AIAA 2005-5189 Dispersed Droplet Momentum Characterization with Particle Image Velocimetry in Helicopter Icing Studies M. Milanez and G. F. Naterer University of Manitoba, Canada G. Venn Westland Helicopters Ltd, UK G. Richardson University of Cambridge, UK
Momentum exchange between droplets and co-flowing air affects the droplet impact, ice shape and capture efficiency in aircraft icing problems. In these problems, it is desirable for the aircraft surface to have a geometrical configuration with low capture efficiency, so it is less ice prone. During icing conditions, incoming droplets impinge on the surface, while air is deflected away and around the surface. Interfacial drag and gravity affect the momentum exchange between droplets and the airstream. This exchange and droplet trajectories are studied with Particle Image Velocimetry (Dantec Dynamics; FlowManager 4.20.25). Results are presented for motion of droplets in a co-flowing airstream.
I. INTRODUCTION
In aircraft icing conditions, impinging
droplets on the surface are affected by various forces between dispersed (droplet) and carrier (air) phases. These forces include interfacial drag, pressure and gravity, which contribute to droplet deflection near the icing surface. The resulting ice shape depends on the mass flux of impinging droplets. Momentum displacement of droplets in a diffusion layer entails cross-phase interactions of interfacial pressure and velocity (Milanez et al., [1]). Convective acceleration of the dispersed phase requires depends on the volume fraction of the dispersed phase [2]. In this article, these processes of interfacial momentum exchange are studied. In particular, deceleration of dispersed droplets due to interfacial drag is investigated with PIV (Particle image Velocimetry).
A dilute flow assumption can be adopted in multiphase flow analysis, provided the fluid motion is not largely affected by droplet / droplet interactions [2]. Distinct interfacial and bulk pressures affect the droplet dynamics of dilute flows (Milanez et al., [3]). Various averaging procedures have been used previously for predicting such interfacial transport, including time averaging, spatial averaging, ensemble averaging and combinations of these procedures [4]. But certain microscopic information may be lost through such averaging procedures, so additional information must be supplied back through other relations, such as constitutive or macroscopic / microscopic relations [5]. Dilute flows occur when the dispersed (droplet) phase is mainly controlled by the carrier (air) phase. For example, when a helicopter moves through a cloud of supercooled droplets, the impinging droplets on the helicopter surfaces are immersed in moving air. Their motion is not dominated by droplet / droplet interactions.
Past advances have developed experimental
methods of characterizing droplet dynamics in multiphase flows. PDS (Planar Droplet Sizing) is an example of a technique for characterizing droplet diameters in multiphase flows. In PDS, the intensity emitted by a fluorescent dye added to a liquid is proportional to the volume of resulting atomized droplets. Taking the ratio of this intensity with the scattered light intensity yields the SMD (Sauter Mean Diameter) of droplets. Past developments [6] have predicted the effects of scattering angle, refractive index, droplet size and dye concentration on the PDS method. Unlike dense sprays considered by Domann and Hardalupas [6], this article focuses specifically on the dispersed phase of dilute multiphase flows.
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Phase Doppler Interferometry, phase-doppler analyzers and Phase Doppler Anemometry are other useful techniques for characterizing droplet sizes and velocity distributions in multiphase flows. Jazayeri and Li [7] have investigated the spatial distribution of sprays with Phase Doppler Anemometry, including the breakup of liquid sheets in a co-flowing air stream. At the center-line, the authors have reported that the mean velocity of droplets reached a maximum value, while the Sauter mean diameter is a minimum. In the transverse direction, a self-similar distribution of droplet mean velocity was observed. Spatial effects of droplet entrainment, migration, secondary atomization and droplet coalescence at downstream locations affect the momentum exchange betweens dispersed and carrier phases. In contrast to these liquid sheet breakup mechanisms, this article focuses on uniformly dispersed droplets throughout a dilute flow field.
Both deterministic and stochastic aspects of
droplet flows have been reported by Kim et al. [8], particularly for droplets in spray modeling. The deterministic portion includes unstable wave motion. The breakup length, mean diameter and droplet distributions of the unstable growth at various wavelengths are investigated. In the stochastic model, a maximum entropy principle is used for the final stage of droplet formation after the liquid bulk breakup. Both deterministic and stochastic parts can be combined through source terms containing liquid / gas interactions.
