Experiments in Fluids 29 (2000) 532±544 Ó Springer-Verlag 2000

Measurements of aerosol product in an axisymmetric co-flow jet T. P. Jenkins, I. M. Kennedy

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Abstract An experimental investigation explored the effects of varying reactant concentration and Reynolds number on the formation of product in a jet of air/N2/HCl ¯owing into a co-issuing stream of air/NH3. Turbulent mixing resulted in the production of NH4Cl particles by a chemical reaction with negligible heat release. Laser light was elastically scattered in the transition regime between Rayleigh and Mie scattering from the particles. Scattered light intensity served as an indicator of particle mass concentration. Radial pro®les of mean and root mean square concentrations were obtained in the self-similar far ®eld region of the jet. The stoichiometric mixture fraction was varied by varying the concentration of NH3 in the co-¯owing stream. It was found that the ``¯ame'' length decreased with increasing stoichiometric mixture fraction, and was independent of Reynolds number. The overall amount of product decreased as the stoichiometric mixture fraction was increased from 0.06 to 0.27, while the amount of limiting reactant was the same in both cases.

1 Introduction Turbulent reacting ¯ows have a great deal of practical importance. They include combusting ¯ows, such as those occurring in engines and incinerators, as well as noncombusting ¯ows, such as those occurring in the atmosphere. In the laboratory, reacting ¯ows can be classi®ed into fast chemistry and slow chemistry regimes. In ¯ows with fast chemistry, the rate of reaction is fast compared with the rate of mixing, so the mixing process limits the amount of product formed. Briedenthal (1981) and Dahm and Dimotakis (1987) have studied fast chemistry ¯ows for the purpose of investigating mixing phenomena. In both studies, chemical reaction was used as a diagnostic to indicate the extent to which mixing had occurred. These studies employed the product of a fast reaction to mark

Received: 28 April 1998/Accepted: 16 November 1999

T. P. Jenkins1, I. M. Kennedy (&) Department of Mechanical and Aeronautical Engineering One Shields Ave., University of California Davis, CA 95616, USA Present address: 1 Department of Mechanical Engineering Stanford University Stanford, CA 94305-3032, USA

regions in the ¯ow that contained ¯uid that had mixed on a molecular level. Mungal and Frieler (1988) showed how the kinetics of a reaction determine its applicability to the study of mixing. A dimensionless number, the DamkoÈhler number (Da), may be used to describe the regime of a reacting ¯ow with respect to the relative rates of mixing and reaction. The Da is de®ned as the ratio of the characteristic mixing time scale to the characteristic chemical time scale. A high Da is indicative of a mixing limited, or fast chemistry, ¯ow. For a Da less than unity, where the rate of chemistry is slow relative to the rate of mixing, details of the impact of turbulence on chemistry may be investigated. Practical applications that may involve low DamkoÈhler numbers include combustion engines and furnaces, in which oxides of nitrogen and soot are produced in relatively slow reactions, and atmospheric mixing of primary pollutants that react to form secondary pollutants (Seinfeld 1986). The study of atmospheric aerosols has gained increased attention in recent years owing to the discovery of adverse health effects associated with ®ne particulate matter (Finlayson-Pitts and Pitts 1997). When the product of reaction is a condensable species, the rate of nucleation of particles and their size can depend upon the turbulence characteristics. Lesniewski and Friedlander (1995) investigated the effect of turbulence on the particle nucleation rate in a turbulent jet using a numerical model, and found that the calculated local nucleation rates were signi®cantly reduced with the presence of turbulence from those without turbulence. The dynamics of large-scale motion and mixing in turbulent jets and shear layers have received some attention with regard to their roles in the overall mixing mechanism. Many experimentalists have reported the presence of large structures of nearly uniform concentration that dominate the mixing process. Mungal and Dimotakis (1984) measured temperatures (indicating product of reaction) instantaneously at eight positions across a planar shear layer, and discovered large structures extending across the shear layer. They also discovered that the cores of these structures were at a nearly uniform temperature across the layer, similar to structures observed by Koochesfahani et al. (1985) in a liquid shear layer. Flow visualization experiments by Sherikar and Chevray (1982) using gaseous NH3/HCl in a shear layer showed large, relatively periodic structures that have wellmixed cores. It was apparent from their images that entrainment was primarily a result of engulfment by the large structures.

Dahm and Dimotakis (1987) investigated a liquid jet in which ¯uorescence of a pH-sensitive dye was used to mark regions in the ¯ow that were above a critical mixture fraction, effectively marking the region of a ``¯ame'' of selectable stoichiometric mixture fraction. They reported that the ``¯ame'' length oscillated, owing to the location of ``burn out'' at the tip changing in a nearly periodic manner, with the characteristic period of oscillation being on the order of the jet width divided by the jet velocity. The average length of the visible jet, or ``¯ame'' length, decreased with increasing stoichiometric mixture fraction. Their ®ndings led to a simple conceptual picture in which the jet concentration ®eld is made up of discrete large structures spanning the width of the jet, the concentrations being uniform inside each structure and decreasing among the structures in the streamwise direction. A similar experiment was conducted by Mungal et al. (1991) in a ¯ame in which movie sequences were taken and a computer graphic volume rendering technique was employed, which provided a unique view of the ¯ow evolution. Characteristics of ¯ame tip oscillation were observed that were similar to those seen by Dahm and Dimotakis (1987), and it was concluded that the organized component of the jet motion is responsible for the oscillations. Even in the simplest cases, modeling of the dynamics of momentum in turbulent ¯ows is still uncertain. Consequently, understanding chemical reaction in turbulent mixing layers in which the chemistry is largely dependent on the turbulence dynamics is a signi®cant challenge. To make the problem tractable, simpli®cations are necessary. The present experiment removes the dif®culties associated with heat release and complex chemical kinetics. A turbulent reacting ¯ow problem is investigated in a simple co-¯ow jet at isothermal conditions by employing a simple kinetic mechanism. The goal of the experiment is to study the effects of turbulence on the molecular mixing and the accompanying chemical reaction of gases by investigating the product, primarily in the slow chemistry regime. The present experimental technique uses NH4Cl aerosol as a marker of product. It differs from past techniques at low DamkoÈhler number because the product is essentially nondiffusing. Regions of high production are more easily located than with a gaseous product that quickly diffuses away.

