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Experimental and numerical investigations of mechanisms in fluidic spray control
International Journal of Multiphase Flow 61 (2014) 48–61
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International Journal of Multiphase Flow j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / i j m u l fl o w
Experimental and numerical investigations of mechanisms in fluidic spray control Kuo-Tung Tseng ⇑, Steven H. Collicott School of Aeronautics and Astronautics, Purdue University, West Lafayette, IN 47907, United States
a r t i c l e
i n f o
Article history: Received 21 September 2013 Received in revised form 8 January 2014 Accepted 10 January 2014 Available online 30 January 2014 Keywords: Spray control Cavitation Droplet measurement Flow structure Two-phase flow
a b s t r a c t A fluidic control method in an axisymmetric spray orifice is investigated experimentally and numerically. In this method, a nominally steady secondary flow is introduced through an annular slot placed near the vena contracta along the orifice wall to control the cavitation, and thus the spray, at pressures up to 550 kPa driving pressure difference. Images of cavitation, measurements of droplet sizes and discharge coefficients, and CFD modeling are combined to explore the flow physics leading to the production of small droplets. Experimental results suggest that the secondary flow is incapable of confining cavitation to the region upstream of the slot, and generally a larger secondary flow rate results in a lower discharge coefficient, and a larger fraction of small droplets. The homogeneous model-based CFD code of Chen and Heister was employed to model the internal flows, which indicated that a high pressure region upstream of the slot, large pressure fluctuations in the orifice, and long cavitation lengths are the favorable conditions for atomization. The CFD simulations, together with experimental measurements, correlate the orifice geometry and flow structures to droplet sizes. Understanding the relationship between flow structures and droplet sizes helps to design orifices in favor of production of small droplets. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction Spray control is important. For example, fuel sprays might be optimized for engine load or bio-fuel blends on a daily basis. Spray coating of contoured surfaces may have a spray that adapts to changes in contour, and hydro-entanglement of unwoven textiles may benefit from maximizing momentum flux with minimal droplet production. Recent research on the connection between smallscale internal flow cavitation and droplet sizes has demonstrated a promising approach for a new spray control method. Compared to a plain orifice (Fig. 1(a)), an orifice with a small step placed at a strategic location (Fig. 1(b)) (where the flow reattaches to the orifice wall for a plain orifice at a pressure below that for hydraulic flip) can substantially increase the pressure for hydraulic flip, and produce a large fraction of tiny droplets (Ong, 2000; Ong et al., 2003). The success of the small step motivated us to devise a circular orifice with an annular slot (through which a secondary flow is introduced to the orifice) placed at the strategic location (Figs. 1(c) and 2(a)), namely orifice 1, which is not the target in this paper. ⇑ Corresponding author. Tel.: +886 2 33665062; fax: +886 2 33665690. E-mail addresses: [email protected] (K.-T. Tseng), collicott@ purdue.edu (S.H. Collicott). http://dx.doi.org/10.1016/j.ijmultiphaseflow.2014.01.003 0301-9322/Ó 2014 Elsevier Ltd. All rights reserved.
Orific 1 is found to work exactly like a step orifice does (Tseng and Collicott, 2011) at certain secondary flow rate, wherein the advantages of a fluidic spray control orifice are demonstrated— the secondary flow is proved to be able to influence the cavitation distribution, spray and droplet size, and the strength of this control effect can be modulated. Since the location of the slot is merely based on the successful small steps (Ong, 2000; Ong et al., 2003) which were guesses at what would work well, the question—how the slot location will influence the cavitation distribution—has inspired us to devise another orifice, namely orifice 2, as shown in Fig. 2(b), where an annular slot is placed near the vena contracta. Unless specified, the results in this paper are all from orifice 2. Historical research has demonstrated that orifice geometry may greatly affect droplet distribution in several ways. Hiroyasu et al. (1991) and Hiroyasu (2000) showed that cavitation and turbulence significantly influence atomization, which can be manipulated by installing a wire mesh over the inlet of the orifice and a gap at the middle of the orifice hole (Hiroyasu, 2000). The wire mesh transforms the jet from non-cavitating hydraulic-flipped flow to cavitating flow; a larger ratio of gap length to orifice length is capable of atomizing the jet more rapidly, and enabling a larger spray angle, where a higher degree of atomization has proven to be ascribed to a strong disturbance arising from cavitation in the nozzle (Tamaki et al., 1998, 2001; Hiroyasu, 2000). In Hiroyasu’s
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Fig. 1. Diagram of the (a) plain orifice, (b) step orifice, and (c) orifice 1.
Fig. 2. Plane section views of the main housings and the inner plugs of orifice 1 and orifice 2, which form the annular plenum and the conical void terminating in the annular slot. The region circled in (c) corresponds to (b).
experiment, the orifice diameter is 0.3 mm, the gap length is 0.3 mm, and the ratios of gap to orifice length are between 5 and 41. The spray has also been observed to be affected by different inlet geometries (Laoonual et al., 2001). Plain, counterbore,
rounded, and beveled inlets of different angles result in different spray distributions, among which the beveled nozzle with a bevel angle of 60 , and the rounded nozzle having an inlet radius of curvature approximately the same as the orifice radius are shown to be capable of greatly increasing the pressure for hydraulic flip. This effect is an analogy to that of a small step placed at a strategic axial location (Ong, 2000). In their study, the nozzle diameter is 6 mm, the length-to-diameter ratio is either 5 or 10, and the pressures are up to 2 MPa. In addition to straight orifices, orifices inclined at different angles (including 0 ; 14 ; 80 ; 85 , and 90 ) to the axis of the injector have also been investigated by some researchers (Ganippa et al., 2001; Li, 1999), wherein an asymmetric nozzle is found to be responsible for asymmetric cavitation distributions, and thus different degrees of atomization. The side with a higher degree of atomization has thicker cavitation on the same side upstream. To simulate the actual geometry of a diesel engine injector, Li et al. (1998) and Li (1999) employ orifices angled at 14 with respect to the surface normal, and having diameters in the range of 0.206–0.397 mm. In their experiment, UCF-1 calibrating fluid was used as the working liquid, and the pressure was as high as 200 MPa. Some features of the asymmetric unsteady cavitation extending downstream from the inlet are also observed later by Ganippa et al. (2001). Recent work at Purdue further demonstrated that either a small step (Ong, 2000; Ong et al., 2003) or a slot placed at a strategic axial location (Tseng and Collicott, 2011) changes the inlet cavitation, discharge coefficient, and droplet size distribution, and substantially increases the pressure for hydraulic flip. That one small change in the orifice can create such a wealth of changes in the flow indicates that a control mechanism likely exists to exploit further. Extending the investigation to explore the influence of the orifice geometry for a fluidic spray control orifice as well as the flow physics will assist in affording us in-depth knowledge of how cavitation may be more effectively manipulated.
2. Purpose Although cavitation has long been known to affect fluid spray, the links between droplets and flow structures are poorly
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understood. For example, there is no effective method to measure the pressure field, velocity field, void fraction, etc., of the flow inside of a small orifice without disturbing the flow field, and thus little of the internal flow details have been explored. Despite pressure measurements that have been made previously inside a larger orifice, the data do not really reflect the actual conditions in a small orifice since the nucleation and the periodic behavior of the cavitating flow have long been known to be influenced by absolute size (Bergwerk, 1959). To overcome the said problem, we adopt a numerical approach in this paper. In addition to yielding non-intrusive insight into quantities such as pressure, and giving a wealth of information to improve understanding of the flow structures inside the orifice, which are crucial for enabling a better control of sprays, Computational Fluid Dynamics (CFD) is also used to predict the influence of the slot location on flow properties at a lower cost, and assisted us in developing the geometry of another orifice, called orifice 2. The numerical solutions are then compared to data from experimental observations and measurements to identify conditions that are favorable in atomizing flows.
3. Experimental and CFD approach 3.1. Experiment The flow rig for this experiment consists of an air compressor supplying air up to 1 MPa, a reservoir, an optically accessible orifice formed by two pieces: the main housing and the inner plug, a Xenon flash lamp, a digital CCD, a camera lens, a pressure transducer, an in-line flow rate meter and a Sympatec laser diffraction
particle-sizer (Fig. 3). The water in the reservoir is split into the main and secondary flows prior to reaching the test section. Flow rates of the secondary and total flows are measured by an in-line flow meter and collection of the efflux, respectively. Based on the measurement results, the percentage of the secondary flow, that is, the ratio of secondary to total mass flow rates, and the discharge coefficients, defined as the ratio of the measured total mass flow _ to the product of water density (q), the orifice cross-secrate (m) tional area (A) and the Bernoulli velocity (V), are calculated (Eq. (1)). Measurements of the total flow rate were repeated thrice to increase accuracy.
