fuelregressionratecharacterizationusingalaboratoryscalenitrousoxidehybridpropulsionsystem...

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Fuel Regression Rate Characterization Using a

Laboratory Scale Nitrous Oxide Hybrid Propulsion

System

Kevin Lohner, Jonny Dyer, Eric Doran, and Zachary Dunn

Stanford University, Stanford, CA, 94305, USA

Greg Zilliac

NASA Ames Research Center, Moffett Field, CA

The purpose of this study was to characterize the regression rates of three traditional

hybrid rocket fuels along with one novel fuel using nitrous oxide as the oxidizer. In order

to complete these tests, a robust test facility was developed for use in this study as wellas in future hybrid rocket programs at Stanford University. This stand allowed for rapid

successive hot fire testing and the capability to test multiple fuel grain configurations. To

date it has been used to conduct 40 hot fire tests. Performance values and fuel regression

rate data are presented for HTPB, PMMA, HDPE, and sorbitol.

Nomenclature

m Mass flow rater Regression ratea Regression rate coefficientA1 Venturi inlet areaA2 Venturi throat area

At Nozzle throat areac Characteristic exhaust velocityCv Coefficient of velocityD Port diameterE Error valueG Mass fluxIsp Specific impulseL Fuel grain lengthm Length exponentmfuel Fuel massn Flux exponentO/F Oxidizer-to-fuel ratio

Pc Chamber PressureR Final to initial diameter ratiotb Burn timex Port length coordinate

Subscriptsf Finalfuel Fuel propertyi Initialox Oxidizer property

Conventions

Averaged variable

Symbols

P Pressure difference across venturic c efficiency Density

I. Introduction

The original goal of this study was to develop a hybrid rocket motor with a nominal thrust level of15 pounds and a burn time of 45 seconds to be used in the proposed NASA Ames Mars Advanced

Technology Airplane for Deployment, Operations, and Recovery (MATADOR) project. However, a lack of

Graduate Student, Department of Mechanical Engineering, Stanford, CA, AIAA Member.Graduate Student, Department of Aeronautics and Astronautics, Stanford, CA, AIAA Member.Research Scientist, NASA Ames Research Center, AIAA Member.

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American Institute of Aeronautics and Astronautics

42nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit9 - 12 July 2006, Sacramento, California

AIAA 2006-467

Copyright 2006 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
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published hybrid fuel regression data motivated the need to experimentally determine much of this databefore a fully-characterized, robust engine system could be built.

Nitrous oxide (N20) was chosen as the oxidizer for this hybrid motor because it is non-toxic, storable atroom temperature, self-pressurizing, inexpensive, and easy to handle. This list of attributes far outweighedthe slightly inferior performance of nitrous oxide when compared to liquid oxygen or exotic, more hazardousalternatives.

Once oxidizer selection was complete, a literature search was performed in an attempt to determineregression rate data for nitrous oxide hybrid rocket engines. This information would be essential in the design

of the MATADOR engine. However the search returned very few results, and in talking with members ofindustry and the research community it became apparent that such work had either not been completed orat least had not been reported in the open literature despite the wide use of nitrous oxide in the propulsioncommunity. A proper test program was required before an optimized flight weight system could be developed.This test program would also serve to fill the apparent gap in academically published nitrous oxide hybridfuel rocket regression data.

To serve as the backbone of this test program, a portable, self-contained test stand was developed tosupport system hardware including the combustion chamber, nitrous oxide tank, plumbing, control system,data acquisition (DAQ), and safety equipment. This stand was developed with interchangeability in mind andeasily allowed for the testing of many different fuel grain configurations. Beyond the MATADOR program,this stand was built to test engines capable of delivering up to 100 pounds of thrust. The oxidizer fluxof these larger engines would be on a scale comparable to levels commonly found in industry applications.Regression rate data gathered in this study are not limited to extremely low flux MATADOR-scale engines,but cover a wide-range of practical oxidizer flux values.

Fuel selection was the final step prior to hot fire testing. High density polyethylene (HDPE) and poly-methyl methacrylate (PMMA), two slower burning fuels were selected along with the faster burning hydroxyl-terminated polybutadiene (HTPB). In addition to these commonly used diffusion-limited fuels, a higherregression rate liquefying fuel, sorbitol, was selected to complement existing work with paraffin at StanfordUniversity. Sorbitol is a naturally occurring sugar alcohol that has theoretical performance metrics similarto those of sucrose.

