Calibration of a planar laser induced fluorescence technique for use in large scale water facilities

Measurement 46 (2013) 2597–2607

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Calibration of a planar laser induced fluorescence technique for use in large scale water facilities Luis A. Torres, Brian A. Fleck, David J. Wilson, David S. Nobes ⇑ Department of Mechanical Engineering, University of Alberta, Edmonton, Alberta, Canada T6G 2G8

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Article history: Received 10 February 2013 Received in revised form 11 April 2013 Accepted 23 April 2013 Available online 15 May 2013 Keywords: Planar laser induced fluorescence Fluid mixing Co-flowing jet Calibration Image correction Powell lens

a b s t r a c t A calibration process for planar laser induced fluorescence (PLIF) is presented and employed to investigate the mixing field of a co-flowing jet in a water channel flow. The calibration technique uses individual calibration curves for each pixel in the image array that correct for the non-uniformities of the laser sheet, optics and digital sensor and account for parameters that affect fluorescence efficiency of the dye. A unique commercial optic is introduced into the optical train to generate a thin laser sheet with an approximately uniform laser intensity distribution. The performance of the calibration procedure is investigated by analysis of the calibration data and through the investigation of a coflowing jet. The results compare well with the results documented in the literature for this flow field. The work shows that the simple approach designed specifically for application in large-scale facilities is suitable for calibration of PLIF style techniques. Ó 2013 Elsevier Ltd. All rights reserved.

1. Introduction In industrial applications, jets are often used to introduce and control the mixing of one fluid into another. Jets in a co-flow have been extensively studied experientially and numerically, with only a small sample of the existing literature cited here [1–5]. Predominately the velocity field has been investigated with the aim to develop simple scaling models of the flow. An understanding of the scalar field of concentration is important when investigating a mixing process, though this is difficult to determine when the scale of the jet flow, the flow field of interest or flow facility itself is large. A useful and powerful technique for studying turbulence and mixing in free shear flows such as jets is laser induced fluorescence (LIF) [6] and its planar variant (PLIF) [7] which are spectroscopic techniques commonly used in quantitative measurements of concentration. In the PLIF process, a fluorescent dye is used as a fluid tracer and a laser is used to excite the dye in a plane using a laser sheet. ⇑ Corresponding author. Tel.: +1 780 492 7031; fax: +1 780 492 2200. E-mail address: [email protected] (D.S. Nobes). 0263-2241/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.measurement.2013.04.066

As the dye de-energies from its excited state, fluorescing photons are emitted that are captured by a 2D imaging sensor. The number of photons collected is correlated to the concentration of the dye in the marked fluid and a 2D image of the concentration field is generated. The earliest works demonstrated the applicability of LIF to obtain quantitative information of the scalar concentration field [6–8] and PLIF has become popular within the fluid dynamics community. It has been commonly used in qualitative and quantitative analyses of mixing and of the structures and dynamics of jets [9] and shear layers [10]. Overviews of the LIF/PLIF technique [6,11] have highlighted that the main factors controlling the fluoresced light intensity If(i,j) at a location (i,j) in an image are,

If ði;jÞ ¼ f ðIlði;jÞ ; C ði;jÞ ; vði;jÞ Þ

ð1Þ

where Il(i,j) is the local intensity of the fluorescing laser, C(i,j) is the local concentration of the fluorescing dye and v(i,j) is a parameter that captures phenomena that affect the efficiency of the fluorescence of the dye. Properties of the dye, such as extinction efficiency, laser saturation, temperature and pH dependence affect the overall performance of the technique. In previous investigations the fluorescence

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intensity of the dye has also been found to have a dependence on the mixing characteristics of the dyed flow [12– 15]. This dependence is related to the susceptibility of a dye to thermal blooming and photo-bleaching processes that are influenced by laser intensity, dye concentration, and the geometry of the measured volume [12–15]. Additionally, Crimaldi [11] showed that the method used to generate the laser sheet has a significant impact on the quality of the image collected. The performance of the detector in terms of quantum efficiency, response across the 2D array and noise characteristics have a significant impact on the counting of fluoresced photons. This brief review highlights that every component of a PLIF system needs to be considered when attempting to make quantitative scalar measurements. An important part of the experimental PLIF procedure therefore is the determination of suitable calibration and data correction processes [6,11,12–15]. Several works have described different correction and calibration processes to obtain scalar concentration from fluorescence intensity [16–18]. The most common method is to obtain the constants that relate fluorescence intensity with laser intensity and dye concentration through the use of the PLIF system in situ on a sample of known concentration. This method requires maintaining the same known concentration of dye at every location within the interrogation region. Consequently, all fluid for the complete flow system will also be required to have the same dye concentration, independent of the scale of the system. Other works have identified aspects of the PLIF approach that should be addressed to obtain accurate measurements. Ferrier et al. [18] proposed a correction process for the attenuation of the laser through the region-of-interest that requires the determination of all correction parameters before every experiment and for every scan-line in the image array. A scan-line is defined as the row of pixels that is parallel to the direction of a laser ray. Ferrier et al. [18] also suggested a method to correct images for the vignette error associated with the imaging optics. This method also included a correction for errors that accumulate when converting the captured signal to a digital signal. Diez et al. [19] showed that some geometrical considerations could be used to correct images, due to the variation of the light intensity distribution in the laser sheet. The recent work of Crimaldi [11] describes a relatively simple image processing procedure that is an extension of the algorithms used by Crimaldi and Koseff [20], Prasad and Sreenivasan [21], and Koochsfahani et al. [22] and requires the calculation of parameters such as an attenuation coefficient and a concentration constant. While the above methods have been shown to provide quantitative scalar data, these approaches are difficult to implement in large scale facilities. As an example, in a large scale water channel or flume facility, the basic methodology would call for the seeding of the entire facility with a uniform known concentration of dye and this would need to be maintained at a constant temperature and pH during the calibration. The facility would then also need to be flushed to allow the experiment to continue. This requires a significant amount of time to exchange and de-gas purified water to be used in the experiment.

