Experimental and numerical study of a water spray in the wake of an axisymmetric bluff body

ELSEVIER

Experimental and Numerical Study of a Water Spray in the Wake of an Axisymmetric BluffBody X.-Q. Chen C. Freek J. C. F. Pereira Instituto Superior T~cnico / Technical University of Lisbon, Mechanical Engineering Department, 1096 Lisbon Codex, Portugal

• An experimental and numerical study was made of a water spray issuing into a recirculating flow behind a bluff body disk mounted in a nozzle. A two-component laser-Doppler/phase-Doppler anomometry system was used to characterize the mean and turbulent dispersed phase. The numerical prediction of the hollow-cone spray was based on an EulerianLagrangian stochastic hybrid model. The continuous gas flow field was predicted using a differential Reynolds stress transport model whereas the particulate droplet flow field was predicted using an improved Lagrangian stochastic dispersion model. Comparison of numerical predictions and experimental measurements was carried out for droplet mean and fluctuating velocities, number mean diameters, and mass fluxes. Results indicate that the droplet dispersion characteristics are strongly influenced by the presence of flow recirculation due to different particle Stokes numbers, yielding recirculation or penetration of particles through the separated flow region. Predictions of droplet axial and radial rms velocities obtained with the Lagrangian stochastic model are less satisfactory than those of other simple gas spray flows. Keywords: spray flow, L D A / PDA measurements, EulerianLagrangian model, Reynolds stress model

INTRODUCTION Spray flows behind a disk are widely encountered in various combustion systems. These flows are characterized by the presence of strong flow recirculation in the near wake of a flame-stabilized disk. Therefore, investigation of spray flows under nonreactive conditions behind a disk becomes a prerequisite not only for spray combustors but also more generally for understanding droplet dispersion inside separated flows. So far, there has existed detailed knowledge of spray characteristics such as spray angle and mean droplet sizes averaged over the spray for different exit Weber numbers and spray types. A large number of studies related to spray characteristics with spatial resolution have been obtained with a laser-Doppler/phase-Doppler anemometry ( L D A / P D A ) system [1-7]. Most of the experimental studies are associated with the physics of droplet-gas interaction in the presence of separated flow and are in particular related to swirling flows. Wang et al. [8, 9] and Rosa et al. [10, 11] have provided insight into the coupling of the droplet phase with the gaseous phase as well as the influence that swirl has on the velocity and turbulence of gas fields and its overall effect on the properties of isothermal sprays. Very few experiments

have been reported on spray flows without swirl in the near wake of bluff bodies. Hardalupas et al. [12] reported experimental studies on disk-stabilized kerosene-fueled flames in which isothermal flow conditions were also considered. Their research was mainly focused on the particle behavior near the stagnation point behind the disk. Recent comprehensive reviews on two-phase flow models can be found in [13-15]. It is widely accepted that the hybrid Eulerian-Lagrangian stochastic separated flow (SSF) modeling of dilute two-phase flows constitutes the state-of-the-art tool to predict engineering dilute two-phase flows. However, detailed inlet conditions for Lagrangian computations have been found to play an important role in appropriately assessing Lagrangian stochastic models, particularly for sprays. Sturgess et al. [16] used the Lagrangian stochastic model to predict the experimental hollow-cone spray of Mellor et al. [17] without complete inlet conditions, yielding unsatisfactory predictions. Shuen et al. [18] performed a sensitivity study of the effect of assuming inlet conditions on the prediction of droplet properties. Their study also demonstrated the importance of assuming dropletphase initial conditions to accurate prediction of droplet

Address correspondence to Professor J. C. F. Pereira, Mechanical Engineering Department, Instituto Superior T6cnico/Technical Universityof Lisbon, 1096 Lisbon Codex, Portugal.

Experimental Thermaland Fluid Science 1996; 13:129-141 © Elsevier Science Inc., 1996 655 Avenue of the Americas, New York, NY 10010

0894-1777/96/$15.00 PII S0894-1777(96)00037-4

130

X.-Q. Chen et al.

