An additive manufactured fuel grain for a hybrid rocket engine

Abstract

Additive-manufactured fuel grains for hybrid rocket engines (HREs) and method of manufacturing the same are disclosed herein. The additive-manufactured fuel grain has an infill density and an infill geometry selected to provide a predetermined burn profile. The method of manufacturing the fuel grain comprises operating an additive-manufacturing system to fabricate a fuel grain having an infill density and an infill geometry selected to provide a predetermined burn profile.

Description

ELECTRONICALLY TRANSMITTED: 12 / 04 / 2024 PATENTINVENTION TITLEAN ADDITIVE MANUFACTURED FUEL GRAIN FOR A HYBRID ROCKET ENGINECROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to the provisional patent application identified by U.S. Serial No. 63 / 495,932, filed April 13, 2023, the entire content of which is hereby expressly incorporated herein by reference.BACKGROUND ART

[0002] Innovations in ammonium perchlorate composite propellant (APCP) primarily focus on rocket assisted take-off (RATO) applications. Test stands to gather thrust data, as well as the fabrication method of propellant, were created for academic research and for future commercialization purposes. In one implementation, the propellant is made of three primary ingredients; ammonium perchlorate (AP) for the oxidizer, aluminum powder (AL) for the fuel, and hydroxyl-terminated polybutadiene resin (HTPB) as the binder. Trimodal compositions were studied with three AP sizes; 400, 200, and 90 microns. An equal particle distribution was found to give very consistent and reliable performance results which is desirable for RATO projects. AP is a fuel as well as an oxidizer, but AL is added to increase solid rocket energetic potential. Different percentages of AL were evaluated at 0%, 5%, and 10% of the overall composition. Adding any amount of AL was shown to produce a more neutral thrust curve during the burn time. A 5% AL composition was selected due to the neutral thrust curve and superior performance over the 10% composition. The fabrication and testing methods are continuously being improved to further future commercialization. Also, other APCP additives like burn rate catalysts and curatives are being investigated.

[0003] Additionally, the infill percentages and infill shape designs of rocket motors were studied. The present disclosure describes effects of additive-manufactured fuel grain geometry on small-scale hybrid rocket performance. Understanding and increasing hybrid rocket performance can allow it to be a more viable option when compared to solid and liquid rocket propulsion systems. This disclosure evaluates the use of additive manufactured polylactic acid filament as a potential propellant in a hybrid rocket propulsion system. Additive-manufactured fuel grains provide an engine system capable of reduced operational expenses, reduced operational hazards by having separate fuel and oxidizer, and highly-tailorable rocket performance with custom grain geometry and composition. On top of all that, these fuel grainsprovide a safer alternative to the volatile nature of solid rocket propellants, as well as simplifying manufacturing and easing storage requirements associated with fuel grains.

[0004] Hybrid rocket engine (HRE) systems consist of two different propellant components: a solid fuel grain and a liquid or gaseous oxidizer. A primary goal of this disclosure is to observe the variances in HRE performance as a function of differing infill densities and infill geometries present within the fuel grain. Because the practice of additive-manufactured fuel is relatively new, the parameters associated with manufacturing fuel grains are largely not well understood when related to rocket engine performance. By adjusting the infill percentage and infill shape print pattern of the fuel, different thrusts, burn times, and burn rates can be achieved due to the change in surface area, density, and its reaction with the oxidizer flow. Performance variances were evaluated on a 38-mm diameter HRE system over fuel grains with three different infill densities of 30%, 50%, and 70% with cubic infill geometry. Performance variances were then evaluated on the same motor system over fuel grains with three different infill geometries of cubic, triangular, and concentric with a 50% infill density. Results from this disclosure show that as the infill percentage increases, burn rate decreases while burn time increases. The observations from this disclosure show the potential use of these hybrid rocket motors for rocket-assisted take-off for high-speed unmanned aircraft and for space transportation.

[0005] H ereinafter is presented a disclosure of effects of additive-manufactured fuel grain geometry on small-scale hybrid rocket performance. The motivation of this disclosure is to understand and increase hybrid rocket performance to be a more viable option when compared to solid and liquid rocket propulsion systems. This disclosure evaluates the use of additive manufactured polylactic acid filament as a potential propellant in a hybrid rocket propulsion system. Additive-manufactured fuel grains provide an engine system capable of reduced operational expenses, reduced operational hazards by having separate fuel and oxidizer, and high ly-tailorable rocket performance with custom grain geometry and composition. On top of all that, these fuel grains provide a safer alternative to the volatile nature of solid rocket propellants, as well as simplifying manufacturingand easing storage requirements associated with fuel grains. HRE systems consist of two different propellant components: a solid fuel and a liquid or gaseous oxidizer. The primary goal of this disclosure is to observe the variances in HRE performance as a function of differing infill densities and infill geometries present within the fuel grain. Because the practice of additive-manufactured fuel is relatively new, the parameters associated with manufacturing fuel grains are largely not well understood when related to rocket engine performance. By adjusting the infill percentage and infill shape print pattern of the fuel, differentthrusts, burn times, and burn rates can be achieved due to the change in surface area, density, and its reaction with the oxidizer flow. Performance variances were evaluated on a 38-millimeter (mm) diameter HRE system over fuel grains with three different infill densities of 30%, 50%, and 70% with cubic infill geometry. Performance variances were then evaluated on the same motor system over fuel grains with three different infill geometries of cubic, triangular, and concentric with a 50% infill density. Results from this disclosure show that as the infill percentage increases, burn rate decreases while burn time increases. The observations from this disclosure show the potential use of these hybrid rocket motors for rocket-assisted take-off for high-speed unmanned aircraft and for space transportation.

[0006] Historically, HREs have been looked over due to not shining in terms of overall performance or efficiency. However, there have been technological advances recently that have launched HREs back into the forefront of research and business alike. An HRE system is a classification that combines the characteristics of both solid and liquid propulsion systems. In an HRE, one of the components, either fuel or oxidizer, is in a solid state while the other is in a gaseous or liquid state. This combination of states allows the system to utilize benefits from both solid and liquid rocket engines, creating a unique envelope that neither system could operate in alone. Compared to solid rocket motors, HREs provide on-demand start and stop capabilities, and reduced storage hazards by storing the oxidizer and fuel separately. Hybrid engines differ from liquid engines by offering a less hazardous system with greater fuel density. Due to having only one liquid or gaseous compound, HREs offer a cheaper and simpler option where throttling is necessary. HRE systems have a variety of applications, including sounding rockets, suborbital and orbital launch vehicles, and RATO. These applications appeal to both military and commercial providers, making hybrid rocketry an interesting research topic over the last few decades.

[0007] SpaceShipOne (SSI) was an experimental space vehicle designed and developed by Scaled Composites, an aerospace company founded by aircraft designer Burt Rutan in 1982. SSI was part of a broader vehicle program known as Tier One, made up of SSI, a launch aircraft coined White Knight, an HRE system, and an avionics suite. SSI was entered into the Ansari X Prize, a space competition in which the X Prize Foundation offered $ 10 million for the first private organization to launch a reusable manned aircraft into space twice within the span of two weeks. Thousands watched as SSI reached an apogee of over 350-thousand feet within a two week span in the fall of 2004. This date represents one of the first successful employments of an HRE. This configuration was so successful that Sir Richard Branson of Virgin Galactic partnered with BurtRutan to build SpaceShipTwo and White Knight Two. More recently, companies like Firehawk Aerospace have begun work on HREs for potential military applications.

[0008] Although the implementation of HREs has been sparse until recently, studies have been conducted for over fifty years on their performance trends. More recently, researchers from all around the world have focused on improving regression rate behaviors that are inherent in HREs, mostly by changing fuel types, fuel additives, and internal port geometries.

[0009] Kevin Lohner et. al. (Kevin Lohner, Jonny Dyer, Eric Doran, Zachary Dunn, and Greg Zilliac. Fuel regression rate characterization using a laboratory scale nitrous oxide hybrid propulsion system. In 42nd AIAA / ASME / SAE / ASEE Joint Propulsion Conference & Exhibit, Reston, Virigina, July 2006. American Institute of Aeronautics and Astronautics.) performed a regression rate study on traditional and novel HRE fuels in a laboratory scale nitrous oxide hybrid propulsion system. The four HRE fuels tested include HTPB, high-density polyethylene (HDPE), polymethyl methacrylate (PMMA), and sorbitol. The scale explored in this work was a 2-inch (in) (54 mm) casing, scaled for 100 pounds of thrust. 40 hot fire tests were performed to characterize the burn rates of fuels over a range of oxidizer flow rates, oxidizer-to-fuel (O / F) ratios, and chamber pressures. This study characterizes the burn characteristics of hybrid rocket fuels with nitrous oxide as an oxidizer.

[0010] Stephen Whitmore et. al. (Stephen Whitmore, Zachary Peterson, and Shannon Eilers. Analytical and experimental comparisons of HTPB and ABS as hybrid rocket fuels. In 47thAIAA / ASME / SAE / ASEE Joint Propulsion Conference & Exhibit, Reston, Virigina, July 2011. American Institute of Aeronautics and Astronautics.) evaluated acrylonitrile butadiene styrene (ABS) as a potential fuel for HREs and is compared to the widely used HTPB, with nitrous oxide used as oxidizer. Analytical predictions for formation, products of combustion, and motor performance were compared against static fire tests for ABS fuel grains. Chemistry and performance of the ABS fuel grains are compared against fuel grains cast from HTPB of equivalent physical volume and dimensions. Tests were conducted using 98-mm motors for both ABS and HTPB. The ABS fuel grains were manufactured using direct digital manufacturing, now known as additive manufacturing, or 3-D printing. 20 successful separate static fire tests including 6 ABS and 14 HTPB fuel grains were performed. However, data from several of the tests were discounted due to known instrumentation, software, and test apparatus difficulties. The presented time history profiles include thrust, total impulse, injector and chamber pressures, and oxidizer mass flow. For each case, HTPB exhibited a small but well-defined advantage in overall performance, including thrust, total impulse, and specific impulse. HTPB outperformed ABS inthrust and impulse by 4.9% and 6.6%, respectively. Although HTPB offered better overall performance, ABS offered a slightly greater run-to-run consistency, with an average standard deviation of ± 17.2 N, compared to ± 32.2 N for its HTPB counterpart. This is likely due in part to the fabrication process of the ABS grains. This serves as one of the pioneering experiments when discussing ABS as a potential alternative to HTPB in HREs. Stephen Whitmore et. al. continued his study of regression rates with a development campaign where modern additive manufacturing methods are used to fabricate HRE fuel grains with embedded helical ports. The experiments featured ABS and gaseous oxygen as the oxidizer. Helical port structures, enabled through additive-manufacturing (AM), increase the volumetric efficiency of the fuel grain by lengthening the internal flow path for a given port length. 16 static test firings were performed measuring the time histories of thrust and chamber pressure. The results of this experiment demonstrate that the centrifugal flow patterns introduced by the helical port structures increases fuel regression rates significantly. Mean regression rates as a function of oxidizer mass flux were increased by greater than four for the aggressive helical port structures, and greater than 2 for the modest port structures.

