GLOBAL RAINBOW REFRACTOMETRY FOR DROPLETS TEMPERATURE MEASUREMENT

Transcription

1 The 11 th International Topical Meeting on Nuclear Reactor Thermal-Hydraulics (NURETH-11) Paper: 081 Popes Palace Conference Center, Avignon, France, October 2-6, ABSTRACT GLOBAL RAINBOW REFRACTOMETRY FOR DROPLETS TEMPERATURE MEASUREMENT Lemaitre Pascal (1), Porcheron Emmanuel, Nuboer Amandine, Malet Jeanne, Vendel Jacques, Bouilloux Laurent Institut de Radioprotection et de Sûreté Nucléaire DSU/SERAC, BP 68, Gif-sur-Yvette Cedex, France. Phone: , Fax: , mailto : pascal.lemaitre@irsn.fr Gérard Grehan UMR 6614 CORIA, Laboratoire d Electromagnétisme et Systèmes Particulaires Site Universitaire du Madrillet, Avenue de l'université BP 12, Saint Etienne du Rouvray Cedex, France. mailto : Grehan@coria.fr In order to study the heat and mass transfers between the spray droplets and the atmosphere for thermal-hydraulic conditions representative of a severe accident in a Pressure Water Reactor, the French Institute for Radioprotection and Nuclear Safety (IRSN) developed the TOSQAN facility. This paper is devoted to present the development and the qualification of the global rainbow refractometry in order to measure falling droplets temperature. KEYWORDS Optical diagnostics, droplets temperature, global rainbow refractometry. 1. INTRODUCTION During the course of an hypothetical severe accident in a nuclear Pressure Water Reactor (PWR), hydrogen can be produced by the reactor core oxidation and distributed into the reactor containment according to convection flows, water steam wall condensation and interaction with the spraying droplets. In order to assess the risk of detonation generated by a high local hydrogen concentration, hydrogen distribution in the containment has to be known. The TOSQAN experimental program has been created to simulate typical accidental thermal-hydraulic flow conditions of the reactor containment and to study different phenomena such as water steam condensation on droplets in presence of non-condensable gases. This large experimental facility (7 m 3 ) is suitable for optical diagnostics and the PIV, LDV and Spontaneous Raman Scattering are already operational on it (Porcheron et al., 2002). In order to measure droplet temperatures, different non-intrusive techniques were envisaged like LIF (Lavieille, 1997), infrared thermography, and global rainbow refractometry. Because of TOSQAN geometrical conditions, we adopted the last one. The aim of this work is to present this optical diagnostic (van Beeck, 1997 ; Roth, 1991), to measure the mean temperature of falling droplets. This technique is now implemented on the TOSQAN facility. This work is divided into four parts. The first one is devoted to explain the principle of the technique. 1 Corresponding author

2 The 11 th International Topical Meeting on Nuclear Reactor Thermal-Hydraulics (NURETH-11) 2/13 The second one will present the code we developed and the simulations we realized in order to measure the effect of different parameters on the temperature and diameter measurements (Lemaitre et al., 2002). The third part will present our experimental set-up, and finally we will present our results on the global rainbow technique. 2. PRINCIPLE OF THE TECHNIQUE The rainbow is a phenomenon that occurs for example when a single droplet intercepts a laser beam (figure 1). The standard rainbow refractometry is a non-intrusive technique for measuring size and temperature of a single droplet (van Beeck, 1997). This technique is based on the detection of the rainbow issued from the interference between one time internally reflected rays and externally reflected ray (figure 1). This technique suffers of major problems related to temperature gradients inside the droplet (Corbin et al., 1995), droplet non-sphericity (van Beeck et al., 1995) and, especially for small particles, the ripple structure (issued from the interference between internally and externally reflected rays, figure 2) that strongly disturbs the rainbow pattern. It is to overcome the last two problems that van Beeck introduced the global rainbow refractometry. The principle of the technique is to superimpose the rainbow pattern issued from about a hundred droplets (van Beeck et al., 2002), so that the ripple structure totally disappears. This phenomenon was first observed by Roth (1991) for a single droplet with diameter variations ; the nonspherical droplets (as far as they are randomly oriented) will interfere destructively and then they will create a uniform background, so that they will not disturb the measurement anymore. Incident wave τ rg Droplet Externally reflectedray Rainbow pattern region Internally reflected rays Rainbow ray? θ rg Figure 1 : Rainbow phenomenon Figure 2 : Standard rainbow pattern (Beeck, 1997) 3. SIMULATIONS OF THE GLOBAL RAINBOW To have a good understanding of the global rainbow pattern and so to be able to invert it to a mean temperature, we made a Fortran program to compute the global rainbow pattern. As mentioned before, the global rainbow is not sensitive to the ripple structure because small variations in the droplets diameter totally dam this ripple structure. As a consequence, the Airy theory, which takes into account the interferences between internally reflected rays, is suitable to compute the light scattered by a single 2 droplet; this theory allows us to compute the scattered intensity Ω rw as a function of the scattering angle θ and the particle diameter d (equation 1 and 2).

