Reseach Plan

A: Focus/Question: Regression rate behavior of liquefying hybrid rocket fuels with varying melting points that form hydrodynamically unstable melt layers resulting from sheer stresses induced in a combustion port boundary layer. How are the ballistic coefficients in the axially average regression rate equation dependent on the melting points of n-paraffin fuels using nitrous oxide oxidizer?

B: Hypothesis/Goal: If there is a relationship between the melting point of n-paraffins and regression rate, then as melting point decreases an increase in regression rate will be observed at some or all oxidizer flux levels. Ultimately, the burn rate performance of liquefying fuels should be maximized at little or no expense to energetic performance as quantified by density specific impulse or mechanical properties of the fuel.

C: Methods: (Preliminary: These will likely change as the experiment is conducted and refined)

Propellant Grain Casting:

1. Cut enough 3” sections of propellant casting tube to completely fill the intended casing.
2. Mass each casting tube.
3. Tape each casting tube to a casting mandrel assembly.
4. Melt the mass of paraffin in grams corresponding to 4.5 times the length of the motor casing in centimeters.
5. With the aid of a spoon and gloves, pour the molten propellant evenly into the casting assemblies. Avoid trapping bubbles or allowing the paraffin to cool before the casting assembly is filled.
6. Allow the fuel to cool. During cooling, the grains should be centrifuged to ensure good bonding with the liner.
7. Remove the tape from casting assemblies and apply a twisting motion to remove the mandrel from the fuel port cast into each grain.
8. Determine the fuel port diameter, outer diameter of the fuel, fuel grain volume, and mass of the individual fuel grains. Record these data both in a log and in sharpie on the side of each grain.

Thermodynamic Prediction Using RPA Code or CAE

1. Select a range of O/F ratios and possible chamber pressures, dividing each range into several intervals of equal size.
2. The following procedure iterates thermodynamic calculations for each O/F ratio under each possible chamber pressure in order to obtain every possible combination of the interval elements for pressure and O/F.
3. At the given pressure, vary the O/F ratio and record the effect on Isp, C*, Tc, and k.
4. Graph the results to determine the O/F ratio that produces the maximum C* and Isp at the given pressure.
5. Repeat with varying pressures and graph the optimal C* and Isp with respect to chamber pressure. The C* at any given mixture ratio should not be highly dependent on pressure!

Injector Flow Calibration

1. Before each firing, mass the oxidizer tank before and after the filling operation is carried out.
2. During each firing, record the chamber pressure and the nitrous oxide pressure in feed system over time.
3. Numerically integrate the square root of the pressure drop across the injector over the entire duration of the firing. This value is proportional to the total oxidizer mass flow.
4. Determine the constant of proportionality for each firing.
5. Average the values for each firing to arrive at a coefficient relating the time-dependent oxidizer mass flow rate to the instantaneous pressure drop across the injector.

Firing and Data Acquisition

1. Using a razor saw, carefully slice one of the fuel grains to adjust the overall length of the fuel to fit the motor casing.
2. Mass the fuel grains. Measure the total fuel port length.
3. Measure the nozzle throat diameter.
4. Slide the fuel grains into the liner and assemble the fuel section of the motor. This includes the nozzle, retention rings, pre-combustion chamber, post-combustion chamber, and pressure transducer tap.
5. Mass the combustion chamber assembly.
6. Mass the oxidizer feed system tank.
7. Fill the tank completely with liquid nitrous oxide, allowing air to vent out of the top until the liquid reaches the venting port. Close the venting port at this time. Close the fill valve
8. Mass the filled oxidizer feed system tank
9. Secure the electrically actuated solenoid valve and pressure transducer tap upstream to the injector assembly.
10. Connect the oxidizer tank to the solenoid valve.
11. Connect the compressed air feed system to the oxidizer tank.
12. Secure the constructed motor to the test stand.
13. Insert an igniter and pre-heater grain through the nozzle and to the back of the combustion port.
14. Open the compressed air valve and pressurize the oxidizer.
15. Move to a safe distance (100ft) trailing the connections to the two pressure transducers, solenoid valve, and igniter.
16. Connect the transducer leads to the amplifier and computer interface. Start the data acquisition software.
17. Remotely fire the igniter. Once lit, quickly activate the solenoid valve, allowing nitrous oxide to flow.
18. Record the chamber pressure versus time trace for the firing along with the pre-injector oxidizer pressure trace.
19. When oxidizer flow stops, immediately close the solenoid valve.
20. Allow the motor to cool.
21. Mass the combustion chamber assembly.
22. Remove the fuel grains and mass them.

