Solving Chemical Equilibrium Concentrations Within a Rocket Nozzle

[BrandonBerchtold]

TL;DR

Looking for a comprehensive resource from which to learn how to solve chemical equilibrium concentrations along a rocket nozzle.

I would like to write a program to calculate the equilibrium concentrations of 10 or more chemical species at any axial location along a quasi 1D isentropic methane-liquid oxygen rocket nozzle. Is anyone aware of any good textbooks that cover this topic in depth, specifically dealing with large numbers of species and the process for solving for their concentrations?

I'm trying to create a program similar to the CEARUN program (https://cearun.grc.nasa.gov/).

 

[boneh3ad]

Are you already familiar with non-reacting computational fluid dynamics?

 

[BrandonBerchtold]

I am familiar with CFD theory though I have limited hands on experience with implementing it. I took an FEM course during my undergrad where we solved thermal conduction problems using our own FEM code. I'm currently half way through reading "Modern Compressible Flow: With Historical Perspective by John Anderson" which outlines the theory behind fluid dynamic problems and I feel quite comfortable working with the governing equations outlined in the book.

 

[boneh3ad]

First, I'm not a computationalist; I do experiments, so I won't be able to entirely solve your problem, but maybe I can point you in the right direction. What sort of fidelity are you looking for here?

 

[BrandonBerchtold]

From what I found in "Rocket Propulsion Elements" and "Modern Engineering for Design of liquid Propellant Rocket Engines", generally nozzle design can be done by assuming frozen composition flow throughout the nozzle (which generally underestimates temperatures), equilibrium composition flow (which usually overestimates temps), and finite rate reacting flow (which is closest to reality). I designed a nozzle using frozen flow so now I'd like to design one for an equilibrium flow to give a bound on the temperatures my nozzle could experience.

The fidelity I'm looking for is not very high considering I'm already assuming the flow is quasi-1D, isentropic, inviscid, and is always at equilibrium(infinitely fast reaction rate regardless of temperature).

From what I've read, I think I'm looking for a way to algorithmically minimize gibbs energy for a given group of chemical species?

 

[boneh3ad]

I am not familiar with the books you cite (my background is external aerodynamics with a bit of a branch into some internal stuff), but I do have a few thoughts on this that may or may not be helpful.

Be careful with things like isentropic assumptions here. How do you even define a ratio of specific heats appropriately in a reacting flow? You'll definitely want to be careful with your equation of state such that it takes such real gas effects into account.

You'll need some kind of kinetic modeling here, I imagine. You might check some of the the high temperature and/or combustion texts out there for examples of what is common. Something like Anderson's Hypersonic and High-Temperature Gas Dynamics would have a discussion of modeling chemistry, dissociation, ionization, etc., though is focus is external. It has a raft of citations as well that might point you in the right direction. Your rocket propulsion texts likely have references in the sections they talk about the different methods for doing this as well.

 

[BrandonBerchtold]

Thanks for the suggestions boneh3ad. I haven't worked much with real gases so I will definitely be getting myself a copy of Anderson's Hypersonic and High-Temperature Gas Dynamics to hopefully get a better understanding of treatment of such gases.

 

[bigfooted]

Joe Shepherd from Caltech has written a compressible 'shock and detonation' solver called SDT that connects to the thermodynamics and chemistry package Cantera. It looks like you want to write something similar.
Cantera is the go-to code for 0D and 1D incompressible reacting flow problems in the combustion community. If you do something with combustion, you might already know it:
https://cantera.org/
SDT is less well known:
https://shepherd.caltech.edu/EDL/PublicResources/sdt/nb/sdt_intro.slides.html
And here is a lot of documentation that you can use if you want to write your own code:
https://shepherd.caltech.edu/EDL/publications.html
And here is a theoretical introduction from Shepherd:
https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.181.1150&rep=rep1&type=pdf

As you can see from the examples on the SDT website, just *using* the software already takes considerable effort and some programming skills. it took several years to write these codes, so you should really focus on a specific problem if you want to write something yourself.

Next to the suggestion of @boneh3ad I can recommend 'Combustion Physics' by C.K. Law. It's a classic textbook on combustion theory with a large chapter on supersonic combustion. If you are not familiar with combustion, you should read this book first, or at least the first 8 chapters (supersonic flows is chapter 14).

 

[BrandonBerchtold]

Oh wow, that's perfect @bigfooted! I am definitely going to have to read up on combustion physics before touching the code but that looks like it'll be perfect for my project.