The aim of the current study is to develop a process that would allow the calibration of a PLIF system in situ in a ‘‘large’’ scale water facility. A PLIF system is described along with the important features of the flow facility. A detailed description of the calibration method and an assessment of important parameters are outlined. This is followed by a brief investigation of the scalar mixing field of a co-flowing jet. The co-flowing jet system is used to highlight the performance of the calibration process by comparing results with current understanding of this flow field and results that have been presented in the literature. 2. Experimental setup The calibration process was developed experiments to be carried out in a closed loop water channel facility that has been extensively used in the past to investigate atmospheric boundary layers and jets [23–26]. A schematic of the facility is shown in Fig. 1 and depicts a section of the channel with a co-flowing jet nozzle located on its centerline. The channel is 5.24 m long by 680 mm wide and 470 mm deep with glass sides and bottom for complete optical access to the entire test section. It has a return section and two pumps for general water flow placed in between an inlet and exit plenum that were designed to control flow profiles and water height in the working section and has a total water volume of 5000 l. Refreshing this volume is a 2–3 day process to allow the system to drained, be re-filled and have enough time to pass to allow it to de-gas. A uniform grid was placed at the inlet of the water channel built with flat stainless steel bars of 19.2 mm  5 mm with a total open area of 56% with a mesh spacing of 76.2 mm. This grid turbulence generates a near uniform velocity profile for the stream-wise component in the measurement test section located 3–4 m from the grid with variations found to be within 5% [23–26]. In the test section the turbulence intensity was found to be 4% of the mean horizontal velocity [23–26] which was 4.8 cm s1 for all experiments presented here. A glass pane (labeled Surface Glass Screen in Fig. 1) was placed on top of the free surface to avoid any distortion due to the small waves that could appear on a free surface.

Fig. 1. Schematic of the experimental set-up of the co-flowing jet.

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The jet flow was generated by a long cylindrical pipe with an internal jet diameter (D) of 8.81 mm located 3.2 m downstream from the water channel entrance. It was designed to have an inlet length of 104D in order to obtain a fully developed flow. The jet was fed from a pressurized tank (125 l) to maintain a steady flow. This coflowing jet was set 200 mm from the bottom of the water channel and the level of water was maintained at a height of 400 mm for all experiments. Three different jet mean exit velocities (Uo) were studied, ranging from laminar to turbulent flow at the pipe exit of 19, 38.4, and 67.4 cm s1 giving a maximum run time of 3, 1.5 and 1 h for this system. The corresponding jet to co-flowing velocity ratios (Ur) were: 4, 8, and 14 with pipe diameter based Reynolds numbers (ReD) of 1665, 3366, and 5908. From standard dimensional analysis [27,28], the corresponding dissipative scales (Kolmogorov) of the jet (at x = 0) range from 36 to 13 lm respectively and scale with the jet spread, increasing in a linear fashion with distance from release. Fluorescein sodium salt (FSS) (also known as disodium fluorescein, fluorescein, and uranine) was used as the dye marker of the jet fluid. It is important that the characteristics of the specific dye to be used in a flow mixing investigation are known a priori. FSS dye has been commonly used in scalar measurements [15]. It possesses a high quantum efficiency and solubility in water, low temperature dependence, low toxicity, and the pH effects can be easily controlled [6,29]. FSS (pH > 8) has a maximum absorption of energy at a wavelength of 490 nm and emission maximum at 515 nm [6]. Like most salts, this compound has a high Schmidt number in water, so the smallest scalar diffusive scales for this experiment are roughly 45 times smaller than the Kolmogorov scales. A schematic of the optical equipment used to generate the laser sheet is shown in Fig. 2. The laser used in this investigation was a 2.1 W argon ion laser (Coherent, Innova 70) operated in single TEM(0, 0) mode at a wavelength of 488 nm that falls on the absorption maxima of FSS [6]. Two £25.4 mm laser line dielectric mirrors (Newport) were used to re-direct the laser through the sheet forming optics and allow accurate positioning. A coated £25.4 mm spherical focusing lens with a focal length of 1000 mm was used to focus the laser at the center of the camera field-ofview. The beam emitted from the laser had a diameter of 1.5 mm which resulted in a calculated minimum sheet