2 Chemical system The reaction of dilute NH3 with dilute HCl is employed as a model system with HCl as a jet into NH3 in a surrounding co-¯ow. The maximum possible temperature rise from the exothermic NH3/HCl reaction is calculated to be about 1.0 K, so the ¯ow is essentially isothermal. Near the nozzle, the DamkoÈhler number is small so that turbulence/chemistry interactions are relevant, while further downstream the DamkoÈhler number is large enough that mixing studies of the jet are possible. Control of the DamkoÈhler number is also achieved by varying the reactant concentrations.

The rate of the reaction employed in the present experiments is enhanced by the presence of NH4Cl particles due to surface effects. When the total particle surface area is small, the system behaves as a second-order gas phase reaction followed by a conversion from gas to particles (Dahlin et al. 1981). The two steps are: k1

NH3 …g† ‡ HCl…g† ! NH4 Cl…g† k2

NH4 Cl…g† ! NH4 Cl…s†

…1† …2†

where k1 is the gas phase rate constant, and k2 can be modeled as being zero below a critical partial pressure of NH4Cl, and in®nity above a critical partial pressure, or supersaturation. When the total particle surface area is large, the system may be modeled as k3

NH3 …g† ‡ HCl…g† ! NH4 Cl…s†

…3†

where k3 depends upon the total particle surface area present (Jenkins 1997). In the present experiments, particle concentrations were great enough that Eq. (3) was the dominant mechanism throughout most regions of the reacting zone.

3 Stoichiometric mixture fraction In a two-stream mixing problem, it is convenient to de®ne a quantity known as the mixture fraction to characterize the degree of molecular mixing. In the present experiment, the mixture fraction, f, at a point in the ¯ow®eld is de®ned by f ˆ Yi/Yi,1, where Yi is the mass fraction of an inert species at that point, and Yi,1 is the mass fraction of that species entering the ¯ow in stream 1. Thus, f takes on values between 0 in the freestream and 1 at the nozzle exit and, in the present experiment, can be thought of as the mass fraction of jet pipe ¯uid remaining after it has been diluted with co-¯ow ¯uid. Figure 1 shows a diagram of iso-surfaces of mean mixture fraction in a co-¯ow jet. The iso-surface corresponding to the stoichiometric mixture fraction may be thought of as a reaction zone or ``¯ame''. Quotation marks are used here to indicate that the reaction takes place at room temperature in the present experiments, as opposed to a real ¯ame that involves higher temperatures. Stream 1 issues from the jet pipe, and stream 2 is the co¯ow. The outermost surface, denoted ``f ˆ 0.06'', represents locations at which the ¯uid is composed of 6% jet pipe ¯uid by mass, the remaining 94% being co-¯ow ¯uid. Likewise, the inner surface represents locations at which the ¯uid contains 27% jet pipe ¯uid. When the ¯ow is turbulent, the values represent mean concentrations. The values for f of 0.06 and 0.27 are the two stoichiometric mixture fractions examined in the present experiments. For a second-order reaction of the type A + B ! C, as in the present case, the stoichiometric condition occurs when the concentrations of reactants A and B are equal. Most of the product will be formed in regions where stoichiometric proportions prevail, since at this condition the reaction rate, given by d[C]/dt ˆ k[A][B], is fastest. Here, the square brackets denote concentrations. In the

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Fig. 2. Wind tunnel facility producing a co-¯ow reacting jet with HCl in the jet pipe, and NH3 in the co-¯ow Fig. 1. Iso-surfaces of mean mixture fraction, f, in a co-¯ow jet. A reaction zone, or ``¯ame'', may be de®ned as the iso-surface of the stoichiometric mixture fraction. The values of f given are the stoichiometric mixture fractions in the present experiments measurement indicated that the HCl concentration in the

4 Experimental apparatus

cylinder was 4.8 ‹ 0.3%. NH3 with a guaranteed purity of 99.97 ‹ 0.03% was supplied from a gas cylinder, also controlled by a rotameter, and injected into the air inlet of the wind tunnel fan where it mixed with the wind tunnel air stream. Both the HCl and NH3 rotameters were calibrated with a soap bubble ¯ow meter. Two different jet ¯ow rates were investigated, corresponding to jet pipe exit velocities of 40 and 78 m/s. The corresponding Reynolds numbers, Re, were 11,400 and 20,600, respectively, based on the jet pipe exit diameter and exit velocity. A ®xed concentration of HCl in the jet pipe of 1,630 ppm was maintained for all experiments. Two different NH3 concentrations in the co-¯ow were examined, 100 ppm and 600 ppm. The co-¯ow velocity was 4.0 m/s for all experimental runs.

4.1 Flow facility A jet was produced by a mixture of air, N2, and HCl issuing from a stainless steel tube with an inside diameter of 4.6 mm. The tube was held in place with wires along the axis of a vertical wind tunnel, which provided a co¯owing stream of air and NH3, as shown in Fig. 2. Zero grade air was supplied to the jet from a gas cylinder, and was combined with a mixture of 5% HCl in N2 from another cylinder before the stream entered the jet pipe. The ¯ow of the HCl/N2 mixture was controlled by a rotameter. Certi®cation supplied with the cylinder guaranteed that the HCl concentration was 5.0 ‹ 0.25%. A check of the concentration in the cylinder was performed by passing some of its contents through a gas washing bottle to dissolve the HCl in an aqueous phosphate buffer solution, and then using a chloride ion probe to measure the concentration of chloride ions. The resulting

4.2 Aerosol sampling Aerosol samples from the co-¯ow jet were obtained by drawing gas samples containing NH4Cl particles from the region of interest with a probe and passing it through a ®lter that was later examined with a scanning electron microscope (SEM). The ®lters were cellulose nitrate with a pore size of 0.1 lm. Gas samples were drawn through the probe by means of a vacuum pump. Ideally, the aerosol extracted from the ¯ow ®eld would not be changed by the sampling. However, the time scale of reaction is on the order of the time scale of the extraction process, so that the sample needed to be diluted by N2 during extraction to halt the reaction. The interior walls of the probe were made of sintered metal through which N2 ¯owed, controlled by a rotameter, to dilute the sample.

present experiment, with HCl in stream 1 and NH3 in stream 2, the stoichiometric mixture fraction, fs, is the value of f for which there are equal concentrations of each reactant. Initial concentrations of the reactants in the two streams determine the value of fs. For the present experiment, the value of 0.06 was chosen as one of the two values of fs because it is near that of a hydrocarbon diffusion ¯ame burning in air. Referring to Fig. 1, the ``¯ame'' may be expected to be longer and more distended when fs ˆ 0.06 than when fs ˆ 0.27.

