Abstract

In this work, the dynamics of a liquid film on the surface of NACA 0012 airfoil placed in a high-speed air flow is investigated. The findings complement previous results obtained on time averaged ligament behavior and droplet sizes generated by the same airfoil. Experimental studies were carried out to assess the film thickness, droplet shedding, and the dynamics of the sheet. In the present work, air velocities up to 175 m/s were used with water films flowing between 1.4 and 2.6 cm2/s. The water film was introduced onto one side of the airfoil surface through a series of 0.5 mm holes separated by 1 mm at a location 35 mm downstream of the leading edge of the vane. The results were obtained using four experimental tools. The first is a point measurement of the dynamic film thickness using a confocal laser induced fluorescence method. This spatially resolved measurement provides time resolved measurement of the instantaneous liquid film thickness at specific points on the vane surface. This is complimented by time averaged images of the film thickness on the entire vane surface. Third, high speed videos are obtained to study the accumulation and breakup of the liquid at the trailing edge of vane. Finally, laser diffraction and Phase Doppler interferometry were used to document the spray dynamics downstream of the vane. The results illustrate that the average film thickness decreases with air velocity and increases with the water flowrate. The results are consistent with the previous studies and suggest that the dominant frequency of liquid film wave, ligament breakup length, drop size and spray concentration increase with the air velocity and is modestly affected by water flowrate. Finally, design tools are provided to predict the average film thickness and dominant frequencies of the film thickness, ligament breakup, spray concentration and droplet average size.

Introduction

The atomization of filmed liquid from a surface is found in numerous applications including fuel injection, annular film flow in pipes, and those involving vanes. In fuel injection, this phenomenon is central to prefilming-air-blast type atomizers where high-speed air flowing in the combustor of gas turbine is utilized to atomize thin liquid film. This results in a narrow droplet size distribution which promotes a homogeneous air-fuel mixture, stable flame, and lower pollutant emissions [16]. Similarly, in heat exchangers, thin annular film helps maintain efficient heat transfer and subsequent atomization enhances the cooling process [79].

The focus of this study extends to situations involving vanes, particularly in steam turbines for power generation. These turbines operate in wet steam stream in several stages downstream of a low-pressure turbine. A wet steam stream contains droplets in it and most of them are less than 1 microns in diameter. Thus, they flow at the same speed as steam and contribute to the generation of rotational force. Steam expands in turbine and then cools down below the saturation temperature, leading to condensation which forms a liquid film on the surfaces of the turbine vanes and eventually dispersing downstream as coarse droplets shed from the vane trailing edge. Due to inertial forces, these droplets cannot follow the steam flow and impact the tips of the downstream blades, which are rotating at high speed, damaging the blade surfaces and possibly causing “water droplet erosion” [10,11]. Options to address this include (1) the liquid film on the vane surface can be removed by slits, (2) the distance between stator and rotor blades is increased and/or (3) accelerating the droplet flow with steam. To make these countermeasures more effective, it is important to understand the behavior of the water film on the blade surface driven by the high-speed steam flow, the process of shed droplets from the blade trailing edge and atomization into droplets.

In the investigation of liquid film behavior in above applications, studies have been performed on a flat plate [12], atomizer [13,14], an airfoil [15,16], or an annular flow pipe [17]. Liquid is introduced onto the surface, often through porous materials or small holes, while air flows in parallel with the liquid film. The objective of these studies is to understand the behavior of liquid film on the surface, its accumulation at the edge, and atomization downstream. Previous studies have highlighted that when turbulent air coflows with a smooth liquid film, it results in a film with an inherently three-dimensional nature. This behavior is attributed to a combination of Kelvin-Helmholtz instabilities in the streamwise direction and Rayleigh-Taylor instabilities in the transverse direction [18]. These instabilities lead to the formation of elongated ligaments at the film's edge, which subsequently break into smaller droplets further downstream [19].

The early studies established that suitable time averaged simulations were able to capture the interface behavior between the gas phase and liquid and that the gas phase velocity field and liquid film thickness could be appropriately estimated [12,20,21]. Yet recent efforts illustrate that the process is dynamic and connected to wave formation and evolution. The earlier works also focus on the release of material from the liquid surface and subsequent entrainment into the air. Much of this work concentrates on behavior over an “infinitely long” domain. In the present work, an airfoil is used so the film evolution is effectively truncated at the trailing edge. Of particular interest has been the relationship between the gas phase velocity and liquid flow rates on the breakup behavior (e.g., ligament formation and length at breakup) and subsequent droplet sizes produced.

