FDM Hybrid Rocket Grains

Fused Layer ABS Rocketry Experiment (F.L.A.R.E.)

Critical Design Review

EML 4501/EAS 4700-Mechanical/Aerospace Engineering Design

April 20, 2015

Point of Contact:

Amy Besio

Team Members:

Jonathan Benson, Richard Horta, Joshua Rou, John Seligson

Faculty Advisor:

Justin Karl, Ph.D.

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Ethics Statement As engineer, we will uphold ourselves to the code of ethics set forth by the American

Society of Mechanical Engineers [1].

We, as engineers will uphold and advance the integrity, honor and dignity of the engineering

profession by:

I. using our knowledge and skill for the enhancement of human welfare;

II. being honest and impartial, and serving with fidelity their clients and the public;

III. striving to increase the competence and prestige of the engineering profession.

By signing this document, we agree to abide by these fundamental principles. We acknowledge

that this work is our original work and will provide credit when paraphrasing work that is not our

own.

Signatures Date

Amy Besio ________________________________________ _________________

Jonathan Benson ________________________________________ _________________

Richard Horta ________________________________________ _________________

Joshua Rou ________________________________________ _________________

John Seligson ________________________________________ _________________

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Abstract This project explores utilizing fused deposition modeling (FDM) for optimization of hybrid

rocket fuel grains. FDM will allow for custom tailoring of fuel grain geometries, in order to target

desirable performance characteristics unobtainable through traditional manufacturing. The solid

propellant will be composed of acrylonitrile butadiene styrene (ABS), a common additive

manufacturing material. When exposed to an oxidizer, ABS performs comparably to commercially

available hydroxyl-terminated polybutadiene (HTPB) fuel grains. The liquid propellant will be

composed of nitrous oxide (N2O) and will provide the oxygen content to the fuel.

The scope of this project includes design, manufacturing, testing, and data review of the fuel

grains. Development of the grains entails forming appropriate mathematical models for solid and

liquid propellant characterization. Manufacturing encompasses fabrication of the ABS grains

using FDM and assembly of test bed components, which includes the test stand, thrust chamber,

and data acquisition and processing. Testing will consist of a baseline run, followed by subsequent

test fires. Data review includes the testing analysis and a comparison with computational

prediction.

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Table of Contents Ethics Statement ...................................................................................................... Error! Bookmark not defined.

Abstract ……………………………………………………………………………………………………………….

iError! Bookmark not defined.

List of Figures ....................................................................................................................................................... iv

List of Tables ......................................................................................................................................................... v

Nomenclature ........................................................................................................................................................ vi

1.0 Project Overview .............................................................................................................................................. 1

2.0 Design Parameters ............................................................................................................................................ 2

3.0 Parametric Design............................................................................................................................................. 5

4.0 Detail Design ..................................................................................................... Error! Bookmark not defined.

5.0 Bill of Materials………………..…………………………………………………………………………………27

References…………………………………………………………………………………………………………….29

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List of Figures Figure 1.1: Classical Hybrid Configuration…………………………………………………………….....2

Figure 2.1: Fuel Grain Geometries By Casting…………………………………………………………....3

Figure 3.1: Example of Fuel Grain CAD Model…………………………………………………….….…6

Figure 3.2: I_sp vs. O/F Ratio……………………………………………………………………….….…8

Figure 3.3: Nitrous Oxide Phase Diagram…………………………………………………………..…….8

Figure 3.4: Commercial Rocket Configuration (Not Drawn to Scale)…………………………………...10

Figure 4.1: Combustion Chamber………………………………………………………………………..16

Figure 4.2: Forward Bulkhead (Front and Rear View) …………………………………………….……16

Figure 4.3: Aft Bulkhead (Front and Rear View)………………………………………………………..17

Figure 4.4: Thrust Chamber FEA-Displacement…………………………………………………...……17

Figure 4.5: Thrust Chamber FEA-Von-Mises Stress……………………………………………………18

Figure 4.6: Nozzle Design……………….………………………………………………………………18

Figure 4.7: Oxidizer Feed System………………………………………………………………….……19

Figure 4.8: Rail Frame Design…………………………………………………………………………...20

Figure 4.9: Platform Design……………………………………………………………………………...20

Figure 4.10: Platform and Wheels- Cross Section………………………………………………………20

Figure 4.11: Superstrut Bed with Clamps………………………………………………………………..21

Figure 4.12: Assembled Test Stand- Isometric View…………………………………………………....21

Figure 4.13: Assembled Test Stand- Top View………………………………………………………….22

Figure 4.14: Finite Element Analysis of Rail Frame- Displacement…………………………………….22

Figure 4.15: Measurement Apparatus……………………………………………………………………23

Figure 4.15: Pressure vs Burn Times………………………………………………………………….…25

Figure 4.16: Tiva™ C Series TM4C123G LaunchPad [Texas Instruments] ……………………………26

Figure 4.17: Control System Diagram…………………………………………………………………...27

Figure 6.1: Conduction Coefficient Formulation………………………………………………………..29

Figure 6.2: Temperature Equation Array………………………………………………………………..30

Figure 6.3: Temperature Distribution Per Node (Temp in K) ………………………………………….30

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List of Tables Table 4.1: Enthalpy of Formation………………………………………………………………………15

Table 5.1: Bill of Materials…………………………………………………………………………......27

vi

Nomenclature

𝑨𝟐 Nozzle Exit Area

𝑭 Thrust

𝑮 Free Stream Velocity

𝒈 Acceleration Due to Gravity

𝑰𝒔𝒑 Specific Impulse

�̇� Propellant Mass Flow Rate

𝒑𝟐 Nozzle Exit Pressure

𝒑𝟑 Atmospheric Pressure

�̇� Fuel Grain Regression Rate

𝒗𝟐 Exhaust Velocity

𝒙 Axial Location for Combustion Port

𝜷 Non-Dimensioned Fuel Mass Flux from Fuel Vapor

𝝁 Combustion Gas Viscosity

𝝆𝒇 Solid Phase Fuel Density

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1.0 Project Overview

1.1 Background

Bipropellant liquid and solid rocket motors that combine volatile and energetic propellants

have been the industry standard for the last fifty years [2]. Liquid engines have a high specific

impulse, Isp, and thrust-to-weight ratio necessary for launching large payloads. Typical liquid

engines use a liquid oxidizer and liquid fuel that are combined and burned in a combustion chamber

[2]. If the complex turbomachinery that mixes the two propellants fails, the combustion becomes

unstable and causes a loss of thrust and eventual loss of the vehicle. Solid rocket motors use a solid

fuel grain that consists of solid fuel and oxidizer particles that are mixed together with a binding

agent. For optimum solid motor performance, the oxidizer and fuel must be mixed to a specific

ratio as defined by the desired total impulse. The regression of the solid fuel grain depends greatly

on combustion chamber pressure. If the pressure increases too quickly, the motor is likely to

explode. Structural imperfections in the fuel grain can also cause an over pressurization of the

chamber as a result of an increase in local burning rate [3]. Both conventional launch systems have

a high susceptibility to failure of 8% according Claude Lafleur’s Spacecraft Encyclopedia. As

space exploration shifts from government to civilian space, a new market arises that is confronted

with cost, performance, and safety challenges that will not be satisfied by the aforementioned

launch systems [2].