4.3 Optical system The beam from an argon ion laser, operated at 200 mW at a wavelength of 488 nm, was directed into the wind tunnel across the test section and was focused by a 0.50-m focal length lens onto the center region of the test section (see Fig. 2). Laser light scattered from NH4Cl particles in the jet was collected at 90° to the laser direction, and measured by a photomultiplier (PM) tube to infer particle mass concentrations. The non-dimensional size parameter pd0/k (where d0 is a characteristic diameter of the particles de®ned as the modal diameter of a lognormal ®t to the size distribution, and k is the laser wavelength) is about 0.6 for these particles, putting them in the transitional regime between Rayleigh and Mie scattering. To collect the scattered light, a segment of the beam waist was imaged at a right angle to both the propagation and polarization directions of the incident beam by a 50mm f/1.7 camera lens onto a pinhole aperture, 85 lm in diameter, in front of the PM tube. The geometrical arrangement of the light collection optics resulted in a measurement volume that was approximately cylindrical in shape, with a diameter of about 60 lm and a length of about 770 lm. A small fraction (about 4%) of the beam energy was re¯ected into a photodiode to monitor ¯uctuations in the laser output. The signal from the PM tube was conditioned with a low-pass ®lter with a cut-off frequency of 15 kHz, and ampli®ed so that it was on the order of a few volts. Analogto-digital conversion of the signal was accomplished with a Lecroy model 8812 A/D converter. Data were stored at a rate of 313 Hz for measurements used for calculating statistical quantities such as means and variances, and at a rate of 50 kHz for measurements used for calculating a frequency spectrum. The rate of 313 Hz ensured that the samples were statistically independent, while the 50 kHz rate was fast enough that motions in the ¯ow up to 25 kHz, by the Niquist criterion (Smol'yakov and Tkachenko 1983), were resolvable in the energy spectrum. At each axial station, Rayleigh scattering from propane gas at the jet exit was used as a reference signal with the same optical system as used for the scattering from the NH4Cl particles. Because the scattering cross section of propane was much less than that of the particles, the signal was ampli®ed by changing a resistor in the signal conditioning circuit. The propane scattering measurements were used for normalizing the scattering signal from the particles. To check that the ¯ow structure in the test section was consistent with well-established characteristics of jets, velocities in the jet were measured using a laser Doppler velocimeter (LDV) system. The system consisted of a twocolor laser to measure both axial and radial velocity components simultaneously using the 488-nm and 514.5nm modes, respectively, of an argon ion laser. Spherical glass particles with a mean diameter of 3.3 lm were seeded into the jet pipe. Scattered light from the measurement volume was collected in forward-scatter mode by two photomultiplier tubes with optical ®lters to select the component measured. The signal from each photomulti-

plier tube was processed by a TSI model 1980 counter, and the data were stored on a computer. Planar images of NH4Cl particle distribution were obtained by passing a laser sheet through the axis of the jet and capturing images of elastically scattered light with a CCD camera. A pulsed Nd:YAG laser source was used at 532-nm wavelength with pulse durations of about 10 ns. Scattered light was imaged with a 50/1.4 camera lens onto a CCD array with 577 ´ 384 elements. The camera was triggered by the Q-switch output from the laser; images were stored on a computer.

4.4 Calibration apparatus The system for measuring scattered light as an indicator of aerosol product concentration was calibrated with a stream containing a known concentration of NH4Cl aerosol. A stream of HCl diluted in nitrogen and air was combined with a stream of NH3 diluted in air. Each of the streams ¯owed through a tube made of polypropylene with an inside diameter of 8 mm. The two tubes were connected at a tee ®tting and the combined stream ¯owed through a third tube, the ``calibration tube''. In the calibration tube, NH4Cl aerosol was produced by chemical reaction. The exit of the calibration tube was placed in the test section of the wind tunnel so that laser light scattered by the aerosol was measured using the same optical system that was used for the turbulent reacting jet measurements. Separate measurements were made in which pure propane was fed into the calibration tube while Rayleigh scattered light from the propane molecules was measured as a reference signal. Care was taken to ensure that the incident beam was polarized vertically so that the maximum Rayleigh signal was measured. Calibration was accomplished by measuring the intensity of light scattered by NH4Cl particles at the exit of the calibration tube for a range of initial reactant concentrations. As the length of the calibration tube was increased from 3 to 6 m, the scattered light intensity increased by less than 3%, indicating that the chemical reaction had essentially gone to completion. This enabled the molar concentration of NH4Cl to be estimated by equating it to the initial molar concentration of HCl, the limiting reactant. A relationship was obtained between the scattered light intensity from NH4Cl particles and the estimated particle mass concentration. 5 Results 5.1 Velocity profiles Some results from the LDV measurements are shown in Figs. 3 and 4. Figure 3 shows the axial evolution of the inverse of the centerline velocity excess, de®ned as Ucl ± Uco, where Ucl is the mean centerline velocity and Uco is the co-¯ow velocity. The lines are least-squares-linear curve ®ts to the data. The inverse of the centerline velocity excess is linear with axial distance from the nozzle exit, consistent with other experimental studies in co-¯ow jets

