5
Comparison to CFD
The CFD code that experiments were compared against; STUBE, is specifically designed for nonequilibrium nozzle flow calculations for Free Piston Shock Tunnels. It was developed at the ANU and
generates the free stream conditions that are used as the input to CFD. While there are some approximations
that are not made in other more detailed CFD codes, its use in ALDiR for input to other CFD makes it
important to test. The main approximations in the code are the sudden freezing approximation and it's
calculation using the Landau-Teller model, discussed earlier in section 2.5. The validity of these
approximations in predicting the temperature was tested as the concentration of oxygen in the flow increased.
5.1
Pure Nitrogen Flow
For these shots the Shock Tube was filled with 99.99% N2 which had the lowest concentration of water
available (<12ppm). The water content is important due to it being a very efficient vibrational relaxer of N2.
As can be seen from figure 5.?? The agreement between CFD and experiment is very good. The results at the
5" exit are scattered around the value predicted by CFD. Therefore this work supports the validity of the
Figure 5.??: Comparison of experimental measurements
to STUBE prediction for a pure nitrogen flow
STUBE calculation, and its use of the sudden freezing approximation for 5" exit calculations.
Results for the 12" exit do not agree as well and while the CFD prediction is within the error bounds,
the measurements indicate that the actual temperature is lower. Despite the flow conditions changing
significantly faster than vibrational energy can be redistributed some redistribution is occurring. This indicates
that the sudden freezing model is not accurate when the flow has been vibrationally frozen for a long time.
The rotational temperature shows good agreement at both positions in the flow. As expected, in light
of the previous discussion of intensity driven cross talk, the rotational temperatures are consistently higher
temperatures than CFD predicts. Furthermore the disagreement is proportionally greater at the 12" exit, when
there is less rotational structure and the cross talk will have a more significant effect on temperature.
5.2
Air Flow
The composition of the gas used was: N2: 78.1%; O2: 20.9% and Ar: 0.9%. This gas mixture also had
the minimum amount of water, being <25ppm. The results of experiments at both the 5" and 12" exits are
shown in figure 5.??. Clearly the CFD prediction of the vibrational temperature is wrong. This is because the
dominant collision partner of molecular nitrogen is assumed to be molecular nitrogen when molecular oxygen
Figure 5.??: Comparison of STUBE predictions
to experimental measurements in an air flow
is 2.5 times better at vibrationally relaxing nitrogen than molecular nitrogen. Furthermore atomic oxygen is
also very effective at relaxing nitrogen and while the mole fraction never exceeds 0.7% even these
concentrations have been shown to have a significant effect [Eswar].
The results also demonstrate that in the presence of these collision partners the sudden freezing model
is not a good assumption. There is a significant change in the vibrational temperature as the flow evolves
down the nozzle and clearly more sophisticated modelling is required for this flow. A quasi one dimensional
model that does not assume vibrational non-equilibrium has been proposed by Anderson, however this is only
for a pure Nitrogen flow, requiring a non-trivial extension to multiple species flows.
A study of vibrational non-equilibrium and the effect of small concentrations of effective collision
partners have shown that the vibrational temperature of the minor species can increase to levels above the
resivour temperature [Rich et al]. The study by Rich et al showed that vibrational freezing was not a simple
matter given the complex nature of the vibrational coupling between species. Rich et al studied 5% CO in 95%
N2 flow and they derived the following relation:
N
2
T N 2

 CO
T C O

 N   CO
2
Tr
5.1
This indicates that the coupling of vibrational energy from N2 to CO is more significant when the
translational temperature is lower. Assuming that a similar relation holds for N2-O2 vibrational coupling would
help explain the results presented in section 4.2.4, where the vibrational temperature shows little change as the
oxygen concentration is increased from 5% to 21% at the 5" exit, while a significant change occurs at the 12"
exit. As the translational and rotational temperatures are in equilibrium, the coupling of vibrational energy
would become more efficient as the flow evolves down the nozzle. Therefore the concentration of oxygen has
a more significant effect at lower temperatures
These results also agree with Palma and recent results by O'Byrne for NO vibrational temperatures in
ALDiR's T2 FPST nozzle expansion flows containing 1% NO. Measured vibrational temperatures were 400
degrees higher than predicted by the Landau-Teller sudden freezing model while the rotational temperature
displayed near perfect agreement. Palma also reported a small rise in the NO vibrational temperature as the
flow expanded, however this is not observed by O'Byrne.