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Solid Combustion

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  1. Solid Combustion Zack Brimhall 12/13/07

  2. Solid Combustion • Motivation • 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.

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