To date, a connection between the filming behavior, the accumulation, and the resulting breakup and atomization process has not been fully established. For example: Sattelmayer and Witting [12] and Gepperth et al. [22,23], have argued that film thickness has no significant impact on resulting droplet size, suggesting a limited connection between these factors. Lefebvre's work [24] suggested that increased film thickness always increases drop size while others [15] indicated that the effect of film thickness may vary depending on whether gas velocity is high or low. Similarly, Chaussonnet [25] discovered a strong link between the SMD of primary atomization and liquid accumulation at the wall's edge. In contrast, Okabe et al. [26] and Inamura [27] concluded that the liquid accumulation depends on the trailing edge thickness which becomes a decisive factor in the droplet size.

Given these varying findings, the relationship between film flow on the surface and subsequent atomization remains ambiguous. As a result, the main goal is to analyze water film dynamics (using FFT) and establish a connection. The particular focus is paid to the liquid sheet mode and higher air velocities up to 175 m/s.

Objectives.

This study is part of ongoing research on liquid film behavior on an airfoil surface in a High-Speed flow and the subsequent atomization downstream of the trailing edge. Previous research [28] investigated the effect of airfoil shape on the liquid flow airfoil surface and atomization downstream trailing edge. The effects of liquid physical properties were also assessed [29] and correlations were developed to predict key parameters including average ligament breakup length, and droplet size [16]

The present effort focuses on the understanding of water film dynamics and establishes a connection between liquid film flowing on the surface and atomization from the trailing edge. A total of 24 conditions are tested under three liquid flow rates at eight air velocities. The objectives are to obtain a detailed time and space resolved dataset associated with (1) the film behavior on a NACA 0012 vane in a high-speed flow (2) the subsequent accumulation, ligament formation and breakup process (3) the dynamics of the resulting spray and droplets downstream. The aim is to establish a clear and definitive link between film flow and atomization phenomena.

Methods

This work involves several experimental tools, i.e., average film thickness measurement with arrangements of LIF methods, liquid accumulation and ligament breakup visualization with high-speed video camera, and droplet characterization with Phase Doppler and laser diffraction methods.

Experimental Setup

Test Section.

The test stand, test section and vane dimensions are shown in Figs. 13, respectively. Details can be found from Ref. [16]; however, a brief description on each experimental setup will be provided in the following subsections.

Fig. 2
Final test section geometry (mm)
Fig. 2
Final test section geometry (mm)
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Fig. 3
NACA 0012 vane details (mm)
Fig. 3
NACA 0012 vane details (mm)
Close modal

The test section used was developed by considering reasonable air flow limits for the facility (∼0.8 kg/s), desired test section velocities (up to 200 m/s), minimized overall pressure loss, and desired liquid flow rates expressed as volume flow per unit width of the vane (0.01 to 5 cc/(cm s)). A maximum water flowrate of less than 8 liters per hour was desired. A combination of analytical and CFD simulations were utilized to guide the design.

First, one-dimensional isentropic flow analysis was performed. Mach number and velocity for compressible flow are defined as in Eq. (1)
(1)

where γ is specific heat ratio of air (1.4), Po is the stagnation pressure and ρ0 is the stagnation density of the inlet and pb is the static pressure at the outlet. To achieve a flow velocity of up to 200 m/s at the outlet, a pressure ratio, P0/pb, of at least 1.2 or more is required. The airfoil dimensions and test section cross-sectional area were established considering 1D compressible flow analysis. The vane width was determined from the target water flow requirements. The area of the test section was determined by the 0.8 kg/s air mass flowrate limit, and the duct height was set to 100 mm in this study to minimize wall effects. In this study, an NACA 0012 vane was utilized and scaled in length and thickness to attain the desired velocities with the air flow limit considered. The resulting vane thickness was set to 12 mm, and area ratio was set to 1.14. According to the one-dimensional choke flow analysis, the critical pressure ratio was set to 1.3 in this study.

The duct width was set to 40 mm based on the 0.8 kg/s maximum air flowrate. To condition the air flow approaching the vane, a transition section was developed, and a 50 mm long honeycomb straightener used. As a result, the final test section design consists of four-parts: inlet pipe, honeycomb, chamber, and vane section. The flow area in the honeycomb section is larger than that at the maximum thickness of the vane to avoid choking the flow.

