Article pubs.acs.org/IECR
The Two-Phase High-Speed Stream at the Centerline of a HollowCone Spray Produced by a Pressure-Swirl Nozzle Wei Du, Ze Sun, Guimin Lu,* and Jianguo Yu National Engineering Research Center for Integrated Utilization of Salt Lake Resource, East China University of Science and Technology, Shanghai 200237, China S Supporting Information *
ABSTRACT: The flow characteristics of hollow-cone sprays produced by pressure-swirl nozzles were investigated by particle image velocimetry (PIV) and computational fluid dynamics. Two high-speed characteristic droplet velocities were observed by PIV captures at the periphery and centerline of the spray cone. Such flow characteristics were also simulated by two-dimensional axisymmetric simulations. In the simulation, in addition to the two high-speed characteristic droplet velocities, a high-speed air stream at the spray centerline was also observed. This high-speed air stream converged and accelerated small droplets to form the high-speed droplet stream. After further simulation, it was found that the largest droplets carried by the high-speed air stream at the centerline were most efficient in the momentum transfer process between two phases. The influence of the two-phase high-speed stream on the heat- and mass-transfer process is meaningful for related spray operation research and should be seriously considered. airflow. Santolaya et al.9 found that the smallest droplets were transported to the spray core by the incoming air flow rate, and the velocities of both phases were coupled at this region. Durdina et al.10 also found the central high-speed stream apart from the main stream at the spray periphery, but no flow structure in the PIV velocity data could support this effect. They hypothesized that the central droplets flowed in a cloud formation which helped to keep their momentum, while the main-stream droplet structure expanded with downstream distance and its interaction with the surrounding air increased. Computational fluid dynamics (CFD) is an effective approach to further investigate the two-phase flow which was hardly measured by experimental methods. The Eulerian approach considers the multiphase flow as a single phase of liquid−gas mixture which is usually used to simulate the breakup process of liquid sheet in the near field of the spray. Siamas et al.11,12 examined an annular liquid jet by Eulerian approach and found a recirculation zone adjacent to the nozzle exit, which was a consequence of the annular configuration.13,14 In a twodimensional (2-D) axisymmetric swirl calculation developed by Sheen et al., the predicted axial droplet velocity showed a good agreement with PDA data, but the calculated maximum velocity at the outer edge of the conical spray pattern was nearly 50% lower than that measured by PDA.15 After the breakup of the liquid sheet, the dispersed droplets transported further in the ambient air, then the Eulerian-
1. INTRODUCTION Pressure-swirl atomizers are widely used in many engineering applications because of their geometrical simplicity and good atomization characteristics. The operation of pressure-swirl atomizers is based on the high angular momentum of the fluid inside the atomizer. Liquid emerges from the discharge orifice as an annular sheet, which spreads radially outward to form a hollow-cone spray. The spray evolution and the two-phase flow induced by spray droplets significantly affect the heat and mass transfer during drying and thermodecomposition processes in related applications. Many researchers have investigated the spray structures of hollow-cone spray by means of spray measurement and numerical simulations. It is commonly accepted that in the absence of any significant external air flow field, large droplets tend to remain in the initial direction along the spray cone periphery with higher velocity, while smaller droplets couple to the local induced airflow.1 Actually, two kinds of spray profiles of hollow-cone sprays had been observed which contradicted each other. Some researchers found local minima of axial velocity in the spray centerline,2−4 while others presented high centerline velocity.5−7 Droplet velocity and flux were compared by Xie et al.3 through phasedoppler anemometry (PDA) and particle image velocimetry (PIV), and a higher local droplet flux corresponding to a higher local droplet velocity was found at the periphery of the spray cone. Though the droplet mass flux might be low, local high velocity was found at the spray centerline in certain conditions. Choi et al.8 analyzed the spray structure by a PDA system and found that entrained airflow accelerated axial velocity near the spray axis and formed vortex flow in the outer edge of the spray, and droplets with diameter less than 15 μm mostly followed this © XXXX American Chemical Society
Received: Revised: Accepted: Published: A
August 16, 2016 December 6, 2016 December 9, 2016 December 9, 2016 DOI: 10.1021/acs.iecr.6b03140 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
Article
Industrial & Engineering Chemistry Research Lagrangian method is efficient to simulate the two-phase flow, especially the trajectory of particles. In this approach, the air is treated as a continuum by solving the Navier−Stokes equations, while the dispersed phase is solved by tracking a large number of droplets through the calculated flow field. Most simulations of spray dryer and similar processes involving spray operation were performed using a mixed Eulerian−Lagrangian approach.16 Huang et al.17 and Mezhericher et al.18−23 performed several calculations on a cylinder-on-cone spray chamber, for which a 2D axisymmetric model was proved to be suitable for fast and lowresource-consumption numerical calculations and predict values of velocity, temperature, and vapor mass fraction in the spray chamber with reasonable accuracy. It was also found that the 2D model predicts greater values of air velocity in the central core region, whereas the 