.. cea_tdk_rpa

CEA vs TDK vs RPA
=================

There are three major computer programs, of which I'm aware, that calculate one dimensional equilibrium (ODE)
performance of rocket engines, **CEA**, **TDK** and **RPA**. Back in 2006 I was interested in comparing the results of these three codes for common propellant combinations,
just to see if they all gave similar results.
I created charts of the **difference** in ODE Isp performance for **CEA** vs **TDK** and for **RPA** vs **TDK**.


Currently these codes are available at:

    `CEA at NASA Glenn Research Center <https://www1.grc.nasa.gov/research-and-engineering/ceaweb/>`_
    
    `TDK at Software & Engineering Associates <http://www.seainc.com/productsTDK.php>`_
    
    `TDK at Sierra Engineering & Software, Inc. <http://sierraengineering.com/TDK/tdk.html>`_
    
    `RPA at Rocket Propulsion Software+Engineering UG <http://www.propulsion-analysis.com/index.htm>`_


The **TDK** code is the accepted standard for the `JANNAF <https://www.jannaf.org/>`_ 
performance calculation method.
As far as I know, `JANNAF <https://www.jannaf.org/>`_  only controls a version of `TDK from 1993 <https://www.jannaf.org/products/codes>`_
and the only modern versions are the two commercial versions above.

One very important reason that **TDK**  is the  `JANNAF <https://www.jannaf.org/>`_  standard is that,
unlike CEA and RPA, the **TDK** code can calculate the **kinetics loss** in the nozzle.
(i.e. ODE assumes infinite time for combustion product chemistry to come to equilibrium
everywhere in the nozzle, whereas the kinetics
calculation accounts for the actual time available for the chemistry to approach equilibrium in the nozzle.)

This **kinetics loss** can be a very important consideration for rocket performance, especially in
small thrust, low pressure, high area ratio engines.

It is my understanding that the developers of **TDK** started with a version of **CEA**
developed by `Bonnie J. McBride and Sanford Gordon <https://www1.grc.nasa.gov/glenn-history/hall-of-fame/biographies/bonnie-mcbride/>`_
and added more capabilities to it,
so there is some expectation that those two codes should agree reasonably well on ODE Isp.

The developers of **TDK** `(Software & Engineering Associates) <http://www.seainc.com/index.php>`_ 
also created the `SPP (Solid Performance Program) <http://www.seainc.com/productsSPP.php>`_
code that calculates performance of solid propulsion Isp.
Because of this, it's probably true that **TDK** handles condensibles and particulates better
than **CEA** or **RPA**. (This likely also explains why **RPA** crashes and **CEA** gets divergent
answers at very high area ratio, where condensibles are likely to occur.)
Note that **SPP** is also available from 
`Sierra Engineering & Software, Inc. <http://sierraengineering.com/SPP/SPP.html>`_.

Although I do not know which code creates the most accurate values, I used **TDK** as the basis 
because it is the `JANNAF <https://www.jannaf.org/>`_  standard. 
Each chart displays a very large spectrum of runs over a range of 
area ratios(2 to 512), chamber pressures(50 to 3200 psia) and 
mixture ratios that cover the 
maximum expected range of operation as well as extending to extremely ox rich and fuel rich.

The main observations are:

- For common propellants, all of the codes agree very well in expected MR range of operation.
- For some storable propellants, RPA predicts higher Isp ODE than both CEA and TDK
- When extremely ox or fuel rich, **CEA** diverges and **RPA** crashes.
- Large differences (and **RPA** crashes) tend to happen at extremely large area ratios.

Bear in mind that these numbers were run in 2006.
I don't think much has changed in any of the codes that would affect these results, however,
that is strictly a **GUESS** on my part.

Chart Description
-----------------

Each chart color-codes the difference in Isp ODE between two software packages (**CEA** vs **TDK**) and (**RPA** vs **TDK**)
with the following scale.

.. image:: ./_static/ode_diff_scale.jpg

Cyan, Light Blue, Dark Blue indicate lower  than **TDK** by -1 to -2, -2 to -3 or <-3 seconds of Isp respectively.

Green indicates agreement within 1 second of Isp.

Yellow, Orange, Red indicate higher than **TDK** by 1 to 2, 2 to 3 or >3 seconds of Isp respectively.


The X and Y axes are obvious and labeled as Area Ratio and Mixture Ratio.

Notice, however, that there are horizontal bars on the mixture ratio axis indicating the 
minimum and maximum expected MR operating range.


.. raw:: html

    <table width="100%">
    <tr>
    <td valign="top" width="40%">
    Chamber pressure on the charts is somewhat less obvious. 
    For each Mixture Ratio and Area Ratio, the range of Chamber Pressure results (50 to 3200 psia)
    are shown as a bar of colors, one for each Pc.
    </td>
    <td><img src="./_static/pc_scale.jpg" width="160"></td>
    </tr>
    </table>


LOX/LH2
-------

LOX/LH2 has very good agreement between all three codes.

High area ratio, low MR is where differences occur. 

