International Journal of Aeronautical Science & Aerospace Research (IJASAR)  /  IJASAR-2470-4415-06-101

Parameters Influencing Regression Rate of Solid Rocket Fuels


Osemwengie O1*, Abdallah SA2, Morgan HP3, Fanegan JO4

1 CEO, Ubiquity Interface Incorporated, USA.
2 Aerospace Engineering Department, CFD Research Lab, University of Cincinnati, USA.
3 Undergraduate Researcher, CFD Research Lab, University of Cincinnati, USA.
4 Ubiquity Interface Incorporated, USA.

*Corresponding Author

Osatohanmwen Osemwengie,
CEO, Ubiquity Interface Incorporated, USA.
Tel: 817-298-4617
Email: dr.osemwengie@ubiquityinterface.com

Received: December 11, 2018; Accepted: January 08, 2019; Published: January 09, 2019

Citation: Osemwengie O, Abdallah SA, Morgan HP, Fanegan JO. Parameters Influencing Regression Rate of Solid Rocket Fuels. Int J Aeronautics Aerospace Res. 2019;6(1):164-170. doi: dx.doi.org/10.19070/2470-4415-1900019

Copyright: Osemwengie O© 2019. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution and reproduction in any medium, provided the original author and source are credited.



Abstract

This review paper provides a compilation of works from 1966 to 2018 pertaining to the study of altering the burn rate for solid fuel rockets. This paper serves to catalog the current state of research on burn rate altering additives and other common methods for tailoring the burn rate of solid rocket fuels for specific applications. Solid rocket motors (SRM) and hybrid rocket engines (HRE) both utilize solid fuels, while SRMs use a solid oxidizer mixed into the fuel and HREs use liquid or gas oxidizer separated from the fuel. There are many different methods for controlling the burn rate of these motors and engines, such as: fuel and oxidizer choice and concentration, additives, grain configuration, and combustion chamber pressure. The methods for controlling burn rate for each particular rocket type are discussed in their own sections, however most additives that mix with the solid fuel remain the same across the SRMs and HREs with the exception of those that behave as oxidizers. The main goal of this study of the modification, not just increasing, of the burn rate for these fuels is their use in long distance unmanned aerial vehicle (UAV) applications. HREs have many benefits that make them ideal for UAVs, including: low cost, added safety and ease of storage, and low burn rate. HRE have the added benefit of increased safety due to the physical separation of the fuel and oxidizer, and any additives that release oxygen during decomposition would not be ideal. Additives are a key element discussed in this paper, as the concentration can be varied to precisely tailor the burn rate of a mixture. The additives alter the burn rate by influencing the activation energy, heat of reaction, and efficiency of energy feedback.



1.Keywords
2.Abbreviations
3.Introduction
4.Modifications for Solid Rocket Motor Regression Rate
5.Choice of Fuel and Oxidizer for SRM
6.Additives for SRM Propellant
7.Modifications for Hybrid Rocket Engine Solid Fuel Regression Rate
8.Choice of Fuel and Oxidizer for HRE
9.Additives for HRE Propellant
10.Rocketry Applied to Power Generation
11.Demand for Hybrid Energy Sources for UAVs
12.Method for Staging Multiple Solid Propellants in a Combustor
13.Conclusions
14.References

Keywords

Burn Rate Modification; Solid Rocket Motors; Hybrid Rocket Engines; Propellant Additives, UAV.


Abbreviations

SRM: Solid Rocket Motors; HRE: Hybrid Rocket Engines; UAV: Unmanned Aerial Vehicle; LRE: Liquid Rocket Engine; AP: Ammonium Perchlorate; HTBP: Hydroxyl-Terminated Polybutadiene; ABS: Acrylonitrile Butadiene Styrene; GOX: Gaseous Oxygen; NOX: Nitrous Oxide; TAGzT: Triaminoguanidinium Azotetrazolate.