1.2 Hybrid Rockets

Hybrid rocket motors have the ability to fulfil the above-mentioned flight requirements, as

they provide a cost effective and safer alternative to liquid and solid systems. A classical hybrid

configuration consists of a liquid oxidizer and solid fuel grain that are housed separately as seen

in Figure 1.1. They employ non-toxic and non-explosive propellants which makes them inherently

safer and reduces the cost of development, handing, and transportation. When compared to liquid

engines, hybrid motors exhibit mechanical simplicity, reduced fire and explosion hazards, and

higher fuel density.

Figure 1.1: Classical Hybrid Configuration

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When referenced to solid rocket motors, hybrids are chemically simpler, have throttling

and command shutdown capability, and higher Isp. Unlike the regression of solid fuel grains, the

regression rate of hybrid rocket solid fuel grains are most dependent on the oxidizer mass flow

rate. This property increases the tolerance to grain flaws and allows for geometry changes over the

length of the fuel grain.

Although advantageous, these motors are confronted with several technical and non-

technical challenges. Hybrid propulsion systems lack technological maturity and will have to

compete with systems currently implemented in industry. Integration of hybrids may prove

difficult as they typically suffer from lower performance characteristics and low regression rates

when compared to liquid and solid motors respectively.

1.3 Research Goals

The objective of this research is to design, fabricate, and test 3D-printed fuel grains that

optimize performance characteristics. This project seeks to enhance solid fuel grain burn rate by

increasing the surface area exposed in hybrid rocket fuel grains. The fuel grains will be

manufactured though Fused Deposition Modeling (FDM) as opposed to traditional manufacturing

methods. As the burn rate increases, the performance of the rocket improves significantly.

Individual goals for this project are four-fold and listed as follows:

1) Verify the feasibility of replacing HTPB with 3D-printed ABS plastic.

2) Characterize the performance of 3D-printed ABS/Nitrous Oxide fuel/oxidizer

combination.

3) Develop appropriate mathematical models for AB/Nitrous Oxide regression.

4) Apply the findings of (3) in the modeling, printing, and test firing of various ABS

fuel geometries.

2.0 Design Parameters

2.1 Problem Formulation

2.1.1 Design Problem Formulation

A major disadvantage of hybrid rocket systems is insufficient regression rate. Regression

rate is dependent on oxidizer contact with the fuel grain and is limited to the inner surface area. To

control resulting thrust curves, the geometry of the fuel grain surface area can be tailored for

increasing, decreasing, and constant surface area during combustion resulting in progressive,

regressive, or neutral burning respectively. The thrust curves and their respective fuel grain

geometries manufactured by casting shown in Figure 2.1 demonstrate the effect of surface area

design. Traditional methods of casting, tapping holes, and introducing air pockets in the fuel grain

have been used in an attempt to improve regression rate. These methods introduce complications.

Casting limits fuel grain geometry to constant cross-sectional area. Tapping holes and introducing

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air pockets can compromise the structural integrity of the fuel grain and present unreliable

performance characteristics.

Figure 2.1: Fuel Grain Geometries By Casting [Braeunig]

The most favorable method for fuel grain manufacturing would be capable of tailoring any possible

geometry with structural stability and consistent results. Such a method, FDM utilizes layer-by-

layer deposition, allowing for unlimited geometry tailoring. The results of FDM vary only in

proportion to layer resolution; high resolution layering leads to consistent results. FDM is currently

unavailable for commercially used fuel, HTPB. As an alternative, FDM is available for ABS, a

viable hybrid fuel source as seen in a study by Utah State. In the study, hybrid fuel grains of 82.6

cm diameter HTPB produced a mean thrust level of 755 N. ABS fuel grains of the same size

produced a mean thrust level of 717.8 N [4].

This project will first compare the performance of ABS by FDM to tubular casted ABS

and HTPB fuel grains. Second, FDM is expected to optimize control of hybrid fuel grain thrust

curves. Third, tailoring for optimal fuel grain geometry will attempt to increase hybrid rocket

motor performance up to low end solid rocket motor performance. Finally, improving the

performance of hybrid fuel grains necessitates increased safety requirements. The combustion

chamber and test apparatus must be designed with sufficient factors of safety to prevent test failure

and ensure operation personnel safety.

2.1.2 Design Variables

Hybrid rocket motor design variables are thrust, propellant mass flow rate, chamber

pressure and temperature. For total thrust 𝐹𝑇

𝐹𝑇 = �̇�𝑣2 + (𝑝2 − 𝑝3)𝐴2 [Equation 1]

the above equation shows the first product as the momentum of the motor, propellant mass flow

rate, m, and the exhaust velocity, v2. The second product that affects total thrust is the difference

of atmospheric p3, and nozzle pressure, p2 to the area A2, at the nozzle exit. The desired output is

to have exhaust pressure equal to or slightly higher than the ambient fluid pressure. As the exhaust

pressure reaches atmospheric pressure, the right side of the equation becomes negligible, and thrust

relies on mass flow rate of the propellant with the corresponding exhaust velocity. Known as

optimal expansion ratio.

Chamber pressure and propellant mass flow rate are related by the same equation. Chamber

pressure is calculated in 𝑀𝑃𝑎 and will be measured using a hardline pressure transducer while

propellant mass flow rate is measured in 𝑘𝑔

𝑠. The chamber pressure is related to propellant mass

flow rate by,

𝑝1 =�̇�𝑐∗

𝑔𝐴𝑙 [Equation 2]

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where the equation shows the product of the propellant mass flow rate m, and characteristic

velocity c*, divided by the product of gravity g, and initial nozzle throat area At. As the propellant

mass flow rate increases, the internal combustion chamber pressure increases due to increased fuel

consumption.

In the design process of a hybrid rocket, temperature is related to the regression rate through heat

transfer rate. Temperature is related to heat transfer by,

�̇�𝑠 = 𝐹𝑇𝜕𝑇

𝜕𝑦|𝑦=0 [Equation 3]

in which the heat transfer rate per unit area of the active combustion zone to the fuel surface is

equal to that conducted [5]. The heat transfer rate 𝑄�̇�, is equal to the product of the change in

temperature dT, per change in area 𝑑𝑦, to the conductivity of gas kg. The temperature per area of

fuel is proportional to the heat transfer.

Hybrid rocket motor design performance variables are regression rate, specific impulse and fuel-

to-oxidizer ratios. For regression rate,

�̇� = .36𝐺 .8

𝜌𝑓(

𝜇

𝑥)

.2

𝛽.23 [Equation 4]

the free stream propellant mass velocity, 𝐺, is a main factor in the relation to the regression rate �̇�.

As the axial location x increases, the free stream propellant mass velocity increases which increases

regression rate. As solid phase fuel density decreases, there is an increase in the mass velocity

which increases regression rate. From equation 4, as the fuel density decreases, the regression rate

increases due to increased mass velocity. Blowing coefficient, 𝛽, is an aerodynamic and

thermochemical parameter that describes the enthalpy relationship between fuel surface and the

flame zone, as well as regression rate [6].

A characteristic operating feature of hybrids is that the fuel regression rate is typically less

than one-third of composite solid rocket propellants [7]. Hybrid rocket motors have lower

regression rates because of their combustion process and combustion port to oxidizer mass flow

rate. During the combustion process the heat transfer rate is decreased by the vaporized fuel leaving

the fuel surface during combustion. This decrease in heat transfer rate causes a decrease in

regression rate.

