light field imaging of fuel droplets and...

16th Int Symp on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 09-12 July, 2012

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Light Field Imaging of Fuel Droplets and Sprays Alexandra H. Techet1,*, Barry E. Scharfman1, Thomas B. Milnes1, and Douglas

P. Hart1

1: Department of Mechanical Engineering, Massachusetts Institute of Technology, USA *Correspondent author: [email protected]

Abstract Light field imaging (LFI) and synthetic aperture (SA) refocusing techniques are married to achieve three-dimensional (3D) reconstruction of fuel droplets and unsteady spray flow fields. A multi-camera array is used to capture the light field and raw images are reparameterized to digitally refocus the flow field post-capture into a volumetric image. LFI with SA refocusing facilitate full 3D reconstructions and allow the camera array to effectively “see through” partial occlusions in the scene. Flow features, such as individual droplets, can be located in three-dimensions by refocusing throughout the volume and extracting features on each plane, making this method particularly attractive for use in multiphase flows that contain many fine features, such as droplets or bubbles, which limit visibility in the depth direction. It is also well suited to turbulent, unsteady flow problems. In this paper, three-dimensional light field imaging and synthetic aperture refocusing techniques have been applied to several experiments to demonstrate a wide range of applications to fuel sprays and combustion studies, including the sprays produced by the atomization of liquid jet in cross flow and the breakup of a turbulent liquid sheet. Water and air are used to simulate these flows and highlight the benefits of the technique. Both fine and coarse structures within these multiphase flows have been identified and located in three dimensions. We present fundamentals of the system hardware and software involved in light field imaging and the synthetic aperture technique as applied to these flows. 1. Introduction

A fundamental challenge in experimental fluid mechanics is the accurate spatial and temporal resolution of three-dimensional, multiphase fluid flows. Whether for determining new fluid phenomena, evaluating new designs, or benchmarking computational codes, fully spatially- and time-resolved experimental data is paramount. Given recent advances in camera and imaging technologies, and the growing prevalence of commercially available light field imaging systems, the opportunities for obtaining such data is achievable at a lower cost and with greater resolution and computational savings. Stemming from the computer vision communities, light field imaging (LFI) and synthetic aperture (SA) refocusing techniques have been combined in a new method to resolve three-dimensional flow fields over time (Belden et al. 2010). This technique is aptly suited for sprays, particle laden and multiphase flows, as well as complex unsteady and turbulent flows.

At the core of light field imaging, a large number of light rays from a scene are collected and subsequently reparameterization based on a calibration to determine a 3D image (Isaksen et al. 2001). In practice, one method used by researchers in the imaging community for sampling a large number of rays is to use a camera array (e.g. Vaish et al. 2004, 2005) or more recently, a single imaging sensor and a small array of lenslets (lenslet array) in a plenoptic camera (e.g. Lynch 2011). The novelty of the approach presented herein is the application of the reparameterization methods to 3D spray fields and fluid flows.

Light field imaging involves the reparameterization of images captured using an array of cameras, or from a single senor and lenslet array (i.e. a plenoptic camera), to digitally refocus a flow field post-capture. All cameras record a volumetric scene in-focus, and by recombining images in a specific manner, individual focal planes can be isolated in software to form refocused


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images. Flow features, such as individual droplets, can be located in three-dimensions by refocusing throughout the volume and extracting features on each plane. An implication of the refocusing is the ability to “see through” partial occlusions in the scene.

The new method extends measurement capabilities in complicated flows where knowledge is incomplete. Utilization of this technique allows for finer measurements of flow quantities and structures that would have been impossible with prior methods. In particular, this imaging system is designed to measure and locate features such as bubbles, droplets and particles in three spatial dimensions over time in multiphase flows. Other measurement systems often only allow practitioners to measure average quantities or envelopes of flow regions that do not require such high resolution. This new technique has already demonstrated the capability to resolve very fine flow features, which is especially important in multiphase and turbulent flow fields that contain very minute flow structures and length scales. An instrument of this kind is of great aid in a variety of engineering applications in areas such as air-sea interaction, naval hydrodynamics, aerospace, turbulence and beyond. 2. Principle

To obtain three-dimensional volumetric data sets for spray fields, we implemented a planar array of cameras to record the scene from different angles. Synthetic aperture refocusing techniques were applied to the raw camera array images, each with large depths of field, to obtain a stack of post-processed images, with narrow depth of field, where each image in the stack is located on a specific focal plane. In general, the post-processing for synthetic aperture refocusing involves projecting all images onto a focal surface (planar or otherwise) in the scene on which the geometry is known, averaging the projected images to generate one image, and repeating for an arbitrary number of focal planes (see Belden et al. 2010 for more details).

