Abstract
This paper describes a measurement technique to quantify temporal variations in the thickness of an unsteady liquid film with a resolution which is independent of the thickness. The optical transformation function has been derived for fringes of equal inclination and, for a temporally varying film, allows the unsteady component of film thickness to be measured in terms of frequency modulated signal analysis of light intensity variations. As it does not require calibration, the method is suited to in-situ measurements of complex and rapidly varying films as encountered in engineering two-phase flows. It requires the inversion of the frequency time-series of the light intensity observed by a photodetector which represents the absolute values of the time-derivative of the thickness variation.
The technique has been used to measure the thickness of the film formed as a result of impingement of a pulsating two-phase jet onto a heated flat plate with surface temperatures of 150 °C and 240 °C and located 143 nozzle exit diameters downstream of the nozzle. The angle between the jet axis and the surface normal was 20 degrees and the injection frequency was 16.7 Hz corresponding to a flow rate of 7.2 mm3 per injection. The results along the line of incidence showed that the ensemble-averaged space-time structure of the film was qualitatively independent of the plate temperature with three peaks, two of which occurred at large radial distances and disappeared in less than 10 ms. The third peak was close to the impingement region and persisted for more than 50 ms due to the small velocities of the incoming two-phase jet as the nozzle needle closed and the low momentum wall jet which was unable to transport the droplets radially outwards. At the higher surface temperature, the rate of evaporation and the amplitude variation of the unsteady component of the overall film thickness increased, and the film covered a smaller area.
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Abbreviations
- A :
-
amplitude of electric field
- E :
-
electric field produced at a point
- f i (t):
-
instantaneous frequency
- f PMT (t) :
-
frequency observed by photomultiplier tube
- h δ :
-
thickness resolution
- h m :
-
minimum thickness that can be measured
- h (t, x) :
-
unsteady film thickness
- h s (x) :
-
steady film thickness
- h t (t,x) :
-
overall film thickness
- H :
-
nozzle-to-plate distance
- i :
-
\(\sqrt { - 1} \)
- I :
-
light intensity at a point
- \(\Im \) :
-
interference term
- k :
-
wavenumber of the monochromatic point source
- n :
-
refractive index of the air
- ń :
-
refractive index of thin film material
- r :
-
radial distance from the geometrical impingement point
- rms:
-
root-mean-square
- t :
-
time
- t 0 :
-
zero-crossing time defined in Fig. 2
- t r :
-
rise-time defined in Fig. 2
- T w :
-
wall temperature
- x :
-
position vector in 3-D space
- α:
-
angle of impingement
- β:
-
angle of reflection
- ɛ:
-
integration constant defined in Eq. (15)
- ɛ c :
-
integration constant at r = 0
- δ:
-
phase angle
- ΔP :
-
optical path difference
- ΔP :
-
minimum optical path difference
- φ:
-
azimuthal coordinate defined in Fig. 3 a
- χ:
-
initial phase angle defined as χ = ζh s (x)
- λ:
-
wavelength of the illuminating source
- ψ:
-
initial phase of an electric field produced by a source
- σ f (t) :
-
ensemble-averaged rms series for f PMT (t)
- θ:
-
angle of incidence
- θ′:
-
angle of refraction
- ω:
-
angular frequency of the electric field produced by a source
- ζ:
-
optical transformation function
References
Black, H. S. 1953: Modulation theory, p. 191. Toronto Van Nostrand
Born, M.; Wolf, E. 1975: Principles of optics, electromagnetic theory of propagation, interference and diffraction of light, 5th Ed., pp. 256–369. Oxford: Pergamon Press
Fansler, T. D.; French, D. T. 1988: Cycle-resolved laser velocimetry measurements in a reentrant-bowl-in-piston engine. SAE Paper 880377
Gohar, R.; Cameron, A. 1967: The mapping of elastohydrodynamic contacts. ASLE Trans. 10, 215–225
Hardalupas, Y. 1989: Experiments with isothermal two phase flows. Ph.D. Thesis, Univ. of London
Hoult, P. D.; Lux, J. P.; Wong, V. W.; Billian, S. A. 1988: Calibration of laser fluorescence measurements of lubricant film thickness in engines. SAE Paper 881587
Johnston, G. J.; Wayte, R.; Spikes, H. A. 1991: The measurement and study of very thin lubricant films in concentrated contacts. Tribology Trans. 34, 187–194
Lux, J. P.; Hoult, D. P. 1990: Lubricant film thickness measurements in a diesel engine piston ring zone. STLE Preprint 90-AM-1H-1
Özdemir, İ B. 1991: Impingement of single and two-phase jets on unheated and heated flat plates. Ph.D. Thesis, Univ. of London
Özdemir, İ. B.; Whitelaw, J. H. 1990: Impingement of an axisymmetric jet on unheated and heated flat plates. Mechanical Eng. Dept. Thermofluids Section Report FS/90/13. Imperial College, London
Özdemir, İ. B.; Whitelaw, J. H. 1991: Impingement of an unsteady two-phase jet on unheated and heated flat plates. Mechanical Eng. Dept. Thermofluids Section Report TF/91/20. Imperial College, London
Pliskin, W. A.; Esch, R. P. 1965: Refractive index of SiO2 films grown on silicon. J. Appl. Phys. 36, 2011–2013.
Reizmann, F.; Van Gelder, W. 1967: Optical thickness measurement of SiO2-Si3N4 films on silicon. Solid-State Electron. 10, 625–632
Shin, K.; Tateishi, Y.; Furuhama, S. 1983: Measurement of oil film thickness between piston ring and cylinder. SAE Paper 830068
TSI Instruction Manual 1985: Model 1990 C Counter-type Signal Processor, TSI Inc.
Twyman, F. 1952: Prism and lens making. 2nd Ed., p. 388, London Hilger and Watts
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Özdemir, İ.B., Whitelaw, J.H. An optical method for the measurement of unsteady film thickness. Experiments in Fluids 13, 321–331 (1992). https://doi.org/10.1007/BF00209505
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DOI: https://doi.org/10.1007/BF00209505