II. Test Facility

A. Test Stand

0:00:00

0:20:00

0:40:00

1:00:00

1:20:00

1:40:00

2:00:00

25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

Tests

T

ime(hr:min:sec)

Average Time BetweenTests: 47:44 (min:sec)

Figure 1. Turn-around Time Between Hot Fire Tests

To carry out the required testing in a relatively shorttime frame, a completely self-contained mobile testfacility was developed. The safety features and smallscale of the facility allowed testing to be conductedlocally. Oxidizer and pressurization tanks with suf-ficient capacity for several tests were mounted di-rectly to the test stand. The stand had an inte-gral power supply utilizing 12 volt lead-acid batter-ies, and all instrumentation and control was handledover a single USB cable. Set-up time was minimizedby mounting the test stand on pneumatic tires sothat the entire system could be rolled to the testsite in ready configuration. The test article design

and plumbing allowed for a simple safing procedureand minimal reassembly time between tests. Thisenabled up to 16 hot fire tests on a typical day withturn-around times as low as 20 minutes. Figure 1shows a chart of test turn-around times for a numberof tests and Figure 2 shows a photo of the test stand.

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Figure 2. Test Stand for a 100 lb Thrust, Supercharged Nitrous Oxide Hybrid Rocket

B. Test Article

The test article was designed to be robust, allowing multiple fuel configurations and ease of fuel grainreplacement. The main combustion chamber consisted of a cylindrical center section and two square endcaps, all machined from 6061T6 grade aluminum. The center body had an outer diameter of 2 inches anda 0.25 inch wall thickness. The assembly was compressed axially using four high strength threaded steelrods with bore seals between the mating parts. Pre- and post-combustion chamber insulation inserts for thefore and aft end caps were manufactured from graphite. The layout of the test article assembly is shown in

Figure 3.

Fuel GrainInjector

Pre-combustion

Chamber

Phenolic

Insulation

Post-combustion

Chamber

Nozzle

Main Combustion

Chamber

Igniter

Figure 3. Section View of Test Article

The test article accommodated fuel grains of different lengths by replacing the center section. Chamberswith lengths of 6, 7, and 10 inches were manufactured to fit 5, 6, and 9 inch fuel grains, respectively. This

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versatility enabled adjustment of oxidizer-to-fuel (O/F) mass ratios for a given oxidizer mass flow rate.The aft end cap contained the nozzle insert. The standard nozzle had a throat diameter of 0.250 inches,

a contoured convergent section, and a conical divergent section with a half angle of 15 degrees and anexpansion ratio of 4. Molybdenum (Mo) was used as the nozzle material due to its ability to withstand ahigh temperature oxidizing environment with little-to-no throat erosion. This served to eliminate chamberpressure decay - a common problem in graphite nozzles.

The injector was designed to cavitate the liquid nitrous oxide, thus controlling the oxidizer mass flowrate while isolating the test article from the feed system. Multiple showerhead injectors were fabricated

by drilling 0.025 inch diameter holes through a standard Swagelok brass cap. Depending on the flow raterequired for each test, injectors with 1 to 6 holes were installed.

C. Feed System

The feed system was composed of a main nitrous oxide feed line and an auxiliary helium system. Thehelium provided supercharging capability, pneumatic pressure for valve operation, and high and low pressurecombustion chamber purges. The plumbing and instrumentation diagram (P&ID) is shown in Figure 4.

He N2O

T

DP1T1

OV-3OV-2

OV-1

OV-0R-1

R-2

PV-1

PV-3

PV-4

OV-5

CV-2

CV-1

RV-1P-1

P-2

P-3

OV-4

TV-1TV-2

OV-0 - Ox Press IsoOV-1 - Ox Main IsoOV-2 - Ox Pre-ValveOV-3 - Ox Main ValveOV-4 - Ox Bleed valveOV-5 - Ox Vent Valve

R-1 - Helium Regulator 1R-2 - Helium Regulator 2

PV-0 - Helium Bottle IsoPV-1 - Press/Purge IsoPV-2 - Low Pressure IsoPV-3 - Low Purge ThrottlePV-4 - Low Purge SolenoidPV-5 - Hi Purge solenoid