Introduction

This review is about solid rocket propellants and how to customize their burning rates for applications that require long time/ range thrust operations. Rockets can be divided into different categories based on the states of matter their oxidizers and fuel are in. Figure 1 illustrates the breakdown of the different classifications of rockets. Rockets that utilize a solid fuel mixed with a solid oxidizer are referred to as solid rocket motors (SRM). These motors are commonly used as boosters for spacecraft launches or other long-range payloads. Compared to their liquid rocket engine (LRE) counterparts that utilize both liquid fuel and liquid oxidizer, SRMs are less complex but are also more dangerous. With the fuel and oxidizer already premixed in SRM, once the propellant mixture is ignited, the burning continues to propagate and cannot be shut off easily. SRMs also have increased sensitivity to accidental ignition and must be stored and transported safely, this leads to an increase in cost. Liquid rocket engines separate the fuel and oxidizer while having the ability to throttle the fuel and oxidizer mixture ratio, providing thrust adjustability and additional safety but also increasing complexity by having pumps and multiple injectors. Hybrid rocket engines (HRE) offer the safety benefits of liquid rocket engines by separating the fuel and oxidizer while also having some of the benefits of solid rocket motors in terms of the simplicity and performance.


Figure 1. Classification of rockets from propellant states.


The hybrid rocket engines discussed in this paper are the solid fuel hybrid engines. There exists liquid or gas fuel with solid oxidizer hybrid rockets, commonly referred to as reverse hybrid engines, but the most popular hybrid engines are those that utilize a solid fuel and either a liquid or gaseous oxidizer. The focus of this paper is to compile the various methods of altering the burn rate for rockets composed of solid fuel with a centralized focus on hybrid rocket engines. HREs are more ideal for UAV applications, for reasons that will be discussed in detail in later sections. Burn rate determines the rate of energy release, and the flame temperature. The linear burning rate, or regression rate, of a propellant is usually measured in mm/sec while the mass burning rate of a propellant is measured in g/sec. There are many factors that can influence the regression rate for each type of rocket fuel and each section will list several of them. However, the focus of the paper is to evaluate the regression rate of several common propellant mixtures combined with common regression rate modifying additives. Propellant additives are chemicals that are added to the mixture that do not have the primary role as a fuel, oxidizer, binder, or cross-link agent.


Modifications for Solid Rocket Motor Regression Rate

The regression rate of most composite (discussed in later sections) SRM propellants can be expressed using St. Robert’s Law:



where r is the regression rate, ro is a constant (usually taken as zero), a is the regression rate coefficient, and n is the pressure exponent, Pc is the pressure of the combustion chamber. The values of a and n are determined empirically for each propellant formulation. On log-log scales, the relationship between chamber pressure and regression rate is linear for propellant that obeys St. Robert’s Law. However, for propellants that do not obey this equation, the slope of the relationship might not be constant for all pressures due to the influence of additional variables as explained in [20] through experimental data. For the two limits of n=1, and n=0, the regression rate changes from linear relationship to constant value respectively. To relate the erosive burning rate to the gas flow in the combustion chamber, various empirical laws are used:



where k is a constant, and G is the specific mass flow rate of the main flow, and G* is a threshold flow rate.



where k is a constant, and u is the velocity of the main flow.

There are many different factors that influence the regression rate of a mixed fuel and oxidizer propellant; several examples of the most influential factors are provided in Table 1.

There are many more factors that control regression rate beyond what is listed in Table 1, for example, Control of Pyrotechnic Burn Rate [23] lists up to 15 methods. The burning rate differs significantly between different fuels and oxidizers while the addition of additives in small fractions of the total mixture can precisely tailor the mixture to achieve the desired burning rate.



Table 1. List of common factors that control the regression rate of solid rocket propellant.


Choice of Fuel and Oxidizer for SRM

The main SRM propellant type being reviewed in this section is a composite type which consists of separate fuel, oxidizer, binding agent, and additives all mixed together. The other type of solid propellant is referred to as “double base propellants” which contain nitrocellulose and nitroglycerine; both of which are oxyhydrocarbons, meaning they each contain the fuel and oxygen necessary for combustion.

Composite propellants that utilize metal fuels typically have a higher regression rate due to the amount high amount of heat given off during their exothermic combustion as well as having high thermal conductivity values, meaning the temperature increase can penetrate deeper into fuel grain. This increase in temperature corresponds to an increase in energy of the mixture prior to combustion, therefore, there is less energy required to reach the activation energy necessary for the combustion reaction to occur. Space Propulsion Analysis and Design [20] outlines a list of solid metal fuels organized by their efficiency of combustion. Control of Pyrotechnic Burn Rate [23] summarizes several fuels and their heat of combustion, which is how much heat energy they put back into the system for further combustion. Aluminum powder is on the higher end of the spectrum with 7400 cal/g and Sulfur is on the low end with 2200 cal/g.

