AN EXPERIMENTAL AND NUMERICAL STUDY OF PARTICLE-LADEN COAXIAL JET FLOWS

Abstract A detailed experimental and numerical study of the developing region of coaxial jet flows with and without glass beads is performed. A two-component phase/Doppler interferometer is used to measure mean and fluctuating velocity components for each phase and particle-number density. The numerical calculation is based on a stochastic Lagrangian treatment for the particles and a recently proposed two-equation turbulence model for two-phase flows.1 Results show that the particle-number density profile becomes narrower than the corresponding profile for round jet flow and that the particles attain a uniform velocity across the jet radius. The particles attenuate the level gas turbulence and increase their anisotropy level. The numerical calculations yield reasonable and encouraging agreement with the measurements.


Introduction
Gas turbine combustor performance and durability are strongly influenced by injector-spray characteristics and the attendant interaction with the combustor's internal flow field. To improve understanding of spray-swirler interaction, we conducted a comprehensive experimental and numerical investigation in a stepwise manner. As a first step, we recently presented a detailed study on the developing region of a single particle-laden axisymmetric jet. 1 As a follow-up, the present study deals with the developing region of unconfined turbulent axisymmetric coaxial jets with and without particles.
A number of investigations have contributed to identifying the general features of single-phase coaxial jet flows.2-4 M atsumoto et al., 4 Chigier and Beer, 5 and Durao and Whitelaw 6 have provided considerable information on the effect of nozzle conditions--such as nozzle-wall thickness and boundary layers on the inside and outside walls of the nozzle--on jet mixing within the developing region. Others 7.s have investigated the effect of the jet momentum ratio on the flow field with test configurations in which the radial distance separating the coaxial jets was negligible. The general features of this class of single-phase flows are reasonably well understood. However, the effect of seeding the central jet with particles on the mixing of the developing region should be studied to obtain a first-order simulation of a liquid fuel injector surrounded by an annular jet.
A phase/Doppler interferometry was utilized in the present study to make detailed point measurements for both phases. This instrument is capable of providing simultaneous particlesize and velocity measurements, particle number density, and size-velocity correlation. Radial profiles at seven axial locations downstream of two coaxial jets with and without particles are reported. The measurements include mean and root mean square (rms) velocity components, Reynolds stresses of both phases, and particle-number density.
Our calculations are based on a recently proposed model for two-phase flows. This model is based on a Eulerian formulation for the gas and a stochastic Lagrangian method for the particles. The modeled conservation equations for the mean motion of the gas are supplemented by a two-equation turbulence model for two-phase flows. 9'~° This turbulence model accounts for the additional energy dissipation caused by the particles. The stochastic Lagrangian method considers the effects of both particle inertia and gas turbulence fluctuations on particle motion and interphase transport quantities. The governing equations of the two phases are fully coupled through the mean and fluctuating relative velocities.

Test facility
The testing facility shown in Figure l(a) was designed to characterize a wide variety of flows under isothermal conditions. For the present study, an unconfined flow configuration was selected, operating with an axial jet injector surrounded by a nonswirling annular jet, as shown in Figure l(b). In this configuration, the injector is directed vertically downward within a 457-mm square wire mesh screen. The pipe extends 59 diameters upstream from the injector to obtain fully developed profiles at the exit plane. The entire test assembly is surrounded by a flexible plastic enclosure, which serves two primary purposes. First, the enclosure helps damp out extraneous room drafts. Second, and most important, the enclosure allows uniform seeding of the entrained air, thereby permitting unbiased measurements in the jet's outer region. Test-section air flows into a sealed collection drum and then into a suction vent connected to an exhaust blower. A slide valve on the vent allows for a variable duct back pressure. The support cage is mounted on an optics table from below by means of a two-axis traverse system, allowing two degrees of freedom horizontally. The injector is mounted on a vertical spar to provide the third degree of freedom--vertically. The control-volume spatial location is monitored through a three-axis digital indicator that permits positioning to within 0.01 mm. Data were obtained at seven axial stations: 15,25,35,50,75,150, and 300mm from the exit plane of the injector. At each axial station, between 10 and 20 radial points were scanned, as determined by the desired level of profile resolution.

Diagnostics
A two-component phase/Doppler system (Aerometrics, Inc., Model No. 2100-3) was used to map the relevant flow field. This instrument simultaneously measures size and two orthogonal components of velocity for individual particles. 11 The phase/ Doppler measurement technique was evaluated against other techniques in a series of studies 12,13 and gave accurate measurements of three components of mean and fluctuating velocities of gas and particles, two cross components of gas-phase Reynolds stresses, particle-size distribution, and particle-number density. Distinguishing between positive and negative flow directions was made possible by frequency shifting provided by the rotating gratings.
Discrimination of phases or of different particle sizes is inherent in the operation of the system 14. Our approach was to size all scatterers and then use the size measured to discriminate between phases when calculating velocity statistics. Figure 2 shows a typical distribution obtained from measuring the gas phase in the presence of glass beads.

