Abstract

Two-color, toluene-based, planar laser-induced fluorescence (PLIF) is utilized to characterize the thermal structure of a turbulent, free jet. The PLIF technique has been used to measure concentration gradients for combustion applications, but its use to quantify thermal gradients is limited. To validate the method, compressed air is seeded with toluene particles. The seeded airflow is heated to temperatures varying from 300 to 375 K, and the heated jet exits a 1.27-cm diameter orifice into quiescent, room temperature air. The jet Reynolds number is varied from 5000 to 15,000. As the jet exits the orifice, the toluene particles fluorescence across a 266 nm laser light sheet which ultimately provides a two-dimensional temperature distribution of the free jet. The rigorous calibration procedure for the PLIF technique is described along with the seeding nuances needed to quantify the thermal structure of the jets. The PLIF technique has been demonstrated for this fundamental flow field, and it has proven to be applicable to more complex heat transfer and cooling applications. Furthermore, the time-averaged temperature distributions obtained in this investigation can be used in the validation of turbulent computational fluid dynamics (CFD) solvers.

Introduction

Experimental methods are important for analyzing heat transfer surfaces and thermal flow fields. Having a better understanding of the temperature distribution within the flow field, and over the surface (through thermal boundary layer), leads to improved system performance. Several experimental methods have been developed to obtain measurements of a surface temperature. Characterizing the boundary layer has always been a challenge. Using a direct method to measure the temperature, such as thermocouples, interrupts the flow structure. Thus, there is a need to develop a nonintrusive method to measure the temperature gradient within the boundary layer.

Surface visualization methods have recently become very popular for surface heat transfer measurements [1,2]. In addition to surface thermal characterization, it is also crucial to characterize the flow behavior above the surface especially within the thermal boundary layer. Planar laser-induced fluorescence (PLIF) could be a solution to this challenge by providing a quantitative relationship between the fluid temperature and fluorescence intensity [3].

PLIF is a two-dimensional, nonintrusive, optical diagnostic method with a potential to measure the flow field parameters such as concentration and temperature. PLIF has been widely used to measure the concentration, particularly in many combustion and flame studies [47]. The purpose of this study is to develop a novel PLIF-based technique. While the current work applies this PLIF method to a heated, free jet, the opportunity exists to apply the method to near-wall flows to quantify thermal boundary layer development. Having the capacity to measure the near-wall temperature profile provides unparalleled insight into convective heat transfer. This method has the potential to be used in other applications that require the knowledge of fluid temperature gradients. In addition, with the application of this process to highly turbulent flows (as seen in gas turbine cooling applications), the results can also be used to validate state-of-the-art computational fluid dynamics (CFD) models.

PLIF History.

Laser-induced fluorescence (LIF) has made significant contributions toward flow visualization, quantification, particularity, and concentration characterization. Long et al. [8] initially demonstrated planar visualization based on laser Rayleigh scattering for concentration measurements within turbulent jets in the late 1970s. A short time later, in 1982, linear and planar imaging using hydroxide-LIF was presented. Kychakoff et al. [9] applied linear LIF for concentration measurement of hydroxide within combustion gases. Additionally, Dyer and Crosley [10] mapped the hydroxide concentration using PLIF. In 1985, Allen and Hanson [11] used PLIF for vapor and liquid visualization in fuel spray. McDaniel et al. [12] also used PLIF to measure the velocity distribution within a plane of gaseous flow using iodine-PLIF. In the same year, Seitzman et al. [13] proposed nitrogen oxide-PLIF for quantitative temperature visualization in combustion flows. Recently, the PLIF technique was applied to a methane flame to obtain temperature and velocity distributions within the flame [14].

Technical improvements in optical systems such as cameras, filters, and lenses have assisted in allowing PLIF diagnostics for other parameters, particularly, temperature measurements. In 1999, Thurber [15] studied the fluorescence dependency of acetone aimed to make PLIF more applicable for quantitative temperature measurements. Shortly after that, Thurber and Hanson [16] demonstrated temperature imaging using acetone-PLIF.

Flow pressure and laser energy are two factors that can be controlled during an experiment. It is almost impossible to keep the seeding concentration uniform. To overcome this challenge, Thurber [15] and Thurber et al. [17,18] introduced the dual wavelength excitation strategy to remove the concentration dependency of the fluorescence. Ratioing of fluorescence intensities resulting from exciting the tracer at two different wavelengths cancels the concentration impacts. For the dual wavelength excitation method, intensities are collected at two different wavelengths, simultaneously. This strategy solves the concentration dependency issue. However, providing two different wavelengths would bring more complexity to the experiment.

Others have utilized PLIF to measure multiple wavelengths to obtain temperature distributions [19,20]. Rather using multiple tracers or multiple wavelengths from a single tracer, researchers have attempted to remove the effect of concentration dependency to obtain fluid temperature distributions. Over the years, researchers have demonstrated the ability to measure temperature distributions based on the fluorescence behavior of various tracers. However, these studies have been completed at relatively high temperatures, and the ability to measure small temperature gradients, as seen in thermal boundary layers, has not been demonstrated. If PLIF can be used in flows with relatively small temperature changes, the possibility exists to apply the method to near-wall flows and nonintrusively measure near-wall temperature gradients, and thus convective heat transfer coefficients.

Laser-Induced Fluorescence Equation.

The fluorescence signal is related to specific tracer characteristics such as concentration and temperature [21]. A relationship for the fluorescence signal, Sf (in units of photons), was developed by Thurber [15], and it is shown in Eq. (1)
$Sf=Ehc/ληtolσ(T)∫270−400nmFi(λ)ϕ(λ,T)ni(λ)dλ$
(1)

Absorption cross section (σ) and fluorescence quantum yield or FQY (ϕ) are two photo-physical features for LIF measurements that describe the probability of a molecule absorbing and emitting photons, respectively [22]. These two parameters are functions of temperature, pressure, and wavelength [23]. These two features play important roles within selecting an appropriate tracer for a PLIF experiment. At a given excitation wavelength and isobaric condition, the fluorescence signal is expressed as Eq. (1). Hence, the fluorescence signal is only a function of temperature, concentration, and optical system response.

PLIF Tracer Selection.

Selecting a proper tracer is an important factor when using an LIF technique. Several tracers have been used based on flowfield features and applications [5]. Examples include OH, NO, acetone, 3-pentanone, and toluene. Each tracer has to retain the following specifications to be applied in a LIF diagnostic. The tracer must possess a vigorous nonresonant fluorescence spectrum within an ultraviolet (UV) excitation wavelength. The absorption spectrum needs to be accessible using a high power light source. Also, it is preferable that the tracer has a high vapor pressure at room temperature to make the seeding process more convenient [22]. Three tracers, which meet the needed requirements, are acetone, 3-pentanone, and toluene.

Acetone has been used in a variety of applications from flow visualization to concentration measurements within gaseous flow near room temperature and atmospheric pressure [24]. 3-pentanone has been mostly used in combustion systems. Toluene has been recently applied in a variety of fields such as thermal stratification, concentration measurement, and flow visualization [23]. Due to its spectroscopic and fluorescence characteristics, toluene separates itself as an ideal tracer for quantitative temperature measurement applications. Toluene has the best temperature sensitivity in comparison with the other tracers (80% increase in fluorescence intensity with 100 K increase in temperature).

It is important to note that a specific excitation approach is required for each tracer because the excitation wavelength influences the fluorescence emission. There are three standard laser excitations choices: 248 nm, 266 nm, and 308 nm. Toluene has higher FQY and absorption cross section in comparison with the other tracers considered. Therefore, toluene is chosen in this study as the tracer for quantitative temperature field measurements.

Two-Color Thermometry Method.

As shown previously, the fluorescence signal is a function of pressure, temperature, and tracer concentration. It is impossible to keep the tracer concentration constant through the entire fluid domain. As a result, the toluene fluorescence intensity depends on both temperature and tracer concentration. Therefore, a need exists to control the tracer concentration and remove the effect of its concentration for thermometry measurements.