Oxidizers also vary in their decomposition temperature, which is the temperature required for reactants to form, and by the amount of heat released after combustion. The lower the decomposition temperature and the higher amount of energy released after combustion, the faster the regression rate of the propellant. The mass percentage of oxygen in the molecule of the oxidizer is also a good indicator of performance. A common oxidizer molecule such as Ammonium Perchlorate (AP) has a chemical formula NH4ClO4 which results in 59.5% of the molecular weight coming from the oxygen molecules. Another common oxidizer, Potassium Nitrate (KNO3), has a lower performance compared to AP, partly due to the lower mass percentage of oxygen at 47.5%. Another aspect of regression rate comes from the strength between the bonds of the reactants (fuel and oxidizer) and products (chemicals formed after combustion). Usually the stronger the bonds are in the products relative to the bonds in reactants, the greater the net generation of heat from combustion. KNO3 also has an endothermic decomposition, which means it will it will take more energy to decompose than the amount of energy given off by the formation of its products. Thus, to provide a net positive heat generation to the fuel grain to keep burning, a fuel or additives must be used that release more energy on combustion than is required by the amount of KNO3 in the mixture.


Additives for SRM Propellant

Additives can be used to precisely control the burn rate of a fuel mixture through altering the additives concentration. Burn rate retardant additives usually work by increasing the activation energy of a mixture, by having an endothermic decomposition reaction, or both. Catalysts work by lowering the activation energy required for the decomposition of the oxidizer, which releases more oxygen to use for combustion of the fuels. Unlike other additives, catalysts are not typically consumed in the reaction.



Table 2. Common additives for suppressing regression rate of SRMs.



Table 3. Common additives for accelerating regression rate of SRMs.


Modifications for Hybrid Rocket Engine Solid Fuel Regression Rate

Hybrid rocket engines have been known to have comparably low regression rates to their SRM counterparts. Much work has been done finding methods of increasing the burn rate or thrust output for HREs. Since the fuel and oxidizer are not already mixed like in SRMs, the regression rate of the solid fuel in a HRE is dependent on the amount of liquid oxidizer being put into the combustion chamber, therefore the regression rate equation is different than that for SRMs:



Where r is the fuel regression rate in m/s, G is the total propellant mass flux in kg/m2*s, x is the distance down the port in m, and a, n, and m are regression rate constants which are determined experimentally for individual propellants. This regression rate equation applies to a particular axial distance along the combustion port, therefore an average regression rate is usually calculated along the entire length of the HRE for comparison purposes. These regression rate equations apply to the system if the effects of radiation heat transfer are negligible and convective heat transfer dominates. If the instantaneous regression rate down the port is approximately constant, the average regression rate can be described with:



Where ravg is the average fuel regression rate along the port in m/s, Gavg is the average total propellant flux rate along the port in kg/m2*s, and Lp is the port length in m. There are many different equations and models for evaluating the burning rate for a particular fuel depending on which mass flow regime it exists in. The equation provided in this paper is used as a rough estimate of regression rate and is not the most accurate model for a system.

Like SRMs, the heat transfer rate into the solid fuel as well at the net heat generation from fuel combustion are major controlling factors of combustion. However, there are different regimes governed by the amount of mass flux out of the engine. For high mass flux, combustion is controlled by chemical kinetics. For medium mass flux, combustion is controlled by diffusion. For low mass flux, radiation heat transfer becomes more dominant as convective heat transfer starts to diminish. If the regression rate is very low, there is the potential issue that the fuel grain underneath the current burning surface begins to melt or cook because of its long exposure in the thermal layer. This cooking of the fuel can result in engine chuffing, which is the melted fuel being removed from the engine and exposing a new layer of combustible fuel. The burning profile of the fuel in HREs are different than that of an SRM, the section of fuel that is closest in axial distance to the oxidizer injector usually burns at a faster rate than the fuel further down the chamber. For single cylindrical port HREs, this results in a truncated cylindrical burning surface that may present differences in thrust profile than a SRM equivalent configuration.

