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Temperature Measurement in Laminar Free Convection Using Electro-Optic Holography
G. Schirripa Spagnolo, D. Ambrosini, A. Ponticiello, D. Paoletti
To cite this version:
G. Schirripa Spagnolo, D. Ambrosini, A. Ponticiello, D. Paoletti. Temperature Measurement in Lam- inar Free Convection Using Electro-Optic Holography. Journal de Physique III, EDP Sciences, 1997, 7 (9), pp.1893-1898. �10.1051/jp3:1997230�. �jpa-00249688�
Temperature Measurement in Lwninar Free Convection Using Electro-Optic Holography
G. Schirripa Spagnolo (*), D. Ambrosini, A. Ponticiello and D. Paoletti
Dipartimento di Energetica, Universith dell'Aquila, Localith Monteluco di Roio, 67040 Roio Poggio (AQ), Italy
(Received 9 September 1996, revised and accepted 10 June 1997)
PACS.42.30 Yc Other topics m imaging and optical processing
PACS 07.20.Dt Thermometry
PACS 44.25.+f Convective and constrained heat transfer
Abstract. In this paper, a system based on electro-optic holography is proposed to measure
temperature in larninar free convection. Special attention is payed to data treatment Some experimental results are given
1. Introduction
Temperature measurement can be performed by contact or non contact methods. Typical
contact devices are thermocouples and thermistors ill, while pyrometers iii are typical non
contact ones. Among non contact type devices, great attention has been given to those op-
tical methods in which the temperature dependence of the refractive index is used to make the temperature field visible [2]. Schlieren methods [3], interferometry [4], holographic inter-
ferometry [5], MoirA deflectometry [6] and speckle photography [7,8] have been studied. As
they are non contact, optical methods do not disturb the temperature field because in most
cases the energy absorbed by the medium is small compared to energy exchange by heat trans-
fer. Rapidly changing processes can be monitored, as there are practically no inertial errors and full-field temperature data can be provided [2]. In particular, holographic interferometry
is a well known and established technique is,9] but it requires stringent stability and good quality optics. There is always a time delay (due to developing procedures), furthermore, a
quantitative analysis is difficult.
A significant improvement in flexibility of use and information treatment can be obtained by electro-optic holography also known as Electronic Speckle Pattern Interferometry (ESPI)
A detailed description of ESPI can be found in literature [10-13]. This technique has already
been used to measure the isothermal diffusion coefficient in binary liquid mixtures [14,15].
In free convection, heat transfer takes place first by pure conduction. Then, when a tem-
perature gradient is established in the fluid, the temperature variation will generate a density gradient, that is, in a gravitational field, a convective motion as a result of buoyancy forces [16].
(* Author for correspondence (e-mail: schirripfling.univaq it)
@ Les (ditions de Physique 1997
1894 JOURNAL DE PHYSIQUE III N°9
90/10 Coupler
/
HeNe Laser
~
Lens coupler
~constant
Computer
~~~~~~~~~~~ ~~~~
Aperture
~
Horizontal
~ isothermal plate
CCD Camera
~
Beam sphtte~ ~g
lefts
~nd
glass
Fig. I Experimental set-up for temperature measurements by electro-optic holography.
Energy transfer by free convection arises in many engineering applications such as refrigera-
tion coils, heating elements and electric transformers. Free convection is in evidence in nature also. Typical examples are the convective motions in the atmosphere, short-term circulations of water due to the solar heating and the seasonal thermal inversion of lakes.
Free convection is more difficult to study than forced convection (in which the fluid motion is
imposed externally), and experimental data are often desirable to develop reliable heat transfer relations.
In this work, the application of electro-optic holography to temperature measurement in laminar free convection is considered. Special attention is payed to data treatment using an
iterative procedure. Some experimental results are given.
2. Basic Theory
The principle of the standard electro-optic holography is based on the recording of a holographic speckle patterns sequence on the photosensor of a TV camera.
ESPI can be described as an image holography (an image hologram is recorded of a real image of the object instead of the object itself), with an in-line reference beam, where the TV target has replaced film as the recording medium. The reconstruction process is performed by
the computer
We consider now an interferometer like the one presented in Figure I. Basically, the ESPI system consists of a continuous wave HeNe laser, a CCD camera, a monitor and a computer with an image processing board. The light coming from the laser is coupled with a single mode fibre. A fibre optics 10/90 directional coupler splits the light into signal and reference beams.
A beamsplitter cube, placed between the photo sensor and the imaging lens, couples the light diffused by the object to the reference beam. The pattern recorded by the TV camera is then stored in a digital memory.
A speckle interferogram is generated arithmetically by subtracting two digitized speckle patterns.
If a squared difference is performed between two intensity speckle patterns, recorded at different states of the object, the fringe pattern can be described by ii?]
i (xi Y) = a (xi Y) + C(z, v) + C* (z, Y) (1)
with
C(xi Y)
= )b(xi Y) exP iiA§2(xi Y)1 (2)
where a (z, y) and b(z, y) describe background variation and local contrast of the pattern, respectively, i is the imaginary unit and the asterisk denotes the complex conjugate. The
interference phase A~2ix, y),containing the residual deformation, can be evaluated by Fourier
analysis
117, 18].
A Fourier transform of equation ii usually
117] gives a trimodal function. After a band-pass filtering and an inverse Fourier transform, the phase term is obtained as
1 iC(x, Y)1
/~l~(~~ Y~ " ~~~ ~~ (3)
ll ic(xi Y)1
where 11 denotes the real part and I the imaginary part. We filtered the signal in an asymmetric
way (taking only one lateral lobe), then the retrieved phase is correct only if the phase function is monotonic 11?,19]. As the phase is computed by an arc tangent function, its values are
within the range [-~, ~]. These discontinuities must be corrected by adding or subtracting the unknown multiple of 2~ to all points. A review of phase unwrapping algorithms can be found in literature [20].