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5.2 Aerosol sampling Particle sizes were observed with the SEM in the aerosol samples collected on the nitrocellulose ®lters. It was found that the particle sizes were dependent upon the sampling time, with longer sampling times resulting in larger particles. For example, a sampling time of 7 s resulted in particle diameters about half the size of those found with a time of 20 s, indicating that they were growing on the ®lter as the reactant gases were passing by. In order to obtain an accurate representation of the particle sizes, the minimum possible sample time was used, about 6 s. This was close to the estimated time it took for the gas to move from the entrance of the probe to the ®lter on which the particles were collected. All of the samples that were used for size determination were taken with sample times of 6 s. SEM micrographs of particles were obtained at the axial Fig. 3. Inverse of centerline axial velocity excess varying with axial location locations x/D ˆ 40 and 80 for both Reynolds numbers and stoichiometric mixture fractions. The circumference of each particle was measured with the aid of software. From the circumferences, equivalent spherical diameters were calculated, and size distributions were obtained from the images. The results indicated that the particle diameters grew by less than 5% from x/D ˆ 40 to x/D ˆ 80. Figure 5 shows the size distributions obtained from the SEM images, along with the size distribution of NH4Cl particles obtained by Carabine et al. (1971). The latter distribution was obtained in a different ¯ow system with a different sampling method, but with similar initial reactant concentrations. The ordinate represents the probability density function, or PDF, de®ned such that the area under the curve is equal to unity, and the abscissa represents the particle diameter. A zeroth-order lognormal distribution (ZOLD) (Espenscheid 1964) provided a reasonable ®t to the data. An increase in the modal diameter of the ZOLDFig. 4. Mean axial velocity distribution ®tted functions can be seen with increasing initial NH3 concentrations. Aerosol samples were also collected for Re ˆ 20,600, which showed no detectable difference in the with large jet to co-¯ow velocity ratios (Antonia and Bilger particle sizes from the samples for Re ˆ 11,400. 1973; Nickels and Perry 1996). As a check on the observations of particle growth, In Fig. 4, radial pro®les of non-dimensional mean ve- calculations were made using simple monodisperse locities are shown for a range of axial positions. The mean velocities are normalized by the centerline velocity excess, and the radial positions are normalized by the velocity half radius, b, which is the radial location at which the velocity excess is half its centerline value. It can be seen that the mean ¯ow is self-preserving by x/D ˆ 20, consistent with other studies (Wygnanski and Fiedler 1969; Antonia and Bilger 1973). A Gaussian curve ®t provides an excellent description of the behavior, as previously established (Daily and Harleman 1966). Radial distributions of the root mean square (rms) of the axial velocity (not shown) indicated that self-similarity of the variance was achieved by about x/D ˆ 40. The rms magnitudes normalized by the mean were about 0.28 on the centerline at x/D ³ 40, in excellent agreement with other studies (Wygnanski and Fiedler 1969; Antonia and Fig. 5. Size distributions of NH4Cl particles measured from SEM Bilger 1973; Nickels and Perry 1996). Reynolds shear micrographs. Dashed lines are zeroth order log-normal distribustresses showed self-similarity by x/D ˆ 40, and had tion (ZOLD) functions ®tted to the data. Data from Carabine et al. magnitudes consistent with the other studies previously (1971) are shown for equal NH3 and HCl concentrations within mentioned. the range indicated

coagulation theory (Hinds 1993). The theory assumes that the particles will stick together if they come into contact with 100% ef®ciency. Collision rates of the particles are determined by their Brownian motion. The rate of decrease in aerosol number concentration is given as

dN ˆ dt

KN 2 :

…4†

The coagulation coef®cient, K, is given by

Kˆ

4kTCc 3l

…5†

where k is the Boltzmann constant, T is the gas temperature, Cc is a slip correction factor, and l is the gas viscosity. For the particle sizes measured in the present experiment (near 0.1 lm), the coagulation coef®cient is about 8.6 ´ 10)10 cm3/s. A condensation nucleus counter was used to measure particle concentrations in the test section, which were found to be on the order of 106 particles/cm3. For this concentration, the estimated time for the number concentration of particles to halve, by solving Eq. (4), is about 2000 s. This is well beyond the residence time of particles in the test section, which is on the order of 1 s, indicating that coagulation should not be signi®cant. Kinematic coagulation due to turbulence (Saffman and Turner 1956) is not included in this analysis, but is unlikely to be important for these very small particles. NH4Cl particles are known to be weakly hygroscopic, with deliquescence occurring at ambient relative humidities above 86% (Hayakawa 1962). In all of the experiments conducted in the present work, the relative humidity did not rise above 68%, so particle growth due to absorption of water was not signi®cant.

scattered light (KoÈyluÈ and Faeth 1994). The depolarization ratio, qp, is de®ned as the ratio of scattered light intensity collected with the beam polarized horizontally to that with it polarized vertically. A computer code was used to calculate depolarization ratios from the two measured size distributions, corresponding to fs ˆ 0.06 and 0.27, using Mie theory for spheres. A value of qp of 0.039 was predicted for the smaller size distribution, which corresponds to fs ˆ 0.06. For the larger distribution, which corresponds to fs ˆ 0.27, the predicted value of qp was 1.34. It can be seen that qp is very sensitive to the size distribution. Scattered light from the particles was measured on the centerline of the jet at x/D ˆ 40 with the incident beam polarization both vertical and horizontal in separate experiments. The measured value of qp was 0.022 and 0.0304 for fs ˆ 0.06 and 0.27, respectively. Thus, for fs ˆ 0.06, the value of qp agrees within a factor of two between the Mie theory approximation and the measurement, while for fs ˆ 0.27 the measured value of qp is nearly two orders of magnitude lower than that calculated from the measured size distribution, and not much greater than that for the case of fs ˆ 0.06. Mie theory assumes that the particles are perfect spheres, but examination of the SEM micrographs showed that some particles are quite non-spherical. It may be reasonable to attribute the difference in the predicted and measured values of qp for fs ˆ 0.06 to the limitations of the Mie theory approximation. However, the difference in the predicted and measured values of qp for fs ˆ 0.27 is probably too large to attribute likewise. It can be concluded that the actual differences in the in situ size distributions are probably less than indicated in Fig. 5. The discrepancy is probably due to a large extent to an artifact of the aerosol sampling.

