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Hybrid rocket fuel combustion and regression rate study

The objectives of this study are to develop hybrid fuels (1) with higher regression rates and reduced dependence on fuel grain geometry and (2) that maximize potential specific impulse using low-cost materials. A hybrid slab window motor system was developed to screen candidate fuels - their combustion behavior and regression rate. Combustion behavior diagnostics consisted of video and high speed motion pictures coverage. The mean fuel regression rates were determined by before and after measurements of the fuel slabs. The fuel for this initial investigation consisted of hydroxyl-terminated polybutadiene binder with coal and aluminum fillers. At low oxidizer flux levels (and corresponding fuel regression rates) the filled-binder fuels burn in a layered fashion, forming an aluminum containing binder/coal surface melt that, in turn, forms into filigrees or flakes that are stripped off by the crossflow. This melt process appears to diminish with increasing oxidizer flux level. Heat transfer by radiation is a significant contributor, producing the desired increase in magnitude and reduction in flow dependency (power law exponent) of the fuel regression rate.

Strand, L. D.↗

Photothermal Monitoring Of Curing Of Polymers

Time-resolved infrared radiometry (TRIR) adapted to monitoring curing of some polymers in production. Proposal part of continuing effort to perfect production of hydroxy-terminated polybutadiene for use in liners of solid-fuel rocket motors. Applicable to monitoring changing states of many other materials in process. TRIR, non-contact technique implemented with remotely situated equipment and better suited to use in production.

Rooney, Michael↗

Development and testing of 11- and 24-inch hybrid motors under the joint government/industry IR&D program

Establishment of a test facility and associated 11-in.-diameter motor for hybrid propulsion technology development at NASA's George C. Marshall Space Flight Center is discussed in this paper. Results of twenty 11-in.-diameter motor tests with a UTF-29901 (60 percent polycyclopentadiene, 40 percent hydroxyl-terminated polybutadiene)/gaseous oxygen propellant system are presented. Tests at this scale have developed fuel regression correlations for comparison with results of yet-to-be-completed, 24-in.-diameter motor tests; demonstrated combustion efficiency levels in the 95 percent range for both single- and multiple-port grain configurations; have shown smooth and stable throttling characteristics over flight-type throttle ranges; and have begun to establish criteria for stable combustion in hybrid motors. The testing of 24-in. motors has not as yet been initiated and is not addressed.

Boardman, T. A.↗

Fuel decomposition and boundary-layer combustion processes of hybrid rocket motors

Using a high-pressure, two-dimensional hybrid motor, an experimental investigation was conducted on fundamental processes involved in hybrid rocket combustion. HTPB (Hydroxyl-terminated Polybutadiene) fuel cross-linked with diisocyanate was burned with GOX under various operating conditions. Large-amplitude pressure oscillations were encountered in earlier test runs. After identifying the source of instability and decoupling the GOX feed-line system and combustion chamber, the pressure oscillations were drastically reduced from +/-20% of the localized mean pressure to an acceptable range of +/-1.5% Embedded fine-wire thermocouples indicated that the surface temperature of the burning fuel was around 1000 K depending upon axial locations and operating conditions. Also, except near the leading-edge region, the subsurface thermal wave profiles in the upstream locations are thicker than those in the downstream locations since the solid-fuel regression rate, in general, increases with distance along the fuel slab. The recovered solid fuel slabs in the laminar portion of the boundary layer exhibited smooth surfaces, indicating the existence of a liquid melt layer on the burning fuel surface in the upstream region. After the transition section, which displayed distinct transverse striations, the surface roughness pattern became quite random and very pronounced in the downstream turbulent boundary-layer region. Both real-time X-ray radiography and ultrasonic pulse-echo techniques were used to determine the instantaneous web thickness burned and instantaneous solid-fuel regression rates over certain portions of the fuel slabs. Globally averaged and axially dependent but time-averaged regression rates were also obtained and presented.