3 The 11 th International Topical Meeting on Nuclear Reactor Thermal-Hydraulics (NURETH-11) 3/13 Ω 1/3 ( 12 ) Ai ( 12 ) 2 2 1/3 2 3 ( ) cos ( ) 2 rw z = zη η dη = 2 z ² ² 0 π π π (1) 1/3 16 tan τ rg sin ² τ rg ² z ( θ) = ( θ θ rg ) d 180 λ² (2) π The angles θ rg and τ rg are represented on figure 1. So, we compute the global rainbow by summing the light scattered by every single droplet (equation 3). i max 7 / 3 Globow( θ ) = Ω ²( di, θ ) di (3) The d 7/ 3 i factor describes the dependency of the scattered light intensity to the droplet diameter. Therefore, as long as all the droplets are perfectly spherical, we can compute the global rainbow pattern. Using this program, we can simulate the effect of droplets temperature on the global rainbow. The simulation of the global rainbow scattered from droplets of the same granulometry at different temperatures is presented on figure 3. i 1,2 1 I rw /I max Irw/Imax 0,8 0,6 0,4 T = 293 K T = 313 K T = 323 K 0, θ ( ) Figure 3 : Effect of droplets temperature on the global rainbow pattern We can see on figure 3 that the droplets temperature increase induces a translation of the global rainbow towards small angles. I/I max σ g = = ,2 1 0,8 0,6 θ rg 0,4 0, Scattering angle (degree) d = 300 mm δ = 300 µm d = mm δ = 100 µm δ = d = 50 µm mm Figure 4 : Global rainbow simulations Figure 5 : Non-sphericity effect on the rainbow We can see on figure 4 that for different log-normal distributions the different global rainbow patterns are superimposing at the geometrical rainbow angle θ rg which is very close to the first inflexion point of the global rainbow.

4 The 11 th International Topical Meeting on Nuclear Reactor Thermal-Hydraulics (NURETH-11) 4/13 Thus, as long as all the droplets forming the global rainbow are perfectly spherical, we can deduce the droplets averaged temperature by searching the angular position of the first inflexion point of the global rainbow, or more precisely using equations 4 and 5 (van Beeck et al., 2002). 3/ 2 ( θ ) D = λ θ (4) Airy inf1 inf 2 2/3 θ rg = θinf λ (5) DAiry To take into account the impact of nearly spherical droplets C η = < 1.04%, Figure 5 on the B scattered global rainbow, we can compute their contribution using the Moebius theory. This theory assumes that the rainbow pattern issued from a non-spherical droplet will be shifted of a θ rg quantity computed using equation 6. So to take this effect into account, we introduce this θ rg shift into equation 2. 3 C B cosτ cosτ rg rg θ 16 sin arccos rg = cos 2 + rg C B m m ( θ ψ ) (6) In our application of the global rainbow refractometry, all the droplets in the probed volume will not have the same temperature, moreover it will exist a relationship between the droplets size and temperature. We now interest in simulating the global rainbow scattered from a spray with a log-normal distribution (representative of the spray we will experimentally investigate) supposing an arbitrary relationship between droplet size and refractive index, and we interest in interpreting the meaning of the deduced mean temperature (figure 6). 1,2 1 Irw/Imax 0,8 0,6 0,4 θ inf1 θ inf2 m = d <m> 0, scattering angle θ ( ) Figure 6 : Effect of an arbitrary size temperature relationship on the temperature deduced We can see on this simulation that if we suppose that all droplets have the same refractive index equal to <m> (<m> is computed using equation 7), the simulated global rainbows are superimposing around θ inf1 and θ inf2 which are the characteristic angles used for the inversion, thus, the refractive index deduced from such global rainbow will be equal to < m >.