[0011] Xiaodong Yu et. al. (Xiaodong Yu, Hongsheng Yu, Wei Zhang, Luigi T DeLuca, and Ruiqi Shen. Effect of penetrative combustion on regression rate of 3D printed hybrid rocket fuel. Aerospace, 9(11):696, November 2022.) performed a study on the mechanism and combustion performance based on fuel packing density of ABS. Grid-like structure fuels with different packing densities were prepared to assess performance characteristics of penetrative combustion. Fuel grains with packing densities ranging between 60% and 100% were testing across separate burning times in a hybrid 2-D radial burner. The results of this study show that, compared with solid grains, the regression rates of 3-D printed ABS fuel grains increase to different degrees under the influence of penetrative combustion. Yu notes several challenges remain to be addressed in future work, including deeper studies on the effect of this penetrative combustion mechanism, extensive analysis of other materials, quantitative evaluations of the critical density, and more complex internal structural design.

[0012] Mitchell McFarland et. al. (Mitchell McFarland and Elsa Antunes. Small-scale static fire tests of 3d printing hybrid rocket fuel grains produced from different materials. Aerospace, 6(7), 2019.) performed small-scale static fire tests of 3-D printed fuel grains produced from different materials for an HRE. Their material selection was based on commercially available filaments including ABS, acrylonitrile styrene acrylate (ASA), polylactic acid (PLA), polyethylene terephthalate glycol (PETG), nylon, and polypropylene (PP). Tests were conducted in a 38-mmmotor configuration. ABS and ASA were shown to have the best burning rate by inspection. A regression rate model showed that ABS and PLA performed similarly, further validating that PLA can be used in a HRE setting. Although many AM filaments were considered, their infill density and geometry were set as control variables. Further studies varying infill density and infill geometry are needed to see their effect on regression rate of AM filament HRE fuels.

[0013] Byeonguk Ahn et. al. (Byeonguk Ahn, Jeongmoo Huh, Vikas Khandu Bhosale, and Sejin Kwon. Three-dimensionally printed polylactic acid as solid fuel for hydrogen peroxide hybrid rockets. J. Propuls. Power, 37(1):171-175, January 2021.) ran a laboratory-scale hybrid propulsion system using PLA and hydrogen peroxide. Hot fire testing was executed to investigate PLA as a potential fuel in HRE applications. The estimated specific impulse of PLA in conjunction with hydrogen peroxide was about 223 s, just slightly lower than HDPE. These hot fire results validate that PLA can be used as an alternative material for the solid fuel grain in an HRE. PLA was also shown to be optimal at a lower O / F ratio range, 3.0 compared to 7.8 with HDPE. Although the specific impulse was lower with PLA, this implies that a much more compact oxidizer tank design may be available for PLA fuel HREs. PLA exhibits a higher mean mass flow rate and higher characteristic velocity efficiency.

[0014] Additive-manufacturing has brought a resurgence of research into rocket propulsion systems due to the versatility this manufacturing process can provide. Additive-manufacturing, more colloquially known as 3-D printing, is the process of layering material onto a flat surface, called a build plate, through a series of complex computer-controlled algorithms. Additivemanufacturing allows for a safe, scalable, reliable, and automated process that produces parts with tighter tolerances and less waste. Hybrid and liquid systems usually have small intricately designed components that would be too difficult to design by hand, such as nozzles with internal cooling passages and swirl-inducing injectors, that can only be additive-manufactured. But more than that, the use of additive-manufacturing has become an attractive candidate to design and fabricate fuel grains for HREs. A fuel grain is a cylindrical segment of solid fuel that varies in length and diameter based on the amount of thrust the propulsion system wishes to produce. Recent advances in additive-manufacturing technologies have allowed for the ability to design and rapidly produce HRE fuel grains with countless parameters to fine-tune the performance and operability of the engine. Due to this technology, the door to a wide research field as opened. Materials such as ABS, paraffin, and others have shown potential as high-energy plastics that, when combined with oxidizer, show good potential to succeed has a hybrid rocket fuel. PLA is a cheap, high-density thermoplastic that can be economically produced from renewable resources.Utilizing additive-manufacturing in HRE fuel provides other inherent characteristics that can alter the way in which the fuel grain burns. Control of those computer algorithms modifies the amount, known as infill density, and pattern, known as infill geometry, of material added to the component. Changes in infill density and infill geometry alter burn characteristics of the fuel grain. By way of additive-manufacturing, fuel grains with complex core geometries can be made to create HREs with unique burn characteristics to accommodate a wide range of mission profiles.

[0015] Due to this technological advancement being rather new, the design space for additive-manufactured fuel grains is vast. Printers are being updated with software that allow the printers to print in new patterns and with different materials. Thus, there is a need to characterize the effects of these geometries on the performance and operability of HREs.SUMMARY OF THE INVENTION

[0016] A method and system are disclosed. In one implementation, the present disclosure includes an additive-manufactured fuel grain for a hybrid rocket engine (HRE), the additive- manufactured fuel grain having an infill density and an infill geometry selected to provide a predetermined burn profile. In another implementation, the present disclosure includes a method of manufacturing a fuel grain for a hybrid rocket engine (HRE), comprising operating an additive-manufacturing system to fabricate a fuel grain, the fuel grain having an infill density and an infill geometry selected to provide a predetermined burn profile.

[0017] The foregoing Summary provides an overview of certain selected implementations or embodiments disclosed herein, and is not intended to describe every aspect, embodiment, implementation, feature, or advantage of the disclosure exhaustively or comprehensively. Therefore, this Summary should not be construed in such a way to limit the scope of this disclosure or to limit the scope of the claims. The details of one or more implementation or embodiment disclosed herein are set forth in the accompanying drawings and descriptions below. Other aspects, features, implementations, embodiments, and advantages will become readily apparent in view of the description, the drawings, and the claims set forth herein.BRIEF DESCRIPTION OF THE DRAWINGS

[0018] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate one or more implementations described herein and, together with the description, explain these implementations. The drawings are not intended to be drawn to scale, and certain features and certain views of the figures may be shown exaggerated, to scale or in schematic in the interest of clarity and conciseness. Not every component may be labeled inevery drawing. Like reference numerals in the figures may represent and refer to the same or similar element or function. In the drawings:

[0019] FIG. 1 is a diagrammatic view of an exemplary implementation of an HRE constructed in accordance with the present disclosure.

[0020] FIG. 2 is a graphical view of a plurality of modes of a boundary layer that are present during HRE combustion in accordance with the present disclosure.

[0021] FIG. 3 is a graphical view of the mass flux regime phenomenon with respect to regression rate in accordance with the present disclosure.

[0022] FIG. 4 is a perspective view of a multi-port fuel grain and a single-port fuel grain constructed in accordance with the present disclosure.

[0023] FIG. 5 is a perspective view of a fused deposition modeling (FDM) printer constructed in accordance with the present disclosure.

[0024] FIG. 6 is a diagrammatic view of a plurality of solid grain port geometries and their respective thrust curves in accordance with the present disclosure.

[0025] FIG. 7 is a perspective view of an exemplary implementation of a fuel grain constructed in accordance with the present disclosure.

[0026] FIG. 8 is a perspective view of an igniter holder disposed within a port of the fuel grain shown in FIG. 7.

[0027] FIG. 9 is a cross-sectional view of the fuel grain shown in FIG. 8, taken from the line 9-9 and in the direction of the arrows.

[0028] FIG. 10 is a diagrammatic view of a plurality of infill densities and infill geometries in accordance with the present disclosure.

[0029] FIG. 11 is an exploded perspective view of an exemplary implementation of a solid fuel assembly constructed in accordance with the present disclosure.

[0030] FIG. 12 is a graphical view of thrust curves of four different nozzle geometries as a function of time in accordance with the present disclosure.

[0031] FIG. 13 is a diagrammatic view of an exemplary implementation of a method of manufacturing a fuel grain for an HRE in accordance with the present disclosure.DETAILED DESCRIPTION

[0032] The following detailed description refers to the accompanying drawings. The same reference numbers in different drawings may identify the same or similar elements.

[0033] As used herein, the terms "comprises," "comprising," "includes," "including," "has,""having" or any other variation thereof, are intended to cover a non-exclusive inclusion. Forexample, a process, method, article, or apparatus that comprises a list of elements is not necessarily limited to only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Further, unless expressly stated to the contrary, "or" refers to an inclusive or and not to an exclusive or. For example, a condition A or B is satisfied by anyone of the following: A is true (or present) and B is false (or not present), A is false (or not present) and B is true (or present), and both A and B are true (or present).

[0034] In addition, use of the "a" or "an" are employed to describe elements and components of the implementations herein. This is done merely for convenience and to give a general sense of the inventive concept. This description should be read to include one or more and the singular also includes the plural unless it is obvious that it is meant otherwise.

[0035] Further, use of the term "plurality" is meant to convey "more than one" unless expressly stated to the contrary.

[0036] As used herein, qualifiers like "substantially," "about," "approximately," and combinations and variations thereof, are intended to include not only the exact amount or value that they qualify, but also some slight deviations therefrom, which may be due to manufacturing tolerances, measurement error, wear and tear, stresses exerted on various parts, and combinations thereof, for example.

