On the Formation of Nitrogen Oxides During the Combustion of ...

3 Experiments on Droplet Array Combustion
stream of the probe orifices in the plane that is flush with the combustion
chamber ceiling). It is driven by the pressure gradient between the evacuated
sample cylinder and the isobaric combustion chamber. To provide the
necessary input for this boundary condition, the total time of the gas sampling
process ∆t sampling was empirically determined by hardware tests, but the
remaining parameters could be derived from gas dynamics. Choked flow is
assumed downstream of the physical probe orifices, where the four probes
are fitted to one piping joint. The fluid properties in the combustion chamber
are expected to be homogeneous everywhere and are equal to the stagnation
properties, denoted by the subscript zero [224, 396]. Thus, sonic (critical)
conditions are reached at the “throat” of the piping. They are denoted by an
asterisk. Employing the ratio of specific heats of a gas,
κ≡ c p
c v
, (3.14)
where
c p = κ
κ−1 R, c v = 1
κ−1 R, and R = c p− c v , (3.15)
critical temperature T ∗ and critical pressure p ∗ can be calculated via the isentropic
relations of Equations (3.16) and (3.17), respectively. As a first estimate,
κ= 1.4 is applied here, as generally valid for diatomic gases.
T ∗
= 2
T 0 κ+1
p ∗ ( 2
=
p 0 κ+1
) κ
κ−1
(3.16)
(3.17)
Introducing the definition of the speed of sound for a perfect gas, the onedimensional
continuity equation for steady flows gives:
ṁ ∗ = p ∗ A ∗( κ
) 1
2
. (3.18)
R T ∗
Everything but the throat area A ∗ is given, which is derivable from the total
sampling time ∆t sampling and the sampling time under critical conditions ∆t ∗
using a goal seek function. The time ∆t ∗ , in turn, can be obtained from the total
mass collected during critical flow (Eq. (3.19)) and the sample temperature
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