Chiaverini, Martin J.↗

Combustion of solid fuel slabs with gaseous oxygen in a hybrid motor analog

Using a high-pressure, two-dimensional hybrid motor, an experimental investigation was conducted on fundamental processes involved in hybrid rocket combustion. HTPB (Hydroxyl-terminated- Polybutadiene) fuel cross linked with diisocyanate was burned with GOX under various operating conditions. Large amplitude pressure oscillations were encountered in earlier test runs. After identifying the source of instability and decoupling the GOX feed line system and combustion chamber, the pressure oscillations were drastically reduced from +/- 20% of the localized mean pressure to an acceptable range of +/- 1.5%. Embedded fine-wire thermocouples indicated that the surface temperature of the burning fuel was around 1000 K depending upon axial locations and operating conditions. Also, except near the leading-edge region, the subsurface thermal wave profiles in the upstream locations arc thicker than those in the downstream locations since the solid-fuel regression rate, in general, increases with distance along the fuel slab. The recovered solid fuel slabs in the laminar portion of the boundary layer exhibited smooth surfaces, indicating the existence of a liquid melt layer on the burning fuel surface in the upstream region. After the transition section, which displayed distinct transverse striations, the surface roughness pattern became quite random and very pronounced in the downstream turbulent boundary-layer region. Both real time X-ray radiography and ultrasonic pulse-echo techniques were used to determine the instantaneous web thicknesses and instantaneous solid-fuel regression rates over certain portions of the fuel slabs. Globally averaged and axially dependent but time-averaged regression rates were also obtained and presented. Several tests were conducted using, simultaneously, one translucent fuel slab and one fuel slab processed with carbon black powder. The addition of carbon black did not affect the measured regression rates or surface temperatures in comparison to the translucent fuel slabs.

Chiaverini, Martin J.↗

Combustion Processes in Hybrid Rocket Engines

In recent years, there has been a resurgence of interest in the development of hybrid rocket engines for advanced launch vehicle applications. Hybrid propulsion systems use a solid fuel such as hydroxyl-terminated polybutadiene (HTPB) along with a gaseous/liquid oxidizer. The performance of hybrid combustors depends on the convective and radiative heat fluxes to the fuel surface, the rate of pyrolysis in the solid phase, and the turbulent combustion processes in the gaseous phases. These processes in combination specify the regression rates of the fuel surface and thereby the utilization efficiency of the fuel. In this paper, we employ computational fluid dynamics (CFD) techniques in order to gain a quantitative understanding of the physical trends in hybrid rocket combustors. The computational modeling is tailored to ongoing experiments at Penn State that employ a two dimensional slab burner configuration. The coordinated computational/experimental effort enables model validation while providing an understanding of the experimental observations. Computations to date have included the full length geometry with and with the aft nozzle section as well as shorter length domains for extensive parametric characterization. HTPB is sed as the fuel with 1,3 butadiene being taken as the gaseous product of the pyrolysis. Pure gaseous oxygen is taken as the oxidizer. The fuel regression rate is specified using an Arrhenius rate reaction, which the fuel surface temperature is given by an energy balance involving gas-phase convection and radiation as well as thermal conduction in the solid-phase. For the gas-phase combustion, a two step global reaction is used. The standard kappa - epsilon model is used for turbulence closure. Radiation is presently treated using a simple diffusion approximation which is valid for large optical path lengths, representative of radiation from soot particles. Computational results are obtained to determine the trends in the fuel burning or regression rates as a function of the head-end oxidizer mass flux, G=rho(e)U(e), and the chamber pressure. Furthermore, computation of the full slab burner configuration has also been obtained for various stages of the burn. Comparisons with available experimental data from small scale tests conducted by General Dynamics-Thiokol-Rocketdyne suggest reasonable agreement in the predicted regression rates. Future work will include: (1) a model for soot generation in the flame for more quantitative radiative transfer modelling, (2) a parametric study of combustion efficiency, and (3) transient calculations to help determine the possible mechanisms responsible for combustion instability in hybrid rocket motors.