3D model calculates higher velocity in the periphery of the chamber.19 The difference in velocity distribution raised the necessity of verifying the predictive veracity of spray models. Based on Eulerian−Lagrangian approach, 2-D and 2-D axisymmetric simulations were modeled in standard KIVA-3 V code by Gao et al.24 and Zhao and Xie,25 respectively. The droplets were found to distribute in the periphery of the spray cone, and no centerline streams was predicted. Shim et al. calculated the spray process with a linearized instability sheet atomization (LISA) model implemented with KIVA code, and the calculated results compared favorably with the experimental results on the spray extension and spray tip penetration.26 Bafekr et al.27 calculated the primary breakup of liquid with MATLAB code, and the results were imported to FLUENT code as initial conditions. Then the spray process within a few milliseconds was studied. No centerline droplet stream was found, but a vortex cloud at the tip of the main spray was observed. The above computed results bring out the contradiction in predicting the droplet velocity distribution of the spray structure, especially the velocity at the centerline of the spray cone, which has been the main focus of our research. Both the experimental measurements and simulation results reported by different researchers showed evidence of a contradiction in the existence of high-speed streams along the centerline of the spray cone, which should be investigated because they have influence on the heat- and mass-transfer process in a spray chamber. To determine the formation of this two-phase high-speed stream, both experiments and computational simulations were employed in this work. PIV measurement was used to investigate the spray structures of four pressure-swirl nozzles with water as feeding liquid. To simulate the spray, a 2-D axisymmetric model was built through CFD codes Fluent version 14.0, in which the high-speed stream at the spray centerline was well predicted compared with the PIV results. The formation of a two-phase high-speed stream at the centerline of the spray cone was verified and interpreted through the PIV and CFD results.
Figure 1. Test rig: (a) tank, (b) ball valve, (c) filter, (d) piston pump, (e) pressure sensor, (f) gasbag accumulator, (g) pressure regulator, (h) atomizer, (i) collecting vessel, (j) collection cone, and (k) exhaust fan.
Four types of pressure-swirl nozzles produced by Spraying Systems Co. were tested under different pressures to confirm the general existence of the high-speed droplet stream at the centerline of the spray cone. The performance data of nozzles with different orifice diameter are listed in Table 1. The PIV system from TSI Inc. was used for investigating the velocity distribution in the vertical section across the spray core. The tangential velocity was ignored because it was 1 order of magnitude lower than the axial velocity component for a pressure-swirl spray.10 A vertical laser light sheet of approximately 1 mm thickness was produced by a double-pulse Nd:YAG laser (Continuum; 50 mJ per pulse; max. repetition rate, 15 Hz) conditioned through a cylindrical lens. The light sheet illuminated an axial cross section of the spray. A chargecoupled device camera was oriented perpendicular to the light sheet, and the processed data yielded a two-component velocity field. Timing of the PIV system was controlled by a TSI LaserPulse synchronizer connected with an acquisition computer. The PIV images were acquired and processed by TSI Insight 4G software package. For each experimental run, 500 paired images were captured and subsequently interrogated using a recursive cross-correlation algorithm. The pass spot sizes were 64 × 64 px. The time delay of laser pulses was about 60 μs depending on the droplets’ velocity. Spray droplets were used as the tracer particles for the calculation of the velocity vectors.
3. MULTIPHASE FLOW MODELING 3.1. Mesh Schemes. The flow field of water spray droplets interacting with ambient air was simulated. The ambient air was considered as a large cylinder with the radius of 2 m and the height of 3 m, as shown in Figure 2. Based on the spatial symmetry, the computational region was set in a 2-D axisymmetric model, which was considered as a low-resourceconsumption numerical calculation with reasonable accuracy.20,22 The atomizer was treated as a group injection at the axis of the 2-D axisymmetric model, 2 m in height. The software package ICEM 14.0 was used to generate rectangular grids in the computational region, in which smallest grids were located around the injection point, as shown in Figure 2. To make the simulating result independent with the mesh size, the computed region was designed with the smallest mesh sizes of 2.5, 5, 10, 20, 40, and 80 mm. 3.2. Two-Phase CFD Model. The two-phase CFD model was based on the assumption that the noninteracting spherical particles (or water droplets) were dispersed and the turbulent air flow was incompressible. Droplet evaporation was ignored because the spray was implemented at room temperature. In
2. EXPERIMENTAL SETUP Experiments were performed using the spray test rig shown in Figure 1 under room temperature of 23 °C. This facility enabled the production of steady sprays under liquid pressures up to 5 MPa. Water was used as feeding liquid which was driven from the tank to the nozzle through a pumping line with the temperature of 15 °C. A filter was installed ahead of the pump to avoid undesirable solid particles, and a gasbag accumulator was used to obtain a steady flow. A pressure atomizer was installed in the vertical direction. The spray droplets were collected in a vessel with mist extraction to avoid the influence of back-flow droplets. B
DOI: 10.1021/acs.iecr.6b03140 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Industrial & Engineering Chemistry Research Table 1. Parameters of the Four Types of Pressure-Swirl Nozzles capacity (L/h)a
a
nozzle no.