properties. In addition, Chen and Pereira [19] used an Eulerian-Lagrangian stochastic model to predict the evaporating spray of Yule et al. [20] without detailed experiments at the inlet. The inlet droplet sizes were assumed to be of the R o s i n - R a m m l e r type. They once again came to the conclusion that the prediction of droplet volume concentration was influenced by the assumption of droplet sizes at the inlet. Sommerfeld et al. [7] performed a complete set of measurements of an evaporating spray almost immediately (4 mm) after the nozzle. However, their test rig was arranged in such a way that the flow recirculation could be minimized. It is clear that most of the existing experimental measurements were characterized by the presence of either weak or no flow recirculation [5-7]. Moreover, numerical predictions of these measurements were based on the isotropic eddy viscosity k - e model, which clearly fails to predict the anisotropy of turbulence in complex recirculating flows as investigated in this work. Therefore, the objective of the present work is twofold: experimental measurements of a water spray immediately after the nozzle (4 mm from the disk) and numerical predictions of the measured spray used a second-moment Reynolds stress transport model for the continuous gas phase together with an improved Lagrangian stochastic model for the particulate droplet phase. EXPERIMENTAL METHODS Air was discharged downward through a nozzle with a diameter of 80 mm surrounding a disk with a diameter of 45 mm. A pressure swirl atomizer was located in the center of the disk, as shown in Fig. la. The complete experimental setup is shown in Fig. lb. Air was discharged from an l l-kW fan and then passed through a Henchel venturi flow-rate meter. The air was fed with tracer particles before entering the settling chamber of the test facilities. The settling chamber was 950 mm long with maximum inner diameter of 240 mm. The first part corn-

28

mrn

....7 i~": ' ;/ i /

" !, . ... ,

45 rnm rI 80

mm

Figure 1. Experimental setup. (a) Spray configuration; (b) test rig.

prises a 640-mm diffuser with an opening half-angle of 7 ° and a maximum inner diameter of 240 ram. It follows a 60-mm-long straight tube containing a "honeycomb" and a mesh screen that were used to maintain a low turbulence level. This unit is connected with a flange to a 190-mm-long converging tube, which was designed by applying Morel's method to form a nozzle with a diameter of 80 ram. A disk was mounted at the nozzle of the above-described chamber. A pressure swirl atomizer operating at a pressure of 4 bar produced droplets ranging from 10 to 100 /zm. The complete system was mounted in a 2 x 2 m rig with a height of 4.5 m; see Fig. 1. A basin connected to a fan was placed under the settling chamber to catch tracer particles, to keep the laboratory air clean, and to remove the water droplets. The distance between the outlet and the basin is 1.5 m so that they have no influence on each other. Detailed measurements of the two-phase velocities and droplet sizes and the droplet mass flow rate were performed at a number of cross sections downstream of the inlet by employing a Dantec two-component fiber-optics phase-Doppler anemometer (PDA) with a multiline argon ion laser of 800 mW. Figure 2 shows the optical setup of the P D A and the data processing system. A 400-mm focal length lens was used for transmitting purposes. The receiving optics were mounted 73 ° off-axis from the scattering direction. The droplet scattering light is received in four photomultipliers. Three detectors at different elevation angles are used to evaluate the particle diameter. The advantage of using three different signals is to broaden the working distance and to increase the sensitivity and the ability to validate the spherical shape in the two-dimensional configuration. One of the three detectors also provides the Doppler frequency for the two velocity components. Furthermore, a validation criterion is used according to the comparison between the phase measurements from the first and second detectors as well as between the phase measurements from the first and third detectors. The signal will be rejected if the comparison lies beyond a prescribed tolerance. In addition, another criterion can also be used to compare the spherical shape for the two dimensions, which can also result in a rejection for a given tolerance. The signal validation is completed by a particle dynamics analyzer connected and controlled by a common personal computer. The software also controls a 3D custom-made traversing system for the P D A optics. The main characteristics of the L D A / P D A systems are summarized in Table 1. The mean diameters were determined from 10,000 individual values. Incorrect size measurements may be due to trajectory effect or Gaussian beam effect [21, 22] and the slit effect [23] that becomes relevant for droplet diameters greater than 75% of the sample l / e 2 beam diameter. A detailed report on sizing errors can be found in Xu and Tropea [23] for the same commercial measuring device as the one we used. With a similar droplet and probe volume relation, they found that theoretically in a maximum error may be as large as 13% in the size measurements, but the reported error in measurements was only around 5%, including the error due to the slit effect. The droplet mass flux error comprises the error in the droplet size and in the counting rate. In addition, it is influenced by the dropout of signals due to the validation rate of the sampies. Since the probability of the system detecting larger

Waternet

Compressor

©

Pressuretank

V3

V2

V1

?

Manometer Pressure tank

®

i~Dmin

PDAProbe t

Manometer

I

Ventilator

lingchamber

Figure1.Continued

i I

[

Ventudaxial

Ethylengl.

|

/

Electricalresistence

Ventilator

,.<

o

03

132 X.-Q. Chen et al.

I

!