5 The 11 th International Topical Meeting on Nuclear Reactor Thermal-Hydraulics (NURETH-11) 5/13 The m( d). f( d). d 7/3dd 0 < m >= (7) f( d) d 7/3dd 0 7 / 3 d factor describes the dependency of the scattered light intensity to the droplet diameter (as in equation 3). This result means that the deduced temperature is more influenced by the biggest droplets. 4. EXPERIMENTAL SET-UP Our experimental set-up sketched on figure 7 is composed of a laser beam issued from an argon laser (λ = nm) and transmitted via a monomode optical fibre. Measurements are achieved on a full cone spray generated by a nozzle (UniJet TG03, Spraying System company) at 0.20 m from the injector and at a water pressure of Pa. The optical set-up for global rainbow collection is composed of two large diameter planoconvexe lenses, a camera and a pinhole. The first lens has a 1 m focal length and is placed at 1m from the probed volume, the second lens placed just behind the first one has a 0.25 m focal length. The pinhole is situated at the image plan of this second lens; this pinhole allows us to spatially select a short volume of measurement and so to avoid an angular spread of the global rainbow. To calibrate the magnification factor of the camera, a millimetre transparent paper is placed on the first lens. So, we deduce the relationship between the pixel number and the scattering angle θ. To make sure that there are enough droplets in the probed volume, for a statistically representative sample of the spray droplets, we achieve a temporal summation of the signal. Nozzle Monomode optical fiber Lens 1 Lens 2 42 Camera Pinhole Figure 7 : Experimental set-up This nozzle has been characterized by laser sheet visualization (figure 8).

6 The 11 th International Topical Meeting on Nuclear Reactor Thermal-Hydraulics (NURETH-11) 6/13 Figure 8 : Visualization of spray of the TG03 injector Then, we achieved P.D.A. measurements to characterize the granulometry generated by this nozzle (figure 9). 140 Diameter ( µm) D10 D D32D radial position (cm) Figure 9 : Droplet size profile of the TG03 injector at 20 cm from the nozzle using PDA. 5. GLOBAL RAINBOW EXPERIMENTAL RESULTS Using this experimental set-up, we acquire two-dimensional images of the global rainbow (figure 10). In order to eliminate the high frequencies due to the noise and so to have a better signal quality, first we achieve a FFT (Fast Fourier Transform) of the collected signal, then we eliminate the high frequencies and finally we calculate the inverse FFT (figure 11).

7 The 11 th International Topical Meeting on Nuclear Reactor Thermal-Hydraulics (NURETH-11) 7/13 1,2 1 θmax 0,8 I rw /I max 0,6 θinf1 θinf2 0,4 θrg 0, pixel Figure 10 : Global rainbow pattern Figure 11 : Filtered global rainbow Then, we make a comparison of the mean droplets temperature measurement using the global rainbow refractometry with another technique, at different droplets temperatures. Our only issue was to achieve global rainbow measurements at 20 cm from the nozzle with different injection temperature (from 293 K to 360 K), and to measure the mean droplet temperatures by collecting the water spray within an isolated vessel placed at the probed volume and measuring its temperature with a thermocouple (Lemaitre et al. 2003). Then, we plot the pixel number of the first inflexion point of the global rainbow versus this measured temperature (figure 12). This result is important because theoretically the relationship between θ rg and the droplet temperature is linear between 293 K and 307 K. Inf1 (pixel) T measured (K) Figure 12 : Experimental relationship between the position of the first inflexion point and the mean droplet temperature measured In order to improve our inversion method, we could apply the algorithm proposed by Vetrano (2002), which consists in finding all spray parameters of the model that minimise the difference between the experimental and the simulated global rainbow, and so to avoid mistakes on temperature measurement mainly due to droplets non-sphericity.