[0037] The use of the term "at least one" or "one or more" will be understood to include one as well as any quantity more than one. In addition, the use of the phrase "at least one of X, V, and Z" will be understood to include X alone, V alone, and Z alone, as well as any combination of X, V, and Z.

[0038] The use of ordinal number terminology (i.e., "first", "second", "third", "fourth", etc.) is solely for the purpose of differentiating between two or more items and, unless explicitly stated otherwise, is not meant to imply any sequence or order or importance to one item over another or any order of addition.

[0039] Finally, as used herein any reference to "one implementation" or "an implementation" means that a particular element, feature, structure, or characteristic described in connection with the implementation is included in at least one implementation. The appearances of the phrase "in one implementation" in various places in the specification are not necessarily all referring to the same implementation.

[0040] Referring now to the drawings and in particular to FIG. 1, shown therein is a diagrammatic view of an exemplary HRE 100 (also referred to herein as the "engine 100") constructed in accordance with the present disclosure. HRE systems, such as the HRE 100 shownin FIG. 1, have a variety of applications, including sounding rockets, suborbital and orbital launch vehicles, and RATO. These applications appeal to both military and commercial providers, making hybrid rocketry an interesting research topic over the last few decades.

[0041] As shown in FIG. 1, the HRE 100 generally comprises a pressurizing gas tank 104 configured to contain and pressurize a gas 106 therein, a liquid oxidizer tank 108 configured to contain a liquid oxidizer 110 therein, a control valve 112, an igniter 116, an injector 120, a solid fuel grain 128 contained therein defining a port 130 therethrough, and a nozzle 132.

[0042] The scale explored in this disclosure comprises a rocket motor with a casing having a diameter such as, for example, 38 mm. This size represents the lower end of what is still considered high powered rocketry, with thrust measurements ranging between number to number. A researcher from Oklahoma State has explored solid rockets ranging from 38 mm diameter to 76 mm diameter, where the observed peak thrust translated to around 10 to 25 Ibf and 500 to 600 Ibf, respectively.

[0043] HRE Fundamentals

[0044] The performance of rocket engines may be evaluated based on a set of several key performance parameters. Typical measurables for rocket engines include mass flow rate (m), thrust (F), burn time (tb), total impulse (I), and specific impulse (lsp). Due to the nature of hybrid rockets, there are other performance parameters that apply known as oxidizer mass flow rate (rhox), and feed pressure (Po). The combination of these different parameters is related to determining what type of rocket is used and what configuration that rocket is used in, especially in regards to propellant composition and nozzle geometry. Thrust is a measure of the reaction force produced by combustion of the fuel and oxidizer within the engine 100, which expels hot gases out of the nozzle. Specific and total impulse are measures of the energy that the propellant releases over the length of the burn. Burn time specifies the length of the burn for a rocket engine, while burn rate refers to the rate at which the propellant burns to completion within the engine 100. In orderto accurately understand these forces at play, the control volume in question can be considered. In accordance with the present disclosure, an HRE 100 provided with plumbing is mounted on linear bearings with the forward closure direct transferring the force into the load cell. If we consider only the engine 100 and load cell, we can include the propellant temperature, pressure, and other properties that occur within the chamber.

[0045] Mass flow rate (m), often times also referred to as mass flux, is a measure of the rate a fluid flows through a certain cross section during a length of time. Mass flow rate is an important metric for engines as it determines the amounts of substances used during thecombustion process that are used to determine thrust, efficiency, and other performance metrics. In HREs, mass flow rate is commonly applied to the fuel and oxidizer. Knowing the values of these parameters is pivotal in determining fuel regression rates and oxidizer remaining in supply. Mass flow rate is defined by Equation (1), where p, A, and v are equal to the density of the fluid, the area of the cross section, and the velocity of the fluid in that cross section, respectively. m = p * v * A (1)

[0046] By using Newton's second law of motion, while also assuming the flow field is steady and one-dimensional, the momentum equation can be rearranged and simplified to be equated to the sum of pressure and momentum forces exiting the control volume. This simplification is characterized in a new form shown in Equation (2).

[0047]

[0048] The right side of the simplified thrust equation can be separated into two separate pieces, each with their own unique contribution to overall thrust. Mass flow rate multiplied by the normal component of exit velocity divided by the gravitational constant is known as momentum thrust, while the difference in pressures multiplied by the exit area is known as pressure thrust. The momentum term will account for the majority of the thrust. The second term is a tuning mechanism to determine the total thrust with respect to altitude, and can be positive, negative, or zero depending on the design of the exit pressure of the nozzle 132. Ideal nozzle 132 performance occurs when the ambient pressure matches the exit pressure and the exit velocity of the nozzle 132 is maximized. This results in the pressure thrust being equal to zero. Most nozzles are considered over-expanded at sea level due to the high ambient atmospheric pressure. This phenomenon is due to the atmospheric pressure being greater than the nozzle exit pressure, causing to push back on the exhaust plume, producing a negative pressure thrust. A positive pressure thrust does not always mean better performance, however. Anything other than perfectly-expanded nozzles do not perform with an ideal normal velocity component.

[0049] An engine's 100 burn time (tb) can be characterized by using the thrust profile during the duration of its burn. A normal thrust profile for an engine 100 is characterized by three distinct stages of an engine's 100 burn: rise, sustain, and fall. During the rise time, the igniter 116 will ignite the engine 100 causing a sharp increase in pressure and thrust. Depending on the propellant composition and geometry of the grain, the engine 100 can exhibit differentcharacteristics during the sustainment period of the burn. Motors can exhibit progressive, regressive, or neutral burn profiles depending on the slope of the thrust curve in the sustainment period. The end of the burn time is characterized by a sharp drop in thrust, indicating the end of the burn period.

[0050] Total impulse (I) is characterized as the integral of thrust with respect to the burn time. Total impulse is a metric used to determine the overall energy a rocket propulsion system has to offer, and is commonly employed in determining the energy required for various stages during a rocket's mission. The units for total impulse are a force multiplied by time, such as (N * s) or (Ibf * s). Equation (3) serves as a reference to the relationship of thrust, burn time, and total impulse. This value can also be calculated by multiplying the average thrust by the engine's 100 burn time.1 = ^bF dt = F * tb(3)

[0051] Specific impulse (lsp) is the ratio of a rocket's total thrust per unit weight flow of propellant through its nozzle 132. This metric serves as a propulsive efficiency, where the higher the specific impulse, the more efficient the engine 100 is at producing thrust per propellant weight. Due to having a solid fuel and liquid or gaseous oxidizer, HREs typically have a middle of the road specific impulse. This is due to the fact that the solid fuel portion is usually heavy compared to other liquid fuels. The expression for specific impulse can be shown in Equation (4) for reference. The units for specific impulse are expressed as seconds (s).

[0052] Due to the nature of HREs, the burn rate of the fuel is measured differently than both solid and liquid systems. Regression rate (f) is the measure of the length the solid fuel grain regresses, or burns away, over time. Typically, hybrid rockets are characterized as having low regression rates which is not good for rocket performance. Regression rate is an important metric for HREs in order to compute fuel flow and overall performance. In accordance with this disclosure, regression rate will be separated into its longitudinal component and calculated using the mass flow rate of fuel and oxidizer. The time-averaged longitudinal regression rate is shown in Equation (5). Note that these values are all in terms of the fuel.

[0053] fport is known as the mean fuel combustion chamber radius. This value can be calculated using the initial port radius of the fuel (fo), the total mass loss of the fuel (AM), andlength of the combustion chamber L. Equation (6) can be seen showing the relationship between these values.

[0054] HRE Combustion

[0055] Due to HREs having a combination of solid fuel and liquid or gaseous oxidizer, the combustion they experience is unlike its solid or liquid counterparts. FIG. 2 provides a graphical view of different modes of the boundary layer 200 that are present in HRE combustion. Boundary layer combustion is the primary mechanism of hot gas generation in HREs. Upon ignition, a diffusion flame forms over the surface of the fuel 202 along the length of the port (i.e., in a diffusion flame zone 204). The combustion is sustained by heat transfer from the flame to the solid fuel 202 causing continuous fuel vaporization until the oxidizer 206 flow is turned off. On top of a velocity gradient that is present within the flow, there is a temperature gradient based on the mixing that occurs between the fuel 202 and oxidizer 206 during the combustion process. Below the diffusion flame zone 204, there is a fuel vapor zone 208 in which there is a fuel-rich portion of flow, while above the diffusion flame zone 204, there is an oxidizer-rich zone 212. The diffusion flame zone 204 is characterized by the highest combustion temperature in the flow, which occurs where the O / F ratio is the most ideal for the given fuel 202 and oxidizer 206 combination. The flame height is set by the competition between the energy from the flame vaporizing the fuel, the turbulent boundary layer development along the fuel port, and the blowing of the fuel of the gases departing the surface.

[0056] Regression Rate Behavior

[0057] Fuel regression rate behaviors are closely linked to mass flux (G), where different regions can be identified within different mass flow regimes, as shown in FIG. 3. The middle region (i.e., a conductive heat transfer region 300) is where regression rate is diffusion dominated. When G gets too high (i.e., as in a chemical kinetics region 304), the combustion process is controlled by the chemical kinetics and not diffusion. This is where the regression rate becomes pressure dependent and eventually reaches an upper bound, known as the flooding limit. The flooding limit is generally characterized by very oxidizer-rich conditions, and will extinguish the flame. At too low of a G value (i.e., as in a radiation heat transfer region 308), convective heat transfer no longer plays a significant role and will be dominated by radiation.

[0058] Marxman laid the foundation for describing and understanding fuel regression rate. According to his studies from 1963-1965, regression rate is most accurately correlated to theconvective heat transfer from the boundary layer to the surface of the fuel grain. In most cases, regression rate is assumed to be constant across the length of the grain. Therefore, it is a safe assumption to correlate regression rate with mass flow entering the solid fuel port. Equation (7) outlines the correlation Marxman and company derived, where Go = rho, rho is mass flow of oxidizer, and Apis area of the fuel grain port. r = a * GQ (7)

[0059] a and m are both experimentally-derived constants for a given Go range and depend on engine dimensions, fuel grain geometry, injector geometry, and internal flow features of the HRE 100.