To evaluate the flow in the test section, numerical simulations were performed by ansyscfx 2019 r3. Reference [16] shows the computational model. In the numerical works, the actual honeycomb structure geometry was modeled. To obtain the relationship between pressure ratio and inlet mass flowrate, the inlet mass flow boundary condition was varied from 0.5 to 1.0 kg/s, and outlet boundary condition was set to ambient pressure. The computational mesh was generated by ansysfluentmeshing 2019 r3. The turbulent model was set to SST k-omega, and steady-state simulation was performed to assess the flow field in the test section. The relationship between the inlet mass flowrate and the pressure ratio of the vane section is also shows in Ref. [16]. According to it, the pressure ratio across the test section is 1.27 at an inlet mass flowrate of 0.8 kg/s—this essentially matches the critical pressure ratio originally targeted.

Mach number contours around the NACA 0012 vane with the inlet mass flowrate of 0.8 kg/s are also presented in Ref. [16]. The peak Mach number is up to approximately 0.7 and no separation occurs around the test vane. Thus, the CFD indicates that the overall test bed, designed using one-dimensional theory, has the critical pressure ratio as intended. The CFD results also confirmed that there was no separation under the maximum flow condition.

The water film holes are positioned 35 mm downstream of the leading edge which is upstream of typical boundary layer separation. Moreover, the location of 35 mm was chosen to allow sufficient development of the water film and to avoid disturbances that could be caused by leading-edge effects. The span of the airfoil used is 40 mm. The test section has transparent walls and the airfoil is held with four screws. The transition from round to rectangular and the flow conditioning honeycomb were 3D printed using Accura 5530 material (polycarbonate like) and postcured to withstand temperatures up to 170 deg C. The vane surface finish was specified at 3.2 Ra. Air was fed using a series of Ingersol Rand air compressors generating flow at up to 10 bars. The air flowrate was set by parallel manual control valves and monitoring the pressure upstream of a critical flow orifice with a 22.25 mm throat diameter (Flow Technologies, Inc., Tempe, AZ). A pitot probe (Dwyer Series 160 Stainless Steel) was used to measure the freestream velocity at the exit of the test section to confirm the analysis. The expression is shown in the following equation:
(2)

where pv is the velocity pressure in inches of water, D is the air density in lb/cu. ft. calculated from D=1.325pBT, where Barometric Pressure in inches of mercury and T is absolute temperature. On the other hand, pressure vessels were used to hold and pressurize the distilled water. These vessels were pressurized using nitrogen and delivered into the liquid lines via ball valves. The Coriolis mass flowmeter was used to accurately determine the flow rates of water. The line was controlled by needle valves and tubes were used to push the water into the airfoil. The liquid film was introduced onto one side of the airfoil surface via 26 holes, each measuring 0.5 mm in diameter and spaced 1 mm apart. These holes are positioned 35 mm downstream from the leading edge and 65 mm upstream from the trailing edge.

High Speed Video.

A FASTCAM Nova S9 type 900K-M-16GB high speed video (HSV) camera was used to document the liquid behavior. The camera field of view was aligned to the trailing edge of the vane with a resolution of 1024 x 576 pixels corresponding to 40 mm × 22.5 mm view. An Infinity long-distance microscope with a CV-4 objective lens was used to collect the images. Figure 4(a) illustrates the two setups used for the high-speed imaging results. The first imaging setup obtained images of the liquid film on the vane surface. These images were obtained using front illumination (Light Source A in Fig. 4(a)). Video was recorded at 15,000 frames per second (fps) with a 10-microsecond exposure time and a record duration of 0.1667 s.

Fig. 4
(a) Experimental setup to visualize liquid film flow and sheet breakup and (b) image processing for ligament length
Fig. 4
(a) Experimental setup to visualize liquid film flow and sheet breakup and (b) image processing for ligament length
Close modal

The second type of images were obtained using backlit shadowgraphs produced by illuminating the liquid sheet with a 500 W halogen lamp (Light Source B in Fig. 4(a)) which was diffused with a frosted glass plate positioned between the lamp and the test section.