RV-1 - Ox Tank ReliefRV-2 - Low Press Relief

TV-1 - Pre-Valve Actuator ThrottleTV-2 - Main Valve Actuator Throttle

CV-1 - Main Ox Check ValveCV-2 - Low Purge Check ValveCV-3 - Hi Purge Check Valve

RV-2PV-2

PV-0

CV-3

PV-5

Figure 4. Plumbing and Instrumentation Diagram for the Test Facility

The nitrous oxide feed system was supercharged 100-150 psi above N20 vapor pressure to extend theliquidous range of the oxidizer. This helped prevent cavitation in the feed line to ensure accurate mass flowrate measurements through the sub-critical venturi. Helium was chosen as the pressurant due to its inertproperties and its insolubility in nitrous oxide. The helium pressurant was introduced through a port at thetop of the nitrous oxide tank and liquid nitrous oxide was extracted from a separate port through a dip tube

extending to the bottom of the tank.The main oxidizer feed line was plumbed using 0.25 inch diameter stainless steel tubing with 0.030 inch

wall thickness. Two pneumatically actuated ball valves in series were used to control the oxidizer flow. Ahigh point bleed upstream of the main oxidizer valve was used to vent any gaseous nitrous oxide in the feedline before testing.

D. Ignition System

The ignition system was a simple electrically-initiated pyrotechnic igniter housed within a standard Swagelokunion fitting. External lead wires were passed through a crimped section of tubing, which was filled with

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epoxy to create a pressure seal. A 24 gauge nichrome bridge wire was used as the initiator. Each ignitercontained 0.5 grams of the following mixture: 60% potassium nitrate (KNO3), 20% magnesium (Mg), and20% epoxy binder (based on percent mass). A schematic of the igniter is shown in Figure 5.

Figure 5. Igniter Design

E. Instrumentation

For temperature measurement, Omega type K grounded thermocouples were used with cold-junction com-

pensated signal conditioning integrated circuits from Analog Devices (AD595C). This chip had a calibrationerror of1C at 25C and a gain error of0.75%. Nitrous oxide tank temperature and nitrous oxide linetemperature just upstream of the sub-critical venturi were measured.

Two Senstronics Storm type 0 to 2000 psia pressure transducers (P/N: OL01 10840-002) with an accuracyof0.25%FS were used to measure the nitrous oxide tank pressure along with the nitrous oxide pressureupstream of the combustion chamber injector. These transducers have built-in temperature sensors, and thenitrous oxide tank pressure transducers temperature output was used to verify line temperature. In additionto the two Storm pressure transducers, a Measurement Specialties, Inc. 0 to 1000 psia MSP-600 pressuretransducer with an accuracy of0.25%FS was utilized to measure the combustion chamber pressure justdownstream of the injector.

The flow rate was measured using a sub-critical venturi with a throat diameter of 0.096 inches and anentrance diameter of 0.190 inches. The convergent and divergent sections were conical, with half angles of11 degrees and 7 degrees, respectively. Pressure taps of 0.040 inch diameter were drilled at the throat and

upstream of the convergent section. The pressure difference across the pressure taps was measured using aStellar Technology, Inc. differential pressure transducer with a range of30 psid (P/N: DT400-30BD-119).A schematic of the venturi is shown in Figure 6.

(a) Venturi Body (b) Throat Section

Figure 6. Venturi Design Schematic

The density of the nitrous oxide passing through the venturi was calculated using the pressure measured

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at the oxidizer tank and the temperature measured in the main oxidizer feed line. This calculation wascarried out using data for nitrous oxide from the National Institute of Standards and Technology 1 (NIST).Using the calculated density, ox, and the measured pressure difference across the venturi, P, the oxidizermass flow rate was calculated using Eq. (1).

mox = CvA2

2oxP

1 A2A1

2(1)

The venturi was calibrated by experimentally determining the velocity coefficient of the venturi, Cv.Nitrous oxide was flowed through the feed line while measuring P and calculating ox. The Cv was deter-mined by comparing the measured change in tank mass with the integrated mass flow calculated assuminga Cv of 1. Several tests were conducted in order to confirm the results and minimize the error.