5.4 Shot noise 5.3 Because of the particulate nature of the light-scattering Size distribution impact on light scattering Because the size distribution was seen to vary with initial medium, marker shot noise could provide a signi®cant NH3 concentration, as shown in Fig. 5, calculations were contribution to the signal. For a system containing an Ä is the number of partiperformed to investigate the effect of size distribution on integer number, N, of particles, N cles that represents continuum behavior. Then the intenscattered light intensity. For a given aerosol concentration, sity of the marker shot noise is given by Becker et al. the intensity of scattered light per unit volume, Is, is (1967) as proportional to a ratio of integrals,  R1
1=2 ~ 2 i … d †N … d †dd N N 1 ; …6† shot noise ˆ Is / R0 1 3 ˆ …7† d N … d †dd  N  †1=2 0 …N where N(d)dd is the number of particles with diameters between d and d + dd. Using a computer code to calculate the scattering function i(d) from the Mie theory for spheres, these integrals were evaluated numerically for the two size distributions measured. For the larger size distribution, Is was 10.4% less than for the smaller. However, the behavior of the scattered light signal as it varied with HCl concentration, to be presented later, suggests that the actual value of Is was essentially invariant in the present experiments. Thus, the effect of size distribution on scattering intensity was insigni®cant. Variation in the particle size distribution was also investigated by checking the depolarization ratio of the

where an overbar indicates a mean value. As the size of the measurement volume is reduced, the shot noise increases owing to a decrease in the mean number of particles. Thus, there is a trade-off between spatial resolution and shot noise. To investigate the magnitude of marker shot noise in the present measurements, the ¯ow rates in the jet were reduced so that a laminar ¯ow was produced. The variance of the scattered light signal was measured over a range of reactant concentrations. Means and variances were calculated from 4,000 individual measurements of scattered light intensity at each set of reactant concentrations investigated. The shot noise varied with particle mass

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Fig. 6. Intensity of shot noise in the signal from light scattered from NH4Cl particles in a laminar ¯ow over a range of particle concentrations

concentration, as shown in Fig. 6. The square root of the variance (rms) of the measured voltage signal, normalized by the mean, is plotted on the ordinate. The horizontal axis represents the mean mass concentration of particles, C, as inferred from the measured mean voltage. From the graph, it can be seen that the rms of the signal varies as C)1/2, in agreement with the behavior described by Eq. (7). The slope of )1/2 con®rms the presence of particle shot noise. It can be seen from Fig. 6 that the shot noise is less than 10% for mass concentrations greater than 7 ng/cm3. Since the number of scatterers is directly related to the size of the measurement volume, the latter should be large to avoid shot noise. The size of the measurement volume that was selected for these measurements was a compromise that allowed its longest dimension to be within an order of magnitude of the Kolmogorov length scale, while most of the measurements had a shot noise of less than 10%.

5.5 Calibration measurements Figure 7 shows a plot of the scattered light intensity at the exit of the calibration tube as a function of the initial concentration of HCl, denoted [HCl]0. The initial concentration of NH3 was held ®xed at 605 ppm. Hence, with a maximum concentration of 400 ppm, HCl was the limiting reactant. The scattered light intensities were normalized by the intensity of scattering from propane. It can be seen that at low [HCl]0, there were no particles present until a critical concentration of about 40 ppm. Between 40 and 170 ppm, there was a non-linear relationship between scattered light intensity and [HCl]0, and above 170 ppm the relationship was linear. The linearity in the data for [HCl]0 >150 is consistent with the notion that the size distribution was essentially invariant over this range. Not all of the NH4Cl product existed as aerosol. Gaseous product may have existed where a molecular cluster of NH4Cl had not reached a critical size for homogeneous nucleation and there was no surface present (Dahlin et al. 1981). To obtain a calibration relationship, the data of Fig. 7 were modeled by the approximation shown as a

Fig. 7. Intensity of scattered light from NH4Cl particles, normalized by Rayleigh scattering from propane molecules, measured at the exit of a mixing tube. The initial concentration of NH3 was ®xed at 605 ppm

heavy line in the ®gure. In this approximation, it was assumed that no particles were produced until a critical NH4Cl vapor concentration was reached This was the same molar concentration as the critical value of [HCl]0 assuming the gas phase reaction of NH3 and HCl went to completion. In the ®gure, the critical concentration is seen to be about 120 ppm. Each mole of HCl added beyond this critical concentration was completely converted to a mole of particulate NH4Cl in this approximation. A mass concentration of NH4Cl particles was calculated from the excess in the known initial concentration of HCl above the critical concentration. The molar concentrations of NH4Cl aerosol were converted to mass concentrations by multiplication by the molecular weight of NH4Cl, WNH4 Cl, which is 53.5 g/mol. A calibration constant K is de®ned by WNH4 Cl/Slope, where Slope is the slope of the linear portion of Fig. 7. Aerosol mass concentrations, c, were related to the scattered light intensity by

cˆK

I Iprop

…8†

where K has the value 1.33 ng/cm3.

5.6 Uncertainty in aerosol mass concentrations The uncertainty in the values of NH4Cl particle mass concentration was calculated using the standard ANSI/ ASME approach (Steele et al. 1994). For a result R calculated from N measured variables, the uncertainty dR is related to the uncertainties of the individual measurements dxi by the equation ( 2  2 )12 oR oR dR ˆ dx1 ‡


‡ oxN : …9† ox1 oxN Table 1 lists the uncertainties attributed to the individual measurements. To obtain the uncertainty in PM tube response, neutral density ®lters of known optical density were used to ®lter light from a steady source. It

Table 1. Uncertainties in measured quantities

Quantity

Symbol

Maximum uncertainty

Intensity of scattered light Volume ¯ow rate of HCl/N2 mixture Volume ¯ow rate of dilution air for HCl stream Volume ¯ow rate of dilution air for NH3 stream Mole fraction of HCl diluted in N2 in the cylinder

dI/I dQHCl/N2 dQair 1 dQair 2 dXHCl,cyl

0.05 0.0234 l/min 1.22 l/min 0.795 l/min 0.0025

was found that the relationship was linear to within 5% for the range of light levels measured in the present experiments. Uncertainties in the volume ¯ow rates of gases were taken to be one half of the least scale reading, divided by the scale reading of the ¯owmeter. Table 2 presents the results of evaluating the propagated uncertainties using equations similar to Eq. (9) with the measured values of Table 1. The ®nal result is a maximum uncertainty in the NH4Cl aerosol mass concentration of 19.5%.