For the present work, the emphasis was on the ligament breakup process immediately downstream of the trailing edge of the vane. An example still image of ligaments is shown in Fig. 4(b). An in-house matlab code was developed to (1) process high speed video images, (2) binarize images, (3) isolate the ligament in each frame, and (4) determine the length of the ligament at its breakpoint. The basic approach is derived from SAE Surface Vehicle Recommended Practice J2715 [30]. However, the binarization threshold was challenging due to the broad and flat “valley” that forms between the two peaks of the gray level histogram (e.g., the intensity behavior from 25 to 150 pixels. To address this, Otsu's method was incorporated to automatically determine the threshold between background and ligament by considering the maximum interclass variance (product of the variance of the intensity values and the probability of number of pixels for each class) on each frame [31,32]. The binary images were filtered by extracting the largest blob and filling holes (Fig. 4(c)). Figure 3 depicts the complete process used within the code.

The breakup length was determined using 24 sets (24 conditions) of high-speed video images. Each image was divided into four equal sections (each with a 10 × 22 mm view) and the middle two sections were chosen to determine the ligament length. The center of the vane location was consistent with other experimental measurements reported in this work. Approximately 500 images from each condition were used to find the maximum average length at the point of breakup.

Spray Concentration and Droplet Characteristics.

A Malvern Insitec ST97 ensemble particle concentration and size instrument (EPCS) with rtsizer software was used to collect and process the data [16]. The data acquisition was performed with “flashmode” which records 2500 snapshots of data each second. Measurements were taken at 10 and 50 mm downstream of the trailing edge of the vane. At 10 mm, only the intensity of the transmitted light was of interest as the ligaments present would affect the accuracy of any droplet sizing [14,26]. The transmitted light is an indicator of the relative spray concentration. As a result, a time varying record of the relative spray concentration is recorded.

Phase Doppler interferometry (PDI; TSI FSA 4000) was used to measure droplet size and velocity. PDI is a nonintrusive method that measures the droplet characteristics on the interferometry principle [33]. This diagnostic technique consists of transmitter and receiver components. The transmitter emits four laser beams converging at one focal point forming an interference pattern. A receiver collects the refracted light at 30 deg with respect to the transmitter centerline. The droplet diameter is measured based on the fringe spacing difference in the inference pattern whereas velocity is measured by monitoring the movement of these fringes. Consistent with the laser diffraction method, the PDI measurements were taken at 70 mm downstream of trailing edge.

Liquid Film Thickness.

Two methods were used for measuring film thickness. The first is a confocal laser induced fluorescence (LIF) method and the second is a LIF imaging system. The confocal system was used to determine the time resolved film thickness at a point using a LIF approach. This method was adopted after consideration of various approaches summarized by Tibiriçá [34]. For the current setup with the airfoil positioned in the center of the rectangular duct, a noninvasive method was desired, especially considering the high air velocities tested. Ultimately, of the optical approaches considered (e.g., interferometry, absorption, fluorescence), confocal LIF method was selected based on the desired attributes for the experimental configuration used. This method has been used in the past, possibly first for the measurement of film thickness in liquid fuel atomizers in the early 1980s by Driscoll, Schmitt, Stevenson and coworkers [35,36].

Figure 5 illustrates the details of the setup used. A 75 mm focal length f/5 transceiver lens was used with a 488 nm diode laser. A dichroic mirror (Semrock FF505-SDi01-25x36) was used to reflect the redshifted fluorescence emitted from the fluorescein dyed water. A concentration of 3.4 mg/litter of water was used to attain a reasonable signal while ensuring transmittance into the liquid film of at least 90%. A Thorlabs photodiode (SM05PD1A) was used to collect the backemitted fluorescence light. A Yokogawa digital oscilloscope (DLM3034) was used to record 10 s chunks of data at a rate of 125 kHz. The spot size of the focused beam is approximately 90 microns.

Fig. 5
Confocal LIF System
Fig. 5
Confocal LIF System
Close modal
To convert the voltage signal into film thickness, a calibration process was utilized in which sample cells (Starna) with optical paths of 100, 200, 500, and 1000 microns were filled with the dyed test liquid. In addition, a blank cell was used to establish any signal offset. A typical calibration curve is shown in Fig. 6. As shown, the voltage signal has an exponential dependence with the film thickness. This is consistent with the relationship between the film thickness and the fluorescence signal as given in Eq. (3) [35]
(3)
Fig. 6
Typical calibration curve for confocal LIF System
Fig. 6
Typical calibration curve for confocal LIF System
Close modal

To validate the point measurement method, the air and water flow conditions of Inamura [15] were set and LIF point measurements of film were obtained at 2 mm upstream of the vane trailing edge at the center of the vane. A comparison of the results is shown in Fig. 7 and exhibits satisfactory agreement and trend with water flow and air velocities. An advantage of the current optical setup, besides being nonintrusive, is that it can also provide time resolved information.