A valuable spectroscopic property of toluene, strong temperature dependency of its fluorescence signal, nominates this tracer for a quantitative thermometry. Toluene fluorescence shows a red shift by increasing the temperature. The general fluorescence behavior of toluene consists of two regions: (a) the spectra peak shows a shift by increasing the temperature and (b) no shift is observed by increasing the temperature. In other words, near the wavelength of 280 nm, the fluorescence spectra are insensitive to temperature (blue spectra), and at wavelengths greater than 305 nm, the fluorescence spectra are sensitive to temperature (red spectra).

The emission intensity of toluene, in both regions (280 nm and 305 nm), is dependent on the tracer concentration. As the emission intensity is similarly affected at both wavelengths, this effect can be removed by dividing the emission signals measured at both wavelengths. With the effect of concentration removed, the only remaining factor affecting the fluorescence intensity of the toluene is the temperature of these tracer particles. To obtain the fluorescence intensity of the toluene at two different wavelengths, two optical filters are required to pass separate fluorescence wavelengths. The fluorescence signal passing through each filter Sf–Red and Sf–Blue can be expressed using Eq. (1). The ratio of these two intensities, Eq. (2), is only a function of temperature and optical system response
$Sf−RedSf−Blue=∫270−400nmFi−Red(λ)ϕ(λ,T)ni−Red(λ)dλ∫270−400nmFi−Blue(λ)ϕ(λ,T)ni−Blue(λ)dλ$
(2)
The optical system response comes from variation of the image’s brightness and camera uniformity. In order to remove this effect from the integral, the intensity ratios are normalized by the intensity ratio at a known temperature (Eq. (3))
$Sf−Red(T)/Sf−Red(298)Sf−Blue(T)/Sf−Blue(298)=∫270−400nmFi−Red(λ)ϕ(λ,T)dλ/∫270−400nmFi−Red(λ)ϕ(λ,298)dλ∫270−400nmFi−Blue(λ)ϕ(λ,T)dλ/∫270−400nmFi−Blue(λ)ϕ(λ,298)dλ$
(3)

A variety of tools exists to measure surface temperatures, and in recent years, optical techniques have quickly developed to provide detailed surface temperature distributions. In addition, optical methods have rapidly advanced to provide detailed, quantitative information across flowfields. To complement the tools commonly used in laboratory investigations, it is desirable to have a method capable of providing detailed temperature distributions within a fluid. The objective of this investigation is to develop and implement a technique to obtain two-dimensional temperature distributions of a fluid operating near room temperature. To demonstrate the method, a heated, free jet is used. The full calibration and testing procedures are presented along with the details of the data reduction process. Upon benchmarking of the process, the method can be applied to more complex flow fields.

PLIF Experimental Facility

In PLIF imaging, flow is seeded with a fluorescing material known as a tracer (toluene for this investigation). A laser beam spreads into a laser sheet (using optics) and excites a two-dimensional region of the flow. The laser wavelength is proportional to the resonant transition of the tracer. Molecules within this region move to a higher energy level resulting from absorption of the laser’s energy. The excited molecules then return to an equilibrium level of energy by fluorescing (emitting energy at a longer wavelength). The intensities corresponding to the fluorescence are collected using optical detectors such as charged coupled device (CCD) cameras and lenses. Two-color thermometry, single-excitation wavelength (266 nm), and single camera image detection are established in this work for quantitative temperature measurements. This study focuses on the development of an experimental arrangement of toluene-based PLIF, the data collection process, and the data reduction procedure.

Facility Overview.

All experimentation was performed in the Convective Heat Transfer Laboratory at Baylor University. The flow line is made of aluminum tubing with a round cross section, 0.0254 m in diameter. An inline heater is used to generate elevated temperature flow conditions required for the PLIF method development. The entire line is wrapped in fiberglass insulation to reduce heat loss from the test section. Standard T-type thermocouples are placed at desirable locations to monitor the flow temperature. The thermocouple output is monitored and recorded using labview software from National Instruments. The output temperatures are recorded every second and written to a data file.

A laser system is used as a primary excitation source for PLIF diagnostics. The detection system consists of a CCD camera, optical lenses, and data collection computer. The experimental setup was designed and built for the purpose of PLIF diagnostic development and validation.

Figure 1 shows the schematic of the general PLIF setup used for this study.

Fig. 1
Fig. 1
Close modal

Laser System.

The laser is one of the crucial components for the PLIF method. A Neodymium-doped Yttrium Aluminum Garnet (Nd:YAG) laser from Litron Laser is used for this study. The excitation wavelength selected for this study, due to the fluorescence features of toluene, is 266 nm, and this wavelength is producible using an Nd:YAG laser. A laser beam is spread into a thin plane using a cylindrical lens with f = −20 mm. In order to create an instantaneous visualization, a pulse width about 100 ns is used for the laser. The laser energy output is in the range of 40–120 mJ/cm2.

Optical Detection System.

The fluorescence signals are collected by an optical system that consists of an intensified CCD camera, equipped with an intensify relay optics (IRO) from LaVision. The camera has a 172 × 260 pixel CCD array with 6.45 μm pixel size and it is 4 × 4 hardware binned. The camera exposure time is set at 6000 μs. The combination of a CCD camera and IRO increases the sensitivity of the system to measure the ultraviolet fluorescence signal range. The optical system is equipped with an IRO controller that allows for the adjustment of the timing of the camera and laser. The optical system is placed at a right angle to the laser sheet.

A UV lens from Nikkor-UV is used to focus the images on the camera. The lens is set at its lowest f-number to achieve the highest photon efficiency. Two filters are used for two different wavelength ranges for the toluene emission spectrum. The first wavelength range is temperature independent while the second is temperature dependent. The temperature-independent filter (blue detector) and the temperature-dependent filter (red detector) passes 285 nm and 320 nm wavelengths, respectively. Both the 285 nm and 320 nm optical filters are narrow bandpass filters. For the “red” detector, maximum transmission efficiency is achieved at 285 ± 2 nm (with a full width-half max of 10 ± 2 nm). The 320 nm fluorescence passes through a separate filter with a peak transmission efficiency at 320 ± 2 nm. With a full width, half max range of 12 ± 2 nm, the fluorescence passing through the “red” filter does not overlap that of the “blue” filter. The ratio of these two signals gives the temperature information without dependence on tracer concentration.

Toluene Seeding System.

A toluene seeding system, made out of a 0.0762 m diameter aluminum pipe and sealed with two flanges at each end, disperses the toluene into the flow line. This system works based on the bubbling principle and provides a saturated air and toluene gas mixture. Two rotameters are used to monitor the flowrate of the air through the heater and bubbling system. Air enters the bubbling system through a 0.0127 m inlet pipe and provides a saturated air and toluene gas mixture. The mixture leaves the bubbling system through a 0.0127 m outlet pipe and meets the heated air at a T-junction. Two check valves are installed after the outlets of the heater and the bubbling system to avoid a reverse flow.

Data Collection Procedure.

The PLIF experimental procedure consists of three main image recording steps: background images, reference images, and air/toluene images at different temperatures. For each step, two sets of 500 images are recorded: temperature dependent (using red filter) and temperature independent (using blue filter). Background images are captured while the laser is on and there is only airflow in the system, because it is desired to record the optical noise that is created by the surrounding light. Reference images are taken while the mixture of air and toluene is flowed in the system at room temperature (297 K) and the laser is on. After the system reaches the desirable steady-state condition, the air/toluene images are recorded while the laser in on. davis 8.3 software from LaVision is used to record the raw images. For each step, flow and ambient temperatures, gauge pressure, and flowrate are monitored and recorded. Images are exported from davis in the tagged image file (TIF) format then postprocessed using in-house matlab code.

PLIF Calibration Procedure

PLIF is a nonintrusive method that quantitatively measures the flow field parameters. As previously mentioned, the scope of this investigation is to develop PLIF to study the temperature field within a fluid. The fluorescence intensity of the tracer particles is captured within a PLIF experiment. A calibration must be completed to determine the relation between the fluorescence intensity and the fluid temperature.

Calibration Setup.

The first step of this study is to develop an empirical relationship between the temperature of the tracer and its florescence intensity. Figure 1 shows the schematic of a calibration setup for the PLIF measurement, and an overview of the flow line was presented in the Facility Overview section. The toluene fluorescence wavelength is within the range of 270–370 nm. It requires a specific window to pass the mentioned wavelength range without changing the fluorescence properties. Since this method is highly dependent on the fluorescence intensity, using any glass window to perform the calibration is avoided. The temperature profile is uniform throughout the central region of a steady-state jet cross section. Therefore, the calibration experiment is carried out through a cross section of a free jet.

