Light Scattering from Particles and Molecules

Figure 1. Mie scattering spectral content.

First we consider the characteristics of the light scattering process. This scattering arises when an incident light ray encounters a perturbation due to a small particle or molecule. When this occurs, a portion of the energy reradiates in all directions centered at the particle. It is common, as in our discussions, to separate Mie scattering and Rayleigh scattering by the relative diameter of the particle (l) although Mie scattering theory is fully capable of describing the scattering in the Rayleigh regime). Mie scattering is generally defined as scattering from particles which are greater than 1/10 of the incident light wavelength (and Rayleigh scattering is defined as scattering from particles with diameters less than 1/10 [McCartney, 1976]. Scattering from particles (liquid or solid) can be in either the Mie or Rayleigh regime, but in general all molecules fall into the Rayleigh scattering regime for visible wavelengths. There are however other attributes of the scattering process which are different for particles and molecules, therefore the remainder our discussion on light

Figure 2. Vector definitions.

Scattering will be separated into two regimes: scattering from particles and scattering from molecules. When the scattered signal is collected from particles, two spectral characteristics are important in our application to molecular filtered based diagnostic techniques as illustrated in Figure 1. First, the scattering from particles is generally not broadened due to thermal motions, therefore it has approximately the same line width as the illuminating laser light (Figure 1). Secondly, the particle Mie/Rayleigh scattering will exhibit a Doppler shift in frequency which is given by:

Df = 1/l (k_s - k₀) . V

where k_s and k₀ are the observation and incident unit light-wave vectors, respectively, V is the flow velocity vector (as illustrated in Figure 2), and is the wavelength of the incident light. From Equation 1 it can be seen that the direction of velocity sensitivity is defined by the bisector of the directions defined by k_s and negative k₀.

 

 

 

 

Figure 3. Rayleigh scattering spectral content.

If the scattering is from molecules in the Rayleigh regime the intensity of the scattered light varies as the sixth power of the equivalent particle diameter and as the inverse of the incident wavelength to the fourth power [McCartney, 1976]. The strong dependence on wavelength results in a significant improvement in scattered signal levels when shorter wavelengths are used. Unlike scattering from particles, the scattering from molecules will be affected by the thermal motions of the fluid. Therefore, the spectral profile of the molecular/scattered light is changed from the incident light spectra as illustrated in Figure 3. The scattered intensity is proportional to the density. The Rayleigh scattering frequency line-width (FWHM) is a function of the temperature (due to thermal induced molecular motions The shape of the scattered spectrum (as illustrated in Figure 3) is governed by the y-parameter which is also a unction of the density and governs the onset of Brillouin scattering effects. The y parameter is the ratio of the collisional frequency to the acoustic spatial frequency. It is recognized that for y of order unity or greater (the kinetic regime), Brillouin components become important and kinetic models must be used. For y <<1 (low pressures or high temperatures) the scattering spectrum is Gaussian and the Brillouin components can be neglected [Tenti et al., 1974]. As y is increased (typical of air at atmospheric conditions), Brillouin lobes become more apparent in the Rayleigh scattering frequency profile.

 

Molecular/Atomic Absorption Filter

Figure 4. Iodine absorption profile in tuning range of Nd:YAG.

Figure 5. Change in absorption line used in FRS experiments due to iodine number density.

