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

3.3 Numerical Study of the Fluid Dynamics Within the Combustion Chamber
T sample after its isentropic expansion into the sample cylinder. The latter correlation
is derived from the first law of thermodynamics by using Equation (3.20)
and assuming an adiabatic sample cylinder, which is justified due to the short
duration of the sampling process [224, 322, 396, 419].
m ∆t ∗ = p∗ V sample
R T sample
(3.19)
κ= T sample
T piping
(3.20)
Finally, the throat area A ∗ can be attained including its respective diameter
D A ∗ = 0.73 mm. This value is well below the physical pipe diameter of
D i = 2.16 mm but confirms the expectations towards boundary layer thickening
and local flow separation [389].
Figure 3.23 illustrates the gas sampling process modeled with the total mass
flow ṁ implemented as an outlet boundary condition. The mass flow of fresh
air through the same outlet is shown, too. It is a function of the fluid dynamics
10 x 10 −5
kg s −1
8 x 10 −5
Mass flow of total gas collected
Mass flow of fresh air collected
Fresh air content in combustion chamber
Fresh air content at probe orifice
100
%
80
Mass flow m
6 x 10 −5
4 x 10 −5
2 x 10 −5
60
40
20
Fresh air content χ
0 x 10 −5
0
0.0 0.2 0.4 0.6 0.8 1.0
Dimensionless time t/∆t sampling
Figure 3.23: Evolution of Fresh Air Content During Gas Sampling.
113