orifice dia. (mm)
0.2
0.3
0.4
1/4LN-ss0.6 1/4LN-ss3 1/4LN-ss6
0.41 0.71 1.10
− 9.7 19.3
− 11.8 24.0
− 13.7 27.0
0.7
spray angle (deg)
1.5
2.0
3.5
4.5
0.3
0.6
2.0
− − 18.1 26.0 36.0 53.0 capacity (L/h)a
27.6 31.0 61.0
33.6 40.0 81.0
36.0 46.0 92.0
− 35 65 65 70 73 73 79 81 spray angle (deg)
nozzle no.
orifice dia. (mm)
0.07
0.10
0.15
0.20
0.30
0.40
0.60
0.70
0.07
0.15
0.60
1/4A-ss1
1.60
22.8
27.6
33.6
38.4
47.4
54.6
66.0
72.0
−
53
67
At the stated pressure in MPa.
1 ∂ 1 ∂ ∂ (ρvr ) + (rρvxvr ) + (rρvrvr ) ∂t r ∂x r ∂r ∂v ⎞⎤ ∂p 1 ∂ ⎡ ⎛ ∂vr + + x ⎟⎥ =− ⎢rμ⎜ r ∂x ⎣ ⎝ ∂x ∂r ∂r ⎠⎦ ⎞⎤ v 1 ∂ ⎡ ⎛ ∂vr 2 2μ (∇·v ⃗) + − (∇·v ⃗)⎟⎥ − 2μ r2 + ⎢rμ⎜2 ⎠⎦ 3 3r r ∂r ⎣ ⎝ ∂r r +ρ
addition, droplet collision was not introduced in the model because the relative velocities between droplets are negligible when injecting into quiescent air.19 The influence of droplet evaporation, collision, and breakup on the droplet velocity and induced air are presented in the Supporting Information. All these submodels were ignored because they have little influence on the formation of the two-phase high-speed stream; therefore, the research was focused on the basic interactions of dispersed droplets and the ambient air. The numerical solution of the model equations and computational simulations has been performed by transient 2-D axisymmetric pressure-based solvers incorporated in CFD package Fluent 14.0. The two-way coupled Euler−Lagrange method was used for the treatment of continuous and discrete phases, where the transport of fluid is described by a continuity equation as
du p dt
= FD(u⃗ − u⃗ p) +
g ⃗(ρp − ρ) ρp
+ F⃗ (4)
where FD(u⃗ − u⃗p) is the drag force per unit particle mass, F⃗ is an additional acceleration (force/unit particle mass) term, and FD =
18μ C DRe ρp d p2 24
(5)
Here, u⃗ is the fluid-phase velocity; u⃗p the particle velocity; ρ the fluid density; ρp the density of the particle; μ the molecular viscosity of the fluid; dp the particle diameter; CD the drag coefficient; and Re the relative Reynolds number, which is defined as Re ≡
ρd p|u⃗ p − u⃗ | μ
(6)
A spherical droplet was assumed to define the drag coefficient, for the Weber numbers were less than unity in the simulations, in which a unity Weber number corresponds to droplet diameter of 390 μm. The drag coefficient is defined as a a C D = a1 + 2 + 32 (7) Re Re
(1)
and axial and radial momentum conservation equations as 1 ∂ 1 ∂ ∂ (ρvx) + (rρvxvx) + (rρvrvx) r ∂x r ∂r ∂t ⎞⎤ ∂p 1 ∂ ⎡ ⎛ ∂vx 2 =− + − (∇·v ⃗)⎟⎥ ⎢rμ⎜2 ⎠⎦ 3 r ∂x ⎣ ⎝ ∂x ∂x ∂v ⎞⎤ 1 ∂ ⎡ ⎛ ∂vx + + r ⎟⎥ + Fx ⎢rμ⎜ ⎝ r ∂r ⎣ ∂r ∂x ⎠⎦
(3)
where ρ is the fluid density, x the axial coordinate, r the radial coordinate, vx the axial velocity, vr the radial velocity, vz the swirl velocity, v⃗ the fluid velocity, and p the pressure. The force balance on a discrete phase particle is written in a Lagrangian reference frame as (for the x direction in Cartesian coordinates)
Figure 2. Physical model and mesh scheme in 2-D axisymmetric simulation.
