Experiments in Fluids 31 (2001) 588595 Springer-Verlag 2001

2D temperature measurements in the wake of a heated cylinder using LIF

588

Abstract A technique is described to measure the instantaneous 2D temperature distribution in the wake of a heated cylinder using `laser-induced uorescence'. Rhodamine B, a uorescent dye, is used as a temperature indicator. The relation between uorescence intensity and temperature is determined by means of calibration experiments in the temperature range of 2035 C with an accuracy of 0.1 C. The temperature distribution behind the heated cylinder is well visible and can be measured with a high spatial resolution. Corrections for variation in laser energy and intensity distribution in the laser sheet have to be made to further improve the accuracy of the measuring method.

Introduction When a heated cylinder is exposed to a horizontal crossow, the induced temperature differences may have a large inuence on the occurring wake ow. The interaction between the two different sources of motion, forced and free convection, may result in enhanced mixing properties compared to the purely forced convection case. The mixing process is of interest in many applications, e.g. electronics cooling, where dispersion of heat and mass is a key aspect. Kieft et al. (1999) and Kieft (2000) investigated the effect of heat addition on the behaviour of the vortices behind a heated cylinder. In that study most information was obtained from 2D and 3D velocity measurements. Besides, 2D calculations on the wake ow offered detailed information on the instantaneous velocity and temperature elds. To be able to measure the temperature eld behind a heated cylinder, a non-intrusive measuring method with a high temperature resolution is aimed at. In the present study, a method based on laser-induced uorescence (LIF) is used, where temperature-sensitive uorescent dyes are excited by laser light. Nakajima et al. (1990) were one of the rst to use this technique to measure the temperature in one point. Sakakibara et al. (1993, 1997) used the technique to measure the 2D temperature eld in a therReceived: 3 January 2001/Accepted: 18 May 2001

mally stratied pipe ow and in the stagnation region of an impinging plane jet, while Coolen et al. (1999) measured temperature elds in a thermally driven cavity. Sakakibara and Adrian (1999) further developed this measurement technique and measured 3D temperature elds using two uorescent dyes as temperature indicators. Typically, the accuracy in the aforementioned studies is 1.5 C for a temperature range of 40 C or more. In the present study, the temperature range is about 5 C. Therefore the temperature eld should be measured with a higher accuracy than in the previous studies. Most of the aforementioned studies make use of a continuous argonion laser. In the present study, a pulsed Nd:YAG laser is employed because its typical wavelength is close to the wavelength of maximum absorptivity of the dye used. Due to the relatively large variation in pulse energy of the Nd:YAG laser, special attention is given to the pulse-topulse correction. LIF is based on natural uorescence of molecules and atoms which is induced by absorption of a photon. This absorption causes a transition from the ground state to an excited state. Part of the absorbed energy is re-emitted during spontaneous transition from the excited state to the ground state (uorescence). The uorescence occurs at a longer wavelength than absorption due to energy loss in the excited state. The uorescence intensity I (W m)3) emitted per unit volume can be described by the following equation, according to Berlman (1971) and Bindhu et al. (1996),

I Ie Cue

ke ; kf

H. J. Seuntiens, R. N. Kieft, C. C. M. Rindt (&) A. A. van Steenhoven Energy Technology Division Department of Mechanical Engineering Eindhoven University of Technology P.O. Box 513, 5600 MB Eindhoven, The Netherlands e-mail: C.C.M.Rindt@tue.nl

where Ie (W m)2) is the intensity of the excitation laser sheet, C (mol m)3) is the concentration of the dye solution, e (m2 mol)1) the molar absorptivity and u ()) the quantum efciency. The wavelength ratio ke/kf accounts for the energy loss in the excited state. For some organic dyes, the quantum efciency turns out to be temperature dependent, resulting in a temperaturedependent uorescence intensity. This dependence makes LIF useful for temperature measurements. In the present study, Rhodamine B has been selected as the uorescent dye, because of its high temperature sensitivity (23% per C). In Fig. 1, the absorption and emission spectra of Rhodamine B are shown. The absorption spectrum maximum of Rhodamine B dissolved in water is near 550 nm. From this gure it can be concluded that a Nd:YAG laser (k 532 nm) can be used for excitation. The emission spectrum has its maximum at about