The oxidizers in HREs are typically in liquid state during storage and then are converted into their gaseous state upon entry into the combustion chamber. While a compressed gas oxidizer would work, storing the oxidizer as a liquid is much more efficient in terms of space and fuel density. This method of providing a more compact storage of the oxidizers has the most potential applications and is why most research on direct HREs pertains to those which utilize a liquid oxidizer and solid fuel.

Another method for increasing the regression rate of solid fuel in HREs is the grain configuration. Fuel Regression Rate in Hydroxyl- Terminated-Polybutadiene/Gaseous Oxygen Hybrid Rocket Motors [19] has experimentally seen a dependence on grain port diameter and regression rate. Through advancements in 3D printing technology, the solid propellant grain in HREs can be printed into geometries that were previously impossible with casting or extruding manufacturing, e.g. helix port configuration. These complex 3D structures cause increased friction on the surface of the grain, resulting in increased heat transfer to the fuel grain and consequently lowering the energy required for combustion.


Choice of Fuel and Oxidizer for HRE

There are various types of fuels used for HREs, most of the work being done utilizes hydroxyl-terminated polybutadiene (HTPB) or a type of wax. It should be noted that not all of these fuel and oxidizers may be compatible. Approaches to Low Fuel Regression Rate in Hybrid Rocket Engines [32] lists several common combinations of fuels and oxidizers. Table 4 and Table 5 list several commonly used fuels and common oxidizers, respectively.


Table 4. Common solid fuels used for HREs



Table 5. Common liquid oxidizers used for solid-liquid HREs.


Because of its energy density as well the ability to safely handle it, HTPB is a very popular fuel choice for hybrid engines. HTPB is also commonly used in SRMs as binder that also behaves as a fuel. The most common gaseous oxidizers, for those few rockets that use a compressed gas oxidizer reservoir, are gaseous oxygen (GOX) and nitrous oxide (NOX), however most rockets further compress or chill these gasses until they are in their liquid phase which allows for more oxidizer to be carried on the rocket. Liquid oxidizers are transformed into gaseous phase upon entry to the combustion chamber to react with solid fuel, hydrogen peroxide for example is injected across a heated catalyst bed of silver to be effectively and rapidly decomposed into hydrogen and oxygen gasses for combustion.


Additives for HRE Propellant

The list of additives in Table 6 used to modify the regression rate for HREs is scarce compared to that of SRMs due to the fact that molecules that could act as oxidizers are not desirable in most cases. Many additives for increasing the regression rate of the fuels in HREs are metals that have high heats of reaction and high thermal conductivity. High nitrogen ingredients such as triaminoguanidinium azotetrazolate (TAGzT) can also be used to increase the regression rate, even though they do not have any oxygen atoms, they still provide positive heats of reaction and react at a fast rate. High temperature nitrogen can also react with aluminum particles to form AlN which may be beneficial to conserve oxygen for combusting compounds that require it.


Table 6. Common additives for accelerating regression rate of solid fuel in HREs.


Much research being done on rockets, and hybrid rocket engines specifically, focuses on increased the regression rate of the fuel to provide higher thrust. Since HREs have characteristically low fuel regression rates, there has not been a lot of research into further lowering the regression rate using additives. If the desired regression rate is less than what is naturally achieved for a given fuel and oxidizer mixture, it is reasonable to assume several of the additives listed in Table 2 that do not behave as oxidizers could be used to further lower the regression rate.

In direct hybrid engines the oxidizer traditionally goes from a liquid state to a gaseous one, which would require any oxidizers to also change state at the same properties as the oxidizer, which is why most additives are added to the solid fuel to modify the regression rate. However, liquid oxygen has been doped with fluoride (FLOX), to create a high performing oxidizer, but it is also highly toxic, thus increasing safety concerns.