F. Control System and Data Acquisition

The test sequence was controlled remotely and executed via a National Instruments LabVIEW interface. Tofacilitate hot-fire tests in which timing was critical, the order and timing of operations was pre-programmedinto an auto test fire sequence, ensuring a repeatable testing procedure. Burn times were set for each testbased on expected regression rate and initial port diameter of the fuel grain. The main oxidizer valve wasadjusted to have an opening slew rate of approximately 1 second to reduce the possibility of compression

heating of nitrous oxide in the line. Igniter firing occurred 0.5 seconds before the opening of the mainoxidizer valve. After the predetermined burn time had elapsed, the oxidizer main valve was closed and ahigh pressure gaseous helium purge was opened. This swept out all remaining nitrous oxide downstream ofthe main valve through the test article. A typical test sequence is represented in Figure 7.

-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11

Time, seconds

Event

Igniter

Low He Purge

High He Purge

Main Ox Valve

Figure 7. Nominal Test Sequence for 10 Second Burn Time

All valves and the igniter relay were actuated remotely using an EasyDaq USB8SR eight channel USBrelay control board interfaced with LabVIEW. The test computer was linked to the test stand via a 100 footUSB connection. A Data Translations 9804 USB board was used for data acquisition. Data was sampled

at 800 Hz and passed through a first order, low pass RC filter with a cut-off frequency of 320 Hz prior toanalog-to-digital conversion.

III. Fuel Characteristics and Processing

The NASA thermochemical program CEA (Chemical Equilibrium with Applications) was used to char-acterize specific impulse (Isp) as a function of O/F. The results for the four fuels used in this study areplotted in Figure 8.

Sorbitol is a naturally occurring sweetener used as a sugar substitute in products such as diet drinksand toothpaste. While often classified with sugars due to its sweetening uses, sorbitol is actually a sugar

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0 1 2 3 4 5 6 7 8 9140

160

180

200

220

240

260

O/F

Isp(s)

Nitrous/Sorbitol

Nitrous/HDPE

Nitrous/HTPB

Nitrous/PMMA

Figure 8. Isp vs. O/F Assuming Equilibrium Combustion at 500 psia Expanding to Sea Level Pressure

alcohol with the chemical formula C6H14O6. It has a density of 1.489 g/cm3,2 melting point of 96.8 degrees

Celsius,3 a resistance to caramelization, and an enthalpy of formation of -1353.7 kJ/mol. 4 From Figure 8,sorbitol has a maximum Isp value of 232 seconds at an O/F of 3.

Granular sorbitol was melted and a small amount of carbon black was added as an opacifying agent.The melt was cast in a 2 inch diameter 0.063 inch thick paper phenolic tube liner with a 0.75 inch mandrel

to form a single port. The casting was allowed to cool for 36 hours to ensure complete solidification. Themandrel was removed and the grain was machined to length.

HTPB is a rubber commonly used as a binder in solid rockets and as a fuel in hybrids. It is a polymerof butadiene (C4H6) terminated at each end with a hydroxyl functional group (-OH). Properties of HTPBare dependent on the the mixture and curing of the specific blend, therefore standard properties are notavailable and must be determined for each individual blend.

The HTPB composition consisted of 83% polybutadiene resin (Sartomer R-45HTLO), 15% isocyanatecurative (Desmodur E 744), 1% antioxidant (CAO-5), and 1% carbon black by mass. These chemicals wereobtained from RCS Rocket Motor Components, Inc. The ingredients were mixed together under vacuumand poured into a 2 inch diameter phenolic liner with a 0.75 inch mandrel. The casting was cured for 24hours at 38 degrees Celsius.

PMMA, commonly known as acrylic, is a transparent thermoplastic with the chemical formula C5H8O2and a density of 1.19 g/cm3. Grains were machined from clear cast 2 inch diameter PMMA rod stock that

was obtained from McMaster-Carr (www.mcmaster.com).HDPE is an opaque thermoplastic that is created through the polymerization of ethene (C 2H4) and has

an average density of 0.948 g/cm3. Grains were machined from extruded 2 inch diameter HDPE rod stockobtained from McMaster-Carr.

