The present work was conducted with the intent of developing a high-fidelity numerical model of a unique combustion flow problem combining multi-phase fuel injection with substantial momentum and temperature into a highly complex turbulent flow. This important problem is very different from typical and more widely known liquid fuel combustion problems and is found in practice in pulverized coal combustors and ducted rocket ramjets. As the ducted rocket engine cycle is only now finding widespread use, it has received little research attention and was selected as a representative problem for this research. Prior to this work, a method was lacking domestically and internationally to effectively model the ducted rocket engine cycle with confidence. In the ducted rocket a solid fuel gas generator is used to deliver a fuel-rich multi-phase mixture to the combustion chamber. When a valve is used to vary the fuel generator pressure, and thereby the delivered fuel flowrate, the engine is known as a Variable Flow Ducted Rocket (VFDR). The Aerojet MARC-R282 ramjet engine represents the worlds first VFDR flown, and the first in operational use. Although performance requirements were met, improvements are sought in the understanding of the ramjet combustion process with a future aim of reducing the visible exhaust and correcting uneven combustor heating patterns. For this reason the MARC-R282 combustor was selected as the baseline geometry for the present research, serving to provide a documented baseline case for numerical modeling and also being a good candidate to benefit from an improved understanding of the combustion process. In order to proceed with the present research, experiments were first carried out to characterize the gas generator particulate exhaust in terms of composition and particle size. Equilibrium thermochemistry was used to supplement these data to develop a gas phase combustion model. The gas phase reactions and resulting particle definition were modeling using the FLUENT Computational Fluid Dynamics (CFD) code for the baseline GQM-163A Supersonic Sea Skimming Missile (SSST) operating conditions. These results were compared to direct-connect ramjet ground tests in order to validate the analysis tool. Data were developed to understand the gas and solid phase fuel exhaust characteristics at the propellant surface, exiting the gas generator injector, and following secondary combustion with air. Particles were collected and analyzed from the fuel generator exhaust. While exhibiting some variation with time in the firing, they were roughly an average of 20 microns in diameter, in line with prior experience with pulverized coal combustion experiments. A computational model was developed based on coal combustion parameters using FLUENT. However, despite considerable effort, the CFD analysis was not able to predict effective burning of the carbon particles to the degree seen in testing. In addition, using equilibrium thermochemistry as a basis for determining the carbon particle content in the fuel exhaust, the CFD analysis resulted in trends in performance opposite to the test results. These facts led to a hypothesis that there was actually a significant fraction of small particles or much less carbon produced than equilibrium thermochemistry would predict. A parametric analysis was performed replacing the 20 micron soot particles with fine fraction particles, representing a fraction of the predicted equilibrium carbon soot being still in the gas phase as higher molecular weight hydrocarbons, or in the form of sub-micron particles. When almost all particles were replaced with fine fraction particles, the model was able to correctly predict absolute values of combustion efficiency as well as trends for different injector geometries. The presence of particles was apparent from the visible exhaust and collection data, however they were found not to play a significant role in the combustion process for this fuel and engine configuration. The robustness of the computational model was also evaluated by examining the effects of turbulence model, order of discretization, and grid size. Comparable trends and results were seen for all cases examined. With the successful development of this modeling tool and an improved understanding of the combustion process, future work is enabled to develop improved combustor flow management and fuel injection schemes to improve existing designs and develop new configurations. This research has served to advance the field of combustion modeling by providing: 1) a solid ducted rocket combustion modeling tool considering solid and gas phase combustion, 2) a correlation between primary combustion theory and particulate exhaust sampling, 3) low length/diameter ratio ducted rocket combustor modeling, and 4) combustor CFD coupled with solid particle tracking and combustion models. / Ph. D.