1 – Laser 2 – Diaphragm 3 – Focusing lens 4 – Reflective mirrors 5 – Powell lens 6 – Laser sheet

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thickness of 400 lm for this long focal length lens. The long focal length focusing lens was chosen as a tradeoff to allow the focal point to be located within the regionof-interest in the experiment, a significant length from the sheet forming optics and the need for a thin sheet to maximize out-of-plane spatial resolution and laser power. A large width light sheet is used here to allow a large region-of-interest to be investigated. A unique single optic (Laserline Optics Canada Inc., Powell lens) [30], consisting of a cylindrical aspheric lens with hyperbolic profile that has been designed to transform the Gaussian intensity profile of the laser into a near top-hat profile was used to expand the laser into a sheet. The two reflective steering mirrors shown in Fig. 2 are used to position the laser onto the apex of the Powell lens to achieve the even intensity distribution. The generated laser sheet performs two tasks. It defines essentially a two dimensional (2D) region in the working section at which the measurement will take place, as well as providing the energy at the correct wavelength to fluoresce the marker dye. The thickness of the sheet defines the out-of-plane spatial resolution while the in-plane resolution is set by the imaging system. An important characteristic of the laser sheet is the intensity distribution across the region-of-interest, defined in Eq. (1) as II(i,j). This distribution may be a function of time but is generally assumed to be constant over the duration of the calibration and experiment. A 2D array CCD camera was used in this study to collect the fluorescence signal. The camera (PCO AG, SensiCam) has an image resolution of 1280  1024 pixels, is 12 bit and has maximum quantum efficiency (40%) at approximately 500 nm, close to the spectral emission wavelength of FSS. In order to avoid photons from others sources affecting the emitted signal of the fluorescent dye, a filter (Kodak Wratten filter No. 12) was placed in front of the lens of the camera. The filter has effectively zero transmittance [31] at the excitation wave length (490 nm) of FSS and at the laser wavelength (488 nm), while allowing 55% of transmittance at 520 nm and reaches a maximum of 78% transmittance at 530 nm. The main drawback of choosing this filter is that at the peak of the emission spectrum of the dye, a considerable percentage of the emitted fluorescence light is wasted. This drawback is however outweighed by the advantage of removing all Mie scattering and scatter from the high intensity emission from the laser. For all presented data, the camera was placed at 1.2 m from the axis of the co-flowing jet, perpendicular to the light sheet. A 100 mm SLR camera lens (Nikkor) was used to image the region-of-interest, resulting in an in-plane average spatial resolution of 300 lm across the camera array. For this optical arrangement and laser sheet, captured intensity of the fluoresced signal for each camera pixel emanates from a volume of 300 lm  300 lm  400 lm deep over which the concentration signal is averaged.

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Fig. 2. Configuration of optical components used to deliver the laser beam and form the laser sheet.

3. The PLIF calibration process An important objective of this calibration approach for PLIF is to setup the process to resemble as closely as possi-

