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Research Papers: Techniques and Procedures

# Feature Correlation Velocimetry for Measuring Instantaneous Liquid Sheet Velocity

[+] Author and Article Information
K. S. Siddharth

Department of Applied Mechanics,
Chennai 600036, India
e-mail: sidacmiitm@gmail.com

Mahesh V. Panchagnula

Professor
Mem. ASME
Department of Applied Mechanics,
Chennai 600036, India
e-mail: mvp@iitm.ac.in

T. John Tharakan

Liquid Propulsion Systems Centre,
Indian Space Research Organization,
Thiruvananthapuram 695547, India
e-mail: tharakan12@yahoo.com

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received March 6, 2016; final manuscript received March 22, 2017; published online June 20, 2017. Assoc. Editor: Peter Vorobieff.

J. Fluids Eng 139(9), 091401 (Jun 20, 2017) (10 pages) Paper No: FE-16-1141; doi: 10.1115/1.4036593 History: Received March 06, 2016; Revised March 22, 2017

## Abstract

We describe a novel nonintrusive velocimetry technique for measuring the instantaneous velocity field on a liquid sheet. Short wavelength corrugations are naturally formed on the surface of a liquid sheet when the sheet interacts with ambient air. This method, called feature correlation velocimetry (FCV), relies on cross-correlation of such short wavelength corrugations visualized on the liquid sheet surface when captured using a high-speed camera. An experimental setup was created for producing a liquid sheet of known thickness and velocity. After imaging the liquid sheet with a high-speed camera, cross-correlation was employed at various spatial locations on the liquid sheet. To examine the fidelity of the method, laser Doppler velocimetry (LDV) measurements were obtained for a range of flow rates at the same spatial locations and were compared with the FCV values. The FCV values were found to be consistently within 7% of the LDV readings with the FCV measurements being consistently less than those from the LDV. In order to examine the cause of the bias error, a theoretical model of the liquid sheet has been developed. Based on the model predictions, the bias error was observed to scale as $U3/2$, where $U$ is the local instantaneous liquid sheet velocity. After correcting for this bias error, a good match was observed between the FCV and the LDV readings. As an application of the FCV method, the near-nozzle region of an annular sheet exiting a spray injector has been characterized.

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## Figures

Fig. 1

The schematic of the calibration experimental setup is shown in Fig. 1(a). The imaging arrangement has been aligned as shown. Figure 1(b) shows a bright field photograph of the liquid sheet exiting the slit. The liquid sheet can be seen adhering to the two 1 mm SS rods. The dot shown in Fig. 1(b) represents our region of interest.

Fig. 2

Collage of three successive images showing the advection of four different features present on the surface of the liquid sheet. The dotted line represents the approximate center of the random shaped features. The images were captured at 6000 fps. Feature advection can be noticed from this collage.

Fig. 3

Comparison of the inbuilt high-pass filters in PIVlab®. High-pass filtering eliminates the long wavelength corrugations. Among the set of filters, 100px filter represents the filter with the lowest cutoff wavenumber and 25px is one that has the highest cutoff wavenumber. 25px filter is used throughout this study.

Fig. 4

Velocity vector map obtained from postprocessing one of the image pairs. 25px filtering was applied prior to the postprocessing. Most of the vectors can be seen pointing in the axially downward direction indicating the general motion of the liquid sheet. Each vector represents different spatial locations where velocity measurements could be obtained.

Fig. 5

The schematic showing the location of the 2D miniLDV™. The dotted lines represent the laser beams. The probe volume is aligned inside the liquid sheet and located 10 mm beneath the slit exit along the centerline of the liquid sheet to get the actual sheet velocity.

Fig. 6

Comparison of the PDFs obtained using different high-pass filters in PIVlab®. PDF obtained from the LDV measurements is also shown. The velocity PDF from the 25px filter is closest to the PDF from the LDV.

Fig. 7

Comparison of LDV mean and FCV mean at two spatial locations of 10 mm and 15 mm from the slit exit along the centerline of the liquid sheet. The figure has been cropped for easy demonstration. The mean and the standard deviation of the velocity PDF at the same locations from both the LDV and FCV measurements are shown in the inset table.

Fig. 8

The instantaneous LDV velocity values from six realizations of the draining experiment. The six vertical lines named (a)–(f) represent the six time instants where the high-speed imaging was performed. FCV data was obtained for a time span of 0.28 s (1000 images from FCV) at each of the instants. The measurements from LDV and FCV were both obtained at 10 mm from the slit exit along the centerline.

Fig. 9

Instantaneous images of the 25px preprocessed images of six different times instants considered (in the order of decreasing velocities from left to right) of the draining phase. Each image represents the cropped area of the near slit region for corresponding velocity of the liquid sheet. All the images were captured at 3600 fps.

Fig. 10

Temporal mean velocity and corresponding standard deviations from FCV and LDV measurements for six different flow rates considered. The six flow rates correspond to the six different time instants of draining where the FCV measurements were obtained.

Fig. 13

Collage of three successive images of near-nozzle region of GCSC injector. The flow conditions were 3.96 lpm of water and 100 lpm of air. The dotted white box in each of the images encloses one of the corrugations visualized. The set of images were recorded at 6000 fps.

Fig. 12

Plot of c versus U from the draining phase of the slit experiment. FCV for all the cases were calculated at the same spatial location of 10 mm from the slit exit along the centerline. The solid line is the prediction from Eq. (12), which is also shown in the plot.

Fig. 11

Schematic of the interface of a liquid sheet. U represents the true velocity of liquid sheet, c represents the velocity of the short wavelength corrugation, y0  represents the infinitesimal amplitude of the corrugation, and λ represents the wavelength of the corrugation. The dotted wave denotes the motion of the short wave on the surface of the liquid sheet at the next time instant.

Fig. 14

Plot of instantaneous axial velocity versus time (a) before the FCV bias velocity correction and (b) after the bias velocity correction. The mean values are also represented in both the graphs.

Fig. 15

Plot of instantaneous corrected swirl velocity versus time. The mean value is also represented in the graph.

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