Master Equation Study of Vibrational and Rotational Relaxations of Oxygen

Abstract

Transition rates in O 2 -O collisions for each vibrational and rovibrational state are generated by means of the quasiclassical trajectory method using potential energy surfaces of different fidelities. The first potential energy surface, obtained via the double many-body expansion method, is adopted to obtain vibrational transition rates assuming transrotational equilibrium. The trajectory simulation on a simpler potential surface, based on the two-body pairwise interaction, generates a complete set of rates for each internal state. Vibrational and rotational relaxations of oxygen in a heat bath of parent atoms are modeled by a system of master equations at translational temperatures between 1000 and 20,000 K. It is shown that the vibrational relaxation becomes less efficient at high temperatures, in contrast with the conventional equation for relaxation time proposed by Millikan and White ("Systematics of Vibrational , Paper 3209). Rotational and vibrational relaxation times are the same order of magnitude in the range of temperatures observed in hypersonic flows. The excitation of the vibrational mode in O 2 -O collisions under typical postshock conditions occurs earlier than in other molecular systems. The exchange channel plays an important role in the internal energy randomization.

State-to-State Master Equation and Direct Molecular Simulation Study of Energy Transfer and Dissociation for the N2–N System

“…The most well-known high-fidelity approach to simulating non-equilibrium chemical processes is the state-to-state master equations (StS-ME) method. − It is a deterministic approach in which all relevant internal energy states are treated as separate pseudo-species and their populations are tracked directly through the system of master equations. This has been done at varying levels of detail by tracking either electronic, − vibrational, or rovibrational − ,, states. The highest-fidelity master equation approach currently feasible for air species such as nitrogen and oxygen is the rovibrational StS-ME method; this requires a complete kinetic database comprised of rate coefficients for all relevant processes ( e.g.…”

“…Recent work has focused on the construction and application of both rovibrational- and vibrational-specific StS models for chemical systems relevant to air chemistry. There have been several rovibrational StS-ME studies of the N 2 –N system − and the O 2 –O system. , There has been extensive work on both vibrational-specific StS-ME and coarse-grained methods on the systems of interest to air chemistry. This includes vibrational StS-ME studies of the O 2 –O , and O 2 –O 2 systems, combined oxygen systems, and N 2 –N, − N 2 –N 2 , , N–O 2 , and N 2 –O 2 systems.…”

Can vibrational pumping occur via O2–N2 collisions in nonequilibrium vibrationally excited air?

“…However, it is shown, theoretically [50,51] and experimentally [52][53][54], that the O2-O VT reaction is extremely efficient at low translational temperatures, and trace amounts of O can influence the vibrational relaxation process significantly. This is further demonstrated in Figure 3 which shows, at three different translational temperatures, the ratio of the O2 vibrational energy source terms between set B (the pumping process) and the three equilibrating processes -O2-N2 VVT set A, O2-O2 VVT, and O2-O VTfor an equilibrium 5-species air composition, calculated using Cantera [55], equilibrated at the given vibrational temperature and defined pressure.…”

Application of the 3D Forced Harmonic Oscillator Model in the DSMC Method

“…In recent years, there has been significant effort aimed at better understanding of the thermal processes of air species, and much recent work has examined internal energy excitation at detailed state-to-state trajectory calculations and the direct molecular dynamics level. Examples are [9,10] for N 2 -N 2 collisions, [11,12] for N 2 -N, and [13,14] for O 2 -O. The use of complete transition cross sections [Eq.…”

“…The drawbacks of this approach were the limited range of temperatures that it captured [23] and the lack of accuracy in collisions that included nitrogen or oxygen atoms. One can also use the transition data obtained in recent QCT computations [9][10][11][12][13][14], although the limiting factor may be the shear amount of information that needs to be stored and used in the modeling of reacting air. Due to this limitation, an alternative approach is currently under development that aims at reducing the prohibitively large number of level-by-level transitions to a set manageable from the computer implementation perspective [24].…”