# In-Situ Optical Measurements of Solid and Hybrid-Propellant Combustion Plumes

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Tests Systems

#### 2.1. Optical Systems Design

#### 2.2. Thrust Chamber Assembly

^{®}hardware”, http://pro75.com/products/pro75/pro75.php, (accessed on 15 April 2020)). Full details of the motor systems are presented by Whitmore et al. [6].

#### 2.3. Motor Instrumentation and Test Assembly

## 3. Analytical Methods

#### 3.1. FTIR Analysis of the ABS Fuel Material

_{4.399}H

_{5.357}N

_{0.337}. Table 1 also lists the enthalpy contributions for each of the ABS copolymers including the monomer enthalpy of formation ΔH

_{f}and energy required for depolymerizing a particular monomer from the polymer chain ΔQ

_{p}. Table 1 also lists the ABS material chemical formula and molecular weight M

_{w}. The total enthalpy of the polymer is less than the sum of the enthalpies of the individual monomers and the net enthalpy contribution of each monomer given by the difference between ΔH

_{f}and ΔQ

_{p}. Because the polymer reaction is exothermic, ΔQ

_{p}must be returned to the fuel material in order to break the polymer bonds, and that energy is not available to support the combustion reaction.

#### 3.2. Thermochemical Analysis of the Exhaust Plume

_{0}is allowed to vary across a range of useful combustion pressures for the GOX/ABS propellants. Figure 8 plots the theoretical flame-temperature T

_{0}and characteristic velocity c* as a function of oxidizer-to-fuel ratio O/F. The different curves of Figure 8 represent the combustion chamber pressure levels, varying from approximately 1000 kPa (145 psia) 6000 kPa (870 psia) in 1000 kPa (145 psi) increments. Increasing values for T

_{0}and c* are associated with the higher combustion pressures. The CEA analysis predicts the stoichiometric O/F ratio to be approximately 2.89. This value is also plotted in Figure 8a,b as the vertical dashed lines.

#### 3.3. Motor Performance Analysis

_{sp}, and (5) characteristic velocity. As shown by Figure 5 an inline Venturi flow meter directly measures the oxidizer flow rate in real-time; however, the test stand was not configured to directly measure the fuel mass flow. Instead, before and after each hot-firing the fuel grains were weighed to give the total fuel mass consumed during the test. These mass measurements were used to anchor the “instantaneous” fuel mass flow rates, calculated as the difference between the nozzle exit and oxidizer mass flows:

_{0}, using the 1-dimensional choking mass flow equation, (Anderson [23], Chapter 4)

_{0}and mean O/F ratio as lookup variables. Calculated parameters included the gas constant R

_{g}, ratio of specific heats γ, and flame-temperature T

_{0}. Defining the combustion efficiency as:

_{exit}is the nozzle exit pressure calculated from the nozzle expansion ratio and chamber pressure, and p

_{∞}is the operating ambient pressure. A close and consistent comparison between the load-sensed and calculated thrust levels will be used to verify the verisimilitude of the previously outlined mass flow and O/F ratio calculation procedure.

## 4. Summary of Test Results

#### 4.1. Motor Performance Data

#### 4.2. Plume Spectra Measurments

_{λ}, although technically representing the mean-square signal-to-noise ratio of the unknown true input signal, can be approximated by the square of the signal-to-noise ratio (S/N) of the measured output signal. The S/N values were selected a priori based on the observed noise threshold of the raw spectra signals. Figure 12 shows how this S/N scaling parameter was estimated. Figure 12a plots a typical snapshot of the unfiltered-spectrum, overlaid with the spectrometer transfer function. The measured spectrum, heavily filtered with a 100-pont averaging window is also plotted. The S/N ratio is estimated by dividing the Hamamatsu transfer function coefficients, by the absolute differences between the raw and filtered spectra:

_{λ}for all follow-on calculations.