In aircraft icing problems, the accreted ice
mass and shape are directly affected by the droplet collection [9]. Aerodynamic characteristics are largely affected by this ice shape, including the drag and lift forces. Such aerodynamic characteristics have been measured by a force balance and surface pressure taps connected to an ESP (Electronically Scanned Pressure) system by Lee, Dunn and co-workers [10]. Side windows for laser droplet measurement were utilized by Chintamani and Belter [11]. Impinging droplets on the ice surface affect the ice thickness and transition between grime ice and glaze ice. An ultrasonic pulse-echo technique to measure the ice thickness was reported by Hansmann and Kirby [12]. A transducer was mounted flush with the surface (below the ice), and it emitted a brief compression wave. After the pulse travels through the ice and it is reflected by the external ice surface, it returns to the transducer as an echo signal. Then, the resulting ice thickness is calculated, based on the time elapsed and the speed of sound in ice.
In addition to aircraft icing problems, droplet flow characterization is important in numerous other practical applications. For example, other applications include cooling of high temperature surfaces with water / air sprays [13] and spray systems for fire suppression [14]. Cooling of high temperature surfaces by incoming droplets has been studied with thermocouple data gathered below the surface of the test piece [13]. An experimental study of the flux of droplets delivered from a spray system was performed for controlling and suppressing fires [14]. A PIV system was used to measure the droplet velocities and water densities leaving the sprinkler. It was observed that larger droplets traveled further horizontally from the sprinkler than smaller droplets, since the momentum of larger droplets was proportionally larger than the drag force.
In this article, new insight regarding such
momentum exchange and interfacial drag forces is provided with data collected from PIV (Particle Image Velocimetry). PIV is a non-intrusive technique, since probes or wires are not directly placed into the flow field [15]. Unlike other methods of anemometry, where velocity measurements are obtained at a single point, the PIV technique permits whole-field measurements of velocity. Past studies have mainly applied PIV techniques to continuous, single-phase flows [16]. However, in this article, applications of the method to dispersed (droplet) phase motion are studied, particularly for applications to aircraft icing problems.
II. ICING PROBLEM DESCRIPTION
The practical motivation of this work is better
understanding of droplet motion and impact on iced helicopter surfaces (see Fig. 1). In particular, ice protection of the engine bay cooling intake may involve active and passive methods. Active methods of de-icing involve electrical heating elements, or hot bleed air re-directed from the compressor of the engine system. On the other hand, passive methods include alterations of the surface geometry to reduce droplet capturing and water adherence to the surface. Controlled surface roughness, such as the specially designed micro-channels, may allow the local air stream to eject water from the surface before it re-freezes downstream [17]. In each method, a main purpose is deflecting droplets away from the ice surface and reducing the collection efficiency, thereby reducing the mass of ice accretion. Compromises involving effects of aerodynamic performance, manufacturing and so forth must be considered.
understanding of droplet impact and droplet momentum exchange between dispersed (droplet) and carrier (air) phases. The droplet velocities near the ice surface contribute to collection efficiency of the surface. This efficiency refers to the ratio of mass flow of impinging droplets on the upstream side of the iced surface, to the mass flow that would contact the same surface if the droplets were not deflected by the airstream. By measuring droplet velocities for assessing the collection efficiency, the detailed effects of surface shape on droplet capturing can be better understood. In this way, individual aircraft components can be designed to become less ice prone during in-flight icing conditions. In the following section, a method involving Particle image Velocimetry will be discussed for purposes of droplet tracking and momentum exchange in multiphase flows.
III. DROPLET TRACKING PROCEDURE
In Particle Image Velocimetry, a planar laser
light sheet is pulsed twice. Then, images of seed particles in the flow field are recorded with a video or photographic camera. The displacement of a group of particles is determined, typically by dividing the image plane into small interrogation regions and cross correlating images from two time exposures. The displacement that yields the maximum cross-correlation, based on statistical analysis, approximates the average displacement of the particles in the interrogation region. Dividing the displacement associated with each interrogation cell by the time between laser pulses then gives the measured velocity field. The conventional PIV method typically measures velocities on a 100 x 100 grid with accuracy between about 0.2% and 5% and a spatial resolution of about 1 mm. Extensions of this technique to 3-D flows can be readily accomplished with a stereographic system using two lenses.