[0060] HRE Advantages and Disadvantages

[0061] HREs experience a wide variety of advantages and disadvantages when compared to their solid and liquid counterparts that apply to distinct aspects of the engine's 100 design, performance, and operability. Some of the earliest work with rockets involved HREs due to the simplicity, safety, cost, and versatile operation envelope.

[0062] Advantages

[0063] One of the earliest studies on HREs was performed by General Electric in 1956, which outlined an HRE employing a 90% hydrogen peroxide oxidizer and polyethylene fuel "solidliquid" rocket. The reasoning that led to this employment method and its advantages were also outlined. Compared to solid rocket motors, HREs exhibit theoretical higher specific impulse and the ability to throttle the engine 100 for better control during burn. The ignition range is smooth over a wide range of oxidizer to fuel ratios. When compared to their liquid counterparts, HREs require much less mechanical sophistication, due to only having one liquid or aseous propellant. Due storing the fuel and oxidizer separately, HREs are typically safer than both liquid engines and solid motors. Separate storage also allows for ease of storage requirements usually associated with solid fuels. Hybrid rockets also do not typically have toxic exhaust products, which makes them better for the environment than solid motors and liquid engines. The combination of these traits allows for a cheap option where throttling is necessary. Table 3 shows a more in-depth breakdown of HREs advantages compared to solid and liquid rocket systems.

[0064] Table 3: Advantages of HREs over Solid and Liquid

[0065] Disadvantages

[0066] Although there are quite a few advantages that make hybrid rockets seem attractive, they are usually not implemented due to the drawbacks that come with the system. One of the main hindrances of HREs is that the combustion process relies on a relatively slow mechanism of fuel melting, evaporation, and diffusive mixing shown in FIG. 2. As a rough comparison, solid rockets at a typical combustion pressure may be near 1.0 cm / s whereas HREs using a classic polymeric fuel may have a regression rate on the order of 0.1 cm / s. Solid rocket motors also lack plumbing and turbomachinery because they have no moving fluids. This makes them the option of choice when thrust-to-weight ratio is of consideration. Due to still having one solid fuel grain, liquid systems can exhibit a higher specific impulse than HREs, making liquid systems the standard for lightweight rocket engines. Due to not having the best thrust to weight ratio, nor being able to produce the most efficient thrust, HREs are rarely chosen in the systems of today.

[0067] As with most chemical combustion processes, an ideal mixture ratio exists. Due to the boundary layer effects on temperature and velocity, a non-uniform burning profile occurs along the length of the fuel grain. As the flow within the fuel grain port fully develops, it experiences more consistent burning with better mixing as the flow proceeds through the casing towards the nozzle. Better mixing of fuel and oxidizer leads to a higher combustion temperature. As the combustion temperature rises, so does the vaporization rate of the solid fuel, which causes the fuel grain to burn faster towards the nozzle than the injector. This phenomenon is known as O / F shift. O / F shift makes it difficult to design for a perfect fuel grain and is an inherent disadvantage of a hybrid rocket propulsion system that results in non-optimal performance.

[0068] Solutions

[0069] There are a few known paths to solutions to low regression rates. One such path is the use of fuels that experience good vaporization during the process of combustion. In the 1990s, the U.S. Air Force studied cryogenic fuels designed for HREs. In their efforts, they discovered pentane burns around 3 to 4 times faster than normal fuels. Pentane produces a thin, low viscosity, low surface tension liquid layer on the fuel surface during combustion. This instability driven by the shearing effect of the oxidizer flow in the port leads to the entrapment of fuel droplets into the gas stream, greatly increasing overall fuel mass transfer rate. This mechanism acts as continuous spray injection distributed along the port, which leads to muchhigher regression rates than conventional polymeric fuels that rely solely on evaporation. Lower required energy for vaporization results in a more uniform burn profile throughout the fuel grain.

[0070] Another way to compensate for low regression rates is through surface area manipulation of the fuel grains. The more surface area in contact with the oxidizer, the faster the solid fuel grain will burn. This can be accomplished through the use of multi-port grains 400 (as opposed to single-port grains 404) depicted in FIG. 4. One of the main problems with this is that the volume of the fuel decreases, which decreases the amount of energy the fuel can store. Most attempts to improve fuel regression rate involve increasing heat transferto the fuel surface. This can be done by inducing turbulence to the fuel by adding roughness. Complex helical geometries have shown to increase regression rates due to producing a more turbulent flow that results in better mixing of the fuel and oxidizer.

[0071] H RE Types

[0072] While HREs exhibit properties from both solid and liquid engines, there are many different configurations to employ these characteristics. Different types of hybrid engines include mono-propellant, bi-propellant, and even reverse hybrid engines. A reverse hybrid is a hybrid that is employs a solid oxidizer with a liquid or gaseous fuel, which was first attempted by William Avery in 1952. The most common employment of the hybrid engine is a solid fuel and liquid or gaseous oxidizer, due to its simplicity, reliability, and cost-effectiveness. These reasons are way this configuration was chosen for this disclosure.

[0073] Additive-Manufacturing Overview

[0074] Additive-manufacturing (AM) is the process of building an object by adding material until the object is the desired shape. Technically, this encompasses any build process that involves adding material, such as molding, but more recently has been used as the production name to three-dimensional (3-D) printing. 3-D printing is a computer-controlled process that creates highly- customizable 3-D objects by depositing layers of material. While concepts date back to the early 20th century, AM technology has not provided reliable and functional parts until recently. AM parts usually begin in a computer-aided design (CAD) software. Common CADs include SolidWorks, CATIA, and Sketchllp. These CAD software applications use precise geometry and a series of sketches, extrusions, and cuts, along with many other possible design processes, that ultimately assist the user in designing a part with precise geometry. Once the part has been designed, it is saved and sent through a slicer software that translate the CAD design into a layer- by-layer design that interfaces with the 3-D printer. This design is then sent to the 3-D printer, where it executes the design by layering material in certain patterns to achieve the desired partgeometry. There are a wide range of 3-D printer types and materials, each providing its own set of benefits and drawbacks.

[0075] Common AM Techniques Vat Photopolymerization

[0076] Vat photopolymerization, or stereolithography apparatus (SLA), is when a vat of liquid photopolymer resin is cured through the selective exposure to light (via laser or projector) which initiates polymerization and converts exposed areas into solid parts. SLA prints typically use ultraviolet (UV)-curable photopolymer resins, feature high level of accuracy and complexity, accommodates large build areas, and allows for a smooth surface finish. This was the first commercialized AM printing technique.

[0077] Powder Bed Fusion

[0078] Powder bed fusion is one of the most commonly employed AM techniques. Also known as selective laser melting (SLM), powdered material is selectively consolidated by melting it together using a heat source such as an electron beam. The powder surrounding the consolidated part acts as support material for the overhanging features. SLM prints have a wide range of materials such as plastics, metals, ceramics, and even sands. This AM technique allows for a high complexity in part shape.

[0079] Directed Energy Deposition

[0080] Directed energy deposition (DED) is an AM technique that is most closely related to welding. DED printers utilize powder or wire that is fed into a melt pool which has been generated on the surface of the part where it adheres to the underlying part or layers by using an energy source such as an arc, laser, or electron beam. DED printing benefits include no axis limitation, allows for repairs, and the ability to use multiple materials in a single part.

[0081] Material Extrusion

[0082] Of the numerous printing techniques, material extrusion (commonly referred to as "FDM") is the most widely used AM printing technology due to its ease of use. In FDM printing, material is extruded through a nozzle ororifice in tracks or beads, which are combined into multilayer models. Varieties include heated thermoplastic extrusion and syringe dispensing. It is conceptually simple, does not require health concerning glue or solvents, and most of the printing apparatus is cheap and tabletop size. Typical materials for this technique are thermoplastic filaments and liquids. That allows for parts that are very economical, can be printed in multiple colors, offer strong structural properties, and can usually be used in office environments. An exemplary FDM printer 500 is shown in FIG. 5. A thermoplastic filament 504 is continuously fed into a small heated chamber where it melts, becoming a highly viscous fluid.The melt is then extruded by an extruder 508 through a nozzle 512 and then deposited layerwise on a heated table 516, following the pattern specified by the CAD file and slicer software to form a printed part 520.

[0083] The process by which FDM printing occurs depends on a long list of parameters that define the way the part is printed. These parameters can be seen in Table 4 with a brief description. Because FDM printers have so many different parameters by which the designed parts are constructed, the design space is large. Nozzle and filament diameter are usually correlated to the type of filament or size of print. Infill parameters such as geometry and density specify the way in which the prints are constructed and with how much filament. These parameters affect structural properties as well as weight. FDM printers were chosen due to the largely undiscovered design space, along with its cost-effectiveness, ease of use, and minimal health risk.

[0084] HRE Composition

[0085] The composition of fuel and oxidizer in a HRE system plays a large role in the overall performance and operability of the system. As described above, there is a delicate balance of energies at play in hybrid rocket combustion that produces the best burn characteristics. Choosing the best combination for performance may be a long and tedious process. However, there are many different perspectives to consider when deciding the best composition for the application, such as cost, storability, and simplicity. Depending on the type of HRE, the fuel and oxidizer may come in many different combinations, and sometimes even different states within the same component. There are other materials, aside from the main fuel material, that can be added into hybrid fuel to change the density or alter burn rate characteristics.

[0086] Table 4: FDM Printing Parameters

[0087] Fuel in an HRE is usually responsible for providing the energy needed forthrust during combustion. Stereotypical fuels for HREs are generally comprised of solid hydrocarbon materials due to the fact that they have the molecules necessary to create high flame temperatures. Themost widely used hybrid rocket fuel is HTPB. One of the main problems with HTPB is the intensive manufacturing process that takes place with the fuel grain. HTPB can be uniformly mixed in a liquid form with other additives, degassed in a vacuum, cast into its desired shape, then left to cure for an extended period of time before it is ready for use. This manufacturing process often leaves small amounts of gas trapped in the fuel grain, causing density impurities that could affect performance. Because of the nature of the casting process, it is practically impossible to cast complex internal geometries.