A second area of understanding required before describe molecular filtered based diagnostic techniques is the idea and attributes of a molecular absorption filter. First consider an optical cell, which is basically a glass cylinder with to flat windows attached to both ends. The optical cell can then be filled with a molecular vapor which has an absorption spectra within the wavelength (or frequency tuning range) of a narrow-linewidth laser. If the laser can be varied in frequency across the absorption lines, several distinct lines may be realized in the transmission spectra. For example (and due to their relevance to our current work) the absorption lines of iodine are a result of overlapping vibration-rotation transitions in the resonant B(0+u3 ) X(0+g1 ) electronic band and has been calculated by the model of Forkey (1996). A portion of this spectra is accessible by the second harmonic of a Nd:YAG laser (Figure 4) where the transmission is defined by the ratio of the spectral intensity of the incoming light (I0 ) to the spectral intensity of the transmitted light (I ). Within the tuning range of these lasers are frequencies where the molecular species absorbs the laser light to varying degrees. For example Figure 5 gives an absorption line of iodine measured by tuning a Nd:YAG laser through a 10 cm long optical cell with iodine at a partial pressure of 1.03 torr and a cell body temperature of 373 K. As can be seen, the absorption line is not discrete, but have a varying spectral line profile depending on the broadening processes (i.e. natural broadening, temperature broadening, pressure broadening etc.) determined by the thermodynamic conditions and species present in the cell. Here the profiles illustrate the variation in absorption spectra due to the change of the colder side arm temperature which changes the number density (or partial pressure) of the iodine vapor.

 

 

 

APPLICATIONS OF MOLECULAR FILTERS TO FLOW DIAGNOSTICS

Figure 6. Typical FRS set-up.

Returning to the concept of the optical cell filled with an absorbing species (also termed a molecular absorption filter) we now consider placing the absorption filter in front of a camera or other light detecting device (i.e. Photomultiplier tube) as illustrated in Figure 6. A shown in the figure for imaging the laser beam is generally spread out into a planar sheet of light to illuminate the flow. If the light is collected from scattering off of particles or molecules in the flow field, the absorption filter will act as a notch filter in the frequency domain. The subsequent effect to the intensity recorded by the camera is dependent on the frequency of the laser relative to the absorption lines of the filter, the transmission profile of the filter, the incident light direction, the observation direction, characteristics of the scattering, and properties of the flow field. There are three general applications in which molecular filtered based diagnostic techniques are utilized in the study of fluid dynamics and combustion which will be briefly described here and in more detail in the articles which appear in the special issue.

 

 

 

Flow visualization

Figure 7. Filter and scattering spectra for flow visualizations.

Figure 7 illustrates the advantage afforded by molecular filtered based diagnostics in collecting weak scattered signals for flow visualizations. In general, there are two sources of unwanted scattering: surface scattering due to walls and windows and scattering due to particles present in the flow. As shown in Figure 7, both these unwanted sources of scattering exhibit a narrow linewidth. If the laser is tuned to the center of the absorption profile, the scattering from walls and windows (that experience no shift in frequency) will be significantly–although many times not completely–absorbed. By judiciously selecting the observation and incident laser directions (k_s and k₀) such that the scattering from particles or molecules in flow experience a Doppler shift they can be shifted in frequency outside the absorption profile. Additionally if the scattering is from molecules in the Rayleigh regime a portion of the scattering can pass outside of the absorption profile due to thermal broadening, even when the center of the profile coincides with line-center of the iodine transition. Although not presented in this special issue, several research groups have employed molecular filters to improve the flow visualizations to investigate a variety of flow fields, including supersonic boundary layers (Miles and Lempert, 1990, Baumgartner et al., 1997, Arnette et al. 1998), compressible shear layers (Elliott et al., 1992), and supersonic shock boundary layer interactions (Forkey et al., 1994).

 

Figure 8. FRS of an underexpanded jet.

Figure 8 gives an example of the potential of molecular filtered Rayleigh scattering to improve the flow visualizations using molecular Rayleigh scattering. The FRS images were taken of a 12.5-mm-diameter underexpanded jet (equivalent Mach number of 2.0 and stagnation pressure of 786 kPa) issuing from a converging axisymmetric nozzle. The supersonic flow is from left to right and the laser sheet propagation direction is from top to bottom of the image. With this arrangement, the FRS system is not sensitive to Doppler shift in the streamwise direction; thus, the scattering intensity variations result primarily from density and temperature variations (as the thermal broadening causes some of the Rayleigh scattering to pass outside of the absorption profile). Both instantaneous (Figure 8a) and average images (Figure 8b, an ensemble average of 300 instantaneous images) are shown. Clearly visible in both the average and instantaneous images is the presence of the Mach disk, shock/expansion cells, and the shear layer. In the instantaneous image, the signal-to-noise ratio is still sufficient to observe the turbulence structures in the flow field. Again, it should be kept in mind that no filtering of the flow field has been done and if the absorption filter were not present, the image would be saturated by particle and background scattering.