Flow with a Reynolds number of approximately 10,000, based on the inner tube diameter, is used for the calibration. The air supplied from a compressor is divided into two separate streams: 80% of the flow goes to the heater and the rest goes to the seeding system. A valve and a rotameter control the flow in each line. Standard T-type thermocouples are placed at the inlet and outlet of the heater and within the central region of the jet cross section to record the air temperatures. The calibration process is performed at a variety of temperatures between room temperature and 400 K. For each measurement, the flow first passes only through the heater to reach the desired temperature at the exit of the tube. When the system reaches the steady-state condition (no changes in temperature), toluene is introduced into the flow line through the seeding system. The heated and seeded flow meet at a T-junction. In order to provide a uniform mixture of toluene and air, an insert of twisted aluminum tape is placed in the tube. A 0.0127 m diameter aluminum tube with a length of 0.254 m is used to produce a fully developed flow for calibration purposes. The 0.0127 m diameter tube is connected to the main flow line tubing using a reducer fitting. A 90-deg pipe elbow is used to provide a cross section perpendicular to the optical system. The camera is equipped with a filter switch, which can remotely change the filter that is required for the PLIF experiment.

Calibration Image Processing.

The fluorescence intensity is a function of parameters such as temperature, pressure, tracer concentration, and laser energy. In a general PLIF experiment, it is possible to control some factors such as temperature, pressure, and laser energy. However, it is almost impossible to control the concentration of the tracer. As a result, there is a need to apply the two-color thermometry to remove the effect of concentration. The procedure toward this method is illustrated for the purpose of developing an empirical relation between the temperature and toluene fluorescence intensity.

The PLIF experimental procedure consists of three main image recording stages: background images, air/toluene images at a reference temperature (known as reference images), and air/toluene images at different temperatures. For each stage, two sets of 500 images are recorded: temperature dependent (using red filter) and temperature independent (using blue filter). Red and blue filters pass 320 nm and 285 nm wavelengths, respectively. Since one camera is used for this study, it is not possible to capture both types of images simultaneously. Temperature-dependent data are first taken using the red filter, and then the filter is switched to the blue filter using the filter switch. The filter switch is controlled remotely by the same computer that is used for data acquisition.

Images are captured when the system reaches the steady-state condition at a desirable temperature. For background images, the laser is illuminating the jet cross section; however, the flow is not seeded (no toluene in the flow). The purpose of capturing the background images is to record the optical noise that is created by the surrounding light. Background images are captured at each temperature. When capturing the background images for both filters is complete, the toluene is spread into the flow line through the seeding system. The seeding system uses the air at ambient temperature; therefore, the temperature at the jet cross section is closely monitored and recorded to assure the system is working under the steady-state condition. After the system reaches the uniform desirable temperature, the air/toluene images are recorded while the laser is illuminating the cross section. Reference images are air/toluene images taken while the mixture of air and toluene flows in the system at room temperature (297 K). davis 8.3 software from LaVision is used to record the raw images. The images are exported from davis in the TIF format then postprocessed using in-house matlab code. The procedure is repeated for a variety of temperatures between room temperature and 400 K.

The image processing includes the following steps: background subtraction, time-averaging, two-color thermometry, and normalizing the fluorescence intensity. The offset from camera noises and surrounding light is removed by subtracting the background intensity. For this purpose, 500 background images are averaged and then the averaged background image is subtracted from each single PLIF image. At this time, the surrounding noise is eliminated from the single PLIF images and they are ready to be time averaged.

Many pixels do not capture fluorescing tracer particles. The matlab code is written in a way that it includes the pixels with fluorescence intensity greater than zero for calculating the average. The two-color method is applied on the time-averaged results; red filter intensities divided by blue filter intensities. The ratio eliminates the effect of concentration. Finally, the two-colored intensities are normalized by the two-colored results at the reference temperature. The primary reason for normalizing is to reduce effects of inconsistencies in spatial illumination and camera sensitivity. A flowchart providing the postprocessing procedure is shown in Fig. 2. Insets are used to show sample intensity distributions for each step in the process. Examples of calibration images (radial profile of free jet) are provided for every step in the process. Free jet images (full streamwise distributions) are provided for the latter stages of the data reduction process. The procedure is repeated for images at a variety of temperatures between room temperature and 400 K with the step size of 25 K.

Fig. 2
Fig. 2
Close modal
In order to apply this method to measure the fluid temperature, the relation between the fluorescence intensity and the fluid temperature must be determined. Therefore, a 10 × 10 pixel frame is created at the center area of the jet cross section for each temperature (box shown in the center of the jet for the “Normalized Intensity Ratio @ Given Temperatures,” Fig. 2). This region in the center of the jet is located above the type-T thermocouple, located at the outlet of the pipe forming the jet. The temperature drop from the exit of the pipe to the measurement plane is taken into account through a separate set of tests. This 10 × 10 area allows for a sufficiently large number of pixels to be averaged while not moving outside the area of the thermocouples. Normalized intensity ratios (Eq. (4)) within the frame are averaged and recorded for each temperature. The normalized temperature is fitted as a function of normalized fluorescence signal ratio IN using the method of least squares regression with a 95% confidence interval. This function will then be applied to assign temperatures corresponding to each pixel for the measured PLIF ratio image. Figure 3 presents the data points that are used in the calibration process as well as the calibration curve. Six sets of data, each including five data points, were collected at different times and used to create the calibration curve. The fitted equation for the linear method that describes the relation between the normalized temperature and normalized fluorescence signal ratio is
$IN=(IRed−IBack−RedIBlue−IBack−Blue)|T/(IRed−IBack−RedIBlue−IBack−Blue)|TRef$
(4)
Fig. 3
Fig. 3
Close modal

Repeatability of Calibration Experiment.

For this study, the calibration is conducted under specific experimental conditions. The flow Reynolds number is approximately 10,000, the seeding setup is arranged in a way that 20% of the flow goes to the seeder and the rest goes to the heater, and 500 images are captured for each filter. In order to verify the repeatability of the calibration data, impacts of the three factors on calibration data are investigated: different Reynolds numbers, seeding setups, and number of images.

Two sets of calibration experiments are conducted at Re ≈ 5000 and Re ≈ 15,000 and the results are compared with the data used for calibration curve at Re ≈ 10,000. As can been seen in Fig. 3, data from varying the Reynolds number falls within the 95% confidence interval.

Three different seeding setups are used to validate the repeatability of the two-color method at higher toluene concentrations. The setup arrangements are summarized in Table 1, and the results are compared in Fig. 3. Seeding setup I is used to create the calibration data. As shown in Fig. 3, the two-color PLIF method successfully removes the effect of seed concentration, as varying the amount of toluene in the air does not affect the measured temperature. Finally, the impact of number of images on the calibration data is studied. For this purpose, calibration experiments were conducted on four different days. Different numbers of images, with the range of 100–400, were captured on each day. Again, the calibration curve represents the calibration data over a wide range of seeding and flow conditions. The range of all data is captured within ±6% of the calibration equation. As mentioned previously, for calibration postprocessing, a small area within center of the jet is used to collect the intensity information. However, for other applications that require a larger area, more images may be required.

Table 1

Toluene seeding setup arrangements for PLIF calibration

Seeding setupHeater flow (%)Seeder flow (%)
Seeding setup I8020
Seeding setup II7525
Seeding setup III5050
Seeding setupHeater flow (%)Seeder flow (%)
Seeding setup I8020
Seeding setup II7525
Seeding setup III5050

In order to obtain fluid temperature distributions using the PLIF technique, the relationship between the measured intensity (during the flow test) and the tracer temperature must be known. Therefore, the calibration data must be robust and reliable. Given the variety of individual data sets shown in Fig. 3, many alternatives exist to analyze the data and develop the intensity–temperature relationship (i.e., including only the baseline data, including all the data, including subsets of the data, etc.). The baseline data covers the entire range of temperatures with the smallest temperature increments. Therefore, this data set was used for the primary calibration. Other options of data analysis were investigated, and choosing different subsets of data produced slopes that changed by less than 1.5%. While additional options could produce improved R2 values for the calibration relationships, the most robust data set was chosen for analysis of the actual PLIF data.