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ble the experimental conditions. There are a number of factors that affect the performance of a PLIF system that have been investigated in the literature. In developing the design of the calibration approach, as many as possible of these factors were addressed. Walker [6] investigated the effects of pH, temperature, dye concentration and laser power on FSS fluorescence intensity, If. It was found that fluorescence intensity changed with pH and temperature. The fluorescence intensity was found to increase with pH, reaching a plateau for values of pH > 8 [6,32]. Walker [6] found only a change of 6% in the fluorescence intensity of FSS for a 20 °C variation in temperature. One important factor was the attenuation of the laser intensity as a function of FSS concentration. An integral formulation to calculate how much the dye attenuated the laser along a straight beam path was presented. It was determined that if the FSS concentration is lower than 0.04 mg L1, the attenuation of the laser results in a <1% error in the calculation of dye concentration [1]. Saylor [12] investigated the effects of photobleaching of FSS when LIF is used to measure concentration. The work compared the photobleaching of FSS using a continuous wave laser (CWL) and a pulsed laser (PL). It was found that the average fluorescence half-life (s1/2) intensity was approximately four times greater when a PL is used compared to a CWL (2.9 ms and 12.3 ms respectively). This suggests that the use of a PL is more effective because it allows a significant amount of photobleaching recovery in between laser pulses. However, the experiments of Saylor [12] were performed with the fluid at rest, where photobleaching has an additive effect. Wang and Fiedler [14] performed a study of the combined effect of photobleaching and thermal blooming on concentration measurements when using PLIF. The effect of thermal blooming is that it reduces the fluorescence intensity. Wang and Fiedler [14] showed that thermal blooming has a strong dependence on laser intensity (Il) and FSS concentration (C). With an increase of Il and C, thermal blooming becomes more significant. Thermal blooming is avoided by cooling the measuring volume, which is achieved by maintaining continuous flow above a threshold while the dyed fluid is transported through the illuminated region [14]. Crimaldi [13] studied the effect of photobleaching and velocity fluctuations in scalar measurements using FSS and rhodamine 6G (R6G). It was found that FSS was significantly more susceptible to photobleaching than R6G and that If decreases as fluid mixing is reduced at lower velocities. This result was also found by Wang and Fiedler [14]. In the investigation presented by Crimaldi [11], If reaches a constant value for velocities higher than 45 cm s1, while for the study presented by Wang and Fiedler [14] this threshold value of If was achieved at velocities > 20 cm s1. The works presented by Saylor [12], Crimaldi [11], and Wang and Fiedler [14] were based on single-point LIF configurations for which the geometry of the measurement volume is different than that of the PLIF configuration. A later work presented by Larsen and Crimaldi [15] showed that photobleaching has little effect when using PLIF. Thermal blooming and photobleaching have both been proven to be affected by laser intensity, dye concentration and the measure volume geometry [13,14]. The effects of photoble-

aching and thermal blooming are a function of both the PLIF system and of the mixing characteristics of the flow. This implies that the effects of thermal blooming and photobleaching on scalar measurements have to be tested for every specific experimental system configuration. To take into account these effects on the performance of PLIF, the approach taken in this work is to place a calibration cell in the same location in the flow at the region-ofinterest of the investigation. The design of the cell allows for the conditions of the flow: pH, temperature, mixing, etc. to be tested. In developing the design and the calibration procedure, two assumptions are made. First, it is assumed that the attenuation of the laser intensity due to the absorption to the dye is negligible. This can be achieved by using a low dye concentration. Secondly, the light distribution in the laser sheet remains constant throughout the execution of the experiment. This is possible using a laser that has high temporal and modal stability. To achieve this, the laser was operated for approximately 2 h before the calibration and experiment, to allow it to reach thermal equilibrium. 3.1. The calibration cell A schematic of the calibration equipment used in situ within the water channel is shown in Fig. 3. A calibration cell consisting of a square cross-section acrylic tube measuring 30 mm  30 mm  300 mm long, was placed within the camera’s field-of-view on the center-line of the 400  400 mm cross-section water channel. A small cross-section cell is used rather than one that covers the full field-of-view to maintain movement and mixing within the cell and to ensure negligible light extinction along the incoming laser sheet rays. A circulation pump with a control valve and rotameter was used to flood the calibration cell with a dye/water mix from a controlled mixture that was maintained in an 80 l dye tank. This allowed control of the concentration of the dye in a volume that was large compared to the measurement volume of the laser sheet but small compared to the total volume of the flow facility. The calibration cell was held in a traversing rig that could translate the cell across the camera’s field-of-view maintaining the long axis of the cell parallel to the light sheet. The cell was positioned for this experimental setup, normal to the direction of the laser and aligned with the direction of the bulk flow of the water channel. 3.2. The calibration procedure The developed procedure for the calibration of the PLIF system uses a target of a known dye concentration in the calibration cell in order to obtain the relationship between If and C. For the instrumentation used in this work, the camera showed a linear response to fluorescence intensity, therefore, a data point within the highest (peak) and lowest concentration is sufficient to obtain a linear fit. A master solution of dye is prepared and used to obtain the desired dye concentration. This dye is stored in the dye tank shown in Fig. 3 and is circulated through the calibration cell. The water used to obtain the desired dye concentration in the calibration images must be the same as is to

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Fig. 3. Schematic of the equipment used to perform the in situ calibration.