Specific impulse of the rocket is the efficiency of a rocket. In equation,

𝐼𝑠𝑝 =𝐹𝑇

𝑚𝑔̇ [Equation 5]

the total thrust FT, is divided by the mass flow rate m , and gravity g. The specific impulse of the

rocket is how much thrust the rocket generates for how much fuel is used. This relates how much

force is being produced per propellant quantity being burned.

Fuel-to-oxidizer ratio, given by

𝑟 =�̇�𝑜

�̇�𝑓=

𝑂

𝐹 [Equation 6]

is the mass of the solid fuel grain to the mass of oxidizer in the mixture as the propellant burns

during combustion. The mixing ratio continually changes during combustion because surface area

of the fuel grain ports and oxidizer in the fuel grain are changing. The constant change in the

mixture ratio causes the specific impulse to vary with burn time [7]. This causes the overall

performance of the rocket to be less efficient.

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2.1.3 Solution Evaluation Parameters

Manufacturing methods for hybrid motor fuel grain cannot produce thrust outputs that

compare to solid rocket motors. Casting is a manufacturing method for solid fuel grains. Casting

takes a cylindrical mold of the fuel grain with a removable casting tube down the middle of the

casted fuel grain. The oxidizer port is made once the casting tube is removed. Casted hybrid rocket

fuel grains are limited to simplistic geometries which exhibit low regression rate. Optimizing the

solid fuel grain geometry will increase regression rate and overall rocket performance. 3D printed

fuel grain geometries can be modified to increase thrust characteristics that casting cannot achieve.

Designing interstitial vacancies in the fuel grain will increase surface area and increase regression

rate.

2.1.4 Testing

A test stand and combustion chamber designed for specified factors of safety will be

manufactured to run multiple tests for the characterization of fuel grain performance. The

combustion chamber will include a removable rear bulkhead for installation of fuel grains. To

allow for multiple test runs, a phenolic lining will separate the combustion chamber from the fuel

grain, allowing for removal of a post-burn fuel grains. As a safety system, a pressure release valve

will be included in the forward bulkhead to prevent explosions. The test stand will incorporate

superstrut channels for modularity and a concrete foundation for stability. Another safety system

will incorporate a scatter shield, covering the test apparatus. The test stand will be oriented

horizontally, incorporating several measurement systems. Systems measuring thrust, combustion

chamber temperature, combustion chamber pressure, and propellant mass flow rate will be

incorporated on and around the test stand. Thrust will be measured by a load cell on the front end

of the test stand. Combustion chamber temperature will be related to measured plume temperature

by a multiwave IR meter. Combustion chamber pressure will be measured by a hardline inserted

through the forward bulkhead leading to a pressure transducer mounted on the test stand.

Propellant mass flow rate will be averaged by the addition of measured before and after weight of

the combustion chamber and the oxidizer supply. These measurement systems will be connected

to a data acquisition device, relaying data to a computer for measurement processing.

3.0 Parametric Design

3.1 Fuel Grain

3.1.1 Improving Regression Rate

Various solutions have been demonstrated to mitigate low regression rates in hybrid

rockets. The addition of oxidizer particles to the fuel grain matrix can increase burn rate due to

greater heat transfer via added surface reactions [8]. Oxidizing agents have included ammonium

perchlorate and iron oxide. Combined propellants pose similar safety risks to solid rocket systems

and diminish start-stop-restart capabilities. Microscopic particle additives, consisting primarily of

metals, can increase regression rate by promoting radiative heat flux from the grain surface [9].

These additives have include aluminum, lithium, and boron. Limitations in this method are due to

specific particle sizing in each application and combustion chamber pressure dependencies [8].

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Another method of boosting the regression rate is to increase the exposed surface area of

fuel grains, enabling more oxidizer to react at the surface [9]. Fuel grains with multiport designs

offer a way of increasing surface area without extending the length of the grains. Multiport grains

can lead to unburned portions of solid propellant and a weakened grain structure. The complex

design of multiport grains can be difficult to fabricate using traditional manufacturing methods

and may require additional support framework. Further drawbacks to multiport designs have

included requiring an injector for each combustion port and the need of a large pre-combustion

chamber [8].

3.1.2 Proposal of a Novel Method

The proposed solution is to optimize the exposed surface area of hybrid rocket fuel grains

through the use of FDM, commonly referred to as 3D printing. Components of a 3D printer

mainly consist of an extruder, print bed, filament spool, and a control system [10]. The process

of 3D printing requires converting a computer aided design (CAD) model to a standard

tessellation language (STL) file format [11].

Figure 3.1: Example of Fuel Grain CAD Model

This involves splitting the three-dimensional CAD model into successive layers of variably

numbered and spaced triangular geometries [12]. Printing can commence once the STL file is

interpreted by the 3D printer control system. 3D printing involves dispensing filament into a

heating element and extruding the resulting semi-liquid material through the extruder. Numerically

controlled motors actuate the extruder and print bed, precisely forming the designed geometries of

each layer.

3D printing offers advantages unobtainable through traditional casting methods. Support

material can be printed under ABS layers and dissolved in a lye bath to show the final geometry

[13]. This process allows flexibility in tailoring complex fuel grain geometries [14]. The precision

of 3D printing provides greater uniformity in fuel grain structure, while streamlining the

production process [4]. The material chosen to compose the fuel grain is ABS. It is a widely used

3D printing material and burns intensely when ignited in the presence of an oxidizer. Research at

Utah State University has demonstrated the viability of using ABS as hybrid rocket fuel grains and

has shown ABS to perform comparably to industry standard HTPB grains [4]. Additional benefits

of using ABS include being readily available and relatively inexpensive [14]. Fuel grains will be

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modeled to load into a 54 mm diameter commercially available hybrid rocket, with a maximum

anticipated thrust range of 500-1000 N.

3.1.3 Evaluation

ABS

The manufacturing precision of ABS, through the use of 3D printing, leads to consistent

performance. ABS is not a regulated substance and is relatively inexpensive. ABS is supplied in

spools of filament that are heated and extruded. Other chemicals are not required to be mixed with

ABS, and both ABS and the manufacturing method are readily available. Filament can be

purchased from multiple suppliers in a variety of lengths. It is limited in mixture composition but

is unlimited in sizing capabilities because of 3D printing. ABS burns intensely when ignited in the

presence of an oxidizer and is comparable to HTPB in terms of 𝐼𝑠𝑝 and regression rate. Precision

of manufacturing process promotes increased consistency between fuel grains. Unlimited fuel

grain geometries greatly increases tailorability. Fabrication time ranges from two to five hours

depending on size of the object, printing resolution, and infill. 3D printing allows the geometry of

the exposed fuel grain surface area to be tailored to meet desired performance characteristics.

Underlying layers of ABS can be structured to enhance regression rate and promote a more

uniform and complete burn.

HTPB

HTPB is a relatively safe material by itself. It burns intensely in the presence of an oxidizer.

HTPB grains are a combination of HTPB resin and a plasticizing agent such as PAPI 94 curative.

These chemicals are purchased separately which may increase shipping costs. Preliminary research

shows that the casting process requires a vacuum pump to remove interstitial air pockets and a

curing oven to set the rubber. HTPB is available from suppliers such as Aerocon or RCS Rocket

Motor Components. It is not as widely available as ABS. The performance of HTPB has been well

established by research and industry. HTPB is a very effective solid fuel grain for hybrid rockets

and is an industry standard, but is affected by low regression rates attributed to hybrid rockets.