IV. Hot Fire Testing

Four rounds of hot fire testing, comprised of 40 individual tests, were performed during the months ofApril to June 2006. The initial round (tests 1-4) was a facility check-out series. Subsequent tests were

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performed to characterize the burn rate of the fuels over a range of oxidizer flow rates, O/F ratios, andchamber pressures. Figure 9 shows the test parameter envelope for each of the four types of fuel. As can beseen, tests were performed at O/F ratios both rich and lean of stoichiometric at chamber pressures rangingfrom 300 psia to over 650 psia. Individual tests can be cross-referenced to Table 2 containing test conditions.Test durations were varied from 3 to 15 seconds in order to achieve steady-state burns at targeted conditions.

Figure 9. Hot Fire Test Parameter Envelope

The fuel grains were made to different lengths depending on the fuel mass flow target for each test. Portdiameters were nominally 0.75 inches, however smaller ports were used for some tests to achieve a higheraverage oxidizer mass flux. All fuel grains were measured dimensionally and massed before and after test.These values, combined with the data from the instrumentation, were used to determine the average fuel

mass flow rate, O/F ratio, c

efficiency, oxidizer mass flux, and regression rate (see Table 3).A pressure-time trace for a typical hot fire test (#30) is shown in Figure 10. Chamber pressure fluctuations

were less than 5% for PMMA, HDPE, and HTPB tests, while sorbitol tests had fluctuations as high as10%. A photograph of a typical hot fire test (#12) is shown in Figure 11.

V. Regression Rate Analysis

A. Space and Time Averaging

The classic hybrid regression rate formula derived by Marxman5

r = aGnxm (2)

expresses the instantaneous time derivative of port radius as a function of total mass flux in the port, G, portlength coordinate, x, and three ballistic coefficients, a, n, and m. Regression rate analysis aims to determinethese coefficients for a given fuel and oxidizer combination. It is generally easier to deal with the regressionrate formula in the form

r = aGnoxxm (3)

where Gox is the oxidizer mass flux in place of the total mass flux. In order that the data be widely applicable,it is important to choose data analysis and regression methods that are consistent and reliable. Due to thediscrete nature of fuel mass measurements in a hybrid rocket, averaging in both space and time is necessaryto obtain time derivatives for regression rate analysis. In this section longitudinal variation in regression ratewill be ignored by assuming a simple average value in space making m = 0. Karabeyoglu et al.6 have shown

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Figure 10. Pressure-time Trace for Hot Fire Test #30

Figure 11. Photograph of Hot Fire Test #12

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that space-averaged regression rate, r, can be recast with Gox as the independent variable in the followingform.

r =aGnoxL

m(1 n)

(1 + m)

1 + 1O/F

O/F

(4)

Although determining r from measurements is trivial using Eq. (5), space-averaged oxidizer mass flux is notuniquely determined due to its non-linear relationship to port diameter. Diameter averaging using Eq. (6)produces the smallest averaging induced error when calculating space-averaged oxidizer mass flux.6

r =DfDi

2tb(5)

Gox =16 mox

(Di + Df)2(6)

Initial diameter, Di, is easily measured prior to test. Determining the space-averaged Df is more difficult,as it involves measuring the port diameter as a function of chamber longitudinal coordinate and taking anaverage value. Alternatively, one can use the density, change in mass and initial diameter to determine finaldiameter according to Eq. (7), which is the method used in this analysis.

Df =

4(mfueli mfuelf )

fuelL+ D2i (7)

B. O/F Correction

It is very difficult to completely isolate mass flux as the independent variable, holding other variables likechamber pressure and O/F ratio constant across all tests. Classic diffusion-limited hybrid regression theorystates that regression rate is not a function of pressure over most of the useful range of oxidizer mass fluxes.However, space-averaged regression rate from Eq. (4) is a function of O/F ratio as well as the traditionalballistic coefficients a, n and m. To reduce regression scatter, Karabeyoglu6 suggests recognizing that theO/F dependent terms in Eq. (4) can be isolated such that

r

aGnoxLm

=(1 n)

(1 + m) 1 +1

O/FO/F= fo(O/F) (8)

which is a function of O/F only. By choosing a standard (O/F)0 when performing a regression analysis onecan correct the raw space-averaged regression rate for changes in O/F by applying

rcorrected = rrawfo(O/F)ifo(O/F)0

(9)

repeatedly until the mass flux coefficient n converges. The (O/F)0 was chosen at the peak Isp of eachpropellant: 3 for sorbitol, 4.4 for PMMA, 6.5 for HTPB, and 8.1 for HDPE.