L r

I

Particle DynamicsAnalyzer i

T

hotomultiplier

Four

J

Channel

Oscilloscope

L- B~nch I 3 D traversing / I system + ~ e i v i n g

Back scattering fiber not in use BB-

optics

[

t/ 73.50o \It

IlJl I1,11 _

,BeamProbe

'

'/__ " " 7 "

\

'1

/

/

Figure 2. Optic arrangement and phase-Doppler anemometry signal processing system. droplets greater than that of detecting smaller droplets, signals from small droplets passing outside the measuring volume center have lower signal amplitudes; therefore, signals from small droplets may be rejected by the system due to the low signal-to-noise ratio. The largest uncertainty in the data to be reported is in droplet mass fluxes. Although some remedies have been put forth [24], no modifications were made to our existing equipment. For the present experiment, the combined error in droplet diameter and size-dependent cross-sectional area, to which the flux measurements are referenced, was estimated by integrating mass flux balance, yielding ___35%. THEORETICAL METHODS The Eulerian-Lagrangian hybrid prediction of two-phase flows treats the continuous gas phase by using an Eulerian formulation whereas it treats the particulate droplet phase by using a Lagrangian formulation. To predict the anisotropy of gas turbulence, the Reynolds stress trans-

Ii

I

I

beam splitter

I

I

I

Laser (Ar+ - ion )

port (RST) model is used here to write the governing equations for the continuous gas flow field. The governing equations for mass and momentum can thus be written tensorially as

0p uj - -

0xj

Op UiUj OXj

OP OX i

c~ ( q-

OXj

where the Reynolds stresses, own equations,

=

0,

c?Ui --- [3tliU j ~ OXj

(l)

) -~- SPi,

(2)

uiuj, are governed by their

0

Oxk (pU~iuj) = Pij - ~ij + qbij + Dij + S ~ ,

(3)

where Pi,J ei,J . 4aij,. and. Dij . are the generation, dissipation, pressure-strain correlation, and diffusion terms, respectively. The source term S ~p , is due to the droplet-gas

Water Spray in the Wake of a Bluff Body Table 1. Transmitting and Receiving Optics Parameters

TransmittingOptics Two-Laser power Focal length of focusing lens Three-Beam intersection One-Wavelength of laser a Size of measuring volume Major axis of the ellipsoid Minor axis of the ellipsoid Velocimeter transfer constants

0.3 W 400 mm 5.44 ° 514.5 nm (green); 488.0 nm (blue)

interactions. In this study, it is only accounted for in the normal-stress equations, S~

3.947 mm (green); 3.742 mm (blue) 0.183 mm (green); 0.178 mm (blue) 5.429 ms- 1/ MHz (green); 5.143 ms- 1/MHz (blue)

Maximum particle concentration Scattering mode Aperture I.D. Scattering angle Focal length Refractive index Polarization orientation

UiS~j)~ij

= 2(~-

(no summation),

(4)

where S~ is the source term for the momentum equations and is determined in Lagrangian computations. The other terms on the right-hand side of Eq. (3) are determined as follows:

[

OUi

ei, = -p uJukT Tx Dij = ~X k

Receiving Optics Diameter range Phase factor U1-2, U1-3

133

Og } + .i. 7 7x

2 =

•amk + DCs--UkUml ° ~ i g . e ]aX m ]

(s) (6)

0-255.7/,m 1.017 deg/tzm 2.034 deg//xm 100,000 (number)

The pressure-strain correlation term of flbijconsists of the slow part ~bij' 1 and the rapid part ~bij' 2; that is,

Refraction ,~ (small particles) 73.5 ° 400 mm 1.334 Parallel

and

4)ij = 4)ij, 1 -}- 4)ij,2

(7)

¢~ij,l = -Cl P k (UiUj - 2kSij), ~)ij, 2 = - C 2 ( Pij - 2 G S u ) ,

llll

b

Figure 3. Measured two-phase velocity vectors. (a) Gas; (b) droplet.

(8)

134 X.-Q. Chen et al. where the production G = ekk/2. Finally, the equation governing the dissipation rate of the turbulent kinetic energy reads

--(pUjs) OXj

= --~ + C,sp--uittj--I OXj ],L¢~Xj 8 OXi ]

__ dt

+-£(C=1G - C=2p=) + C=3~SL (9) where the droplet-gas interaction term is given by Sp = ~S~j~. 1 p

(10)

The modulation of the droplet phase on the turbulence of the gas phase, Eqs. (4) and (1), was accounted for here following Berlemont et al. [25]. The RST model constants are given as follows: (Cs,

Due to the large ratio of droplet density to gas density, the Lagrangian equation of motion for each of the droplet parcels can be written [27] as

C1, C2, C~, Ct2, Cel, C=2, Ce3)

-

+ Fpi ,

(II)

.Cp

where t)// = U/+ u i is the instantaneous gas velocity and Fpi is the sum of the external forces, i.e., gravity, centrifugal, and Coriolis forces, in cylindrical coordinates. The relaxation time of droplets, ~-p,is defined as "rp = p p D 2 / 1 8 t ~ f p ,

(12)

where the drag correction coefficient f p is used to account for the non-stokesian flow and depends on the relative Reynolds number between the gas and droplet phases. As proposed by Cliff and Gauvin [28], it is given by fp = 1 + 0.15 nK e p0 687

(0 < Rep < 1000), (13a)

= (0.22, 1.8, 0.6, 0.5, 0.3, 1.45, 1.9, 1.1). The determination of the droplet sources in the gas-phase equations can be found in detail elsewhere [26]. It should be stressed that for the present dilute spray, the turbulence modulation of the droplet phase on the gas phase is not significant; however, these sources are still included for completeness.

