Overview

We collect the transport equations for a multi-component, multi-temperature ^[8] non-equilibrium flow. All transport equations have been discussed in Chapter 4, as well as in Chapters 5, 6, 7 (see also ^[1], ^[2], ^[3]). We write the equations in (conservative) flux-vector formulation, which we have used already for the energy equation in Sub-Section 4.3.2, and for three-dimensional Cartesian coordinates:

Q is the conservation vector, E, F, G are the convective (inviscid) and E _uisc F _uisc, G _uisc the viscous fluxes in x, y, and z direction. S is the source term of mass and of vibration energy.

The conservation vector Q has the form:

where ? _i, are the partial densities of the involved species i, Section 2.2, ? is the density, u, v, w are the Cartesian components of the velocity vector V, e _t = e + 1/2 V ² is the mass-specific total energy ( V = V), Sub-Section 4.3.2, and ?e _uibr,m the mass-specific vibration energy of the molecular species m. The convective and the viscous fluxes in the three directions read:

The convective flux vectors E, F, G represent from top to bottom the transport of mass, Sub-Section 4.3.3, momentum, Sub-Section 4.3.1, of total energy, Sub-Section 4.3.2, and of non-equilibrium vibration energy ^[9], Section 5.4. In the above h _t = e _t