Unlike conventional applications of PIV to continuous, single-phase flows, this article considers how measurements can be performed for dispersed droplets in dilute multiphase flows (see Fig. 2). Various different setups will be considered. Large droplets (up to about 1 mm diameter) are seeded with polyamide particles (20 micron diameter) and emitted horizontally in quiescent air (see Fig. 3). Also, small droplets (on the order of 10 microns) are sprayed from a series of air atomizing nozzles (see Fig. 4).
pulsed laseroptics
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Figure 2: PIV Schematic
In these cases, the PIV camera is aligned
perpendicular to the planar laser sheet. The test section is contained within a plexiglass region within an empty water tunnel, which collects water after it is sprayed. Reflecting optics below the test section are adjusted, in order that the emitted laser light is reflected at the proper angle relative to the camera positioning. Once the camera matches a sequential pair of images of dispersed droplets, the average displacement of a group of droplets within an interrogation region is calculated. This approach yields a grid of measured velocity vectors in the plane of the laser sheet.
In the large droplet case (Fig. 3), the vertical
pipe is fed by a constant water mass flow rate from the top. The horizontal pipe can be replaced with pipes of different diameters, in order to produce a jet type flow with various emitted droplet characteristics. The mass flow, pressure and pipes diameter are the main parameters controlling the flow characteristics, such as the droplet breakup diameter. The seeding particle feeder (upright mixer at midpoint of horizontal pipe) mixes polyamide seeding particles with the flowing water stream, thereby immersing particles within the emitted droplets for PIV measurements.
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The seeding particle feeder supplies particles into the water stream by gravitational and pressure effects induced within the adjoining horizontal pipe. Without particle seeding of large droplets, it was observed that an inadequate number of droplets passed through the interrogation region for PIV image analysis.
Figure 3: Experimental Setup of Jet Flow
Various factors affect the accuracy of capturing images from the seeded droplets. These factors include light intensity from the laser, droplet diameter, number of sprayed droplets, diameter of droplets, distance from the laser and specific trajectories of droplets passing across the light plane.
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Figure 4: Laser Illumination of Dispersed Droplets
In the small droplet case (Fig. 4), the droplets are emitted from a spray bar containing nozzles and atomizers. The role of this atomizer is to produce controlled droplet sizes for the PIV velocity measurements. Since the atomizer’s nozzles cannot produce sufficiently dispersed droplets, pressurized air is used to disperse the water stream. In order to improve controllability of this pressurized flow, valves and additional fittings were assembled into the spray bar. The valves were used to control the mass flow rate for each nozzle and the special fittings were used to control the flow directionality. In this way, the velocity field of dispersed droplets could be measured directly with the PIV setup, without the seeding particle feeder. Additional measures were studied to improve the measurement capabilities These steps would ensure additional camera sensitivity for capturing the images digitally. For example, a smaller spreading angle of laser light could be achieved with a custom-made cylinder type laser lens.
IV. RESULTS AND DISCUSSION
In this section, experimental results will be presented for horizontal jet flows with large droplets (cases 1 – 2), vertical jet flow (case 3) and dispersed droplet flows (cases 4 – 5). Case 1: Horizontal Jet Flow (High Pressure)
A liquid water stream is emitted horizontally with seed particles in surrounding quiescent air. Without such particles, insufficient illumination would be provided for the PIV method. In this problem, the exit mass flow rate of water is 55.6 mL/s and the supply line pressure is 65 psi.
Figure 5: Illuminated Particles in Jet Flow Problem
Sample results are shown in Figs. 6 – 9. From right to left in Fig. 8, it can be observed that the horizontal component of fluid velocity decreases. Diffusion through the liquid layer, adjacent to the quiescent air stream, contributes to momentum exchange and such velocity variations.
Similar trends for the vertical velocity component are observed in Fig. 9, except that gravity contributes to acceleration of the fluid from right to left. Although pressure and diffusion affect this vertical motion, a straightforward analysis of gravitational acceleration alone shows close agreement with the measured data (solid line in Fig. 9). The results suggest that the measured data is closely representative of fluid motion within the liquid jet.