C. Least Squares Regression Analysis

Taking m = 0, Eq. (3) reduces tor = aGnox (10)

and Eq. (8) to:r =

aGnox(1 n)1 + 1O/F

O/F

= aGnoxfo(O/F) (11)

To obtain the least squares fit the O/F correction term is initially ignored and Eq. (10) is manipulated asfollows:

lnr

a= n ln Gox

ln r

ln Gox=

ln a

ln Gox+ n

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Recasting as a standard matrix equation, Ax = b, results in:

1

lnGox

1

1...

...1

lnGox

j

1

ln a

n

=

ln rlnGox

1

...ln r

lnGox

j

(12)

Applying the linear least squares solution x = (ATA)1ATb gives the ballistic coefficients n and ln a as thecomponents of x.

The regression rate curves are shown in Figure 12 and ballistic coefficients are listed in Table 1 for eachof the four fuels. One can see the relative range in regression rate with HDPE being the slowest and sorbitolbeing the fastest burning fuel. Note that the data represent a work in progress and the coefficients are onlyapplicable within the illustrated range of Gox values. In particular, the correlation for sorbitol is weak andthe regression rate curve plotted is purely notional as more data points are needed to refine the curve.

Table 1. Ballistic Coefficients for Four Fuels Us-

ing N20 as the Oxidizer

Fuel a* n*

HDPE 0.104 0.352

PMMA 0.111 0.377

HTPB 0.198 0.325

Sorbitol 0.286 0.310

* To be used when r is in mm/s and Gox is in g/cm2-s. Coefficients are approximate due to weak correlation.

D. Averaged c* Method

Another technique for obtaining regression rate coefficients, termed the averaged c method, has been sug-gested by Wernimont.7 This method assumes that c remains constant over the course of a test run todetermine the time-resolved fuel flow rate.

c =Attb

0Pc(t)dttb

0mox(t)dt + mfuel

mfuel(t) =Pc(t)At

c mox(t) (13)

Using Eq. (13) and assuming m = 0, the instantaneous regression rate is:

r(t) =mfuel(t)

fuelLD(t)(14)

An explicit discrete approximation can be defined as:

rj =1

fuelLDjPcjAt

c

moxj (15)Dj Dj1 + 2rj1dt (16)

Finally, Goxj can be calculated as:

Goxj =4 moxjD2j

(17)

The method outlined in Eq. (12) can be used to find the least squares coefficient fits from the rj and Goxj .Figure 13 shows the regression rate curve calculated using average c method for a typical test. As canbe seen, the ballistic coefficients match quite well to those determined using the space and time averagingmethod.

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Figure 13. Regression Rate Using Averaged c Method for PMMA Test #25

in Eq. (6). Determining the error in the mass flow rate, a calculated parameter, begins with quantifying theindividual errors in the measured values that go into the mass flow rate calculation according to Eq. ( 1).These values include the diameter of the venturi, the discharge coefficient of the venturi, the pressure dropacross the venturi, and the upstream temperature and pressure of the nitrous oxide fluid (used to determine

fluid density). The mass flow rate is therefore quite sensitive to the Cv, which was known to within 1%based on repeated calibrations of the venturi. Thus, again for test #30, the relative error in mass flow ratewas determined to be 0.019, yielding an overall relative random error of 0.057 in oxidizer mass flux. Thiscorresponds to a absolute error value of 0.77 g/(cm 2s).

Acknowledgments

Financial support for the MATADOR project was provided by Stanford Department of Aeronautics andAstronautics Gift Funds. NASA Ames Research Center and Pratt & Whitney Rocketdyne generously loanedequipment that was instrumental for this project. The authors wish to thank Stanford Consulting ProfessorArif Karabeyoglu for his advice in test operations and analysis.

References

1Lemmon, E. W., McLinden, M. O., and Friend, D. G., Thermophysical Properties of Fluid Systems, NIST ChemistryWebBook, NIST Standard Reference Database Number 69, edited by P. J. Linstrom and W. G. Mallard, National Institute ofStandards and Technology, Gaithersburg MD, 20899 (http://webbook.nist.gov), June 2005.

2Physical Constants of Organic Compounds, CRC Handbook of Chemistry and Physics, edited by D. R. Lide, CRCPress, 86th ed., June 2005.

