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The thermally perfect gas model allows Cp = Cp(T) and Cv = Cv(T) while still using P = RT as the equation of state. This model allows for a variation of γ through the flow field.
The user must provide a file containing discrete values of Cp/R vs. T or γ vs. T. The user is required to copy this file to $SCRATCH/specific_heats.tpg prior to the CoMPIRUN script executing. This can be accomplished by adding a copy command to the file in the top of the job file.
specific_heats.tpg file************************************************
gamma vs T Test File -- linear gamma (-0.02 for every +1000* R)
************************************************
TEMPERATURE UNITS (1=KELVIN, 2=RANKINE) DATA TYPE (1=GAMMA, 2=Cp/R)
2 1
************************************************
TEMPERATURE GAMMA
50.00 1.4090
290.00 1.4042
500.00 1.40
1000.00 1.39
2500.00 1.36
4000.00 1.33
6000.00 1.29
8000.00 1.25
The specific heats file starts with a few header lines. The user then must specify the units of temperature and type of the discrete data provided in the last section. The last section lists values of temperature and or Cp/R. This data is cubic spline fit within Cobalt.
The equilibrium air module uses the curve fits of Tannehill, et al. to calculate the thermodynamic and molecular properties of air when intermolecular forces become important. As temperature becomes large, dissociation and eventually ionization occurs. The thermodynamic properties of air become dependent on two variables (T = T(P,e)). For hypersonic flows, this has the effect of weakening the strength of a shock wave. The table below shows the temperatures at which dissociation and ionization become important. Molecular vibrations start occurring around T=600 K which is the temperature value where starts γ changing.
| Temperature Range | Chemical Composition |
|---|---|
| T < 2500 K | 78% N2, 21% O2 |
| 2500 K < T < 4000 K | Oxygen dissociation regime. Some NO is formed |
| 4000 K < T < 8000 K | Nitrogen dissociation regime. Oxygen is fully dissociated. |
| 8000 K < T | Ionization of atomic constituents occurs |