Rocketry Applied to Power Generation

Hybrid rocket engines have been the subject of much research over the past several decades with many fuels and oxidizers being tested. One common characteristic of the fuels evaluated in that research is low cost materials. Low cost materials such as ABS and polyethylene can be utilized in combustion chambers and mixed with simple oxidizers such as liquid or gaseous oxygen. Through several modifications and advancements, a traditional gas turbine engine combustor could be modified to handle solid propellant grains. This modification would provide an alternative energy source for power generation if the engine components downstream of the combustor can handle the increased temperature of and pressure from solid fuel combustion. If these engines components are equipped with high-temperature materials, the increased heat generation from burning solid fuels compared to that of gasoline could provide greater output to the shaft turbine.


Demand for Hybrid Energy Sources for UAVs

Hybrid electric propulsion systems with more than one energy sources for powering UAVs have been the focus of intensive research. The reason for this is the huge success of applying hybrid power to highway vehicles. It significantly improved pollution and energy efficiency. UAVs that require increased distance and long duration flights could benefit significantly from a method of charging the on-board batteries. Traditional methods of charging on-board batteries, such as solar panels, are very inefficient in the terms of power generation per unit of mass. The US Department of Defense has been the leading organization funding research and the application of hybrid engine to its UAVs. Because it provides military UAVs long flight duration, reduced exhaust, and better efficiency.

Other commercial organization prefers the hybrid to a single conventional internal combustion because the electric side of the hybrid gives the UAVs more thrust in demanding task such as climbing and maneuvering in disaster, hazard environments while the liquid fuel, solid fuel or fuel cell is used for longer flight time. The electric – batteries which are continually being charged as the UAVs undergo their mission serves as a backup energy source. A hybrid energy source could allow drones to be used at higher altitudes for longer, travel further distances, or pollute less.


Method for Staging Multiple Solid Propellants in a Combustor

A pulse rocket motor design allows the solid propellants to be burned in sections however contained in a single case. The objective is to control the burn rate by using multiple solid propellants attached to each other with a buffer, a thick thermal barrier membrane, in between the solid propellants. The initial propellant is ignited and completely burn while the barrier inhibits the next section to be burnt only until after its ignited thus allowing us to control the start of the burn hence timing. Once ignited, the burn from the next propellant section destroys the barrier membrane. This provides control since each section can use the same or different solid propellant material to control the thrust level, burn rate and specific impulse. How quickly the barrier membrane burns can also be controlled to achieve desired performances since it’s protected from the high temperature burning heat by the first propellant. Chiyako Mihara and Katsunori Ieki in their patent US8397486B2 achieved this by creating a two-pulse rocket motor with multiple ignitors set at the end of the propellants. As mention in the article, “According to the two-pulse rocket motor of the second or third means, the barrier membrane is divided into two pieces and a joint part is provided to weaken a portion to be broken or a slit is formed in the barrier membrane to break the barrier membrane. Therefore, the barrier membrane is surely broken at an expected position (weak part) by the pressure of gas generated by the operation of the second igniter or second ropellant combustion.”


Conclusion

From the research evaluated in this paper, multiple elements must be considered upon choosing a solid fuel for an application. Utilizing a SRM comes with multiple tradeoffs compared to using an HRE. SRMs have reduced complexity, increased thrust output, and the regression rate can be easily modeled. However, these motors cannot be easily shut off, there is no way to throttle the thrust output, and the premixed oxidizer and fuel have increased instability and safety is a concern. In contrast, HREs can be throttled and they have increased safety from separating the fuel and oxidizer. The tradeoff of using HREs are the lower regression rate, complex burning characteristics, and increased design complexity by adding an oxidizer tank, routing pipes, and injectors. Each of these elements should be considered when choosing a rocket for a particular application. After the decision to either mix the oxidizer with the fuel or keep them separated has been resolved, methods for altering the regression rate for both SRMs and HREs stem from the fuel and oxidizer choice and the addition additives. The choice of fuel and oxidizer seems to have the greatest influence on fuel regression rate and should be used to get the system in a close range to the target regression rate. To precisely tailor the regression rate, additives can be chosen for the appropriate propellent (either oxidizer mixed or separate) and varied in concentration to achieve the desired effect.