3Gombas, A., Szabo-Revesz, P., Regdon, G., and Eros, I., Study of Thermal Behaviour of Sugar Alcohols, Journal ofThermal Analysis and Calorimetry, Vol. 73, 2003, pp. 615621.

4Afeefy, H. Y., Liebman, J. F., and Stein, S. E., Neutral Thermochemical Data, NIST Chemistry WebBook, NISTStandard Reference Database Number 69, edited by P. J. Linstrom and W. G. Mallard, National Institute of Standards andTechnology, Gaithersburg MD, 20899 (http://webbook.nist.gov), June 2005.

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5Marxman, G. A., Wooldridge, C. E., and Muzzy, R. J., Fundamentals of Hybrid Boundary Layer Combustion, Progressin Aeronautics and Astronautics , Vol. 15, 1964, pp. 485522.

6Karabeyoglu, M. A., Cantwell, B. J., and Zilliac, G., Development of Scalable Space-time Averaged Regression RateExpressions for Hybrid Rockets, 41st AIAA/ASME/SAE/ASEE Joint Propulsion Conference , AIAA, Tucson, AZ, July 2005.

7Wernimont, W. J. and Heister, S. D., Combustion Experiments in Hydrogen Peroxide/Polyethylene Hybrid Rocket withCatalytic Ignition, Journal of Propulsion and Power, Vol. 16, No. 2, 2000, pp. 318326.

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Table 2. Test Conditions

TestFuel

GrainTest Duration

Injector OpenArea

ThroatDiameter

mfueli L Di

(s) (mm2) (mm) (g) (cm) (cm)

1 PMMA-1 5.4 0.950 3.56 255.9 12.7 1.91

2 SP1A-1 3.5 0.633 5.56 245.6 12.7 1.91

3 SORB-1 3.0 0.633 5.56 299.9 12.7 1.91

4 SORB-1 4.6 0.633 5.56 299.9 12.7 1.91

5 HDPE-1 9.9 0.317 3.56 208.7 12.7 1.91

6 PMMA-2 14.9 0.317 3.56 311.4 15.2 1.92

7 HDPE-2 10.0 0.633 3.56 209.1 12.7 1.91

8 PMMA-3 9.8 0.633 3.56 312.1 15.2 1.97

9 HDPE-3 9.5 0.633 3.56 210.1 12.7 1.91

10 PMMA-4 9.7 0.633 3.56 259.2 12.7 1.94

11 SORB-4 4.2 0.633 3.56 187.1 7.6 2.03

12 SORB-3 7.2 0.950 5.56 307.6 12.7 1.91

13 PMMA-5 7.2 0.633 3.56 341.0 15.3 1.33

14 HDPE-4 14.7 0.633 3.56 272.2 15.3 1.33

15 PMMA-6 9.9 1.267 6.35 506.7 22.9 1.34

16 HDPE-5 12.8 1.267 6.35 405.3 22.8 1.35

17 PMMA-7 9.7 1.267 6.35 502.6 22.9 1.34

18 HDPE-6 12.8 1.267 6.35 400.8 22.8 1.35

19 HTPB-1 6.8 1.267 6.35 382.7 22.8 1.91

20 SORB-8/5 4.0 1.267 6.35 558.1 22.9 1.91

21 HTPB-2 6.8 1.267 6.35 218.6 12.7 1.91

22 HTPB-3 6.8 1.267 6.35 217.1 12.7 1.9123 SORB-6 4.9 1.267 6.35 309.1 12.7 1.91

24 SORB-10 4.8 1.267 6.35 310.3 12.7 1.91

25 PMMA-8 9.8 1.583 6.35 505.1 22.9 1.33

26 HDPE-7 9.8 1.583 6.35 403.5 22.8 1.28

27 HTPB-6 4.9 1.583 6.35 402.8 22.9 1.92

28 PMMA-9 6.8 1.900 6.35 512.4 22.8 1.27

29 HDPE-8 9.9 1.900 6.35 413.9 22.7 1.16

30 HTPB-7 5.8 1.900 6.35 396.9 22.6 1.93

31 SORB-7/9 2.8 1.900 6.35 555.5 22.9 1.89

32 SORB-13 4.8 1.900 6.35 548.0 22.9 1.90

33 SORB-14 6.9 1.583 6.35 539.7 22.3 1.9034 SORB-11 7.9 1.267 6.35 306.2 12.7 1.91

35 SORB-12 4.9 1.267 6.35 310.9 12.7 1.90

36 HTPB-4 7.8 0.950 6.35 211.4 13.0 2.24

37 HTPB-5 9.8 0.633 6.35 212.3 12.8 2.13

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Table 3. Test Results

TestFuel

GrainPc

*

(atm)Mean-to-PeakPc Roughness

mox*

(g/s)mfuel

*

(g/s)O/F* c

Gox

(g/cm2s)rfuel

(mm/s)