_{2}, H

_{2}O, and N

_{2}; all species predicted in observable concentrations in the exhaust plume. The magnitude-adjusted spectral also tend to show another weak “hump” at around 950–970 nm, corresponding to second emission wavelength for N

_{2}.

#### 4.3. Estimating the Internal Flame-Temperature

_{B}is Boltzmann’s constant, lambda is the emission wavelength, T is the absolute gas temperature, and A is the amplitude scaling factor. The parameters {A,T} are the minimum-variance curve fit variables. The non-linear regression algorithm, as applied to this problem, is derived in the Appendix A of this paper. Figure 14 shows this comparison. Plotted are the data of Figure 13b overlaid with the black-body spectrum curve fit (dashed green line), and the wavelength (dashed blue line) corresponding to the curve fit maximum radiance value, approximately 957 nm. From Wien’s displacement law [29]:

#### 4.4. Student-t Significance Test

_{student}= 0.00285. In Equation (12) N is the degrees of freedom, and {μ,σ} represent the sample mean and standard deviations for the CEA- and optically-derived flame-temperatures. Figure 16 overlays this t-statistic value on the student-t probability density curve for four degrees of freedom. The observed differences are statistically insignificant. Clearly, the limited data collected thus far demonstrate that the optically-sensed flame-temperature agrees with a very high level of confidence with the theoretically-predicted values.

## 5. Proposed Future Work

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Symbols | |

$\stackrel{\u2322}{\mathbb{A}}$ | Average absorbance of total polymer |

{a,b,c} | FTIR least-squares curve fit coefficients |

A | amplitude scaling factor |

A_{c} | fuel port cross-sectional area, cm^{2} |

A_{exit} | nozzle exit area, cm^{2} |

A* | sectional area at which local flow chokes, cm^{2} |

$\mathbb{A}$ | residual vector for estimated amplitude |

B | black body spectral radiance, W/rad^{2}-m^{3} |

c | speed of light in a vacuum, 2.998 × 10^{8} m/s |

c* | characteristic velocity of propellants, m/s |

F | curve fit function, W/rad^{2}-m^{3} |

F_{thrust} | thrust level, N |

g_{0} | normal acceleration of gravity at sea level, 9.8067 m/s^{2} |

h | Planck’s constant, 6.62607015 × 10^{−34} J/Hz |

i | wavelength index |

j | iteration index |

k_{B} | Boltzmann constant, 1.380649 × 10^{−23} J/K |

${\dot{m}}_{fuel}$ | fuel mass flow, g/s |

${\dot{m}}_{ox}$ | oxidizer mass flow, g/s |

${\dot{m}}_{total}$ | total mass flow through the nozzle, g/s |

N | degrees of freedom |

n | number of wavelength points in a given spectrum |

O/F | oxidizer-to-fuel ratio |

p_{exit} | nozzle exit pressure, kpa |

p_{∞} | operating ambient pressure, kpa |

P_{0} | combustion chamber pressure, kpa |

S | spectrum radiance at a single data point, W/rad^{2}-m^{3} |

$\mathbb{S}$ | residual vector for estimated radiance, W/rad^{2}-m^{3} |

$\hat{S}$ | spectrum radiance adjusted for spectrometer response transfer function, W/rad^{2}-m^{3} |