Fig. 1. Absorption (- -) and emission () spectra of Rhodamine B for 20, 30, 40, 50, 60 and 70 C (Coolen et al. 1999). k 532 nm is the wavelength of the Nd: YAG laser

575 nm. As one can see, a higher temperature results in an overall decrease of the emission spectrum. In Sect. 2, the experimental setup used is described and the calibration experiments done to determine the relation between temperature and uorescence intensity are discussed. The temperature measurements behind the heated cylinder are discussed in Sect. 3. Here, special attention is given to the reconstruction of the temperature eld and the correction technique which is needed to compensate for intensity variations in the laser sheet. Finally, some conclusions are drawn.

at 29 Hz. One laser pulse has a duration of about 6 ns and a maximum energy of about 200 mJ. The pulse-to-pulse uctuation of the laser intensity is about 3%. The longterm variation (O(1 h)) of the laser intensity is about 5%. A beam attenuator is used to adjust the laser energy. By means of two glass plates part of the laser energy is split off. In this way, the pulse-to-pulse energy variation of the laser can be measured by means of a pyroelectric head. The pyroelectric head is able to measure the pulse energy at a maximum pulse rate of 1 kHz and has an accuracy of 4%. A negative lens is used to make a laser sheet. The laser sheet has a thickness of about 8 mm. In the test section water with Rhodamine B dissolved in it is present. The uorescence signal from the laser sheet is recorded by means of a CCD camera (Kodak Megaplus Camera, Model ES 1.0, 8 bits, 1,008 1,019 pixels) with a maximum frame rate of 29 frames per second. The signal from the CCD camera was stored using a frame grabber (Bitow Road Runner). In order to obtain synchronization between the camera and the laser, the camera was used to trigger the laser pulse. This means that exactly one pulse during the integration time of a frame is achieved. A colour lter (a holographic notch lter: %0% transmission for k 532 nm and %80% transmission for k 575 nm) is used to remove the scattered light of the laser beam out of the uorescence signal to be detected by the camera.

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Calibration experiments In order to measure temperatures, the relation between temperature and uorescence intensity has to be known. To determine this relation, calibration experiments are done. In the test section a vessel is placed, containing Rhodamine B dissolved in tap water with a concentration Experimental setup C 4.0 10)4 mol m)3. For this concentration, selfThe optical conguration used is shown in Fig. 2. The absorption can be neglected, according to Coolen et al. main objects in this setup are a Nd:YAG laser, a beam attenuator, an energy meter, a negative lens, a test section, (1999). The vessel contains 4 l of the dye solution. The water is rst boiled and then cooled to 35 C before the a colour lter and a camera. A pulsed Nd: YAG laser Rhodamine B is added. By means of a heater and a cooling (Spectra-Physics) is used to generate a laser beam. The laser emits light with a wavelength of 532 nm and operates system the temperature in the vessel can be varied. In order to have a uniform temperature, the water in the vessel was stirred continuously. In one calibration experiment, the temperature was rst decreased and then increased over a temperature range of 2035 C. At different temperatures three variables are recorded: the uorescence intensity I, the temperature T and the pulse energy of the laser Ep. The pulse energy of the laser is measured because the laser energy is changing about 5% in time during the experiment. Therefore, the intensity measured must be corrected for this change in laser energy. The measuring section recorded by the CCD camera has the dimensions 55 55 mm. At each temperature, 50 images are recorded at a rate of 5.8 frames per second. The uorescence intensity I is determined by taking the mean value of the intensity in one image averaged over the 50 images. Besides, the pulse energy Ep is measured at a rate of 5.8 Hz during 30 s. The mean  value of the pulse energy Ep is taken to correct for the change in laser energy. K-type thermocouples are used to measure the temperature. In Fig. 3, the relation between the corrected uoresFig. 2. The experimental setup cence intensity Icor and the temperature T is given for two

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Fig. 3. The corrected uorescence intensity Icor plotted against temperature T for two calibration experiments