With the extensive research done into low cost fuels and the naturally low regression rate of hybrid rocket engines, HREs seem to be a likely candidate for power generation. Specifically, these HREs could be utilized aboard long distance/duration UAVs to provide power and charge on-board batteries. The UAVs primary propulsion method would still primarily be electric batteries for the ideal maneuverability, with power generation stemming from a turbine downstream of the HRE combustor. The hybrid rocket engine adds many benefits to the system compared to that of traditional gasoline engines charging on-board batteries. One of the greatest being the ability to operate at high altitudes due to the oxidizer being carried on-board the UAV. This type of innovation would also put safety at the forefront with propellants that have low sensitivity to impact and can be transported easily and less costly.


References

  1. Akhter MZ, Hassan MA. Characterisation of paraffin-based hybrid rocket fuels loaded with nano-additives. J Exp Nanosci. 2018 Feb 28;13(sup1):S31-44.
  2. Altman D. Hybrid rocket development history. In 27th Joint Propulsion Conference; 1991. p. 2515.
  3. Author G. Space Safety Magazine [Internet]. 2014. Hybrid Rocket Motor Design. Available from: http://www.spacesafetymagazine.com/aerospaceengineering/rocketry/hybrid-rocket-overview-part-2/
  4. Bath A. Performance characterization of complex fuel port geometries for hybrid rocket fuel grains. All Graduate Theses and Dissertations. 2012.
  5. Walker SD. High regression rate hybrid rocket fuel grains with helical port structures. Logan: Utah State University; 2015.
  6. Braeunig RA. Basics of Space Flight [Internet]. 2008. Rocket Propellants. Available from: http://www.braeunig.us/space/propel.htm
  7. Cantwell B. Aircraft and Rocket Propulsion Ch 11. Stanford: California, United States of America; 2016 May 13.
  8. Carmicino C, Russo Sorge A. Experimental investigation into the effect of solid-fuel additives on hybrid rocket performance. J Propul Power. 2014 Dec 17;31(2):699-713.
  9. Chaturvedi S, Dave PN. Solid propellants: AP/HTPB composite propellants. Arab J Chem. 2015 Jan 8.
  10. Kenneth KK, Chiaverini MJ. Review of Solid-Fuel Regression Rate Behavior in Classical and Nonclassical Hybrid Rocket Motors. Fundamentals of Hybrid Rocket Combustion and Propulsion, Progress in Astronautics and Aeronautics. 2007:37-26.
  11. Chiaverini MJ, Kuo KK, Peretz A, Harting GC. Regression-rate and heattransfer correlations for hybrid rocket combustion. J Propul Power. 2001 Jan;17(1):99-110.
  12. Chiaverini MJ, Serin N, Johnson DK, Lu YC, Kuo KK, Risha GA. Regression rate behavior of hybrid rocket solid fuels. J Propul Power. 2000 Jan;16(1):125-32.
  13. National Research Council. Uninhabited Air Vehicles: Enabling Science for Military Systems. Washington, DC: The National Academies Press; 2000.
  14. Conkling JA, Mocella C. Chemistry of pyrotechnics: basic principles and theory. Boca Raton: CRC Press; 2010 Dec 23.
  15. Doran E, Dyer J, Lohner K, Dunn Z, Cantwell B, Zilliac G. Nitrous oxide hybrid rocket motor fuel regression rate characterization. In 43rd AIAA/ ASME/SAE/ASEE Joint Propulsion Conference & Exhibit. 2007. p. 5352.
  16. Risha G, Harting G, Kuo K, Peretz A, Koch D, Jones H, et al. Pyrolysis and combustion of solid fuels in various oxidizing environments. In 34th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit. 1998 Jan 1. p. 3184.
  17. Fuller J, Ehrlich D, Lu P, Jansen R, Hoffman J. Advantages of rapid prototyping for hybrid rocket motor fuel grain fabrication. In47th AIAA/ASME/ SAE/ASEE Joint Propulsion Conference & Exhibit. 2011 Aug. p. 5821.
  18. Jones RD, inventor; Additive manufactured thermoplastic-nanocomposite aluminum hybrid rocket fuel grain and method of manufacturing same. United States patent application US 20180169937. 2018 Jun 21.
