Solid Combustion
Zack Brimhall
12/13/07
Solid Combustion
•
Motivation
–
–
–
–
•
Project Goal
–
•
Model the burning rate of carbon as a function of temperature and pressure.
Objectives
–
–
•
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.
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
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.
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.
Math Model
Math Model (contd.)
Math Model (contd.)
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.
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).
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.
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.