Data Analysis: The averaged characteristic velocity approach will be taken in order to numerically approximate the instantaneous regression rate and internal ballistics during any given trial. Pressure drops across the injector orifice are used to calculate instantaneous nitrous oxide mass flow rates once a proportionality constant has been calibrated by the above procedure. Based on time-averaged characteristic velocity information, nozzle throat cross-sectional area, instantaneous oxidizer mass flow rate data, and a chamber pressure versus time trace, a Runge Kutta-4 time integration scheme is adopted to iteratively determine the internal ballistics over the duration of the trial through application of an augmented regression rate relation. An iteratively converging least squares algorithm is derived in order to approximate the ballistic coefficients in the O/F shifted regression rate equation. The ballistic coefficients are compared across the range of melting points, resulting in a best-fit curve which approximates the relationship between an n-paraffin's melting point and a given ballistic coefficient. The mathematical construct relevant to this approach is detailed in my Tuesday, October 18, 2011 post titled Mathematical Construct of Data Acquisition

Bibliography: (Documents so far pertaining to liquefying hybrid rocket fuels)

 
Karabeyoglu, M. A., Greg Zilliac, Brian J. Cantwell, Shane De Zilwa, and Paul Castelluci. "Scale-Up Tests of High Regression Rate Liquefying Hybrid Rocket Fuels." The American Institute of Aeronautics and Astronautics (2003). Print.

 
Brown, Timothy R., and Michael C. Lydon. "Propulsion." Testing of Paraffin-Based HybridRocket Fuel Using Hydrogen Peroxide Oxidizer. Proc. of 2005 Undergraduate Space Research Symposium and Career Fair, University of Colorado, Boulder Colorado. Colorado Springs: United States Air Force Academy Department of Astronautical Engineering, 2005. 2005 Undergraduate Space Research Symposium and Career Fair. Colorado Space Grant Consortium, 5 Apr. 2005. Web. 16 Sept. 2011. <http://spacegrant.colorado.edu/COSGC_Projects/symposium_archive/2005/docs/115.pdf>.

Arena, Zach, Alexander Athougies, and Alden Rodulfo. Hybrid Rocket Motor. Diss. California Polytechnic State University, 2010. Print.

 
Karabeyoglu, M. A., B. J. Cantwell, and D. Altman. "Development and Testing of Paraffin-Based Hybrid Rocket Fuels." The American Institute of Aeronautics and Astronautics (2001). University of Minnesota. Stanford University, 8-11 July 2001. Web. 4 Oct. 2011. <www.d.umn.edu/~rrosandi/Hybrids/Combustion/AIAA2001-4503.pdf>.

 
Chiaverini, Martin J., Nadir Serin, David K. Johnson, Yeu-Cherng Lu, Kenneth K. Kuo, and Grant A. Risha. "Regression Rate Behavior of Hybrid Rocket Solid Fuels." Journal of Propulsion and Power 16.1 (2000): 125-32. Planete Sciences. Pennsylvania State University. Web. 15 Sept. 2011. <www.planete-sciences.org/espace/basedoc/.../RegressionRateGOx-HTPB.pdf>.

 
Lohner, Kevin, Jonny Dyer, Eric Doran, Zachary Dunn, and Greg Zilliac. "Fuel Regression Rate Characterization Using a Laboratory Scale Nitrous Oxide Hybrid Propulsion System." Kevin Lohner: Selected Publications. Proc. of 42nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, Sacramento, California. Stanford University, 12 July 2006. Web. 16 Sept. 2011. <http://www.stanford.edu/~klohner/Publications/JPC_hybrid_propulsion.pdf>.

Sutton, GP., & Biblarz, O. (2010). Rocket Propulsion Elements. Hoboken, NJ: John Wiley & Sons Inc.

Karabeyoglu, M. A., David Altman, and Brian J. Cantwell. High Regression Rate Hybrid Rocket Propellants. The Board of Trustees of the Leland Stanford Junior University, assignee. Patent US 6684624 B2. 3 Feb. 2004. Print. 

 

Lazarev, Alexander, and Alon Gany. Experimental Investigation of Paraffin-Fueled Hybrid Combustion. Tech. Print. 

 

Karabeyoglu, M. A., Greg Zilliac, Paul Castellucci, Paul Urbanczyk, Jose Stevens, Gohkan Inalhan, and Brian J. Cantwell. "Development of High-Burning-Rate Hybrid-Rocket-Fuel Flight Demonstrators." AIAA/ASME/ASEE Joint Propulsion Conference, Huntsville, AL, July 2003. Print. 

  

Karabeyoglu, M. A., Brian J. Cantwell, and Greg Zilliac. "Development of Scalable Space-Time Averaged Regression Rate Expressions for Hybrid Rockets." AIAA/ASME/ASEE Joint Propulsion Conference, Tucson, AZ, July 2005. Print. 

 

Grosse, Matthias. "Development Work on a Small Experimental Hybrid Rocket." AIAA/ASME/ASEE Joint Propulsion Conference, Seattle, WA, July 1997. Print.