The Mechanical Engineering Department at California Polytechnic State University in San Luis Obispo currently maintains a lab-scale hybrid rocket motor for which nitrous oxide is utilized as the oxidizer in the combustion system. Because of its availability, the same two-phase (gas and liquid) nitrous oxide that is used in the combustion system is also routed around the throat of the hybrid rocket’s converging-diverging nozzle as a coolant. While this coolant system has proven effective empirically in previous tests, the physics behind the flow of the two-phase mixture is largely unexplained. This thesis provides a method for predicting some of its behavior by modeling it using the classic gas dynamics scenarios of Rayleigh and Fanno flows which refer to one-dimensional, compressible, inviscid flow in a constant area duct with heat addition and friction. The two-phase model produced utilizes a separated phase with interface exchange model for predicting whether or not dryout occurs. The Shah correlation is used to predict heat transfer coefficients in the nucleate boiling regime. The homogeneous flow model is utilized to predict pressure drop. It is proposed that a Dittus-Boelter based correlation much like that of Groeneveld be developed for modeling heat transfer coefficients upon the collection of sufficient data. Data was collected from a series of tests on the hybrid rocket nozzle to validate this model. The tests were first run for the simplified case of an ideal gas (helium) coolant to verify the experimental setup and promote confidence in subsequent two-phase experimental results. The results of these tests showed good agreement with a combined Rayleigh-Fanno model with a few exceptions including: (1) reduced experimental gas pressure and temperature in the annulus entrance and exit regions compared to the model and (2) reduced experimentally measured copper temperatures uniformly through the annulus. These discrepancies are likely explained by the geometry of the flowpath and location of the copper thermocouples respectively. Next, a series of two-phase cooled experiments were run. Similar trends were seen to the helium experiment with regards to entrance and exit regions. The two-phase Rayleigh homogeneous flow model underpredicted pressure drop presumably due to the inviscid assumption. Ambiguity was observed in the fluid temperature measurements but the trend seemed to suggest that mild thermal non-equilibrium existed. In both cases, the dryout model predicted that mist flow (a post-CHF regime) occurred over most of the annulus. Several modifications should be implemented in future endeavors. These include: (1) collecting more data to produce a heat transfer coefficient correlation specific to the nitrous oxide system of interest, (2) accounting for thermal non-equilibrium, (3) accounting for entrance and exit effects, and (4) developing a two-phase Fanno model.

Nitrous oxide (N2O) is an inexpensive and readily available non-toxic rocket motor oxidizer. It is the most commonly used oxidizer for hybrid bipropellant rocket systems, and several bipropellant liquid rocket designs have also used nitrous oxide. In liquid form, N2O is highly stable, but in vapor form it has the potential to decompose exothermically, releasing up to 1865 Joules per gram of vapor as it dissociates into nitrogen and oxygen. Consequently, it has long been considered as a potential "green" replacement for existing highly toxic and dangerous monopropellants. This project investigates the feasibility of using the nitrous oxide decomposition reaction as a monopropellant energy source for igniting liquid bipropellant and hybrid rockets that already use nitrous oxide as the primary oxidizer. Because nitrous oxide is such a stable propellant, the energy barrier to dissociation is quite high; normal thermal decomposition of the vapor phase does not occur until temperatures are above 800 C. The use of a ruthenium catalyst decreases the activation energy for this reaction to allow rapid decomposition below 400 C. This research investigates the design for a prototype device that channels the energy of dissociation to ignite a laboratory scale hybrid rocket motor.