_ qAVÞ C d ¼ m=ð
ð1Þ
Orifice 2, having Ls ¼ 0:41 mm with a ¼ 75 (Fig. 2(b)), and inlet bluntness approximately 5% of the orifice radius (the ratio of the inlet radius of curvature to the orifice radius is approximately 0.05), was machined from transparent acrylic. The nominal slot length (h) is 0.08 mm, and may be slightly widened at a large driving pressure difference. The droplets in the spray are measured with a Sympatec Helos laser diffraction particle-sizer, providing measurement accuracy to ±1% and operated by Windox software from Sympatec GmbH. When interacting with droplets, the light source of the particlesizer, a Helium–Neon-laser with 632.8 nm wavelength, is diffracted, or otherwise concentrated on central parts of the detector. Generally, the diffraction angle decreases as the droplet size increases. The graphical presentations of the results include mass density distributions defined as the mass fraction for a range of droplet sizes, to the width of that range, wherein the adequacy of sample sizes and class sizes is justified according to the ASTM E799-03 testing standard (Tseng, 2006). For the measurements in this study, the smallest class size is centered at 2.12 lm, but in the area very close to 0 lm, the measurement results may be influenced by particles in air, which are likely to cause noise signals. An EG&G xenon arc lamp (Model No. FTO-1130) flashing at 15 Hz with 2 ls duration, enabling the capture of fast-moving cavitation or droplets, and activated by a function generator is utilized as the light source to backlight the test section. The light radiated from the lamp, focused by an aspheric lens and diffused by a ground glass, finally gets to the orifice. A Nikon lens (Model No. AF 70-210 f/4-5.6) is used on the other side to image the cavitation in the orifice onto the Redlake 1024 by 1024 square-pixel 8-bit grayscale CCD camera (Model No. ES 1.0) equipped with a builtin electronic shutter. Exposure time for the shutter can be as short as 127 ls, which is longer than the duration of the arc. The high resolution CCD camera, triggered by operating the XCAP software developed by Redlake MASD, INC., is capable of capturing 30 images per second. When light passes through a region with two-phase flows, it is refracted or scattered by the liquid–vapor interface as a result of the different refractive indices of the vapor and the liquid. Light refracted outside of the imaging lens aperture is unable to reach the CCD detector. Therefore, the appearance of cavitation is always indicated by a dark region in the images. This technique differentiates two-phase from single-phase flows, but it cannot distinguish vapor from air. Hence, a dark region also emerges in response to a hydraulic flip.
3.2. CFD
Fig. 3. Schematic of the flow rig.
The numerical model used in this paper was developed by Chen and Heister (1996) and students. They treated the flow as an unsteady two-phase flow. In addition to momentum (Navier– Stokes) and continuity equations, an extra expression is constituted to deal with the pseudo-density, which varies from pure vapor, 0.001, to pure working liquid, 1. The additional expression
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only applies to the cavitation region, wherein the density change of fluid is assumed to be proportional to the product of the pressure difference between the local pressure (P) and vapor pressure (P v ), characteristic length, and characteristic velocity, which enables the pressure to recover at the end of the cavitation region without using a separate wake model (Chen and Heister, 1995). In this expression, the hydrodynamic non-equilibrium effects are taken into account. Later, Bunnell and Heister (2000) extended the code to three-dimensional flows. Physically, the secondary flow enters the orifice through the annular slot, wherein a velocity profile is of course created. However, numerically, a uniform velocity is specified across the slot length for simplification. Moreover, the simulation assumes that the orifice is symmetric with respect to the central axis, although a certain degree of asymmetry, which is likely to induce a strong 3-D effect at a large secondary flow rate, inevitably exists. The specified velocity direction is determined by the slot orientation, and the magnitude is based on the experimental measurements. 3.3. Dimensionless parameters The dimensionless pressure is given as:
P ¼
1 ðP P2 Þ 2 ðP1 P2 Þ
ð2Þ
where P1 , and P2 indicate the upstream pressure and downstream pressure, respectively. P1 and P 2 , the dimensionless upstream and downstream pressures, are 0.5 and 0, respectively, calculated from Eq. (2). Vapor pressure for water, P v , changes with temperature and pressure. At 550 kPa driving pressure difference with temperature between 21 C and 28 C; Pv is approximately 0.089. Time, t , is defined as:
t ¼ tV=D
ð3Þ
where D is the orifice diameter, t is time, and V is the Bernoulli velocity defined by:
V¼
sffiffiffiffiffiffiffiffiffi 2DP
q
ð4Þ
Here DP is the indicated driving pressure difference and q is the water density. Other parameters, v and q are the corresponding axial velocity and density normalized by the Bernoulli velocity and the liquid density, respectively; z and r denote the axial and radial coordinates normalized by the orifice diameter (z ¼ 0 and
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r ¼ 0 correspond to the orifice inlet plane and the centerline in the axial direction, respectively). Prior to simulation, a grid convergence study (Tseng, 2006) is conducted, wherein pseudo-density profiles, axial velocity profiles and wall pressures are scrutinized. 4. Results 4.1. Experiment Spray from an orifice is actually affected by both primary and secondary atomization. The former, determined by the interaction of the jet with the ambient air (Chryssakis and Assanis, 2005), causes the jet to break up into droplets, and the latter, influenced by droplet size, droplet velocity and the properties of the system such as pressure, temperature, viscosity and surface tension (Faeth et al., 1995), may transform the large droplets into smaller ones (Ranger, 1968; Ranger and Nicholls, 1969) through both shear (Chou et al., 1997; Chryssakis and Assanis, 2005) and catastrophic breakup (Chryssakis and Assanis, 2005) for flows with sufficiently large Weber numbers (100), as in this experiment. If the Weber numbers fall in the range of 13–20, the parent droplet may be deformed into a thin bag, and its breakup yields droplets with diameter approximately 4% of that of the parent droplet, depending on the conditions such as Reynolds numbers, Ohnesorge numbers, and liquid/gas density ratios (Chou and Faeth, 1998). Although the effect of secondary atomization, supposed to exert an important influence on the flows in this experiment, is not explored, the measurements and images recorded here still deliver meaningful information in that the link between internal flow structures and droplet sizes has been confirmed by several researchers (Hiroyasu et al., 1991; Tamaki et al., 1998, 2001; Hiroyasu, 2000). Seven secondary flow rates at 350 kPa and 550 kPa driving pressure differences, respectively, have been investigated (fourteen cases in all), but in this paper, only five cases at 550 kPa driving pressure difference are presented because a lower driving difference, generally enabling a lower degree of atomization (Chaves et al., 1995), is of less interest. Note that the back pressure for all cases is atmospheric. Fig. 4 displays the cavitation with no secondary flow. At 550 kPa driving pressure difference, two flow states—hydraulic flip (Fig. 4(a)) and cavitating flow (Fig. 4(b))—are present alternately. The cavitated state, likely to be triggered by a minor disturbance upstream, does not greatly atomize the flow, and only a very small fraction of tiny droplets, referring to those with diameters smaller
Fig. 4. Flow visualization and droplet size distributions (35 cm downstream) for orifice 2 with 0% secondary flow at: DP ¼ 550 kPa. For details in the shaded region in (c), please see Fig. 5.
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Fig. 5. Mass density distribution per lm for the shaded region in Fig. 4(c). Note that the vertical axis is on a nonlinear scale, the lower limit for which is taken as 5 106 .
than approximately 100 lm, are shaped, as exhibited in Fig. 4(c), wherein the left peak in the bimodal distribution, caused by the slot effect, is not important. The details in the shaded region in Fig. 4(c) are shown in Fig. 5. Note that a large dark region appears in the ‘‘no flow’’ photo, which results from refraction from the orifice wall, and thus, any new black regions in the flow photos show two-phase boundaries, or cavitation (Fig. 6). Obviously orifice 2 does not behave like a plain orifice when there is no secondary flow, pointing out that the slot effect cannot be ignored even without the secondary flow. That is, with no secondary flow, the slot acts as a constant geometrical perturbation to the internal flow, much like the step of Ong (2000). In the droplet size distributions, two measurements are made to give an indication of the repeatability, wherein at least 300,000 droplets are measured, respectively. With the secondary flow rate increased to 2%, cavitation is seen to appear irregularly upstream (Fig. 7(a)) or downstream (Fig. 7(b)) of the slot. Compared to the 0% case, the elimination of hydraulic flip does not discernibly increase the number of small droplets
(Fig. 7(c)), suggesting the effects of secondary flow and the slot are approximately equal in atomizing the flow. Although the local enlarged view (Fig. 8) reveals that the former causes a slightly larger fraction of tiny droplets than the latter (Fig. 5), the difference is so small, rendering the comparison results uncertain to some degree, which may be improved by more detailed measurements or orifice design. With the secondary flow turned on at 4%, cavitation extends well downstream, as shown in Fig. 9(a) and (b), representing the cases of upper and lower limits of cavitation lengths. This phenomenon was not observed in the small step orifice, suggesting that at the moment, the fluid efflux from the slot does not create a sufficiently large high-pressure region neighboring the slot, and thus seems to cause the inception of cavitation therein. Compared to prior cases, the more downstream distribution of cavitation appears to constitute a more favorable condition for atomizing the flow, as shown in Fig. 9(c). The mass density per lm for tiny droplets is still small but perceivable. Note that the value of the right peak (Fig. 9(c)) is also larger than those for the 0% and 2% cases (Figs. 4(c) and 7(c)), indicating the influence of the slot is reduced, thus causing a more flat central region. At the maximum two secondary flow rates in this experiment, 15% and 20%, cavitation persists at the exit plane (Figs. 10(a) and 11(a)), creating a strong 3-D flow structure that prevents air from penetrating upstream, and thus prevents hydraulic flip from occurring. In fact, cavitation continues to prevail at the orifice exit plane even at pressures up to 600 kPa. Compared to the 4% case, the minor change in cavitation distribution is thought to boost the turbulence level significantly, whereby velocity profiles are modified at the orifice exit (Tafreshi and Pourdeyhimi, 2004), and hence the mass density per lm for tiny droplets (Figs. 10(b) and 11(b)) is substantially increased, as is affirmed by Gopalan and Katz (2000). During the measurement period (10 s), the numbers of droplets created by the 20% secondary flow and sized in 50–60 lm, 90–100 lm, and 1450–1750 lm ranges are approximately 5,650,000, 1,700,000, and 9800, respectively, while the 0% secondary flow creates approximately 28,000 droplets sized in 1450– 1750 lm range, but only a small amount of tiny droplets.
