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Measurements of temperature, density, pressure, and their fluctuations in supersonic turbulence using laser-induced fluorescence

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Abstract

A laser-induced fluorescence (LIF) method has been developed that provides simultaneous measurements of temperature, density, and their fluctuations owing to turbulence in unheated compressible flows. Pressure and its fluctuations are also deduced using the equation of state. Fluorescence is induced in nitric oxide that has been seeded into a nitrogen flow in concentrations of 100 ppm. Measurements are obtained from each laser pulse, with a spatial resolution of 1 mm and a temporal resolution of 125 ns. The method was applied to a supersonic, turbulent, boundary-layer flow with a free-stream Mach number of 2. For stream conditions in the range from 150–300 K and 0.3–1 atm, temperature is measured with an uncertainty of approximately 1% rms, while density and pressure uncertainties are approximately 2% rms.

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Abbreviations

B lu :

Einstein B-coefficient for transitions from state |l〉 to state u〉

c :

speed of light

C D :

calibration factor for density measurement [see Eq. (20)]

C T :

calibration factor for temperature measurement [see Eq. (18)]

C lu :

collision broadening function constant [see Eq. (14)]

d :

Voigt parameter [see Eq. (9)]

E f :

fluorescence energy per pulse

E 0 :

laser pulse energy

E l :

energy of molecular state |l〉

F i :

spectral function for laser i (i = 1, 2) [see Eq. (17)]

g l :

degeneracy of state |l〉

G lu :

spectral convolution integral [see Eq. (3)]

h :

Plank's constant

J′, J″:

upper and lower rotational quantum numbers respectively

k :

Boltzmann's constant

L :

length of observed sample volume

m f :

molecular mass per molecule of the fluorescent species

M ∞ :

free-stream Mach number

N :

total number density

N i :

number density in state |i〉

N l * :

number density in state |l〉 at thermal equilibrium

p, p′:

Voigt parameters [see Eqs. (10) and (15)]

P :

pressure

Re δ :

Reynolds number based on boundary layer thickness

S i, S i′:

sample and reference signals respectively, from las i

t :

time

T :

kinetic temperature

v′, v″:

upper and lower vibrational quantum numbers respectively

V(p, d) :

Voigt function

X i :

mole fraction of species i

Z :

partition function

δ:

boundary layer thickness

δv :

detuning frequency

Δv :

spectral width (full width at half maximum)

ζJ″, J′ :

rotational line-strength factor

v :

frequency

v :

average band frequency

τ0 :

collisional decay time

τ f :

fluorescence decay time

τ T :

total radiative decay time

τ ui :

quenching time of state |u〉 by species i

Φ(v 0, v):

spectral distribution function centered at frequency

D :

Doppler

G :

Gaussian

lu :

state |l〉 to state |u〉 transition

L :

Lorentzian

r :

reference condition

0:

property of the laser

t :

flow stagnation condition

∞:

flow free-stream condition

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Author notes

  1. K. P. Gross

    Present address: Tencor Instruments, 94043, Mountain View, CA, USA

Authors and Affiliations

  1. Polyatomics Research Institute, 94043, Mountain View, CA, USA

    K. P. Gross

  2. Ames Research Center, 94035, Moffett Field, CA, USA

    R. L. McKenzie

  3. Dept. of Aeronautics and Astronautics, Stanford University, 94305, Stanford, CA, USA

    P. Logan

Authors
  1. K. P. Gross
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  2. R. L. McKenzie
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  3. P. Logan
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Gross, K.P., McKenzie, R.L. & Logan, P. Measurements of temperature, density, pressure, and their fluctuations in supersonic turbulence using laser-induced fluorescence. Experiments in Fluids 5, 372–380 (1987). https://doi.org/10.1007/BF00264400

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  • DOI: https://doi.org/10.1007/BF00264400

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