Rep =

/x

(13b)

The droplet trajectories are computed as d'Xpi __ Upi.

(14)

dt

Note that Eqs. (11)-(14) represent each droplet size considered. For conciseness, the subscript for droplet sizes is neglected. STOCHASTIC D R O P L E T DISPERSION M O D E L

Figure 4. Droplet drag forces and diameters. (a) Drag force vector; (b) drag force contours; (c) number-mean diameter contours.

It is known that the time-averaged Eulerian equations can only provide the gas mean properties. However, an instantaneous gas flow field is required in Lagrangian equations of motion. Therefore, the main difficulty in Lagrangian computations is the unknown instantaneous gas field. For the time being, the stochastic model of Gosman and Ioannides [29] is often used to determine the instantaneous gas flow field. This model is, however, in essence an isotropic stochastic dispersion model. It treats the droplet dispersion by employing the instantaneous gas velocity through the concept of droplet-eddy interactions. The droplets are assumed to interact with a sequence of randomly sampled turbulent eddies. The droplet-eddy interaction time is determined by minimizing two time scales: the eddy lifetime and eddy transit time. The fluctuating velocity is obtained by randomly sampling a Gaussian pdf with a standard deviation proportional to the local turbulent kinetic energy. This model does not account for the effect of temporal and directional correlations of gas velocity fluctuations on droplet dispersion along droplet trajectories and as a consequence fails to account for the anisotropic effect of gas turbulence on droplet dispersion. To overcome the shortcomings of this model, Zhou and Leschziner [30] proposed a time-correlated model that accounts for temporal and directional correlations of velocity fluctuations between two successive time steps. The recent comparative study [31] of these two dispersion models shows that the time-correlated dispersion model can adequately account for the anistotropy of turbulence, thus giving better prediction of droplet rms velocities than

Water Spray in the Wake of a Bluff Body

r" O

,4

J

J

135

136

X.-Q. Chen et al.

the isotropic dispersion model. However, using cylindrical coordinates, the prediction of droplet mass fluxes tends to accumulate unrealistically near the centerline far downstream with both droplet dispersion models. Therefore, the conventional SSF model was recently improved by Chen and Pereira [32] to solve this problem. To account for the anisotropic effect of gas turbulence on droplet dispersion, we use u i = o'i~jSij,

(15)

the centerline far downstream [31, 33], the Gaussian variable for the transverse component is obtained by ~cL, = ~:" + ~-~-pap

Yv

where sc~7 is the Gaussian variable having zero mean and unity deviation and Odp is a controlling parameter to switch this modification on or off, depending on the local radial gas mean velocity.

where ~:j is the Gaussian variable having zero mean and unity deviation and ~i is the standard deviation of gas fluctuating velocity given by = ~/2.

(16)

Instead of using the local turbulent kinetic energy [29], the normal stresses, u/z, are used in Eq. (16), which can be appropriately predicted with the RST model. To get rid of the unrealistic accumulation of mass flux predictions near

(17)

O/p =

0, 1,

V < O, V>_ O,

(18)

where V is the radial mean velocity of the gas phase. The idea behind Eq. (18) is that the modification is switched off at V < 0, which corresponds to the region of flow recirculations. Equations (17) and (18) have been successfully used to solve the problem of the unrealistic accumulation of mass flux predictions near the centerline for turbulent evaporating sprays. The details of this model

Figure 4. Continued

Water Spray in the Wake of a Bluff Body 137

._-,o,,

.oe-_-------O

_

.

_

.

.

.

.

.

Figure 5. Predicted gas flow pattern and droplet trajectories. can be found elsewhere [32]. It should be pointed out that the mass flux accumulation occurs for many axisymmetric two-phase flows, whether the centrifugal and Coriolis forces are included or not [31]. The finite-volume method is employed to solve the Eulerian equations together with a staggered grid arrangement. The third-order discretization of the Q U I C K algorithm was used for convection discretization, together with a blend flux correction for Reynolds stress equations -50

5 1015-50

5 1015-50

and the dissipation equation, in which the coefficient matrix incorporates only the contribution from the firstorder upwind and the source term induces the difference between the first-order upwind and quadratic upwind. For the present flow configuration, this procedure avoided wiggle errors. The droplet phase field is calculated by tracking the droplet parcels throughout the computational domain. The initial conditions at the inlet were obtained by interpolating the experimental measurements. At the

5 1015-50

5 1015-50

5 1015-50

Y [mm] 50

I

~

I

I

D

9

-50

10

5 1015 U~[m/s] I

20

30

o

Measured

40

60 Computed

Figure 6. Comparison of droplet axial mean velocities.

