How to calculate these engine parameters on my own?

I am a space enthusiast and am intrigued mostly by rockets. I recently found a book HOW to DESIGN, BUILD and TEST SMALL LIQUID-FUEL ROCKET ENGINES and have been fiddling around with rocket engine calculations and calculated a theoretical engine. But there is one problem with the chamber parameters. In the book/pdf and also on this site from Robert Braeunig it shows tables and graphs of parameters and their correlation, mostly in the chamber pressure. Now, I would like to make an engine with other parameters that are not used in the graphs/tables(let's say a different mixture ratio). Where can I get data or formulas to make this graphs by my self? Thank you for your answers.

Disclaimer: I have no intention of building a real rocket engine as I do not have manufacturing knowledge nor tools to make it (so even if I wanted to I couldn't).

• You will need to be more specific. Right now this says 'teach me to compute every kind of engine parameter'. for example, pick one parameter and say what you want to vary to see the effect. Jun 8, 2020 at 12:27
• Why would you change a mixture ratio away from optimum thrust: weight ratio? Jun 8, 2020 at 15:29
• This is a valid problem even if poorly written. "How to model a liquid combustion engine" is a very big question, but it can be answered. Ponomarenko (2009) provides a very broad overview, including much more of the non-combustion considerations that I do not cover in my answer. 87.106.90.141/downloads/1.0/docs/… Jun 8, 2020 at 16:23
• @CarlWitthoft How were those optimum thrust/weight ratios determined in the first place? Jun 8, 2020 at 16:25

You will need to write a solver for the incomplete combustion of your propellant. This can be done by hand, but I recommend writing a program to implement it.

These days, such calculations are primarily done by solving for the maximum entropic state of the system (the system being the mixture of reactants at the chamber temperature & pressure). The equivalent problem to the maximization of the entropic state is the minimization of the Gibbs free energy (or the Helmholtz free energy, depending on whether you allow pressure or temperature, respectively, to vary in your calculations).

Traditionally, Gibbs minimization problems are solved in R-space, where R is the number of different reactions between species. Because we are modeling non-ideal combustion, we do not just consider the dominant species. For example, consider the very simple reaction 2H2 + O2, a hydrolox reaction.

Besides the obvious H2O product, you must also consider H2, O2, H, O, O3, OH, etc. and, depending on the robustness of your method, e- and all associated molecular and monatomic ions. Multiple reactions might be considered per species. For example, 2H2 + O2 --> 2H2O, but so does OH + H --> H2O, O + H2 --> H2O, OH- + H+ --> H2O, H3O+ + e- --> H2O + H, etc. All reverse equations are also implicitly considered during solving. As you can see, this produces a very large, non-linear system. The hydrolox reaction is the simplest you are likely to find in rocketry. Large CHON systems can grow to hundreds of reactions, & thus dimensions.

However, by the method of Reynolds (1986), you may reduce the dimensionality by rejecting the traditional method of balancing the reactions & instead converting the problem to a less-physical one. The concept of element potentials arise when implementing the constraint of atomic population (aka: no matter how the atoms are redistributed in the product species, there must be no net change in the total number of atoms in the system, per change in Gibbs energy) as Lagrangian multipliers.

As these Lagrange multipliers are as many as the types of atom in the system, they far less numerous than the number of reactions, or even the number of species. A CHON system only has 4 types of element, but it can have 100s of reactions & dozens of species. Remarkably, the element potentials can be solved for, and in doing so, solve the system. From the aforementioned paper:

This method is also more robust to the influence of rare but high-energy species, such as solid phases like elemental C (soot), and ionized species. These species can have a large influence on the thermodynamics of the system while existing in population several orders of magnitude lower than the reactants & dominant products.

While you are still solving a non-linear system, Reynolds demonstrates that the dual problem can be solved by a minimaxing method of steepest descent/ascent, followed by the applications of a second-order Newton method to rapidly approach the optimal solution from near the solution, where the solution space shallows out, becomes difficult for gradient descent methods to operate, and the space becomes well-approximated by second-order polynomials.

I am still parsing the work of Gordon & McBride (1994) but I will update my answer with their additions to the science when I am done re-reading their paper for the umpteenth time.

Once you have the energy of your reaction, it is relatively trivial to determine your thrust & specific energy using the adiabatic & isentropic mass flow equations. You will also know the composition of your exhaust, so you can determine the parameter gamma, the ratio of specific heats, which is required for said mass flow equations.

• +1. Crikey, no wonder its called rocket science! ;-). Would you be able to give an indication of how one determines how many lesser species its worth including given the intended fidelity of the effort? Jun 10, 2020 at 20:36
• @Puffin It really depends on the system & your intended application. Perhaps being a few seconds off of your Isp calculations for a simple hydrolox engine is fine, but when you're trying to model weird complex hypergolics & hydrocarbons, or if there's many-bonding, heavy metals like sulfur & boron involved, then the accuracy of your model will start going down the tubes, as even small amounts of these lesser condensed species will absorb a lot of heat (lots of vibrational modes) & reduce your pressure. Jun 10, 2020 at 21:38

Anton must really love chemistry or pain. NASA's CEA is a robust tool for analyzing combustion thermo-chemistry which was developed by the same Gordon & McBride mentioned in Anton's answer while they were working at NASA. They also make MATLAB wrappers for the thing, but I'm not sure where to find a publicly available option. It will save you a million years of headache and provide useful rocket design parameters (Chamber Temp, Gammas, Cstar, etc.)

• +1. Actually, CEA is the program developed in that paper I linked. Not doing it yourself is a great alternative to chemistry & pain. Jun 10, 2020 at 21:36