 

Figure 9. Experimental setup for laser induced breakdown FRS experiments.

The process by which focused laser energy deposited into a gas is sufficient to induce optical breakdown has been studied since the development of the laser and continues to be studied in the context of various applications [Raizer, 1977, Adelgren et al., 2001, and Dors et al., 2000]. This process can be described by four progressive states [Adelgren et al., 2001]: 1) initial release of electrons by a multi-photon effect; 2) ionization of the gas in the focal region by the cascaded release of electrons; 3) absorption and reflection of the laser energy by the plasma, rapid expansion of the plasma and detonation wave formation; and 4) the propagation of the detonation wave into the surrounding gas and relaxation of the focal region plasma. Figure 9 shows the optical arrangement used to study the flow field susequent to laser-induced breakdown in air. The laser sheet is formed and propagates from left to right in the images, with the laser beam which induces the breakdown propagating top to bottom. The laser used for the FRS imaging was tuned to the center of the absorption line (18789.28 cm-1) so that background emission and particle scattering is absorbed by the filter while a portion of the thermally broadened Rayleigh scattering passes to the intensified camera. Images were taken at varying time delays from the initiation of optical breakdown. A second Q-switched, frequency-doubled Nd:YAG laser was used to achieve dielectric breakdown of quiescent air; this laser delivered ~200 mJ per pulse and the beam was focused by a 250-mm focal-length lens.

 

 

Figure 10. FRS of laser induced breakdown in air.

Figure 10 shows the FRS image/movie of the laser-induced breakdown at increasing time delays from the initiation of the breakdown pulse to the initiation of the FRS imaging pulse. In the first two images, the emission from the breakdown is still visible. Subsequent images show the formation of the weak blast wave that emanates from the breakdown until it exits the viewing area by 50 s. This is visible because the density and velocity behind the wave change the transmitted scattering intensity. Also clearly visible is the evolution of a ringed vortex of the heated fluid which grows and propagates in time. Since the sheet cuts through the structure, the ringed vortex appears as two circular dark regions, since the density is decreased and the temperatures increased by the optical breakdown. This ringed vortex induces a jet from the center which appears to have a secondary vortex pattern at the end. The evolution of the flow field from laser induced optical breakdown has been studied computationally by Dors et al. (2000) and is described in more detail or a variety of quiescent and supersonic flow fields by Adelgren et al. (2001).

 

Velocity Measurement

Figure 11. PDV setup for velocity measurements.

Figure 12. Filter and scattering spectra for PDV.

Figure 13. Intensity velocity function for PDV.