100

X [me]

138

X.-Q. Chen et al. 10 33 57 80 10 33 57 80 10 33 57 80 10 33 57 80 10 33 57 80 10 33 57 80 Do[#m] i

Y [mm]

~

50

D

i

i

D

DD

-50

0

20

30

[]

40

60

Meosured

1O0

X [mrn]

Computed

Figure 7. Comparison of droplet number-mean diameters. inlet, the droplet size distribution was measured at each point. The computational droplet size is selected in such a way that it approaches the measured probability density function (pdf). Depending on the total number of droplet trajectories, the selected droplet size distribution may be almost continuous at the inlet. This is also the particular advantage of the Lagrangian trajectory model over the Eulerian continuum model. Each selected droplet size at the inlet represents a set of droplets having the same size and initial conditions. The droplet equation of motion is presently solved in terms of the Cartesian coordinates to avoid the singularity that the droplet radial position may approach zero in the application of cylindrical coordinates. Therefore, the centrifugal and Coriolis forces are implicitly included in the Cartesian equations of motion. The droplet source terms determined in Lagrangian computations are distributed into gas Eulerian equations in accordance with the residence time of droplets in an Eulerian control volume. The gas properties at current droplet positions are interpolated using an accurate second-order algorithm similar to that used by Rangel and Sirignano [34]. 0.0

0.1

0.00

i

Y [mm]

0.02 0.00

0.0:

!

i

50

RESULTS AND DISCUSSION Detailed experimental measurements of radial profiles were performed radially at X = 4, 10, 20, 30, 40, 60, and 100 mm. The first radial profile at X = 4 mm was used as the initial conditions required for the numerical computations of the dispersed phase. The remaining profiles were used as the validation of the numerical results. The first profile of measurements provides such detailed droplet properties as droplet sizes and their corresponding pdf, mean and rms velocities for each of the droplet sizes, mass fluxes, and droplet mean diameters at each measured point. Experimental measurements indicate that the spray could be satisfactorily considered axisymmetric. Therefore, only half of the flow domain was considered in the numerical calculations. For the present unconfined spray, it is required to choose a computational domain that covers the jet expansion. The dimensions of the computational domain were 350 mm axially by 95 mm radially. On the free boundary, entrained fluid was implicitly calculated. The details on the implementation of free boundary conditions can be found elsewhere [35]. The present nu0.00

0.02

LO0

i

0.02 0.00

0.01 F,[kg/sm']

i

i

,>

0

-50

10

50

2O n

Meosured

40

60 Computed

Figure 8. Comparison of droplet mass flux.

100

X [me]

Water Spray in the Wake of a Bluff Body 139 merical computations were performed using a grid of 73 X 71 in the axial and radial directions, respectively, and to resolve well the flow near the nozzle, refined grids were employed in the region close to the nozzle. To achieve a statistically significant solution for the Lagrangian computations, especially in the central region close to the nozzle, a total of 9000 droplet trajectories were employed for trajectory calculations. Comparing the results obtained with a grid comprising 36 x 35 nodes and using the Richarson extrapolation it has been shown that the error in mean axial velocity is about 10% of the inlet velocity. This clearly shows that the 73 x 71 grid does not yield grid-independent results. However, it was considered satisfactory based on the impossibility of conducting calculations using 145 x 142 nodes in our workstation to further use the Richarson extrapolation. Figures 3a and 3b show the measured axial and radial velocity components for the gas and droplet phases, respectively. Obviously, the motion of droplets is influenced by the presence of flow recirculation. Only large droplets have enough momentum to penetrate the separated flow region, and they are less influenced by the gas phase. This is due to the fact that the dispersion behavior of a droplet is governed by its Stokes number, defined as the ratio of the relaxation time to the characteristic time of the turbulent gas flow. Shown in Figs. 4 a - c are the measured mean drag force vectors, mean drag force contours, and mean droplet diameter contours. The mean drag forces are evaluated as - - m p , %