Image capture is performed using an array of cameras typically arranged in a multi-baseline stereo configuration, which view the scene from different viewpoints (figure 1). The cameras can be placed at arbitrary locations and angles as long as the desired refocused planes (image volume) are in the field of view of each camera. The depth of field of each camera is set large enough such that the entire volume of interest is in focus. Accurate calibration is also critical in the reparameterization and requires advanced auto-calibration algorithms.

a) b)

Fig. 1: Nine and ten camera arrays of Flea 2 model FL2-08S2M/C from Point Grey Research, Inc. CCD cameras, with 50mm Nikkor lenses, typical of those used for the experiments presented.


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The starting point for volume reconstruction is the implementation of the synthetic aperture algorithm to generate refocused images on planes throughout the volume. Thereafter, the actual particle field must be extracted from the refocused images and organized into a volume with quantifiable locations. First, mapping functions must be established between the camera image planes and world coordinates

𝒖!! = 𝐹 𝑿!;𝑝! , (1)

where 𝒖! is the 2x1 vector of the 𝑗!! image point coordinates, [𝑢! , 𝑣!]!, 𝑋! is the 3x1 vector of the 𝑗!! world point coordinates, [𝑋! ,𝑌! ,𝑍!]!, 𝑝! is a set of parameters defining the model of the 𝑖!! camera, and F defines the form of the model. This model allows each image from each of the N cameras in the array to be projected onto k focal planes. 𝐼!"!" denotes the image from camera 𝑖 aligned on the 𝑘!! focal plane. The resulting, refocused SA image, 𝐼!"!, may be generated by averaging each of these images over the number of cameras in the array

𝐼!"! =1𝑁 𝐼!"!"

!

!!!

, (2)

where 𝐼!"! is the image from camera 𝑖 aligned on the 𝑘!! focal plane and N is the number of cameras (Belden et al. 2011). Combining images using this averaging technique is known as additive refocusing. A variant of the additive SA algorithm that can enhance signal-to-noise ratio for well calibrated images is given by the multiplicative refocusing algorithm

𝐼!"! = (𝐼!"!")!

!

!!!

, (3)

where 𝑛 is an exponent between 0 and 1. This allows for enhancement of the signal-to-noise ratio without letting any camera with an occluded view of an object prevent that object from being refocused, because a small number raised to an exponent between 0 and 1 is non-zero. It has been determined that n in the range !

!≤ n ≤ !

! works best.

It has been found that the most efficient number of cameras is in the range of 10–15 (Belden

et al. 2010). This was determined by comparing a synthesized image intensity field to a reconstructed one. The value of 𝑄, defined as follows, is maximized in the range of 10–15 cameras

𝑄 =[𝐸! 𝑋,𝑌,𝑍 ∗ 𝐸! 𝑋,𝑌,𝑍 ]!,!,!

𝐸!! 𝑋,𝑌,𝑍!,!,! ∗ 𝐸!! 𝑋,𝑌,𝑍!,!,!

(4)

where 𝐸! is the reconstructed intensity field and 𝐸! is a synthesized intensity volume based on the known particle locations.


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3. Experiments

For the purposes of illustration of applications of this 3D imaging techniques within the fluid community, we present two distinct experiments, each with complex flow presentations such as dense spray droplets and unsteady flow features: break up of a turbulent sheet along a solid boundary and a liquid jet in air cross flow. Each of these experiments involved the use of a planar camera array with nine or ten cameras. The images were processed using the light field imaging and synthetic aperture refocusing algorithms as described above that were written in MATLAB.

The cameras used in all of the experiments presented herein were Flea 2 model FL2-08S2M/C from Point Grey Research, Inc. All ten cameras in the array were synced and simultaneously captured 1024 x 768 pixels, 8 bit, monochromatic images at 30 frames per second maximum. Although this frame rate was not high enough to achieve fine temporal resolution, it was effective for recording images that could be refocused and from which flow structures, such as droplets and ligaments, could be extracted and investigated. High-speed cameras were used by Belden et al. (2012) with similar success but significant cost increase. Each Flea camera was equipped with a Nikon Nikkor 50 mm lens and F-to-C mount adapter. The cameras were arranged in a planar array mounted on 80/20® aluminum rails, in various configurations. All cameras were oriented at angles such they could all record the same image volume simultaneously. The spray was back illuminated by a pulsed LED light bank, which could be synchronized with the camera frame rate; a common light diffuser, such as that used by professional photographers, was used to create uniform, diffuse lighting. An auto-calibration method relying on a pinhole model was utilized to establish a mapping function between the image planes and world coordinates (Belden 2011). For all calibrations, a checkered grid (2 mm2 grid spacing) was randomly moved and recorded in different orientations throughout the focal volume for each set of experiments. It was important to make sure that the calibration plate was in focus in every image by each camera in the array to ensure that the auto calibration and refocusing algorithm would succeed in reconstructing the volume. 3.1 Turbulent Sheet Breakup The light field imaging and synthetic aperture refocusing techniques were applied to the investigation of the atomization of an unsteady turbulent sheet of water in air. The goal of this project is to characterize the size range and spatial distribution of droplets formed by the unsteady, turbulent atomization of a sheet of water launched into the air at an angle (figure 2). For this project, three-dimensional imaging was performed with a multiple CCD sensor array consisting of ten cameras arranged in three rows (Fig. 1b).