Fig. 4. The relation between the normalized uorescence intensity Inorm and temperature T

calibration experiments. The differences in the absolute value of Icor for the two experiments occurs because a new Rhodamine B solution is used for each experiment. This means that the concentration of Rhodamine B in the vessel will slightly differ in the two experiments. Also the mean laser energy in the two experiments is not necessarily the same. However, differences in the concentration of Rhodamine B and the laser energy do not affect the relation between temperature and normalized uorescence intensity, as is shown by Nakajima et al. (1990). The relation between the corrected uorescence intensity Icor and the temperature T is approximated by a second-order least square t. From these two experiments, one calibration curve is constructed. To this end, the corrected uorescence intensity Icor is normalized at T 20 C. Out of the results of the two experiments one calibration curve Inorm(T) is constructed by approximating the relation between Inorm and T by a second-order least square t (Fig. 4). The calibration curve found is in good agreement with the relation found by Sakakibara and Adrian (1999). The accuracy of the calibration curve is 0.1 C (95% condence). In the case of the temperature measurements behind the heated cylinder, the inverse function of the calibration

curve T(Inorm) will be used. Once the uorescence intensity eld Inorm(x,y) in the region of interest is determined, the temperature eld T(x,y) can be found using the calibration function T(Inorm). The procedure to determine Inorm(x,y) is discussed in Sect. 3.2.

Temperature measurements behind a heated cylinder Measuring configuration The temperature measurements behind a heated cylinder are done in a water tank, shown in Fig. 5a, which has the dimensions (length width height) 500 cm 50 cm 75 cm. The experimental setup is basically the same as shown in Fig. 2, with the difference that the test section is replaced by the water tank. The windows of the water tank are made out of 15-mm-thick glass which has special demands with respect to thickness variations. These variations are not allowed to exceed 50 lm, to minimize lens effects caused by the translation of the camera along the test section's glass wall. The whole water tank is supported by a steel frame. In the setup, the cylinder with a diameter D 8.5 mm and length L 495 mm is kept in position by two perspex plates (see Fig. 5b). The plates are connected to a stiff

Fig. 5a, b. The water tank construction: a overview of the water tank, b conguration of the cylinder and measuring equipment

structure carrying the cylinder and measuring equipment. The carrier is translated along two guiding rails mounted on top of the water tank. The cylinder is heated using a rod heater with a maximum heat density of 8.0 W cm)2. More information about the setup can be found in Kieft et al. (1999). The optics used consist of a positive lens with focal distance f 200 cm and a negative lens with focal distance f )12.8 mm. The negative lens is used to create the laser sheet, while with the positive lens the thickness of the laser sheet can be installed. This is necessary because the laser beam has travelled over a distance of about 8 m from the laser head to the lens system. The measuring section recorded by the CCD camera has a length of 7.7 cm and a height of 7.4 cm and is situated immediately behind the cylinder. To reduce the spatial noise of the camera, the recorded images are divided in clusters of 6 6 pixels, resulting in a spatial resolution of 0.46 0.44 mm. About one week before the temperature measurements are done, the water tank is lled with tap water. The Rhodamine B is added a few days before the experiments. The water surface of the tank must be made free of dust particles and other contaminations, because they can disturb the intensity in the laser sheet. Before the actual measurements are done, it is veried whether the temperature of the water in the tank is uniform. This is done by measuring the temperature of the water at different positions in the tank using calibrated K-type thermocouples. The variation of the water temperature appears to be about 0.1 C.

is entering the measuring section from above. The intensity distribution shown is caused by the divergence of the laser light and by vignetting, caused by the lens system in front of the CCD camera. To correct for these disturbing effects it is necessary to normalize the uorescence intensity in each experiment. To this end, a reference uorescence intensity distribution Iref (x,y,Tref) has to be determined at a reference temperature Tref. Here, the reference eld is measured by moving the cylinder through the tank with velocity U0. The cylinder is not heated, so Tref equals the water temperature in the tank. Then 140 images of the uorescence intensity eld are recorded by the CCD camera at a frame rate of 4.84 frames per second. The reference uorescence intensity eld Iref(x,y,Tref) is determined by averaging over the 140 images taken. Then the cylinder is brought back to its original position. After about 2 h, when the water in the tank has come to rest again, the cylinder is heated to the desired temperature and moved through the tank with velocity U0. A total of 400 images of the intensity distribution behind the heated cylinder I(x,y,T) are recorded by the CCD camera at a frame rate of 4.84 frames per second. The normalized uorescence intensity Inorm(x,y) is found using the following equation,