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be used in the experiment in order to account for the effect of pH and temperature on dye fluorescence intensity. For the calibration and results presented later, city water with pH = 7.9 and temperature of 18 °C was used. This dyed calibration cell water was replaced after each run and was found to have stable conditions over the course of experiments. For calibration, the desired dye concentration was circulated through the calibration cell and calibration images were collected. Calibration images can be taken before or after experiments, however for the present results, images were taken after the execution of the experiments. A calibration image sequence was obtained by placing the calibration cell at a known location within the camera’s field-of-view and acquiring an image. An example calibration image sequence at a single location is shown in Fig. 4. This image was taken using an FSS concentration of 0.05 mg L1. Moving the calibration cell through the camera field-of-view allows the dye target to approximate the ideal situation when an image of FSS emission within the dimensions of a row of pixels is taken at every row. Camera settings for the calibration are also set to match the settings to be used for experiments. The observed variation of signal intensity shows the strong relationship to the distribution of laser energy in the light sheet. The method requires that a calibration image be obtained pixel-by-pixel. For each pixel, an arithmetic mean of the camera count was calculated, but only measurements obtained when the calibration cell was present over that pixel were used to calculate this mean. Fig. 5 depicts the built calibration image for a dye concentration of 0.05 mg L1. This image was obtained by averaging a sequence of images similar to the one shown in Fig. 4. Note the fan shape of the laser sheet incoming from above and

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visible streaks due to non-uniformities in the Powell lens pattern. Horizontal makings in the image are a result of the compellation of this image from many individual images similar to that shown in Fig. 4. The purpose of the calibration process is to correct for these non-uniformities. After the calibration images were obtained for each dye concentration, data post-processing was used to subtract the average background pattern of the images (B(i,j)) from the calibration images and to determine the coefficients of the linear fit for each pixel in the array. For each pixel (i,j) in the image a unique linear fit was determined of the form:

C ði;jÞ ¼ ðIf ði;jÞ  Bði;jÞ Þaði;j;2Þ þ aði;j;1Þ

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where If(i,j) is the fluorescence intensity image in digital counts that is being converted into the dye concentration matrix C(i,j) and a(i,j,2) and a(i,j,1) are the slope and offset from the least squares fit for each individual pixel in the 2D array. 3.3. Correction of laser sheet intensity profile A plot of the raw signal scaled with a reference intensity along the axis of the calibration cell of the fluorescence distribution in the laser sheet for two dye concentrations is shown in Fig. 6. The profile clearly does not reflect the typical Gaussian intensity distribution of a CW laser but shows a more even distribution to be expected from a Powell lens [30] with the intensity profile relatively uniform through the center of the range and intensity peaks at the edges. The distribution depends on the quality of the laser beam and is sensitive to alignment of the laser onto the axis of the Powell lens. Evidence of the stability

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Fig. 7. Averaged fluorescence light intensity (dotted line) and the corresponding dye concentration (solid line) obtained using the calibration equation (Eq. (2)) along the calibration cell. Three different concentrations of FSS were used in this experiment, 0.00, 0.03, and 0.05 mg L1.

of the PLIF system over longer time periods is also seen in Fig. 6 by comparing the two profiles of different dye concentration. Common features within the profiles related to laser intensity are apparent and are only scaled by the different dye concentrations. In order to quantify the error associated to the calibration process, a set of 400 images of three known FSS dye concentrations, 0.00, 0.03, and 0.05 mg L1 were analyzed. Fig. 7 shows the average fluorescence light intensity and the corresponding dye concentration along the calibration cell obtained using the calibration process. The concentration data has also been scaled for physical location. It can be seen that this calibration process is able to correct the uneven distribution of the light intensity in the laser sheet (dotted line), resulting in more uniform value of the dye concentration (solid line). Several positions across the calibration cell were analyzed. For the worst case scenario the resulting dye concentration was found to be within 5% of the expected value. The errors in the calibration process were found to be larger for instantaneous FSS dye concentration. Therefore, the errors in measuring the dye concentration using the calibration images are minimized when the mean dye concentration field is desired. The background noise level for the average case was found to be approximately 0.0005 mg L1. This noise level is related to the temporal noise component in the signal, which becomes part of the uncertainty in the measurements and can be only minimized by time or ensemble averaging [18]. 3.4. Influence of mixing

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The calibration cell allows the control of the velocity of dyed fluid in the region-of-interest. To investigate the influence of mixing of the calibration fluid on the calibration, If was measured at nine different velocities from Uf = 0 to 16 cm s1 through the calibration cell. For each velocity, 764 images were taken using a frame rate of approximately 39 Hz, with an exposure time of 10 ms.

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Eight different concentrations of FSS were studied, where the dye concentration was varied from 0.01 to 0.10 mg L1. The sets of images were averaged in order to calculate the average intensity value for every dye concentration at the corresponding velocity. Fig. 8 shows the average intensity plotted against the velocity of the dye in the calibration cell. The results show that velocity has a negligible effect on fluorescence intensity for flow velocities > 4 cm/s. A maximum error of 3% was found when the dye was at rest for a dye concentration of 0.10 mg L1. A stronger relationship between fluorescence intensity and velocity was found by Wang and Fiedler [14], however this investigation was undertaken for a single point LIF and the results cannot be transferred to PLIF geometries [15]. For dye concentrations lower than 0.05 mg L1, the relative deviation was not more than 2%, therefore low concentrations of FSS can be used with less uncertainty. Similar results have been reported in previous investigations, in which minimal effects of photobleaching on PLIF were observed [15].