Combustion instability (CI) has been persistent in all forms of propulsion since their inception. CI is characterized by pressure oscillations within the propulsion system. If even a small fraction of the dense energy within the system is converted to acoustic oscillations the system vibrations can be devastating. The coupling of combustion and fluid dynamic phenomena in a nonlinear system poses CI as a significant engineering challenge. Drawing from previous analysis, second order acoustic energy models are taken to third order. Second order analysis predicts exponential growth. The addition of the third order terms capture the nonlinear acoustic phenomena (such as wave steepening) observed in experiments. The analytical framework is derived such that the energy sources and sinks are properly accounted for. The resulting third order solution is compared against a newly performed simplified acoustic closed tube experiment. This experiment provides the interesting result that in a forced system, as the 2nd harmonic is driven, no energy is transferred back into the 1st mode. The subsequent steepened waveform is a summation of 2nd mode harmonics (2, 4, 6, 8...) where all odd modes are nonexistent. The current third order acoustic model recreates the physics as seen in the experiment. Numerical experiments show the sensitivity of the pressure wave limit cycle amplitude to the second order growth rate, highlighting the importance of correctly calculating the growth rates. The sensitivity of the solution to the third order parameter is shown as well. Exponential growth is found if the third order parameter is removed, and increased nonlinear behavior is found if it retained and as it is increased. The solutions sensitivity to this term highlights its importance and shows the need for continued analysis via increasing the models generality by including neglected effects. In addition, the affect of a time varying second order growth rate is shown. This effect shows the importance of modeling the system in time because of the time lag between changes in the growth rate to a change in the limit cycle amplitude.

Combustion instability is a problem that has plagued the development of rocket-propelled devices since their conception. It is characterized by the occurrence of high-frequency nonlinear gas oscillations inside the combustion chamber. This phenomenon degrades system performance and can result in damage to both structure and instrumentation. The goal of this dissertation is to clarify the role of unsteady combustion in the combustor instability problem by providing the first quantified estimates of its effect upon the stability of liquid rocket engines. The combination of this research with a new system energy balance method, accounting for all dynamic interactions within a system, allows for the isolation of combustion effects for this study. These effects are quantified through use of classical linear stability analysis to calculate the unsteady combustion heat release growth rate. Since combustion modeling can become very involved, including the mixing process and multiple reactions concerned, for this initial evaluation the model is limited to a one-dimensional flame analysis for a one-step premixed chemical reaction. Using classical analysis of oscillatory burning, the governing combustion equations are expanded into sets of steady and unsteady equations adapted for premixed liquid rockets. From this expansion process, the first real treatment of the effects of unsteady combustion in a rocket system is presented, and the first quantified values of the unsteady heat release in a rocket system are computed. Finally, the corresponding linear heat release growth rate for the system is then calculated for the first quantified effects of unsteady combustion on the overall system stability. The mechanism of unsteady combustion is shown to behave as a driving mechanism, serving as one of the more important stability mechanisms comparable to the magnitude of the nozzle damping mechanism. This analysis confirms that unsteady combustion is an important stability mechanism that warrants further investigation. This study also creates a firm foundation upon which to extend the analysis of this important mechanism to fully understand all of its effects within a rocket system.

State of the art research in hydrodynamic stability analysis has moved from classic one-dimensional methods such as the local nonparallel approach and the parabolized stability equations to two-dimensional, biglobal, methods. The paradigm shift toward two dimensional techniques with the ability to accommodate fully three-dimensional base flows is a necessary step toward modeling complex, multidimensional flowfields in modern propulsive applications. Here, we employ a two-dimensional spatial waveform with sinusoidal temporal dependence to reduce the three-dimensional linearized Navier-Stokes equations to their biglobal form. Addressing hydrodynamic stability in this way circumvents the restrictive parallel-flow assumption and admits boundary conditions in the streamwise direction. Furthermore, the following work employs a full momentum formulation, rather than the reduced streamfunction form, accounting for a nonzero tangential mean flow velocity. This approach adds significant complexity in both formulation and implementation but renders a more general methodology applicable to a broader spectrum of mean flows. Specifically, we consider the stability of three models for bidirectional vortex flow. While a complete parametric study ensues, the stabilizing effect of the swirl velocity is evident as the injection parameter, kappa, is closely examined.