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Inorm x; y Inorm Tref

Ix; y; T Ioff x; y ; Iref x; y; Tref Ioff x; y 2

Temperature reconstruction The temperature eld T(x,y) in the measuring section is proportional to the height of the uorescence intensity I(x,y,T). However, the uorescence intensity in turn is not only dependent on temperature, but also on the height of the excitation energy, on the position in the measuring section, on deformations due to the lens system in front of the CCD camera, etc. In Fig. 6 the measured uorescence intensity is given for a uniform temperature eld. The laser

in which Inorm(Tref) is the value of the calibration curve Inorm(T) at temperature Tref and Ioff(x,y) is the offset of the camera. The offset of the camera is the intensity the camera records when it is not illuminated and is about 1% of the uorescence intensity I(x,y,T). The term Inorm(Tref) is needed to correct for the difference in the normalization temperature in the calibration experiment (which is 20 C here) and the reference temperature Tref. When these temperatures are the same, Inorm(Tref) equals one. Using the calibration function T(Inorm), the temperature eld T(x,y) can now be determined. Equation 2 would hold if the energy output of the laser is constant. However, as mentioned before, this energy varies by about 3%. The most direct way to correct for this energy uctuation is to measure the pulse energy Ep, because the uorescence intensity I is proportional to the uctuating laser energy Ie (Eq. 1). The normalized uorescence intensity in Eq. 2 then has to be replaced by
H Inorm x; y : Inorm x; y

Ep;ref ; Ep;exp

in which Ep,ref is the mean laser energy for the reference eld and Ep,exp is the laser energy per pulse in case the cylinder is heated. However, the energy meter, a pyroelectrical head, has a pulse-to-pulse accuracy of 4%. This means that the error in the energy measurement is in the same order of magnitude as the uctuation in laser energy itself. Therefore, another correction method has to be Fig. 6. Distribution of the uorescence intensity in the measuring used. In the case of the measurements behind the heated section when no heat source is present and the temperature is cylinder, the temperature in part of the measuring section uniform. The rectangle shows the area in which the temperature remains uniform when the cylinder is heated remains uniform even when the cylinder is heated. This

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Fig. 7. Temperature distribution in the vortex street behind the heated cylinder

feature is used to correct for the uctuation in laser energy. In that part of the image where the temperature is uniform, the measured uorescence intensity I is proportional to the uctuating laser energy Ie. In Fig. 7, the specic area used in which the temperature remains uniform is given. For both the uniform temperature eld and the eld in case the cylinder is heated, the spatial mean uorescence intensity I is determined in that specic area. The ratio between these two mean values is used to correct for the variation in laser energy. With this correction made, the normalized uorescence intensity Inorm becomes

ref I H Inorm x; y : Inorm x; y  : 4 Iexp In this equation, ref is the mean uorescence intensity for I Inorm Tref ; 5 the reference eld and exp the mean uorescence intensity Fc x; y yT I Inorm x; y yT in case the cylinder is heated. Inorm Tref Fc x; y yB ; 6 Temporal variation of the intensity distribution Inorm x; y yB in the laser sheet The velocity of the cylinder and the temperature difference with Inorm(Tref) the value of the calibration function Inorm between the cylinder and the water are respectively set to at temperature Tref. The correction factor Fc(x,y) for the U0 1.54 cm s)1 and TH TC 20.5 C, resulting in a whole image is then constructed as a linear interpolation between the correction factors at the top and bottom, Reynolds number ReD 130 and a Richardson number RiD GrD/Re2D 1.5, with GrD the Grashof number. The taking into account the shift Ds between the proles,