Fig. 6. Schematic of causes of dark regions (in the orifice with no flow), and the orifice structure. The dark regions are from refraction from the orifice wall, and thus, any new black regions in the flow photos show two-phase boundaries, or cavitation.
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Fig. 7. Flow visualization and droplet size distributions (35 cm downstream) for orifice 2 with 2% secondary flow at: DP ¼ 550 kPa. For details in the shaded region in (c), please see Fig. 8.
Fig. 8. Mass density distribution per lm for the shaded region in Fig. 7(c). Note that the vertical axis is on a nonlinear scale, the lower limit for which is taken as 5 106 .
4.2. Discharge coefficient In the flow regime without a hydraulic flip at 0% secondary flow, occurring approximately between 480 kPa and 550 kPa driving
pressure difference, the C d values are found to be generally inversely proportional to the secondary flow rates (Fig. 12). Cavitation lengths, increasing with secondary flow rates, appear to be responsible for this unique trend. With cavitation spanning further downstream, more vorticity is deemed to be created, which is capable of increasing the level of turbulence (Ruiz and He, 1998, 1999), a phenomenon probably evidenced by the seemingly thicker cavitation acting like an obstruction by displacing the high-momentum flow. As the pressure is increased to 550 kPa, the most highly cavitated flow resulting from the maximum flow rate achieves the minimum discharge coefficient (0.68), a value even smaller than that achieved by 0% and 1% secondary flows that cause hydraulic flip and cavitating flow to alternate. This indicates that the 20% secondary flow highly obstructs the flow, and thus substantially reduces the effective flow area. Discharge coefficients for other cases, including 2%, 3% and 4% secondary flows, exceed those for the 0% case, but are not significantly different from those for the 1% case. Excluding the two lowest flow rate cases, the aforementioned C d values versus secondary flow rate relationship still applies. Note that the C d values increase as the pressure rises beyond 550 kPa, especially for the 15% and 20% cases, which might be due to the combined effect of the strong 3-D flow structure and cavitation distribution.
Fig. 9. Flow visualization and droplet size distributions (35 cm downstream) for orifice 2 with 4% secondary flow at: DP ¼ 550 kPa.
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Fig. 10. Flow visualization and droplet size distributions (35 cm downstream) for orifice 2 with 15% secondary flow at: DP ¼ 550 kPa.
Fig. 11. Flow visualization and droplet size distributions (35 cm downstream) for orifice 2 with 20% secondary flow at: DP ¼ 550 kPa.
Fig. 12. Measured discharge coefficient for orifice 2 versus driving pressure difference for seven secondary flow rates.
4.3. CFD Fig. 13 displays the CFD results for the baseline case (0% secondary flow). The cavitation histories imply that at 550 kPa driving pressure difference, the flow becomes hydraulic flipped, a state
that cannot be really predicted by CFD here. On average, the portion prior to t ¼ 70 in the cavitation histories, regarded as the transient state, is excluded in the subsequent discussions. Although the code is capable of predicting the behavior of many small-scale, unsteady, non-equilibrium cavitating flows, it does not capture the hydraulic flipped flow because the model assumes that only vapor and working liquid appear in the orifice. In other words, the calculation proceeds as if the orifice were submerged in the working liquid, instead of flowing into the atmosphere. Note that the contour legends in Fig. 13 also apply to the other figures in this paper. The numerical results for 2% secondary flow are exhibited in Fig. 14, where the pressure created is not sufficiently large in the region upstream of as well as around the slot, allowing the onset of cavitation at the orifice inlet. The dimensionless cavitation lengths (i.e., the streamwise extents of cavitation measured from the inlet) are estimated to oscillate approximately between 0.42 and 0.93 (Fig. 14). Although the computational domain extends downstream to the exit plane and well upstream of the orifice inlet, only the region in the vicinity of the slot that is of more interest is shown here for easy reference. On the other hand, experiments show that the ratio of cavitation length (Lc ) to orifice length (L) varies approximately between 0.25 and 0.6 (Fig. 7(a) and (b)). The differences may be attributed to the non-uniform slot that is likely to result in a 3-D effect.
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Fig. 13. Cavitation histories, pressure contours, streamlines and pseudo-density contours for orifice 2 with 0% secondary flow; the latter three figures correspond to t = 180, wherein the left-hand border is the orifice centerline, and the exit plane is at z ¼ 6:25.
Fig. 14. Cavitation histories, pressure contours, streamlines and pseudo-density contours for orifice 2 with 2% secondary flow; the latter three figures correspond to t = 180, wherein the left-hand border is the orifice centerline, and the exit plane is at z ¼ 6:25.
The predictions for the 4% case seem to be in more agreement with the experimental results compared with the 2% case. CFD predicts that Lc =L ranges approximately from 0.52 to 0.93 (Fig. 15), while experiments indicate an Lc =L range of approximately 0.7–1 (Fig. 9(a) and (b)). CFD appears to underestimate the pressure upstream of the slot, causing cavitation developed at the orifice inlet to propagate downstream to below the slot, whereas physically the onset of cavitation seems to occur in the vicinity of the slot. (Due to an inevitable certain degree of asymmetry of the orifice, there could be a very small amount of cavitation in the region upstream of the slot.) The predictions of pressure contours, streamlines and pseudo-density contours show little difference from those for the 2% case.
At large secondary flow rates, 15% and 20%, CFD shows no trace of cavitation (Figs. 16 and 17) throughout the region upstream of the slot, consistent with the cavitation images (Figs. 10 and 11). Obviously, the high pressure covers the said region, inhibiting the onset of cavitation. 4.4. Causes of small droplets In addition to cavitation, historical efforts have proved that droplet sizes are also influenced by liquid turbulence, the location where the turbulent primary breakup begins, the cross stream dimension of the free jet (Sallam et al., 1999), small-scale turbulent
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Fig. 15. Cavitation histories, pressure contours, streamlines and pseudo-density contours for orifice 2 with 4% secondary flow; the latter three figures correspond to t = 180, wherein the left-hand border is the orifice centerline, and the exit plane is at z ¼ 6:25.
Fig. 16. Cavitation histories, pressure contours, streamlines and pseudo-density contours for orifice 2 with 15% secondary flow; the latter three figures correspond to t = 180, wherein the left-hand border is the orifice centerline, and the exit plane is at z ¼ 6:25.
eddies in the vicinity of the jet exit, and Weber numbers (Sallam et al., 2002) based on which correlations for breakup lengths were developed (Sallam et al., 2002). These mechanisms are of course very important in the atomization process, which, however, are not discussed here in that this research mainly focuses on the internal flow physics. In our experiment, the degree of atomization was found to depend on driving pressure difference, streamwise extent of cavitation, and the mechanism determining how cavitation is distributed, which is conjectured to be the magnitude of pressure in the vicinity of the slot. A larger driving pressure difference and a longer cavitation length are obviously advantageous to liquid jet atomization. Also, the numerical approach further suggests additional mechanisms in favor of breaking liquid streams into tiny droplets. To this end,
a series of figures concerning pseudo-density variations over time, axial velocity variations over time, and wall pressure variations over time are explored, wherein the former two are investigated at several planes perpendicular to the orifice axis (Tseng, 2006). Pseudo-density distributions appear not to be the critical conditions, the variations of which over time at different planes are larger for the 2% case than for the 15% case that results in a much larger fraction of small droplets, as is, without loss of generosity, shown in Fig. 18. By the same token, the axial velocity is also ruled out as the important condition for atomization. The typical axial velocity distribution in the vicinity of the slot is exhibited in Fig. 19. The likely conditions favoring production of small droplets appear to be: high pressure in the vicinity of the slot, large high pressure variations over time, and long cavitation lengths
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Fig. 17. Cavitation histories, pressure contours, streamlines and pseudo-density contours for orifice 2 with 20% secondary flow; the latter three figures correspond to t = 180, wherein the left-hand border is the orifice centerline, and the exit plane is at z ¼ 6:25.
Fig. 18. Pseudo-density profiles for orifice 2 with 2%, 4%, 15% and 20% secondary flows at: z = 0.95.
(Fig. 20). The 20% secondary flow leads to the highest pressure near the slot, the largest high pressure variations over time, and the greatest extent of cavitation, and, therefore, achieves the highest degree of atomization. For the two largest secondary flow rate cases, a large magnitude pressure drop is found in the region neighboring the slot, which may result in more violent cavitation collapse therein, and consequently to produce cavitation effects which propagate to the exit plane.