By far the most common use of molecular based filtered diagnostics is for velocity measurements of seeded flow fields. The molecular filtered based velocimetry techniques go by several achronimes (Plannar Doppler Velocimetry - PDV, Doppler Global Velocimetry - DGV (Meyers and Komine, 1992), Filtered Planar Velocimetry - FPV, Absorption Filter-Planar Doppler Velocimetry [Smith er al., 1996], and Filtered Rayleigh Scattering (FRS) Velocimetry [Miles and Lempert, 1990]). PDV uses a narrow-linewidth laser to illuminate a plane of the flow field as illustrated in Figure 11. As illustrated, the laser sheet is imaged by one camera which views the illuminated plane through a molecular filter, termed the filter or signal camera (or signal image), and a second camera which views the plane without a filter, termed the reference camera (or reference image). Through judicious selection of the absorption line used, the filter can be operated in the optically thin regime or pressure broadened with a nonabsorbing molecule resulting in a transmission profile with finite sloping edges as shown in Figure 12. The flow field contains small particles which are seeded into the flow or occur naturally (such as condensation) and scatter the illuminating light from the laser sheet. The spectral intensity of the light which passes through the molecular filter is the convolution of the scattered spectral intensity from the particles illuminated in the flow field, and the absorption profile of the molecule present within the cell (as illustrated in Figure 12). As an example, consider a case where the laser frequency, f₀, is tuned to the midpoint of the transmission profile. The scattered light experiences a change in frequency, due to the Doppler shift (Equation 1), causing the transmission from the scattered light to either increase or decrease depending on whether the frequency increases or decreases. Note, also, that there is no ambiguity in the direction of the shift: positive and negative frequency shifts are distinguished by the increase or decrease in transmission respectively. The pixels of the signal camera CCD array, record the integrated spectral intensity which is transmitted through the molecular filter's absorption profile and is given by I (i.e. I = I d with the limits on the integration dependent on the spectral sensitivity of the camera and optics). The second reference camera (or a separate portion of the same camera) is used to collect images of the flow field without the molecular filter. The reference camera is used to account for intensity fluctuations due to laser energy (and/or sheet energy distribution) or seed-concentration variations. The reference camera records I₀, which is the integrated spectral intensity of the unfiltered light (i.e. I₀ = I₀ d ). The integrated transmission through the cell (TR) is obtained by dividing the intensities of the signal (I) and reference (I₀) cameras at corresponding pixels. Figure 13 shows a plot of the integrated transmission as the independent variable and the frequency shift as the dependent variable with points taken from Figure 12 highlighted. In a PDV experiment, once the integrated transmission (TR) is determined from the two cameras at each corresponding pixel, the Doppler shift can be found at each pixel using the frequency function of the filter used (Figure 13). The velocity is then calculated at each pixel of the image using this measured Doppler shift and Equation 1. As may be noted in Equation 1, the measured Doppler shift is dependent on the angle between the illumination and observation directions, respectively. This fact may be exploited in order to make multi-component velocity measurements—either by viewing the flow field from more than one direction (changing the observed unit light-wave vector k_s), or by illuminating the flow field from multiple directions (changing the incident light wave vector, k₀). Both approaches have been used by researchers in order to make multi-component velocity measurements.

 

Figure 14. Velocity field behind a delta wing measured using PDV and computed using CFD .

Three-component velocity systems have been developed by our research staff in association with Innovative Scientific Solutions Incorporated and have been used to test a variety of models in large-scale facilities. Shown in Figure 14 is the velocity at 97% chord of a delta wing at 23 degrees angle of attack simulated by Rizzetta (1996) and measured using Planar Doppler Velocimetry at AFRL. The dominant flow direction is directed out of the page and the velocity component shown is predominately in the vertical direction with the vortex pair clearly visible. This same system has been used to make velocity measurements of the flow field above various aircraft models in addition to supersonic jets with a forced shear layer. Using a Mach 1.34 jet, large scale structures were forced in the compressible shear layer using a focused laser beam at the edge of the jet (Figure 15). For moderate Mach numbers, shear layer large scale structures exist and are generally described as a roller-type structure

Figure 15. Experimental setup for laser induced jet excitation.

characterized by a central vortex core and braid region which contain regions of streamwise vorticity. The study of these structures is motivated by an interest to increase our fundamental understanding of the flow physics, and also possible applications of energy deposition to enhance mixing of supersonic shear layers. This method of forcing allows the synchronization of the velocity measurements with the large scale structure as it convects downstream. Figure 16 shows the three velocity components measured using PDV. The velocity content of the large scale structure is clearly evident in all the images. The streamwise velocity component, shows an indentation into the core flow caused by the large scale structure. The vorticity of the structure is clearly seen in the positive and negative peaks in the lateral velocity component and the spanwise component shows positive and negative peaks which indicate the braid region. Measurements were also taken at other delay times so that the evolution of the large scale structure and velocity content can be described.

Figure 16. Three velocity components of forced jet measured using PDV.

