Question 6.6: Isothermal Relaxation: Pair Selection versus Particle Select...
Isothermal Relaxation: Pair Selection versus Particle Selection Prohibiting Double Relaxation
As a further demonstration, a similar isothermal relaxation simulation is conducted using the pair selection procedure (selection procedure (A)). Specifically the form of Eq. 6.93 is used.
P_{rot}= \frac{\zeta _{tr}+\zeta _{rot}}{\zeta _{tr}} \frac{1}{Z_{rot}} = \frac{C}{Z_{rot}} (6.93)
This simulation considers only rotational relaxation and the rotational collision numbers are modified from Table. 6.3 to be Z_{rot} = 10 for collisions 1|2 and 2|1, and to be Z_{rot} = 20 for collision 2|2.
Table 6.3 Simulation Parameters Specific to Each Collision Pair
| j|k | Z_{rot} | Z_{vib} | ω | d_{ref}(×10^{-10}m) | T_{ref}(K) |
| 1|1 | 5 | 40 | 0.74 | 4.17 | 273 |
| 1|2 | 8 | 60 | 0.755 | 4.12 | 273 |
| 2|1 | 10 | 80 | 0.755 | 4.12 | 273 |
| 2|2 | 15 | 60 | 0.77 | 4.07 | 273 |
The results using the particle selection prohibiting double relaxation procedure are shown in Fig. 6.16(a) and the results from the pair selection procedure are shown in Fig. 6.16(b). Clearly, the results using the pair
selection procedure do not agree with the analytical solution for the mixture, whereas the particle selection prohibiting double relaxation procedure exactly reproduces the analytical solution.