Venkateswaran,S.↗

CFD Analysis of the 24-inch JIRAD Hybrid Rocket Motor

A series of multispecies, multiphase computational fluid dynamics (CFD) analyses of the 24-inch diameter joint government industry industrial research and development (JIRAD) hybrid rocket motor is described. The 24-inch JIRAD hybrid motor operates by injection of liquid oxygen (LOX) into a vaporization plenum chamber upstream of ports in the hydroxyl-terminated polybutadiene (HTPB) solid fuel. The injector spray pattern had a strong influence on combustion stability of the JIRAD motor so a CFD study was initiated to define the injector end flow field under different oxidizer spray patterns and operating conditions. By using CFD to gain a clear picture of the flow field and temperature distribution within the JIRAD motor, it is hoped that the fundamental mechanisms of hybrid combustion instability may be identified and then suppressed by simple alterations to the oxidizer injection parameters such as injection angle and velocity. The simulations in this study were carried out using the General Algorithm for Analysis of Combustion SYstems (GALACSY) multiphase combustion codes. GALACSY consists of a comprehensive set of droplet dynamic submodels (atomization, evaporation, etc.) and a computationally efficient hydrocarbon chemistry package built around a robust Navier-Stokes solver optimized for low Mach number flows. Lagrangian tracking of dispersed particles describes a closely coupled spray phase. The CFD cases described in this paper represent various levels of simplification of the problem. They include: (A) gaseous oxygen with combusting fuel vapor blowing off the walls at various oxidizer injection angles and velocities, (B) gaseous oxygen with combusting fuel vapor blowing off the walls, and (C) liquid oxygen with combusting fuel vapor blowing off the walls. The study used an axisymmetric model and the results indicate that the injector design significantly effects the flow field in the injector end of the motor. Markedly different recirculation patterns are observed in the vaporization chamber as the oxygen velocity and/or spray pattern is varied. The ability of these recirculation patterns to stabilize the diffusion flame above the surface of the solid fuel gives a plausible explanation for the experimentally determined combustion stability characteristics of the JIRAD motor, and suggests how combustion stability can be assured by modifications to the injector design.

Liang, Pak-Yan↗

Combustion of solid fuel slabs with gaseous oxygen in a hybrid motor analog

Using a high-pressure, two-dimensional hybrid motor, an experimental investigation was conducted on fundamental processes involved in hybrid rocket combustion. HTPB (Hydroxyl-terminated Polybutadiene) fuel cross-linked with diisocyanate was burned with gaseous oxygen (GOX) under various operating conditions. Large-amplitude pressure oscillations were encountered in earlier test runs. After identifying the source of instability and decoupling the GOX feed-line system and combustion chamber, the pressure oscillations were drastically reduced from plus or minus 20% of the localized mean pressure to an acceptable range of plus or minus 1.5%. Embedded fine--wire thermocouples indicated that the surface temperature of the burning fuel was around 1000 K depending upon axial locations and operating conditions. Also, except near the leading edge region, the subsurface thermal wave profiles in the upstream locations are thicker than those in the downstream locations since the solid-fuel regression rate, in general, increases with distance along the fuel slab. The recovered solid fuel slabs in the laminar portion of the boundary layer exhibited smooth surfaces, indicating the existence of a liquid melt layer on the burning fuel surface in the upstream region. After the transition section, which displayed distinct transverse striations, the surface roughness pattern became quite random and very pronounced in the downstream turbulent boundary-layer region. Both real-time X-ray radiography and ultrasonic pulse echo techniques were used to determine the instantaneous web thicknesses and instantaneous solid-fuel regression rates over certain portions of the fuel slabs. Globally averaged and axially dependent but time-averaged regression rates were also obtained and presented. Several tests were conducted using, simultaneously, one translucent fuel slab and one fuel slab processed with carbon black powder. The addition of carbon black did not affect the measured regression rates or surface temperatures in comparison to the translucent fuel slabs.

Chiaverini, Martin J.↗

Computational and Experimental Study of Energetic Material in a Counterflow Microgravity Environment

Ground based (normal gravity) combustion studies can provide important information on the processes by which monopropellants and composite systems burn. The effects of gravitational forces, however, can often complicate the interpretation of the models and the implementation of experiments designed to help elucidate complex issues. We propose to utilize a combined computational/experimental approach in a microgravity environment to understand the interaction of oxidizer-binder diffusion flames in composite propellants. By operating under microgravity conditions we will be able to increase the length scales and suppress the gravitational forces on melting binders such that increased resolution of both major and minor species will be possible thus reducing the demands placed on both the computational and diagnostic tools. Results of a detailed transport/finite rate chemistry model will be compared with nonintrusive optical diagnostic measurements of the structure and extinction of diffusion flames in which oxidizers such as ammonium perchlorate (AP) and ammonium dinitramide (ADN) are counterflowed against realistic binders such as hydroxyl-terminated polybutadiene (HTPB) and 3,3-bis(azidomethyl)oxetane (BAMO). The work proposed herein represents a collaborative effort among the research groups at Yale University, Princeton University and the Combustion Diagnostics Laboratory at the Naval Air Warfare Center in China Lake, CA.