A numerical analysis was conducted to study the effects of geometrically scaling scramjet inlet-combustor isolators. Three-dimensional fully viscous numerical simulation of the flow inside constant area rectangular ducts, with a downstream back pressure condition, was analyzed using the SolidWorks Flow Simulation software. The baseline, or 1X, isolator configuration has a 1” x 2.67” cross section and 20” length. This baseline configuration was scaled up based on the 1X configuration mass flow to 10X and 100X configurations, with ten and one hundred times the mass flow rate, respectively. The isolator aspect ratio of 2.67 was held constant for all configurations. To provide for code validation, the Flow Simulation program was first used to analyze a converging-diverging channel and a wind tunnel nozzle. The channel case was compared with analytical theory and showed good agreement. The nozzle case was compared with AFRL experimental data and showed good agreement with the entrance and exit conditions (Pi0= 40 psia, Ti0= 530ºR, Pe= 18.86 psia, Te= 456ºR, respectively). While the boundary layer thickness remained constant, the boundary layer thickness with respect to the isolator height decreased as the scale increased. For all the isolator simulations, a shock train was expected to form inside the duct. However, the flow simulation failed to generate this flow pattern, due to improper sizing of the isolator and combustor for a 3-D model or having a low pressure ratio of 2.38. Instead, a single normal shock wave was established at the same relative location within the length of each duct, approximately 80% of the duct length from the isolator entrance. The shape of the shock changed as the scale increased from a normal shock wave, to a bifurcated shock wave, and to a normal shock train, respectively for the 1X, 10X, and 100X models.

A computer model of a blow-down free-jet hypersonic propulsion test facility exists to validate facility control systems as well as predict problems with facility operation. One weakness in this computer model is the modeling of an air ejector diffuser system. Two examples of facilities that could use this ejector diffuser model are NASA Langley Research Center's 8-ft High Temp. Tunnel (HTT) and the Aero-Propulsion Test Unit (APTU) located at Arnold Engineering Development Center. Modeling an air ejector diffuser system for a hypersonic propulsion test facility includes modeling three coupled systems. These are the ejector system, the primary free-jet nozzle that entrains secondary airflow from the test cell, and the test article. Both of these facilities are capable of testing scramjets/ramjets at high Mach numbers. Compared with computer simulation data, experimental test cell pressure data do not agree due to the current modeling technique used. An improved computer model was derived that incorporates new techniques for modeling the ejector diffuser. This includes real gas effects at the ejector nozzles, flow constriction due to free-jet nozzle and ejector plumes, test article effects, and a correction factor of the normal shock pressure ratio in a supersonic diffuser. A method was developed to account for the drag and thrust terms of the test article by assuming a blockage factor and using a drag coefficient*Area term for both the test article and thrust stand derived from experimental data. An ideal ramjet model was also incorporated to account for the gross thrust of the test article on the system. The new ejector diffuser model developed improved the accuracy and fidelity of the facility model as compared with experimental test data while only negligibly affecting computational speed. Comparisons of the model data with experimental test data showed a close match for test cell pressure (within 1 percent for final test cell pressure). The model accurately simulated both the unstarted and started modes of ejector flow, in which test cell pressure increases with nozzle total pressure once in started mode.

A numerical analysis was conducted to study the effects of geometrically scaling scramjet inlet-combustor isolators. Three-dimensional fully viscous numerical simulation of the flow inside constant area rectangular ducts, with a downstream back pressure condition, was analyzed using the SolidWorks Flow Simulation software. The baseline, or 1X, isolator configuration has a 1” x 2.67” cross section and 20” length. This baseline configuration was scaled up based on the 1X configuration mass flow to 10X and 100X configurations, with ten and one hundred times the mass flow rate, respectively. The isolator aspect ratio of 2.67 was held constant for all configurations. To provide for code validation, the Flow Simulation program was first used to analyze a converging-diverging channel and a wind tunnel nozzle. The channel case was compared with analytical theory and showed good agreement. The nozzle case was compared with AFRL experimental data and showed good agreement with the entrance and exit conditions (Pi0= 40 psia, Ti0= 530ºR, Pe= 18.86 psia, Te= 456ºR, respectively). While the boundary layer thickness remained constant, the boundary layer thickness with respect to the isolator height decreased as the scale increased. For all the isolator simulations, a shock train was expected to form inside the duct. However, the flow simulation failed to generate this flow pattern, due to improper sizing of the isolator and combustor for a 3-D model or having a low pressure ratio of 2.38. Instead, a single normal shock wave was established at the same relative location within the length of each duct, approximately 80% of the duct length from the isolator entrance. The shape of the shock changed as the scale increased from a normal shock wave, to a bifurcated shock wave, and to a normal shock train, respectively for the 1X, 10X, and 100X models.