Chemicals are mixed and poured into a mold for casting. Set time varies depending on the size of

the grain. Molds must be fabricated, and the portion of the mold that forms the core of the grain

must be removed. It is possible to construct the core mold out of styrofoam and dissolve it with

acetone. The casting process limits the tailorability of HTPB to single or multi-cored grains. HTPB

is difficult to manufacture complex internal geometries and requires considerable cure time.

3.2 Oxidizer Feed Design

3.2.1 Oxidizer

Nitrous oxide (N2O) will be the oxidizer used in this experiment and was chosen for being

non-toxic, self-pressurizing, and readily available. Its viability as a liquid propellant in hybrid

motors has been well established by research [3] and is relatively benign compared to other liquid

propellants [13]. N2O must be maintained at optimal pressure and temperature within the holding

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tank. Safety guidelines for the handling, use, and disposal of N2O have been outlined by Scaled

Composites and will be adhered to in the overall design [14].

The nitrogen within N2O serves the purpose of cooling the graphite nozzle [Newlands],

which aids in nozzle reuse for multiple test runs. The large mass flow content of nitrogen promotes

erosion rate of the fuel, and in turn, increases regression rate by exposing more oxygen to the fuel.

An oxidizer to fuel ratio by mass of 7:1 is common for burns in hybrid rockets. Oxygen content is

not greatly affected by changes in 𝑂/𝐹 ratio over the stoichiometric range, meaning it concedes

higher 𝐼𝑠𝑝 for a wider effective range in 𝑂/𝐹 ratio.

Figure 3.2: 𝐼𝑠𝑝 vs. O/F Ratio [Newlands]

N2O is subcritical at room temperature, which means the liquid and vapor phase exist

simultaneously within the tank. The liquid to vapor ratio of N2O varies with change in temperature.

N2O becomes supercritical at 309 K, so special care must be taken into consideration for launches

in high heat. A high temperature environment would necessitate a special injector.

Figure 3.3: Nitrous Oxide Phase Diagram [15]

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When N2O is subcritical, small pressure drops within the tank will produce an increase in

gas content of the mixture. This additional gas content then increases the pressure, effectively

returning steady pressure within the tank. Pressure drops at the outlet of the thrust chamber injector

indicate a change from liquid to a vapor phase will occur, so a maximum injector outlet diameter

of 1.5 mm must be used. The critical point indicates where the liquid and vapor saturation lines of

N2O incurs the largest density and pressure change. A drop from room temperature will cause a

loss of pressure in the run tank, meaning a reduction in thrust. Nitrous oxide entering the

combustion chamber through the injector is usually a lower density liquid. The low density liquid

content of N2O will be shot into the injector at high pressure due to the high vapor pressure of N2O

at room temperature of around 800 psi. This added benefit allows the thrust chamber to operate at

high pressure while still maintaining the pressure gradient. Aspirespace hybrid rockets were

designed to operate at higher combustion chamber pressures of 507 psi, which produced a higher

specific impulse. Nitrous requires a high temperature to break molecular bonds for release of

oxygen content, making it relatively benign.

3.2.2 Delivery System

A feed system will provide oxidizer to the injector of the thrust chamber. The system will

be comprised of a holding tank, valves, regulators, and routing lines [4]. The holding tank contains

the oxidizer at a prescribed temperature and pressure. A valving system will be implemented for

manual and remote cut-off of the flow. Regulators can be integrated into the system to control the

mass flow rate of the oxidizer and will cut off oxidizer flow in the event of backflow from the

thrust chamber. The oxidizer regulation system may be connected to a computer or microcontroller

for remotely controlling sequencing. Routing lines will connect all components of the feed system

and must withstand the self-pressurizing oxidizer [16].

3.3 Thrust Chamber Design

3.3.1 Design Considerations

Maximizing grain performance and obtaining accurate data, while minimizing cost and risk

of failure are integral to the design of this project. A two part test device will be developed in order

to adequately test the grains. The first subassembly, or thrust chamber, includes the combustion

chamber, an injector, and a nozzle. The combustion chamber will house the grains during

combustion with the oxidizer and is comprised of a cylindrical vessel sealed by a pair of bulkheads.

The injector distributes the oxidizer into the combustion chamber. After ignition, the vaporized

propellants will build pressure and are expelled out of the aft end of the chamber through a nozzle

that is optimized to increase motor performance.

The heat and stresses of combustion will subject components of the thrust chamber to

conditions that may cause failure if not properly accounted for. The melting point of materials

must be taken into consideration and relevant heat transfer analysis should be performed.

Materials and coatings need to be selected to minimize the oxidation of metals and erosion

of components [18]. Exposure to high temperatures and an oxygen rich environment may corrode

components, while high speed of combustion gases will deform the thrust chamber over multiple

uses.

The thrust chamber components must be designed to contain the combusting propellant

and allow pressure to build, resulting in an increase of exhaust velocity. The oxidizer entering the

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combustion chamber must exceed the pressure of combustion in order to prevent catastrophic

failure from hot gases flowing back into the oxidizer reserve. It is ideal to integrate a pressure relief

system to vent the gases, should combustion pressure exceed tolerable limits. The capability of

performing multiple tests is an important requirement of this experiment. Solid fuel grains, nozzles,

and supply of oxidizer must be replaced with minimal downtime between runs. A phenolic liner

will insulate the combustion chamber and prevent grain adhesion to the inner surfaces, facilitating

quick, repeated testing. The thrust chamber will be statically fired and must be mounted to a

restraint apparatus, which will subject the assembly to rapid accelerations and vibration.

3.3.2 Conceptual Solutions

Three solutions are available to develop the thrust chamber. The first method entails

performing testing on a pre-fabricated, commercially available hybrid rocket motor with minimal

modifications to the design. This method simplifies the design process and enables testing to be

performed on a reliable platform that integrates the thrust chamber and oxidizer reserve. A

commercial motor includes the oxidizer delivery system, nozzle, combustion chamber, bulkheads,

o-rings, and features the ability to be reloaded for multiple uses. This solution lacks a method to

relieve combustion pressure and poses a safety risk by storing the oxidizer supply near the

combustion chamber. The structural integrity of the rocket body could be compromised due to the

use of weaker, flight-weight materials, as a commercial flight rocket is not designed for repeated

static testing. This solution would not be cost effective to replace as it may employ proprietary

internal components that cannot be purchased as stand-alone parts. Attempting to implement

custom components could damage the motor as a whole. The budget may not allow for the

purchase of a replacement motor.

Figure 3.4: Commercial Rocket Configuration (Not Drawn to Scale)

The second solution attempts to mitigate some of these concerns by highly modifying a

commercial motor. A separate oxidizer Delivery system may be implemented to relocate the

reserve tank away from the thrust chamber, thus minimizing the risk of both components

simultaneously failing. A relief valve may be integrated with the combustion chamber and would

be activated if the pressure approaches a critical threshold. Though heavily modifying the

commercial rocket motor can give more freedom in the routing of oxidizer, this method still carries

some of the drawbacks that ruled out the slightly modified method. Dismantling the flight motor

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to better suit static testing may decrease its structural integrity and damage components that are

expensive to replace. Purchasing a prefabricated motor is costly, especially in the event of a failure.

The third solution addresses the deficiencies of the previous methods directly by

fabricating the thrust chamber from the ground up with cost-effective and easy to replace

components.