S/N_{λ} | measured spectrum signal to noise ratio at a given wavelength |

T | radiant temperature, K |

T_{0} | stagnation temperature, K |

t_{student} | student t-statistic value |

t_{burn} | burn time, s |

$\mathbb{T}$ | residual vector for estimated temperature, K |

X | estimation coefficient vector |

Γ | Jacobian Matrix |

ΔH_{f} | Molar enthalpy of formation, kJ/g-mol |

ΔQ_{p} | Molar enthalpy of polymerization, kJ/g-mol |

Φ | equivalence ratio |

λ | wavelength, nm |

λ_{max} | wavelength of maximum radiance, nm |

$\mathsf{\Upsilon}$ | spectrometer response transfer function |

μ | mean value |

σ | standard deviation |

η* | combustion efficiency |

γ | ratio of specific heats |

Acronyms | |

ABS | Acrylonitrile Butadiene Styrene |

ATR | Attenuated Total Reflection |

BLAST | Battery and Survivability Limits Testing |

CEA | Chemical Equilibrium with Applications |

CMOS | Complementary Metal Oxide Semiconductor |

FDM | Fused Deposition Manufacturing |

FTIR | Fourier Transform InfraRed Spectroscopy |

GOX | Gaseous Oxygen |

HVPS | High Voltage Power Supply |

IR | InfraRed |

P&ID | Piping and Instrumentation |

USU | Utah State University |

## Appendix A. Non-Linear Regression Algorithm for Fitting Planck’s Law to the Optical Sensor Data

#### Appendix A.1. Derivation of the Non-Linear Regression Algorithm

^{(j}

^{)},T

^{(j)}):

#### Appendix A.2. Derivatives of Planck’s Function

^{(j)},T

^{(j)}), Equation (A7) is iterated using successive substitutions until the differences between iterations for the parameters become acceptably small. The resulting solution gives the minimum variance fit between Planck’s law and the observed spectra. Only the data that lie between the sensitivity limits of the spectrometer, between 640 and 1050 nm, were allowed into the data set that were fit to Equation (A1).