Fluorescence Intensity Standard Deviation and Error.

The PLIF temperature distribution is determined in the following steps: background subtraction, two-color method, and normalizing. The accuracy of each step contributes to the overall precision of the temperature measurement. Using the theory of propagation for a given function, the standard deviation of the function can be calculated. As shown in Fig. 3, a linear relationship exists between the measured normalized, intensity ratio, and the temperature ratio. From these ratios, the fluorescence intensity of the raw images, reference images, and background images are contributing to the overall precision of the PLIF method.

The standard deviation of temperatures corresponding to the data used to create the calibration curve has been calculated. The maximum standard deviation, based on postprocessing of 500 images, is equal to 12.50 K at 334.87 K. The maximum relative standard deviation for this study is approximately 3.73%. Sensitivity of the standard deviation to each step varies at different temperatures. However, the calculations show that the background subtraction and two-color method have the lowest and highest contribution to the standard deviation, respectively. At a maximum standard deviation of 3.73%, the proportion of background subtraction, two-color method, and normalizing steps are, namely, 16.25%, 54.12%, and 29.63%.

The standard deviation is in agreement with literature standard deviations corresponding to LIF experiments. As an example, Kearney and Reyes [25] estimated the standard deviation of 1.8% for temperature measurement in a turbulent, thermal convection study using acetone-LIF. O’Byrne et al. [26] reported a standard deviation of 4.5% in PLIF temperature measurement in laminar hypersonic flat plate flows.

In addition, standard deviations corresponding to the slope and intercept of the calibration curve have to be considered to obtain the uncertainty of the calibration tests. Since a linear least squares curve fit is made for the calibration set of data, a standard error of regression can be applied to calculate the standard deviation corresponding to the slope and intercept [27]. Using this method, the standard deviation for the slope and intercept of the calibration relationship is equal to 0.068 (9.94%) and 0.041 (12.75%), respectively. The theory of propagation can be used to combine the standard deviations of fluorescence intensities, calibration curve slope, and intercept. The overall uncertainty corresponding to calibration tests is equal to 16.59%. Other investigations using the two-color PLIF method at temperatures greater than 500 K have estimated the experimental uncertainty to be as low as 4% [28]. However, with the application of PLIF to flows approaching room temperature, the experimental uncertainty of the temperature measurements have been reported as high as 20% in water [29] and 10% in air [30].

The major sources of uncertainty for the PLIF calibration study could be related to camera noise, filter detectability error, laser energy, and toluene purity. Cameras create dark and shot noises. In the PLIF study, the majority of dark noise is removed through the background subtraction process. The shot noise is a result of capturing undesirable information and impacting the image resolution. Sensitivity of the standard deviation to each of the steps (background subtraction, two-color method, and normalizing) is calculated. It is found that the background subtraction step has the lowest impact on the standard deviation.

The standard deviation for the PLIF calibration has the highest sensitivity to the two-color method step. In the PLIF calculation, the intensity ratio of the temperature dependent images to temperature independent images is calculated to eliminate the effect of concentration. For this study, a single camera is used to capture the temperature-dependent and temperature-independent fluorescence signals. Therefore, the two types of images are not recorded simultaneously. The delay between switching the filters and capturing two types of images could create errors.

For this study, a planar laser is used to excite toluene molecules. The laser energy may change within its plane and results in creating an uncertainty. The two-color method and normalizing can partially remove this effect. However, since two types of images (temperature dependent and independent) are recorded separately, the possibility that the laser energy varies during the data collection and its gradient affects the florescence quality. To reduce the laser energy error, the laser energy has to be monitored and adjusted during image collection using laser power meters.

Toluene impurity could contribute to error production. The PLIF method works based on capturing the toluene fluorescence intensity. The toluene molecules absorb the energy of the laser and travel to a higher energy state. The excited molecules emit energy, in the form of fluorescence, while they are reaching the equilibrium state. The presence of contamination and impurities in toluene could affect the energy absorption and photon emission.

Results and Discussion

This study focuses on developing a novel, nonintrusive method to measure the flow field temperature. An empirical relationship between the temperature and fluorescence intensity was developed. Now the experimental results of a PLIF application on free jets can be presented. To start, a general background behind free turbulent flows is summarized. Second, features of the experimentation for the free jets are outlined. Finally, the results of PLIF experimentation are provided.

Turbulent Jets.

Free turbulence flows are shear streams with high Reynolds number flow through an open environment fluid. A free jet is formed when a flow leaves a nozzle or orifice and is discharged into a flow with a negligible velocity. Free jet flows are widely used in many engineering applications such as drying, cooling, propulsion, and air conditioning systems. The jets are flows with a specific momentum that spread into another fluid (usually a stagnant fluid).

The traditional, critical Reynolds number indicating transition from laminar to turbulent flow for an unbounded jet has been shown to range from 0.3*102 to 2*102 [31]. Fully turbulent jets exist for Re > 2000 [32]. Heat and mass transfer enhancement are special characteristics of the turbulent jets. Fellouah et al. [33] investigated the effects of jet Reynolds number at different distances downstream from the jet exit (0 < Z/D < 25) using a hot-wire technique to determine the differences in mean velocity and turbulence intensity distribution. The Reynolds numbers used for the experiment were 6000, 10,000, and 30,000. It was shown that the impact of Reynolds number varies at different regions of the jet. The effect of the Reynolds number is more significant within the shear layer region. It was also found that by increasing the Reynolds number, the thickness of the boundary layer at the jet exit decreases and the length of the potential core increases.

Researchers have also used flow visualization techniques to characterize the behavior of free jets. Popiel and Trass [34] visualized the behavior of natural free jets, for two Reynolds numbers of 10,000 and 20,000, at regions near the nozzle exit using the smoke-wire flow visualization technique. It was found that the creation of vortices near the nozzle exit disturbs the boundary layer and leads to the elongation of the jet core. Kwon and Seo [35] used the particle image velocimetry (PIV) method to obtain the jet mean velocity and study the impact of Reynolds number on development of flow regions within free jets. It was found that the turbulent flow spreading rates gradually decreased by increasing the Reynold number. Dimotakis et al. [36] used laser induced fluorescence and particle streak velocity methods to obtain some physical insights into the structure and dynamics of turbulent jets. While recent researchers have used PIV methods to study the flow field, there is still a need to investigate the thermal flow fields, especially within the boundary layers where obtaining measurements is complicated.

Free Jet Facility.

The flow path of air for the free jet is very similar to the calibration setup. The jet cross section was used for the calibration purposes. For the free jet study, a streamwise cut at the center of the jet is desirable. In order to produce a free jet, a 0.0127 m diameter aluminum tube is connected to the PLIF flow line using the appropriate fitting. The tube length and jet diameter are 0.254 m and 0.0127 m, respectively. The ratio of the jet length to diameter is equal to 20. The entrance length for turbulent flow is approximately equal to ten pipe dimeters [37]; for this study, the tube is long enough to produce fully developed flow.

A schematic of the free jet setup is shown in Fig. 1. The camera is placed at a distance from the jet to record the length equal to 0.127 m downstream of the jet exit. The jet temperature is measured at the center of the jet at the nozzle exit and varies between 300 K and 375 K with the step size of 25 K. Three Reynolds numbers of 5000, 10,000, and 15,000 are used to produce turbulent free jets. This range of jet Reynolds numbers is typically seen in applications utilizing jet impingement for surface cooling/heating. Decreasing the Reynolds number yields uneven heating or cooling on the target surface, and increasing the Reynolds number can be costly in terms of mass flow and pressure losses. The jet exit, jet streamwise cut, origin, and the coordinate system used to present the free jet results are also illustrated in Fig. 1.

Experimental Procedure.