ρv ∂ρ ∂ ∂ + (ρvx) + (ρvr ) + r = 0 ∂t ∂x ∂r r
vz2 + Fr r
where a1, a2, and a3 are constants taken from Morsi and Alexander.28 Two additional forces (F⃗ ) incorporated in eq 4 were introduced. The “virtual mass” force required to accelerate the fluid surrounding the particle can be written as F= (2) C
1 ρ d (u⃗ − u⃗ p) 2 ρp dt
(8) DOI: 10.1021/acs.iecr.6b03140 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Industrial & Engineering Chemistry Research Table 2. Diameter and Mass Flux of Droplets Injected by the Nozzle droplet no.
0
1
2
3
4
5
6
7
8
9
diameter (×10−6m) mass flux (×10−4kg/s) droplet no.
11 1.07 10
14 1.42 11
18 1.76 12
22 2.08 13
25 2.37 14
29 2.64 15
32 2.88 16
36 3.09 17
39 3.26 18
43 3.40 19
diameter (×10−6m) mass flux (×10−4kg/s) droplet no.
47 3.50 20
50 3.57 21
54 3.60 22
57 3.60 23
61 3.56 24
64 3.50 25
68 3.42 26
72 3.31 27
75 3.18 28
79 3.03 29
diameter (×10−6m) mass flux (×10−4kg/s) droplet no.
82 2.87 30
86 2.70 31
89 2.53 32
93 2.35 33
97 2.17 34
100 1.99 35
104 1.82 36
107 1.65 37
111 1.49 38
114 1.33 39
diameter (×10−6m) mass flux (×10−4kg/s)
118 1.19
122 1.05
125 0.93
129 0.81
132 0.71
136 0.61
139 0.53
143 0.45
147 0.39
150 0.33
Another additional force caused by the pressure gradient in the fluid is written as ⎛ ⎞ ρ F = ⎜⎜ ⎟⎟u p∇u ⎝ ρp ⎠
The characteristic lifetime of the eddy is defined as
τe = −TL ln(r )
where r is a uniform random number between 0 and 1 and TL is the fluid Lagrangian integral time, which is obtained as
(9)
The standard k−ε model is utilized to describe turbulent flow, in which the turbulence kinetic energy, k, and its rate of dissipation, ε, are obtained from the following transport equations ∂ (ρk) + ∇·(ρk u⃗ ) ∂t ⎡⎛ μ⎞ ⎤ = ∇·⎢⎜μ + t ⎟∇k ⎥ + G k + G b − ρε ⎢⎣⎝ σk ⎠ ⎥⎦
TL ≈ 0.30
(10)
∂ (ρε) + ∇·(ρε u⃗ ) ∂t ⎡⎛ μ⎞ ⎤ ε ε2 = ∇·⎢⎜μ + t ⎟∇ε⎥ + C1ε (G k + C3εG b) − C2ερ ⎢⎣⎝ k k σε ⎠ ⎥⎦ (11)
In these equations, Gk is the generation of turbulence kinetic energy due to the mean velocity gradients; Gb represents the generation of turbulence kinetic energy due to buoyancy; σk and σε are the turbulent Prandtl numbers for k and ε, respectively; C1ε, C2ε, and C3ε are constants. Stochastic tracking was used to predict the dispersion of particles due to turbulence. The instantaneous value of the fluctuating gas flow velocity, u′, is added to the mean fluid-phase velocity, u,̅ as (12) u = u ̅ + u′
(13)
where ζ is a normally distributed random number. Because the kinetic energy of turbulence is known at each point in the flow, these values of the root-mean-square fluctuating components can be defined as v′2 =
w′2 =
2k /3
(16)
4. RESULTS AND DISCUSSION 4.1. Visualization of Flow. The axial sections of the sprays generated by different nozzles under different pressures were captured with PIV laser sheet to obtain a general characteristic of the spray structure. The spray morphologies in Figure 3 show good atomization generated by different types of nozzles. Processed PIV captures provided the droplet velocity distribution in the axial section of the sprays, which was visualized in Tecplot software and plotted in Figure 4a−f. Two kinds of highspeed characteristic velocities can be distinguished at the periphery and centerline of the spray cone. The high-speed stream at the centerline of the spray cone was more apparent with a smaller nozzle orifice (consequently smaller droplets) under the same liquid pressure, as shown in Figure 4a,c,e. On the other hand, the high-speed stream at the spray periphery became obvious with the increase of liquid pressure and droplet velocity (Figure 4b−d). Nozzle 1/4A-ss1 was designed to produce spray under relatively low pressures, in which the droplets were larger than those produced by the other three 1/4LN types. Therefore, in Figure 3f, the liquid pressure was set to 0.8 MPa and the highspeed stream at spray periphery was primarily on account of the inertia of large droplets.