3.3.3 Our Solution

It is possible to fabricate a thrust chamber that is comparable with commercial performance

and meets the requirements of a repeated static experiment. The thrust chamber will be compatible

with 54mm commercially available HTPB and 3D printed ABS grains. Baseline performance of

the fabricated motor will be determined by testing HTPB and forming a comparison to similarly

sized commercial motors. The thrust chamber will be over-designed to withstand pressures of 3000

kPa, delivering a minimum factor of safety of two. Excessive combustion pressure is to be vented

out of the chamber by via the actuation of a relief valve. Finite element analysis will assist in

determining an appropriate set pressure to actuate the relief valve. The diverted propellant should

be directed away from equipment and personnel, and in a manner that will not cause a torque about

the testing apparatus.

The prototype rocket motor will be manufactured by machining a metal housing with

bulkheads. A reload system will be implemented on the aft end of the motor to streamline the grain

and nozzle loading process. It is preferred to fabricate the test bed from materials used on a live-

fire flight rocket, but this is not a primary concern due to the static nature of this experiment. It is

more important to account for the heat transfer from the hot gasses to the housing, as the

propellants of hybrid motors can reach temperatures up to 3500 K [17]. It is also feasible to apply

extra insulation to the combustion chamber by increasing the phenolic liner thickness to mitigate

these concerns.

The nozzle will be machined from graphite stock. A precedent for graphite nozzles has

been well established because of its low density and high temperature resistance [18]. Large

graphite stock machines well, but is abrasive and can quickly dull out tooling bits [18]. Graphite

is prone to brittle failure and requires high technical proficiency to prevent fracturing. Graphite

stock can be purchased from various industrial suppliers.

The oxidizer injector will be fabricated to provide an optimum amount of liquid propellant

for various grain geometries

3.3.5 Nozzle Evaluation

Purchase

Defined nozzle dimensions would simplify the grain making process and promote

consistency between tests. It is limited in terms of suppliers and sizing of length and diameters.

Purchasing a nozzle with known dimensions increases performance consistency between runs,

assuming the material does not deteriorate. If the material does deteriorate, the performance and

safety of the nozzle will be affected and may necessitate replacement. Purchasing the nozzle

reduces the fabrication process but may require modification for compatibility with the motor

casing.

Fabricate

A graphite rod is much more cost effective than buying a nozzle, but machining costs are

present. G raphite is very abrasive to tooling bits and may dull them out quickly. Rod stocks may

12

be cut to length to fabricate multiple nozzles but may require a significant amount of time

to fabricate. Multiple sizes of graphite are readily available. Performance of graphite fabrication

is based on machining precision, which is determined by tolerances in the machining process and

the skill of the machinist. The material has a high temperature threshold leading to durability and

possible repeated use.

3.4 Test Stand Design

3.4.1 Design Considerations

The second subassembly of the testing apparatus is the test stand, which is used to restrain

rocket thrust chamber during live-fire testing for fuel grain characterization purposes. The test

stand includes the frame, foundation, and rocket motor restraint system [4]. A transparent scatter

shield may also be incorporated to contain debris and allow observations to be made safely. The

frame members must withstand thrust and transfer those forces to a foundation secured to the

ground. Materials used to construct the test stand are selected based on maintaining structural

integrity through numerous test runs. The minimum factor of safety for the test stand will be 5

times the maximum expected thrust output of 1000 N.

3.4.2 Conceptual Solutions

Three rocket test stand orientations are commonly used in industry and research. Two

vertical orientations include upward or downward firing exhausts, while the third orientation is a

horizontal exhaust configuration [17]. Both vertical test stand orientations require a high strength

structure affixed to the ground, in order to withstand large bending moments from the additional

height. The downward exhaust design enables a relatively simple oxidizer routing system at the

forward bulkhead and emulates test flight conditions. Upward exhaust orientation allows for the

test stand to be positioned in an excavated hole, providing added safety in the event of a failure.

This orientation requires an oxidizer Delivery system that can be difficult to route. In terms of test

stand rigidity and economic viability, both vertical orientations require additional material for

structural support, meaning an increase in overall cost.

3.4.3 Idealized Solution

In contrast to the vertical orientations, the horizontal structure is closer to the ground,

decreasing the bending moment and stresses on the members and in effect, reducing the required

members and the cost of materials. It also provides a simple oxidizer routing system via the

forward bulkhead. The thrust chamber will be mounted and secured with clamps to a linear rail

system, which will constrain the motor laterally in the thrust direction. The stand will be

compatible with thrust chambers of varying lengths and diameters by changing the clamps and

distance between them. The frame will be fastened to a solid foundation comprised of concrete, to

prevent any test stand movement. Transportation of the stand will be possible by unbolting the

frame from the foundation. High strength, corrosion resistant materials will be used for the frame

13

members to combat high stress levels, vibrations, high temperatures, and possible sources of

corrosion. These measures will ensure overall test stand robustness for numerous uses.

Modifying Existing Prototype

The existing test stand prototype is a functioning proof of concept, but requires significant

modifications to the rail system and to its supports to be a viable testing apparatus. The platform

requires additional wheels to keep it from sliding off the rails laterally and moving vertically.

Components must be purchased and cut to size and existing welds must be grinded off for new

members to be welded on. The structure is very heavy and rigid, yet collapsible and portable. The

prototype's main structural elements are mostly fabricated which decreases labor and material

costs. The platform needs heavy modifications as well as the foundation. This test stand must also

be compatible with measurement devices and mounting brackets. Overall, this method has less

control over the design parameters than a ground up build.

Full Fabrication

The integration of measurement devices, restraint system, and foundation can be addressed

directly by fabricating the test stand from the ground up. This method allows the most control of

design parameters and the parts from the existing test stand can be repurposed to develop a new

stand. New components of the test stand would be higher quality than the existing prototype parts.

A linear rail system will constrain the platform and the rolling supports can be developed to fix all

motion in the lateral and vertical direction. Building from the ground up also allows for a more

rigid foundation to be made. All of the frame members and a full linear rail system will need to be

purchased. The components of the test stand are readily available in a variety of sizes and

configurations.

3.5 Measurements

Obtaining accurate measurements plays a vital role in characterizing grain performance,

and all measurement devices used for the experiment must be properly calibrated.

3.5.1 Thrust

Thrust will be measured by a load cell attached to the test stand. Important qualities of a

load cell are its effective loading range, measurement sensitivity, and cost. The anticipated thrust

range is 500 N to 1000 N and the ideal sensitivity is less than or equal to 1N. It is important to

account for oscillations of high-impact members and apply appropriate damping.

Thrust data may be obtained in two different ways. The first and least cost effective method

is to purchase a load cell that operates within the desired thrust range. The second option is to

create a force transducer using strain gauges on a metal block but may require more time to

fabricate and calibrate.

Fabricate Load Cell

The load cell will have the total thrust bearing down on it. The load cell will be mounted

onto the test stand using brackets. By fabricating the load cell, the manner by which it is mounted

can be addressed directly in the design. Cost of fabrication would include the block of metal and

machining tools, strain gauges, developing a wheatstone bridge out of wires and resistors, and the

necessary wires and connectors to the DAQ. These components are not very expensive and easily

14

obtained. The strain gauges, bridge, and DAQ connections are more difficult to acquire.

Fabricating the load cell gives a degree of control of the effective range and device sensitivity.

Developing the bridge, making the device compatible with the DAQ, machining and calibration

time, all play a factor in fabrication time.

