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Measurement of temperature field of a Rayleigh-Bénard convection using two-color laser-induced fluorescence

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Abstract

The two-color laser-induced fluorescence technique developed by Sakakibara and Adrian (1999) for the measurement of planar turbulent temperature fields in water has been refined to reduce the RMS error of the instantaneous measurement by an order of magnitude. The technique achieves higher sensitivity by employing two high-resolution 14-bit monochrome CCD cameras. Further refinement is achieved by post-processing the data using a convolution method that matches the degree of the image blurring of the two images. The method is demonstrated by application to turbulent Rayleigh-Bénard convection wherein the random error is shown to be less than 0.17 K.

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Abbreviations

B (1/K):

thermal expansion coefficient

C (kg/m3):

dye concentration

d B (m):

e –1diameter of laser beam

f (m):

focal length

g (m/s2):

gravitational acceleration

G :

point spread function

I :

fluorescent intensity without background intensity, \( I = \ifmmode\expandafter\tilde\else\expandafter\~\fi{I} - I_{b} \)

I b :

background intensity

I c :

corrected intensity

I s :

intensity of fluorescence excited by stationary laser beam

\( \ifmmode\expandafter\tilde\else\expandafter\~\fi{I} \) :

light intensity detected by CCD cameras

ΔI :

absorbed light intensity

k (m2/s):

thermal diffusivity

Pr:

Prandtl number

Q 0 (mK/s):

kinematic heat flux at lower (and upper) surface

Ra:

Rayleigh number

T (K):

temperature

T 0, T 1 (K):

temperature for reference images

T L (K):

temperature of lower surface

T U (K):

temperature of upper surface

T RMS (K):

RMS temperature

T b (K):

mean temperature at mid-height of cell

\( \ifmmode\expandafter\bar\else\expandafter\=\fi{T}{\left( {\text{K}} \right)} \) :

mean temperature

ΔT (K):

temperature difference between upper and lower surface ΔT= T L− T U

Δt (s):

time period of excitation against local fluorescent molecule Δt= d B/ V S

V s (m/s):

beam speed in vertical direction

w * (m/s):

Deardorff’s velocity scale, w *=( gBQ 0 z *)1/3

X (pixel):

image coordinate (horizontal)

x (m):

physical coordinate (horizontal)

Y (pixel):

image coordinate (vertical)

z (m):

physical coordinate (vertical)

z * (m):

layer half-depth

ε (m2/kg):

absorption coefficient of dye

φ :

quantum yield

γ :

ratio of fluorescent intensities at each pixel location

γ 0, γ 1 :

ratio of fluorescent intensities at T = T 0 and T = T 1, respectively

κ (1/K):

temperature sensitivity

λ R (m):

reflected wavelength of beam splitter

λ T (m):

transmitted wavelength of beam splitter

λ abs (m):

wavelength yielding maximum absorption

λ em (m):

wavelength yielding maximum emission

λ ex (m):

wavelength of laser beam

ν (m2/s):

kinematic viscosity

θ * (K):

Deardorff’s temperature scale, θ *= Q 0/ w *

σ I :

noise level of intensity averaged over 10 by 10 pixels

σ γ :

noise level of intensity ratio, σγ=(2σ I 2)1/2

σ T (K):

standard deviation of measured temperature

ξ :

coefficient for mapping function ( X)

η :

coefficient for mapping function ( Y)

RhB:

Rhodamine B

Rh110:

Rhodamine 110

α :

camera α for Rhodamine B

β :

camera β for Rhodamine 110

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Acknowledgments

This research was supported by the Hoeft Chair of the University of Illinois at Urbana-Champaign. JS held a Zaigai Kenkyuin of Ministry of Science and Education of Japan (No.13-WAKA-41).

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Authors and Affiliations

  1. Institute of Engineering Mechanics and Systems, University of Tsukuba, Tennodai 1-1-1, Tsukuba 305-8573, Japan

    J. Sakakibara

  2. Department of Theoretical and Applied Mechanics, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA

    R. J. Adrian

Authors
  1. J. Sakakibara
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  2. R. J. Adrian
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Sakakibara, J., Adrian, R.J. Measurement of temperature field of a Rayleigh-Bénard convection using two-color laser-induced fluorescence. Exp Fluids 37, 331–340 (2004). https://doi.org/10.1007/s00348-004-0821-3

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  • DOI: https://doi.org/10.1007/s00348-004-0821-3

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