The discrete random walk (DRW) model was used to simulate the interaction of a particle with a succession of discrete stylized fluid-phase turbulent eddies. Each eddy is characterized by a Gaussian distributed random velocity fluctuation, u′, v′, w′, and a time scale, τe, so that
u′2 =
k ε
Pressure-outlet type was used as the boundary condition, while axis boundary was used along the axis. A droplet was reported as “escaped” when it encountered the pressure-outlet boundary. Droplet diameter parameters were taken from Spraying Systems Co. The droplet diameters and mass fluxes used are presented in Table 2. The total flow rate of the spray was 31 L/h, and a Rosin− Rammler distribution was used to describe the droplet distribution, in which 11 μm for the minimum diameter, 150 μm for the maximum diameter, 77 μm for the average diameter, and 2.05 for the spread parameter were fitted. A group injection of 40 particle streams was employed with measured spray angle of 76° and droplet velocity of 17.35 m/s from PIV results. Spray droplets were regarded as inert particles, because the main focus of the simulation was the flow field of two-phase velocities and no evaporation was considered.
and
u′ = ζ u′2
(15)
(14) D
DOI: 10.1021/acs.iecr.6b03140 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Industrial & Engineering Chemistry Research
droplet velocity. To quantify this characterized high-speed stream, the velocity distribution in Figure 4c was inspected in detail. The axial velocity along a series of horizontal lines (distance from 60 to 210 mm downward from the nozzle orifice, the same as shown in Figure 7) in Figure 4c were extracted into Figure 5, with the radial position as abscissa and the axial velocity
Figure 5. Axial velocity distribution of droplets along horizontal lines in the axial section of spray field (from axis to periphery on the right, based on nozzle 1/4LN-ss3 with operating pressure under 2 MPa). Figure 3. Spray morphology of four pressure swirl nozzles captured by PIV camera.
as vertical coordinate. Only half of the whole spray field was considered according to the symmetry of the spray cone, in which the spray axis was located on the radial position of 0 mm. As shown in Figure 5, droplet velocity at the periphery decelerated quickly in ambient air, while the droplets along the spray centerline remained at high speed for a relatively long distance. The central high-speed stream was unexpected in conventional sense, for the central part of the spray contained smaller droplets which were supposed to be less affected by gravity and more inclined to decelerate because of drag forces.10 To reveal the mechanism of the central high-speed stream, CFD simulations were performed to investigate the interactions between spray droplets and the ambient air. 4.2. Verification of Simulation Results. To make the simulating result independent with the mesh size, the computing region was meshed with the smallest sizes of 2.5, 5, 10, 20, 40, and 80 mm. The corresponding nodes in each case were 12312, 7735, 4641, 2368, 1118, and 459. Figure 6 presents the effect of the number of nodes on the max axial air velocity caused by spray droplets. Compared with the mesh of 12312 nodes, the difference in velocity with the mesh of 7735 nodes is no more than 2%. Hence, the mesh with 7735 nodes was selected to
Figure 4. Distribution of the spray droplet velocity of the four pressureswirl nozzles measured by PIV.
Based on the discussion above, the high-speed stream in the spray centerline was affected by droplet diameters and initial
Figure 6. Effect of number of nodes on the max axial air velocity as simulated by CFD. E
DOI: 10.1021/acs.iecr.6b03140 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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high-speed droplet stream at the spray centerline. Hence, the 2-D axisymmetric model was used to further investigate the twophase interactions. 4.3. Air Flow Field and Droplet Behavior. The air flow field induced by spray droplets is presented in Figure 9 with
obtain reasonable simulation results with appropriate computational cost. The spray evolution and droplet velocities predicted by the 2D axisymmetric simulation is plotted in Figure 7, in which six
Figure 9. Pathlines and contour lines of the continuous phase flow field (colored by air velocity). Figure 7. Computed droplet velocity distribution (colored by droplet velocity magnitude).
symmetrical plane to obtain a whole image. The injection point was located at radial position of 0 m and axial position of 1 m. Flow pathlines of the air are shown in Figure 9a, where air is attracted to the injection point and then flows downstream along the axis of the spray cone. Finally, the air flow expanded again as the velocity was getting lower. The induced air flow produced two vortexes on both sides of the axis and a high-speed air stream along the centerline of the spray cone. The high-speed air stream at the spray centerline in a smaller range is magnified in Figure 9b, where the major characteristic of the air sream could be described as a sharp velocity drop in the radial direction and a speed that remains for a long distance at the axial direction. This narrow high-speed air stream induced by spray droplets was believed to transport small droplets with high speed at the spray centerline. To reveal the transport mechanism of spray droplets under the influence of the high-speed air stream, the movement and velocity of a single droplet of 11 μm was investigated with the local air flow. The smallest droplet size in the spray range was chosen for its smallest Stokes number, which means better tracing accuracy to the flow field. In Figure 10, the injection point was set to 0 mm on both the axial and radial positions, from where the droplet trajectory plotted as a gray line was started. The limited radial fluctuation of the droplet as shown in the gray line was caused by the difference between radial velocities of the droplet and the local air, plotted in red and green lines,
horizontal lines are presented to identify the location where the droplet velocities were extracted for verification. The axial droplet velocities predicted by the CFD calculation were compared with the PIV results on the six levels in Figure 8, in which satisfied verification results were found, especially for the
Figure 8. Verification of simulated axial droplet velocities with PIV data on the six levels with a distance of (a) 60 mm, (b) 90 mm, (c) 120 mm, (d) 150 mm, (e) 180 mm, and (f) 210 mm from the spray orifice.