 

Thermodynamic Property Measurement

Now that we have demonstrated that molecular filter diagnostic techniques have the ability to improve flow visualizations and make velocity measurements in flow fields, we now turn our attention to other thermodynamic properties (i.e. temperature, density, pressure, and velocity) which can be measured. The majority of the molecular filter based techniques which are used to make multiple thermodynamic measurements fall under the class of techniques termed Filtered Rayliegh Scattering (FRS) by the originators of the technique Miles and Lempert [1990]. This is due to the fact that FRS relies on Rayleigh scattering from molecules in order to obtain thermodynamic data (other than velocity). Returning to our discussion of Rayleigh scattering and Figure 3 we can see that all of the flow properties (temperature, density, pressure and velocity) have some effect on the spectral intensity of the Rayleigh scattering. For example the density is proportional to the integrated intensity, the width of the scattering is related to the temperature of the flow, and the position of the center of the profile is related to the Doppler shift or velocity. Also we have the ideal gas law which relates the temperature, pressure, and number density together. The question becomes how to separate these effects and calculate the desired flow properties in a real flow field.

Figure 17. Schematic of FRS process to measure multiple properties.

One of the first methodologies to measure the multiple properties in a flow was proposed by Miles and Lempert in 1990 and further developed by Forkey et al. (1996) was to scan the frequency of the laser across the absorption line and measure the subsequent transmission of the Rayleigh scattering through the iodine cell at each frequency. Figure 17 gives a schematic of the process proposed by Miles and Lempert (1990) and Forkey (1996) where the absorption line, laser frequency, and Doppler shifted Rayleigh scattering is shown at five representative points throughout the scan. Also shown is the spectrally integrated intensity which would be recorded by the detector observing the flow through the iodine cell. At the first frequency location (a), the laser and all of the Rayleigh scattering spectral profile is outside the filter and therefore the integrated intensity is unaffected by the absorption profile. At frequency positions (b) and (d) half of the Rayleigh scattering spectra has been attenuated by the absorption filter. Forkey [1996] demonstrated that the slope of this frequency (or near to it) will change as the temperature and pressure of the flow changes. It also is observed that not only does the slope at each edge of the profile change with temperature as mentioned by Forkey [1996], but also the minimum intensity of the profile decreases as the temperature decreases [Elliott et al. 2001]. The frequency when the Rayleigh scattering profile is absorbed the greatest by the filter is shown at (b), which indicates the velocity of the flow. This can be accomplished by comparing the minimum intensity frequency with the minimum in the transmission profile of the absorption profile. The difference between these two frequencies is the Doppler shift of the flow, which can be used to calculate the flow velocity using equation 1. Summarizing these effects: the intensity outside of the filter results in the density of the flow, the shape of the profile determines the temperature and pressure, and the frequency location of the intensity minimum relative to the absorption profile minimum results in the velocity. Therefore solving for the properties from the scattered intensity scan becomes a curve fitting process to fit the intensity profile from the computational model of the scattering process (using the S6 model of Tenti, transmission profile of the iodine filter, ideal gas law, and Doppler shift equation) to the one measured experimentally. The flow parameters ( density, temperature, pressure, and velocity of the flow field) are found by minimizing the error between the experimental and modeled curves. Forkey [1996] gives a complete description of one possible curve fitting methodology which can be used to deduce the flow quantities efficiently from the experimentally obtained profile.

Again the camera arrangement for the frequency scanning FRS is similar to Figure 6 except for this technique only one camera is needed. For the example results given here the laser propagates in the images from top to bottom so that the Doppler shift in the flow direction is maximized while still imaging the flow orthogonally to the flow direction. FRS was applied to a converging jet which has an exit diameter of 5.5 mm and a very slow co-flow of dry air is provided to minimize the number of particles in the flow and prevent condensation of moisture which would occur if the jet were allowed to interact with the moisture in the ambient air. For this demonstration of FRS, the jet was operated in an under expanded condition with a stagnation pressure and temperature of 370 kPa and 300 K respectively resulting in an equivalent Mach number of 1.65.

Figure 18. Pressure, density, temperature, and velocity measured using FRS.