1 PMMA-1 - - - - - Test Facility Checkout

2 SP1A-1 - - - - - Test Facility Checkout

3 SORB-1 - - - - - Igniter failure4 SORB-1 19.6 6.0% 21.6 15.0 1.4 96% 4.8 1.11

5 HDPE-1 22.4 1.8% 12.6 3.4 3.7 92% 3.2 0.39

6 PMMA-2 23.8 1.5% 12.1 5.7 2.1 92% 2.5 0.40

7 HDPE-2 43.5 1.6% 23.9 3.3 7.2 96% 5.8 0.38

8 PMMA-3 45.5 1.0% 23.3 6.0 3.9 96% 5.1 0.44

9 HDPE-3 43.7 1.2% 23.9 3.2 7.4 97% 6.0 0.38

10 PMMA-4 44.4 1.6% 24.0 4.9 4.9 96% 5.4 0.44

11 SORB-4 - - - - - Failed to ignite

12 SORB-3 26.5 5.1% 38.4 11.0 3.5 86% 7.3 0.79

13 PMMA-5 40.6 0.8% 19.2 6.8 2.8 99% 7.4 0.66

14 HDPE-4 40.5 0.7% 23.3 4.9 4.8 90% 6.8 0.5115 PMMA-6 26.8 1.0% 44.2 13.6 3.2 92% 12.5 0.76

16 HDPE-5 24.6 1.1% 41.0 8.8 4.7 99% 11.4 0.61

17 PMMA-7 24.9 1.1% 39.1 13.6 2.9 96% 11.3 0.77

18 HDPE-6 24.7 1.0% 42.8 8.8 4.9 95% 11.9 0.61

19 HTPB-1 29.8 0.5% 46.9 17.0 2.8 98% 9.0 0.98

20 SORB-8/5 34.0 3.3% 47.2 35.9 1.3 99% 9.5 1.43

21 HTPB-2 31.0 2.3% 53.1 8.7 6.1 95% 10.4 0.92

22 HTPB-3 26.6 2.4% 44.8 8.1 5.5 95% 9.2 0.87

23 SORB-6 36.3 6.5% 59.2 17.8 3.3 98% 11.6 1.26

24 SORB-10 34.6 4.7% 55.7 19.4 2.9 95% 11.0 1.35

25 PMMA-8 33.1 1.6% 57.5 12.3 4.7 94% 17.6 0.7126 HDPE-7 32.7 1.5% 57.6 9.1 6.4 94% 19.0 0.68

27 HTPB-6 35.8 1.6% 57.5 16.3 3.5 97% 12.2 1.00

28 PMMA-9 40.2 2.0% 72.3 13.1 5.5 94% 26.4 0.84

29 HDPE-8 37.0 2.6% 67.4 8.7 7.8 93% 25.0 0.70

30 HTPB-7 37.1 1.8% 63.7 14.8 4.3 91% 13.4 0.91

31 SORB-7/9 42.6 5.1% 64.1 35.1 1.8 94% 15.0 1.50

32 SORB-13 43.5 5.5% 65.5 35.9 1.8 94% 12.5 1.38

33 SORB-14 37.3 4.1% 57.9 28.4 2.0 92% 10.6 1.09

34 SORB-11 38.0 0.3% 53.6 18.2 2.9 - 8.6 1.15

35 SORB-12 34.7 9.6% 63.0 16.1 3.9 92% 13.0 1.16

36 HTPB-4 25.8 4.1% 47.8 8.3 5.8 88% 7.5 0.76

37 HTPB-5 19.3 1.7% 33.6 7.7 4.3 91% 5.4 0.72

* Averaged over a steady-state portion of the test. Diameter averaged over test duration. Length averaged over test duration. Value not available due to malfunctioning Pc transducer.

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