In the aerospace propulsion sector safety is an important driver to costs, vehicle design and mission capabilities. Hybrid rockets are considered some of the safest forms of chemical propulsion. That factor alone makes hybrid rocket propulsion systems desirable options. Hybrid systems often benefit from multiple additional advantages over conventional solid and liquid propellant systems, including: minimal environmental impact, higher density impulses, start-stop-restart capabilities, simplistic random throttle control, low development costs, and basic transportation and storage requirements. A major issue that continues to impact the effective use of hybrid systems, is that classical hybrid rocket fuels suffer in low regression rates. If fuel regression rates can be improved upon without diminishing any of the other beneficial factors to a hybrid rocket motor then a far greater market for such systems can be generated. In this work, additively manufactured polypropylene solid fuel grains were infused with gels as a means of significantly altering the fuel burning rates in a lab scale hybrid rocket motor. Gels based on Jet-A were created using both particulate (fumed silica, micro aluminum, nano aluminum) and polymeric (paraffin wax) gellants. The particle structure of the aluminum powders was characterized by means of microscopic imaging, particle size measurement, and thermal mass response analysis. The rheological behavior of the gels was characterized in order to determine the relationship between melt layer viscosity, viscoelastic properties, and combustion performance. High speed color video recording was used on select grains for spatially and temporally resolved three-color camera pyrometry analysis. The process showed promise in determining aluminized gel burn time across an entire rocket firing. The performance of the gel infused grains was compared to a traditional center perforated fuel grain, under similar flows of gaseous oxygen. Rocket motors fired with gel infused grains exhibited pressure increases of greater than 40%. Gel infused fuel grains demonstrated regression rate enhancements up to 90% higher than the baseline. The estimated gel regression rates were over 500% higher than the host polypropylene fuel. When the O/F was maintained near stoichiometric or lean conditions, c∗ efficiencies of the gel infused grains were similar to that of the baseline indicating thorough combustion of the gels. At low oxygen mass flows, the effects of gel infusion are not as significant, which is consistent with the liquefying fuel entrainment concept. / Master of Science / In the field of air and space flight, safety is an important driver to costs, vehicle design and mission capabilities. Hybrid rockets are considered some of the safest forms of vehicle lift systems compared to similar forms. That factor alone makes hybrid rockets desirable options. Hybrid systems often benefit from multiple additional advantages over similar systems often used, including: minimal environmental impact, greater force for a given time and volume of fuel, start-stop-restart capabilities, simplistic random motor control, low development costs, and basic transportation and storage requirements. A major issue that continues to impact the effective use of hybrid systems is that classical hybrid rocket fuels suffer in low burn rates. If fuel burn rates can be improved upon without diminishing any of the other beneficial factors to a hybrid rocket motor then a far greater market for such systems can be generated. In this work, specially manufactured solid fuel grains were combined with gels as a means of significantly altering the fuel burning rates in a small scale test setup. Gels based on a type of jet fuel were created using multiple gel forming and modifying materials. The structure of two types of small scale aluminum powders was characterized by means of microscopic imaging, particle size measurement, and weight response to thermal changes. Properties specific to the gels were characterized in order to determine performance relationships to individual material properties. High speed color video recording was used on select grains for space and time resolved three-color camera temperature analysis. The process showed promise in determining aluminized gel burn time across an entire rocket firing. The performance of the gel modified grains was compared to a traditional fuel grain design, under similar flows of gaseous oxygen. Rocket motors fired with gel modified grains exhibited pressure increases of greater than 40%. Gel modified fuel grains demonstrated burn rate enhancements up to 90% higher than the traditional fuel grain design. The estimated gel burn rates were over 500% higher than the host polypropylene fuel. When ideal conditions were maintained, fuel burn efficiencies of the gel modified grains were similar to that of the traditional fuel grain design indicating ideal burning of the gels. At low oxygen flow rates, the effects of gel addition are not as significant, which is consistent with an expectant similar concept.

The problem of maximizing the altitude of a rocket in vertical flight has been extensively analyzed by many writers since the early days of rocketry. In the beginning, solutions were obtained using the classical theory of the Calculus of Variations, and later using Optimal Control theory. For strict assumptions on the drag law and the thrust, solutions were found, even in a closed, analytic form. Nevertheless, for more realistic conditions, the problem becomes a very complex one, and the solution is far from complete. In addition to this, complexity increases if an isoperimetric constraint is added to the problem. Such a case is, for example, the problem of extremizing the rise in altitude for a given time. In the present work an attempt is made to treat the problem under the most realistic assumptions used so far, for both the system of equations and the drag model. The analysis of the problem reveals that a more complex thrust history exists than the classical sequence of full-singular-coast subarcs, for both the time-constrained case, and for the case of a drag model with a sharp rise in the transonic region. In the first case, a second full-thrust subarc is generated at the end of the singular subarc, owing to the boundedness of the thrust, while, in the second case, a full-thrust subarc appears in transition from the subsonic to the supersonic branch of the singular path. Both are new results, at least for the bounded-thrust case, and the drag law assumed, insofar as the author knows. Discussion is also provided for the limitations of such a switching structure, and it is shown that the composition of an optimal trajectory is heavily dependent on the assumed drag law. / Master of Science