The PLIF experimental procedure for free jet tests consists of three main image recording steps: background images, reference images, and air/toluene images at different experimental conditions. For each step, two sets of 500 images are recorded: temperature dependent (using red filter) and temperature independent (using blue filter). Background images are captured while the laser is on and there is only airflow in the system (no tracer particles). Reference images are taken while the mixture of air and toluene is flowing in the system at room temperature (297 K) and the laser is on. Background images are taken for each filter at each temperature. There are two thermocouples located at the center of the jet at the nozzle exit. The temperature is closely monitored. After the jet reaches the steady-state condition (constant temperature at the tube outlet), the toluene is introduced to the flow line from the seeding system. The toluene is added to the flow by passing 20% of the air through the seeder. The seeded air mixes with the hot air from the heater and the mixture exits the nozzle into the measurement area. While the 80/20 division of the air is chosen for the experiments, it is not critical to maintain a precise seeding concentration, as this two-color PLIF method eliminates seed concentration variations. It is important to monitor the total flowrate to maintain the same Reynolds number. The air/toluene images are recorded while the laser is on. davis 8.3 software from LaVision is used to record the raw images. Images are exported from davis in the TIF format then postprocessed using an in-house matlab code.

Data Reduction.

The data reduction for the free jet experiments is very similar to the calibration data reduction. However, in order to reduce the noise, the two-color method process is slightly different for the free jet experiment. For the calibration image processing, a very small area located at the center of the jet cross section was desirable to collect the intensity information. However, for the free jet tests, the whole jet is studied for the PLIF validation. As was mentioned in the description of the calibration procedure, there are pixels that do not capture fluorescing tracer particles. Including these pixels in the time-averaging process and two-color method would lead to increased uncertainty of the experiment as well as including additional noise.

For this investigation, the 500 single raw images are background subtracted and time averaged. It is important to note that only pixels that carry an intensity magnitude greater than zero are considered in the time-averaging process. A distribution of the number of images that carry desirable intensities (intensity greater than zero) for the time-averaged images is created. This distribution, known as count, is used later as a threshold for the two-color method procedure. The count distribution presents how many images at each pixel are used for the time-averaged process. In other words, it shows the distribution of the number of images that capture a fluorescence tracer particle at each pixel. Figure 2 includes samples of the time-averaged images for temperature-dependent (red filter) and temperature-independent (blue filter) signals.

In order to apply the two-color method, propagation of the temperature-dependent and the temperature-independent count is calculated as
$Combinedcount=(Temperature−dependentcount)2+(Temperature−independentcount)2$
(5)

From the combined count distribution, the median value of the combined count is extracted and used as a threshold for the two-color method. Pixels of the time-averaged images that carry a count greater than the median value of the combined count are used in the two-color method. The same procedure is repeated on the free jets at higher temperatures. Figure 2 includes the postprocessing results on the free jet at T = 324.60 K and Re = 10,000.

The room temperature is the reference temperature for this experiment. The intensity ratio at the reference temperature is used in the normalizing procedure. The normalized image is the result of dividing the intensity ratio distribution at a given temperature by the intensity ratio obtained at the reference temperature. The normalizing procedure reduces the effect of inconsistencies in spatial illumination and camera sensitivity. In order to calculate the temperature distribution, the PLIF calibration correlation is applied to the normalized intensity ratio. The temperature distribution for T = 324.6 K at Re = 10,000 is shown as the last step in Fig. 2.

For the free jet experiments, 500 images are recorded for each test. The impact of number of images on the experiments is studied to confirm that 500 images are an adequate number. For this purpose, a comparison was conducted among a variety of number of images that are used for the postprocessing. Figure 4 presents the impact of the number of images on the radial temperature distribution at downstream location of Z/D = 5 for free jets at T = 324.60 K and Re = 10,000. As is seen, the data corresponding to 50 images are dispersed. As the number of images is increased, the data consistency improves. The impact of the number of images on the PLIF results is studied for all cases. At a 95% level of confidence, the data provide sufficient evidence that using more than 350 images does not affect the results.

Fig. 4
Fig. 4
Close modal

PLIF Free Jet Results.

For this study, free jet tests are created at nozzle temperatures ranging from 300 K to 375 K with the step size of 25 K. From these cases, the impact of jet Reynolds number on thermal development is investigated to validate the PLIF technique. The test cases are summarized in Table 2.

Table 2

Free jet test cases

Jet Reynolds numberOutlet temperature (K)
5000300, 325, 350, 375
10,000300, 325, 350, 375
15,000300, 325, 350, 375
Jet Reynolds numberOutlet temperature (K)
5000300, 325, 350, 375
10,000300, 325, 350, 375
15,000300, 325, 350, 375

Detailed, time-averaged, temperature distributions for cases with Re = 10,000 are presented in Fig. 5. The temperatures at the jet nozzle exit, recorded by thermocouples, are provided above the distribution. The PLIF experimental results near the jet exit closely agree with the thermocouple data. The relative error of the temperature near the jet exit, |TPLIFTTC|/TTC, for all cases are less than 6%. The standard deviation analysis for full jets is performed on the case with Re = 10,000. The relative uncertainties for the free jets at jet nozzle temperatures equal to 300.30 K, 324.60 K, 347.70 K, and 372.40 K are equal to 0.98%, 1.58%, 3.18%, and 2.76%, respectively. The uncertainties calculated for free jets agree with the calibration uncertainties described previously. The free jet experiments were conducted on different days. Thus, the reference temperature (room temperature) is not constant for all cases. The impact of this change is mostly eliminated through the normalizing process.

Fig. 5
Fig. 5
Close modal
A dimensionless temperature, θ, is defined (Eq. (6)) to maintain the consistency in comparing the results of the PLIF free jet cases. The reference temperatures (room temperatures) for this calculation are provided from thermocouple data; the jet (nozzle outlet) temperatures are directly extracted from the PLIF results. The dimensionless temperature, θ, varies between the range of zero and one. θ equal to zero means that the local temperature is equal to the reference temperature, and θ equal to one means that the local temperature is equal to the jet temperature at the nozzle exit. When the turbulent flow exits the nozzle, a mixing occurs between the jet core and ambient flow. The dimensionless temperature illustrates the extent of the mixing between the jet core and the ambient flow. For the areas with θ approaching unity, there is no mixing effect and jet is maintaining the nozzle exit temperature. The mixing effect is at its highest for areas with θ equal to zero when jet reaches the room temperature
$θ=T−TRefTJet−TRef$
(6)

Detailed, time-averaged, dimensionless temperature distributions for cases with Re = 10,000 are presented in Fig. 6. The θ distributions show similar magnitudes independent of the jet temperature. This figure also provides information about the jet core region. The jets retain the nozzle exit temperature in their potential cores. Moreover, the potential cores remain intact until approximately the same distance from the jet outlet Z/D ≈ 5 for all four cases, which is expected to be observed for cases with the same Reynolds number. For the momentum potential cores, it is expected to observe the uniform velocity until approximately seven diameters downstream from the jet outlet [38,39]. Available experimental investigations on free jets have primarily focused on jet velocity. Theory has shown the core of the turbulent, free jet is expected to remain intact until approximately 5.65 diameters downstream from the nozzle exit [31]. The thermal potential cores observed from PLIF tests only for cases with Re = 10,000 agree with the theoretical solutions.

Fig. 6
Fig. 6
Close modal

Before exploring the effect of Reynolds number on the thermal structure of the jet, it is necessary to discuss several artifacts of the proposed PLIF technique. Although the distributions shown in Figs. 5 and 6 represent “time-averaged” temperature profiles, the distributions do not take on the notable characteristics of time-averaged distributions. Each temperature distribution shown in Fig. 5 is the culmination of eight different image sets (each set consisting of 500 images). The small insets in Fig. 2 show typical intensity distributions obtained throughout the process. The “background subtracted” intensity distributions depict a more typical time-averaged jet structure. However, the pixel-by-pixel ratioing of these distributions introduces scatter into the distributions. Also, the magnitudes of the intensity distributions obtained using the temperature-dependent and -independent filters are relatively close to one another, so pixel-to-pixel variation can appear amplified.

