INTRODUCTION Motivation Recent interest from military and commercial sectors in small scale propulsion Pursuing a new field in propulsion systems Has not been performed before on vast quantity Project Goal By simplifying the micro-thruster problem with a numerical approach using a Propane-Air reaction, it is hoped to yield an understanding and building of a more complex model for the HAN monopropellant. Objectives To measure the temperature range, and mass fractions in the reactants and products in Ethane-Air and Propane-Air reactions in the Well-Stirred. Investigate blow-off limits Numerically model and asses the Propane-Air combustion in a U-shaped cell using Fluent Approach Literature review Development of a math and CFD model Quantification of the math model mathematically Computation of the CFD model numerically Solution of the math and CFD model Analysis of the results

LITERATURE REVIEW The 5 most important papers are: Turns, “An Introduction to Combustion” 2nd edition Not only our text book for class, but an important reference for combustion equations Glassman, “Combustion” 3rd edition Excellent source for species properties and chemical reactions Kirk, Mento, Homitz; “Mainstream Proposal # 703CAM7030 for Microthrusters” Initial information on micro-combustors and summary Sitzki, Borer, Schuster and Ronney, “Combustion in Microscale Heat-Recirculating Burners” Explained “Swiss-Roll” assumptions, geometry and various catalysts Hisatsune, Izumi, Tsutaya and Furukawa, “Development of Han-based liquid propellant thruster” Explained various fuel advantages and disadvantages Found the best catalyst for microcombustion

PHYSICAL MODEL Spiral counterflow heat-recirculating “Swirl Roll” burner (chosen for motivation)

MATH MODEL 4 governing equations for a well-stirred reactor: Global rate coefficient:

Partial derivates of governing equations with respect to species concentrations and temperature

NOMENCLATURE Mass Flow Rate (kg/s) Yf,in Fuel Mass Ratio into WSR Yox,in Oxidizer Mass Ratio into WSR Yf Fuel Mass Ratio in WSR Yox Oxidizer Mass Ratio in WSR Ypr Products Mass Ratio in WSR kG Global Rate Coefficient MW Molecular Weight (kg/kmol) V Volume (m^3) U Velocity (m/s) P Pressure (N/m^2) Ru Universal Gas Constant h enthalpy (J/kg) T Temperature in WSR (K) Tin Temperature into WSR (K) (A/F)s Stoichiometric Air-Fuel Ratio Hf,F Heat of Formation of Fuel (J/kg) Cp Specific Heat (J/kg-K)

Equations f1, f2, f3, and f4 derived in the textbook in example 6 Equations f1, f2, f3, and f4 derived in the textbook in example 6.2 page 192. To solve four nonlinear equations with four unknowns the Newton-Raphson method was used, each involves the Jacobian Matrix. The Jacobian matrix is the partial differential of each equation with respect to each unknown. For further information see Appendix E in the Turns text. Newton-Raphson solved in Excel

We can see the mass flow rate limit for each equivalence ratio We can see the mass flow rate limit for each equivalence ratio. We see the oxidizer mass ratio grows greater than the fuel mass ratio at increased mass flow rates. Also evident is the inability to sustain combustion at greater mass flow rates with larger equivalence ratios. The increase in fuel can not be turned into products. The mass ratios for fuel, oxidizer, and products at different equivalence ratios and mass flow rates. The inlet temperature is 298 K The same results are seen here as in the case of an inlet temperature of 298 K. We do see that with an increase of inlet temperature the limits are extended for each equivalence ratio. Combustion sustained at higher mass flow rates and high fuel and oxidizer mass ratios. The mass ratios for fuel, oxidizer, and products at different equivalence ratios and mass flow rates. The inlet temperature is 500 K

Here we see the temperatures inside the WSR for varying cases of mass flow rates and equivalence ratios for two different inlet temperatures 298 and 500 K The temperatures inside the WSR were higher for lower mass flow rates and equivalence ratios closer to unity Also higher inlet temperatures increased the temperatures inside the WSR for both the upper and lower limits of each equivalence ratio

CFD MODEL Geometry chosen to be square shaped from initial proposal. Inlet Outlet Solid: Steel Fluid: Propane-Air Complete combustion equation: Propane properties: Tad = 2267 K MW = 44.096 kg/kmol Cp = 1650 J/kgK Initial conditions: T = 300 K, U = 50 m/s YC3H8 = 0.060343 YO2 = 0.218952 YN2 = 0.720705

This shows the velocity contours for the channel. Ranges from 0 m/s to 373.4 m/s Temperature in the channel is shown to the left. Here we see the flame zones wrapping around the channel as well the temperature of the flow. The temperature for the solid center: steel, is also shown. Ranges from 300 K to 2061 K

From the previous slide, we saw the temperature change across the cell. Here we see the “excess” enthalpy of the channel is re-heating the incoming flow, as seen at the upper wall. This “swirl-roll” channel was chosen due to its higher enthalpy, heat recirculating characteristics. This shows the temperature on the solid walls; upper in red, lower in black. The combustion of the mixture heats up the solid by conduction, and that transfers the heat into the incoming flow.

SUMMARY OF RESULTS MATH MODEL Inlet temperature cases: T = 298, 500 K Equivalence ratio cases: Φ = 1, 2, 3 Mass flow rates range from 0 kg/s to allowable blow-off limits CFD MODEL Tmax = 2061 K , have (on solid) = 590873.06 J/kg, at exit = 0.5987 kg/s As inlet velocity increases, temperature in the channel will decrease These results show that inlet temperature affect the flow rates and blow-off limits With higher mass flow rates and equivalence ratios, combustion process becomes increasingly unstable.

CONCLUSIONS Conclusions Learned steps in solving numerical problems for Ethane-Air, Propane-Air small-scale combustion Information can be used to numerically approach the micro-thruster solution using more complex combustion The following things went well: Ethane-Air model was verified in Turns, example 6.2 Different inlet temperature cases were accurate in the Ethane-Air model. Propane-Air CFD model yielded results consistent with expectations. What needs to be improved Develop a transient Propane-Air math model, and an unsteady flow in Fluent Consider different geometries for computation in Fluent Improve heat transfer modes in the numerical simulation The development of a full kinetic model for HAN propellant has not been done