Purchasing Load Cell

Externally purchased load cells have already been tested by the manufacturer to perform

within the specified load range. Pricing depends on supplier, load capacity, and configuration of

load cell. Suppliers and variety of load cells are more limited in the higher thrust range.

Performance is very high due to quality of materials. Fabrication time is minimal and consists of

mounting the load cell to the test stand.

3.5.2 Temperature

Temperatures during testing are expected to range from 293 K to 3500 K [15] and can be

measured by an infrared (IR) thermometer or IR camera. The cost of these solutions is directly

proportional to their respective measurable temperatures, with the IR thermometer being more cost

effective than the IR camera. The IR thermometer takes measurements at a point and would be

better suited to measure high temperatures further into the plume or chamber. An IR camera can

pinpoint critical temperature sites on the verge of failure and displays important information about

heat transfer. Using both devices in tandem is preferred, and it may be possible to acquire them

from outside sources, mitigating the high cost of these solutions

3.5.3 Propellant Mass Flow Rate

The mass flow rate of the propellant will be obtained by the addition of fuel mass flow rate

and oxidizer mass flow rate. A scale will be used to weigh the combustion chamber and oxidizer

supply before and after each test run. A mass loss calculation will give the difference in weight,

and dividing the difference by gravitational acceleration and the burn time will give the average

mass flow rate for each system. To acquire an accurate burn time, a digital image correlation of

the combustion chamber will indicate the transition of oxidizer blowdown to steady state

combustion, taken as the initial time. The end time will be indicated by the extinguishing of the

combustion. Once the initial flux of oxidizer is burned through the flame and plateaus, the oxidizer

mass flow rate can be calculated using a piecewise function. The two average mass flow rates are

summed, resulting in average propellant mass flow rate. This mass flow rate will be recorded and

used in data processing.

4.0 Detail Design

4.1 Thrust Chamber

4.1.2 Thermochemical Evaluation

Before testing the fuel grains, chemical equilibrium analysis was completed for

combustion of ABS and 𝑁2𝑂. The thermodynamic properties of ABS were obtained from the

research done by Utah State University which analyzed HTPB and ABS fuel grains. The ABS

filament available

15

for 3D printing consists of 50% butadiene, 43% acrylonitrile, and 7% styrene. Table 4.1 shows the

mole fractions, heats of polymerization Δ𝑄𝑝𝑜𝑙𝑦 , the corresponding polymer heat of formation Δ𝐻𝑓0,

and the enthalpy contributions of the individual monomers completed by Utah State [4].

Table 4.1: Heat of Formation of ABS

Monomer Δ𝐻𝑓𝑜, monomer

(kJ/mol)

Δ𝑄𝑝𝑜𝑙𝑦

(kJ/mol)

Δ𝐻𝑓𝑜 polymer

(kJ/mol)

Mole

Fraction

Enthalpy

Contribution

(kJ/mol)

Acrylonitrile 172.6218 74.3119 98031 0.43 42.27

Butadiene 104.1 72.1020 32.00 0.50 16.00

Stryene 146.9121 84.60 63.31 0.07 4.63

ABS Total 62.63

The stoichiometric reaction for combustion that corresponds to the reduced chemical

formula from the calculated value of Δ𝐻𝑓𝑜 is seen below. Using the mole numbers found from

chemical equilibrium and the molecular weights, the oxidizer to fuel ratio 𝑂

𝐹 is found to be 8:1.

Using this formula, properties of the combustion products including mole fractions, density𝜌𝑝, and

gas constants 𝑅𝑝 are found for future reference.

𝐶15𝐻17𝑁 + 38.5𝑁2𝑂 → 15𝐶𝑂2 + 8.5 𝐻2𝑂 + 15.5 𝑁2 [Equation 7]

𝑂

𝐹=

𝑚𝑜𝑥̇

𝑚𝑎𝑏𝑠̇=

𝑀𝑛2𝑜𝑁𝑛2𝑜

𝑀𝑎𝑏𝑠𝑁𝑎𝑏𝑠 [Equation 8]

The adiabatic flame temperature, 𝑇𝐹, is the maximum temperature of combustion achieved

adiabatically, without heat entering or leaving the system. Assuming complete combustion, the

expected 𝑇𝐹 is 3500 K. The properties of the combustion products for the expected 𝑇𝐹 are

calculated using equations 9,10,11.

𝑐�̅� = 𝑎 + 𝑏𝑇 + 𝑐𝑇2 + 𝑑𝑇3 [Equation 9]

𝐶𝑣 = 𝐶𝑝 + 𝑅𝑝 [Equation 10]

𝛾 =𝐶𝑝(𝑇)

𝐶𝑣(𝑇) [Equation 10]

4.1.2 Fuel Grain

The length of the fuel grain is directly dependent on the burn time. For this application, the

desired burn time is five seconds which leads to a fuel grain length of 180 mm. The fuel grain will

be inside a phenolic liner with a thickness of 2.03 mm. This limits the fuel grain to have a maximum

outer diameter of 51 mm.

16

4.1.3 Combustion Chamber

To compare the performance to those used in industry, the combustion chamber will have

an inner diameter of 54mm. The combustion chamber has a length of 200 mm. The additional 20

mm will act as a post combustion chamber, ensuring complete combustion of the reactants.

Figure 4.1 Combustion Chamber

The combustion chamber will be sealed by two bulkheads constrained with threaded rods

and hex nuts. The forward bulkhead will house the injector and pressure hardline, whereas the aft

bulkhead will contain the nozzle. Each bulkhead will have an appropriately sized O-rings that will

aid in the sealing of the chamber.

Figure 4.2 Forward Bulkhead (Front and Rear View)

17

Figure 4.3 Aft Bulkhead (Front and Rear View)

The combustion chamber and bulk heads will be manufactured from 6061-T6 round

aluminum stock. This material was chosen for its affordability, strength, and ease of

manufacturing. To comply with the specified factor of safety, the chamber was analyzed using

FEA as seen in figures 4.4 and 4.5.

Figure 4.4 Thrust Chamber FEA-Displacement

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Figure 4.5 Thrust Chamber FEA-Von-Mises Stress

4.1.4 Nozzle

Once combustion is complete, the nozzle converts the chemical energy produced into

kinetic energy. For performance efficiency, supersonic flow is achieved through the design of a

converging-diverging nozzle. The flow at the throat will reach Mach 1 and will be supersonic in

the diverging section.

The thermodynamic properties of the combustion produces as defined above, were used to

calculate the initial velocity, Mach number, and initial area of the nozzle. Assuming the nozzle is

ideally expanded, the expansion ratio 𝜖, is 2.3. This relates the nozzle exit area to the area at the

throat as seen in Figure 4.6.

Figure 4.6 Nozzle Design

19

4.2 Oxidizer Delivery System

An aluminum N2O tank with a 10lb. capacity will comprise the holding tank and features

a high-flow valve with a siphon tube to aid in liquid N2O removal [19]. Stainless steel braided

hoses of 1/4in. diameter will be used to form the routing lines connecting the components [20].

Prevention of flowback in the feed line will be accomplished with a brass one way male to male

check valve of 1/4in. diameter, which is capable of withstanding up to 3000psi [21]. A 2-way

normally closed Gem solenoid valve with a 900psi rating will be used to remotely actuate oxidizer

release and shut-off [22]. Compatibility between fitting sizes will be accomplished through the use

of adapters [23]. T-junctions will function to connect the the solenoid valve to the routing lines

[24].