Another distinct feature of the distributions appears along the outer edges of the jet. Again, looking at the intensity distributions shown in Fig. 2, the gradual decrease of the intensity from the seeded jet to the unseeded quiescent air is captured. The temperature distributions shown in Figs. 5 and 6 show a much more abrupt change from the jet to the stagnant surrounding air. The outer boundaries of the jet are defined based on the “threshold” from the combined count of the temperature-dependent and -independent intensity distributions. The threshold value has been set to increase the confidence of the primary features within the core of the jet. Reducing the number of instances occurring from the 500 images would provide a wider signature of the jet. With more mixing occurring along the edges of the jet, a single pixel will provide an intensity for the instances when the jet fluid covers the pixel. However, when the surrounding air occupies the pixel, no intensity is measured for that instant in time. For the current study, regions of high shear are not fully portrayed due to the thresholding procedure. This is further complicated by the use of a single camera and separate image sets obtained with the two filters. However, the core region of the jet is adequately represented by the PLIF distributions.

Reynolds Number Influence on the Jet Core.

The Reynolds number has the most influence on the free jet development [35]. In this study, the impact of increasing the jet Reynolds number is investigated. Figure 7 presents the detailed distribution of the temperature and dimensionless temperature at TJet ≈ 325 K for three different Reynolds numbers of jets. While the results are shown for the fixed temperature of 325 K, the non-dimensional distributions shown in Fig. 6, indicate at a given Reynolds number, the thermal structure of the jet does not change as the jet temperature changes. Therefore, the jet outlet temperature is constant as the Reynolds number changes. As shown in Fig. 7, an increase in the Reynolds number leads to an increase in the length of the jet potential core zone. The jets with a lower velocity (lower momentum) start exchanging the energy of the jet with the surrounding flow at a distance closer to the nozzle exit; thus, jets with lower Reynolds numbers have a shorter potential core. The impact of the Reynolds number depends on the jet region. As is seen in Fig. 7, the effect of the Reynolds number is more significant in the shear layer region where larger spread of momentum exists. The impact of the turbulent flow structure at the edge of the jet increases with increasing Reynolds number. Clearly, at higher Reynolds numbers, the jet shear layer vortices exist at a further distance downstream.

Fig. 7
Fig. 7
Close modal

Figure 7 also shows mixing layer development within free jets. Mixing layers are created between two flows with different velocities. For this study, turbulent jets spread into ambient flow with zero velocity. Figure 7 shows that mixing layers are formed near the nozzle exit lip and grow toward the end of jet core. The dimensionless temperature distribution in Fig. 7 provides a better visualization between jets at different Reynolds number. As is seen, the angle of spread of the mixing layer is the same for all Reynolds numbers.

Figure 8 shows the impact of the jet Reynolds number on the radial, dimensionless temperature distribution. Data are categorized based on four distances from the jet nozzles: one, three, five, and seven diameters. As mentioned earlier, the dimensionless parameter shows the impact of mixing. At the lowest Reynolds number of Re = 5000, the temperature of the jet clearly decreases as it moves away from the nozzle exit (Z/D increases). The jet is carrying the least momentum, and the ambient air readily mixes with the jet. The entrainment of the ambient air reduces the temperature of the jet.

Fig. 8
Fig. 8
Close modal

As the Reynolds number increases, the increased momentum of the jet resists the entrainment of the lower temperature, quiescent, ambient air. Therefore, the thermal core of the jet remains intact further downstream as the Reynolds number increases. With the faster moving jet, the shear layer developing along the edge of the jet is thinner, and mixing between the two fluids is reduced. As the jet continues to move further from the nozzle, the thickness of the shear layer increases, and more mixing occurs. The energy transport across the mixing layer is similar to the mass and momentum transport. As the Reynolds number increases, the breakdown of the jet is observed at Z/D > 5.

These radial temperature distributions reveal the decay of the turbulent jet as a function of Reynolds number. Additional data could be extracted from the jet two-dimensional distributions: in the radial direction at additional axial locations, or in the axial direction at multiple radial locations. The PLIF technique described in this paper is applied to jet impingement on a flat surface. With the jet impingement, the axial jet profiles are presented as an avenue to obtain the temperature gradient near the impingement surface. With the near-wall thermal gradient, it is possible to calculate the surface heat transfer coefficients. Therefore, more discussion of the turbulent jet can be seen with the application of the PLIF method [40].

PLIF Comparison With Analytical Solution for a Round, Free Jet.

Laser-induced fluorescence techniques have been used extensively in the past to acquire concentration gradients and more sparingly in flows at relatively high temperatures. With this study, detailed temperature distributions have been obtained within a heated jet under a variety of flow conditions and temperatures. From the detailed distributions, radial temperature profiles were extracted to quantitatively discuss the thermal development of the fee jets.

The discharge of jets into a stagnant fluid reservoir has been studied for decades. Analytical solutions for the development of both “slot” and “round” jets are readily available in literature [31]. For both types of flows, the free shear layer surrounding the jet governs the velocity and temperature profiles. Downstream of the potential core (Z/D > 5), an analytical solution can be used to describe the profile of the time-averaged, turbulent jet. Beginning with the mass and momentum equations in cylindrical coordinates, a solution for the time-averaged velocity profile can be obtained using a similarity variable [31].

The present case focuses on the temperature distribution of the jet. Bejan [31] expands this discussion and provides the following equation to describe the thermal behavior of a round jet (the nomenclature has been modified to match the current study):
$T−TRefTJet−TRef=exp[−(Rbt)2]$
(7)
Equation (7) directly shows the temperature distribution is dependent upon the radial location, R, within the jet. In addition, the thermal profile is changing in the streamwise direction, and this is represented by bt. Experiments have indicated that this streamwise (transversal) length scale is linearly proportional to the downstream location from the exit of the nozzle [41]. Taking into account the range of bt and rewriting the equation in terms of the current nomenclature and coordinate system, an analytical solution for the radial temperature profile of a free jet is shown by Eq. (8)
$T−TRefTJet−TRef=−exp[−(2.5⋅RD⋅DZ)2]+2$
(8)

The temperature profiles obtained using the PLIF technique are compared with those generated from the analytical, similarity solution (Eq. (8)) in Fig. 9. As indicated by Bejan [31], this similarity solution applies to developed jets (Z/D > 5). Therefore, comparisons are included for Z/D = 3, 5, and 7 with a jet Reynolds number of Re = 15,000. As shown in the figure, the overall the PLIF data is in good agreement with the profile proposed by the analytical solution. The most noticeable variation between the experimental data and the analytical solution is with the radial spread of the jet.

Fig. 9
Fig. 9
Close modal

Building on the previous work, the streamwise variation in the temperature should be captured with the constant, bt. As this is believed to be linearly related to the downstream distance from the nozzle, Eq. (8) should properly capture this effect. Therefore, the source of this variation may lie with the data reduction process. With the time-averaging and filtering of the raw images, each pixel must satisfy a minimum threshold for the number of images returning a measurable intensity. In the mixing layer, along the outer perimeter of the jet, the seeded jet is mixing with the unseeded surrounding air. Therefore, with the mixing, it is possible for pixels along the edge to return more images without intensity than with a measured intensity from the tracer particles. The outer structure of the jet is directly affected by this data reduction process. Lowering the threshold could present a jet with more radial spread at any streamwise location. However, lowering the threshold also increases the uncertainty of the measured temperature. Therefore, the threshold has been set to compromise between these two factors. However, this process could be responsible for the discrepancy shown between the PLIF measurements and the analytical solution.

Extension of the PLIF Method.

With this novel attempt to study the thermal development of a heated, free jet, several points should be carefully considered with further implementation. In order to remove the effect of seed concentration, the ratio of images using two separate filters are needed. In the current investigation, two separate sets of 500 images were recorded at different instances in time. Utilizing two cameras simultaneously or image doubling hardware could reduce any uncertainty associated with taking the ratio of two different image sets. Furthermore, the proposed procedure includes eight different sets of images to yield the final temperature distribution.

Only time-averaged temperature profiles have been presented in this work. Providing a more comprehensive data set is needed for complete validation of CFD codes. With the recording of 500 images for each filter for each flow/thermal condition, the opportunity exists to further analyze the raw intensity images to obtain root-mean-square (RMS) temperature distributions. The coupling of instantaneous temperature and velocity measurements will provide the complete reconstruction of turbulent flow and heat transfer.