5.7 NH4Cl concentration measurements Autocorrelation functions were calculated from the data, de®ned as q…s† ˆ

V …t†V …t ‡ s†

…10†

2

V …t †

where V(t) is the voltage signal as a function of time, and s is a given time shift. Quantities with an overbar are time average quantities. Autocorrelation functions obtained from the data were helpful in selecting the sampling frequency of data from which the means and variances were calculated. Statistically independent samples of the time series were obtained by meeting the criterion T > T0, where T is the sampling time interval and T0 is the integral time scale obtained from the autocorrelation function (Smol'yakov and Tkachenko 1983). The integral time scale, T0, was calculated from

data points collected at each measurement location for a given set of experimental conditions as follows:

Cˆ

n 1X ci n iˆ1

…12†

and

r2 ˆ

n X

1 n

1

…ci

C †2 ;

…13†

iˆ1

where n is the number of points (4,000). Measurement locations covered a range of radial locations at ®ve axial stations, viz., x/D ˆ 20, 40, 60, 80, and 96. At each axial location, two NH3 concentrations in the wind tunnel stream were examined, fs = 0.06 and 0.27, and two values of Reynolds number: Re ˆ 11,400 and 20,600. Figure 8 shows radial pro®les of the mean concentration at all axial locations and both stoichiometric mixture fractions for Re ˆ 11,400, while Fig. 9 shows the same for Re ˆ 20,600. In both ®gures, the concentrations are normalized by the centerline value, and on the abscissas the radial coordinates are normalized by the concentration half radius at fs ˆ 0.27, denoted d0.27. The concentration half radius, d, is de®ned as the radial coordinate corresponding to a concentration of one half the centerline value. The ®lled symbols correspond to fs ˆ 0.06, and the open symbols to fs ˆ 0.27. It can be seen that at both

Z1 T0 ˆ

q…s† ds

…11†

0

and found to be about 8.0 ´ 10)4 s on the centerline at x/D ˆ 96. A sampling frequency of 313 Hz, corresponding to a sampling time interval of 3.2 ´ 10)3 s, was selected. Mean and rms concentrations A sample mean, C, and a sample variance, r2, of particle mass concentrations were calculated from a set of 4,000 Table 2. Uncertainties in calculated quantities Quantity

Symbol

Intensity of scattered light, normalized by propane scattering Molar concentration of HCl Calibration constant K, de®ned I as c ˆ K Iprop Mass concentration of NH4Cl aerosol

d



I



Iprop

d[HCl] dK=K dc=c

Maximum uncertainty 29.16 27.5 ppm 0.182 0.195

Fig. 8. Mean concentrations of NH4Cl particles in a reacting co¯ow jet from 20 to 96 diameters downstream from the jet exit, with stoichiometric mixture fractions of 0.06 and 0.27, for Re ˆ 11,400

539

radius reported for jets (Becker et al. 1967; Ooms and Wicks 1975; Sautet and Stepowski 1994). The mean concentrations along the centerline are plotted for both stoichiometric mixture fractions and both Reynolds numbers in Fig. 11. A spline curve is drawn through each set of data. Data for fs ˆ 0.06 are represented by solid lines and ®lled symbols, while data for fs ˆ 0.27 are represented by dashed lines and open symbols. It can be seen that there is little effect of Reynolds number on the trends with both fs and axial location, other than a decrease in the magnitudes with increasing Reynolds number due to the shorter residence times. Fluctuations in the magnitudes of measured concentrations are characterized by the root mean square (rms) of the instantaneous concentration. Figure 12 shows the axial variation of the rms of NH4Cl concentration on the centerline normalized by the mean concentration. The

540

Fig. 9. Mean concentrations of NH4Cl particles in a reacting co¯ow jet from 20 to 96 diameters downstream from the jet exit, with stoichiometric mixture fractions of 0.06 and 0.27, for Re ˆ 20,600

Reynolds numbers the product concentration pro®les for fs ˆ 0.27 collapse onto the same curve when normalized this way, while for fs ˆ 0.06 the pro®les are different at each axial location up to x/D ˆ 80, beyond which they collapse onto the same curve as that for fs ˆ 0.27. The distribution of product at fs ˆ 0.27 is the same in both Figs. 8 and 9, and resembles data from measurements of passive scalars in jets (Becker et al. 1967; Gladnick et al. 1990; Sanders and Lamers 1992; Sautet and Stepowski 1994). On the other hand, pro®les of product concentrations at fs ˆ 0.06 close to the nozzle exhibit a distinct maximum off-axis. Figure 10 presents the axial variation in d0.27. For each Reynolds number, a linear least-squares ®t is shown. It can be seen that d0.27 increases linearly with axial location, similar to the axial variation of the mixture fraction half

Fig. 11. Axial distribution of mean NH4Cl particle mass concentrations in a co-¯ow jet

Fig. 10. Axial variation in the concentration half radius of NH4Cl Fig. 12. Axial variation of rms of NH4Cl concentration for fs ˆ 0.27

data points are connected by splines. The rms ¯uctuations are very large initially for fs ˆ 0.06, and fall sharply by x/D ˆ 40, eventually rising to about the same levels as for fs ˆ 0.27. The magnitudes for fs ˆ 0.27 gradually increase over the range of axial locations investigated, resembling the trend shown by mixture fraction measurements in jets, although with somewhat greater magnitudes (Becker et al. 1967; Ooms and Wicks 1975). Figures 13 and 14 present the radial distributions of rms concentration of NH4Cl at both stoichiometric mixture fractions for Re ˆ 11,400. The magnitudes have been normalized by the centerline rms. As shown in Fig. 13, at fs ˆ 0.27 the pro®les collapse to a self-similar form by x/D ˆ 40 when plotted this way. The self-similar form is similar in shape to the form observed from measurements of mixture fraction in jets (Becker et al. 1967; Ooms and Wicks 1975; Dahm and Dimotakis 1990; Gladnick et al. 1990; Sautet and Stepowski 1994). At fs ˆ 0.06 (Fig. 13), the signi®cant maxima are exhibited off axis at low values

Fig. 13. Radial distribution of rms of NH4Cl concentration at fs ˆ 0.06 and Re ˆ 11,400

of x/D; the pro®les reach a self-similar form by x/D ˆ 80. Results obtained for Re ˆ 20,600 (not shown) exhibit the same patterns. DamkoÈhler numbers were calculated according to Da ˆ d/(scDU), where d is the concentration half width of the jet, DU is the local velocity excess on the centerline, and sc is a characteristic time scale of the chemistry, taken to be the time it takes for the concentration of the limiting reactant, HCl, to fall to 1/e of its initial value in a stoichiometric mixture. The value of sc was calculated using the rate constant measured in a separate experiment (Jenkins 1997). Calculated values of Da for Re ˆ 11,400 ranged from 0.054 at x/D ˆ 20 to 0.66 at x/D ˆ 96 for fs ˆ 0.27, and from 0.012 to 0.15 for fs ˆ 0.06, at the same axial locations, respectively. These results are summarized in Table 3.