Orifice 1 behaves differently. The degree of atomization reaches the peak at 4% secondary flow, wherein the cavitation persists in the region upstream of the slot (Tseng and Collicott, 2011). Although the two maximum secondary flow rates (15% and 20%) result in the highest pressure (Fig. 21), the absence of cavitation (throughout the entire orifice) as well as the nearly steady high pressure profiles (Fig. 21) seem to greatly weaken the atomization effect. In the 2% case, the pressure neighboring the slot is lower than that in the 4% case, which, together with the occurrence of
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Fig. 19. Axial velocity profiles for orifice 2 with 2%, 4%, 15% and 20% secondary flows at: z = 0.95.
Fig. 20. Wall pressure for orifice 2 with 2%, 4%, 15% and 20% secondary flows; vapor pressure is P v = 0.089.
hydraulic flip that alternates with the cavitating flow, reduces the atomization efficiency. Similar to orifice 2, pseudo-density variations (Fig. 22) and axial velocity variations (Fig. 23) are not the important conditions for atomization.
Note that, taking into account the numerical results for both orifice 1 and orifice 2, we also exclude the magnitudes of pseudo-density and axial velocity as the crucial conditions.
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Fig. 21. Wall pressure for orifice 1 with 2%, 4%, 15% and 20% secondary flows; vapor pressure is P v ¼ 0:089.
Fig. 22. Pseudo-density profiles for orifice 1 with 2%, 4%, 15% and 20% secondary flows at: z ¼ 2.
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Fig. 23. Axial velocity profiles for orifice 1 with 2%, 4%, 15% and 20% secondary flows at: z ¼ 2.
5. Discussion In addition to driving pressure difference, DP, cavitation length, and frequency in the periodic growth-collapse of cavitation, the droplet size distribution is also seen to be influenced by pressure in the neighborhood of the slot as well as pressure variations over time. Hydraulic flip excluded, the flows are atomized more at a large driving pressure difference than at a low driving pressure difference because a faster-moving stream interacts more violently with the surrounding air. An increased cavitation length presumably provides a greater cavitated region capable of shedding more sub-diameter length scale unsteadiness into the flow, and thus enhances atomization. However, as cavitation length increases, the characteristic frequency in the periodic growth-collapse of cavitation regions is lowered simultaneously. The lower frequency disturbances reduce the unsteadiness of cavitating flow, and hence weaken atomization. Another decisive condition, the high pressure region, created in the vicinity of the slot and varying drastically over time, is induced by a large secondary flow rate, causing cavitation to collapse more fiercely, a condition beneficial to giving rise to a higher level of turbulence and therefore a higher degree of atomization. For this steep slot orifice (orifice 2), the increasing secondary flow simultaneously exerts both favorable and unfavorable influences on atomization. On one hand, it increases the pressure that varies more drastically, causing longer cavitation lengths, and thus a higher degree of atomization in spite that, on the other hand, the unsteadiness triggered by the cavitation grow-collapse cycle is reduced. Apparently, the favorable influences appear to overwhelmingly dominate, accounting for the trend that a larger secondary flow rate creates a larger fraction of smaller droplets. For orifice 1, with the slot placed at a strategic location, a large high pressure region, created throughout the entire neighborhood
of the slot, is found to fully confine cavitation to the region upstream of the slot. As a result, a larger secondary flow rate moves cavitation further upstream, leading to shorter cavitation lengths that lead to higher frequencies in the periodic growth-collapse of cavitation, and at the same time, result in a higher pressure region around the slot, which, along with the degree of high pressure fluctuations, determine the overall atomization performance. The degree of atomization is maximized as the secondary flow rate increases to near 4% (for orifice 1), where the pressure around the slot is lower but the pressure variations over time are larger than at higher secondary flow rates, 15% and 20%. On the other hand, the cavitation length for the 4% and 2% cases is approximately the same (hydraulic flip in the 2% case is excluded), but the former causes higher pressure around the slot than the latter. Considering orifice 1, the combined effects of large high pressure variations over time and long cavitation lengths are regarded as the most influential conditions for promoting the level of atomization. 6. Conclusions A fluidic control method or device is shown to be capable of manipulating droplet sizes. By controlling the secondary flow rate, which at various flow rates can create significantly different distributions of pressure, velocity, streamlines, and density in the orifice, the droplet distribution in the spray is affected. Among all quantities, the internal unsteady pressure field, also critically influenced by the slot location, is verified by CFD simulations as the most critical influence in determining the degree of atomization. As opposed to the previous orifice (orifice 1), orifice 2 does not work like the step orifice works. Perhaps the slot, located in the vena contracta, is too far upstream to subdue the streamwise growth of cavitation. As the secondary flow rate increases, the stronger interaction between the main and secondary flows
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around the slot causes longer cavitation lengths that lead to a larger fraction of small droplets. When the rate of the secondary flow is low, it imposes little influence on the wall pressure as well as the droplet size distribution in spite that the cavitation lengths may change significantly. At large secondary flow rates, the pressure is apparently elevated beyond the threshold for cavitation to occur throughout the entire upstream region, causing cavitation to disappear therein. Production of small droplets is maximized near 20% secondary flow. Although not measured, cavitation appears to thicken as the cavitation length increases, and this effect is surmised to be responsible for producing even more sub-diameter length scale unsteadiness that is crucial in spray control. For orifice 2, cavitation can originate in the vicinity of where the primary and secondary flows meet. That is, cavitation can extend downstream from the neighborhood of the slot, instead of from the orifice inlet, a feature distinguishing orifice 2 from orifice 1. In contrast, the secondary flow in orifice 1 does not allow the onset of cavitation in the region around the slot. Generally, a larger secondary flow rate results in higher pressure spanning from the slot to more upstream regions, which is able to restrict the cavitation occurring at the orifice inlet from propagating downstream, thus leading to shorter cavitation lengths, wherein the important effects exerted by high pressure and cavitation length counteract each other. As a result, the degree of atomization is not necessarily enhanced as the secondary flow rate increases. Compared with orifice 2, the degree of high pressure fluctuation for orifice 1 is much lower. Fluidic spray control, along with the CFD simulations, assists in gaining in-depth insight into the relationship between internal flow physics and droplet sizes, understanding better of which helps to manipulate spray more effectively and economically. After all, improving spray distribution further by shrinking a small circular hole like a Diesel injector, or increasing driving pressure does not hold promise as they both already tax the limits of economic manufacturing. Conclusions in this work appear to show how pseudodensity modeling of the internal flows can be useful in evaluating or optimizing slot design and placement, and secondary flow rates, prior to building experimental nozzles for verification. Acknowledgment The authors would like to express their gratitude toward Purdue Research Foundation for financing much of this research. References Bergwerk, W., 1959. Flow pattern in diesel nozzle spray holes. In: Proceedings of the Institution of Mechanical Engineers, vol. 173, pp. 655–660.