8 The 11 th International Topical Meeting on Nuclear Reactor Thermal-Hydraulics (NURETH-11) 8/13 6. PRESENTATION OF THE TOSQAN FACILITY The TOSQAN experiment (figure 13) consists in a closed cylindrical vessel (7 m 3 volume, 4 m high, 1.5 m internal diameter) into which steam is injected by a vertical pipe located in the central part of the enclosure. The spray injection is achieved using a nozzle located in the upper part of the dome. This nozzle is vertically translatable in order to allow measurements at different distances from the injection. The walls of the vessel are thermostatically controlled. Optical accesses are provided by 14 overpressure resistant viewing windows permitting non-intrusive optical measurements along an enclosure diameter at 4 different levels. A full description of the TOSQAN experiment and of the optical diagnostics implemented on it, is presented in a companion paper (Porcheron et al. 2004). Nozzle Droplets temperature measurements Viewing windows 1.5 m 1.5 m 4 m Pipe injection for water steam and seeding Figure 13 : Scheme of the TOSQAN experiment The implementation of the global rainbow refractometry on this experiment is now going to be presented. It is important at this step of the paper to remind the angular sensitivity of the technique : an error of 0.1 on the measurement of the geometrical rainbow angle θ rg leads to a 5 K mistake on the droplets temperature deduced.

9 The 11 th International Topical Meeting on Nuclear Reactor Thermal-Hydraulics (NURETH-11) 9/13 7. IMPLEMENTATION OF THE GLOBAL RAINBOW REFRACTOMETRY ON THE TOSQAN EXPERIMENT We now aim at achieving global rainbow measurement within the TOSQAN experiment (figure 13). The principal constraint is related to the fact that TOSQAN is equipped with viewing windows for 90 measurements. Thus, to respect the constraint of 138 between the emission and the collection, a mirror is placed in the vessel, in front of the transverse viewing window (figure 14). This mirror is assembled on an engine enabling this mirror to carry out a rotation around its axis with a precision of thousandths of degrees. The collection set-up (figure 15) is exactly the same one as illustrated on figure 7 and that we previously qualified on optical table. This collection set-up is assembled on a rail equipped with an engine allowing the rotation of this entire rail around a vertical axis passing through the centre of the viewing window (figure 14). Mirror Measurement volume Viewing window Lens 1 Lens 2 Spatial filte r Camera PC Figure 14 : Transversal overview of the TOSQAN experiment and its optical set-up for global rainbow measurement With this optical set-up, we are able to acquire global rainbow images with the same quality as the ones acquired with the set-up sketched on figure 7, on optical table. To measure the effect of the viewing windows on the global rainbow measurement, we compared the global rainbow images collected with and without any viewing windows. The only effect of the viewing window is to absorb 30 % of the scattered intensity, and so to reduce the signal upon noise ratio but it does not disturb the angular repartition of the scattered intensity. Laser emission Camera Optical rail TOSQAN viewing window First lens Second lens Spatial filter Figure 15. Picture of the TOSQAN set-up

10 The 11 th International Topical Meeting on Nuclear Reactor Thermal-Hydraulics (NURETH-11) 10/13 To qualify this set-up we inject a water spray at a known temperature in a gas at the same temperature. We use the global rainbow experimental set-up presented above to measure the droplets temperature during their fall. The possible heat absorption due to the interaction between the continuous laser light (350 mw) is considered negligible, thus the droplets measured temperature should be equal to the water injection temperature. Our experimental results and the associated standard deviations are related on table 1. We notice a good agreement between the droplets temperature measured using the global rainbow refractometry and the gas temperature, which is assumed to be equal to the droplets temperature. Water temperature at the injection (K) Gas temperature (K) Droplet global rainbow temperature measured (K) 338 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 2 Table 1 : Experimental result for droplets temperatures Using these experimental data, we compare on figure 16 the droplets temperature measured using the global rainbow refractometry to the expected droplets temperature. The expected droplets temperature is the average between the droplets temperature and the gas temperature. The analysis of the figure 16 shows a good validation of the rainbow measurements achieved on TOSQAN. 352 Experimental validation 350 Droplet Temperature (K) Experimental measurement Theoritical droplets Droplet tempearture temperature T TOSQAN (K) Figure 16 : Validation of Rainbow measurements

11 The 11 th International Topical Meeting on Nuclear Reactor Thermal-Hydraulics (NURETH-11) 11/13 8. DROPLET HEATING MEASUREMENTS INSIDE TOSQAN Using this experimental set-up, we measure the droplets heating during their fall in order to characterize the condensation process. Figure 17 illustrates the averaged droplets temperatures measured using the global rainbow refractometry as a function of the distance from the nozzle. The initial thermal-hydraulic conditions of this test are presented on table 2. The gas is initially composed of Pa of water steam and Pa of dry air at 393 K. The spray is injected with a mass flow rate of 30 g.s -1 and 298 K using a TG_3.5 nozzle. The measurements are achieved during pressure equilibrium. During these measurements, the steam partial pressure is 1.22 Pa and the average gas temperature is 380 K. A complete presentation of all the measurements achieved during a TOSQAN test and their thermalhydraulic interpretations are presented in a companion paper (Porcheron et al., 2004). P steam (Pa) P air (Pa) T gas (K) Q inj (g.s -1 ) T inj (K) Table 2 : Initial thermal-hydraulic conditions of the test 380 Droplet temperature (K) Distance from the injection (cm) Figure 17 : Droplets temperatures vertical profile The figure 17 shows a very strong droplets temperature increase during the ten first centimeters bellow the injection nozzle. This heating is mainly due to the steam condensation on the droplets. Fifteen centimetres after the injection, the droplets temperature stabilizes at about 375 K, this phase corresponds to the droplets vaporization.