[0088] Due to the recent advances in additive-manufacturing, HREs are being explored with other materials to gain further knowledge on the relationships at play between fuel and oxidizer. FDM printers have allowed for complex internal geometries, automated manufacturing, and more consistent results in grain density. The use of additive-manufacturing has allowed for the design space of solid fuel grains to be limitless, allowing very customizable fuel grains for a wide range of mission profiles. Various parameters, such as infill percentage and infill geometry, can be applied to fuel grains that allow for different regression rates and thrust values that cater to the mission. This process is additive, and leaves very little waste because of that.

[0089] FDM printers have a wide variety of filaments available, each with their own properties that are used for different applications. The most common types of filaments employed today are PLA, ABS, PETG, nylon, and others. Structural, thermal, and mechanical properties of these materials can be seen in Table 5.

[0090] ABS is an inexpensive filament material that already has proven applicability as a hybrid rocket fuel. ABS has been shown to be more consistent than hydroxyl-terminated polybutadiene (HTBP) in hybrid rocket combustion due to the more accurate manufacturing process and high energy content of butadiene. Another intriguing FDM filament for hybrid rocket applications is PLA. PLA is similar to ABS in its mechanical properties but has a large advantage in its environmental impact. PLA is a thermoplastic polyester with a chemical formula of (C3H4O2), and is the most common FDM filament for its good mechanical properties and biodegradability. PLA is principally produced from starch saccharification, lactic acid fermentation, oligomerization, cyclic monomer, and ring-opening polymerization of the cyclic monomer. PLA is easily processed on standard plastics equipment, and can be made annually from renewable resources to yield articles for use in either the industrial packaging field or the biocompatible / bioabsorbable medical device market. PLA is degraded by simple hydrolysis of the ester bond and does not require the presence of enzymes to catalyze this hydrolysis. The rate of this degradation is dependent on the size and shape of the article, the isomer ratio, and thetemperature of the hydrolysis. Table 6 compares the material properties of PLA, ABS, and HDPE, a traditional hybrid rocket fuel.

[0091] Table 5: Structural, Thermal, and Mechanical Properties of Common FPM Materials

[0092] Table 6: Material Properties of ABS, PLA, and HDPE

[0093] Note a slight variation in densities occur between Tables 6 and 7. This could be due to environmental differences or differences in the way these materials were tested. The ignition temperature of ABS is 466°C, which is much higher than the other materials listed on this table. A high ignition temperature is not desirable, as it takes more energy to complete the combustion process. High combustion temperatures and pressures could be problematic as they are more difficult to achieve. Further studies have shown that ABS produces several volatile organic compounds in much higher concentrations at a temperature around 250°C, which is much lower than its ignition temperature. PLA presents a lower ignition temperature at 388°C and higher density than ABS. A higher density with a lower ignition temperature is desirable because it does not take as much energy to burn, and higher density material creates more thrust due to higher available mass flow of the fuel. PLA has been known to emit harmful combustion products, but at considerably lower levels than other plastic materials and leaves no residue. Leaving no residue is an attractive characteristic of PLA, as it does not present a harmful impact on reusable hybrid rocket casings. Another study on the thermal degradation and combustion properties of common biodegradable polymers shows that PLA has a combustion temperature of 382°C in a nitrogen environment and 385°C in an oxygen environment. This study is useful because nitrogen and oxygen are the two elements that make up nitrous oxide (N2O), a common oxidizing agent for hybrid rocket propulsion.

[0094] Oxidizer

[0095] Oxidizer is used to control the intensity and rate of the combustion process. There are many different characteristics to consider when deciding on an oxidizer for a hybrid rocket system. Because none of these oxidizers encompass all desirable properties, the selection of an oxidizer is usually a compromise between various factors such as availability, cost, storage requirements, hazards, and performance. The most common oxidizers for HREs are liquid oxygen (LOX), ozone, nitrous oxide (NOS), dinitrogen tetroxide (NTO), nitric acid (RFNA), and hydrogen peroxide. Thermochemical properties of these well-known oxidizers reacted with HTPB can be seen in Table 7.

[0096] Table 7: Thermochemical Properties of Common Oxidizers Reacted with HTPB

[0097] LOX is a widely used oxidizer and burns with a bright yellow flame with most hydrocarbon fuels. It has high attainable performance and is a commonly used oxidizer for large launch vehicles. Although LOX is non-toxic and non-corrosive, it has other qualities that are much more undesirable. Because it boils at such a low temperature, well-insulated storage tanks, pipes, and valves can be used in order to eliminate any boiling losses during plumbing. This drastically increases storage and maintenance costs due to having to store it at such a low temperature. This also involves personnel with advanced training to ensure no one is harmed during the process as cryogenic LOX can cause severe frostbite.

[0098] NOS, also known as laughing gas, is a less potent oxidizer than the majority listed in Table 7, but still facilitates combustion at raised temperatures. Although its liquid temperature range is very small, it is self-pressurizing which eliminates the need for separate pressurization tanks. Combining that with its very basic storage requirements and applicable performance, this makes NOS a very attractive oxidizer in low-cost scenarios.

[0099] NTO is a high-density liquid that is the most common very storable oxidizer today. It is mildly corrosive when pure, but forms very strong acids whenever exposed to water. It is also very toxic during its decomposition process. Because of its high vapor pressure, it can be stored in large tanks with compatible materials. Although this oxidizer permits solid performance, it is very dangerous to employ.

[0100] RFNA stands for red fuming nitric acid and was widely used during the mid-1900s. Specific types of stainless steel, gold, and other materials are used for storage of RFNA due to its high corrosiveness. When exposed to air, its fumes are poisonous. Many other oxidizers today are more desirable.

[0101] Hydrogen Peroxide is a very powerful liquid oxidizer that also permits clean burning. Its organic compounds are non-toxic when exhausted. When used as an oxidizer, its high concentrations cause severe skin reactions and can ignite when in contact with wood, oils, and many other organic compounds. Although this oxidizer shows promise, it has not been employed much in the United States due to its unpredictable storability.

[0102] In one aspect, the oxidizer chosen for this disclosure is NOS. It has favorable combustion characteristics and is non-toxic, non-corrosive, and has a desirable density and vapor pressure. NOS has flown in space since the early 2000s with SSI, showing promise in HRE applications.

[0103] Additives

[0104] Additives perform many functions, including but not limited to shortening or lengthening curing times, improving rheological properties or physical properties, changing the transparency of to prevent radiation heating, or modifying chemical or physical reactions that occur during the burn. Although there will be no comparison of additives in this disclosure, it is important to note their ubiquity in hybrid rocketry, and rocketry in general. In HREs, additives are generally used to enhance performance characteristics of the fuel grain, or ease storage and handling requirements of potentially dangerous oxidizers.

[0105] The use of metal particles in hybrid fuel grains has been pivotal in increasing performance of HREs. By adding metal particles of various sizes to fuel grains, fuel regression rate, combustion efficiency, and motor stability can be modified to better fit the mission statement. Test firings performed by researchers from Naples, Italy show that metal particles such as aluminum, magnesium, and iron increase regression rate by nearly 50%. This is due to the additives reducing the heat of gasification of the bulk fuel and the blocking effect induced by mass blowing. Metal and metal hydride powders raise the flame temperature and radiation feedback from the combustion products.

[0106] The use of additive-manufactured fuel allows for a seamless addition of metal powders whenever desired. It is common for FDM filaments to contain powder metal additives for aesthetic purposes, but for HRE applications, these additives give a boost in performance. There are also machines that can melt, extrude, and wind pellets of FDM filament to allow forthe use of customizable filament. An external hopper is filled with the desired FDM filament pellets along with any metal additives that may be considered. The pellets are then fed into a heated extrusion chamber where they are subsequently melted and mixed. That mixture is then pushed out a small opening and rapidly cooled by external fans to create usable FDM filament. In accordance with the present disclosure, the fuel grain may include a powder metal additive having a granular size between 5 and 30 micrometers (pm). Generally, the powder metal additive may be a metal commonly used as burn rate catalysts in solid rocket motors, such as aluminum or copper chromite, for example.

[0107] In order to facilitate reliable combustion, a pyrogenic igniter will be used. Pyrogenic igniters utilize a small amount of propellant attached to the end of a wire. A current is passed through the wire via a control relay causing the propellant to ignite. This provides a strong flame to ignite the oxidizer flow and begin combustion of the solid fuel. Different igniters are used in different factions of rocketry, but almost always present.

[0108] Theory of Analysis

[0109] This disclosure focuses on six different rocket performance parameters and their statistical variations. These parameters consist of mass flow rate, peak thrust, average thrust, total impulse, specific impulse, and regression rate. Three variations of solid fuel infill density and three variations of infill geometry were chosen in order to evaluate their performance variations. Initially, three different infill densities, 30%, 50%, and 70%, will be varied in a cubic infill geometry. Subsequently, two different infill geometries, triangular and concentric, will be varied with an infill density of 50%. Each different configuration will consist of five separate tests to ensure all assumptions made on the basis of this testing will be accurate and well developed. All five solid fuel configurations will be evaluated on an HRE thrust stand in a 38-mm (1.5in) casing with a total solid fuel length of 3.5 in. Thrust will be recorded as a function of time for all tests, whereas total impulse and specific impulse will be calculated based on the burn characteristics such as burn time and mass flow rate. Oxidizer mass flow rate will be calculated using mass flow parameter of NOS at conditions created in this testing, and physically verified by weighing the testing bottle before and after hot firings. Fuel grains will be weighed before and after each hot fire test to physically track the fuel mass flow rate. Regression rate will be calculated analytically based on the weight of the fuel before and afterfiring using equations characterized by Marxman et al. and further expanded by Whitmore et al. Regression rate will then be physically examined by cutting and measuring the difference in port geometry diameter after each test to determinethe actual fuel regression rate. Nozzle geometry will be determined with preliminary tests to assess the most consistent results.

[0110] EXPERIMENTAL METHODOLOGY

[0111] Fuel Grain Manufacturing

[0112] As stated above, most HRE solid fuels are manufactured through the cast and cure method. Although most of the traditional HRE fuels are highly energetic, this manufacturing method leaves little room for complex geometric design parameters such as non-uniform port geometry structures. Cast and cure manufacturing is also very labor intensive, requires an exact ingredient mixture to ensure proper fuel formation, and can release harmful gases if not protected properly. The use of AM to print solid fuel grains alleviates all of those problems with a passive manufacturing method that produces tight tolerances and complex internal geometries.