Fig. 7
Comparison of confocal LIF system time averaged film thickness results with those of Ref [15]
Fig. 7
Comparison of confocal LIF system time averaged film thickness results with those of Ref [15]
Close modal

The experimental setup for the LIF film imaging method is shown in Fig. 8(a). An Optotune® reluctance force laser despeckler was placed between the 488 nm laser and the test section. The despeckle unit acts as a beam homogenizer and beam expander. An Andor i-Star (1024 × 1024 pixels) ICCD camera with a 50 mm Nikon lens and 532 nm bandpass was used to capture the liquid film images. 10 frames were obtained at a frame rate of 0.79 Hz with an exposure time of 0.011 s and were averaged. The images were saved in 16 bit (0-65535 Gray Value) Tag Image File Format (TIFF). The despeckler did not fully homogenize the intensity of the illumination beam. But this was accounted for by measuring the fluorescence intensity emitted from a paper sheet mounted on the vane and applying a correction factor over the field of view.

Fig. 8
(a) Schematic of LIF imaging setup and (b) typical calibration curve
Fig. 8
(a) Schematic of LIF imaging setup and (b) typical calibration curve
Close modal

To convert gray values into film thickness, a calibration curve was used. The film thickness was measured by the confocal LIF method 2 mm upstream of the vane trailing edge at the center of the vane. Hence, the gray value seen in the LIF Images corresponded to that particular thickness. A typical calibration curve is shown in Fig. 8(b). Figure 9 shows an example instantaneous LIF Film Image at Ug = 100 m/s.

Fig. 9
Example LIF film imaging at Ug = 60 m/s
Fig. 9
Example LIF film imaging at Ug = 60 m/s
Close modal

Test Plan.

To facilitate the development of correlations, a factorial design approach was used to develop the test matrix so that analysis of variance could be applied to the results obtained. The parameters varied were air velocity and the water flowrate. While the plan followed is effectively a two factor, three level design, several sets of data were obtained over the range of parameters to cover the full range shown in Table 1. Analysis of variance identified the statistically significant parameters influencing the measured responses (in this case the frequency containing the peak energy content from an FFT of the time resolved results).

Table 1

Ranges for factorial design

ParameterLowMidpointsHigh
Air velocity, Ug (m/s)30 (We=16.01)a40,60,80,100,125,150175 (We=510)
Water Flow, MFRl (g/s)3.5 (1.4 cm2/s)b5.0 (2.0 cm2/s)6.5 (2.6 cm2/s)
ParameterLowMidpointsHigh
Air velocity, Ug (m/s)30 (We=16.01)a40,60,80,100,125,150175 (We=510)
Water Flow, MFRl (g/s)3.5 (1.4 cm2/s)b5.0 (2.0 cm2/s)6.5 (2.6 cm2/s)
a

We is based on the air velocity and the trailing edge characteristic length of 1 mm.

b

For water, 1.4 cm2/s = 3.5 g/s/2.5 cm = 3.5 cm3/s/2.5 cm.

Results

In this section, several results are presented, starting with the average film thickness, film thickness dynamics, ligament breakup dynamics and the dynamics concentration, and droplet sizes of the spray downstream of the vane.

Experimental Results

Average Film Thickness.

Figure 10 compares average film thickness between Confocal LIF and LIF Imaging. The film thickness was found to decrease with increased air velocity. Further, it was also found to increase with water flowrate. It is noted that, for the conditions studied, the lower air velocities and water flow rates resulted in “rivulet” mode of water flow on the vane rather than a full sheet. In such flow modes, the liquid does not form a continuous, uniform film over a surface but instead forms discrete, elongated channels or rivulets. These rivulets are essentially thin streams of liquid that flow in separate paths rather than spreading evenly across the surface. The behavior of these two modes is significantly different. For the current effort, the focus is on the sheet mode.

Fig. 10
Average film thickness comparison between confocal LIF and LIF imaging
Fig. 10
Average film thickness comparison between confocal LIF and LIF imaging
Close modal

Film Wave, Ligament Breakup, and Spray Concentration Dynamics.