## References

- Gardon, R. An instrument for the direct measurement of intense thermal radiation. Rev. Sci. Instrum.
**1954**, 24, 366–370. [Google Scholar] [CrossRef] - Kidd, C.T.; Nelson, C.G. How the Schmidt-Boelter gage really works. In Proceedings of the 41st 41st International Instrumentation Symposium, Research Triangle Park, NC, USA, 7–11 May 1995; pp. 347–368. [Google Scholar]
- HAMAMATSU MS Series Mini-Spectrometers. Available online: https://www.hamamatsu.com/resources/pdf/ssd/c10988ma-01_etc_kacc1169e.pdf (accessed on 24 December 2021).
- Whitmore, S.A.; Armstrong, I.W.; Heiner, M.C.; Martinez, C.J. High-performing hydrogen peroxide hybrid rocket with 3-D printed and extruded ABS fuel. Aeronaut. Aerosp. Open Access J.
**2018**, 2, 356–388. [Google Scholar] [CrossRef] [Green Version] - Whitmore, S.A.; Martinez, C.J.; Merkley, D.P. Catalyst development for an arc-ignited hydrogen peroxide/ABS hybrid rocket system. Aeronaut. Aerosp. Open Access J.
**2018**, 2, 356–388. [Google Scholar] [CrossRef] [Green Version] - Whitmore, S.A.; Babb, R.S.; Gardner, T.J.; LLoyd, K.P.; Stephens, J.C. Pyrolytic graphite and boron nitride as low-erosion nozzle materials for long-duration hybrid rocket testing, AIAA 2020–3740. In Proceedings of the AIAA Propulsion and Energy 2020 Forum, Virtual Event, 24–28 August 2020. [Google Scholar]
- Whitmore, S.A.; Inkley, N.R.; Merkley, D.P.; Judson, M.I. Development of a power-efficient, restart-capable arc ignitor for hybrid rockets. J. Propuls. Power
**2015**, 31, 1739–1749. [Google Scholar] [CrossRef] - Anon. National Institute for Standards in Technology (NIST) Standard Reference Database Number 69. Available online: http://webbook.nist.gov/chemistry (accessed on 1 June 2019).
- Othmer, K. Butadiene. In Encyclopedia of Chemical Technology; John Wiley & Sons, Inc.: New York, NY, USA, 2006. [Google Scholar]
- Anon. Styrene. National Library of Medicine. PubChem. Available online: https://pubchem.ncbi.nlm.nih.gov/compound/Styrene (accessed on 12 August 2021).
- Cha, J. Acrylonitrile-Butadiene-Styrene (ABS) Resin. In Engineering Plastics Handbook; Margolis, J.M., Ed.; McGraw-Hill: New York, NY, USA, 2006; pp. 101–130. [Google Scholar]
- Bradley, M. FTIR Sample Techniques: Attenuated Total Reflection (ATR). Thermo Fisher Scientific Technical Note. Available online: https://www.thermofisher.com/us/en/home/industrial/spectroscopy-elemental-isotope-analysis/spectroscopy-elemental-isotope-analysis-learning-center/molecular-spectroscopy-information/ftir-information/ftir-sample-handling-techniques.html (accessed on 1 June 2019).
- Junga, M.R.; Horgena, F.D.; Orskib, S.V.; Rodriguez, V.C.; Beers, K.L.; Balazs, G.H.; Jones, T.T.; Work, T.M.; Brignace, K.C.; Royer, S.J.; et al. Validation of ATR FT-IR to identify polymers of plastic marine debris, including those ingested by marine organisms. Mar. Pollut. Bull.
**2018**, 127, 704–716. [Google Scholar] [CrossRef] [PubMed] - Smith, A.L.; Carver, C.D. (Eds.) Propene Nitrile. In The Coblentz Society Desk Book of Infrared Spectra, 2nd ed.; The Coblentz Society: Kirkwood, MO, USA, 1982; pp. 1–24. Available online: https://webbook.nist.gov/cgi/cbook.cgi?JCAMP=C107131&Index=1&Type=IR (accessed on 1 June 2019).
- Smith, A.L.; Carver, C.D. (Eds.) Butadien. In The Coblentz Society Desk Book of Infrared Spectra, 2nd ed.; The Coblentz Society: Kirkwood, MO, USA, 1982; pp. 1–24. Available online: https://webbook.nist.gov/cgi/cbook.cgi?JCAMP=C107131&Index=1&Type=IR (accessed on 1 June 2019).
- Smith, A.L.; Carver, C.D. (Eds.) Styrene. In The Coblentz Society Desk Book of Infrared Spectra, 2nd ed.; The Coblentz Society: Kirkwood, MO, USA, 1982; pp. 1–24. Available online: https://webbook.nist.gov/cgi/cbook.cgi?JCAMP=C100425&Index=1&Type=IR (accessed on 1 June 2019).
- Baxendale, J.L.H.; Madaras, G.W. Kinetics and heats of copolymerization of acrylonitrile and methyl methacrylate. J. Polym. Sci.
**1956**, 19, 171–179. [Google Scholar] [CrossRef] - Seymour, R.B.; Carraher, C.E., Jr. Polymer Chemistry, Revised and Expanded, 6th ed.; Marcel Dekker Publishing, Inc.: New York, NY, USA, 2003; Available online: https://www.academia.edu/29185976/Seymour_Carrahers_Polymer_Chemistry_Sixth_Edition (accessed on 5 December 2021).
- Van Krevelen, D.W.; Jijenhuis, K. Properties of Polymers: Their Correlation with Chemical Structure; Their Numerical Estimation and Prediction from Additive Group Contributions, 4th ed.; Elsevier Science Ltd.: Amsterdam, The Netherlands, 2009. [Google Scholar]
- Prosen, E.J.; Maron, F.W.; Rossini, F.D. Heats of combustion, formation, and isomerization of ten C4 hydrocarbons. J. Res.
**1951**, 46, 106–112. [Google Scholar] - Prosen, E.J.; Rossini, F.D. Heats of formation and combustion of 1,3-butadiene and styrene. J. Res.
**1945**, 34, 59–63. [Google Scholar] [CrossRef] - Gordon, S.; McBride, B.J. Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications; NASA RP-1311; NASA: Washington, DC, USA, 1994. [Google Scholar]
- Anderson, J.D. Modern Compressible Flow, 3rd ed.; The McGraw Hill Companies, Inc.: New York, NY, USA, 2003; Chapter 4; pp. 127–187, ISBN-13 978-0072424430; Available online: https://libcat.lib.usu.edu/search/i0070016542 (accessed on 5 December 2021).
- Whitmore, S.A. A variational method for estimating time-resolved hybrid fuel regression rates from chamber pressure. In Proceedings of the AIAA 2020-3762, AIAA Propulsion and Energy Forum 2020, Virtual Event, 24–28 August 2020. [Google Scholar] [CrossRef]
- Whitmore, S.A. Nytrox as “drop-in” replacement for gaseous oxygen in SmallSat hybrid propulsion systems. Aerospace
**2000**, 7, 43. [Google Scholar] [CrossRef] [Green Version] - Meditch, J.S. Stochastic Optimal Linear Estimation and Control; McGraw-Hill: New York, NY, USA, 1969; pp. 288–322. [Google Scholar]
- Gonzalez, R.; Woods, R.; Eddins, S. Digital Image Processing Using Matlab; Prentice Hall: Saddle River, NJ, USA, 2003; Chapter 4. [Google Scholar]
- Dougal, R.C. The Presentation of the Planck Radiation Formula (Tutorial). Phys. Educ.
**1976**, 11, 438–443. [Google Scholar] [CrossRef] - Walker, J. Fundamentals of Physics, 8th ed.; John Wiley and Sons: Hoboken, NJ, USA, 2008; p. 891. ISBN 9780471758013. [Google Scholar]
- Beckwith, T.G.; Marangoni, R.D.; Lienhard, V.J.H. Mechanical Measurements, 6th ed.; Prentice Hall: Hoboken, NJ, USA, 2006; pp. 43–73. [Google Scholar]
- Whitmore, S.A.; Olsen, K.C.; Forster, P.; Oztan, C.; Coverstone, V.L. Test and evaluation of copper-enhanced, 3-D printed ABS hybrid rocket fuels. In Proceedings of the AIAA 2021-3225, AIAA Propulsion and Energy 2021 Forum, Virtual Event, 9–11 August 2021. [Google Scholar]
- Boyd, S. Lecture 5, Least-squares, EE263 Lecture Notes. 2007. Available online: https://see.stanford.edu/materials/lsoeldsee263/05-ls.pdf (accessed on 25 May 2021).
- Kosinski, A.A. Cramer’s Rule is due to Cramer. Math. Mag.
**2001**, 74, 310–312. [Google Scholar] [CrossRef]