consistent with the typical behavior of a polydispersed spray. In the following paragraphs, numerical results for the droplet phase are compared and discussed according to the experimentally measured radial profiles at X = 10, 20, 30, 40, 60, and 100 mm for droplet axial mean velocity, number-mean diameters, mass fluxes, and fluctuating velocities. To gain an intuitive impression of the motion of droplets in the strongly recirculating gas flow, Fig. 5 displays 10 sampled droplet trajectories with different diameters from Lagrangian trajectory computations, together with the predicted gas flow pattern. Note that the sizes of the circular symbols in the figure are directly proportional to the real droplet sizes in the spray. The flow pattern indicates that a large flow recirculation is formed near the nozzle. In addition, the computed droplet trajectories demonstrate that almost all droplets go outward from the spray core close to the inlet due to the large initial radial velocity at the inlet. Owing to their large inertia, thus large relaxation time, large droplets move farther away from the spray core. This kind of phenomenon has also been observed in the droplet trajectory visualization of Raju and Sirignano [36]. The predominant radial mean velocity at the inlet results in few droplets being present in the spray core region within the flow domain studied, which attributes principally to the computational noise in the prediction of droplet properties, as discussed below. Figure 6 shows a comparison of the predicted and measured droplet axial mean velocities. Reasonably good agreement has been achieved between the prediction and measurement. Compared in Fig. 7 are the radial profiles of the predicted and measured droplet number-mean diameters, which are obtained by averaging all the droplets across an Eulerian control volume. Figure 7 also demonstrates that the droplet number-mean diameters are underpredicted on the spray edge downstream compared to the experimental measurements. The large droplets are moving away from the spray core, which is typical behavior for polydisperse hollow-cone sprays. Note that there are still some large droplets present out of the spray edge. However, the number of large droplets is usually small; there are not enough to achieve a stochastically significant

(19)

where mp denotes the droplet mass. Figure 4 clearly demonstrates that a large drag force is present within the coflowing air region, where there exists a large difference in two-phase velocity. Note that some small droplets with small Stokes numbers may be trapped by the gas flow because of their easy responsiveness to the change in gas flow; therefore, they can be easily influenced by the motion of the gas flow. Figure 4c demonstrates that the large number-mean diameters occur at the spray edge. This is 0 Y [ r a m]

2

4

I

I

6

0

I

5O

2

4

6

I

I

I

0

2

4

I

[

6

0

I

2

4

I

I

6

0

I

2

4

I

I

6 I

0

2

4

6

!

I

I

u,[m/s]

>

-50

10

20

30 n

Measured

40

60 Computed

Figure 9. Comparison of droplet axial rms velocities.

1 O0

X [mm]

140 X,-Q. Chen et al. 0

2

4

6

0

2

4

6

0

2

4

6

0

2

4

6

I

I

I

0

2

4

6

I

I

I

[mml 5O

0

2

1

4

6

I

I

v,[m/s]

.k 1o

20

.30 []

6O

40

Meosured

1 oo

X [ram]

Computed

Figure 10. Comparison of droplet radial rms velocities. average, as was also found in the experimental measurements. Therefore, the predictions out of the spray edge are not shown here. The radial profiles of droplet mass fluxes are shown in Fig. 8. Of particular note is that the droplet mass flux calculations are based on the total number of droplets across a control volume in question. However, the other droplet properties--velocities and diameters--are determined in terms of number-averaged values. Figure 8 indicates that the droplet mass fluxes are very low in the spray core region, which is consistent with the behavior of the plotted droplet trajectories in Fig. 5. The experimental measurements show that the flow deviates slightly from axisymmetry. However, due to the intrinsic experimental errors it is still reasonable to adopt the simplified axisymmetric assumption. The comparison clearly shows that mass flux predictions are qualitatively in satisfactory agreement with the measurements. Evidently, one requires more accurate mass flux measurements before quantitatively judging the accuracy of mass flux predictions. Shown in Figs. 9 and 10 are the radial profiles of the droplet fluctuating velocities, indicating that the droplet rms velocities are underpredicted downstream of X = 30 mm, especially in the spray core region. This is probably due to the underprediCtion of the gas turbulent properties, and in particular the difficulties in predicting the near wake of a disk flow even with different versions of the second-order differential Reynolds stress model. PRACTICAL S I G N I F I C A N C E In the present experimental study, detailed measurements were performed for two phases at the inlet, providing necessary initial conditions for Eulerian-Lagrangian hybrid modeling of two-phase flows. This should be useful for validating existing Eulerian-Lagrangian models. In addition, this study can enhance our understanding of spray behavior in practical combustors with similar flow configurations. CONCLUSIONS AND FINAL REMARKS An experimental and numerical study was conducted of a water spray in the near wake of a disk air flow. To better account for normal stress anisotropy, the gas flow field was predicted using the Reynolds stress transport model instead of two-scale turbulence models. The droplet flow field was predicted using an improved Lagrangian stochastic model that accounts for the anisotropic effect of gas

turbulence on droplet dispersion. It was found that the dispersion of droplets is strongly influenced by the presence of flow recirculation behind the disk. In addition, droplet trajectory visualization has shown that almost all droplets are moving away from the centerline, causing the persistent presence of computational noise in this region. To avoid this, it is necessary to use at least one more order of magnitude in the number of droplet trajectories or to design new efficient Lagrangian trajectory models in the direction proposed by Litchford and Jeng [37]. The detailed comparison of the numerical predictions with the experimental measurements also demonstrates the ability of the Eulerian-Lagrangian stochastic model to predict droplet dispersion in strongly recirculating gas flows.