The ADP rocket pump inducer was studied computationally using a 3-D Navier-Stokes solver, The Moore Elliptic Flow Program. Design and off-design flow rates were simulated to qualitatively and quantitatively study the effects of flow rate on the flow and performance. Several views of the results were created to aid flow visualization. The 3-D laser measurements made by Rocketdyne were used for comparison. The velocity magnitudes as well as the flow patterns within the inducer match well between the calculated and measured results. The axial velocity distribution and the rotary stagnation pressure, losses, are predicted very well by the calculation. The internal flow patterns developed in the simulation as expected, with radial outflow in the blade boundary layers. The tip leakage flow formed a recirculation region, a toroidal shaped vortex at the tip leading edge of the blades. The associated backflow forms a blockage that varies with flow rate. The thermodynamic performance was evaluated by calculating the contributions to pressure rise, the pump characteristic, the contributions to moment of momentum, and the efficiency. The centrifugal effect and relative velocity effect were found to vary with flow rate. The effective inlet throat radius, which governs these two effects, changes with flow rate because of the recirculation blockage. The shear on the blades was found to produce a small fraction of the work in the inducer, and most was produced by the pressure difference across the blade. The inducer efficiency was about 89%, and increased with decreasing flow rate in the range of flow rates considered, from 89% to 110% of the design flow rate. / Master of Science

A nonlinear programming technique is applied to the optimization of the thrust and lift control histories for missiles. The first problem considered is that of determining the thrust history which maximizes the range of a continuously-variable (non-pulsed) thrust rocket in horizontal lifting flight. The optimal control solution for this problem is developed. The problem is then approximated by a parameter optimization problem which is solved using a second-order, quasi-Newton method with constraint projection. The two solutions are found to compare well. This result allows confidence in the use of the nonlinear-programming technique to solve optimization problems in flight mechanics for which no analytical optimal-control solutions exist. Such a problem is to determine the thrust and lift histories which maximize the final velocity of a multiple-pulse missile. This problem is solved for both horizontal- and elevation-plane trajectories with and without final time constraints. The method is found to perform well in the solution of these optimization problems and to yield substantial improvements in performance over the nominal trajectories. / M.S.

Increasing interest in the development of nontoxic monopropellants for the replacement of hydrazine and its derivatives stems from the desire for safer and thus more cost-effective alternatives. Ionic liquid monopropellants based on the hydroxylammonium nitrate and ammonium dinitramide ionic oxidizer salts have received the majority of attention over the last two decades and present a promising alternative with higher performance and more attractive handling qualities than hydrazine. These monopropellants are employed using catalytic methods which lead to their decomposition and ignition. However, the development of compatible catalysts remains a limiting step in the technological readiness of these alternative monopropellants. Due to their ionic nature, the development of ionic liquid monopropellants has led to many investigations on the utilization of electrolysis to achieve combustion. Separately, there has been a longtime interest in the use of gelled propellants for enhanced handling and operating safety. Atomization and combustion inefficiencies associated with gels have continued to limit their use. Monopropellants composed of gel polymer electrolytes present a unique opportunity which combines the safety features of gelled propellants as well as the ionic conductivity seen in ionic liquids, allowing them to decompose and ignite electrolytically. In this research, a family of electrically controlled monopropellants that utilize electrolysis in this fashion was developed from a gel polymer electrolyte. Their fundamental properties, including those pertaining to rheology, conductivity, thermal stability, and combustion, are explored as the composition of the oxidizer salt is varied. / Master of Science / Current advancements in rocket propulsion include interests in developing alternative green propellants for use in spacecraft propulsion systems with the hope of replacing current options which may be toxic to handle and present a serious safety hazard. Alternative propellants are generally thought of as not requiring special safety equipment or protocols in their handling, thereby reducing costs. Several promising options belonging to a category of propellants known as ionic liquids have made significant progress in development since the 1990s and have the potential to be used alongside a novel electrical combustion method known as electrolysis. Gelled propellants are another possible alternative which have been researched for their appealing safety qualities for some time. While not researched for their use as rocket propellants until very recently, gel polymer electrolytes have received interest in this application due to their composition which includes a polymer, commonly used as rocket fuel, and an oxidizer salt. Due to their inherent electrical conductivity, their potential to use electrolysis in a similar manner to ionic liquids to achieve combustion is of interest. The research detailed in this thesis was completed to characterize fundamental material and combustion properties of a gel polymer electrolyte propellant as its oxidizer constituents are varied.

