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Measurements of no rotational and vibrational temperatures behind a normal shock in hypervelocity flow via absorption spectroscopy

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Abstract

Tunable Diode Laser Absorption Spectroscopy (TDLAS) measurements of nitric oxide (NO) using a Quantum Cascade Laser (QCL) in the vicinity of 5.26 μm were conducted in a hypervelocity flow generated in the Texas A&M Hypervelocity Expansion Tunnel (HXT). The nascent NO was produced downstream of symmetric Mach reflections generated in Mach 8.5 flows with stagnation enthalpies from 6.9 to 11.1 MJ/kg. Path-averaged flow parameters of rotational and vibrational temperatures and NO concentration at a measurement rate of 30 kHz were obtained. By probing the R-branch of the fundamental absorption band in NO, thermal nonequilibrium and NO concentration levels in the post-shock region were measured. Measurements are compared to equilibrium calculations. NO equilibrium values during the 1 ms test period differ from the experimental rotational and vibrational measurements across the same time period. The experimental measurements of the rotational temperature show a consistent value around 3000 K larger than the recovered vibrational temperature across any run. The NO concentrations in all runs are near to the reported equilibrium value; often beginning higher than, and over time decaying to, the equilibrium concentration value of the specific tunnel run.

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Data availability

Not applicable.

Abbreviations

\(A\) :

Einstein A-coefficient

\(\widetilde{A}\) :

1st spin-splitting energy term

\({B}_{\text{v}}\) :

Rotational constant for vibronic level

\(C\) :

2nd spin-splitting term

\(c\) :

Speed of light

\({c}_{x}\) :

Constant of x broadening

\({c}_{2}\) :

2nd radiation constant

\({D}_{v}\) :

Centrifugal stretching term for the vibronic level \(v\)

\(d\) :

Lorentzian–Gaussian ratio

\({F}^{{\prime}{\prime}}\) :

Lower-state rotational energy

\({f}_{V}\) :

Voigt convolution function

\({G}^{{\prime}{\prime}}\) :

Lower-state vibrational energy

\({g}_{V}\) :

Voigt convolution function

\(h\) :

Planck constant

\(I\) :

Moment of inertia

\({I}_{\text{t}}\) :

Transmitted signal

\({I}_{0}\) :

Baseline signal

\(J\) :

Rotational quantum number

\({k}_{B}\) :

Boltzmann constant

\(L\) :

Laser pathlength

\(M\) :

Molecular weight

\({M}_{a}\) :

Mach number

\(m\) :

Mass

\({N}_{A}\) :

Avogadro constant

\(n\) :

Molecular density

\({n}_{air}\) :

Temperature dependence coefficient

\(P\) :

Pressure

\(\widetilde{P}\) :

Constant in the expression for \(\Lambda\)-doubling

\(Q\) :

Molecular partition function

\(\widetilde{Q}\) :

Constant in the expression for \(\Lambda\)-doubling

\({r}_{0}\) :

Molecular distance between two atoms of a diatomic molecule

\(S\) :

Linestrength intensity

\({T}_{x}\) :

Temperature of \(x\) mode excitation

\({T}_{\infty }\) :

Freestream temperature

\(t\) :

Time

\(v\) :

Vibrational quantum number

\({Y}_{v}\) :

Term in the ground electronic state rotational energy

\(\alpha\) :

Absorbance

\({\alpha }_{x}\) :

Broadening due to x

\(\gamma\) :

Heat capacity ratio

\({\gamma }_{x}\) :

x-broadened HWHM

\(\widetilde{\gamma }\) :

Spin-splitting term for the excited state

\(\Delta F\) :

Change in rotational energy

\(\Delta f\) :

Optical linewidth

\(\Delta G\) :

Change in vibrational energy

\({\theta }_{x}\) :

Characteristic temperature of x mode excitation

\(\lambda\) :

Wavelength

\(\mu\) :

Ratio of NO vibronic constants

\(\nu\) :

Wavenumber

\(\xi\) :

Average noise uncertainty

\(\sigma\) :

Absorption cross section

\(\tau\) :

Transmission

\(\phi\) :

Hyperfine transition term

\(\chi\) :

Mole fraction

\({\omega }_{e}\) :

1st harmonic oscillator vibrational constant

\({\omega }_{e}{x}_{e}\) :

Anharmonicity constant

\(\tilde\omega\) :

Term in the calculation of rotational energy

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Funding

The authors gratefully acknowledge the Office of the Under Secretary of Defense Vannevar Bush Faculty Fellowship program (Drs. B. Nair and J. Cambier, N00014-18–1-3020) for sponsoring a portion of this study. Its contents are solely the responsibility of the authors and do not necessarily represent the official views of the Department of Defense. The authors also acknowledge support from the National Science Foundation under NSF-2026242 and the DOE under DE-SC0021382.

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Authors and Affiliations

  1. Department of Mechanical, Aerospace, and Biomedical Engineering, University of Tennessee, Knoxville, TN, 37996, USA

    Samuel E. Feltis, Zhili Zhang, Farhan Siddiqui & Mark Gragston

  2. Department of Aerospace Engineering, Texas A&M University, College Station, TX, 77834, USA

    Tyler S. Dean & Rodney D. W. Bowersox

  3. University of Tennessee Space Institute, Tullahoma, TN, 37388, USA

    Farhan Siddiqui & Mark Gragston

Authors
  1. Samuel E. Feltis
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  2. Zhili Zhang
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  4. Rodney D. W. Bowersox
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  5. Farhan Siddiqui
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  6. Mark Gragston
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Contributions

S.F. assisted in the performance of the experiment, wrote the main manuscript text, partially created figure 2 and created figures 4-16, created Tables 3-5, and created the main model used in the research analysis. Z.Z. assisted in the performance of the experiment, assisted in the creation of the model, and reviewed the manuscript. T.D. assisted in the performance of the experiment, partially created figures 2 and 3 and created figure 1, created Tables 1 and 2, and reviewed the manuscript. R.B. assisted in the performance of the experiment and reviewed the manuscript. F.S. assisted in the performance of the experiment, assisted in the creation of the model, and reviewed the manuscript. M.G. assisted in the performance of the experiment, wrote portions of the manuscript text, partially created figure 3, assisted in the creation of the model as well as the frozen temperature analysis, and reviewed the manuscript.

Corresponding author

Correspondence to Samuel E. Feltis.

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Feltis, S.E., Zhang, Z., Dean, T.S. et al. Measurements of no rotational and vibrational temperatures behind a normal shock in hypervelocity flow via absorption spectroscopy. Exp Fluids 65, 112 (2024). https://doi.org/10.1007/s00348-024-03841-w

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