With further implementation and increased sensitivity of image acquisition hardware, the quality of the results will continuously improve. The method has shown the potential for quantitatively assessing the thermal development of an unbounded flow. The application of the method to near-wall flows will extend the capabilities of the PLIF technique to measure temperature gradients near a surface. Not only will these gradients provide information of the thermal boundary layer development, but they will also provide a means to calculate the convective heat transfer coefficient on the surface. A variety of opportunities exists for the widespread application of the PLIF technique presented in this study. A complimentary study demonstrates the direct application of this PLIF method for the characterization of a cool jet impinging on a hot surface. In this work, the near-wall temperature gradient is obtained using the PLIF method, and the surface convective heat transfer coefficients are calculated. Favorable agreement is shown between the heat transfer coefficients obtained using the PLIF method and a more traditional, convective heat transfer experiment [40].

Conclusions

This work has shown that two-color, PLIF thermometry can be used to obtain thermal distributions through fluids with relatively small temperature changes. A toluene-based, two-color method of planar fluorescence measurements has been presented. The details of the experimental setup, calibration procedure, and data reduction method have been provided. After completing the calibration to obtain a relationship between the emission intensity of the toluene and the air/toluene mixture temperature, the method was used to obtain thermal maps within the center of a free jet. In its current form, the proposed method was used to obtain time-averaged temperature distributions in flows ranging from 300 to 375 K. The temperature profiles were obtained for jets issued at different temperatures and varying Reynolds numbers.

The method proved its capability to capture temperature distributions under a variety of flow conditions. With the establishment of the method, it is possible to apply the technique to more complex flow fields and focus on near-wall thermal boundary layer development. In addition, the acquisition of detailed temperature distributions within a fluid will be beneficial for the validation of numerical simulations.

Acknowledgment

This work has been sponsored by the National Science Foundation under award number CBET-1126371. The authors would like to thank Drs. Truell Hyde and William Jordan of Baylor University for their support of this project. In addition, the machine work (and advice) of Mr. Ashley Orr was vital to the completion of the work.

Nomenclature

c=

speed of light in a vacuum (m/s)

f=

focal length (mm)

h=

Planck’s constant (J·s)

i=

laser energy (J)

D=

nozzle (jet) diameter (m)

E=

incident laser energy (J/cm2)

I=

intensity (au)

R=

radial coordinate (from jet center) (m)

T=

temperature (K)

V=

jet velocity (m/s)

Z=

axial coordinate (along jet centerline) (m)

bt=

constant representing the thermal, streamwise length scale (similarity solution) (m)

ni=

tracer number density (cm−3)

ni–Blue=

temperature-independent spectral response of optical system (cm−3)

ni–Red=

temperature-dependent spectral response of optical system (cm−3)

IBack–Blue=

temperature-independent fluorescence intensity of background images (au)

IBack–Red=

temperature-dependent fluorescence intensity of background images (au)

IBlue=

temperature-independent fluorescence intensity of toluene/air images (au)

IN=

normalized fluorescence intensity of toluene/air images (–)

IRed=

temperature-dependent fluorescence intensity of toluene/air images (au)

IRef=

intensity ratio at reference temperature (–)

Sf=

fluorescence signal intensity (number of protons)

Sf–Blue=

temperature-independent fluorescence signal (number of protons)

Sf–Red=

temperature-dependent fluorescence signal (number of protons)

TJet=

jet temperature (outlet of nozzle) (K)

TPLIF=

temperature measured at the exit of the nozzle using PLIF (K)

TRef=

reference (room) temperature (K)

TTC=

temperature measured at the exit of the nozzle using thermocouples (K)

Fi(λ)=

spectral transmission curve (au)

Fi–Blue(λ)=

temperature independent spectral transmission curve (au)

Fi–Red(λ)=

temperature dependent spectral transmission curve (au)

Re=

jet Reynolds number (ρVD/μ) (–)

ηtol=

collection efficiency (–)

θ=

non-dimensional temperature (–)

λ=

wavelength of excitation laser (nm)

μ=

dynamic viscosity (N·s/m2)

ρ=

density (kg/m3)

σ=

absorption cross section (cm2)

ϕ=

fluorescence quantum yield (–)