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Bunnell, R.A., Heister, S.D., 2000. Three-dimensional unsteady simulation of cavitating flows in injector passages. J. Fluids Eng. 122, 791–797. Chaves, H., Knapp, M., Kubitzek, A., Obermeier, F., Schneider, T., 1995. Experimental study of cavitation in the nozzle hole of diesel injectors using transparent nozzles. SAE, 199–211. Chen, Y., Heister, S.D., 1995. Two-phase modeling of cavitated flows. Comput. Fluids 24, 799–809. Chen, Y., Heister, S.D., 1996. Modeling hydrodynamic non-equilibrium in bubbly and cavitating flows. J. Fluid Eng. – Trans. ASME 118, 709–726. Chou, W.H., Faeth, G.M., 1998. Temporal properties of secondary drop breakup in the bag breakup regime. Int. J. Multiphase Flow 24, 889–912. Chou, W.H., Hsiang, L.P., Faeth, G.M., 1997. Temporal properties of drop breakup in the shear breakup regime. Int. J. Multiphase Flow 23, 651–669. Chryssakis, C.A., Assanis, D.N., 2005. A secondary atomization model for liquid droplet deformation and breakup under high weber number conditions. In: ILASS-Americas, May 22–25, 2005, Irvine, CA. Faeth, G.M., Hsiang, L.P., Wu, P.K., 1995. Structure and breakup properties of sprays. Int. J. Multiphase Flow 21, 99–127. Ganippa, L.C., Bark, G., Andersson, S., Chomiak, J., 2001. Comparison of cavitation phenomena in transparent scaled-up single-hole diesel nozzles. In: 4th international symposium on cavitation, California institute of technology, Pasadena, CA. Paper No. CAV2001:session A9.005. Gopalan, S., Katz, J., 2000. Flow structure and modeling issues in the closure region of attached cavitation. Phys. Fluids 12, 895–911. Hiroyasu, H., 2000. Spray breakup mechanism from the hole-type nozzle and its application. Atom. Sprays 10, 511–527. Hiroyasu, H., Arai, M., Shimizu, M., 1991. Break-up length of a liquid jet and internal flow in a nozzle. In: ICLASS-91, Gaithersburg, MD, July 15–18, 1991, pp. 275– 282. Laoonual, Y., Yule, A.J., Walmsley, S.J., 2001. Internal fluid flow and spray visualization for a large scale valve covered orifice (vco) injector nozzle. In: ILASS-Europe, Sept. 2–6, 2001, Zurich. Li, H., 1999. An Experimental Investigation of High Pressure Cavitating Atomizers. Ph.D. Thesis. School of Aeronautics and Astronautics, Purdue University. Li, H., Sanchez, P., Collicott, S., 1998. Visualization of cavitation in low-pressure miniature slot flows. In: ILASS-Americas 98, Sacramento, CA. pp. 138–142. Ong, D., 2000. Investigation of Cavitation in Circular and Slot Orifices with A Step. Master’s Thesis. School of Aeronautics and Astronautics, Purdue University. Ong, D., Yeh, C., Hoverman, T.J., Collicott, S.H., 2003. Effects of a small step in an orifice on liquid jet breakup. Atom. Sprays 13, 297–307. Ranger, A.A., 1968. The Aerodynamics Shattering of Liquid Drops. Ph.D. Thesis. University of Michigan, Ann Arbor. Ranger, A.A., Nicholls, J.A., 1969. Aerodynamics shattering of liquid drops. AIAA 7, 285–290. Ruiz, F., He, L., 1998. Turbulence inside a cavitating injector orifice: a different animal. In: ILASS-Americas, Sacramento, CA, May 17–20, 1998, pp. 133–137. Ruiz, F., He, L., 1999. Turbulence under quasi-cavitating conditions: a new species? Atom. Sprays 9, 419–429. Sallam, K.A., Dai, Z., Faeth, G.M., 1999. Drop formation at the surface of plane turbulent liquid jets in still gases. Int. J. Multiphase Flow 25, 1161–1180. Sallam, K.A., Dai, Z., Faeth, G.M., 2002. Liquid breakup at the surface of turbulent round liquid jets in still gases. Int. J. Multiphase Flow 28, 427–449. Tafreshi, H.V., Pourdeyhimi, B., 2004. Simulating cavitation and hydraulic flip inside hydroentangling nozzles. Textile Res. J. 74, 359–364. Tamaki, N., Shimizu, M., Nishida, K., Hiroyasu, H., 1998. Effects of cavitation and internal flow on atomization of a liquid jet. Atom. Sprays 8, 179–197. Tamaki, N., Shimizu, M., Hiroyasu, H., 2001. Enhancement of the atomization of a liquid jet by cavitation in a nozzle hole. Atom. Sprays 11, 125–137. Tseng, K.T., 2006. Fluidic Spray Control. Ph.D. Thesis. School of Aeronautics and Astronautics, Purdue University. Tseng, K.T., Collicott, S.H., 2011. Demonstration of a fluidic spray control orifice. J. Propul. Power 27, 733–736.
Contents lists available at ScienceDirect
International Journal of Multiphase Flow j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / i j m u l fl o w
Experimental and numerical investigations of mechanisms in fluidic spray control Kuo-Tung Tseng ⇑, Steven H. Collicott School of Aeronautics and Astronautics, Purdue University, West Lafayette, IN 47907, United States
a r t i c l e
i n f o
Article history: Received 21 September 2013 Received in revised form 8 January 2014 Accepted 10 January 2014 Available online 30 January 2014 Keywords: Spray control Cavitation Droplet measurement Flow structure Two-phase flow
a b s t r a c t A fluidic control method in an axisymmetric spray orifice is investigated experimentally and numerically. In this method, a nominally steady secondary flow is introduced through an annular slot placed near the vena contracta along the orifice wall to control the cavitation, and thus the spray, at pressures up to 550 kPa driving pressure difference. Images of cavitation, measurements of droplet sizes and discharge coefficients, and CFD modeling are combined to explore the flow physics leading to the production of small droplets. Experimental results suggest that the secondary flow is incapable of confining cavitation to the region upstream of the slot, and generally a larger secondary flow rate results in a lower discharge coefficient, and a larger fraction of small droplets. The homogeneous model-based CFD code of Chen and Heister was employed to model the internal flows, which indicated that a high pressure region upstream of the slot, large pressure fluctuations in the orifice, and long cavitation lengths are the favorable conditions for atomization. The CFD simulations, together with experimental measurements, correlate the orifice geometry and flow structures to droplet sizes. Understanding the relationship between flow structures and droplet sizes helps to design orifices in favor of production of small droplets. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction Spray control is important. For example, fuel sprays might be optimized for engine load or bio-fuel blends on a daily basis. Spray coating of contoured surfaces may have a spray that adapts to changes in contour, and hydro-entanglement of unwoven textiles may benefit from maximizing momentum flux with minimal droplet production. Recent research on the connection between smallscale internal flow cavitation and droplet sizes has demonstrated a promising approach for a new spray control method. Compared to a plain orifice (Fig. 1(a)), an orifice with a small step placed at a strategic location (Fig. 1(b)) (where the flow reattaches to the orifice wall for a plain orifice at a pressure below that for hydraulic flip) can substantially increase the pressure for hydraulic flip, and produce a large fraction of tiny droplets (Ong, 2000; Ong et al., 2003). The success of the small step motivated us to devise a circular orifice with an annular slot (through which a secondary flow is introduced to the orifice) placed at the strategic location (Figs. 1(c) and 2(a)), namely orifice 1, which is not the target in this paper. ⇑ Corresponding author. Tel.: +886 2 33665062; fax: +886 2 33665690. E-mail addresses: [email protected] (K.-T. Tseng), collicott@ purdue.edu (S.H. Collicott). http://dx.doi.org/10.1016/j.ijmultiphaseflow.2014.01.003 0301-9322/Ó 2014 Elsevier Ltd. All rights reserved.
Orific 1 is found to work exactly like a step orifice does (Tseng and Collicott, 2011) at certain secondary flow rate, wherein the advantages of a fluidic spray control orifice are demonstrated— the secondary flow is proved to be able to influence the cavitation distribution, spray and droplet size, and the strength of this control effect can be modulated. Since the location of the slot is merely based on the successful small steps (Ong, 2000; Ong et al., 2003) which were guesses at what would work well, the question—how the slot location will influence the cavitation distribution—has inspired us to devise another orifice, namely orifice 2, as shown in Fig. 2(b), where an annular slot is placed near the vena contracta. Unless specified, the results in this paper are all from orifice 2. Historical research has demonstrated that orifice geometry may greatly affect droplet distribution in several ways. Hiroyasu et al. (1991) and Hiroyasu (2000) showed that cavitation and turbulence significantly influence atomization, which can be manipulated by installing a wire mesh over the inlet of the orifice and a gap at the middle of the orifice hole (Hiroyasu, 2000). The wire mesh transforms the jet from non-cavitating hydraulic-flipped flow to cavitating flow; a larger ratio of gap length to orifice length is capable of atomizing the jet more rapidly, and enabling a larger spray angle, where a higher degree of atomization has proven to be ascribed to a strong disturbance arising from cavitation in the nozzle (Tamaki et al., 1998, 2001; Hiroyasu, 2000). In Hiroyasu’s
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49
Fig. 1. Diagram of the (a) plain orifice, (b) step orifice, and (c) orifice 1.
Fig. 2. Plane section views of the main housings and the inner plugs of orifice 1 and orifice 2, which form the annular plenum and the conical void terminating in the annular slot. The region circled in (c) corresponds to (b).
experiment, the orifice diameter is 0.3 mm, the gap length is 0.3 mm, and the ratios of gap to orifice length are between 5 and 41. The spray has also been observed to be affected by different inlet geometries (Laoonual et al., 2001). Plain, counterbore,
rounded, and beveled inlets of different angles result in different spray distributions, among which the beveled nozzle with a bevel angle of 60 , and the rounded nozzle having an inlet radius of curvature approximately the same as the orifice radius are shown to be capable of greatly increasing the pressure for hydraulic flip. This effect is an analogy to that of a small step placed at a strategic axial location (Ong, 2000). In their study, the nozzle diameter is 6 mm, the length-to-diameter ratio is either 5 or 10, and the pressures are up to 2 MPa. In addition to straight orifices, orifices inclined at different angles (including 0 ; 14 ; 80 ; 85 , and 90 ) to the axis of the injector have also been investigated by some researchers (Ganippa et al., 2001; Li, 1999), wherein an asymmetric nozzle is found to be responsible for asymmetric cavitation distributions, and thus different degrees of atomization. The side with a higher degree of atomization has thicker cavitation on the same side upstream. To simulate the actual geometry of a diesel engine injector, Li et al. (1998) and Li (1999) employ orifices angled at 14 with respect to the surface normal, and having diameters in the range of 0.206–0.397 mm. In their experiment, UCF-1 calibrating fluid was used as the working liquid, and the pressure was as high as 200 MPa. Some features of the asymmetric unsteady cavitation extending downstream from the inlet are also observed later by Ganippa et al. (2001). Recent work at Purdue further demonstrated that either a small step (Ong, 2000; Ong et al., 2003) or a slot placed at a strategic axial location (Tseng and Collicott, 2011) changes the inlet cavitation, discharge coefficient, and droplet size distribution, and substantially increases the pressure for hydraulic flip. That one small change in the orifice can create such a wealth of changes in the flow indicates that a control mechanism likely exists to exploit further. Extending the investigation to explore the influence of the orifice geometry for a fluidic spray control orifice as well as the flow physics will assist in affording us in-depth knowledge of how cavitation may be more effectively manipulated.