0 10 20 30 40 50 60 70 80 90 mm0
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Figure 7: Measured Droplet Streamlines (Case 1)
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Figure 8: Horizontal Velocity Component (Case 1)
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Figure 9: Vertical Velocity Component (Case 1)
Case 2: Horizontal Jet Flow (Low Pressure)
In this case, the same problem is considered, but with a lower water pressure in the supply line. Measured results for this case are shown in Figs. 10 – 11.
Figure 10: Measured Droplet Velocities (Case 2)
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At a lower supply pressure in this case, the
horizontal velocity component decreases in Fig. 10. The magnitude of the vertical component velocity increases from right to left, due to gravitational acceleration (see Fig. 11). Similar trends in the x-direction are observed at different elevations throughout the jet flow. Figure 11 illustrates these variations at positions of 5, 10, 15 and 20 mm from the base of the camera view region.
This case is depicted in Fig. 12, whereby liquid water falls vertically under gravity in free flow from a liquid supply chamber. The exit mass flow rate of water is 53.3 mL/s. From classical mechanics, the expected fluid velocity in the view region of the camera image can be predicted analytically to be 3.679 m/s. The measured average velocity at this location was 3.821 m/s, thereby representing a measurement error of approximately 3.7%.
seeding particles
vertical outflow
light sheet
in liquid supply
view region
Figure 12: Vertical Jet Flow Schematic
Figure 13: Camera Image; Vertical Jet Flow (Case 3)
Figure 14: Measured Velocities (Case 3)
A sample photographic image of the vertically falling jet with seed particles is illustrated in Fig. 13. Steady state velocity vectors within this jet flow are shown in Fig. 14. Case 4: Dispersed Droplet Flow (High Pressure)
In this case, dispersed droplets are emitted from a spray bar assembly and PIV measurements of droplet velocities are studied. The droplet motion upstream of the helicopter engine bay is studied (see Fig. 15). The air gage pressure in the atomizing nozzles was 100 psi.
Seeding particles are not used, so laser light is
reflected from the droplets themselves, before their motion is analyzed by the PIV software. Figures 16 – 17 show successive images with illuminated droplets.
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Two camera images are needed for each velocity result. The first image shows the positions of the seed particles at one time. Then, a matching second image (after 30 µs) of the final positions of particles determines the movement of the fluid. Both camera images are divided into interrogation regions, which are used to measure the displacement of groups of dispersed droplets (based on a FFT correlation technique).
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Sample results are shown in Figs. 18 – 19. Unlike Cases 1 – 3, this case involves dispersed droplets in a co-flowing airstream. Interfacial drag imparted by emitted air from the spray nozzles contributes to droplet motion. Velocity vectors and streamlines of droplet motion are shown in Figs. 18 – 19. The diverging streamlines correspond to the conical emission of droplets and air from the atomizing nozzles of the spray bar.
The same problem is considered in this case, except that the air pressure in the atomizing nozzles is reduced to 15 psi gage pressure (see Figs. 20 – 22). This reduces effects of airstream inertia on convective acceleration, relative to gravity and interfacial drag.
Figure 20: Measured Velocities (Case 5)
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Figure 21: Horizontal Velocity Component (Case 5)
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Figure 22: Vertical Velocity Component (Case 5)
Measured velocity vectors are illustrated in Fig. 20. From right to left, the magnitude of the horizontal velocity component decreases due to interfacial drag between droplets and the airstream (see Fig. 21). This cross-phase diffusion contributes to decelerating the droplets. Similar trends are observed in Fig. 22. Interfacial drag occurs in the y-direction, while exceeding the influence of gravity, thereby contributing to deceleration of droplets (from right to left in Fig. 22). Similar trends are observed at elevations of 2.5, 5 and 10 mm within the view region of dispersed droplets.
V. CONCLUSIONS
In this article, momentum exchanges of droplets in dilute multiphase flows were investigated with Particle Image Velocimetry. Velocities and streamlines can be effectively characterized for groups of dispersed droplets in this method. Interfacial drag contributes to droplet deceleration in the flow direction. Gravitational effects of droplet acceleration in the y-direction can be measured experimentally with the PIV technique. Such advances have important implications for impinging droplets on iced surfaces. In particular, deflected droplets affect the collection efficiency and resulting ice shape of a helicopter engine bay cooling inlet.
ACKNOWLEDGEMENTS
Support of this research from Westland Helicopters Ltd, Natural Sciences and Engineering Research Council of Canada and Canada Foundation for Innovation are gratefully acknowledged.
