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

- Received:

DOI: 10.1007/BF00264400

- Cite this article as:
- Gross, K.P., McKenzie, R.L. & Logan, P. Experiments in Fluids (1987) 5: 372. doi:10.1007/BF00264400

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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.

### List of symbols

*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

- δ
*v* detuning frequency

- Δ
*v* spectral width (full width at half maximum)

- ζ
_{J″, J′} rotational line-strength factor

*v*frequency

*v*average band frequency

- τ
_{0} 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

### Subscripts and superscripts

*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