3.5. Other sources of uncertainty It has been shown that for high dye concentrations a key effect on If is the attenuation of the laser intensity [6], resulting in decay of the signal along the light ray of the laser sheet. Measurements across the 30 mm width of the cell in the direction of the laser beam showed that there is minimal attenuation of the laser as it passes through the calibration cell. The worst relative decrease was 3% observed for the largest test dye concentration of 0.10 mg L1. These results are similar to those of Walker [6] where the attenuation of the laser was found to be approximately 1% for a concentration of 0.04 mg L1. Correcting for attenuation of the laser signal is difficult in practice since the cumulative attenuation must be integrated due to the changing concentration field of the flow along the skewed and slightly diverging laser beam trajectories as the light fan passes through the flow. The traditional calibration approach for PLIF calibration would

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completely fill the flow volume, in this case the water channel with an even concentration of dye to measure the intensity and attenuation distribution in the laser sheet. In a large scale facility with a long beam path length through the dyed fluid, significant attenuation of the beam may occur. This would lead to a calibration scaling of experimental data where dye is only introduced into the mixing region under investigation that would overcorrect its value due to attenuation. It is expected that this effect would be minimal in small scale facilities, but could have a major impact in large scale facilities. The approach presented here only accounts for attenuation over a minimal region of the field of interest and negates any long beam path length effects related to attenuation. In both cases the effect of laser attenuation can be minimized by using a low concentration of dye. This however leads to low values of If and lower signal-to-noise ratios. In the study of the jet, presented later, a maximum concentration of 0.05 mg L1 is used in order to avoid introducing a correction process due to laser attenuation. Some of the more common problems associated with the 2D imaging detector used in PLIF are investigated by Ferrier et al. [18] where camera lens vignette is presented as the intensity variation across the sensor array. This is where the sensor at the edges of the array receive less light than the locations at the center of the chip (CCD array), causing the image to be brighter at the center. Ferrier et al. [18] corrected this problem by taking an image of a flat board section illuminated by sunlight. This image was then normalized and every image was divided by this normalized flat image. Three other options to correct this problem are also presented by van Cruyningen et al. [17], however, this problem is overcome by the current method of using individual calibration curves for each pixel. A potential source of uncertainty is the additional light introduced due to reflections in the system. It is generally assumed when modeling the PLIF process that the laser only undergoes a single pass through the region-of-interest. As the laser passes through the wall of the calibration cell, light will be reflected off every water/acrylic interface. Based on the Fresnel equation for reflectance for a light beam normal to the surface transmitting from water into acrylic the amount of reflected light is 0.3% of the incident power. This is compared to a laser beam propagating from air into glass where the reflectance is 4%. At this low level, the additional light has negligible effect on the calibration process. There are other uncertainties for each component within the PLIF system that contribute to the overall experimental error. Optical error can be found in the misalignment of the optical components that result in variations of the light distribution in the laser sheet. This light distribution can be affected by temperature variations with time of the cavity of the laser. Other measurement devices can also be a source of significant uncertainties in the system. These include flow and volume measurement devices that are used to control the flow rate for the calibration process and the amount of dye used to generate the desired dye concentration for the calibration images. The combination of these other errors were assessed to be less than 2% [33].

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4. Application of PLIF to a co-flowing jet

5. Experimental results

The experimental setup described in Section 2 consists of a round jet issuing from a long pipe into a co-flow. The mean scalar field was computed and used to generate radial and axial concentration profiles. Images of the jet mixing field were taken with the same 12 bit camera described in Section 2. At every flow condition a set of 1000 images was taken at a rate of 19.32 Hz. The exposure time used in these images was 10 ms to optimize light collect by the camera to generate an acceptable signal-to-noise level. This leads to spatial averaging depending on the local velocity. The presented results are therefore only appropriate for the mean scalar field. Continuous injection of dye into the water channel may introduce background buildup of dye. Using a dye concentration of 0.05 mg L1 in a wellmixed background for a completed injection of 125 l of jet fluid into the 5000 l channel will develop a background of 0.001 mg L1 or 2% of the maximum concentration. Effects of dye buildup in the background for this worst case scenario are therefore small and were found to be negligible during experiments.

