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Local film thickness and temperature distribution measurement in wavy liquid films with a laser-induced luminescence technique

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Abstract

Heat transfer in falling liquid film systems is enhanced by waviness. Comprehension of the underlying kinetic phenomena requires experimental data of the temperature field with high spatiotemporal resolution. Therefore a non-invasive measuring method based on luminescence indicators is developed. It is used to determine the temperature distribution and the local film thickness simultaneously. Results are presented for the temperature distribution measurement in a laminar-wavy water film with a liquid side Reynolds number of 126 flowing down a heated plane with an inclination angle of 2° at two positions in flow direction. The measured temperature distributions are used to calculate the local heat transfer coefficient for solitary waves at two positions in flow direction.

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Abbreviations

c :

Phase velocity, m/s

C :

Molar concentration, mol/m3

d :

Thickness, diameter, m

f :

Frequency, 1/s

F :

Objective functional

H :

Height of channel, m

I :

Intensity, W/m2

K :

Constant device factor, V m/W

L :

Length of channel, m

M :

Measured signal, V

n :

Distribution of effective emission area, m2

N :

Number of nodal points

Pr :

Prandtl number = ν/κ

Re :

Reynolds number \({=\dot{V}/(\nu\ W)}\)

t :

Time, s

u :

Streamwise velocity, m/s

v :

Transversal velocity, m/s

V :

Volume, m3

W :

Width of channel, m

x :

Streamwise coordinate, m

y :

Normal coordinate, m

α:

heat transfer coefficient, W/(m2 K)

η:

dynamic viscosity, kg/(m s)

φ:

regularization parameter

ϕ:

inclination angle, °

κ:

thermal diffusivity, m2/s

λ:

thermal conductivity, W/(m K)

λ:

wave length, m

ν:

kinematic viscosity, m2/s

ϑ:

temperature, °C

ρ:

density, kg/m3

τ:

decay constant, s

d:

disturbance

exp:

experimental

f:

film

g:

gas

i:

interface

l:

liquid, lower bound

m:

mean

max:

maximum value

Nu:

Nusselt

ob:

observation volume

P:

phosphorescence

s:

substrate

sta:

stagnant liquid

u:

upper bound

w:

wave peak, wall

*:

scaled value

\({\Vert \cdot \Vert^2_2}\) :

squared euclidian norm

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Acknowledgments

The authors gratefully acknowledge the financial support of the Deutsche Forschungsgemeinschaft (DFG) within the Collaborative Research Center (SFB) 540 “Model-based Experimental Analysis of Kinetic Phenomena in Fluid Multi-phase Reactive Systems”.

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Authors and Affiliations

  1. Department of Chemical Engineering, Chair of Mechanical Unit Operations, RWTH Aachen University, Aachen, Germany

    A. Schagen & M. Modigell

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  1. A. Schagen
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  2. M. Modigell
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Correspondence to M. Modigell.

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Schagen, A., Modigell, M. Local film thickness and temperature distribution measurement in wavy liquid films with a laser-induced luminescence technique. Exp Fluids 43, 209–221 (2007). https://doi.org/10.1007/s00348-007-0289-z

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  • DOI: https://doi.org/10.1007/s00348-007-0289-z

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