NOMENCLATURE Dij diffusion component mp droplet mass, g u i gas fluctuating velocity, m / s P,7 generation component S,P momentum sources from the droplet phase Rep relative Reynolds number, dimensionless uiu~ Reynolds stresses, m2/s 2 S,-~ Reynolds stress sources from the droplet phase Sp Dp f k P t U V x y

turbulent energy source from the droplet phase droplet diameter, /xm drag force turbulent kinetic energy ( = 0.5u7), m2/s 2 Pressure, mPa time, s axial gas velocity, m / s radial gas velocity, m / s axial coordinate, m radial coordinate, m

Greek Symbols dissipation rate of turbulence laminar dynamic viscosity density, g / m 3 gas velocity (rms), m / s ooij dissipation component ~-p droplet relaxation time, s ap model parameter 8ij Kronecker delta function e /x p o-

Water Spray in the Wake of a Bluff Body

Subscripts i,j,k Cartesian components p droplet phase t turbulent REFERENCES 1. Bachalo, W. D., Houser, N. J., and Smith, J. N., Behavior of Sprays Produced by Pressure Atomizers as Measured Using a Phase/Doppler Instrument, At. Spray Tech., 3, 53-72, 1985. 2. MacDonell, V. G., Samuelsen, G. S., Wang, W. R., Hong, C. H., and Lai, W. H., Interlaboratory Comparison of Phase Doppler Measurements in a Research Simplex Atomizer Spray, J. Propul. Power, 10, 402-409, 1994. 3. Hardalupas, Y., and Whitelaw, J. H., Characteristics of Sprays Produced by Coaxial Airblast Atomizers, J. Propid. Power, 10, 453-460, 1994. 4. Hardalupas, Y., Taylor, A. M. K. P., and Whitelaw, J. H., Characteristics of the Spray from a Diesel Injector, Int. J. Multiphase Flow, 18, 159-179, 1992. 5. Chang, K.-C., Wang, M.-R., Wu, W.-J., and Hong, C.-H., Experimental and Theoretical Study on Hollow-Cone Spray, J. PropuL Power, 9, 28-34, 1993. 6. Bulzan, D. L., Levy, Y., Aggarwal, S. K., and Chitre, S., Measurements and Predictions of a Liquid Spray from an Air-Assist Nozzle, At. Sprays, 2, 445-462, 1992. 7. Sommerfeld, M., Qiu, H. H., Ruger, M., Kohnen, G., and Mulet, D., Spray Evaporation in Turbulent Flow, Second Symp. Eng. Turbulence Modeling and Measurements, Florence, Italy, May 31-June 1, 1993. 8. Wang, H., McDonell, V. G., Sowa, W. A., and Samuelson, S., Experimental Study of a Model Gas Turbine Combustor Swirl Cup, Part I: Two-Phase Characterization, J. Propul. Power, 10, 441-445, 1994. 9. Wang, H., McDonell, V. G., Sowa, W. A., and Samuelson, S., Experimental Study of a Model Gas Turbine Combustor Swirl Cup, Part II: Droplet Dynamics, J. Propul. Power, 10, 445-452, 1994. 10. Rosa, A. B., Bachalo, W. D., and Rudoff, R. C., Spray Characterization and Turbulence Properties in an Isothermal Spray with Swirl, J. Eng. Gas Turbines Power, 112, 60-66, 1990. 11. Rosa, A. B., Wang, G., and Bachalo, W. D., The Effects of Swirl on the Velocity and Turbulence Fields of a Liquid Spray, J. Eng. Gas Turbines Power, 114, 72-81, 1992. 12. Hardalupas, Y., Liu, C. H., and Whitelaw, J. H., Experiments with Disk Stabilized Kerosene-Fuelled Flames, Combust. Sci. Technol. 97, 157-191, 1994. 13. Crowe, C. T., The State-of-the-Art in the Development of Numerical Models for Dispersed Phase Flows, Int. Conf. on Multiphase Flows, Tsukuba, Japan, pp. 49-59, Sept. 24-27, 1991. 14. Sirignano, W. A., Fluid Dynamics of Sprays--1992: Freeman Scholar Lecture, J. Fluids Eng., 115, 345-378, 1993. 15. Elghobashi, S. E., On Predicting Particle-Laden Turbulent Flows, Appl. Sci. Res., 52, 309-329, 1994. 16. Sturgess, G. J., Syed, S. A., and McManus, K. R., Calculation of a Hollow-Cone Liquid Spray in Uniform Airstream, J. Propul. Power, 1, 360-369, 1985. 17. Mellor, R., Chigier, N. A., and Beer, J. M., Hollow-Cone Liquid Spray in Uniform Air Stream, Symp. on Combust. and Heat Transfer in Gas Turbine Systems, Oxford, UK, Vol. 11, pp. 291-305, 1971. 18. Shuen, J.-S., Solomon, A. S. P., Zhang, Q.-F., and Faeth, G. M., Structure of Particle-Laden Jets: Measurements and Predictions, A/AA J., 23, 396-404, 1985.