  19. George P, Krishnan S, Varkey PM, Ravindran M, Ramachandran L. Fuel regression rate in hydroxyl-terminated-polybutadiene/gaseous-oxygen hybrid rocket motors. J Propul Power. 2001 Jan;17(1):35-42.
  20. Humble RW, Henry GN, Larson WJ. Space Propulsion Analysis and Design. New York: McGraw-Hill; 1995.
  21. Khattab M, Galfetti L. Innovative solid fuels for hybrid rocket propulsion. Milan: Politecnico Di Milano; 2011.
  22. Knuth WH, Chiaverini MJ, Sauer JA, Gramer DJ. Solid-fuel regression rate behavior of vortex hybrid rocket engines. J Propul Power. 2002 May;18(3):600-9.
  23. KL Kosanke. Control of Pyrotechnic Burn Rate. 1994.
  24. Kuo KK, Summerfield M. Fundamentals of Solid Propellant Combustion. New York: American Institute of Aeronautics and Astronautics; 1984.
  25. Lengellé G, Duterque J, Trubert J. Combustion of Solid Propellants. Châtillon: National Office for Studies and Aerospace Research (ONERA); 2004.
  26. Lieh J, Spahr E, Behbahani A, Hoying J. Design of hybrid propulsion systems for unmanned aerial vehicles. In 47th AIAA/ASME/SAE/ASEE Joint Propulsion Conference. New York: American Institute of Aeronautics and Astronautics; 2011 Aug. p. 6146.
  27. LIPS H. Metal combustion in high performance hybrid rocket propulsion systems. In 12th Propulsion Conference. 1976 Jul. p. 640.
  28. Marothiya G, Kumar R, Ramakrishna PA. Enhancement of Regression Rate in Hybrid Rockets. 47th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit. 2011.
  29. Mihara C, Leki K, inventors; Mitsubishi Heavy Industries Ltd., assignee. Two-pulse rocket motor. United States patent US 8397486B2. 2013 Mar 19.
  30. Nakka R. Nakka's Experimental Rocketry Web Site [Internet]. Solid Propellant Burn Rate. Available from: https://www.nakka-rocketry.net/burnrate. html
  31. Netzer DW. Hybrid Rocket Internal Ballistics. Springfield: National Technical Information Service; 1972.
  32. Pastrone D. Approaches to low fuel regression rate in hybrid rocket engines. Int J Aerospace Eng. 2012;2012.
  33. Risha GA, Evans BJ, Boyer E, Kuo KK. Metals, energetic additives, and special binders used in solid fuels for hybrid rockets. Prog Astronaut Aeronaut. 2007;218:413-456.
  34. Shah HA, Akram I, Khizar S, Siddique SJ. Design and Prototyping of a Solid Fuel/Liquid Oxidizer Hybrid Rocket Engine. Karachi: DHA Suffa University; 2016.
  35. Price CF, Smoot LD. Regression rates of metalized hybrid fuel systems. AIAA Journal. 1966 May;4(5):910-5.
  36. Price CF, Smoot LD. Pressure dependence of hybrid fuel regression rates. AIAA Journal. 1967 Jan;5(1):102-6.
  37. Stamatis D, Jiang X, Beloni E, Dreizin EL. Aluminum burn rate modifiers based on reactive nanocomposite powders. Propellants, Explosives, Pyrotechnics. 2010 Jun;35(3):260-7.
  38. Strand L, Jones M, Ray R, Cohen N. Characterization of hybrid rocket internal heat flux and HTPB fuel pyrolysis. In 30th Joint Propulsion Conference and Exhibit. 1994 Jun 1. p. 2876.
  39. Strand L, Ray R, Anderson F, Cohen N. Hybrid rocket fuel combustion and regression rate study. In 28th Joint Propulsion Conference and Exhibit. 1992 Jul 1. p. 3302.
  40. Sutton GP, Biblarz O. Rocket propulsion elements. John Wiley & Sons; 2016 Nov 30.
  41. Wernimont EJ, Heister SD. Combustion experiments in hydrogen peroxide/polyethylene hybrid rocket with catalytic ignition. J Propul Power. 2000 Mar;16(2):318-26.
  42. Whitmore S, Peterson Z, Eilers S. Analytical and Experimental Comparisons of HTPB and ABS as Hybrid Rocket Fuels. In 47th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit. 2011. p. 5909.
  43. Jones RD, inventor; Persistent Vortex Generating High Regression Rate Solid Fuel Grain for A Hybrid Rocket Engine. United States patent US 20180209381. 2018.

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