2. Purpose Although cavitation has long been known to affect fluid spray, the links between droplets and flow structures are poorly
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understood. For example, there is no effective method to measure the pressure field, velocity field, void fraction, etc., of the flow inside of a small orifice without disturbing the flow field, and thus little of the internal flow details have been explored. Despite pressure measurements that have been made previously inside a larger orifice, the data do not really reflect the actual conditions in a small orifice since the nucleation and the periodic behavior of the cavitating flow have long been known to be influenced by absolute size (Bergwerk, 1959). To overcome the said problem, we adopt a numerical approach in this paper. In addition to yielding non-intrusive insight into quantities such as pressure, and giving a wealth of information to improve understanding of the flow structures inside the orifice, which are crucial for enabling a better control of sprays, Computational Fluid Dynamics (CFD) is also used to predict the influence of the slot location on flow properties at a lower cost, and assisted us in developing the geometry of another orifice, called orifice 2. The numerical solutions are then compared to data from experimental observations and measurements to identify conditions that are favorable in atomizing flows.
3. Experimental and CFD approach 3.1. Experiment The flow rig for this experiment consists of an air compressor supplying air up to 1 MPa, a reservoir, an optically accessible orifice formed by two pieces: the main housing and the inner plug, a Xenon flash lamp, a digital CCD, a camera lens, a pressure transducer, an in-line flow rate meter and a Sympatec laser diffraction
particle-sizer (Fig. 3). The water in the reservoir is split into the main and secondary flows prior to reaching the test section. Flow rates of the secondary and total flows are measured by an in-line flow meter and collection of the efflux, respectively. Based on the measurement results, the percentage of the secondary flow, that is, the ratio of secondary to total mass flow rates, and the discharge coefficients, defined as the ratio of the measured total mass flow _ to the product of water density (q), the orifice cross-secrate (m) tional area (A) and the Bernoulli velocity (V), are calculated (Eq. (1)). Measurements of the total flow rate were repeated thrice to increase accuracy.
_ qAVÞ C d ¼ m=ð
ð1Þ
Orifice 2, having Ls ¼ 0:41 mm with a ¼ 75 (Fig. 2(b)), and inlet bluntness approximately 5% of the orifice radius (the ratio of the inlet radius of curvature to the orifice radius is approximately 0.05), was machined from transparent acrylic. The nominal slot length (h) is 0.08 mm, and may be slightly widened at a large driving pressure difference. The droplets in the spray are measured with a Sympatec Helos laser diffraction particle-sizer, providing measurement accuracy to ±1% and operated by Windox software from Sympatec GmbH. When interacting with droplets, the light source of the particlesizer, a Helium–Neon-laser with 632.8 nm wavelength, is diffracted, or otherwise concentrated on central parts of the detector. Generally, the diffraction angle decreases as the droplet size increases. The graphical presentations of the results include mass density distributions defined as the mass fraction for a range of droplet sizes, to the width of that range, wherein the adequacy of sample sizes and class sizes is justified according to the ASTM E799-03 testing standard (Tseng, 2006). For the measurements in this study, the smallest class size is centered at 2.12 lm, but in the area very close to 0 lm, the measurement results may be influenced by particles in air, which are likely to cause noise signals. An EG&G xenon arc lamp (Model No. FTO-1130) flashing at 15 Hz with 2 ls duration, enabling the capture of fast-moving cavitation or droplets, and activated by a function generator is utilized as the light source to backlight the test section. The light radiated from the lamp, focused by an aspheric lens and diffused by a ground glass, finally gets to the orifice. A Nikon lens (Model No. AF 70-210 f/4-5.6) is used on the other side to image the cavitation in the orifice onto the Redlake 1024 by 1024 square-pixel 8-bit grayscale CCD camera (Model No. ES 1.0) equipped with a builtin electronic shutter. Exposure time for the shutter can be as short as 127 ls, which is longer than the duration of the arc. The high resolution CCD camera, triggered by operating the XCAP software developed by Redlake MASD, INC., is capable of capturing 30 images per second. When light passes through a region with two-phase flows, it is refracted or scattered by the liquid–vapor interface as a result of the different refractive indices of the vapor and the liquid. Light refracted outside of the imaging lens aperture is unable to reach the CCD detector. Therefore, the appearance of cavitation is always indicated by a dark region in the images. This technique differentiates two-phase from single-phase flows, but it cannot distinguish vapor from air. Hence, a dark region also emerges in response to a hydraulic flip.
3.2. CFD
Fig. 3. Schematic of the flow rig.
The numerical model used in this paper was developed by Chen and Heister (1996) and students. They treated the flow as an unsteady two-phase flow. In addition to momentum (Navier– Stokes) and continuity equations, an extra expression is constituted to deal with the pseudo-density, which varies from pure vapor, 0.001, to pure working liquid, 1. The additional expression
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only applies to the cavitation region, wherein the density change of fluid is assumed to be proportional to the product of the pressure difference between the local pressure (P) and vapor pressure (P v ), characteristic length, and characteristic velocity, which enables the pressure to recover at the end of the cavitation region without using a separate wake model (Chen and Heister, 1995). In this expression, the hydrodynamic non-equilibrium effects are taken into account. Later, Bunnell and Heister (2000) extended the code to three-dimensional flows. Physically, the secondary flow enters the orifice through the annular slot, wherein a velocity profile is of course created. However, numerically, a uniform velocity is specified across the slot length for simplification. Moreover, the simulation assumes that the orifice is symmetric with respect to the central axis, although a certain degree of asymmetry, which is likely to induce a strong 3-D effect at a large secondary flow rate, inevitably exists. The specified velocity direction is determined by the slot orientation, and the magnitude is based on the experimental measurements. 3.3. Dimensionless parameters The dimensionless pressure is given as:
P ¼
1 ðP P2 Þ 2 ðP1 P2 Þ
ð2Þ
where P1 , and P2 indicate the upstream pressure and downstream pressure, respectively. P1 and P 2 , the dimensionless upstream and downstream pressures, are 0.5 and 0, respectively, calculated from Eq. (2). Vapor pressure for water, P v , changes with temperature and pressure. At 550 kPa driving pressure difference with temperature between 21 C and 28 C; Pv is approximately 0.089. Time, t , is defined as:
t ¼ tV=D
ð3Þ
where D is the orifice diameter, t is time, and V is the Bernoulli velocity defined by:
V¼
sffiffiffiffiffiffiffiffiffi 2DP
q
ð4Þ
Here DP is the indicated driving pressure difference and q is the water density. Other parameters, v and q are the corresponding axial velocity and density normalized by the Bernoulli velocity and the liquid density, respectively; z and r denote the axial and radial coordinates normalized by the orifice diameter (z ¼ 0 and
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r ¼ 0 correspond to the orifice inlet plane and the centerline in the axial direction, respectively). Prior to simulation, a grid convergence study (Tseng, 2006) is conducted, wherein pseudo-density profiles, axial velocity profiles and wall pressures are scrutinized. 4. Results 4.1. Experiment Spray from an orifice is actually affected by both primary and secondary atomization. The former, determined by the interaction of the jet with the ambient air (Chryssakis and Assanis, 2005), causes the jet to break up into droplets, and the latter, influenced by droplet size, droplet velocity and the properties of the system such as pressure, temperature, viscosity and surface tension (Faeth et al., 1995), may transform the large droplets into smaller ones (Ranger, 1968; Ranger and Nicholls, 1969) through both shear (Chou et al., 1997; Chryssakis and Assanis, 2005) and catastrophic breakup (Chryssakis and Assanis, 2005) for flows with sufficiently large Weber numbers (100), as in this experiment. If the Weber numbers fall in the range of 13–20, the parent droplet may be deformed into a thin bag, and its breakup yields droplets with diameter approximately 4% of that of the parent droplet, depending on the conditions such as Reynolds numbers, Ohnesorge numbers, and liquid/gas density ratios (Chou and Faeth, 1998). Although the effect of secondary atomization, supposed to exert an important influence on the flows in this experiment, is not explored, the measurements and images recorded here still deliver meaningful information in that the link between internal flow structures and droplet sizes has been confirmed by several researchers (Hiroyasu et al., 1991; Tamaki et al., 1998, 2001; Hiroyasu, 2000). Seven secondary flow rates at 350 kPa and 550 kPa driving pressure differences, respectively, have been investigated (fourteen cases in all), but in this paper, only five cases at 550 kPa driving pressure difference are presented because a lower driving difference, generally enabling a lower degree of atomization (Chaves et al., 1995), is of less interest. Note that the back pressure for all cases is atmospheric. Fig. 4 displays the cavitation with no secondary flow. At 550 kPa driving pressure difference, two flow states—hydraulic flip (Fig. 4(a)) and cavitating flow (Fig. 4(b))—are present alternately. The cavitated state, likely to be triggered by a minor disturbance upstream, does not greatly atomize the flow, and only a very small fraction of tiny droplets, referring to those with diameters smaller
Fig. 4. Flow visualization and droplet size distributions (35 cm downstream) for orifice 2 with 0% secondary flow at: DP ¼ 550 kPa. For details in the shaded region in (c), please see Fig. 5.
