1. Solid Combustion
Zack Brimhall
12/13/07

2. Solid Combustion Motivation Project Goal Objectives Approach
Solid propellants are commonly used for the booster stage of a large rocket. Modeling solid combustion proves to have added complexities over liquid and gas combustion due to the variety of fuels and applications used for solid combustion.
MAE 5310 criteria focuses on liquid and gas combustion. This project enabled me to learn new material independent of the lectures.
Studying solid combustion would be valuable to my thesis work, which involves testing solid motors.
Models for carbon combustion have been developed.
Project Goal
Model the burning rate of carbon as a function of temperature and pressure.
Objectives
Determine the burning rate of carbon and how it is affected by temperature and pressure.
Correlate the burning rate, temperature, and pressure to the thrust of the motor.
Approach
Literature Review
Development of a physical model
Quantification of the physical model mathematically
Solution of the math model
Cases Studied
Analysis of the Results

3. Literature Review Glassman, Irvin. Combustion, Third Edition.
Thermodynamic properties were taken from the source.
Hunley, J.D. “The History of Solid-Propellant Rocketry: What We Do And Do Not Know”
This paper gave me a very good history and outline of solid propellants. However, there was no quantitative analysis, or technical model.
Pierson O. Hugh. Handbook of Carbon, Graphite, Diamond, and Fullerenes.
This was useful as it gave properties of Graphite (hc, hfg) which were used in the models.
Turns, Stephen R. An Introduction to Combustion.
The two-film model was taken from this source. Also, a simple droplet evaporation model was used.
Zarko, V.E. “Stability of Ignition Transients of Reactive Solid Mixtures”
This paper provided an interesting read, but the subject matter was not quite what I was focusing on with the project.

4. Physical Model The two film model for carbon combustion was used.
This model involves two different gas layers which interact in order to burn the carbon.
The cycle begins with the flame producing
The carbon surface is oxidized to carbon monoxide
The carbon monoxide produced diffuses through the first gas layer towards the flame sheet
Here it is consumed in the flame with an inwardly diffusing flow of oxygen.
Also, the simple droplet evaporation model was used for a sphere particle of carbon.

5. Math Model

6. Math Model (contd.)

7. Math Model (contd.)

8. Temperature of Carbon Surface
Equations were iterated to find Ts
The temperature of the carbon surface during combustion was found using the droplet model.
This is similar to the two film model which was applied to find the burning rate of the carbon.
Once a surface temperature was found then the equations for the burning rate of carbon could be solved. All thermodynamic values are assumed constant throughout the gas film for this case.
Because of this assumption the temperature has much room for improvement.

9. Burning Rate of Carbon
The burning rate of a particle was modeled and was plotted against pressure.
This is relevant because in a rocket motor a major factor is combustion chamber pressure, and it can be seen from the graph that higher pressures increase the burning rate of the carbon.
The rate does not change as much as the pressure gets higher. This might be explained by saying that the carbon can only burn so much at a certain temperature no matter what the pressure.
The second graph shows a similar trend with the lifetime of a carbon particle (70um-dia).
These models also ignore chemical kinetics and because of this tend to overestimate the burning rate by about 17% (Turns, 542).

10. Summary
The temperature of the surface of the carbon was found. This was necessary to solve for the burning rate of the carbon.
The burning rate was plotted for a range of pressures (1-100atm). Pressures in a rocket often are very high and can even change during flight. The plot showed that the burning rate increased with pressure up to a point.
The burning rate can be correlated to mass flow rate of the burned gases, and to thrust.

11. Conclusions
The complexity of modeling solid combustion arises from the large variety of models.
I have a good understanding of two models for solid combustion (the one-film and two-film models).
I personally thought using the droplet evaporation model for a solid particle was ingenious.
Modeling carbon was a great start for me. But in the future, I’d like to extend my model to actual solid propellants.
Both models used in Turns are described by the author as being inaccurate. What I don’t know how to do is to create a model that is very accurate to experimental results.