Smooke, Mitchell D.↗

Final Report

This cooperative agreement explored the novel polymerization of vinylsilane, alone and in combination with other alkenylsilanes, alkylsilanes, and/or crosslinking agents, using dimethyltitanocene as homogeneous catalyst. The reactions were found to be initiated photochemically under mild conditions, and no hydrogen gas was evolved when alkenylsilanes were polymerized. The polymers were found to have predominately a carbosilane-type backbone containing -SiH2-CH2-CH2-Si and -SiH2-CH(CH3)-Si type linkages. The mechanism of polymerization was found to be step-growth. Despite the relatively low molecular weight of the polymer (M(sub n) - 500 and M(sub W) - 1500), pyrolysis resulted in conversion to C-rich SiC ceramic in high char yields (-60%). Copolymerization with methylsilane resulted in higher chars and more crystalline polymer. Addition of crosslinking agents such as polybutadiene or methyltrivinylsilane increased the viscosity of the polymer produced and enabled application as coatings to fiber toes.

Source record↗

Development and Application of Tools to Characterize the Oxidative Degradation of AP/HTPB/Al Propellants in a Propellant Reliability Study

The oxidative thermal aging of a crosslinked hydroxyl-terminated polybutadiene (HTPB)/isophorone diisocyanate (IPDI) polyurethane rubber was studied at temperatures between 25 C and 125 C. Changes in tensile elongation, mechanical hardening, polymer network properties, density, O2 permeation, and molecular chain dynamics were investigated as a function of age. The techniques used include solvent swelling, detailed modulus profiling, and NMR relaxation measurements. The Arrhenius methodology, which normally assumes a linear extrapolation of high temperature aging data, is critically evaluated by using extensive data superposition and highly sensitive oxygen consumption measurements. Significant curvature in the Arrhenius diagram of these oxidation rates is observed to be similar to previous results found for other rubber materials that have been evaluated by this technique. Preliminary gel/network properties suggest that crosslinking is the dominant process at higher temperatures. The effect on the oxidation rate of the binder when other constituents found in propellants are present, such as ammonium perchlorate, plasticizer and aluminum powder, is presented.

Celina, Mathew↗

The Three-Dimensional Combustion of Heterogeneous Propellants

A numerical framework is described which permits the calculation of the 3-D combustion field supported by a heterogeneous propellant, allowing for complete coupling between the condensed phase physics, the gas-phase physics, and the unsteady, uneven, regressing surface. A random packing algorithm is used to construct models of ammonium-perchlorate in hydroxyl-terminated-polybutadiene propellants which mimic experimental propellants designed by R. Miller, and these are numerically burnt. Mean burning rates are compared with experimental data for four packs, over a pressure range of 7-200atm.

Massa, L.↗

Nitrous Oxide/Paraffin Hybrid Rocket Engines

Nitrous oxide/paraffin (N2OP) hybrid rocket engines have been invented as alternatives to other rocket engines especially those that burn granular, rubbery solid fuels consisting largely of hydroxyl- terminated polybutadiene (HTPB). Originally intended for use in launching spacecraft, these engines would also be suitable for terrestrial use in rocket-assisted takeoff of small airplanes. The main novel features of these engines are (1) the use of reinforced paraffin as the fuel and (2) the use of nitrous oxide as the oxidizer. Hybrid (solid-fuel/fluid-oxidizer) rocket engines offer advantages of safety and simplicity over fluid-bipropellant (fluid-fuel/fluid-oxidizer) rocket en - gines, but the thrusts of HTPB-based hybrid rocket engines are limited by the low regression rates of the fuel grains. Paraffin used as a solid fuel has a regression rate about 4 times that of HTPB, but pure paraffin fuel grains soften when heated; hence, paraffin fuel grains can, potentially, slump during firing. In a hybrid engine of the present type, the paraffin is molded into a 3-volume-percent graphite sponge or similar carbon matrix, which supports the paraffin against slumping during firing. In addition, because the carbon matrix material burns along with the paraffin, engine performance is not appreciably degraded by use of the matrix.