**Figure 1.**Typical Gardon Gauge Installation. (Wikimedia Commons, free media repository, public domain). (

**a**) Schmidt -Boelter Gardon Gauge (Wikimedia Commons, public domain). (

**b**) Typical Installation. (

**c**) Heat Flux Paths.

**Figure 2.**Proof-of-Concept Tests for Fiber-Optic Sensor. (

**a**) Fiber Optic Fed Through EPDM Rubber Sample. (

**b**) Burning the EPDM/Fiber Optic Sample. (

**c**) Fiber Optic Cable with Melted Tip, Still Transmitting Light.

**Figure 3.**Hamamatsu Optical Sensing System Components. (

**a**) Fiber Optic Connection to Spectrometer via Custom Adapter. (

**b**) Spectrometer Transfer Function. (

**c**) Block Diagram of the Optical Sensor Electronics and Data Acquisition.

**Figure 6.**Ensemble Mean FTIR Spectra for ABS Material Samples: ABSPlus-Red, ABS Plus-Blue, and Extruded.

**Figure 11.**Unscaled Ensemble Spectrum Corresponding to Burn Data of Figure 11.

**Figure 16.**Comparing Flame-Temperature t-Statistic with. Student-t Probability Curve for 4 Degrees of Freedom.

Monomer | Chemical Formula | M_{w} g/mol | ΔH_{f} MonomerkJ/g-mol | ΔQ_{p} PolymerkJ/g-mol | Net ΔH_{f} kJ/g-mol | Mole Fraction | Mass Fraction | Net Enthalpy Contribution kJ/g-mol |
---|---|---|---|---|---|---|---|---|