Images of the uncorrected ensemble averaged fluorescent light intensity for the three different velocity ratios; Ur = 4, Ur = 8, and Ur = 14 are shown in Fig. 9a–c. Here the physical location in the image has been scaled with the inlet diameter of the jet while the color map is of the digital counts from the camera. The contours in the images exhibit light intensity structures that do not correspond to the expected smoothly degrading concentration field of a coflowing jet. These light intensity structures are consistently present in all three data sets, confirming that they are related to the intensity distribution of the laser sheet. The image data, corrected using the developed calibration procedure, are presented in Fig. 9d–f. It can be seen that the light intensity structures have been removed after the images are corrected by the calibration process and the concentration field matches the expected smooth concentration decay. The scalar field is measured in terms of the concentration of the dye marker and hence reaches a maximum of 0.05 mg L1 in the potential core of the jet. Classical features present in the flow include the zone of flow

2 0

1000

0

500

-2

0

-3

10

15

20

25

0

5

10

15

(a)

(d)

1

2500

3

2000

2

1500

0 1000

-1

-2

0

-3

20

25

0

0.05 0.04 0.03

0

500 15

25

0.02

-1

-3

10

20

1

-2 5

0.01

x/D

3

0

0.02

x/D

y/D

5

0.04 0.03

-1

-3

0

0.05

1

-2

2

y/D

2000

2

1500

-1

0.01 0

5

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x/D

x/D

(b)

(e)

20

25

0

3

2500

3

0.05

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2000

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0.04

1

y/D

3

1500

0 1000

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y/D

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y/D

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-2

-3

0

-3

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0.02

-1

500 0

0.03

0 0.01 0

5

10

15

x/D

x/D

(c)

(f)

20

25

0

Fig. 9. A comparison of the uncorrected images (a–c) of the jet in digital counts with corrected/scaled images of the jet (d–f) in mg L1, using the described procedure. Three velocity ratios of the co-flowing jet in the channel of (a and d) Ur = 4, (b and e) Ur = 8, and (c and f) Ur = 14. The pipe feed flow for (a and d) is laminar.

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(a) 1.0 0.8

Cy/Cc

ity of the co-flowing jet is clearly observed once the fully developed region has been reached. These results agree with the work presented by Chu et al. [1], and Antoine et al. [2]. The fit presented in the data of Fig. 10 corresponds to a Gaussian fit of the form:

x/D = 15 x/D = 20 x/D = 25 x/D = 15 x/D = 20 x/D = 25

2 !2 3 Cy y 4 5 ¼ exp  y1=e Cc

0.6

0.4

0.2

0

0

0.5

1.0

1.5

2.0

y/y1/e

(b) 1.0

x/D = 15 x/D = 20 x/D = 25 x/D = 15 x/D = 20 x/D = 25

Cy/Cc

0.8

0.6

0.4

0.2

0

0

0.5

1.0

1.5

2.0

y/y1/e

(c)

1.0

x/D = 15 x/D = 20 x/D = 25 x/D = 15 x/D = 20 x/D = 25

Cy/Cc

0.8

0.6

0.4

0.2

0

0

0.5

1.0

1.5

2.0

where Cy is the local mean concentration, Cc is the mean concentration at the physical centerline of the jet, y is the radial position, and y1/e is the radius at which Cy = e1Cc. This Gaussian fit is commonly assumed for the axial velocities in the fully developed region and is plotted with each data set [3]. In Fig. 10 profiles starting from the jet centerline and extending in both directions are plotted on the same dimensionless axis. This allows a comparison of the data to establish if there is any effect of attenuation of the laser on the radial profile of the jet. The open symbols correspond to one side of the profile and line patterns to the other. The close overlap of the profiles indicates that the calibrated results are effectively unaffected by laser attenuation. From Fig. 10 it is possible to observe that there is one data set which visibly departs from the trend and is for the case of a laminar pipe flow at the jet exit. There is a visible delayed spread due to late transition to turbulence as seen in Fig. 10a. For this flow condition (Ur = 4) the potential core extends until approximately 14D. Therefore, at 15D it is likely that the fully developed region has not been completely established here. Even though the Gaussian function fits well with most of the data shown in Fig. 10, it can be seen that at about 20% of the centerline concentration for all cases, the data starts diverging from the Gaussian fit. This could be the resulting effect of the coflowing stream in the spreading of the jet, which depends on the jet to co-flowing velocity ratio [1]. Similar results to those in Fig. 10 were reported by Davidson and Wang [4]. The dilution of the centerline concentration of the coflowing jet is presented in Fig. 11. The centerline dilution of the concentration is shown using the dimensionless form presented by Chu et al. [1] and Davidson and Wang [4] and reported results from these works are also included in the figure. It is possible to observe that the normalized dilution of the centerline concentration varies linearly with x = lm on a log–log axes, which was also observed in the investigations cited. The length lm is defined as the momentum excess length scale and it is given by

y/y1/e

lm ¼ Fig. 10. Dimensionless radial concentration profiles of the co-flowing jet for (a) Ur = 4, (b) Ur = 8, and (c) Ur = 14. Open symbols correspond to one side of the profile and line patterns to the other. A Gaussian profile (solid line) is also plotted.

establishment in the near nozzle region and the region of developing and fully developed flow further downstream [1]. Radial profiles of the jet are shown in Fig. 10 of the dimensionless ensemble averaged concentration for the three co-flowing velocity ratios. The expected self-similar-