Figure 4.7 Oxidizer Feed System

4.3 Test Stand

4.3.1 Fabrication Process

The process of manufacturing the test stand will involve bolting channeled members and

welding frame members. Before and after each part is assembled, measurements will be made to

ensure accurate geometry. The test stand factor of safety of 5 contributes to the tolerance for error

in geometry. The test stand is divided into three subassemblies: the rail frame, the platform, and

the superstrut bed. The rail frame is the outer structure of the stand and is fabricated completely

out of 1-¼ x 1-¼ square steel tubing welded together. Two vertical rectangles members will

support the horizontal rails on which the platform will roll along. The rails are oriented at a 45°

angle to allow two wheels to constrain the platform at each corner opposed to three in previous

designs. The rail frame will be bolted to pre-formed concrete slabs Provisions for load cell

integration will be implemented onto the rail frame.

20

Figure 4.8: Rail Frame Design

The platform consists of 1-¼ x 1-¼ square steel tubing welded to form a rectangle that fits

within the rail frame. 2” sections of tubing will be welded at a 45° angle at each of the corners.

Two holes will be welded into each of the 2” sections and bolts will be welded into the holes. The

upper set of wheels will be fastened to the bolts, then the stand will be placed onto the rail frame.

The second set of wheels can then be fastened to constrain the platform to the rail frame. A

provision for the hardline pressure transducer will be made onto the platform to enable the system

to move with the thrust chamber.

Figure 4.9: Platform Design

Figure 4.10: Platform and Wheels- Cross Section

21

The superstrut bed consists of two 1-⅞ x 1-⅝ lengths of superstrut welded onto the axial

members of the platform and clamps to restrain the thrust chamber. Two lateral lengths of

superstrut will be bolted onto the axial superstrut lengths and the clamps to restrain the thrust

chamber. This restraint system will be compatible with thrust chambers of varying lengths and

diameters by changing out the clamps and distance between them.

Figure 4.11: Superstrut Bed with Clamps

Figure 4.12: Assembled Test Stand- Isometric View

22

Figure 4.13: Assembled Test Stand- Top View

Figure 4.14: Finite Element Analysis of Rail Frame- Displacement

4.3.2 Scatter Shield

For the safety of operating personnel and testing apparatus, a scatter shield will be

manufactured to surround the test stand, capable of withstanding shrapnel and debris. In order to

observe the test stand during testing, the material of the scatter shield will include acrylic sheets

and metal corner braces covering a 48” x 24” x 18” space over the test stand. Acrylic will be clear

and 0.22” in thickness, covering the forward, sides, and top areas. 5” corner braces will be used to

23

assemble the acrylic sheets and will ensure rigidity. The forward acrylic sheet will be cut for the

entrance of the oxidizer routing and measurement cables.

4.4 Data Acquisition

The signals from the load cell, pressure transducer, and IR meter will simultaneously feed

into a DAQ that will relay the data via USB cable to a computer running LabVIEW software. The

DAQ may be housed on the test stand and wiring must be able to withstand high accelerations and

intense vibrations to prevent loss of contact due to testing. The DAQ will also provide voltage

excitation to power the load cell and pressure transducer. LabVIEW software will be used to

compile the data and an appropriate sampling rate must be selected to minimize aliasing. A virtual

instrumentation subroutine, or VI, will collect the raw voltage outputs from the sensors and record

them for post processing. The sensors must be calibrated before testing by relating the voltage

outputs to known quantities. Calibration data will be processed on Microsoft Excel to perform

statistical analysis, formulate visual representations, and develop models for the interpolation and

extrapolation of data. The data can then be exported for post processing and used to make future

adjustments in the grain geometry. The figure below displays the measurement apparatus.

Figure 4.15: Measurement Apparatus

4.4.1 Load Cell

Manufacturing a load cell in house is advantageous because of design intended for this

project’s specific application. Drawbacks arise with the application of a strain gage to the load

cell’s surface. Strain gages are isolated to measurement in one strain direction while deflection in

any other direction is not observed by the strain gage. This requires the strain gage to be applied

to a manufactured load cell under critical tolerances. Loading applied in a direction non-

perpendicular to the load cell’s surface will also not be measured by the strain gage. To ensure the

uniformity of the load cell’s geometry and the accuracy of its strain gage, an externally purchased

load cell from Omegadyne, Inc. will be included in the measurement apparatus. The LCCD-500

S-beam load cell has a maximum capacity of 2224.11N with accuracy of ±0.25%. A five point

calibration procedure will be performed before operation. In a study at Utah State, the same load

24

cell was used in a similar application testing tubular casted ABS fuel grains. The thrust levels

increased from zero to over 800N within 1s, providing validity to the response time of the load

cell [26]. A hysteresis of ±0.02% also contributes to the load cell’s sufficiency for dynamic

loading. The ultimate overload of 300% maximum capacity extends beyond the factor of safety of

five for the test stand design, ensuring safety and reliability of the measurement system. For

integration to the test stand, a 1/2"-20 male thread bolt will be used to join the load cell to the

superstrut cross member at the front end of the test stand. The 24 AWG jacketed cable containing

excitation and output wiring will be connected to the DAQ for 10V excitation and 3V output [27].

4.4.2 IR Meter

Externally purchased IR meters within this project’s budget are not capable for measuring

maximum combustion chamber temperatures. To compromise, measurements of a single point of

the plume will be related to the combustion chamber’s internal temperature via the following

equation:

𝑇𝑜2 = 𝑇2(1 +𝛾𝑝−1

2𝑀𝑒

2) [Equation 10]

in which 𝑇𝑜2 is the adiabatic internal combustion temperature, 𝑇2 is the exit temperature, 𝛾𝑝 is the

specific heat of the mixed propellant, and 𝑀𝑒 is the exit Mach number. The measurements will be

collected through a DAQ and sent to a computer for data processing, incorporating the equation

above.

An Ircon UX-40P will be loaned for the purposes of this project as a sufficient IR meter

for plume temperatures well above 473 K would be very expensive. The meter covers a spectral

region of 8 mm to 13 mm and is capable of measuring a maximum temperature of 1273 K. The

meter is able to be placed at a safe distance from the plume. An optical resolution of D/40 and

focus distance of 700 mm or larger. The accuracy of the reading is ±1.0% or ±2 K, whichever is

greater. The resolution of the meter is 1 K. The response time of 1.0 sec will be considered during

the burn, as the measurements will be delayed. The analog output of 1.0 V will be connected to

the DAQ for data acquisition. The meter is powered by 4 type AA batteries requiring no excitation

voltage [27].

4.4.3 Pressure Transducer

The expected internal combustion chamber temperature is above the maximum operating

temperature of a pressure transducer within this project’s budget. To decrease the temperature of

the combustion gasses, sufficient heat transfer through the hardline is required for cooling to 398

K. A two dimensional heat transfer solution was implemented to determine the length of the

hardline necessary for this cooling. Considering radial and axial heat transfer, a nodal analysis was

performed with nine nodes with an initial temperature at the first node. Each node incorporated

radial convection with ambient temperatures and axial conduction through the stagnant

combustion gasses present in the hardline. Using the mass percentage of the combustion products,

a conduction coefficient was formulated for the total homogeneous combustion gasses as a

function of temperature. The function of temperature was interpolated from known conduction

coefficient values of the individual combustion products from Fundamentals of Heat and Mass

Transfer [27]. Creating an array of heat transfer equations for each node, a Newton Raphson solver

was used to solve for the axial temperature distribution for the hardline. This solution allowed for

specification of hardline diameter and length, sufficient for the desired heat dissipation. See the

appendix for calculations. The result of the solution specified a 0.12 m hardline of 3.175 mm

25

diameter for heat dissipation reducing the combustion gas temperature at the pressure transducer

to 374.526 K.