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Fig. 5. Mass density distribution per lm for the shaded region in Fig. 4(c). Note that the vertical axis is on a nonlinear scale, the lower limit for which is taken as 5 106 .
than approximately 100 lm, are shaped, as exhibited in Fig. 4(c), wherein the left peak in the bimodal distribution, caused by the slot effect, is not important. The details in the shaded region in Fig. 4(c) are shown in Fig. 5. Note that a large dark region appears in the ‘‘no flow’’ photo, which results from refraction from the orifice wall, and thus, any new black regions in the flow photos show two-phase boundaries, or cavitation (Fig. 6). Obviously orifice 2 does not behave like a plain orifice when there is no secondary flow, pointing out that the slot effect cannot be ignored even without the secondary flow. That is, with no secondary flow, the slot acts as a constant geometrical perturbation to the internal flow, much like the step of Ong (2000). In the droplet size distributions, two measurements are made to give an indication of the repeatability, wherein at least 300,000 droplets are measured, respectively. With the secondary flow rate increased to 2%, cavitation is seen to appear irregularly upstream (Fig. 7(a)) or downstream (Fig. 7(b)) of the slot. Compared to the 0% case, the elimination of hydraulic flip does not discernibly increase the number of small droplets
(Fig. 7(c)), suggesting the effects of secondary flow and the slot are approximately equal in atomizing the flow. Although the local enlarged view (Fig. 8) reveals that the former causes a slightly larger fraction of tiny droplets than the latter (Fig. 5), the difference is so small, rendering the comparison results uncertain to some degree, which may be improved by more detailed measurements or orifice design. With the secondary flow turned on at 4%, cavitation extends well downstream, as shown in Fig. 9(a) and (b), representing the cases of upper and lower limits of cavitation lengths. This phenomenon was not observed in the small step orifice, suggesting that at the moment, the fluid efflux from the slot does not create a sufficiently large high-pressure region neighboring the slot, and thus seems to cause the inception of cavitation therein. Compared to prior cases, the more downstream distribution of cavitation appears to constitute a more favorable condition for atomizing the flow, as shown in Fig. 9(c). The mass density per lm for tiny droplets is still small but perceivable. Note that the value of the right peak (Fig. 9(c)) is also larger than those for the 0% and 2% cases (Figs. 4(c) and 7(c)), indicating the influence of the slot is reduced, thus causing a more flat central region. At the maximum two secondary flow rates in this experiment, 15% and 20%, cavitation persists at the exit plane (Figs. 10(a) and 11(a)), creating a strong 3-D flow structure that prevents air from penetrating upstream, and thus prevents hydraulic flip from occurring. In fact, cavitation continues to prevail at the orifice exit plane even at pressures up to 600 kPa. Compared to the 4% case, the minor change in cavitation distribution is thought to boost the turbulence level significantly, whereby velocity profiles are modified at the orifice exit (Tafreshi and Pourdeyhimi, 2004), and hence the mass density per lm for tiny droplets (Figs. 10(b) and 11(b)) is substantially increased, as is affirmed by Gopalan and Katz (2000). During the measurement period (10 s), the numbers of droplets created by the 20% secondary flow and sized in 50–60 lm, 90–100 lm, and 1450–1750 lm ranges are approximately 5,650,000, 1,700,000, and 9800, respectively, while the 0% secondary flow creates approximately 28,000 droplets sized in 1450– 1750 lm range, but only a small amount of tiny droplets.
Fig. 6. Schematic of causes of dark regions (in the orifice with no flow), and the orifice structure. The dark regions are from refraction from the orifice wall, and thus, any new black regions in the flow photos show two-phase boundaries, or cavitation.
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Fig. 7. Flow visualization and droplet size distributions (35 cm downstream) for orifice 2 with 2% secondary flow at: DP ¼ 550 kPa. For details in the shaded region in (c), please see Fig. 8.
Fig. 8. Mass density distribution per lm for the shaded region in Fig. 7(c). Note that the vertical axis is on a nonlinear scale, the lower limit for which is taken as 5 106 .
4.2. Discharge coefficient In the flow regime without a hydraulic flip at 0% secondary flow, occurring approximately between 480 kPa and 550 kPa driving
pressure difference, the C d values are found to be generally inversely proportional to the secondary flow rates (Fig. 12). Cavitation lengths, increasing with secondary flow rates, appear to be responsible for this unique trend. With cavitation spanning further downstream, more vorticity is deemed to be created, which is capable of increasing the level of turbulence (Ruiz and He, 1998, 1999), a phenomenon probably evidenced by the seemingly thicker cavitation acting like an obstruction by displacing the high-momentum flow. As the pressure is increased to 550 kPa, the most highly cavitated flow resulting from the maximum flow rate achieves the minimum discharge coefficient (0.68), a value even smaller than that achieved by 0% and 1% secondary flows that cause hydraulic flip and cavitating flow to alternate. This indicates that the 20% secondary flow highly obstructs the flow, and thus substantially reduces the effective flow area. Discharge coefficients for other cases, including 2%, 3% and 4% secondary flows, exceed those for the 0% case, but are not significantly different from those for the 1% case. Excluding the two lowest flow rate cases, the aforementioned C d values versus secondary flow rate relationship still applies. Note that the C d values increase as the pressure rises beyond 550 kPa, especially for the 15% and 20% cases, which might be due to the combined effect of the strong 3-D flow structure and cavitation distribution.
Fig. 9. Flow visualization and droplet size distributions (35 cm downstream) for orifice 2 with 4% secondary flow at: DP ¼ 550 kPa.
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Fig. 10. Flow visualization and droplet size distributions (35 cm downstream) for orifice 2 with 15% secondary flow at: DP ¼ 550 kPa.
Fig. 11. Flow visualization and droplet size distributions (35 cm downstream) for orifice 2 with 20% secondary flow at: DP ¼ 550 kPa.
Fig. 12. Measured discharge coefficient for orifice 2 versus driving pressure difference for seven secondary flow rates.
4.3. CFD Fig. 13 displays the CFD results for the baseline case (0% secondary flow). The cavitation histories imply that at 550 kPa driving pressure difference, the flow becomes hydraulic flipped, a state
that cannot be really predicted by CFD here. On average, the portion prior to t ¼ 70 in the cavitation histories, regarded as the transient state, is excluded in the subsequent discussions. Although the code is capable of predicting the behavior of many small-scale, unsteady, non-equilibrium cavitating flows, it does not capture the hydraulic flipped flow because the model assumes that only vapor and working liquid appear in the orifice. In other words, the calculation proceeds as if the orifice were submerged in the working liquid, instead of flowing into the atmosphere. Note that the contour legends in Fig. 13 also apply to the other figures in this paper. The numerical results for 2% secondary flow are exhibited in Fig. 14, where the pressure created is not sufficiently large in the region upstream of as well as around the slot, allowing the onset of cavitation at the orifice inlet. The dimensionless cavitation lengths (i.e., the streamwise extents of cavitation measured from the inlet) are estimated to oscillate approximately between 0.42 and 0.93 (Fig. 14). Although the computational domain extends downstream to the exit plane and well upstream of the orifice inlet, only the region in the vicinity of the slot that is of more interest is shown here for easy reference. On the other hand, experiments show that the ratio of cavitation length (Lc ) to orifice length (L) varies approximately between 0.25 and 0.6 (Fig. 7(a) and (b)). The differences may be attributed to the non-uniform slot that is likely to result in a 3-D effect.
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Fig. 13. Cavitation histories, pressure contours, streamlines and pseudo-density contours for orifice 2 with 0% secondary flow; the latter three figures correspond to t = 180, wherein the left-hand border is the orifice centerline, and the exit plane is at z ¼ 6:25.
Fig. 14. Cavitation histories, pressure contours, streamlines and pseudo-density contours for orifice 2 with 2% secondary flow; the latter three figures correspond to t = 180, wherein the left-hand border is the orifice centerline, and the exit plane is at z ¼ 6:25.
The predictions for the 4% case seem to be in more agreement with the experimental results compared with the 2% case. CFD predicts that Lc =L ranges approximately from 0.52 to 0.93 (Fig. 15), while experiments indicate an Lc =L range of approximately 0.7–1 (Fig. 9(a) and (b)). CFD appears to underestimate the pressure upstream of the slot, causing cavitation developed at the orifice inlet to propagate downstream to below the slot, whereas physically the onset of cavitation seems to occur in the vicinity of the slot. (Due to an inevitable certain degree of asymmetry of the orifice, there could be a very small amount of cavitation in the region upstream of the slot.) The predictions of pressure contours, streamlines and pseudo-density contours show little difference from those for the 2% case.
At large secondary flow rates, 15% and 20%, CFD shows no trace of cavitation (Figs. 16 and 17) throughout the region upstream of the slot, consistent with the cavitation images (Figs. 10 and 11). Obviously, the high pressure covers the said region, inhibiting the onset of cavitation. 4.4. Causes of small droplets In addition to cavitation, historical efforts have proved that droplet sizes are also influenced by liquid turbulence, the location where the turbulent primary breakup begins, the cross stream dimension of the free jet (Sallam et al., 1999), small-scale turbulent
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Fig. 15. Cavitation histories, pressure contours, streamlines and pseudo-density contours for orifice 2 with 4% secondary flow; the latter three figures correspond to t = 180, wherein the left-hand border is the orifice centerline, and the exit plane is at z ¼ 6:25.