temperature of the water is TC Tref 18.9 C and the cylinder temperature TH is 39.4 C. In Fig. 7, the measured temperature distribution in the vortex street behind the heated cylinder is given at a certain instant in time, determined with the method described above. When looking at the reconstructed temperature eld, temperature zones can be seen, although the real temperature is uniform outside the vortex street. The edges of the temperature zones have the same direction as the light in the laser sheet (the sheet is coming from above, see Fig. 5), implying that the error in the temperature eld is originating from intensity variations in the laser sheet. It appears that the light intensity distribution in the laser sheet when recording the referencence temperature eld Iref(x,y,Tref) differed from the light intensity distribution when recording the images of the temperature eld behind the heated cylinder I(x,y,T). This results in a systematic error in the measured temperature eld. In Fig. 8a, the reconstructed temperature proles at the top and bottom of the image shown in Fig. 7 are given. The proles are determined averaging over 6 pixels in width and 30 pixels in height at positions y 2.47 cm and y )2.47 cm. The reconstructed temperature proles have an oscillating course, whereas the real temperature is constant (Tref 18.9 C). It can be seen that the temperature distributions at the top and bottom are highly correlated (the correlation coefcient is 0.95). The temperature prole at the bottom of the image has shifted Ds 0.46 cm to the left. To eliminate the systematic error in the temperature eld, a correction is made on the normalized intensity eld Inorm(x,y). First, the proles of the normalized intensity are determined at the top and bottom of the image (Fig. 8b). With these proles, correction factors are derived at the top and bottom of the image,

Fig. 8a, b. Distribution of a temperature and b normalized intensity at the top and bottom of the temperature eld shown in Fig. 7

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Fig. 9. Temperature distribution in the vortex street behind the cylinder

  Dy H Dy Fc x Ds; y yT Fc x; y H H   Hy Dy Fc x Ds; y yB : H H

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In this equation, Dy yyB and H yTyB (see Fig. 8). When comparing the temperature and normalized intensity proles at the top and bottom of the images, it can be seen that the proles at the bottom are disturbed at the positions where the laser beam has crossed the warm blob (x 12 cm and x 5.57 cm). This is probably caused by the temperature eld in the warm blobs. The temperature variations in the blob result in a spatially varying refractive index n(x,y). The spatial variation of the refractive index then results in a so-called thermal lens effect. This effect deforms the excitation intensity eld Ie. This results in an error in the normalized intensity eld Inorm(x,y), especially in and beneath the warm blobs. The Fig. 10. Temperature distribution in the warm blob inuence of this effect on the accuracy of the temperature measurements is not investigated in the present study.

Results In Fig. 9 the temperature distribution in the vortex street is given. This is done for one period of the vortex-shedding process. The frequency at which the vortex-shedding process occurs is about f % 0.3 Hz, meaning that the Strouhal number of the process is St fD/U0 % 0.17. The cylinder is situated at y/D x/D 0. At t 0 a new blob develops at the upper side of the cylinder. This blob grows until it is shedded off the cylinder. It can be concluded that the blob which develops at the upper side of the cylinder contains more heat than the lower blob, resulting in a higher temperature of the upper blob. This is in agreement with the results of the numerical simulations done by Kieft (2000). The temperature in the center of the upper blob is about 5 C higher than its environment, while the centre of the lower blob is about 3 C higher than its environment. The dimensions of the blob are in the same order of magnitude as the cylinder diameter D. The temperature eld at t 0 is the corrected temperature eld of the distribution shown in Fig. 7. In Fig. 10, the detailed temperature distribution in the warm blob at t 0 is shown. In this case, the image has been divided in clusters of 3 3 pixels, resulting in a spatial resolution of 0.23 0.22 mm. For this smaller spatial resolution, the temperature still is monotonous decreasing when moving away from the centre of the blob. It can be seen that the temperature eld can be measured with a high spatial resolution. The temperature resolution is 0.4 C, which is determined by the 8-bit CCD camera used. When using a 12-bit camera, the temperature resolution can be improved. The maximum resolution is probably limited to about 0.1 C, because then other errors become relatively more important like the correction used for the temporal variation of the intensity in the light sheet and errors in the determination of the calibration curve. The temperature in the centre of a warm blob as function of the downstream position is determined for ve successive warm blobs and shown in Fig. 11. It can be seen