A computer model of a blow-down free-jet hypersonic propulsion test facility exists to validate facility control systems as well as predict problems with facility operation. One weakness in this computer model is the modeling of an air ejector diffuser system. Two examples of facilities that could use this ejector diffuser model are NASA Langley Research Center's 8-ft High Temp. Tunnel (HTT) and the Aero-Propulsion Test Unit (APTU) located at Arnold Engineering Development Center. Modeling an air ejector diffuser system for a hypersonic propulsion test facility includes modeling three coupled systems. These are the ejector system, the primary free-jet nozzle that entrains secondary airflow from the test cell, and the test article. Both of these facilities are capable of testing scramjets/ramjets at high Mach numbers. Compared with computer simulation data, experimental test cell pressure data do not agree due to the current modeling technique used.An improved computer model was derived that incorporates new techniques for modeling the ejector diffuser. This includes real gas effects at the ejector nozzles, flow constriction due to free-jet nozzle and ejector plumes, test article effects, and a correction factor of the normal shock pressure ratio in a supersonic diffuser. A method was developed to account for the drag and thrust terms of the test article by assuming a blockage factor and using a drag coefficient*Area term for both the test article and thrust stand derived from experimental data. An ideal ramjet model was also incorporated to account for the gross thrust of the test article on the system.The new ejector diffuser model developed improved the accuracy and fidelity of the facility model as compared with experimental test data while only negligibly affecting computational speed. Comparisons of the model data with experimental test data showed a close match for test cell pressure (within 1 percent for final test cell pressure). The model accurately simulated both the unstarted and started modes of ejector flow, in which test cell pressure increases with nozzle total pressure once in started mode.

High Efficiency Multistage Plasma Thrusters (HEMPTs) are a relatively new form of electric propulsion that show promise for use on a variety of missions and have several advantages over their older EP competitors. One such advantage is their long predicted lifetime and minimal wall erosion due to a unique periodic permanent magnet system. A laboratory HEMPT was built and donated by JPL for testing at Cal Poly. Previous work was done to characterize the performance of this thruster and it was found to exhibit a large plume divergence, resulting in decreased thrust and specific impulse. This thesis explores the design and application of a magnetic shield to modify the thruster’s magnetic field to force more ion current towards the centerline. A previous Cal Poly thesis explored the same concept, and that work is continued and furthered here. The previous thesis tested a shield which increased centerline current but decreased performance. A new shield design which should avoid this performance decrease is studied here. Magnetic modelling of the thruster was performed using COMSOL. This model was verified using guassmeters to measure the field strength at many discrete points within and near the HEMPT, with a focus on the ionization channel and exit plane. A shield design which should significantly reduce the radial field strength at the exit plane without affecting the ionization channel field was modelled and implemented. The HEMPT was tested in a vacuum chamber with and without the shield to characterize any change to performance characteristics. Data were collected using a nude Faraday probe and retarding potential analyzer. The data show a significant increase in centerline current with the application of the shield, but due to RPA malfunction and thruster failure the actual change in performance could not be concluded. The unshielded HEMPT was characterized, however, and was found to produce 12.1 +/- 1.3 mN of thrust with a specific impulse of 1361 +/- 147s. The thruster operated with a total efficiency of 10.63 +/- 3.66%, an efficiency much lower than expected. A large contributor to this low efficiency is likely the use of argon in place of xenon. Its lower mass and higher ionization energy make it a less efficient propellant choice. Further, the thruster is prone to overheating, indicating that significant thermal losses are present in this design.