Figure 10. Velocity distribution of induced air and droplet 11 μm in diameter. F
DOI: 10.1021/acs.iecr.6b03140 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Industrial & Engineering Chemistry Research respectively. In the meanwhile, the droplet was accelerated by the axial local air velocity plotted as a blue line. Therefore, in the axial direction, the droplet was decelerated at first because of the drag force and then accelerated by the axial air stream; the corresponding axial droplet velocity is shown as a black line in Figure 10. To illustrate different droplet fates on account of the droplet diameters, a series of droplets of different diameters in the whole range of the diameter distribution in the investigated spray is shown in Figure 11. The limited radial fluctuation of droplet
Figure 12. Maximum axial air velocity produced by sprays with single droplet diameters.
This result was unexpected but reasonable because of two factors, the droplet mass (mp) and interaction time (t), which can be written in the axial direction as
ma va = −mpΔvp + FDt
(17)
in which ma is the mass of induced air, va the local air velocity, and vp the droplet velocity. Larger droplets can transport more momentum to the ambient air, but this process takes time. Although the droplets shown in green and blue color sets in Figure 11 were heavier, they exited the narrow region at the spray centerline rapidly, so the interaction time, t, in eq 17 was short; as a consequence, the momentum transported to the ambient air was limited. In our opinion, the high-speed air stream at the spray centerline was caused by the axisymmetric momentum exchange between the continuous and discrete phases. This insight into the formation mechanism is believed to have instructive principles in considering the level of the two-phase high-speed stream at the spray centerline for a hollow-cone spray in certain operating conditions. The influence of droplet size distribution, spray angle, and injection velocity on the axial stream will be investigated in further research. In general, a transient 2-D axisymmetric CFD model with stochastic tracking of droplets was built with reasonable accuracy to describe the two-phase flow in a hollow-cone spray produced by a pressure-swirl nozzle. For nozzle 1/4LN-ss3 with operating pressure under 2 MPa, the three-dimensional model about the axial velocity of droplet and local air in the inspected region in PIV measurement is shown in Figure 13d. The distribution of droplets differing in diameter can be located separately, as shown in Figure 13a−c, in which the small, medium, and large droplets are presented as examples. The axial velocity of most droplets in Figure 13 was a little higher than that of the local air, which indicated the balance between drag force and gravity on droplets. To draw more information on the two-phase flow field in the spray region, the Stokes numbers of dispersed phase and Froude numbers of the continuous phase are plotted in panels a and b of Figure 14, respectively. The spray droplets were generated from nozzle 1/4LN-ss3 under the operating pressure of 2 MPa, with a diameter distribution ranging from 11 to 150 μm. As shown in Figure 14a, droplets of large Stokes numbers detached from the air flow field and remained along the initial direction at the spray periphery, while as the Stokes number decreased, droplets gradually distributed toward the spray centerline. Because droplets of small Stokes numbers follow fluid streamlines closely, the distribution of Stokes numbers inside the spray
Figure 11. Behaviors of three types of particles divided by particle diameter, expressed by (a) radial velocity, (b) axial velocity, and (c) axial velocity change in a longer time scale.
