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Relaxation of chemically-reacting air behind a shock
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.. Author: Rowan J. Gollan <r.gollan@uq.edu.au>
.. Date: 05-Feb-2012

Description
-----------
This example computes the relaxation of air due to chemical
reactions which occurs behind a strong shock.
The free stream air is travelling at Mach 12.3.
This calculation was first presented by Marrone.
The calculation presented here uses a newer set of
reaction rates as compared to those used by Marrone.
The details of this calculation can be found in
Section 4.4.2 of the author's thesis.

This example is found in the code collection at::

  $CFCFD/examples/poshax3/air-Mach-12.3

Files
-----

*User-built files:*

air-Mach-12.3.cfg
  Input file for Poshax3.

air-model.inp
  Input file for describing the gas model.

gupta_etal_with_Keq.lua
  User-built input file containing chemical reaction rates.

run.sh
  A script to execute the example and plot results.

*Gas model input file:*

air-model.lua
  Gas model input file for direct use by Poshax3. This
  file is created using the ``gasfile`` program.

*Output file:*

air-Mach-12.3.data
  Output file from Poshax3 calculation. This contains flow properties
  as a function of distance downstream of the shock. *This file is only
  available after running the calculation.*

*Data files:*

marrone_fig3\_??.g3data
  Mole profiles of various species as calculated by Marrone.

marrone_fig4\_??_ratio.g3data
  Flow property profiles (as ratio of free stream values) as calculated by Marrone.

*Results files:*

plot-data.gplot
  A Gnuplot input file for plotting of results.

profile_moles.*
  Plot of mole profiles of air species (as a ratio of original moles).

profile_T_rho.*
  Plot of temperature and density ratio.


Running the simulation
----------------------

The steps to running and plotting results are contained in the script: ``run.sh``.
This can be executed at the command line, from this working directory as::

> ./run.sh


Results
-------
The results of the calculation show how the flow properties and
species concentrations vary as the flow relaxes downstream
of the normal shock.
The following figure shows the temperature and density
ratio (normalised by free stream values) behind the shock.
A comparison to Marrone's data is shown and the equilibrium
state as computed by CEA2 is plotted.
The calculation comes to the correct equlibrium values as expected.

.. figure:: profile_T_rho.png
   :align: center
   :scale: 30%

   Temperature and density ratio behind a normal shock in air at Mach 12.3.

The next figure shows how the species concentrations change as the
chemical reaction proceed behind the shock.
Again the comparisons to Marrone's calculations are shown and the
equilibrium concentrations calculated with CEA2.
The difference between the present work and Marrone's results
are attributed to differences in the thermodynamic data
and reaction rates used in the two calculations.

.. figure:: profile_moles.png
   :align: center
   :scale: 30%

   Species concentrations behind a normal shock in air at Mach 12.3.