Now, let us consider a light beam through a test section of length I. A phase variation A~2 is related to a refractive index variation An by
A~2 =
~~~ An (4)
where I is the wavelength.
The change in the refractive index of air is usually related to a temperature variation through
a factor approximately constant, if the temperature changes are small, the so-called Gladstone- Dale constant. The refractive index of air at 632.8 nm can be evaluated with greater precision by [21]
~ ~~~~~~ ~~ ~
~ l + 0.36818/x 10-2T ~~~
where T is in degrees Celsius. This equation is based on the Gladstone-Dale relation, with
wavelength dependence calculated according to Meggers and Peters and small corrections due to Tilton.
Hence
An
=
~'~~~~~~ ~ ~~
~
AT. (6)
(1 + 0.368184 x 10- T)
From equations (4) and (6) we easily obtain
~~ l.075152 x
10~~ ~ l
(l + 0.368184 x 10-2T)~ 2~l ~~ ~~~
1896 JOURNAL DE PHYSIQUE III N°9
Fig. 2. Electro-optic holography fringes relative to the central section of the plate The temperature of the plate was 325 + 0.2 K. Room temperature was 295 + 0.2 K
We note that the term in square brackets in equation (7) depends on temperature. In convective heat transfer problems, physical properties are usually evaluated at the so-called film temper- ature, that is at the mean temperature between the object temperature and the undisturbed fluid temperature.
In electro-optic holography, data treatment is inherently digital. Therefore, we can compute the term in square brackets in equation (7) at the mean film temperature in a first iteration.
The temperature determined pointwise in this first iteration can be used again in equation (7).
Usually, after two or three iterations the resulting change in
~~
will be negligible.
AT
3. Experimental Results and Discussion
As an example, let us consider steady laminar free convection on a horizontal aluminum plate (0.7 cm x 25 cm x 25 cm). The plate is maintained at a constant temperature of 325 ~ 0 2 K by pumping water from a constant temperature bath on one surface of the plate. The other side is exposed to quiescent atmospheric air at 295 + 0.2 K The hot surface (that is the surface
exposed to air) faces down, then the flow regime is always laminar. A chromel-constantan thermocouple sandwiched to the plate is used to monitor the surface temperature distribution.
Figure 2 shows ESPI fringes above a central section of the plate. The interferogram is
digitized in 512 x 512 x 8 bit data, with a magnification factor such that I pixel
= 40 x 10~~
m.
In laminar free convection on a plate, we may assume (neglecting the end effect) that the temperature variation AT is one-dimensional and normal to the plate. In this particular case,
a significant reduction of the speckle noise can be obtained taking an average operation over points presenting the same distance from the plate. Figure 3 shows temperature variation with
distance from the plate computed in one, two and three iterations
The accuracy of the proposed method depends on errors in plate and room temperature determination, plate length measurement and phase evaluation. Error in phase determination encloses computational errors, optical non linearities and electronic noise. In our case, compu-
tational errors (due to signal discretization and quantization by CCD) give the most relevant contribution. We assumed an error of i mm on the plate length measurement and an error of
1/20 on the phase determination [22]. The total error in temperature determination depends
on the distance from the plate, and was about ~0.4 K near the plate surface and ~0 57 K at
a distance of about 3 cm from the plate.
The presented system is relatively low cost but it has some limitations. One typical limitation
325
320
315
310
305
285
0 4 8 12 16 20
jmmj
Fig. 3. Temperature variation with distance from the plate computed in
one iteration (full line),
two (dotted line) and three iterations (dashed line)
in electro-optic holography is that the individual speckles must be resolved by the TV camera.
Then the mean speckle size must be equal to the size of a single pixel on the camera. This will optimize both the performance and the fringe visibility With a typical pixel size of
m~
10 pm,
a f-number of16 is necessary. Using relatively large f-numbers will give large speckles, thus
affecting the system performance in several ways. Firstly, the light intensity in the image
is reduced, thus reducing the signal dynamic unless a higher power laser and/or a higher sensitivity camera are used (with a much higher cost). A second consequence is that the speckles are clearly seen in the monitor, their signal-to-noise ratio is unity, therefore the fringe clarity is poor.
A further limitation in ESPI system is the spatial resolution of the camera. The number of
fringes which can be seen and analysed depends on the number of points of the interferogram
In fact, a minimum of about 20 speckles is required to resolve a fringe [12]. Using a typical detector array with 512 x 512 pixels, about 25 equally spaced fringes could be resolved In the present case, because of non linearity of refractive index distribution, fringes spacing is large
in regions of small gradient and small in region of high gradient of the refractive index, i.e.
near the plate. Then a suitable inspection area must be chosen in order to have the required 20 speckles per fringe. Future developments of ESPI systems could consider a larger inspection
area by using large area image sensors.
4. Conclusions
In this work we presented the application of electro-optic holography to temperature measure- ments in a typical problem of natural convection.
The proposed technique, combining the properties of digital speckle pattern interferometry
with the flexibility of optical fiber illumination, has the sensitivity of holographic interferometry
1898 JOURNAL DE PHYSIQUE III N°9
but allows to operate under difficult conditions. The major features of the technique are the ability to present correlation real time fringes displayed directly on a TV monitor and a full
digital data elaboration. Finally, this cheap system can easily operate in day-light by using a
simple interference filter.
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