Figure 18 shows results of the pressure, density, temperature, and velocity calculated from the FRS images and derived by fitting the Rayleigh scattering profile of the model due to the frequency scanning process over a range of subsonic and supersonic equivalent Mach numbers. Note that the images at each frequency were normalized by images taken outside of the absorption profile to correct for intensity variations in the laser sheet. The density is the first quantity which can be measured by simply comparing (i.e. normalizing) the intensity with the measurements made in ambient air. Compression and expansion waves from the underexpanded jet are clearly observed as density variations in the jet develop downstream. The velocity shows the same structures and the decrease in the jet velocity as the jet spreads downstream and interacts with the quiescent air. The thermodynamic properties are from 4% to 8% of the theroretical values for all flows shown here. Currently we are to improving this technique and evaluating the uncertainty.

Figure 19. FARRS experimental arrangement.

There are other methods of measuring thermodynamic properties using FRS than scanning the frequency of the laser. One method proposed by Shirley and Winter [1993] as well as Elliott and Samimy [1996] uses anamorphic optical systems to view an interrogation point from a range of observation angles simultaneously. The anamorphic optical system used in FARRS (first proposed by Elliott and Samimy [1996] for average property measurements ) is shown in Figure 19. This system allows the intensity at different viewing angles to be recorded separately by the ICCD camera. The system utilizes a low f-number photographic lens (i.e. f/1.4) so that the viewing half angle is approximately ± 20 degrees about the center line. The field stop placed at the focal point of the photographic lens prevents off axis light from reaching collimation by the spherical lens. A cylindrical lens then focuses the light into a line which represents the intensity recorded at different viewing angles. A beam splitter separates this signal with one path propagating through the iodine absorption filter (termed the filtered image) and the other path passing outside the filter (termed the reference image) before being focused on the ICCD camera.. This allows the density to be measured directly and the filtered image to be normalized so that the intensity profile can be compared to the computational model and the flow properties (density temperature pressure and velocity) are then deduced.

 

Figure 20. Mean velocity (a) and turbulence intensity (b) measured using FARRS and LDV.

Previously Samimy and Elliott [1996] showed that average properties could be accurately measured, initial experiments were recently been conducted to investigate the capability of FARRS to measure turbulence quantities using a small subsonic axisymmetric jet to quantify the accuracy of the technique. As a first step turbulence intensity measurements were made in a Mach 0.85 axisymmetric jet (with a 12.5 mm exit diameter) using FARRS and Laser Doppler Velocimetry for comparison. The average velocity and turbulence profiles are given in Figure 20 where the agreement is quite good for this preliminary attempt, but it is clear that some discrepancy still exists particularly in the core of the jet. The source of this error has been traced to the stability of the laser frequency, the random intensity fluctuations associated with the intensified CCD camera, and inaccuracies associated with the data reduction routine. This system is currently being investigated to use multiple detectors to obtain the instantaneous quantities of the other flow properties as well. Another approach is to make the FRS system sensitive to only a single property (or two properties which can be related by an equation of state) so that the intensity can be related to that property. Basically the property can be isolated using a combination of an equation of state (i.e. the ideal gas law), if the change of other properties are negligible (i.e. the velocity in the sensitive direction is negligible, or the pressure is constant), or recently investigators have shown that by careful selection of the absorption profile and relative laser frequency individual flow properties can be isolated [Miles et al. 2001]. One of the most popular single properties measured using FRS is the temperature which has been measured in combustion [Elliott et al., 1997,1999, Hoffman et al., 1996] and glow discharge environments [Yalin et al., 2000].

 

Figure 21. Temperature of hydrogen flame above Henkin burner measured using FRS and CARRS.