Fig. 11. The maximum temperature in the warm blob as function of the downstream position

that the temperature measured decays until x/D % 5. The initial temperature in the centre of the warm blobs varies by at most 0.8 C. This variation in blob temperature is probably caused by a disturbance in the ow around the cylinder, resulting in a varying heat transfer from the cylinder to the warm blob. The course of the temperature decay seems to be the same for all blobs until x/D % 5. After x/D % 5, the temperature measured becomes constant or even increases. It is possible that in this area the thermal lens effect is substantial, resulting in an error in the temperature eld measured. Another possibility is that the temperature eld has become (partly) 3D.

Conclusions It has been demonstrated that the instantaneous 2D temperature eld behind a heated cylinder can be measured at a high spatial resolution using LIF. First, the relation between temperature and uorescence intensity has been determined in the range 2035 C. The calibration curve obtained has an accuracy of 0.1 C and is in good agreement with the curve found by Sakakibara

and Adrian (1999). Because the uorescence intensity is not only dependent on temperature, a normalization procedure is used. Because the pulse-to-pulse energy of the laser varies by 3%, a correction is made for this effect. Besides, the intensity distribution in the laser sheet also changes in time. Therefore, an extra correction step is made. To avoid these correction steps, a laser should be used which is much more stable, for example, a continuous argon-ion laser. The temperature eld behind the heated cylinder is well visible and is measured with a temperature resolution of 0.4 C. When using a 12-bit camera instead of an 8-bit camera, the temperature resolution can probably be improved to 0.1 C. From the maximum temperature in the warm blob as function of the downstream position, it can be seen that downstream of the position x/D % 5 deviations occur in the temperature measured. If this originates from refraction of the laser light passing through the thermal eld, the technique used by Sakakibara and Adrian (1999) could be used to improve the temperature measurements. In that case, two uorescent dyes whose emission intensities depend differently upon temperature have to be used as temperature indicators, as the ratio between the two uorescence intensities is nearly independent of the incident-light intensity. However, in addition, 3D ow effects and transition phenomena may occur from that position, which is the topic of future research.

Berlman IB (1971) Handbook of uorescence spectra of aromatic molecules, 2nd edn. Academic Press, London Bindhu CV; Harilal SS; Varier GK; Issac RC; Nampoori VPN; Vallabhan CPG (1996) Measurement of the absolute uorescence quantum yield of rhodamine B solution using a dualbeam thermal-lens technique. J Phys D 29: 10741079 Coolen MCJ; Kieft RN; Rindt CCM; Steenhoven AA Van (1999) Application of 2D LIF temperature measurements in water using a Nd: YAG laser. Exp Fluids 27: 420426 Kieft R (2000) Mixed convection around a heated cylinder. Ph. D. Thesis. Eindhoven University of Technology, The Netherlands Kieft RN; Rindt CCM; Steenhoven AA Van (1999) The wake behaviour behind a heated horizontal cylinder. Exp Therm Fluid Sci 19: 183193 Nakajima T; Utsunomiya M; Ikeda Y (1990) Simultaneous measurement of velocity and temperature of water using LDV and uorescence technique. In: 5th Int. Symposium on Application of Laser Techniques to Fluid Mechanics, 1990, Lisbon, Portugal Sakakibara J; Adrian RJ (1999) Whole-eld measurement of temperature in water using two-color laser-induced uorescence. Exp Fluids 26: 715 Sakakibara J; Hishida K; Maeda M (1993) Measurements of thermally stratied pipe ow using image-processing techniques. Exp Fluids 16: 8296 Sakakibara J; Hishida K; Maeda M (1997) Vortex structure and heat transfer in the stagnation region of an impinging plane jet (simultaneous measurements of velocity and temperature elds by digital particle image velocimetry and laser-induced uorescence). Int J Heat Mass Transfer 40: 31633176

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