Acrylo-nitrile | C_{3}H_{3}N | 53.06 | 172.62 [17] | 74.3 [18] | 98.31 | 0.337 | 0.284 | 33.13 |

Butadiene | C_{4}H_{6} | 54.09 | 104.10 [19] | 72.10 [20] | 32.00 | 0.479 | 0.411 | 15.33 |

Styrene | C_{8}H_{8} | 104.15 | 146.91 [21] | 84.60 [20] | 63.31 | 0.184 | 0.305 | 11.65 |

ABS Total | C_{4.399} H_{5.357} N_{0.377} | 62.95 | 1.00 | 1.00 | 60.11 |

Species | Mass Fraction | Emission Wavelengths, nm |
---|---|---|

CO | 59.8% | 1568, 2330, 4610 |

H_{2} | 23.5% | 410, 434, 486, 656 |

H_{2}O | 8.3% | 605, 660, 750 |

H | 3.0% | 410, 434, 486, 656 |

CO_{2} | 2.8% | 300, 444, 1459 |

N_{2} | 2.1% | 590, 670, 740, 820, 870, 900, 970 |

OH | 0.4% | 304, 307 |

O | 0.03% | 558, 630, 635 |

Burn No. | Burn Time, s | Load Cell Thrust, N | Thrust from P_{0}, N | Chamber Pressure P_{0}, kPa (Psia) | I_{sp}from Load | Mean Total Mass Flow, g/s | O/F | η* | c*, m/s | T_{0}, °C |
---|---|---|---|---|---|---|---|---|---|---|

1 | 5 | 112.8 | 111.1 | 880.1 (127.7) | 208.0 | 55.3 | 1.38 | 0.941 | 1621.7 | 2701.6 |

2 | 15 | 117.4 | 116.3 | 893.1 (129.5) | 213.0 | 56.2 | 1.34 | 0.960 | 1642.9 | 2754.0 |

3 | 15 | 117.5 | 116.1 | 891.0 (129.3) | 214.3 | 55.9 | 1.36 | 0.964 | 1655.6 | 2806.4 |

4 | 25 | 118.2 | 117.5 | 897.1 (130.1) | 213.7 | 56.4 | 1.35 | 0.960 | 1645.8 | 2758.9 |

5 | 15 | 117.9 | 116.7 | 896.2 (130.0) | 215.5 | 55.8 | 1.36 | 0.948 | 1628.1 | 2714.4 |

μ | - | 116.8 | 115.5 | 891.5 (129.3) | 212.9 | 55.9 | 1.358 | 0.955 | 1638.2 | 2747.1 |

σ | - | 2. 24 | 2.54 | 6.82 (0.97) | 2.89 | 0.43 | 0.015 | 0.010 | 13.74 | 41.36 |

95% t-conf. | - | 2.78 | 3.15 | 8.47 (1.20) | 3.58 | 0.52 | 0.018 | 0.012 | 17.04 | 51.32 |

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**MDPI and ACS Style**

Whitmore, S.A.; Frischkorn, C.I.; Petersen, S.J.
In-Situ Optical Measurements of Solid and Hybrid-Propellant Combustion Plumes. *Aerospace* **2022**, *9*, 57.
https://doi.org/10.3390/aerospace9020057

**AMA Style**

Whitmore SA, Frischkorn CI, Petersen SJ.
In-Situ Optical Measurements of Solid and Hybrid-Propellant Combustion Plumes. *Aerospace*. 2022; 9(2):57.
https://doi.org/10.3390/aerospace9020057

**Chicago/Turabian Style**

Whitmore, Stephen A., Cara I. Frischkorn, and Spencer J. Petersen.
2022. "In-Situ Optical Measurements of Solid and Hybrid-Propellant Combustion Plumes" *Aerospace* 9, no. 2: 57.
https://doi.org/10.3390/aerospace9020057