Zubrin, Robert↗

2010 JPC Abstract: Ares I First Stage Propulsion System Status

In November 2005, NASA created the Constellation Program to develop an entirely new fleet of spacecraft to include the Ares I Crew Launch Vehicle and Ares V Cargo Launch vehicles. This mission architecture included the Orion capsule (which would be used to transport astronauts to low-Earth orbit and beyond), the Altair lunar lander, and an Earth departure stage. The Ares First Stage Team has made significant progress on the design of a propulsion system to meet the objectives of the Constellation Program. Work on a first stage element propulsion system capable of lofting a new fleet of spacecraft is well underway. To minimize technical risks and development costs, the Solid Rocket Boosters (SRBs) of Shuttle served as a starting point in the design of a new motor that would meet the requirements of those new vehicles. This new propulsive element will provide greater total impulse utilizing a fifth segment to loft a safer, more powerful fleet of space flight vehicles. Performance requirements, basic architecture, and obsolescence issues were all factors in determining the new first stage element design and configuration. Early efforts focused on creating designs that would be capable of supporting the requisite loads and environments. While the motor casings are Shuttle legacy, because of Ares I s unique in-line configuration, the first stage will require entirely new forward structures (forward skirt, forward skirt extension, aeroshell, and frustum) and a modified systems tunnel. The use of composites facilitated a change in the geometry, which in turn afforded the ability to focus strength where it was needed without additional mass. The Ares First Stage rocket motor casting tooling was designed and built to achieve a propellant grain geometry that produces the specific required ballistic profile. The new propellant formulation is a polybutadiene acrylonitrile (PBAN) copolymer, which has been modified to attain the desired burn rate and retain adequate tailoring capability.

Priskos, Alex S.↗

Heavy Lift for Exploration: Options and Utilization

Every study of exploration capabilities since the Apollo Program has recommended the renewal of a heavy lift launch capability for the United States. NASA is aggressively pursuing that capability. This paper will discuss several aspects of that effort and the potential uses for that heavy lift capability. The need for heavy lift was cited most recent in the findings of the Review of U.S. Human Space Flight Plans Committee. Combined with considerations of launch availability and on-orbit operations, the Committee finds that exploration will benefit from the availability of a heavy-lift vehicle, the report said. In addition, heavy lift would enable the launching of large scientific observatories and more capable deep-space missions. It may also provide benefit in national security applications. The most recent focus of NASA s heavy lift effort is the Ares V cargo launch vehicle, which is part of the Constellation Program architecture for human exploration beyond low Earth orbit (LEO). The most recent point-of-departure configuration of the Ares V was approved during the Lunar Capabilities concept Review (LCCR) in 2008. The Ares V first stage propulsion system consists of a core stage powered by six commercial liquid hydrogen/liquid oxygen (LH2/LOX) RS-68 engines, flanked by two 5.5-segment solid rocket boosters (SRBs) based on the 5-segment Ares I first stage. The boosters use the same Polybutadiene Acrylonitrile (PBAN) propellant as the Space Shuttle. Atop the core stage is the Earth departure stage (EDS), powered by a single J-2X upper stage engine based on the Ares I upper stage engine. The 33-foot-diameter payload shroud can enclose a lunar lander, scientific instruments, or other payloads. Since LCCR, NASA has continued to refine the design through several successive internal design cycles. In addition, NASA has worked to quantify the broad national consensus for heavy lift in ways that, to the extent possible, meet the needs of the user community.

Creech, Steve↗

Processing and Damage Tolerance of Continuous Carbon Fiber Composites Containing Puncture Self-Healing Thermoplastic Matrix

Research at NASA Langley Research Center (NASA LaRC) has identified several commercially available thermoplastic polymers that self-heal after ballistic impact and through-penetration. One of these resins, polybutadiene graft copolymer (PB(sub g)), was processed with unsized IM7 carbon fibers to fabricate reinforced composite material for further evaluation. Temperature dependent characteristics, such as the degradation point, glass transition (T(sub g)), and viscosity of the PBg polymer were characterized by thermogravimetric analysis (TGA), differential scanning calorimetry (DSC), and dynamic parallel plate rheology. The PBg resin was processed into approximately equal to 22.0 cm wide unidirectional prepreg tape in the NASA LaRC Advanced Composites Processing Research Laboratory. Data from polymer thermal characterization guided the determination of a processing cycle used to fabricate quasi-isotropic 32-ply laminate panels in various dimensions up to 30.5cm x 30.5cm in a vacuum press. The consolidation quality of these panels was analyzed by optical microscopy and acid digestion. The process cycle was further optimized based on these results and quasi-isotropic, [45/0/-45/90]4S, 15.24cm x 15.24cm laminate panels were fabricated for mechanical property characterization. The compression strength after impact (CAI) of the IM7/pBG composites was measured both before and after an elevated temperature and pressure healing cycle. The results of the processing development effort of this composite material as well as the results of the mechanical property characterization are presented in this paper.