A MLH01KPSB06A sealed gauge male, 3.175mm 27 NPT port pressure transducer made by

Honeywell manufacturing will be purchased from Digi-Key Electronics. The operating pressure

of the pressure transducer is 0 to 6.894 MPa with a standard output of .5 to 4.5Vdc ratiometric at

.5% accuracy at Full Scale Span (FSS). The FSS is the algebraic difference between the output

signal measured at the maximum pressure and minimum pressure limits of the pressure range [30].

Excitation voltage is 5Vdc with a response time of less than 2ms. The error of the pressure

transducer is the Total Error Band of ± 2% FSS. This pressure transducer is rated for 10 Hertz to

2000 Hertz of vibration which is more than what is expected during testing. With accordance to

MIL-STD-810C, Figure 214.2-5 curve AK, this pressure transducer can withstand a minimum of

20.7 G-rms [29]. The operating and compensated temperature range of this pressure transducer is

233 to 398 K. A pressure transducer like this has been used in ABS hybrid rocket testing by Utah

State University [4]. Using a pressure transducer like Utah State, chamber pressure plot is expected

to be similar to Figure 4.15.

Figure 4.15 Pressure vs Burn Times

Hardline Tube

A ⅛ outer diameter stainless steel hardline tube will connect to the ⅛ diameter pressure

transducer port to dissipate the combustion chamber heat. The tube will be inserted into the forward

bulkhead of the combustion chamber and placed in the middle of the combustion chamber. The tip

of the tube in the combustion chamber will be angled 90° to acquire the static pressure of the

chamber. The stainless steel tube will be coated with LOCTITE Mil Spec Silver Grade Anti-Seize

to protect the tubing from high heat temperatures. This coating will increase the resistance of the

stainless steel by 1143 K. This insulator coat will prevent the stainless steel from melting and

warping. Any failure in the stainless steel tubing will show error in the pressure readings. During

combustion, pressure will increase in the tube and will be read by the pressure transducer. The

stainless steel tube has a melting range of 1673-1723 K which would hold for the five second burn

time of the combustion chamber. After each run, the tube will be inspected for any signs of failure.

Extra hardline tubes will be bought to replace any failing hardline tubes.

26

4.4.4 Combustion Chamber/Oxidizer Supply Scale

Initial and final weight measurements will be conducted for the combustion chamber and

the oxidizer supply. Both the combustion chamber and oxidizer supply will be removed from the

test apparatus and weighed on an externally purchased digital scale. The accuracy of each

measurement will be ±0.1 lbs, relating to ±0.045kg [28]. Initial weight will be subtracted from

final weight and divided by the burn time to give propellant mass flow rate.

4.4.5 DAQ

Once the oxidizer is ignited and the fuel grain burns, the pressure from the combustion

reaction will be recorded through the hardline and to the pressure transducer. To acquire data, the

pressure transducer and load cell will be connected to a NI USB-6008 12 bit, Low-Cost

Multifunction DAQ. The DAQ has 8 analog inputs and 2 analog outputs with a max sampling rate

of 10 kS/s. A single ended input and working range of ±10 Volts. The DAQ’s working range of

10V would power the pressure transducer’s operating voltage of 5Vdc and the load cell’s operating

voltage range of 10 - 15V. The measurements from the pressure transducer and load cell would

be sent to the DAQ and then sent to the computer in LABVIEW.

4.5 Control System

The sequencing of the experiment will be controlled by a Tiva C Series TM4C123G digital

signal controller. The Tiva is simple to code and is compatible with a vast library of open source

Arduino programs.

Figure 4.16: Tiva™ C Series TM4C123G LaunchPad [Texas Instruments]

The Tiva will time the burn, signal a solenoid valve to open and close the valves, and prime

the ignition source. An emergency stop function will be added to the code to close the solenoid

valve in case of failure. A check valve will be implemented to permit oxidizer flow to the thrust

chamber and inhibit backflow into the holding tank. Pressure relief valves on the thrust chamber

and holding tank will vent gasses that reach excessive pressures.

27

Figure 4.17: Control System Diagram

5.0 Bill of Materials

Thrust Chamber

Component Unit Price ($) Quantity Cost

Injector $60.00 1 $60.00

4" Round Aluminum Stock $116.00 1 $116.00

Threaded Rod $9.50 2 $19.00

Hex Nuts $0.20 22 $4.40

Medium Extruded Graphite Rod $27.00 1 $27.00

O-rings $5.00 12 $60.00

Phenolic Liners $8.00 6 $48.00

HTPB $90.00 1 $90.00

Total $424.40

Oxidizer Delivery System

10-pound Aluminum Nitrous Bottle $230.00 1 $230.00

Nitrous oxide 65lb. tank $135.00 1 $135.00

Stainless Steel Braided Hose with -4AN Blue Fittings $43.16 1 $43.16

Inline NPT Check Valve $37.81 1 $37.81

Gem Solenoid Valve 900-1000psi $120.00 1 $120.00

Blue Anodized Aluminum -4AN to 1/8" NPT Straight Flare To Pipe Fitting $6.83 1 $6.83

AN Male to AN Female Swivel on Side T-Fitting $18.99 1 $18.99

Tiva™ C Series TM4C123G LaunchPad $12.99 1 $12.99

$604.78

27

Test Stand

Radial Bearings 0.3750 x 0.8750 x 0.2812 in. $0.99 8 $7.92

Plain Steel Square Tube, 1-¼ in. x 1-¼ in. 1/16 Thickness $0.32 200 $64.00

Concrete Pad, 16 x 16 x 4 in. $4.37 4 $17.48

Total $89.40

Measurements

MLH01KPSB06A Pressure Transducer $110.00 1 $110.00

Stainless Steel Hardline Tube ⅛" Diameter x 6' $31.71 1 $31.71

LOCTITE Mil Spec Silver Grade Anti-Seize, 8oz brushtop, $19.99 1 $19.99

Digital Scale $39.99 1 $39.99

NI DAQ USB-6008 $199.00 1 $199.00

Total $400.69

29

Appendix

Figure 6.1: Conduction Coefficient Formulation

30

Figure 6.2: Temperature Equation Array

Figure 6.2: Temperature Distribution Per Node (Temp in K)

31

References

[1] ASME Publications Committee, 1995, “Ethical Obligations of Authors,” from

https://www.asme.org/shop/proceedings/conference-publications/ethical-standards

[2] McCulley, J.m., 2012, “Design and Testing of Digitally Manufactured Paraffin Acrylonitrile-

Butadiene-Styrene Hybrid Rocket Motors,” M.S. thesis, Utah State University.

[3] “Solid Rocket Motor Failure Prediction” http://ti.arc.nasa.gov/tech/dash/pcoe/solid-rocket-motor-

failure-prediction/introduction/ (accessed February 2015)

[4] Whitmore, S.A., Peterson, Z.W., Eilers, S.D., 2011, “Analytical and Experimental Comparisons to

HTPB and ABS as Hybrid Rocket Fuels,” AIAA Journal, 5909.

[5] Zilliac, G., Karabeyoglu, A. 2006, “Hybrid Rocket Fuel Regression Data and Modeling,” 42nd

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