5.8 Planar images Figure 15 shows an instantaneous NH4Cl particle distribution for the region of the jet between 6.5 and 15 jet pipe diameters downstream from the exit for fs ˆ 0.27. The direction of ¯ow is from left to right in the image. The imaged area is 74 ´ 74 lm per pixel. This is the region where particles ®rst begin to appear. A characteristic turbulent mixing time scale was estimated by smix ˆ L/DU, where L is a characteristic size of the large structures seen in Fig. 15, taken to be 10 mm, and DU is the velocity excess on the centerline, which is about 10 m/s in the middle of the image according to the LDV measurements of Fig. 3. These estimates result in a mixing time scale of 1.0 ´ 10)3 s. A characteristic time scale for diffusion of the particles due to Brownian motion was calculated by sdiff ˆ l2/D, where l is the characteristic width of the long, string-like structures seen in Fig. 15, taken to be 200 lm, and D is the diffusivity of the particles into air, calculated to be 7.5 ´ 10)10 m2/s. The calculated diffusion time scale was 53.3 s. The residence time of particles in the ¯ow in this image is about 3.9 ´ 10)3 s. The chemical time scale was estimated using the rate constant measured in a separate experiment (Jenkins 1997) giving schem ˆ 7.0 ´ 10)2 s. It can be concluded that there is no signi®cant Brownian diffusion of the particles in Fig. 15, but there may be signi®cant turbulent mixing that can transport the particles. It can be seen that there are two kinds of structures in which particles are present in Fig. 15: long, thin strings, and broader more homogeneous regions. The strings appear mostly near the edges of the jet, while the broader structures appear across the jet. The total volume of particles contained in the broader structures appears to be greater than that contained in the strings. From this and similar images, it appears that production occurs both in Table 3. DamkoÈhler numbers, Da, in a co-¯ow jet

Fig. 14. Radial distribution of rms of NH4Cl concentration at fs ˆ 0.27 and Re ˆ 11,400

fs = 0.06 fs = 0.27

x/D = 20

x/D = 96

0.012 0.054

0.15 0.66

541

Fig. 15. Elastic scattering image of NH4Cl particles in a reacting co-¯ow jet for Re ˆ 11,400, fs ˆ 0.27. The laser sheet extends from x/D ˆ 6.5 (left edge) to 15 (right edge)

542

thin strained layers, and in large, relatively uniform structures. The estimated time scale for turbulent mixing is substantially shorter than the estimated time scale for chemistry in this image, so it is likely that more production occurs in the well-mixed large structures (where signi®cant mixing has occurred) than in the thin layers. Figure 16 shows a similar image for fs ˆ 0.06. This image also corresponds to the axial location where particles ®rst appear, which is further downstream than for fs ˆ 0.27. In contrast to the case for fs ˆ 0.27 in Fig. 15, the structures containing particles in Fig. 16 are of only one type, large and relatively uniform in concentration. The lack of production in strained layers, as was seen for fs ˆ 0.27, is due to the slower chemistry. The characteristic reaction time scale is about four times longer for fs ˆ 0.06 than for fs ˆ 0.27. The bright spots in the image are stray particles, either dust or NH4Cl particles that had been building up on the nozzle exit.

6 Discussion The radial distributions of the mean concentration of NH4Cl are shown in Figs. 8 and 9. These results show the effect of stoichiometric mixture fraction on the formation of product. At x/D ˆ 20 for both Reynolds numbers, i.e., in Figs. 8 and 9, the data exhibit a maximum some distance from the axis for fs ˆ 0.06 (®lled squares), and on the axis for fs ˆ 0.27 (open triangles). The shape of the product distribution pro®le at fs ˆ 0.27 shows that most of the chemical reaction has already occurred by x/D ˆ 20, and the product is mixing as a passive scalar. On the other hand, for the case fs ˆ 0.06, the reaction is still occurring at x/D ˆ 20. This interpretation is consistent with the much lower concentrations of product measured for fs ˆ 0.06, which are about an order of magnitude lower than for fs ˆ 0.27 (see Fig. 11). If the reaction were to proceed to completion, the total amount of product would

Fig. 16. Elastic scattering image of NH4Cl particles in a reacting co-¯ow jet for Re ˆ 11,400, fs ˆ 0.06. The laser sheet extends from x/D ˆ 17 (left edge) to 24 (right edge)