Glass beads
From both the experimental and numerical standpoints, using glass beads with an acceptable quality and size distribution is important. Air classification of the beads was necessary to provide a uniform distribution, as shown in Figure 3. The actual sizes of the air-classified beads, determined by microscopic Particle-laden coaxial jet flows: A. A. Mostafa et al. examination, were between 100/~m and 110 #m. This resulting narrow size range provides for (1) better representation of a monodispersed, nonevaporating spray and (2) better discrimination by the phase/Doppler. Figure 4 shows a typical distribution obtained for two sizes mixed together. Clear separation is evident between the data obtained for each size. Figure 4 shows little deviation in mean velocity within a given size group, indicating that the classification method used is sound.

Data sets
This article presents two data sets for the flow conditions given in Table 1. The center jet (D=2.41cm) is surrounded by an annular jet with inner and outer diameters of 2.9cm and 3.67 cm, respectively. The effective area ratio and axial velocity ratio of the annular jet to the central jet are 0.87 and 1.4, respectively. To facilitate direct comparison of data and predictions, we present the results graphically. However, the experiment is documented in ref. 15, and data are tabulated following the format outlined in ref. 16.

Mathematical model
The modeled conversion equations for turbulent two-phase flow along with the modeling assumptions are described in a previous publication.l' 10 Therefore we only briefly describe the modeled equations in the following paragraphs. The equations of particle motion are cast in the Lagrangian form; the equations of carrier-phase transport follow the Eulerian treatment. The governing equations of the two phases are coupled primarily by the momentum interchange and the extra energy dissipation owing to the relative velocity fluctuation between the gas and particles.

Particle equations
In the discrete particles approach of this study, the dispersed phase is represented by computational particles rather than a continuous distribution function. Each of these computational particles characterizes a group of physical particles possessing the same characteristics, such as size, velocity, and temperature. For a large particle-density to gas-density ratio, the only important forces on a particle are inertia, drag, and gravity, in  b Inlet profiles of mean and fluctuating velocities and particle-number density are plotted in Figures 3-8 which case the equation of motion of the kth computational particle in the ith direction is and

Ui = Ui + ui
Assuming that the particles are spherical, we can use the experimental results for the drag coefficient of a solid sphere. 17 We determine the particle location at any instant of time from: In Equations 4-6, the comma suffix notation indicates differentiation with respect to the spatial coordinates z and r. The kinematic eddy viscosity of the carrier phase is

Numerical solution
The carrier-phase governing equations are solved numerically using Spalding's parabolic marching finite difference solution procedure. 2° The present calculations were performed using a fine grid with 100 cross-stream grid points and marching step sizes limited by 3% of the current radial grid width or an entrainment increase of 3%, whichever is smaller. The ordinary differential equations governing particle motion are solved using a second-order finite difference algorithm. Ten thousand particles are used for the stochastic treatment, and two hundred particles are used for the deterministic treatment. The main difference between the two treatments is that the first considers the effect of gas turbulence on particle motion whereas the second ignores it completely.

Results and discussion
The numerical calculations were started at a downstream distance of 0.62 inner nozzle diameter (15 mm from the nozzle exit), where measured profiles for both phases show no reverse flow behind the nozzle wall. This approach allowed the use of the parabolic code with a very fine grid to obtain an accurate numerical solution. The measured profiles of mean and rms quantities at z= 15 mm were used as initial conditions. Consistent with the K-e model, the initial profile for the turbulence energy dissipation rate was obtained from the measured kinetic energy of turbulence, shear stress, and axial velocity gradient.

Single-phase jet
Calculations were made to establish how well the K-e model performs against the data before introducing two-phase effects. Figure 5 shows a comparison between predictions and measurements of mean axial velocity, kinetic energy of turbulence, K, and shear stress at the various axial stations: z/D=0.62 (initial station), 1.04, 1.45, 2.06, 3.10, 6.2, and 12.45. Solid lines refer to the predictions while symbols represent the measurements. As shown, the results are plotted in a dimensionless form versus r/ro, where r o is the radius of the inner jet pipe. The axial velocity is normalized by the centerline velocity, U=,o, at the initial station, whereas the other variables are appropriately normalized by the local centerline velocity, U~,~. Figure 5 shows that the K-e model yields good overall agreement with measurements; however, the discrepancies are high for the kinetic energy distribution. The underpredicted values of the kinetic energy of turbulence are more obvious in the regions where the flow  ~Uz ,c TE88-5262 Figure 6 Measurementsofrmsvelocitycomponentsforthesinglephase coaxial jets changes rapidly: in the developing shear layer between the two jets (first region) and where the shear layer reaches the centerline (second region).
In the first region, the mixing layer between the two flows produced by the inner and outer streams is changing from a thin layer characterized by a high shear stress to a self-similar shear flow where the shear stress is relatively small. In both regions, the flow possesses two significant rate-of-strain components resulting from the velocity gradients in both the axial and radial directions. This type of flow is classified as complex shear flow, which is difficult to predict by using the standard version of the K-e model.
The distribution of the turbulent shear stress and its dependence on the mean velocity gradient is also shown in Figure 5. According to the eddy-viscosity hypothesis, the sign of the shear stress and the velocity gradient is clearly consistent across the flow field. The positive shear stress in the inner jet region indicates that the flow still bears the characteristics of the upstream pipe flow; the gradient of mean axial velocity is still negative but approaching zero. The distributions of K and uzu, reach their more familiar shapes (as in a single free jet) when the mixing takes place across the entire flow and the mean axial velocity gradient becomes negative across the entire jet. Figure 6 presents the experimental data of the three rms velocity components at the different axial locations. The shapes of the three components have maximum values just behind the nozzle wall and minimum values at the central axis. But in the farther downstream region where the mixing layer merges with the central axis, the rms profiles take a uniform shape like that observed in fully developed jet flows. Figure 6 also shows that the radial rms velocity component, u 2, has almost the same value of the axial component.