REFERENCES [1] Milanez, M., Naterer, G. F., Venn, G., Richardson, G., ``Self Similarity of Cross-Stream Droplet Momentum Displacement in Dispersed Multiphase Flow'', Particle and Particle Systems Characterization, vol. 20, no. 1, pp. 62 - 72, 2003 [2] Hetsroni, G., Handbook of Multiphase Systems, Hemisphere Publishing Corp., McGraw-Hill Book Company, USA, 1982 [3] Milanez, M., Naterer, G. F., Venn, G., Richardson, G., “Volume Averaged Pressure Interactions for Dispersed Droplet Phase Modeling of Multiphase Flow”, AIAA Journal, vol. 42, no. 5, pp. 973 – 979, 2004
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[4] Naterer, G. F., Heat Transfer in Single and Multiphase Systems, CRC Press, Boca Raton, FL, 2003 [5] Tsuboi, K., “Computational and Analytical Study on Particle Flow Field Around a Circular Cylinder”, AIAA Paper 2001-2650, AIAA Fluid Dynamics Conference, Anaheim, CA, 2001 [6] Domann, R., Hardalupas, Y., “A Study of Parameters that Influence the Accuracy of the Planar Droplet Sizing (PDS) Technique”, Particle and Particle Systems Characterization, vol. 18, no. 1, pp. 3 – 11, 2001 [7] Jazayeri, S. A., Li, X., “Structure of Liquid-Sheet Sprays”, Particle and Particle Systems Characterization, vol. 17, no. 2, pp. 56 – 65, 2000 [8] Kim, W. T., Mitra, S. K., Li, X., Prociw, L. A., Hu, T. C. J., “A Predictive Model for the Initial Droplet Size and Velocity Distributions in Sprays and Comparison with Experiments”, Particle and Particle Systems Characterization, vol. 20, no. 2, pp. 135 – 149, 2003 [9] Naterer, G. F., “Multiphase Flow with Impinging Droplets and Airstream Interaction at a Moving Gas / Solid Interface”, International Journal of Multiphase Flow, vol. 28, pp. 451 – 477, 2002 [10] Lee, S., Dunn, T., Gurbacki, H. M., Bragg, M. B., Loth, E., ``An Experimental and Computational Investigation of Spanwise-Step-Ice Shapes on Airfoil Aerodynamics'', AIAA Paper 98-0490, AIAA 36th Aerospace Sciences Meeting, Reno, NV, January 12 – 15, 1998 [11] Chintamani, S. H. Belter, D. L., ``Design Features and Flow Qualities of the Boeing Research Aerodynamic Icing Tunnel'', AIAA Paper 94-0540, AIAA 32nd Aerospace Sciences Meeting and Exhibit, Reno, NV, January 10 – 13, 1994 [12] Hansman, R. J., Kirby, M. S., ``Comparison of Wet and Dry Growth in Artificial and Flight Icing Conditions'', AIAA Journal of Thermophysics and Heat Transfer, no. 3, pp. 215 – 221, 1987 [13] Buckingham, F. P., Haji-Sheikh, ``Cooling of High Temperature Cylindrical Surfaces Using a Water – Air Spray'', ASME Journal of Heat Transfer, vol. 117, pp. 1018 – 1027, 1995
[14] Sheppard, D. T., Gandhi, P. D., Lueptow, R. M., ``Understanding Sprinkler Sprays: Trajectory Analysis'', Fifteenth Meeting of the UJNR Panel on Fire Research and Safety, vol. 1, pp. 281 – 288, March 1 – 7, 2000 [15] Buchhave, P., ``Particle Image Velocimetry - Status and Trends'', Experimental Thermal and Fluid Science, vol. 5, pp. 586 - 604, 1992
[16] Yu, S. C. M., ``Steady and Pulsatile Flow Studies in Abdominal Aortic Aneurysm Models Using Particle Image Velocimetry'', International Journal of Heat and Fluid Flow, pp. 74 – 83, vol. 21, 2000 [17] Naterer, G. F., Chomokovski, S. R., Friesen, C., Shafai, C., ``Micro-machined Surface Channels Applied to Engine Intake Flow and Heat Transfer'', AIAA Paper 2003-4054, AIAA 36th Thermophysics Conference, Orlando, FL, June 23 - 26, 2003
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