[0113] Design

[0114] To test an HRE, the process begins at designing and manufacturing solid propellant. In this disclosure, 3-D printed PLA will be the fuel of choice due to its validity of a solid propellant in an HRE system, cost-effectiveness, and lack of health concerns associated with its manufacturing and storage. White Build Series PLA from MatterHackers will be the PLA described in this disclosure, along with a Creality Ender 5 3-D printer. In order to design and manufacture 3-D printed PLA, a CAD software can be used to interface between the designer and printer to ensure the part gets designed correctly. The CAD software used to execute the fuel grain design is SOLIDWORKS, a very common and robust CAD software utilized in academia and industry alike.

[0115] Solid fuel grains generally have a range of different core geometries that correspond to different thrust profiles. FIG. 6 depicts the relationship between solid grain port geometries (also referred to herein as "port geometries") and their corresponding thrust curves. As shown in FIG. 6, a tubular port geometry 600 results in a progressive thrust curve 604, a star port geometry 608 results in a first neutral thrust curve 612a, a rod-and-tube port geometry 616 results in a second neutral thrust curve 612b, a multi-fin port geometry 620 results in a dual thrust curve 624, a double-anchor port geometry 628 results in a regressive thrust curve 632, and a dual-composition port geometry 636 results in a two-step thrust curve 640.

[0116] Due to simplicity and past benchmarking, a port geometry known as Bates grain was selected. Bates grain, or tubular if referring to FIG. 6, is the stereotypical port geometry choice due to its favorable chamber pressure and thrust curve. Bates grain geometry is characterized by a long cylindrical shape. Initial designs for this fuel grain correspond with a 38-mm diameter tofit snugly inside the motor casing, along with a port diameter of 0.65-in and an overall length of3.5 in.

[0117] Referring now to FIG. 7 , shown therein is a fuel grain 700 (e.g., the fuel grain 128 shown in FIG. 1) constructed in accordance with the present disclosure. In accordance with the present disclosure, the fuel grain 700 may be an additive-manufactured fuel grain for an HRE. The fuel grain 700 may have an infill density and an infill geometry selected to provide a predetermined burn profile. The fuel grain 700 may be manufactured using a material selected from a group consisting of ABS, PLA, and HDPE, and may include an additive selected from a group consisting of aluminum, magnesium, and iron.

[0118] The infill density may be in a range between 20% (such as the 20% triangular infill geometry 904 shown in FIG. 10) and 50% (such as the 50% cubic infill geometry 1000 shown in FIG. 10). In one implementation, the infill density is 25% (such as the 25% concentric infill geometry 1008 shown in FIG. 10).

[0119] The port geometry may be selected from a group consisting of a tubular port geometry 600, a star port geometry 608, a rod-and-tube port geometry 616, a multi-fin port geometry 620, a double-anchor port geometry 628, and a dual-composition port geometry 636.

[0120] The infill geometry may be selected from a group consisting of a cubic infill geometry 1000 (shown in FIG. 10), a triangular infill geometry 1004 (shown in FIG. 10), and a concentric infill geometry 1008 (shown in FIG. 10).

[0121] As described elsewhere herein, the predetermined burn profile may include one or more of a burn rate, a burn duration, and a thrust level.

[0122] As shown in FIG. 7, the fuel grain 700 may have a first end 704, a second end 708 opposite the first end 704, and a sidewall 712 extending between the first end 704 and the second end 708. The sidewall 712 may have an inner surface 716 defining a port 720 extending between the first end 704 and the second end 708. As shown in FIG. 7, each of the fuel grain 700 and the port 720 may have a circular cross-section. The port 720 may have a diameter in a range between 0.5 in and 2.0 in, such as 0.65 in, for example. The fuel grain may have a diameter in a range from 38 mm to 76 mm.

[0123] Bates grain is a very common port geometry in solid rocket motors due to simplicity and performance. Its practice in HRE applications is much less trivial, however. Due to the combination of oxidizer flow and pyrogenic igniters, preliminary tests showed difficulty with keeping the igniter 116 in place within the fuel grain 700 to facilitate reliable combustion. As the NOS flows at a very high pressure, it wants to eject the igniter 116 out the back of the casing,rendering it useless and resulting in a failed test. Thus, adjustments to the fuel grain 700 were made to allow the igniter 116 to remain in contact with the fuel grain 700 during the duration of the burn period. In some implementations, the fuel grain 700 may have an igniter holder 800 inside the Bates grain geometry. The igniter holder 800 may be formed integrally with the fuel grain 700. FIG. 8 shows a magnified rendering of the igniter holder 800 within the port 720 of the fuel grain 700. As shown in FIG. 8, the igniter holder 800 may have a seat portion 804 centrally disposed within the port 720 and a plurality of support struts 808 extending outwardly from the seat portion 804 toward the inner surface 716 of the fuel grain 700. The seat portion 804 may have an inner surface 812 defining a cavity 816 sized and dimensioned to receive the igniter 116 and an outer surface 820. As further shown in FIG. 8, the seat portion 804 may have a circular cross-section. The support struts 808 may be circumferentially disposed about the outer surface 820 of the seat portion 804. While the igniter holder 800 is shown as having six of the support struts 808, it should be understood that the igniter holder 800 could have more or less than six of the support struts 808. For purposes of clarity, only one of the support struts 808 is labeled with a reference character. Further, the igniter holder 800 may be configured to promote initial mixing and add turbulence to the flow for better combustion characteristics. Preliminary testing shows the effectiveness of the igniter holder 800 and this fuel grain port geometry. Shown in FIG. 9 is a cross-sectional view of the fuel grain 700 shown in FIGS. 7 and 8.

[0124] Slicing

[0125] After being carefully designed in the CAD software, the fuel grain can be prepared for transmission to the Ender 5 printer. This is accomplished by saving the SOLIDWORKS file as a Standard Tessellation Language (.STL) file. This converts the CAD part into a tesseract of triangular shapes to interface itself with the printer's software. However, before it can be sent to the printer, it can be run through a slicing software to give the new .STL file parameters by which it is printed. In one aspect, the slicing software described in this disclosure is Cura. In Cura, parameters outlined in Table 4 can be altered to further customize the way the part is printed. Many of these settings were left in their default state, while others were critical design parameters of this disclosure.

[0126] The first design parameter that was altered is known as infill density, or infill percentage. Whenever a print is executed, the printer goes through a series of commands to save filament while also making the part as structurally sound as possible. This involves the printer to execute a complex series of algorithms that result in solid wall layers on the outside and a matrix of filament on the inside of the part. While the wall layers have a 100% infill density, the matrixcan be specified based on the user's needs. It is a well-known phenomenon that surface area and volume play an integral role in the rate at which fuel is burned inside any type of rocket engine or motor. In order to understand the role different surface areas and volumes can make, the infill density of the fuel grain prints was varied in Cura between 30%, 50%, and 70%.

[0127] Another design parameter that may be altered is known as infill geometry, or infill shape. Not to be confused with port geometry that was mentioned earlier, infill geometry specifies the shape of the matrix that constructs the part between its wall layers. Cura has many different infill geometries, each with its own practical use such as rigidity, strength, or flexibility whenever needed. A very standard geometry known as cubic is described as the baseline for testing in this disclosure. All three sets of varying infill percentages are printed with cubic infill geometry, as this is what Cura initially recommends due to its strong structural properties. In order to further understand the role of these manufacturing parameters and their relation with regression rates in HRE fuels, two other infill geometries are chosen at a constant infill density of 50%. These two new geometries are known as triangular prism and concentric. As the shapes of the infill changes, so do the amount of filament, surface area for burning, and volume inside the internal matrix of the print. These changes represent key tuning parameters for the rate burning of the solid fuel. FIG. 10 shows a representation of the different infill densities and infill geometries described in this disclosure, such as a 50% cubic infill geometry 1000, a 20% triangular infill geometry 1004, and a 25% concentric infill geometry 1008.

[0128] Most of the other values receive little to no alterations in this disclosure. The PLA was printed at its recommended print speed, nozzle temperature, and bed temperature to ensure proper heating and adhesion to the bed during the print process. Once all the parameters have been adjusted, Cura will slice the part and save it as a file that interfaces with the Ender 5 printer.

[0129] Printing

[0130] In orderto print the part with accuracy and precision, a few pre-print readiness checks can take place. The most important part of a 3-D print is ensuring the build plate is level. While some printers have digital bed leveling capabilities, the Ender 5 is mechanically leveled. There are small screws on the corners of the build plate that can be twisted to move that portion of the build plate up or down according to where the nozzle is located. A common leveling method is to take a sheet of paper and manipulate it underneath the nozzle and on top of the build plate until the sheet is touching both the nozzle and plate, but slides freely with little to no friction between the two. This ensures that the nozzle is close enough to the build plate for proper adhesion, but does not interfere with itself or the print as the molten filament leaves the nozzle.T1The printer is then set to go through a process of preheating the nozzle and print bed to ensure the filament will flow smoothly and properly adhere to the build plate. This also helps remove any filament that was stuck in the nozzle or extruder from past prints. Once the build plate is level, and the printer has been pre-heated, the print can take place. Table 8 shows the different print configurations and their print durations.

[0131] Table 8: Print Time and Print Weight of Fuel Grain Configurations

[0132] Oxidizer Manufacturing

[0133] In order to test an HRE in a safe environment, special care may be taken in order to ensure the fuel and oxidizer are used properly during testing, handling, and storage. Since the fuel described in this disclosure is PLA, the handling requirements are minimal. On the other hand, NOS is a highly compressed gas that boils at ambient conditions and requires attention when used. To mitigate risk, most of the NOS is stored in a mother bottle that is stored in a safe location and transferred to a smaller testing bottle.

[0134] The thrust stand described in this disclosure implements an HRE that nests inside aluminum plates supported by threaded rods. This sled creates room for oxidizer feed and plumbing, so the load created by the HRE 100 does not affect oxidizer flow. These aluminum plates interface with the thrust ring on the casing while also supporting the casing itself to allow for better momentum transfer to the thrust post, and ultimately, the load cell. This sled created by the aluminum plates and threaded rods are interfaced into linear bearings that allow for accurate transmission of thrust through t-slot aluminum that has been rigidly attached to a mobile stand.

