Experiments in Fluids

, Volume 4, Issue 5, pp 269–278 | Cite as

Rayleigh scattering for density measurements in premixed flames

One point, time series data
  • F. C. Gouldin
  • R. N. Halthore
Originals
Received:

Abstract

Rayleigh scattering measurements for molecular number density in turbulent, premixed CH4-air flames are discussed, and data for both flamelet passage time distributions and power spectral density functions are reported and compared to the recent predictions of Bray, Libby and Moss (1984). Measurement problems associated with variations in mixture-averaged Rayleigh scattering cross section, index of refraction fluctuations, finite spatial and temporal resolution and with scattering from particles are discussed. It is concluded that these effects are relatively minor in the reported experiments. Correction procedures are suggested for the effects of cross section variation and of finite resolution.

Passage time and spectral data support the Bray, Libby and Moss hypothesis for the passage time distribution function. Furthermore, model predictions for the variation across the flame brush of mean passage times for both reactant and product eddies are in reasonable agreement with experiment. Finally, the data suggest that these mean times scale in part with Ū and λ in the reactant flow.

Keywords

Power Spectral Density Passage Time Scatter Cross Section Rayleigh Scattering Premix Flame 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols

c=(T − T0)/(T∞ − T0)

reaction progress variable

Eϕϕ (k, Ω)

wave number — frequency spectrum of scalar ϕ

f

frequency (hz)

f (c)

normalized contribution to P (c) from reacting components

Gx, Gt

Fourier transforms of θx and θt, Eqs. (7) and (8)

hx, ht

measurement system response functions, Eq. (8)

K

calibration constant for scattering measurements, Eq. (3)

k

wave number

l

length of scattering measurement volume and turbulence integral scale

m

number of samples in ensemble for ti;

N (t), N (Δt)

photon counting rate and photon countsper period Δt

n

molecular number density; no of reactants and n0 and n∞ of products

\(\hat n\)

Locshmidt's number

P (c) = α δ(c) + βδ (1 − c) + γf(c)

probability density function of c

P (ti)

probability density function of ti

Ps

power of scattered light as detected

Pt

laser power

Re

turbulence Reynolds number (u′ l/ν) in the reactant flow

Rn (τ)

autocorrelation function of n

Rϕϕ (ε, τ)

covariance of scalar ϕ

rp, rR

radial dimensions of scattering volumes, Eq. (12)

Sn (f), Sc (f)

power spectral density function for n, for c

T

temperature T0 of reactants and T∞ of products

ti

passage times: i = r in reactants or i = p in products

\(\bar t_m \)

time scale for passage times; tm ≡ t r , t p at c = 0.5

Ū

mean axial velocity in the reactant flow

\(u'\)

rms axial velocity fluctuations in reactant flow

Xα

mole fraction of species α

x1, x2

spatial coordinates defined in Fig. 2

Greek symbols

α, β, γ

relative contributions of reactant, product and reacting mixture to P (c)

ε

measurement error

η

quantum efficiency of detector

0x, θt

response functions defined by Eqs. (11) and (12)

λ

Taylor microscale;. λ = l (15/ARe)1/2 with A = 1

ν

flamelet crossing frequency

ζ

spatial displacement in covariance

σ

scattering cross section: σ p of particles and σα of species α

σm = Σ xα σα

mean scattering cross section

σn, σN

variance in number density, in photon arrival rate

σϕ

variance in ϕ

τ

transmission efficiency and lag time

ϕ

mixture equivalence ratio and general scalar quantity

Ω

collection solid angle in scattering measurements

ω

radian frequency

Miscellaneous

Overbar

mean quantity

Underbar

vector quantity

Superscript m

quantity derived from measurement

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Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • F. C. Gouldin
    • 1
  • R. N. Halthore
    • 1
  1. 1.Sibley School of Mechanical and Aerospace EngineeringCornell UniversityIthacaUSA

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