A sample set of raw images from each of the ten cameras at a particular time instant is shown in Fig. 3. The notable features in these images are the ligaments and droplets of water emanating from the liquid sheet, which was located above the field of view of the cameras in these images. It is interesting to investigate the nature of the shape and size distribution of these structures, which are formed during the primary breakup phase of the sheet atomization. These ten individual camera images were processed using the multiplicative refocusing method with a multiplicative exponent of 1/5 (Eq. 3).

Sample results are shown in Fig. 4 at various depths throughout the volume. Features that are in focus at each particular plane in the z (depth) direction are indicated. Negative z values indicate image planes that are in front of the reference plane (closer to the camera array) at the center of the volume of interest, while positive values of z are behind the reference plane.


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Fig. 2: Turbulent sheet of water flowing along an inclined plate, imaging was performed in the region where breakup and separation from the plate begins.

Fig. 3: Raw images from individual cameras at a particular instant in time. Image positions correspond to physical camera positions when looking head-on at the array.


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Fig. 4: Synthetic Aperture refocused images corresponding to the raw images in the previous figure.

Those structures that are not depicted in sharp focus, or that appear to be ghosting, are actually located at a different depth in the volume and are not in focus on the given z-plane. The identification of the plane(s) of focus of particular features allows their positions in the volume to be determined. Ultimately a larger overall FOV and depth of field, achieved with different lenses, would yield more data for validation of CFD studies and development of theoretical predictions. Challenges with the Flea cameras arose mainly due to issues with the firewire interface and individual camera gains, which tended to challenge the reconstruction when one camera had brighter overall images than another. Gains were typically adjusted to provide a similarly light/dark background for all ten cameras. For this investigation, the overall field of view was smaller than desired due to the magnification factor of the CCD camera (35mm mount camera lenses were used with a Nikon to C-mount adapter, instead of C-mount). However, we show that it is possible to determine the location of the droplets and the incline of the ligaments in three dimensions, in addition it is possible to place the location of the droplets relative to the turbulent sheet with good position calibration a priori. 3.2 Liquid Round Jet in Gaseous Crossflow The second application we present is the LFI of a round water jet in an air cross flow. Liquid jets in crossflow are multiphase flows that involve dense cores and sprays of droplets and ligaments. Traditional imaging techniques have been unable to successfully resolve these optically dense segments of the flow and to identify the locations of fine structures. The current experiments involved a water jet emanating vertically from an orifice of diameter 0.789 mm and a nozzle length-to-diameter ratio of 16.1 into a uniform perpendicular crossflow of air (Fig. 5).


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Fig. 5: Liquid jet in crossflow experimental setup and close-up 2D image of jet breakup.

Fig. 6: Single time instance of jet captured by nine-camera array arranged into two rows. Images are shown in same position as camera arrangement.

The cross flow was provided by a 3Hp air blower running at 1000 CFM, for gas velocity Ug = 100 m/s. Gaseous Weber number for these tests was Weg = ρg dj Ug

2 /σ = 126. A pressurized water system was used to control the liquid flow rate; Uw = 29 m/s.

An array of Flea cameras, configured similarly to that described in section 3.1, was used to image and resolve this flow field, however the nine cameras were arranged into only two rows with four on the top row and five on the bottom row. Figure 6 shows raw images of the jet in cross flow from the nine cameras from each mounting location, at one instance in time. The two-row arrangement facilitated optical access in a tight space (the vertical height of the visualization


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chamber was only 6 inches tall) and use of the 105mm macro lenses, with F-to-C mount adapters. These lenses, while quite large, were a cost effective (and widely available) option over standard C-mount lenses.

The nine-camera array was calibrated using the techniques in Belden (2011) and the auto-calibration method applied. The multiplicative refocusing was applied with an exponent of 1/3. Fig. 7 shows a sample result of the three-dimensional resolution and post-processing of the jet in crossflow image data at a particular time instant. In the background is a raw image from one of the cameras in the array that recorded the scene head-on (bottom row, middle camera). Colored contours are superimposed over this image, which indicate the z-depth of each particular enclosed feature. Each color corresponds to a particular depth as indicated by the color bar on the left of Fig. 7.

