Rowan-Gollan-PhD-Thesis - Mechanical Engineering - University of ...

50 Chemical Nonequilibrium Chapter 4
takes for the gas particle to pass through the bow shock and transit the vehicle shock layer.
After passing the shock, the thermally perfect gas particle has an excess of sensible internal
energy 1 and during subsequent collisions the gas particle will seek to redistribute that energy
among other modes, including chemical energy if available. In particular, molecules will seek
to break chemical bonds as a means of absorbing the excess internal energy. For certain flow
conditions, often associated with flows tending towards the rarefied limit, the amount of time
required for sufficient collisions for equilibrium is of the same order as the time required for a
gas particle to transit the shock layer. In these cases, the modelling of chemical nonequilibrium
is important to correctly characterise the flow field about the vehicle. On a more practical note,
the correct modelling of nonequilibrium phenomena is required for accurate estimates of heat
loading on the vehicle surface. Sutton and Gnoffo [114] have reported that a little more than
half of the stagnation point heating rate for entry into air at 10.9 km/s is due to recombina-
tion of atomic species of O and N. This effect on heat transfer estimates can only be reliably
modelled by including finite-rate chemistry effects.
The influence of chemical nonequilibrium phenomena in gas dynamics is not limited to
blunt body flows. Its influence extends to combustion processes, detonation waves and nozzle
flows to name a few examples and the same basic theoretical treatment can be applied to each
of theses types of flows.
In this chapter, a computational model for calculating the finite-rate chemical evolution of
reacting gas in nonequilibrium flows is described. In essence this chapter is dedicated to the
term
˙ω
as it appears in Equation 2.2; its theory, implementation, verification and validation is reported.
The theory behind the coding implementation is presented in two sections: the model for a
mixture of thermally perfect gases is presented in Section 4.1 and the model for the chemical
kinetics is described in Section 4.2. The numerical methods for solving the chemical kinetic rate
equation are presented in Section 4.2.3. An oft encountered problem in the numerical solution
of the chemical rate equations is that numerical inaccuracies can lead to problems ensuring
that mass is conserved in the system. In Section 4.3, an original treatment — to the best of my
knowledge — to the numerical solution of the chemical kinetics equations is presented; this
method directly addresses the problems of mass conservation. The implementation is verified
by comparison with an analytical solution to a hydrogen-iodine system in Section 4.4, and,
finally, some validation cases for gas dynamic flows in chemical nonequilibrium are shown in
Section 4.5.
gas.
1 This is a result of shock processing, or consider this a result of indirect transferal of vehicle kinetic energy to the