12 The 11 th International Topical Meeting on Nuclear Reactor Thermal-Hydraulics (NURETH-11) 12/13 9. CONCLUSION We have developed the global rainbow refractometry upon the TOSQAN experiment in order to measure droplets heating on a real spray in thermal-hydraulic conditions representative of a hypothetical nuclear accident. The experimental set-up implemented on TOSQAN has been optimized and qualified on optical table. To be able to invert experimental global rainbow images and to qualify the global rainbow performances to measure droplet mean temperature, we have developed a simulation program. Now, we are able to measure droplets temperature variations using non-intrusive techniques in hostile environments. This set-up can be implemented on others experiments to characterize heat and mass transfers. List of symbols Ai D 10 D 32 Globow m P PDA Q T δ θ σ η λ Airy function Arithmetic mean diameter Sauter mean diameter Global rainbow intensity refractive index Pressure Phase Doppler Anemometry Mass flow rate Temperature Mean diameter of the log normal distribution Scattering angle Standard deviation Sphericity factor Wavelength of the laser beam Subscripts gas Inf1 Inf2 inj rg Relative to the gas Relative to the first inflexion point Relative to the second inflexion point Relative to the injestion Relative to the geometrical rainbow

13 The 11 th International Topical Meeting on Nuclear Reactor Thermal-Hydraulics (NURETH-11) 13/13 REFERENCES AND CITATIONS Porcheron E., Thause L., Malet J., Cornet P., Brun P., Vendel J Simultaneous application of Spontaneous Raman Scattering and LDV / PIV for steam / air flow characterization. 10 th International Symposium on Flow Visualization, Kyoto, Japan. Lavieille P Etude expérimentale du comportement aérothermique de gouttes en écoulement, réactif ou non, par utilisation de fluorescence induite par laser à deux couleurs. Ph.D - thesis, Université Henry Poincaré de Nancy I. van Beeck J.P.A.J Rainbow phenomena, developpement of laser based non intrusive technique for measuring droplet size, temperature an velocity. Ph.D - thesis, Eindoven University of Technology, ISN Corbin F., Garo A., Gouesbet G., Grehan G Réfractométrie d arc-en-ciel : application au diagnostic des gouttes avec gradient d indice. Recueil des actes du 5 e congrès Francophone de Vélocimétrie Laser. Rouen, France, E1.1 - E.1.80 van Beeck J.P.A.J., Riethmuller M. L., Nonintrusive Measurements of Temperature and Size of Single Falling Raindrops. Applied optic 34, pp : Roth N., Andens K., Frohn A., Refractive-Index Measurement for the Correction of Particle sizing methods. Applied optic 30 pp : van Beeck J.P.A.J., Giannoulis D., Zimmer L., Riethmuller M. L., 2002, Global Rainbow thermometry for average temperature measurement of spray droplet. 10 th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon. Porcheron E., Lemaitre P., Malet J., Nuboer A., Bouilloux L., Vendel J Water interaction with air-steam mixtures under containment spray conditions : experimental study in the TOSQAN experiment. 11 th International Topical Meeting on Nuclear Reactor Thermal-Hydraulics, NURETH 11, Avignon, France. Lemaitre P., Grehan G., Porcheron E., Malet J., Cornet P., Brun P., Vendel J Global rainbow refractometry development for droplet temperature measurement in hostile environment. 9 th International Conference on Liquid Atomization and Spray Systems, Sorrento, Italy. Vetrano M.R., van Beeck J.P.A.J. Riethmuller M. L Validation expérimentale de simulation par la méthode globale par arc-en-ciel. 8ème Congrès Francophone de vélocimétrie laser, Orsay, France.