Environmental Engineering Reference
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front at some distance from the surface. Now, the definition for the Spalding
number for this situation becomes
B
q
=
Δ
h
c
=ϑ
+c
p
T
∞
−
ð
T
boil
Þ
h
fg
in which the enthalpy of combustion (
Δ
h
c
) and the oxidizer-to-fuel stoichio-
metric ratio (
ϑ
) have been added. For octane, the enthalpy of combustion is
kg
−1
, and the stoichiometric ratio is given by
Δ
h
c
= 44,791 kJ
ϑ
= 15.03.
Calculate the burnout time based on this information.
9.5
The Spalding theory can also provide a standoff distance and a burning temper-
ature. This temperature can be used to calculate a new temperature in the far field
and one can iterate the procedure. The standoff distance can be expressed as the
ratio of the radii of the flame to the droplet, r
f
/r
s
, and becomes
ln 1 + B
0
,
q
ln 1 +
ð
ð Þ
=ϑ
Þ
Here, the index 0,q denotes the Spalding number for combustion and evaporation.
Evaluate the standoff distance for Problem 9.4.
PROJECTS
P9.1
Visit a biomass-fired power plant and analyze the combustion system. Try to
answer the following questions. What type of reactor is used? What is the aver-
age particle size? What is the residence time of the biomass particles in the
reactor? Which emission reduction measures are taken? Try to set up a global
mass and energy balance.
P9.2
In the analysis for determining the combustion mode, typical concentration
profiles of oxygen are determined. Using these stationary profiles, try to find
a method to estimate the time of total conversion for the different conver-
sion modes.
P9.3
In the analysis of Project P9.2, a quasi-steady state is assumed. Is this correct?
The fraction of time that the steady state exists should be a large part of the total
conversion time for the steady-state solution to be meaningful. Add an
unsteady-state term to the equations and solve them using numerical tools
to see whether this is indeed the case.
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