[0135] Oxidizer Delivery System

[0136] The oxidizer delivery system was designed to safely transport the oxidizer from the testing bottle to the thrust chamber. This delivery system implements the 10-1 b testing bottle, mounting clamps, braided hose, pressure regulator, solenoid valve, orifice plate, and injector. NOS is a self-pressuring gas due to its low boiling point and high vapor pressure. This allows for direct storage underneath the test stand without other needs of cooling or pressurizing. Table 9 shows the pressure of NOS at varying temperatures close to the ambient condition.

[0137] Table 9: NOS Temperature and Corresponding Pressure

[0138] The NOS flows directly to a pressure regulator, where the user is able to regulate the output pressure of the bottle between 200-1100 psi. The ability to vary pressure allows for different mass flow rates of oxidizer on the same stand, which is an inherent plus for testing. In accordance with this disclosure, a single oxidizer mass flow rate of 200 psi may be used. Directly downstream of the pressure regulator sits the solenoid valve. This solenoid valve serves as the on / off switch for the oxidizer and is controlled via an electronic relay board.

[0139] Further downstream of the solenoid is the orifice plate. The goal of the orifice plate is to be able to meter the flow of oxidizer based on mass flow parameter (MFP). The equation for MFP can be seen in Equation (8).

[0140] By using Equation (8), the mass flow rate of oxidizer can be obtained. Assuming a set pressure by the pressure regulator and a temperature that matches that pressure for NOS, the mass flow through the orifice can be adjusted based on the area of the orifice by assuming choked flow through the orifice. Choked flow refers to the velocity of the flow relative to the speed of sound (a). The equation for a can be seen in Equation (9). The MFP can be obtained through gas tables by knowing the ratio of specific heats, (y), and molecular weight (MW) of the fluid.

[0141] After an iterative process, the orifice plate can be machined based on the hole diameter needed for the oxidizer flow selection. The final design of the orifice plate described in this disclosure is shown in FIG. 24. The orifice plate is sandwiched between two flanged fittings to restrict the flow to the orifice. Special care was taken to design the orifice to the correct size for accurate oxidizer flow measurements. Many cold fire tests were conducted to ensure accurate measurements. In these cold flow tests, the oxidizer ran for a set amount of time, and weighed before and after the test. This allowed for calculation between actual mass flow and theoretical mass flow, which were closely correlated. Table 10 displays the parts used for the oxidizer delivery system as well as other parts.

[0142] Table 10: HRE System Parts

[0143] After moving through the orifice, the oxidizer is ready for the combustion chamber. Downstream of the orifice plate is the injector. The injector is what guides the flow into the combustion chamber. The injector described in this disclosure axially injects the flow of NOS into the combustion chamber. This design choice was chosen for simplicity.

[0144] HRE Hot Fire Testing

[0145] Before any hot fire tests can commence, a series of pre-test readiness checks typically take place. These pre-test readiness exercises include prepping the solid fuel grains for integration into the thrust chamber, preparing the testing bottle for oxidizer flow, verifying the pressure of oxidizer in the feed system, assembling the rocket casing, stand integration, and configuration of the LABView virtual instrument (VI). Each of these steps are pivotal in the functioning of the hybrid thrust stand and can be executed with precision and care for a reliable and safe testing environment.

[0146] Solid Fuel Preparation

[0147] Referring now to FIG. 11, shown therein is an exemplary implementation of a solid fuel assembly 1100 constructed in accordance with the present disclosure. As shown in FIG. 11, the solid fuel assembly 1100 generally comprises a casing 1104, an injector 1108 (e.g., the injector 120 shown in FIG. 1), a nozzle 1112 (e.g., the nozzle 132 shown in FIG. 1), a liner 1116, one or more nozzle washer 1120, a solid fuel grain 1124 (e.g., the fuel grain 128 shown in FIG. 1 or the fuel grain 700 shown in FIG. 7), and one or more O-ring 1128.

[0148] After the solid fuel grains 1124 have been designed, sliced, and printed, the fuel grains can be prepared for integration with the thrust chamber and testing. It is common practice within rocketry to use liners 1116 within the thrust chamber in order to ensure the casing 1104 is not exposed to the high temperature ranges created by the fuel and oxidizer burning. Liners 1116 are usually comprised of paper or, in more extreme cases, phenolic material. Phenolic liners aremade of alternating layers of cured resin and fibrous materials such as cotton, paper, or glassbased fabric. These materials are sandwiched under extreme pressure and heat forming a solid thermoplastic that has strong structural and thermal properties, ideal for rocket applications. In order to ensure the hot fire tests were as safe as possible, this disclosure implements phenolic liners as insulation between the solid fuel grain and casing. These liners 1116 are cut with precision and care to ensure a perfect integration within the rocket casing.

[0149] After cutting, a fit check can take place to mitigate risk of failures during hot fire testing. Fit checks consist of assembly of the rocket casing with all parts, including snap rings (not shown), nozzle washers 1120, nozzle 1112, fuel grain 1124, liner 1116, O-rings 1128, injector 1108, and an igniter (e.g., the igniter 116 shown in FIG. 1).

[0150] In this assembly, the injector 1108 acts as the forward closure of the thrust chamber and threads into the oxidizer feed system to allow for secure flow. The forward closure is sealed with an O-ring 1128 that ensures no gas can escape the forward closure. The forward closure is secured into place with a snap ring. Directly downstream of the forward closure is the liner 1116 and fuel grain that interfaces directly with a converging-diverging nozzle 1112 that is sized during the initial tests to ensure for the most reliable analysis of performance. The nozzle 1112 is also pressure sealed with an O-ring 1128 and is sandwiched with another snap ring (not shown) to secure the other end of the thrust chamber. After the fit check, the fuel grains are glued into the liner to ensure there is no movement of the fuel during the burn. This glue may be left to cure for at least six hours to allow for adequate time to dry and adhere to the liner.

[0151] P reliminary Test Results

[0152] Preliminary tests were conducted to find the optimal nozzle performance for an inlet pressure of 200 psi and moxof 0.027 Ib / s, with a burn time of 4 s. The nozzle sizes investigated in the preliminary tests were #13, #16, #19, and #25. The numbers refer to the diameter of their throats in inches as a fraction of 64. FIG. 12 displays the thrust curves of these four different nozzle geometries as a function of time (i.e., a #19 nozzle curve 1200, a #16 nozzle curve 1204, a #13 nozzle curve 1208, and a #25 nozzle curve 1212).

[0153] Each test begins with the opening of the solenoid valve near the 0.75-second mark and the rise in thrust due to ignition around the 1.75 s mark. All burns are considered fairly neutral which is conventional of Bates grain geometry in HRE applications. Table 11 shows the peak thrust, average thrust, total impulse, and specific impulse for each nozzle configuration.

[0154] Table 11: HRE Performance Based on Nozzle Size

[0155] Table 11 shows that optimal performance can be most closely replicated using the 16 / 64 in (#16) nozzle. Therefore, a #16 nozzle is used as a control variable for this disclosure. All subsequent tests were executed using a #16 nozzle to ensure the highest level of confidence related to the results.

[0156] Slight variations in how the test stand was set up have occurred since the preliminary tests. Supports for the solenoid and pressure regulator have been removed, which could account for a slight change in thrust measured. Manual quarter-turn valves were also added to prevent the unwanted flow of NOS.

[0157] Referring now to FIG. 13, shown therein is an exemplary implementation of a method 1400 of manufacturing a fuel grain for an HRE. As shown in FIG. 13, the method 1300 generally comprises operating an additive-manufacturing system to fabricate a fuel grain, the fuel grain having an infill density and an infill geometry selected to provide a predetermined burn profile (step 1304).NON-LIMITING ILLUSTRATIVE EMBODIMENTS

[0158] The following is a number list of non-limiting illustrative embodiments of the inventive concept disclosed herein:

[0159] Illustrative embodiment 1. An additive-manufactured fuel grain for a hybrid rocket engine (HRE), the additive-manufactured fuel grain having an infill density and an infill geometry selected to provide a predetermined burn profile.

[0160] Illustrative embodiment 2. The additive-manufactured fuel grain of illustrative embodiment 1, wherein the additive-manufactured fuel grain is manufactured using a material selected from a group consisting of acrylonitrile butadiene styrene (ABS), polylactic acid (PLA), and high-density polyethylene (HDPE).

[0161] Illustrative embodiment 3. The additive-manufactured fuel grain of illustrative embodiment 2, wherein the material selected from the group consisting of ABS, PLA, and HDPE includes an additive selected from a group consisting of aluminum and copper chromite.

[0162] Illustrative embodiment 4. The additive-manufactured fuel grain of any one of illustrative embodiments 1-3, wherein the infill density is in a range between 20% and 50%.

[0163] Illustrative embodiment 5. The additive-manufactured fuel grain of any one of illustrative embodiments 1-4, wherein the infill geometry is selected from a group consisting of a cubic infill geometry, a triangular infill geometry, and a concentric infill geometry.

[0164] Illustrative embodiment 6. The additive-manufactured fuel grain of any one of illustrative embodiments 1-5, wherein the predetermined burn profile includes at least one of a burn rate, a burn duration, and a thrust level.

[0165] Illustrative embodiment 7. The additive-manufactured fuel grain of any one of illustrative embodiments 1-6, wherein the additive-manufactured fuel grain has a first end, a second end opposite the first end, and a sidewall extending between the first end and the second end, the sidewall having a fuel grain inner surface defining a port extending between the first end and the second end, each of the additive-manufactured fuel grain and the port having a circular cross-section.

[0166] Illustrative embodiment 8. The additive-manufactured fuel grain of illustrative embodiment 7, wherein the port has a port diameter in a range between 0.5 inches (in) and 2.0 in.

[0167] Illustrative embodiment 9. The additive-manufactured fuel grain of illustrative embodiment 7, wherein the additive-manufactured fuel grain has a fuel grain diameter in a range from 38 millimeters (mm) to 76 mm.