In order demonstrate the feasibility FRS for accurate temperature measurements, a hydrogen- air flame was stabilized on a 25-mm-square Hencken burner (Elliott et al., 1997). In order to investigate the accuracy of FRS to measure temperature in combustion environments, Elliott et al., [1997] presented the two-dimensional temperature field for a hydrogen-air flame above a Hencken burner at various equivalence ratios. Figure 21 presents the average temperature from the uniform portion of the flame 2 cm above the burner surface. The temperatures measured with FRS show excellent agreement with the adiabatic-equilibrium flame temperatures and the CARS measurements. The maximum deviations are at the highest temperatures with the FRS measurements always slightly below the CARS measurements and the calculation. It should be noted, however, that in configuring the CARS instrument, we used the temperature near 2200 K as a calibration point, obviating need to normalize the CARS spectrum with that from the broadband dye laser; consequently, the FRS temperatures near the stoichiometric conditions may more accurately reflect the true gas temperatures (i.e., slightly below adiabatic). The percent of temperature fluctuation for the time-average, instantaneous, and instantaneous bin-by-three temperature fields were found to be approximately 2, 8, and 3%, respectively. A detailed uncertainty analysis is given in Elliott et al., 1997 for these flames where it was found that the most significant sources of uncertainty were from the following the uncertainty in the mixture properties of molecular mass M and Rayleigh scattering cross-section R. According to standard uncertainty propagation, the total uncertainty was found to be 8.5% for the instantaneous image (with pixel binning) for the hydrogen-air flame.

 

Figure 22. Temperature field of stagnation flame measured using FRS.

Another flame studied using FRS is stagnation-flow flames arises from their importance to materials processing. Potential applications of these flames (both at atmospheric and sub-atmospheric conditions) include synthesis of polycrystalline diamond films and nano-powders. Figure 22 shows the average (Figure 22a) and instantaneous temperature fields (Figs. 22b-c with 2-by-2 binning) of the premixed methane/air flame with an equivalence ratio of 1.08, substrate/burner separation of 3.8 cm, substrate diameter of 3.2 cm, and adiabatic-equilibrium flame temperature of 2234 K. The water cooled substrate is located at the top of the image with the burner located at the bottom of the image. The laser sheet is propagating left to right. Using FRS the derived flame temperature was 1940 K. The signal to noise ratio was found (by measuring the standard deviation of the signal in a relatively uniform region of the flame and dividing it from the level of the signal) to be approximately 40 for the instantaneous measurements with pixel binning. Under these conditions, the measured temperatures are below the adiabatic value, presumably due to heat loss to the burner and substrate surfaces and mixing with ambient air. Almost all the instantaneous images show vortices rolling up on the edge of the flame and the temperature variation associated with this substrate diameter and separation distance. Figure 22 demonstrates the value of the FRS two-dimensional temperature imaging method: one can quantify the effects unsteadiness within the shear layer while also recording the temperature near burner and substrate surfaces. A detailed uncertainty analysis found that the uncertainty in the flame region where only reactants are present was found to be 19%, while those regions where only equilibrium combustion products were found would have an uncertainty of ~ 4.4% [Elliott et al., 1999]. In both regions the major source of error is due to the neglect of mixture properties, as noted above. Clearly this could be remedied to a large extent by providing some mixture information from the model results; or, one could simply use an iterative approach and infer the mixture from the temperature, though this approach is complicated by having two cold regions, the reactants and the surrounding air. Of course, the reactants, which are responsible for the largest errors, are limited to a region a few millimeters from the burner surface; for the majority of the flow field, the uncertainty is less than 5%. For the instantaneous measurements, the uncertainty for each binned pixel increases to 6.5%. It should be noted that due to the fact theat the filter also rejects particle scattering the flame can be seeded and a simultaneous measurement of velocity could be made using PIV.

 

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Boguszko, M., Elliott, G., and Carter, C., “Filtered Rayleigh Scattering for Fluid/Thermal Systems, AIAA-2002-3233, 22nd AIAA Aerodynamic Measurement Technology and Ground Testing Conference, June, 2002.
Baumgartner ML, Erbland, PJ, Etz MR, Yalin A, Muzas BK, Smits AJ, Lempert WR, Miles RB. Structure of a Mach 8 Turbulent Boundary Layer. AIAA Paper 97-0765, 1997.
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