velocities (Figure 11a) becomes slower and weaker with the increase in diameter, which was caused by the increase in inetia of larger droplets. In addition, the limited radial fluctuation disappeared when droplet diameter exceeded 32 μm, which indicates the escape of larger droplets from near the spray axis. The sharp drop of axial droplet velocity in the blue curves shown in Figure 11b corresponded to the transport of droplet momentum to the induced air in the axial direction. The acceleration effect of larger droplets in the green and red sets was relatively small because they exited the central area rapidly. On the basis of the axial droplet velocities shown in Figure 11c, the droplets can be distinguished into three types, which are small droplets (blue color set) following the high-speed air stream at the spray centerline, large droplets (red color set) decelerated and distributed at the spray periphery, and medium droplets (green color set) distributed between small and large droplets. As discussed above, the momentum transport from injected droplets to the ambient air along the axial direction varied with different droplet diameters. To find out the most intense interactions between droplets and ambient air at the spray axis, a series of simulations were carried out with the same boundary conditions but only one diameter for the injection droplets in each case. In other words, the sprays were treated with extreme narrow droplet size distribution of only one diameter in each case at the same spray angle, flow rate, and initial velocity. The max axial air velocities in the spray centerline induced by the ideal sprays are shown in Figure 12, in which the maximum velocity magnitude was induced by the spray with droplets of 32 μm. It is noteworthy that this diameter was also the largest size of the droplets which were shown in the blue color set in Figure 11. G
DOI: 10.1021/acs.iecr.6b03140 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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their inertia. The complicated axisymmetric momentum exchange between the continuous and discrete phases was considered as the cause of the two-phase high-speed stream at the spray centerline. Small droplets limited at the spray axis had relatively longer momentum transferring time in the axial direction, whereby the heaviest ones had the largest contribution. The droplet fates in the investigated hollow-cone spray were divided into three types, which are small droplets at the spray centerline, large droplets along the spray periphery, and medium droplets in between. The evidence of the two-phase high-speed stream was decided by the component proportion of the three types, which differed under conditions of different nozzle orifice and atomization pressure.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.6b03140. Sub model comparison on the axial velocities of air and droplets (PDF)
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Figure 13. Computed axial velocity distribution of droplets and the local air in half of the inspected region in PIV measurement.
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Guimin Lu: 0000-0001-9629-1372 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the National High Technology Research and Development Program of China (Grant 2013AA064007).
Figure 14. Dimensionless criteria distribution in the spray region.
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cone indicated that the velocity vectors of induced air flow were approximately parallel to the spray axis. At the same time, the induced air flow was most rapid along the spray axis, as shown in Figure 14b, and the air stream of high Froude number along the spray axis would transmit its flow inertia further downstream. In general, the air stream induced by spray operation redistributed the droplets and had significant influence on the heat- and masstransfer process in spray chambers. Appropriate spray model with accurate prediction of the two-phase stream was essential in simulations of chemical unit equipment with spray operation.
NOMENCLATURE dp = particle diameter, m CD = drag coefficient k = turbulence kinetic energy, m2/s2 Gk = turbulence kinetic energy due to the mean velocity gradients, m2/s2 Gb = turbulence kinetic energy due to buoyancy, m2/s2 C1ε, C2ε, and C3ε = constants TL = fluid Lagrangian integral time, s
Greek Symbols
5. CONCLUSIONS Characteristics of sprays generated by four pressure-swirl nozzles were investigated using particle image velocimetry. Except for the main high-speed droplet stream along the periphery of the spray cone, a high-speed droplet stream at the spray centerline was also observed. The high-speed droplet stream was more evident with smaller nozzle orifice and higher atomization pressure. CFD simulations were performed to predict these two characteristic droplet streams. Satisfactory verification with PIV results was made by transient 2-D axisymmetric simulations. The flow field induced by the spray model in ambient air was characterized as a narrow stream in high speed at the spray centerline and a vortex outside the spray periphery. On the other hand, limited by the local radial air velocity, small droplets experienced a limited radial fluctuation at the spray axis, while large droplets kept moving along the spray periphery because of
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ρp = density of the particle, kg/m3 μ = molecular viscosity, Pa·s ε = turbulence energy dissipation rate, m2/s3 σk, σε = turbulent Prandtl numbers for k and ε, respectively
REFERENCES
(1) Sommerfeld, M. Analysis of isothermal and evaporating turbulent sprays by phase-Doppler anemometry and numerical calculations. Int. J. Heat Fluid Flow 1998, 19, 173−186. (2) Xie, J. L.; Gan, Z. W.; Duan, F.; Wong, T. N.; Yu, S. C. M.; Zhao, R. Characterization of spray atomization and heat transfer of pressure swirl nozzles. Int. J. Therm. Sci. 2013, 68, 94−102. (3) Xie, J. L.; Gan, Z. W.; Wong, T. N.; Duan, F.; Yu, S. C. M.; Wu, Y. H. Thermal effects on a pressure swirl nozzle in spray cooling. Int. J. Heat Mass Transfer 2014, 73, 130−140. (4) Herpfer, D. C.; Jeng, S.-M. Planar measurements of droplet velocities and sizes within a simplex atomizer. AIAA J. 1997, 35, 127− 132.