141

19. Chen, X.-Q., and Pereira, J. C. F., Numerical Prediction of Evaporating and Nonevaporating Sprays under Nonreactive Conditions, At. Sprays, 2, 427-443, 1992. 20. Yule, A. J., Seng, C. All., Felton, P. G., Ungut, A., and Chigier, N. A., A Study of Vaporizing Fuel Sprays by Laser Techniques, Combust. Flame, 44, 71-84, 1982. 21. Saffman, M., The Use of Polarized Light for Optical Particle Sizing, in Anemometry in Fluid Mechanics, R. J. Adrian, T. Asanurna, D. F. G. Dur~o, F. Durst, and J. Whitelaw, Eds. LOADOAN-Instituto Superior T6cnico, Lisbon, pp. 387-396, 1986. 22. Sankar, S. V., Wang, G., Brena da la Rosa, A., Rudoff, R. C., Isakovic, A., and Bachalo, W. D., Characterisation of Coaxial Rocket Injector Sprays under High Pressure Environments, AIAA Paper 92-0228, 1992. 23. Xu, T.-H., and Tropea, C., Improving the Performance of TwoComponent Phase Doppler Anemometries, Meas. Sci. Tech., 5, 969-975, 1994. 24. Schone, F., Tropea, C., Xu, T.-H., and Haugen, P., Mass Flux Measurements with Phase Doppler Anemometry, in Two-Phase Flow Modeling and Experimentation, G. P. Celata and R. K. Shah, Eds., pp. 751-758, Edizioni ETS, Pisa, Italy, 1995. 25. Berlemont, A., Desjonqueres, P., and Gouesbet, G., Particle Lagrangian Simulation in Turbulent Flows, Int. J. Multiphase Flow, 16, 19-34, 1990. 26. Chen, X.-Q, Numerical Simulation of Steady and Unsteady Two-Phase Spray Flows, Ph.D. Thesis, Instituto Superior T6cnico, Tech. Univ. of Lisbon, Portugal, 1994. 27. Faeth, G. M., Evaporation and Combustion of Sprays, Prog. Energy Combust. Sci., 9, 1-76, 1983. 28. Clift, R., and Gauvin, W. H., Motion of Entrained Particles in Gas Streams, Can. J. Chem. Eng., 49, 438-448, 1971. 29. Gosman, A. D., and Ioannides, E., Aspects of Computer Simulation of Liquid-Fuelled Combustors, AIAA Paper 81-0323, 1981. 30. Zhou, Q., and Leschziner, M. A., A Time-Correlated Stochastic Model for Particle Dispersion in Anisotropic Turbulence, Presented at 8th Turbulent Shear Flows Symp., Munich, September 1991. 31. Chen, X.-Q., and Pereira, J. C. F., Prediction of Evaporating Spray in Anisotropically Turbulent Gas Flow, Numer. Heat Transfer, 27, 143-162, 1995. 32. Chen, X.-Q., and Pereira, J. C. F., Computation of Turbulent Evaporating Sprays with Well-Specified Measurements: A Sensitivity Study on Droplet Properties, Int. J. Heat Mass Transfer, 34, 441-454, 1996. 33. Adeniji-Fashola, A., and Chert, C. P., Modeling of Confined Turbulent Fluid-Particle Flows Using Eulerian and Lagrangian Schemes, Int. J. Heat Mass Transfer, 33, 691-701, 1990. 34. Rangel, R. H., and Sirignano, W. A., An Evaluation of the Point-Source Approximation in Spray Calculations, Numer. Heat Transfer, PartA, 16, 37-57, 1989. 35. Dur~o, D. F. G., and Pereira, J. C. F., Calculation of Isothermal Turbulent Three-Dimensional Free Multijet Flows, Appl. Math. Modeling, 15, 338-350, 1991. 36. Raju, M. S., and Sirignano, W. A., Multicomponent Spray Computations in a Modified Centerbody Combustor, J. Propul. Power, 6, 97-105, 1990. 37. Litchford, R. J., and Jeng, S.-M., Efficient Statistical Transport Model for Turbulent Particle Dispersion in Sprays, A/AA J., 29, 1443-1451, 1991.

Received March 9, 1995; revised March 25, 1996