In this section, FFTs were taken of the time records of (1) the film thickness, (2) the ligament breakup length, and (3) the spray concentration 10 mm below the vane. Appendix lists all time-average values, and Fig. 11(a) shows the measurement locations. Result for each point is the frequency containing the majority of the power in the spectra of each measurement time series. Figure 11(b) shows an example of the dynamic liquid film behavior using Confocal LIF method at Ql = 2.0 cm2/s, Ug = 100 m/s, whereas Fig. 11(c) shows resulting FFT spectra (amplitude versus frequency). A plot inside Fig. 11(c) shows a zoomed view of a dotted section illustrating the definition of the dominant frequency.

Fig. 11
(a) Measurement locations for film thickness, ligaments length and spray concentration, (b) an example time resolved film thickness at Ql = 2.0 cm2/s, Ug = 100 m/s, and (c) resulting FFT amplitude versus frequency
Fig. 11
(a) Measurement locations for film thickness, ligaments length and spray concentration, (b) an example time resolved film thickness at Ql = 2.0 cm2/s, Ug = 100 m/s, and (c) resulting FFT amplitude versus frequency
Close modal

Figure 12 compares the dominant frequency from the FFT analysis of liquid film wave, spray concentration, and ligament breakup. The results for liquid film wave correspond to the dominant frequency of film thickness measured at 2 mm upstream of the vane trailing edge at the center of the vane using the confocal LIF method. The spray concentration frequency corresponds to the dominant frequency of the laser diffraction transmission intensity measured at 10 mm downstream of the vane trailing edge using laser diffraction method. The ligament breakup frequency corresponds to the dominant frequency at which the ligament reaches its maximum length prior to breaking as recorded by HSV. The image processing method is described in Fig. 4(b) and [16]. The HSV images were divided into five sections each having dimensions of 8 × 22.4 mm. The middle 1/5 section (corresponding to the center segment of the vane trailing edge) was chosen to study the breakup length. As illustrated, no film wave frequency was observed at low air velocities probably because of “rivulet mode.” As a result, since the confocal LIF is a point measurement technique, the film detection for rivulet mode was not indicative of the film mode behavior and results for these cases cannot be compared with full sheet mode. In general, the dominant frequencies are found to increase with increased air velocities. However, little effect due to the increase in water volume flowrate is observed.

Fig. 12
Dominant frequency comparison between liquid film wave, spray concentration and ligament breakup
Fig. 12
Dominant frequency comparison between liquid film wave, spray concentration and ligament breakup
Close modal

Although raw data were obtained at different locations and from different measurement techniques, the dominant frequencies associated with each phenomena exhibit very good agreement. This indicates a strong connection between the dynamic behavior of the liquid film on the vane, its subsequent accumulation and breakup at the trailing edge, and the resulting downstream spray concentration. Hence it is clear that the liquid film thickness is a substantial factor in atomization as it directly influences the spray dynamics.

Droplet Dynamics Downstream of the Vane.

The final result is the impact of the above dynamics on the resulting spray SMD. Figure 13 shows the dominant frequency comparison of SMD and laser transmission using laser diffraction and droplet velocity using PDI at 50 mm downstream of the vane trailing edge at the center of the vane. The 50 mm distance downstream was established as the location at which the droplets were fully spherical (and therefore able to be measured by laser diffraction and PDI) based on the evaluation of the HSV. Ligament fracture was seen to be completed within 20 mm of the vane, and that primary atomization was also complete shortly thereafter. Although, a few traces of secondary breakup were noted at 50 mm for the lower air flow velocities, but at 75 m/s and above, atomization appeared to be completed. This consistency was seen in Ref. [16] and Inamura [15] showed that the average drop size does not change with downstream distances past 50 mm for velocities above 33 m/s [12]. Similar to Fig. 12, Fig. 13 also shows that the dominant frequency increases with an increase in air velocity and doesn't change much with the water volume flowrate. This further connects the atomization process to the origination of waves on the vane surface.

Fig. 13
Dominant frequency comparison between SMD, transmission and droplet velocity at 50 mm downstream of the trailing edge of vane
Fig. 13
Dominant frequency comparison between SMD, transmission and droplet velocity at 50 mm downstream of the trailing edge of vane
Close modal

In summary, a connection between liquid film flowing on the surface upstream of the trailing edge, sheet breakage at the trailing edge, and corresponding droplets generated downstream of the trailing edge was established. The overall behavior in terms of the dominant frequency in the corresponding power spectrum of the parameter studied is depicted in Fig. 14.

Fig. 14
Dominant frequency upstream of trailing edge, at the trailing edge and downstream trailing edge
Fig. 14
Dominant frequency upstream of trailing edge, at the trailing edge and downstream trailing edge
Close modal

Correlations.