A mixed variational statement and corresponding finite element model are developed for an axisymmetric solid body under external symmetric loads using the updated Lagrangian formulation. The mixed finite element formulation treats the nodal displacements and stresses as the variables that can be approximated independently. The method of static condensation is used to keep some stresses across interfaces of a solid of revolution discontinuous. The stiffness matrix is transformed from semi-positive definite to positive definite. A rocket motor is composed of (1) case (2) propellant and (3) hollow air core and is modelled as an axisymmetric solid. The propellant of a rocket motor is treated as a viscoelastic material. Static and dynamic analyses are performed under (1) two opposite line loads (2) two opposite patch loads and (3) one line and one patch load combination. The modified Newton-Raphson method is used in the solutions of nonlinear algebraic equations. The analysis of free vibration is executed first and then the Newmark direct integration method is used in a transient analysis. Results of these analyses are compared with solutions obtained from different methods that are independent of the finite element method. / Ph. D.

Star grain configuration design has been widely used in solid rocket applications for several decades. Although a large number of surface cracks are detected in the rocket motor propellants, the mechanism of these cracks is sull not well known due to the complex geometry of the grain. A stress-freezing photoelastic investigation has been performed to study the deep cracks which emanate from the fingertips of the star-shaped cutout cylinders. Using three-dimensional photoelasticity and proper algorithms in fracture mechanics, the stress intensity factors (SIF's) and the stress singularity orders along the crack front have been calculated. A surface effect on the dominant singularity order is observed and some analytical results are employed as a comparison. Meanwhile, three-dimensional finite element solution to the circular cylinder is used to find the “equivalent” inner radius for the internal star cylinder and the variation of SIF's along the crack border shows a very similar trend to the experimental results once the "equivalent" radius is adopted. / Master of Science

While Newton’s law of gravity suffices for travelling nearby a planetary body, massive objects such as black holes require the more advanced theory of general relativity. To successfully fly a rocket in the vicinity of such an object, a first step is the description of test particle trajectories. In this report, the equations of motion for test particles affected by external forces are derived and used for simulations on a range of examples within the framework of general relativity. An application for these equations is found in the force required to counteract gravity, regardless of any non-radial motion around the black hole. Then, the equations of motion for a rocket test particle, which accelerates by expelling mass, are formulated for radial motion and used to find optimal mass conserving radial trajectories.

<p> Lifted non-premixed turbulent jet flames in the Transverse Instability Combustor (TIC) have been analyzed using qualitative and quantitative methods. Lifted flames in the TIC have been observed to stabilize about zero to five injector exit diameters downstream of the dump plane into the chamber and exhibit pulsating, unsteady burning. Anchored flames immediately begin reacting in the injector recess and burn evenly in a uniform jet from the injector exit through the entire optically accessible region. Statistically significant, repeatable behavior lifted flames are observed. It is shown that the occurrence of lifted flames is most likely for an injector configuration with close wall-spacing, second greatest for a configuration with close middle-element spacing, and lowest for a configuration with even element-spacing. For all configurations, of those elements that have been observed to lift, the center element is most likely to lift while the second element from the wall was likely. Flames at the wall elements were never observed to lift. Evidence is shown to support that close injector element spacing and stronger transverse pressure waves aid lateral heat transfer which supports flame stability in the lifted position. It is hypothesized that the stability of lifted flames is influenced by neighboring ignition sources, often a neighboring anchored flame. It is also shown that instances of lifted flames increase with the root-mean-squared magnitude of pressure fluctuation about its mean (P’ RMS) up to a threshold, after which flames stabilize in the anchored recess position.</p> <p>Dynamic mode decomposition (DMD) and proper orthogonal decomposition (POD) analyses of CH* chemiluminescence data is performed. It is found that lateral ignition of the most upstream portion of lifted flames is dominated by the 1W mode. Furthermore, it is shown that low-frequency high energy modes with spatial layers resemble intensity-pulses, possibly attributable to ignition. These modes are trademarks of CH* chemiluminescent intensity data of lifted flames. It was also shown that the residence time in the chamber may be closely associated with those low-frequency modes around 200 Hz. DMD and POD were repeated for a downstream region on the center element, as well as a near-wall element, highlighting differences between the lifted flame dynamics in all three regions. </p> <p>It is shown that lifted flames are best characterized by their burning behavior and in rare cases may stabilize in the recess, while still being “lifted”. Furthermore, it is shown that flame position differentiation can extend into an initial period of highly stable combustor operation. Dynamic mode decomposition is explored as potential method to understand physical building blocks of proper orthogonal spatial layers. Non-visual indicators of lifted flames within the high-frequency (HF) pressure signal are sought to seek a method that allows for observation of lifted flames in optically inaccessible combustors, such as those in industry. Some attributes of power-spectral diagrams and cross-correlations of pressure signals are provided as potential indicators. </p>