References

1.
Cooper
,
T.
,
Field
,
R.
, and
Meyer
,
J.
,
1975
, “
Liquid Crystal Thermography and Its Application to the Study of Convective Heat Transfer
,”
ASME J. Heat Transfer
,
97
(
3
), pp.
442
450
. 10.1115/1.3450396
2.
Lui
,
T.
, and
Sullivan
,
J. P.
,
2005
,
Pressure and Temperature Sensitive Paints
,
Springer
,
New York
.
3.
Kohse-Hoinghaus
,
K.
,
1994
, “
Laser Techniques for the Quantitative Detection of Reactive Intermediates in Combustion Systems
,”
Prog. Energy Combust. Sci.
,
20
(
3
), pp.
203
279
. 10.1016/0360-1285(94)90015-9
4.
Hanson
,
R. K.
,
Seitzman
,
J. M.
, and
Paul
,
P. H.
,
1990
, “
Planar Laser-Fluorescence Imaging of Combustion Gases
,”
Appl. Phys. B: Lasers Opt.
,
50
(
6
), pp.
441
454
. 10.1007/BF00408770
5.
Schulz
,
C.
, and
Sick
,
V.
,
2005
, “
Tracer-LIF Diagnostic: Quantitative Measurement of Fuel Concentration, Temperature and Fuel/Air Ratio in Practical Combustion Systems
,”
Prog. Energy Combust. Sci.
,
31
(
1
), pp.
75
121
. 10.1016/j.pecs.2004.08.002
6.
Singh
,
V.
,
Parthasarathy
,
R. N.
, and
Gollahalli
,
S. R.
,
2016
, “
Radiative Heat Transfer and Fluorescence Measurements in Laminar Prevaporized Canola Methyl Ester/Diesel Blend Flames
,”
ASME J. Therm. Sci. Eng. Appl.
,
8
(
1
), p.
011006
. 10.1115/1.4030701
7.
Huang
,
R. F.
,
Kivindu
,
R. M.
, and
Hsu
,
C. M.
,
2018
, “
Combusting Jets Issued From Rectangular Nozzles of High and Low Aspect Ratios With Co-Flowing Air
,”
ASME J. Therm. Sci. Eng. Appl.
,
10
(
4
), p.
041009
.
8.
Long
,
M. B.
,
Webber
,
B. F.
, and
Chang
,
R. K.
,
1979
, “
Instantaneous Two-Dimensional Concentration Measurements in a Jet Flow by Mie Scattering
,”
Appl. Phys. Lett.
,
34
(
1
), pp.
22
24
. 10.1063/1.90584
9.
Kychakoff
,
G.
,
Howe
,
R. D.
,
Hanson
,
R. K.
, and
McDaniel
,
J. C.
,
1982
, “
Quantitative Visualization of Combustion Species in a Plane
,”
Appl. Opt.
,
21
(
18
), pp.
3225
3227
. 10.1364/AO.21.003225
10.
Dyer
,
M. J.
, and
Crosley
,
D. R.
,
1982
, “
Two-Dimensional Imaging of OH Laser Induced Fluorescence in a Flame
,”
Opt. Lett.
,
7
(
8
), pp.
382
384
. 10.1364/OL.7.000382
11.
Allen
,
M. G.
, and
Hanson
,
R. K.
,
1988
, “
Digital Imaging of Species Concentration Fields in Spray Flames
,”
Symp. (Int.) Combust.
,
2
(
1
), pp.
1755
1762
. 10.1016/S0082-0784(88)80409-0
12.
McDaniel
,
J. C.
,
Hiller
,
B.
, and
Hanson
,
R. K.
,
1983
, “
Simultaneous Multiple-Point Velocity Measurements Using Laser-Induced Iodine Fluorescence
,”
Opt. Lett.
,
8
(
1
), pp.
51
53
. 10.1364/OL.8.000051
13.
Seitzman
,
J. M.
,
Kychakoff
,
G.
, and
Hanson
,
R. K.
,
1985
, “
Instantaneous Temperature Field Measurements Using Planar Laser-Induced Fluorescence
,”
Opt. Lett.
,
10
(
9
), pp.
439
441
. 10.1364/OL.10.000439
14.
Dong
,
B.
,
Huang
,
Y.
, and
Wu
,
J.
,
2019
, “
Temperature Profile of Thermal Impinging Flow Induced by Horizontally Oriented Rectangular Jet Flame Upon an Opposite Plate
,”
ASME J. Therm. Sci. Eng. Appl.
,
11
(
5
), p.
051019
. 10.1115/1.4043469
15.
Thurber
,
M. C.
,
1999
, “
Acetone Laser-Induced Fluorescence for Temperature and Multiparameter Imaging in Gaseous Flows
,”
Ph.D. dissertation
,
Stanford University
.
16.
Thurber
,
M. C.
, and
Hanson
,
R. K.
,
2001
, “
Simultaneous Imaging of Temperature and Mole Fraction Using Acetone Planar Laser-Induced Fluorescence
,”
Exp. Fluids
,
30
(
1
), pp.
93
101
. 10.1007/s003480000142
17.
Thurber
,
M. C.
,
Grisch
,
F.
, and
Hanson
,
R. K.
,
1997
, “
Temperature Imaging With Single- and Dual-Wavelength Acetone Planar Laser-Induced Fluorescence
,”
Opt. Lett.
,
22
(
4
), pp.
251
253
. 10.1364/OL.22.000251
18.
Thurber
,
M. C.
,
Kirby
,
B. J.
, and
Hanson
,
R. K.
,
1998
, “
Instantaneous Imaging of Temperature and Mixture Fraction With Dual-Wavelength Acetone PLIF
,”
36th AIAA Aerospace Sciences Meeting and Exhibit
,
Reno, NV
, pp.
397
406
.
19.
Kakuho
,
A.
,
Nagamine
,
M.
,
Amenomori
,
Y.
,
Urushihara
,
T.
, and
Itoh
,
T.
,
2006
, “
In-Cylinder Temperature Distribution Measurement and its Application to HCCI Combustion
,”
SAE Paper No. 2006-01-1202
.
20.
Koban
,
W.
,
Koch
,
J. D.
,
Hanson
,
R. K.
, and
Schulz
,
C.
,
2004
, “
Absorption and Fluorescence of Toluene Vapor at Elevated Temperatures
,”
Phys. Chem. Chem. Phys.
,
6
(
11
), pp.
2940
2945
. 10.1039/b400997e
21.
Hanson
,
R. K.
,
1988
, “
Combustion Diagnostics: Planar Imaging Techniques
,”
Symp. (Int.) Combust.
,
21
(
6
), pp.
1677
1680
. 10.1016/S0082-0784(88)80401-6
22.
Yoo
,
J. H.
,
2011
, “
Strategies for Planar Laser-Induced Fluorescence Thermometry in Shock Tube Flows
,”
Ph.D. dissertation
,
Stanford University
.
23.
Koch
,
J.
,
2005
, “
Fuel Tracer Photophysics for Quantitative Planar Laser-Induced Fluorescence
,”
Ph.D. dissertation
,
Stanford University
.
24.
Thurber
,
M. C.
, and
Hanson
,
R. K.
,
1999
, “
Pressure and Composition Dependences of Acetone Laser-Induced Fluorescence with Excitation at 248, 266, and 308 Nm
,”
Appl. Phys. B: Lasers Opt.
,
69
(
3
), pp.
229
240
. 10.1007/s003400050799
25.
Kearney
,
S.
, and
Reyes
,
F.
,
2003
, “
Quantitative Temperature Imaging in Gas-Phase Turbulent Thermal Convection by Laser-Induced Fluorescence of Acetone
,”
Exp. Fluids
,
34
(
1
), pp.
87
97
. 10.1007/s00348-002-0537-1
26.
O’Byrne
,
S.
,
Danehy
,
P. M.
, and
Houwing
,
A. F. P.
,
2003
, “
PLIF Temperature and Velocity Distributions in Laminar Hypersonic Flat-Plate Flow
,”
20th International Congress on Instrumentation in Aerospace Simulation Facilities
,
Gottingen, Germany
, pp.
136
147
.
27.
Coleman
,
H. W.
, and
Steele
,
W. G.
,
1999
,
Experimentation and Uncertainty Analysis for Engineers
, 2nd ed.,
John Wiley & Sons, Inc.
,
New York
.
28.
Scott
,
B.
,
Willman
,
C.
,
Williams
,
B.
,
Ewart
,
P.
, and
Stone
,
R.
,
2017
, “
In-Cylinder Temperature Measurements Using Laser Induced Grating Spectroscopy and Two-Colour PLIF
,”
SAE Int. J. Engines
,
10
(
4
), pp.
2191
2201
. 10.4271/2017-24-0045
29.
Lewis
,
E.
,
Lau
,
T.
,
Sun
,
Z.
,
Nathan
,
G.
, and
Alwabhabi
,
Z.
,
2018
, “
Gas-Phase Temperature Measurement of Particle-Laden Jets
,”
Australasian Heat and Mass Transfer Paper No. 11AHMTC18-16
.
30.
Banks
,
D.
,
Robles
,
V.
,
Zhang
,
B.
,
Devia-Cruz
,
L. F.
,
Camacho-Lopez
,
S.
, and
Aguilar
,
G.
,
2019
, “
Planar Laser Induced Fluorescence for Temperature Measurement of Optical Thermocavitation
,”
Exp. Therm. Fluid Sci.
,
103
, pp.
385
393
. 10.1016/j.expthermflusci.2019.01.030
31.
Bejan
,
A.
,
2013
,
Convection Heat Transfer
, 3rd ed.,
John Wiley & Sons, Inc.
,
New York
.
32.
List
,
E. J.
,
1982
, “
Turbulent Jets and Plumes
,”
Annu. Rev. Fluid Mech.
,
14
(
1
), pp.
189
212
. 10.1146/annurev.fl.14.010182.001201
33.
Fellouah
,
H.
,
Ball
,
C. G.
, and
Pollard
,
A.
,
2009
, “
Reynolds Number Effects Within the Development Region of a Turbulent Round Free Jet
,”
Int. J. Heat Mass Transfer
,
52
(
17–18
), pp.
3943
3954
. 10.1016/j.ijheatmasstransfer.2009.03.029
34.
Popiel
,
C. O.
, and
Trass
,
O.
,
1991
, “
Visualization of a Free and Impinging Round Jet
,”
Exp. Therm. Fluid Sci.
,
4
(
3
), pp.
253
264
. 10.1016/0894-1777(91)90043-Q
35.
Kwon
,
S. J.
, and
Seo
,
I. W.
,
2005
, “
Reynolds Number Effects on the Behavior of a Non-Buoyant Round Jet
,”
Exp. Fluids
,
38
(
6
), pp.
801
812
. 10.1007/s00348-005-0976-6
36.
Dimotakis
,
P. E.
,
Miake-Lye
,
R. C.
, and
Papantoniou
,
D. A.
,
1983
, “
Structure and Dynamics of Round Turbulent Jets
,”
Phys. Fluids
,
26
(
11
), pp.
3185
3192
. 10.1063/1.864090
37.
Cengel
,
Y. A.
, and
Cimbala
,
J. M.
,
2006
,
Fluid Mechanics: Fundamentals and Applications
, 4th ed.,
McGraw-Hill, New York
.
38.
Han
,
J. C.
,
Dutta
,
S.
, and
,
S.
,
2012
,
Gas Turbine Heat Transfer and Cooling Technology
, 2nd ed.,
CRC Press
,
Boca Raton, FL
.
39.
Han
,
B.
, and
Goldstein
,
R.
,
2001
, “
Jet-Impingement Heat Transfer in Gas Turbine Systems
,”
,
934
(
1
), pp.
147
161
. 10.1111/j.1749-6632.2001.tb05849.x
40.
Wright
,
L. M.
, and
Seitz
,
S.
,
2019
, “
Thermal Development of an Impinging Jet Using Planar Laser Induced Fluorescence (PLIF)
,”
ASME Paper No. GT2019-92062
.
41.
Fischer
,
H. B.
,
List
,
E. J.
,
Koh
,
R. C. Y.
,
Imberger
,
J.
, and
Brooks
,
N. H.
,
1979
,
Mixing in Inland and Coastal Waters
,