In this section, correlations are presented for liquid film thickness, film wave frequency, ligament frequency and SMD frequency. An analysis of variance of the measured results was performed to quantify the impact of the parameters studied. 24 individual measurements covering the ranges shown in Table 1 were used.

Average Film Thickness.

The average film thickness correlation is expressed in Eq. (4), and measured versus calculated film thickness is shown in Fig. 15. The fit coefficient of variance (R2) is 0.9732 and the coefficient of variance between the predicted and measured film thickness is, on average, +/− 2.89%
(4)
Fig. 15
Measured versus calculated average film thickness
Fig. 15
Measured versus calculated average film thickness
Close modal

The mass flowrate and air velocity influence on the film thickness is shown in Fig. 16. The lower air velocities have a higher impact in comparison to higher air velocities. Similar results were also reported by the researchers in the past. Gepperth el. al. [23] used laser focus displacement meter to measure the film thickness. They found film thickness to be thinner with the air velocity. Rizk and Lefebvre [24] used prefilming type of atomizer and film thickness was measured using a contact needle probe method. It was concluded that increased air velocity exerts high shear forces on the liquid surface and causes film thickness to be thinner.

Fig. 16
Mass flow rate and air velocity impact on film thickness
Fig. 16
Mass flow rate and air velocity impact on film thickness
Close modal
Also, according to Mayer's model [37,38] expressed in Eq. (5), the liquid film thickness varies directly with the square root of liquid flowrate and inversely with the air velocity
(5)

where fi is the interfacial shear factor which depends on the Reynold's number. For this study, fi=0.016Re0.133 [39].

Film Wave, Ligament Breakup, and Spray Concentration Dynamics.

Analysis of variance was applied to (1) Film frequency (fL) at 2 mm upstream trailing edge of vane, (2) ligament breakup frequency (flb) at the trailing edge, and (3) SMD frequency (fSMD) at 50 mm downstream trailing edge of vane in order to identify the statistically significant factors for each. The correlations are given in Eqs. (6)(8), respectively, and calculations are compared with measurements in Fig. 17. R2 and coefficient of variance between the predicted and measured for fL, flb, fSMD are 0.93, 10.4%; 0.86, 19%; 0.77, 29.2%, respectively
(6)
(7)
(8)
Fig. 17

Measured versus calculated dominant frequencies upstream of trailing edge, at the trailing edge and downstream trailing edge

Fig. 17

Measured versus calculated dominant frequencies upstream of trailing edge, at the trailing edge and downstream trailing edge

Close modal

It is noteworthy that the predictive models in this study are based on the available experimental data and may behave differently if applied outside the studied conditions. For example, the dominant frequency of SMD has been validated only up to an air velocity of 100 m/s. Therefore, calculations for air velocities above 100 m/s may become inaccurate, as shown in Fig. 17.

The results demonstrate that air velocity is the dominant factor with some, but less impact of the water flowrate. The trend is similar to that reported previously [40,41]. An increase in the dominant frequency with the air velocity occurs because high air velocity leads to increased kinetic energy of air which results in stronger interactions with the liquid film. Also, the liquid waves generated on the surface are caused by the Kelvin-Helmholtz instability. Wavelength correlations [15,19,22] suggest that as the air velocity increases the wavelengths of these waves decrease which eventually leads to a contrary effect on the wave frequency.

In comparison with Sattelmayer and Witting [12] and Gepperth et al. [22,23], this study illustrates that the film flowing on the surface is important in determining the mean droplet size, agreeing with Lefebvre' work [24] and Inamura [15].

Conclusions

In this work, an experimental investigation of dynamics of water film flowing on a NACA0012 airfoil was performed. Air velocities up to 175 m/s were used with water film flows between 1.4 and 2.6 cm2/s Conclusions drawn include:

  1. (1)

    Film thickness

    1. 1.1 The average liquid film thickness decreases with an increase in air velocity, while it increases with water flow rate.

    2. 1.2 Two optical methods i.e., Confical LIF and LIF imaging for measuring film thickness are employed and give consistent results. Further, the time average results agree closely with previous work [15] for comparable conditions.

    3. 1.3 The analysis of variance also confirms that both water mass flow rate and air velocity impact the film thickness.

  2. (2)

    Frequency analysis

    1. 2.1 Dominant frequency is directly proportional with the air velocity and is slightly influenced by the liquid flow rate.

