, and it is in the order of
millisecond [42]. The life time t e is important to characterize the combustion effi-
ciency of atomized liquid fuel droplets and the consequent air emissions. If t e is longer
than the residence time of the combustion system, the droplets will not be burned
completely because of incomplete vaporization. As a result, liquid fuel droplets exist
in the flue gas (or exhaust). They may be part of the particulate emissions. Meanwhile
residual fuel evaporation continues but these extra vapors are not burned at low
temperature; this result in extra volatile organic compound (VOC) emissions.
2
Since t e is proportional to the square of initial droplet diameter, r ; it is
s0
imperative that fine spray droplets favor combustion efficiency and lower the air
emissions. However, the upper limit of the droplet size depends on the design of
nozzles employed.

7.2.2 Vapor Combustion

When the combustible vapor is mixed with the oxidizers at high temperature, com-
bustion takes place in a thin flame surrounding the droplet. As depicted in Fig. 7.2,
vapor concentration decreases from the droplet surface r s to the flame r f , and vapor is
oxidized instantaneously in the thin flame. Oxidizer is transported to the flame from
the surrounding environment by diffusion that is driven by the concentration gradient.
Part of the heat produced by the combustion is transferred to the surface of the
fuel droplet to sustain the droplet vaporization. Combustion in the zone between the
flame and the droplet surface is highly fuel rich due to the great fuel vapor concen-
tration, and the combustion products join the vapor as combustible gases. The
combustion at r > r f is fuel lean and complete owing to the sufficient oxygen supply.