ð3Þ

ðMeo Þ1=2 Uo

ð4Þ

where Uo is the ambient fluid velocity and Meo is the excess momentum per unit density defined as,

M eo ¼ ðU j  U o ÞU j

pD2 4

ð5Þ

where Uj is the magnitude of the jet exit velocity and D is the diameter of the jet nozzle. For the developed jet far downstream, the data shown in Fig. 11 agrees well with the experimental studies of Chu et al. [1] and Davidson

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10 Ur = 4 Ur = 8 Ur = 14 Davidson (2002) Chu (1999)

-1

(Ur - 1) . Cj /Cc

1

0.1

0.155 x 0.174 x 0.01 0.1

1

10

x/lm Fig. 11. Centerline dilution of the co-flowing jet for three jet to coflowing velocity ratios, Ur = 4, Ur = 8, and Ur = 14. The results are compared to the linear variations found by Davidson and Wang [23] and Chu et al. [20].

and Wang [4]. This figure also shows that in the near field where the jet is transitioning from laminar to turbulent, this scaling is not appropriate. For the fully developed region of the jet, the centerline mean concentration variation with the axial distance is shown in Fig. 12. The exit concentration of the jet (Cj) is normalized by the local mean concentration on the axis of the jet (Cc). Using the equation for the centerline velocity variation presented by Hussein et al. [34], it is possible to write the centerline mean concentration variation with the form:

Cj 1  x xo  ¼  C c Bc D D

ð6Þ

where the constant Bc is related with the spread constant B as:

Bc ¼

1 1 p2 B 2

ð7Þ

7 Ur = 4 6

Ur = 8 Ur = 14

5

Bc = 6.3, xO/D = -2.6 Bc = 6.7, xO/D = -2.4

Cj /Cc

4

Bc = 4.7, xO/D = 10.9 3 2 1 0 -5

0

5

10

15

20

25

30

x/D Fig. 12. Decay of the axial concentration of the co-flowing jet for three jet to co-flowing velocity ratios, Ur = 4, Ur = 8, and Ur = 14. The functional form of the lines shown in this graph is given by Eq. (6).

As can be seen from Eqs. (6) and (7), the greater the slope of the fitted line, the smaller the value of B which represents a higher decay rate of the centerline concentration. Fig. 12 highlights a higher centerline concentration decay for the jet with the smaller jet to co-flowing velocity ratio (Ur = 4). The values of Bc found for the case of Ur = 8 and Ur = 14, are Bc = 6.7 and Bc = 6.3 respectively and are comparable to the results presented by Antoine et al. [2]. The values for the virtual origins however are found in this study to significantly differ from Antoine et al. [2], mostly likely due to different inlet conditions. Different asymptotic values of turbulence characteristics in the far field have been linked to initial jet initial conditions based on experiments [35] and theoretical work [36] for jets into quiescent surroundings. Studies on the centerline velocity variation have shown a discrepancy in the location of virtual origins with different values for x/D < 50 (xo  3D and Bc  5.7) and for x/ D > 50 (xo  7D and Bc  5.0) [34]. These numbers are comparable to the corresponding results of the turbulent jets presented in this study. Antoine et al. [2] presented data for x/D > 50; this is a significantly larger range compared with the range studied in the current investigation.

6. Conclusion A PLIF calibration approach has been described in this work that uses a relatively small calibration cell in a large-scale flow facility to generate calibration data. The novelty of this approach is that all parameters related to the fluorescence performance of the dye (pH, temperature, and flow characteristics) can be delivered to the measurement test section in a controlled manner. This removes the need to flood the facility with a high concentration of dye. A new method to generate a laser sheet has also been used in this study. A Powell lens improves the distribution of laser intensity across the laser sheet and hence maintains a similar signal-to-noise ratio throughout the field. The investigation demonstrates that the effect of thermal blooming and photobleaching are not significant in the PLIF system described. A simple calibration process to obtain information of the concentration field using image processing was described and is proven to be independent of the light intensity distribution in the laser sheet. The use of the individual calibration curves for each pixel in the array corrects the variation of the quantum efficiency among the pixels of the camera. The calibration process described can be easily performed prior to each experiment and postprocessing of the data does not require an extensive computational effort. The calibration process described can be used independently of the FSS dye used in the PLIF technique and the hardware can be easily scaled for use in very large test flow facilities. The scalar field data for a co-flowing jet in an open water channel was also presented. Measurements were performed for three different co-flowing jet conditions. The ensemble averaged scalar concentration field agreed well with the theory and previous experimental studies carried out in similar geometries providing validation for the presented experimental calibration technique.

L.A. Torres et al. / Measurement 46 (2013) 2597–2607

Acknowledgement This work has been conducted with the support of the Natural Sciences and Engineering Research Council (NSERC) of Canada.

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