    2. 2.2 Frequency analysis of the time resolved measurements of film thickness, ligament breakup, spray concentration, droplet mean size and droplet velocity indicated consistent trends. The dominant frequency for each measurement showed a high level of consistency which indicates a clear connection between the liquid film on the vane, its breakage at the trailing edge and the downstream spray behavior, shown further in Fig. 14.

  3. (3)

    Design tools

    1. 3.1 Correlation are developed to estimate the mean film thickness, the dominant frequencies of the film thickness, ligament breakup and droplet average size. These complement “the previous tools” developed for average ligament length at breakup and average droplet size developed previously [16].

The implications of the present effort are that the film thickness is dependent on the air and water flow rates. Also, the film flowing on the surface is connected to its breakage on the atomizing edge and resulting droplets. In parallel works from the authors, the effects of airfoil shape and liquid physical properties on the film thickness, maximum ligaments length and droplet mean diameter are explored. Future research will explore the impact of body forces on liquid film behavior under relatively low air flow conditions, which may promote the formation of small rivulets on the airfoil surface. Also, the effect of trailing edge thickness and shape on film behavior will be examined. Since the correlations developed in this study use dimensional parameters (Ug and Ql), their application is somewhat limited. By varying trailing edge thickness, future work will encourage the use of nondimensional parameters, such as the Weber number, where the characteristic length will be the trailing edge thickness.

Acknowledgment

The authors would like to thank Mitsubishi Heavy Industries, Ltd., for the financial and technical support provided over the progress of the current project.

Data Availability Statement

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

Nomenclature

A =

absorption coefficient of dye molecule

ANOVA =

analysis of variance

D32 =

Sauter mean diameter (SMD) representative diameter

E =

quantum efficiency of dye molecule

FFT =

Fourier fast transform

fL =

liquid film wave frequency

fT10mm =

spray concentration dominant frequency 10 mm downstream of vane

flb =

ligament breakup dominant frequency

fT50mm =

spray concentration dominant frequency 50 mm downstream of vane

fSMD =

SMD frequency

GV =

gray value

HSV =

high speed video

ICCD =

intensified charge coupled device

L =

film thickness (μm)

LIF =

laser induced fluorescence

MFRl =

liquid mass flow rate (g/s)

Pf =

fluorescence emission power

t =

time (s)

Ug =

gas velocity (m/s)

We =

Weber number (based on the trailing edge characteristic length of 1 mm)

Ρl =

liquid density (kg/m3)

Subscripts
l =

liquid

g =

gas

Appendix: Mean Values at Dominant Frequencies Shown in Figs. 12, 13, and 15.

Table 1
Water MFRAir VelocityLengthThicknessSMDVelocity
g/sm/smmumumm/s
3.53022.0476.52393.92-
4022.01289.5283.38-
6018.01125.08179.8324.44
8018.9169.23133.9432.72
10014.5062.31111.6742.15
12512.3930.2497.01654.85
15011.4835.1784.8563.44
17510.1943.1981.685.89
53022.01498.5383.3-
4022.01274.82280.27-
6022.01161.27181.4923.90
8018.5095.51137.0732.2
10016.3988.97113.3740.45
12515.8047.2891.6152.35
15013.4256.6476.8968.62
17513.1166.1772.5683.31
6.53019.2452.58427.99-
4018.70323.0316.29-
6022.01209.65183.5923.7
8020.12130.05126.3032.55
10021.11117.5109.2440.26
12517.2468.4388.0350.10′
15014.95′80.3175.6765.35
17513.896.0664.3479.59
Water MFRAir VelocityLengthThicknessSMDVelocity
g/sm/smmumumm/s
3.53022.0476.52393.92-
4022.01289.5283.38-
6018.01125.08179.8324.44
8018.9169.23133.9432.72
10014.5062.31111.6742.15
12512.3930.2497.01654.85
15011.4835.1784.8563.44
17510.1943.1981.685.89
53022.01498.5383.3-
4022.01274.82280.27-
6022.01161.27181.4923.90
8018.5095.51137.0732.2
10016.3988.97113.3740.45
12515.8047.2891.6152.35
15013.4256.6476.8968.62
17513.1166.1772.5683.31
6.53019.2452.58427.99-
4018.70323.0316.29-
6022.01209.65183.5923.7
8020.12130.05126.3032.55
10021.11117.5109.2440.26
12517.2468.4388.0350.10′
15014.95′80.3175.6765.35
17513.896.0664.3479.59

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