In those areas, **CEA** gets more than 3 seconds higher than **TDK** and
**RPA** crashes.

.. note::

    Blank areas in the RPA chart is where that code crashes.

.. raw:: html

    <table width="1000">
    <tr>
    <th style="text-align:center;"> CEA </th>
    <th style="text-align:center;"> RPA </th>
    </tr>
    <tr>
    <td>
    <a class="reference internal image-reference" href="./_static/LOX_LH2_cea_minus_ode.png">
    <img src="./_static/LOX_LH2_cea_minus_ode.png">
    </a>
    </td>
    <td>
    <a class="reference internal image-reference" href="./_static/LOX_LH2_rpa_minus_ode.png">
    <img src="./_static/LOX_LH2_rpa_minus_ode.png">
    </a>
    </td>
    </tr>
    <tr>
    <td colspan="2" style="text-align:center;">
    <img src="./_static/ode_diff_scale.jpg">
    </td>
    </tr>
    <tr>
    <td colspan="2">
    <p><cite>Click images to see full size</cite></p>
    </td>
    </tr>
    </table>


LOX/CH4
-------

LOX/LCH4 has very good agreement between all three codes.

Both **CEA** and **RPA** diverge at low MR. 

**RPA** crashes at very high MR for very high area ratios.

.. raw:: html

    <table width="1000">
    <tr>
    <th style="text-align:center;"> CEA </th>
    <th style="text-align:center;"> RPA </th>
    </tr>
    <tr>
    <td>
    <a class="reference internal image-reference" href="./_static/LOX_CH4_cea_minus_ode.png">
    <img src="./_static/LOX_CH4_cea_minus_ode.png">
    </a>
    </td>
    <td>
    <a class="reference internal image-reference" href="./_static/LOX_CH4_rpa_minus_ode.png">
    <img src="./_static/LOX_CH4_rpa_minus_ode.png">
    </a>
    </td>
    </tr>
    <tr>
    <td colspan="2" style="text-align:center;">
    <img src="./_static/ode_diff_scale.jpg">
    </td>
    </tr>
    <tr>
    <td colspan="2">
    <p><cite>Click images to see full size</cite></p>
    </td>
    </tr>
    </table>


LOX/RP1
-------

For LOX/RP1 **CEA** has good agreement with **TDK**, however, **RPA**
calculates as much as 2 seconds lower than **TDK** in the low portion of the expected MR range.

Both **CEA** and **RPA** diverge at low MR. 

**RPA** crashes at very high MR for very high area ratios.

.. raw:: html

    <table width="1000">
    <tr>
    <th style="text-align:center;"> CEA </th>
    <th style="text-align:center;"> RPA </th>
    </tr>
    <tr>
    <td>
    <a class="reference internal image-reference" href="./_static/LOX_RP1_cea_minus_ode.png">
    <img src="./_static/LOX_RP1_cea_minus_ode.png">
    </a>
    </td>
    <td>
    <a class="reference internal image-reference" href="./_static/LOX_RP1_rpa_minus_ode.png">
    <img src="./_static/LOX_RP1_rpa_minus_ode.png">
    </a>
    </td>
    </tr>
    <tr>
    <td colspan="2" style="text-align:center;">
    <img src="./_static/ode_diff_scale.jpg">
    </td>
    </tr>
    <tr>
    <td colspan="2">
    <p><cite>Click images to see full size</cite></p>
    </td>
    </tr>
    </table>

LOX/Ethanol
-----------

LOX/Ethanol results are virtually identical to LOX/CH4 results.

Good agreement between all three codes.

Both **CEA** and **RPA** diverge at low MR. 

**RPA** crashes at very high MR for very high area ratios.


.. raw:: html

    <table width="1000">
    <tr>
    <th style="text-align:center;"> CEA </th>
    <th style="text-align:center;"> RPA </th>
    </tr>
    <tr>
    <td>
    <a class="reference internal image-reference" href="./_static/LOX_Ethanol_cea_minus_ode.png">
    <img src="./_static/LOX_Ethanol_cea_minus_ode.png">
    </a>
    </td>
    <td>
    <a class="reference internal image-reference" href="./_static/LOX_Ethanol_rpa_minus_ode.png">
    <img src="./_static/LOX_Ethanol_rpa_minus_ode.png">
    </a>
    </td>
    </tr>
    <tr>
    <td colspan="2" style="text-align:center;">
    <img src="./_static/ode_diff_scale.jpg">
    </td>
    </tr>
    <tr>
    <td colspan="2">
    <p><cite>Click images to see full size</cite></p>
    </td>
    </tr>
    </table>

Peroxide90/Ethanol
------------------

Peroxide90/Ethanol  has excellent agreement between all three codes.