be the same for the two cases of fs, since the total amount of the limiting reactant, HCl in the jet pipe, is the same in each case. The off-axis maxima for fs ˆ 0.06 in Figs. 8 and 9 may be representative of a ``¯ame'' surface, where the rate of chemical reaction is greatest. The conditions at x/D ˆ 20 correspond to those depicted in the top half of the sketch in Fig. 1, in which a ``¯ame'' surface exists for the lower fs and not for the higher. Referring to Fig. 11, by x/D ˆ 40, the amount of product for the case of fs ˆ 0.06 has increased signi®cantly, to the extent that it is of the same order as that for fs ˆ 0.27. However, the distributions shown in Figs. 8 and 9 are clearly ¯atter near the centerline for the lower fs, indicative of a reaction that is still occurring away from the centerline. By x/D ˆ 80, the shapes of the distributions for fs ˆ 0.06 are quite similar to those for fs ˆ 0.27, indicating that the reaction has progressed to near completion for the lower fs as well. Note that the NH4Cl product concentration on the centerline at x/D ³ 60 in Fig. 11 at fs ˆ 0.06 is greater than at fs ˆ 0.27, even though it is expected that the amount of product would be the same for each fully reacted mixture, since the amount of limiting reactant is the same. Figure 11 together with the radial pro®les of Figs. 8 and 9 demonstrate that at large x/D there is more NH4Cl aerosol for the case fs ˆ 0.06 than for fs ˆ 0.27. At x/D ˆ 96, the concentration for fs ˆ 0.06 is about a factor of two greater than that for fs ˆ 0.27. A likely explanation for the observed behavior follows from a consideration of the effects of the lifetimes of large structures on chemistry. As mentioned in the Introduction, a simple conceptual model of jet mixing was given by Dahm and Dimotakis (1987). The model postulates a series of large structures of uniform concentration moving downstream with a characteristic length scale on the order of the jet width, d. The concentration of each structure is less than that of the one upstream of it, such that the mixture fractions of the individual structures decrease in the streamwise direction. ``Flame'' length oscillations in the experiment of Dahm and Dimotakis (1987) were observed to have a characteristic period of d/U, which can be viewed as the lifetime of a structure in a free jet. In the present co-¯ow jet, the lifetime of a structure would be approximately d/DU. Since the jet width, d, increases linearly with x (Fig. 10), and the velocity excess, DU, decreases hyperbolically, or with the inverse of x (Fig. 3), the lifetime of a structure is proportional to x2. Engulfment by other structures dilutes the structure and forms a new one with a lesser concentration. Assuming that the mixing rate is much faster than the chemical reaction rate, most of the product will be formed inside these uniform structures, rather than at the edges. Since the values of Da listed in Table 3 for x/D ˆ 20 are much less than unity, this assumption should apply to the present results. For a structure with a stoichiometric value of fs, chemical reaction will be occurring at a ®nite rate within the structure. Dilution by engulfment at the end of the structure's lifetime will effectively quench the reaction. In this model, the regions of greatest production in a reacting jet will be the structures that have mixture fractions at or near the stoichiometric value. The amount of product formed is dependent upon the lifetimes of struc-

tures at or near the concentration of the stoichiometric mixture fraction, fs. Recall that the lifetimes of the structures grow with distance from the nozzle as x2. As depicted in Fig. 1, when fs is large the stoichiometric regions are close to the jet pipe, where the structures are short lived, leading to less product than at high fs, for which the stoichiometric structures are further downstream from the jet pipe and longer-lived. Thus, more product is produced in the longer-lived structures, corresponding to the lower stoichiometric mixture fraction. An alternative explanation follows from assuming that most of the reaction occurs in locally strained shear layers where the reactants are initially mixed, rather than in large, well-mixed structures. In this case, formation of particles may be suppressed at the higher fs owing to the surface of mean stoichiometric mixture fraction being in a region of higher strain rates for fs ˆ 0.27 than for fs ˆ 0.06. The results of a numerical model indicate that, in highly strained layers, the nucleation rate of particles was suppressed, owing to slowness of cluster growth compared with the mixing rates (Kennedy 1985). Experiments in a strained laminar mixing layer produced by a stagnation ¯ow support this ®nding by showing that the rate of nucleation of NH4Cl particles from reacting NH3 and HCl was diminished by high strain rates (Kennedy and Chevalier 1991). In addition, Lesniewski and Friedlander (1995) reported results from calculations for a turbulent jet with nucleating particles that showed, when turbulent ¯uctuations were taken into account, that the local maximum in the average nucleation rate was signi®cantly reduced from that calculated based on just the mean concentrations. At the higher stoichiometric mixture fraction (fs ˆ 0.27) the stoichiometric surface is closer, on average, to the centerline (see Fig. 1) where turbulence levels are highest. Mean scalar dissipation rates are expected to follow the distribution of viscous dissipation rates in a jet, and to be fairly uniform across the central part of the jet (Bradbury 1965), where the reaction zone at fs ˆ 0.27 will be located on average. The reaction zone for fs ˆ 0.06 is located, on average, much further from the axis where turbulence production rates, turbulence kinetic energy, and, by inference, mean scalar dissipation rates are smaller. In order for the latter description for suppression of product at high fs to be valid, one would expect Da to be on the order of unity or above, otherwise chemical reaction would be distributed over a large region and reaction rates would not be sensitive to local strain rates. In view of the low values of Da listed in Table 3, the former mechanism is deemed the more likely of the two. The images of Figs. 15 and 16 are consistent with the notion that chemical reaction is for the most part uniformly distributed over relatively large structures. The graphs of normalized ¯uctuations of product concentrations in Figs. 13 and 14 clearly show differences in the data between the two cases of fs for x/D < 80. At x/D ˆ 20, differences occur in the magnitudes and radial locations of the maxima. For the case fs ˆ 0.06 (Fig. 13), the magnitudes at the maxima are signi®cantly higher that at the centerline, and the maxima occur further away from the centerline than for fs ˆ 0.27 (Fig. 14). The maxima for fs ˆ 0.06 most likely occur near the location where the

543

reaction is taking place, since they can be associated with regions of locally high product concentration surrounded by regions of locally pure reactant. At locations further downstream, the curves for fs ˆ 0.06 move progressively toward those for fs ˆ 0.27. By x/D ˆ 80, the data are indistinguishable between the two cases, consistent with the similar shapes of the mean pro®les between Figs. 8 and 9 at the same axial location.

544

7 Conclusions An experimental study was undertaken in a co-¯ow jet that incorporated the reaction of HCl and NH3. The product, NH4Cl aerosol, enabled mass concentrations to be measured by elastic light scattering in the transitional regime between Rayleigh and Mie scattering. Mean and rms values of the product concentrations revealed that the ``¯ame'' length changed with stoichiometric mixture fraction, but not with Reynolds number. A signi®cant reduction in product concentration was observed at the higher of the two stoichiometric mixture fractions that were examined. Two possible mechanisms were proposed to explain the reduction in product; one involving a simple conceptual model in which the bulk of production occurs in large structures of uniform concentration, the lifetimes of which decreased as one moved closer to the jet pipe exit, and the other involving production in localized thin shear layers at the interface between regions of reactants. Since estimates of the DamkoÈhler number are signi®cantly less than unity, the former mechanism is thought to be the more likely. References

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