Grimsley, Brian W.↗

Characterization, Operation and Analysis of Test Motors Containing Aluminized Hybrid Fuels

NASA Marshall Space Flight Center's Materials and Processes Department, with support from the Propulsion Systems Department, has renewed the development and maintenance of a hybrid test bed for exposing ablative thermal protection materials to an environment similar to that seen in solid rocket motors (SRM). The Solid Fuel Torch (SFT), operated during the Space Shuttle program, utilized gaseous oxygen for oxidizer and an aluminized hydroxyl-terminated polybutadiene (HTPB) fuel grain to expose a converging section of phenolic material to a 400 psi, 2-phase flow combustion environment. The configuration allows for up to a 2 foot long, 5 inch diameter fuel grain cartridge. Wanting to now test rubber insulation materials with a turn-back feature to mimic the geometry of an aft dome being impinged by alumina particles, the throat area has now been increased by several times to afford flow similarity. Combined with the desire to maintain a higher operating pressure, the oxidizer flow rate is being increased by a factor of 10. Out of these changes has arisen the need to characterize the fuel/oxidizer combination in a higher mass flux condition than has been previously tested at MSFC, and at which the literature has little to no reporting as well. Testing for fuel regression rate comprised a two-level, full factorial design available over Aluminum loading level, mass flow rate, pressure, and diameter. The data taken significantly surpasses the previous available data on regression rate of aluminized HTPB fuel burning with gaseous oxygen. It encompasses higher mass fluxes, and appears to generate more consistent data. The good test article and facility design and testing work of the Penn State HPCL combined with careful analysis of the data and good planning has made this possible. This should be able to assist with developing rate laws that are useful both for research planning and for developing flight system sizing relationships that can help optimize hybrid rocket concepts for trade studies. The successful approach of this DOE and test setup is applicable to other propellant combinations as well.

Kibbey, Timothy P.↗

Characterization, Operation and Analysis of Test Motors Containing Aluminized Hybrid Fuels

NASA Marshall Space Flight Center's Materials and Processes Department, with support from the Propulsion Systems Department, has renewed the development and maintenance of a hybrid test bed for exposing ablative thermal protection materials to an environment similar to that seen in solid rocket motors (SRM). The Solid Fuel Torch (SFT), operated during the Space Shuttle program, utilized gaseous oxygen for oxidizer and an aluminized hydroxyl-terminated polybutadiene (HTPB) fuel grain to expose a converging section of phenolic material to a 400 psi, 2-phase flow combustion environment. The configuration allows for up to a 2 foot long, 5 inch diameter fuel grain cartridge. Wanting to now test rubber insulation materials with a turn-back feature to mimic the geometry of an aft dome being impinged by alumina particles, the throat area has now been increased by several times to afford flow similarity. Combined with the desire to maintain a higher operating pressure, the oxidizer flow rate is being increased by a factor of 10. Out of these changes has arisen the need to characterize the fuel/oxidizer combination in a higher mass flux condition than has been previously tested at MSFC, and at which the literature has little to no reporting as well. Testing for fuel regression rate comprised a two-level, full factorial design available over Aluminum loading level, mass flow rate, pressure, and diameter. The data taken significantly surpasses the previous available data on regression rate of aluminized HTPB fuel burning with gaseous oxygen. It encompasses higher mass fluxes, and appears to generate more consistent data. The good test article and facility design and testing work of the Penn State HPCL combined with careful analysis of the data and good planning has made this possible. This should be able to assist with developing rate laws that are useful both for research planning and for developing flight system sizing relationships that can help optimize hybrid rocket concepts for trade studies. The successful approach of this DOE and test setup is applicable to other propellant combinations as well.

Kibbey, Timothy P.↗