**RPA** crashes at very high MR for very high area ratios.


.. raw:: html

    <table width="1000">
    <tr>
    <th style="text-align:center;"> CEA </th>
    <th style="text-align:center;"> RPA </th>
    </tr>
    <tr>
    <td>
    <a class="reference internal image-reference" href="./_static/Peroxide90_Ethanol_cea_minus_ode.png">
    <img src="./_static/Peroxide90_Ethanol_cea_minus_ode.png">
    </a>
    </td>
    <td>
    <a class="reference internal image-reference" href="./_static/Peroxide90_Ethanol_rpa_minus_ode.png">
    <img src="./_static/Peroxide90_Ethanol_rpa_minus_ode.png">
    </a>
    </td>
    </tr>
    <tr>
    <td colspan="2" style="text-align:center;">
    <img src="./_static/ode_diff_scale.jpg">
    </td>
    </tr>
    <tr>
    <td colspan="2">
    <p><cite>Click images to see full size</cite></p>
    </td>
    </tr>
    </table>



N2O4/MMH
--------

N2O4/MMH has excellent agreement between all three codes.

**RPA** crashes at very high MR for very high area ratios.

.. raw:: html

    <table width="1000">
    <tr>
    <th style="text-align:center;"> CEA </th>
    <th style="text-align:center;"> RPA </th>
    </tr>
    <tr>
    <td>
    <a class="reference internal image-reference" href="./_static/N2O4_MMH_cea_minus_ode.png">
    <img src="./_static/N2O4_MMH_cea_minus_ode.png">
    </a>
    </td>
    <td>
    <a class="reference internal image-reference" href="./_static/N2O4_MMH_rpa_minus_ode.png">
    <img src="./_static/N2O4_MMH_rpa_minus_ode.png">
    </a>
    </td>
    </tr>
    <tr>
    <td colspan="2" style="text-align:center;">
    <img src="./_static/ode_diff_scale.jpg">
    </td>
    </tr>
    <tr>
    <td colspan="2">
    <p><cite>Click images to see full size</cite></p>
    </td>
    </tr>
    </table>


N2O4/N2H4
---------

N2O4/N2H4 has excellent agreement between all three codes.

**RPA** crashes at both very high and very low MR with high area ratio.

.. raw:: html

    <table width="1000">
    <tr>
    <th style="text-align:center;"> CEA </th>
    <th style="text-align:center;"> RPA </th>
    </tr>
    <tr>
    <td>
    <a class="reference internal image-reference" href="./_static/N2O4_N2H4_cea_minus_ode.png">
    <img src="./_static/N2O4_N2H4_cea_minus_ode.png">
    </a>
    </td>
    <td>
    <a class="reference internal image-reference" href="./_static/N2O4_N2H4_rpa_minus_ode.png">
    <img src="./_static/N2O4_N2H4_rpa_minus_ode.png">
    </a>
    </td>
    </tr>
    <tr>
    <td colspan="2" style="text-align:center;">
    <img src="./_static/ode_diff_scale.jpg">
    </td>
    </tr>
    <tr>
    <td colspan="2">
    <p><cite>Click images to see full size</cite></p>
    </td>
    </tr>
    </table>


MON25/MHF3
----------

for MON25/MHF3, **CEA** has good agreement

**RPA** predicts high everywhere, and has some crashes at very high MR for high area ratio.

.. raw:: html

    <table width="1000">
    <tr>
    <th style="text-align:center;"> CEA </th>
    <th style="text-align:center;"> RPA </th>
    </tr>
    <tr>
    <td>
    <a class="reference internal image-reference" href="./_static/MON25_MHF3_cea_minus_ode.png">
    <img src="./_static/MON25_MHF3_cea_minus_ode.png">
    </a>
    </td>
    <td>
    <a class="reference internal image-reference" href="./_static/MON25_MHF3_rpa_minus_ode.png">
    <img src="./_static/MON25_MHF3_rpa_minus_ode.png">
    </a>
    </td>
    </tr>
    <tr>
    <td colspan="2" style="text-align:center;">
    <img src="./_static/ode_diff_scale.jpg">
    </td>
    </tr>
    <tr>
    <td colspan="2">
    <p><cite>Click images to see full size</cite></p>
    </td>
    </tr>
    </table>



CLF5/N2H4
---------

for CLF5/N2H4, **CEA** has good agreement in the expected MR range, but predicts higher Isp
at the MR extremes.

**RPA** predicts high everywhere, and has some crashes at very high area ratio.

.. raw:: html

    <table width="1000">
    <tr>
    <th style="text-align:center;"> CEA </th>
    <th style="text-align:center;"> RPA </th>
    </tr>
    <tr>
    <td>
    <a class="reference internal image-reference" href="./_static/CLF5_N2H4_cea_minus_ode.png">
    <img src="./_static/CLF5_N2H4_cea_minus_ode.png">
    </a>
    </td>
    <td>
    <a class="reference internal image-reference" href="./_static/CLF5_N2H4_rpa_minus_ode.png">
    <img src="./_static/CLF5_N2H4_rpa_minus_ode.png">
    </a>
    </td>
    </tr>
    <tr>
    <td colspan="2" style="text-align:center;">
    <img src="./_static/ode_diff_scale.jpg">
    </td>
    </tr>
    <tr>
    <td colspan="2">
    <p><cite>Click images to see full size</cite></p>
    </td>
    </tr>
    </table>