Fig. 16. Cavitation histories, pressure contours, streamlines and pseudo-density contours for orifice 2 with 15% secondary flow; the latter three figures correspond to t = 180, wherein the left-hand border is the orifice centerline, and the exit plane is at z ¼ 6:25.
eddies in the vicinity of the jet exit, and Weber numbers (Sallam et al., 2002) based on which correlations for breakup lengths were developed (Sallam et al., 2002). These mechanisms are of course very important in the atomization process, which, however, are not discussed here in that this research mainly focuses on the internal flow physics. In our experiment, the degree of atomization was found to depend on driving pressure difference, streamwise extent of cavitation, and the mechanism determining how cavitation is distributed, which is conjectured to be the magnitude of pressure in the vicinity of the slot. A larger driving pressure difference and a longer cavitation length are obviously advantageous to liquid jet atomization. Also, the numerical approach further suggests additional mechanisms in favor of breaking liquid streams into tiny droplets. To this end,
a series of figures concerning pseudo-density variations over time, axial velocity variations over time, and wall pressure variations over time are explored, wherein the former two are investigated at several planes perpendicular to the orifice axis (Tseng, 2006). Pseudo-density distributions appear not to be the critical conditions, the variations of which over time at different planes are larger for the 2% case than for the 15% case that results in a much larger fraction of small droplets, as is, without loss of generosity, shown in Fig. 18. By the same token, the axial velocity is also ruled out as the important condition for atomization. The typical axial velocity distribution in the vicinity of the slot is exhibited in Fig. 19. The likely conditions favoring production of small droplets appear to be: high pressure in the vicinity of the slot, large high pressure variations over time, and long cavitation lengths
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Fig. 17. Cavitation histories, pressure contours, streamlines and pseudo-density contours for orifice 2 with 20% secondary flow; the latter three figures correspond to t = 180, wherein the left-hand border is the orifice centerline, and the exit plane is at z ¼ 6:25.
Fig. 18. Pseudo-density profiles for orifice 2 with 2%, 4%, 15% and 20% secondary flows at: z = 0.95.
(Fig. 20). The 20% secondary flow leads to the highest pressure near the slot, the largest high pressure variations over time, and the greatest extent of cavitation, and, therefore, achieves the highest degree of atomization. For the two largest secondary flow rate cases, a large magnitude pressure drop is found in the region neighboring the slot, which may result in more violent cavitation collapse therein, and consequently to produce cavitation effects which propagate to the exit plane.
Orifice 1 behaves differently. The degree of atomization reaches the peak at 4% secondary flow, wherein the cavitation persists in the region upstream of the slot (Tseng and Collicott, 2011). Although the two maximum secondary flow rates (15% and 20%) result in the highest pressure (Fig. 21), the absence of cavitation (throughout the entire orifice) as well as the nearly steady high pressure profiles (Fig. 21) seem to greatly weaken the atomization effect. In the 2% case, the pressure neighboring the slot is lower than that in the 4% case, which, together with the occurrence of
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Fig. 19. Axial velocity profiles for orifice 2 with 2%, 4%, 15% and 20% secondary flows at: z = 0.95.
Fig. 20. Wall pressure for orifice 2 with 2%, 4%, 15% and 20% secondary flows; vapor pressure is P v = 0.089.
hydraulic flip that alternates with the cavitating flow, reduces the atomization efficiency. Similar to orifice 2, pseudo-density variations (Fig. 22) and axial velocity variations (Fig. 23) are not the important conditions for atomization.
Note that, taking into account the numerical results for both orifice 1 and orifice 2, we also exclude the magnitudes of pseudo-density and axial velocity as the crucial conditions.
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Fig. 21. Wall pressure for orifice 1 with 2%, 4%, 15% and 20% secondary flows; vapor pressure is P v ¼ 0:089.
Fig. 22. Pseudo-density profiles for orifice 1 with 2%, 4%, 15% and 20% secondary flows at: z ¼ 2.
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Fig. 23. Axial velocity profiles for orifice 1 with 2%, 4%, 15% and 20% secondary flows at: z ¼ 2.
5. Discussion In addition to driving pressure difference, DP, cavitation length, and frequency in the periodic growth-collapse of cavitation, the droplet size distribution is also seen to be influenced by pressure in the neighborhood of the slot as well as pressure variations over time. Hydraulic flip excluded, the flows are atomized more at a large driving pressure difference than at a low driving pressure difference because a faster-moving stream interacts more violently with the surrounding air. An increased cavitation length presumably provides a greater cavitated region capable of shedding more sub-diameter length scale unsteadiness into the flow, and thus enhances atomization. However, as cavitation length increases, the characteristic frequency in the periodic growth-collapse of cavitation regions is lowered simultaneously. The lower frequency disturbances reduce the unsteadiness of cavitating flow, and hence weaken atomization. Another decisive condition, the high pressure region, created in the vicinity of the slot and varying drastically over time, is induced by a large secondary flow rate, causing cavitation to collapse more fiercely, a condition beneficial to giving rise to a higher level of turbulence and therefore a higher degree of atomization. For this steep slot orifice (orifice 2), the increasing secondary flow simultaneously exerts both favorable and unfavorable influences on atomization. On one hand, it increases the pressure that varies more drastically, causing longer cavitation lengths, and thus a higher degree of atomization in spite that, on the other hand, the unsteadiness triggered by the cavitation grow-collapse cycle is reduced. Apparently, the favorable influences appear to overwhelmingly dominate, accounting for the trend that a larger secondary flow rate creates a larger fraction of smaller droplets. For orifice 1, with the slot placed at a strategic location, a large high pressure region, created throughout the entire neighborhood
of the slot, is found to fully confine cavitation to the region upstream of the slot. As a result, a larger secondary flow rate moves cavitation further upstream, leading to shorter cavitation lengths that lead to higher frequencies in the periodic growth-collapse of cavitation, and at the same time, result in a higher pressure region around the slot, which, along with the degree of high pressure fluctuations, determine the overall atomization performance. The degree of atomization is maximized as the secondary flow rate increases to near 4% (for orifice 1), where the pressure around the slot is lower but the pressure variations over time are larger than at higher secondary flow rates, 15% and 20%. On the other hand, the cavitation length for the 4% and 2% cases is approximately the same (hydraulic flip in the 2% case is excluded), but the former causes higher pressure around the slot than the latter. Considering orifice 1, the combined effects of large high pressure variations over time and long cavitation lengths are regarded as the most influential conditions for promoting the level of atomization. 6. Conclusions A fluidic control method or device is shown to be capable of manipulating droplet sizes. By controlling the secondary flow rate, which at various flow rates can create significantly different distributions of pressure, velocity, streamlines, and density in the orifice, the droplet distribution in the spray is affected. Among all quantities, the internal unsteady pressure field, also critically influenced by the slot location, is verified by CFD simulations as the most critical influence in determining the degree of atomization. As opposed to the previous orifice (orifice 1), orifice 2 does not work like the step orifice works. Perhaps the slot, located in the vena contracta, is too far upstream to subdue the streamwise growth of cavitation. As the secondary flow rate increases, the stronger interaction between the main and secondary flows
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around the slot causes longer cavitation lengths that lead to a larger fraction of small droplets. When the rate of the secondary flow is low, it imposes little influence on the wall pressure as well as the droplet size distribution in spite that the cavitation lengths may change significantly. At large secondary flow rates, the pressure is apparently elevated beyond the threshold for cavitation to occur throughout the entire upstream region, causing cavitation to disappear therein. Production of small droplets is maximized near 20% secondary flow. Although not measured, cavitation appears to thicken as the cavitation length increases, and this effect is surmised to be responsible for producing even more sub-diameter length scale unsteadiness that is crucial in spray control. For orifice 2, cavitation can originate in the vicinity of where the primary and secondary flows meet. That is, cavitation can extend downstream from the neighborhood of the slot, instead of from the orifice inlet, a feature distinguishing orifice 2 from orifice 1. In contrast, the secondary flow in orifice 1 does not allow the onset of cavitation in the region around the slot. Generally, a larger secondary flow rate results in higher pressure spanning from the slot to more upstream regions, which is able to restrict the cavitation occurring at the orifice inlet from propagating downstream, thus leading to shorter cavitation lengths, wherein the important effects exerted by high pressure and cavitation length counteract each other. As a result, the degree of atomization is not necessarily enhanced as the secondary flow rate increases. Compared with orifice 2, the degree of high pressure fluctuation for orifice 1 is much lower. Fluidic spray control, along with the CFD simulations, assists in gaining in-depth insight into the relationship between internal flow physics and droplet sizes, understanding better of which helps to manipulate spray more effectively and economically. After all, improving spray distribution further by shrinking a small circular hole like a Diesel injector, or increasing driving pressure does not hold promise as they both already tax the limits of economic manufacturing. Conclusions in this work appear to show how pseudodensity modeling of the internal flows can be useful in evaluating or optimizing slot design and placement, and secondary flow rates, prior to building experimental nozzles for verification. Acknowledgment The authors would like to express their gratitude toward Purdue Research Foundation for financing much of this research. References Bergwerk, W., 1959. Flow pattern in diesel nozzle spray holes. In: Proceedings of the Institution of Mechanical Engineers, vol. 173, pp. 655–660.
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