[0168] Illustrative embodiment 10. The additive-manufactured fuel grain of illustrative embodiment 7, further comprising an igniter holder disposed within the port, the igniter holder having a seat portion centrally disposed within the port and a plurality of support struts extending outwardly from the seat portion toward the fuel grain inner surface of the additive-manufactured fuel grain, the seat portion having a seat inner surface and a seat outer surface, the seat inner surface defining a cavity sized and dimensioned to receive a pyrogenic igniter, the plurality of support struts circumferentially disposed about the seat outer surface.

[0169] Illustrative embodiment 11. A method of manufacturing a fuel grain for a hybrid rocket engine (HRE), comprising operating an additive-manufacturing system to fabricate a fuel grain, the fuel grain having an infill density and an infill geometry selected to provide a predetermined burn profile.

[0170] Illustrative embodiment 12. The method of manufacturing a fuel grain of illustrative embodiment 11, wherein the step of operating the additive-manufacturing system to fabricate the fuel grain is further defined as operating the additive-manufacturing system to fabricate the fuel grain, the fuel grain having the infill density and the infill geometry selected to provide thepredetermined burn profile, wherein the fuel grain is manufactured using a material selected from a group consisting of acrylonitrile butadiene styrene (ABS), polylactic acid (PLA), and high- density polyethylene (HDPE).

[0171] Illustrative embodiment 13. The method of manufacturing a fuel grain of illustrative embodiment 12, wherein the step of operating the additive-manufacturing system to fabricate the fuel grain is further defined as operating the additive-manufacturing system to fabricate the fuel grain, the fuel grain having the infill density and the infill geometry selected to provide the predetermined burn profile, wherein the fuel grain is manufactured using the material selected from the group consisting of ABS, PLA, and HDPE, wherein the material selected from the group consisting of ABS, PLA, and HDPE includes an additive selected from a group consisting of aluminum and copper chromite.

[0172] Illustrative embodiment 14. The method of manufacturing a fuel grain of any one of illustrative embodiments 11-13, wherein the step of operating the additive-manufacturing system to fabricate the fuel grain is further defined as operating the additive-manufacturing system to fabricate the fuel grain, the fuel grain having the infill density and the infill geometry selected to provide the predetermined burn profile, wherein the infill density is in a range between 20% and 50%.

[0173] Illustrative embodiment 15. The method of manufacturing a fuel grain of any one of illustrative embodiments 11-14, wherein the step of operating the additive-manufacturing system to fabricate the fuel grain is further defined as operating the additive-manufacturing system to fabricate the fuel grain, the fuel grain having the infill density and the infill geometry selected to provide the predetermined burn profile, wherein the infill geometry is selected from a group consisting of a cubic infill geometry, a triangular infill geometry, and a concentric infill geometry.

[0174] Illustrative embodiment 16. The method of manufacturing a fuel grain of any one of illustrative embodiments 11-15, wherein the step of operating the additive-manufacturing system to fabricate the fuel grain is further defined as operating the additive-manufacturing system to fabricate the fuel grain, the fuel grain having the infill density and the infill geometry selected to provide the predetermined burn profile, wherein the predetermined burn profile includes at least one of a burn rate, a burn duration, and a thrust level.

[0175] Illustrative embodiment 17. The method of manufacturing a fuel grain of any one of illustrative embodiments 11-16, wherein the step of operating the additive-manufacturing system to fabricate the fuel grain is further defined as operating the additive-manufacturingsystem to fabricate the fuel grain, the fuel grain having the infill density and the infill geometry selected to provide the predetermined burn profile, wherein the fuel grain has a first end, a second end opposite the first end, and a sidewall extending between the first end and the second end, the sidewall having a fuel grain inner surface defining a port extending between the first end and the second end, each of the fuel grain and the port having a circular cross-section.

[0176] Illustrative embodiment 18. The method of manufacturing a fuel grain of illustrative embodiment 17, wherein the step of operating the additive-manufacturing system to fabricate the fuel grain is further defined as operating the additive-manufacturing system to fabricate the fuel grain, the fuel grain having the infill density and the infill geometry selected to provide the predetermined burn profile, wherein the fuel grain has a first end, a second end opposite the first end, and a sidewall extending between the first end and the second end, the sidewall having a fuel grain inner surface defining a port extending between the first end and the second end, each of the fuel grain and the port having a circular cross-section, wherein the port has a port diameter in a range between 0.5 inches (in) and 2.0 in.

[0177] Illustrative embodiment 19. The method of manufacturing a fuel grain of illustrative embodiment 17, wherein the step of operating the additive-manufacturing system to fabricate the fuel grain is further defined as operating the additive-manufacturing system to fabricate the fuel grain, the fuel grain having the infill density and the infill geometry selected to provide the predetermined burn profile, wherein the fuel grain has a fuel grain diameter in a range from 38 millimeters (mm) to 76 mm.

[0178] Illustrative embodiment 20. The method of manufacturing a fuel grain of illustrative embodiment 17, wherein the step of operating the additive-manufacturing system to fabricate the fuel grain is further defined as operating the additive-manufacturing system to fabricate the fuel grain, the fuel grain having the infill density and the infill geometry selected to provide the predetermined burn profile, the fuel grain further comprising an igniter holder disposed within the port, the igniter holder having a seat portion centrally disposed within the port and a plurality of support struts extending outwardly from the seat portion toward the fuel grain inner surface of the fuel grain, the seat portion having a seat inner surface and a seat outer surface, the seat inner surface defining a cavity sized and dimensioned to receive a pyrogenic igniter, the plurality of support struts circumferentially disposed about the seat outer surface.CONCLUSION

[0179] The foregoing description provides illustration and description, but is not intended to be exhaustive or to limit the inventive concepts to the precise form disclosed. Modifications andvariations are possible in light of the above teachings or may be acquired from practice of the methodologies set forth in the present disclosure.

[0180] Even though particular combinations of features are recited in the claims and / or disclosed in the specification, these combinations are not intended to limit the disclosure. In fact, many of these features may be combined in ways not specifically recited in the claims and / or disclosed in the specification. Although each dependent claim listed below may directly depend on only one other claim, the disclosure includes each dependent claim in combination with every other claim in the claim set.

[0181] No element, act, or instruction used in the present application should be construed as critical or essential to the invention unless explicitly described as such outside of the preferred implementation. Further, the phrase "based on" is intended to mean "based, at least in part, on" unless explicitly stated otherwise.

Claims

What is claimed is:

1. An additive-manufactured fuel grain for a hybrid rocket engine (HRE), the additive- manufactured fuel grain having an infill density and an infill geometry selected to provide a predetermined burn profile.

2. The additive-manufactured fuel grain of claim 1, wherein the additive-manufactured fuel grain is manufactured using a material selected from a group consisting of acrylonitrile butadiene styrene (ABS), polylactic acid (PLA), and high-density polyethylene (HDPE).

3. The additive-manufactured fuel grain of claim 2, wherein the material selected from the group consisting of ABS, PLA, and HDPE includes a powder metal additive having a granular size in a range between 5 micrometers (pm) and 30 pm.

4. The additive-manufactured fuel grain of any one of claims 1-3, wherein the infill density is in a range between 20% and 50%.

5. The additive-manufactured fuel grain of any one of claims 1-4, wherein the infill geometry is selected from a group consisting of a cubic infill geometry, a triangular infill geometry, and a concentric infill geometry.

6. The additive-manufactured fuel grain of any one of claims 1-5, wherein the predetermined burn profile includes at least one of a burn rate, a burn duration, and a thrust level.

7. The additive-manufactured fuel grain of any one of claims 1-6, wherein the additive- manufactured fuel grain has a first end, a second end opposite the first end, and a sidewall extending between the first end and the second end, the sidewall having a fuel grain inner surface defining a port extending between the first end and the second end, each of the additive- manufactured fuel grain and the port having a circular cross-section.

8. The additive-manufactured fuel grain of claim 7, wherein the port has a port diameter in a range between 0.5 inches (in) and 2.0 in.

9. The additive-manufactured fuel grain of claim 7 , wherein the additive-manufactured fuel grain has a fuel grain diameter in a range from 38 millimeters (mm) to 76 mm.

10. The additive-manufactured fuel grain of claim 7, further comprising an igniter holder disposed within the port, the igniter holder having a seat portion centrally disposed within the port and a plurality of support struts extending outwardly from the seat portion toward the fuel grain inner surface of the additive-manufactured fuel grain, the seat portion having a seat inner surface and a seat outer surface, the seat inner surface defining a cavity sized and dimensioned to receive a pyrogenic igniter, the plurality of support struts circumferentially disposed about the seat outer surface.

11. A method of manufacturing a fuel grain for a hybrid rocket engine (HRE), comprising operating an additive-manufacturing system to fabricate a fuel grain, the fuel grain having an infill density and an infill geometry selected to provide a predetermined burn profile.

12. The method of manufacturing a fuel grain of claim 11, wherein the step of operating the additive-manufacturing system to fabricate the fuel grain is further defined as operating the additive-manufacturing system to fabricate the fuel grain, the fuel grain having the infill density and the infill geometry selected to provide the predetermined burn profile, wherein the fuel grain is manufactured using a material selected from a group consisting of acrylonitrile butadiene styrene (ABS), polylactic acid (PLA), and high-density polyethylene (HDPE).

13. The method of manufacturing a fuel grain of any one of claims 11-12, wherein the step of operating the additive-manufacturing system to fabricate the fuel grain is further defined as operating the additive-manufacturing system to fabricate the fuel grain, the fuel grain having the infill density and the infill geometry selected to provide the predetermined burn profile, wherein the infill density is in a range between 20% and 50%.

14. The method of manufacturing a fuel grain of any one of claims 11-13, wherein the step of operating the additive-manufacturing system to fabricate the fuel grain is further defined as operating the additive-manufacturing system to fabricate the fuel grain, the fuel grain having the infill density and the infill geometry selected to provide the predetermined burn profile, whereinthe infill geometry is selected from a group consisting of a cubic infill geometry, a triangular infill geometry, and a concentric infill geometry.

15. The method of manufacturing a fuel grain of any one of claims 11-14, wherein the step of operating the additive-manufacturing system to fabricate the fuel grain is further defined as operating the additive-manufacturing system to fabricate the fuel grain, the fuel grain having the infill density and the infill geometry selected to provide the predetermined burn profile, wherein the predetermined burn profile includes at least one of a burn rate, a burn duration, and a thrust level.

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