The depth data were determined by constructing a focal stack of refocused images of the jet in cross flow. Edge detection was performed on each refocused image plane to isolate individual structures. It is clear that there is a complex distribution of structures, such as ligaments and droplets, present in the core of the jet and the dense spray farther downstream. Wishbone-shaped ligament structures can be observed in the spray. The size of the droplets and ligaments in all three spatial dimensions can be determined from these data. Since the flow is optically dense, it would have been impossible to distinguish each of these features from the individual two-dimensional raw camera images.

In a separate, yet similar, jet-in-cross flow facility at MIT, a larger diameter (dj = 5mm) water jet was tested in a slower air flow with gaseous Weber number Weg = ρg dj Ug

2 /σ = 14.6, such that it falls in the bag breakup regime, instead of a shear breakup with more ballistic spray formation seen at higher gaseous weber numbers (e.g. see Salam et al 2004). In this bag breakup regime, fluid bags are formed and then rupture forming a spray of small droplets. The droplets resulting from a bursting bag were imaged using the nine-camera imaging array; the raw images from each camera are shown in figure 8.

Fig. 7: Liquid jet in cross flow features at various refocused volume depths with reference (z=0) to the center of the jet core. Depth in z is indicated by color map. Structures in both the dense core at the bottom of the image and the wishbone structures near the top of the image were extracted with edge detection from the LFI/SA refocused images (Image in collaboration with and courtesy of CREARE, Inc.)


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Fig. 8: Raw images from nine camera square array used in low speed jet in cross flow experiments. Lower right hand quadrant of imagers look up through additional fluid bags that have not yet burst. A fine mist of spray droplets generated from burst fluid bags is observed.

a) b)

c) Fig. 9: Refocused images at three z-planes in focal stack: z = +6.7mm (a), + 10.1mm (b), and + 24.4 mm (c); z = 0 mm was chosen arbitrarily. Select in-focus features in each plane are highlighted with yellow circles.


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Using the LFI/SA reconstruction algorithm we are able to determine position of in-focus

spray droplets at this time instance using the nine raw images in figure 8. Figure 9 shows three planes within the reconstructed volume, highlighting sample individual droplets (yellow circles) that are in focus on one of three z-planes in the focal stack. These images show the density of droplets, and droplet ghosts, during reconstruction. Thresholding and droplet identification algorithms can automate the determination of spray droplet size and location, similar to work on bubbles presented in Belden et al. (2012). Further investigations are ongoing to develop more robust droplet detection algorithms for light field imaging applications. 4. Conclusions Spray flows are typically highly unsteady, three-dimensional and often densely saturated with droplets that impact other droplets, coalesce and breakup. Droplets, fluid ligaments and bags can form from fluid streams and sheets being accelerated in air cross flows or along solid surfaces. This work shows the potential for imaging these complex features with novel three-dimensional imaging methods derived from the combination of light field imaging and synthetic aperture refocusing. Initial applications by Belden et al. (2010) also proved these techniques viable for quantitative flow measurements when combined with 3D particle imaging velocimetry algorithms and special particle identification thresholding. Ultimately these advances, along with others coming from the vision community hold great potential for opening doors to previously under-sampled unsteady, turbulent and multi-phase fluid flows. Acknowledgements The authors acknowledge Drs. Thomas Fu and Erin Hackett, from Naval Surface Warfare Center Carderock Division, W. Bethesda, MD, USA, for their collaboration in the liquid sheet breakup project and Drs. Darin Knauss and Scott Phillips, of Creare, Inc., Hanover, NH, USA, for their collaboration on the high-speed jet in cross flow spray project. Office of Naval Research funding provided under contracts N00014-09-1-1167, Dr. Steven Russell and N00014-11-C-0497, Dr. Clifford Bedford. References Belden J (2011) Synthetic Aperture Imaging for Three Dimensional Resolution of Fluid Flows.

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image velocimetry. Meas Sci Technol 21:1-21. Belden J, Truscott, T T, Ravela S, Techet A H (2011) Three-dimensional synthetic aperture

imaging and resolution of multi-phase flows. Proc ASME-JSME-KSME Joint Fluids Engineering Conf Hamamatsu, Shizuoka, Japan.

Belden J, Truscott TT, Ravela S, Techet AH (2012) Three-Dimensional Bubble Field Resolution Using Synthetic Aperture Imaging: Application to a Plunging Jet, Exp. Fluids in press.


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