Particle-laden jets
The mass loading, defined as the ratio of particle-to-gas mass flow rate of the inner jet at the inlet plane, LR =0.2, was considered. To distinguish between the effects of mean and fluctuating gas velocity on particle transport, we compared predictions using stochastic and deterministic treatments to the measured data. Figure 7 presents the mean axial velocity, kinetic energy, and shear stress of the carrier phase. The high velocity of the external stream (compared to that of the central jet) causes a rapid increase in the axial velocity of the inner jet downstream of the exit plant. Because of this transfer of mass and momentum from the external to the internal stream, the carrier-phase velocity distribution where the particles exist, becomes different from that of the axisymmetric jet flow case observed by M ostafa The present particle loading is fairly small in terms of altering the carrier-phase flow field.~ 9 However, comparison of the last two planes in Figure 7 with those of Figure 5 shows some reductions in turbulence kinetic energy and shear stress in the near centerline region where the particles exist. This turbulence modulation is caused mainly by the fluctuating relative velocity between the particles and the carrier phase. Particles generally cause a reduction in gas turbulence and an increase in the dissipation rate of that energy. This phenomenon was simulated in the present study by introducing extra terms into the turbulence kinetic energy and its dissipation rate equations. Increasing the particle loading increases the turbulence modulation, as pointed out by Mostafa et al. ~ and recently measured by Fleckhaus et al. 2' Figure 7 shows that the present mathematical model yields fairly good agreement with the experimental data. Figure 8 presents the measured values of the three components of fluctuating velocity of the carrier phase when glass beads are present. The effect of the particles on the radial and azimuthal components is higher than that on the axial component. This condition may be attributed to the differences in the mean  w~"e / Vz ,c TE88-5258 Radial profiles of rms of particle-velocity components velocity strain profiles and to the small ratio of v2,/u 2" compared 2 2 to vz/u,. According to Fleckhaus et al., 21 the smaller the ratio of particle to gas velocity fluctuation, the higher is turbulence attenuation. This observation supports the postulate that particles increase the level of anisotropy and shows the need for detailed measurements of mean and fluctuating components of the two phases under different flow conditions. Figure 9 presents the data of the mean axial particle velocity and number density. It also compares the predictions of the stochastic (ST) and deterministic (DT) treatments to the experimental data. The mean particle velocity profile is uniform over the entire cross section of the flow field. This behavior is different from that observed in round jet flow measurements 1 and could be attributed to rapid mixing between inner and outer jets, which subjects the particles to a more uniform gas-velocity distribution. This jet mixing process creates a strong negative radial velocity in the jet's outer region and causes the particle-number density to become narrower than the corresponding profile for axisymmetric round jet flows. 1 Figure 9 also shows that the ST provides good predictions, compared to the experimental data, whereas the DT performs quite poorly at the downstream stations. That is, a particle moves radially because of its initial mean radial velocity and/or the mean radial gas velocity, both of which are very small compared to the axial component. This effect explains the narrow distribution of particle mean axial velocity and number density predicted by DT. Figure 10 presents the measurements of the three components of fluctuating particle velocity and indicates the extent to which ST allows reasonable calculations. Although DT ignores these components entirely, ST simulates these particle-velocity fluctuations as a response to the carrier-phase components. The agreement between predictions and data is less than satisfactory at the last station, which could be attributed to the limitations of the assumptions embedded in the ST's formulation. Figure 10 also shows the high anisotropy of particle turbulent quantities that increase the anisotropy level of the carrier phase discussed in the analysis of Figure 8.

Conclusions
A detailed data set was presented for gas and particle mean and fluctuating velocity and particle-number density within the developing region of particle-laden coaxial jets with 105/~m glass beads. Because of the mixing between inner and outer gas streams, the mean particle velocity becomes uniform over the entire cross section, and the particle-number density profile becomes narrower than the corresponding profile for axisymmetric round jet flows. The presence of the glass beads attenuates the level of the gas turbulence quantities and increases their level of anisotropy. The computations--using the stochastic treatment in conjunction with the recently developed two-phase turbulence model--yield reasonably good agreement with the data.