H
DOI: 10.1021/acs.iecr.6b03140 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
Article
Industrial & Engineering Chemistry Research (5) Madsen, J. Computational and experimental study of sprays from the breakup of water sheets. Ph.D. Thesis, Aalborg University, Aalborg, Denmark, October 2006. (6) Santolaya, J.; Aisa, L.; Calvo, E.; García, I.; Cerecedo, L. Experimental study of near-field flow structure in hollow cone pressure swirl sprays. J. Propul. Power 2007, 23, 382−389. (7) Yang, J.; Chen, A.; Yang, S.; Huang, K. Flow analysis of spray patterns of pressure-swirl micro atomizers. Proceedings of PSFVIP-4, Chamonix, France, June 3−5, 2003. (8) Choi, D. S.; Choi, G. M.; Kim, D. J. Spray structures and vaporizing characteristics of a GDI fuel spray. J. Korean Soc. Miner. Energy Resour. Eng. 2002, 16, 999−1008. (9) Santolaya, J. L.; Aisa, L. A.; Calvo, E.; Garcia, I.; Garcia, J. A. Analysis by droplet size classes of the liquid flow structure in a pressure swirl hollow cone spray. Chem. Eng. Process. 2010, 49, 125−131. (10) Durdina, L.; Jedelsky, J.; Jicha, M. Investigation and comparison of spray characteristics of pressure-swirl atomizers for a small-sized aircraft turbine engine. Int. J. Heat Mass Transfer 2014, 78, 892−900. (11) Siamas, G. A.; Jiang, X.; Wrobel, L. C. A numerical study of an annular liquid jet in a compressible gas medium. Int. J. Multiphase Flow 2008, 34, 393−407. (12) Siamas, G. A.; Jiang, X.; Wrobel, L. C. Dynamics of annular gas− liquid two-phase swirling jets. Int. J. Multiphase Flow 2009, 35, 450−467. (13) Del Taglia, C.; Blum, L.; Gass, J. r.; Ventikos, Y.; Poulikakos, D. Numerical and experimental investigation of an annular jet flow with large blockage. J. Fluids Eng. 2004, 126, 375−384. (14) Belhadef, A.; Vallet, A.; Amielh, M.; Anselmet, F. Pressure-swirl atomization: Modeling and experimental approaches. Int. J. Multiphase Flow 2012, 39, 13−20. (15) Sheen, H.; Chen, W.; Jeng, S. Recirculation zones of unconfined and confined annular swirling jets. AIAA J. 1996, 34, 572−579. (16) Fletcher, D. F.; Guo, B.; Harvie, D. J. E.; Langrish, T. A. G.; Nijdam, J. J.; Williams, J. What is important in the simulation of spray dryer performance and how do current CFD models perform? Appl. Math. Model. 2006, 30, 1281−1292. (17) Huang, L. X.; Kumar, K.; Mujumdar, A. S. A parametric study of the gas flow patterns and drying performance of co-current spray dryer: Results of a computational fluid dynamics study. Drying Technol. 2003, 21, 957−978. (18) Mezhericher, M.; Levy, A.; Borde, I. Droplet-droplet interactions in spray drying by using 2D computational fluid dynamics. Drying Technol. 2008, 26, 265−282. (19) Mezhericher, M.; Levy, A.; Borde, I. Modeling of Droplet Drying in Spray Chambers Using 2D and 3D Computational Fluid Dynamics. Drying Technol. 2009, 27, 359−370. (20) Mezhericher, M.; Levy, A.; Borde, I. Three-dimensional modelling of pneumatic drying process. Powder Technol. 2010, 203, 371−383. (21) Mezhericher, M.; Levy, A.; Borde, I. Three-Dimensional SprayDrying Model Based on Comprehensive Formulation of Drying Kinetics. Drying Technol. 2012, 30, 1256−1273. (22) Mezhericher, M.; Levy, A.; Borde, I. Probabilistic hard-sphere model of binary particle-particle interactions in multiphase flow of spray dryers. Int. J. Multiphase Flow 2012, 43, 22−38. (23) Mezhericher, M.; Levy, A.; Borde, I. Multi-Scale Multiphase Modeling of Transport Phenomena in Spray-Drying Processes. Drying Technol. 2015, 33, 2−23. (24) Gao, J.; Jiang, D. M.; Huang, Z. H.; Wang, X. B. Experimental and numerical study of high-pressure-swirl injector sprays in a direct injection gasoline engine. Proc. Inst. Mech. Eng., Part A 2005, 219, 617− 629. (25) Zhao, Z. G.; Xie, M. Z. Numerical simulation about interaction between pressure swirl spray and hot porous medium. Energy Convers. Manage. 2008, 49, 1047−1055. (26) Shim, Y. S.; Choi, G. M.; Kim, D. J. Numerical modeling of hollow-cone fuel atomization, vaporization and wall impingement processes under high ambient temperatures. Int. J. Automot. Technol. 2008, 9, 267−275.
(27) Bafekr, S. H.; Shams, M.; Ebrahimi, R.; Shadaram, A. Numerical Simulation of Pressure-Swirl Spray Dispersion by Using EulerianLagrangian Method. J. Dispersion Sci. Technol. 2010, 32, 47−55. (28) Morsi, S. A.; Alexander, A. J. An investigation of particle trajectories in two-phase flow systems. J. Fluid Mech. 1972, 55, 193−208.
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DOI: 10.1021/acs.iecr.6b03140 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
