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1Mechanical Engineering Department, University of New Hampshire
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An echo particle image velocimetry (EPIV) system capable of acquiring two-dimensional fields of velocity in optically opaque fluids or through optically opaque geometries is described, and validation measurements in pipe flow are reported.
DeMarchi, N., White, C. Echo Particle Image Velocimetry. J. Vis. Exp. (70), e4265, doi:10.3791/4265 (2012).
The transport of mass, momentum, and energy in fluid flows is ultimately determined by spatiotemporal distributions of the fluid velocity field.1 Consequently, a prerequisite for understanding, predicting, and controlling fluid flows is the capability to measure the velocity field with adequate spatial and temporal resolution.2 For velocity measurements in optically opaque fluids or through optically opaque geometries, echo particle image velocimetry (EPIV) is an attractive diagnostic technique to generate "instantaneous" two-dimensional fields of velocity.3,4,5,6 In this paper, the operating protocol for an EPIV system built by integrating a commercial medical ultrasound machine7 with a PC running commercial particle image velocimetry (PIV) software8 is described, and validation measurements in Hagen-Poiseuille (i.e., laminar pipe) flow are reported.
For the EPIV measurements, a phased array probe connected to the medical ultrasound machine is used to generate a two-dimensional ultrasound image by pulsing the piezoelectric probe elements at different times. Each probe element transmits an ultrasound pulse into the fluid, and tracer particles in the fluid (either naturally occurring or seeded) reflect ultrasound echoes back to the probe where they are recorded. The amplitude of the reflected ultrasound waves and their time delay relative to transmission are used to create what is known as B-mode (brightness mode) two-dimensional ultrasound images. Specifically, the time delay is used to determine the position of the scatterer in the fluid and the amplitude is used to assign intensity to the scatterer. The time required to obtain a single B-mode image, t, is determined by the time it take to pulse all the elements of the phased array probe. For acquiring multiple B-mode images, the frame rate of the system in frames per second (fps) = 1/δt. (See 9 for a review of ultrasound imaging.)
For a typical EPIV experiment, the frame rate is between 20-60 fps, depending on flow conditions, and 100-1000 B-mode images of the spatial distribution of the tracer particles in the flow are acquired. Once acquired, the B-mode ultrasound images are transmitted via an ethernet connection to the PC running the PIV commercial software. Using the PIV software, tracer particle displacement fields, D(x,y)[pixels], (where x and y denote horizontal and vertical spatial position in the ultrasound image, respectively) are acquired by applying cross correlation algorithms to successive ultrasound B-mode images.10 The velocity fields, u(x,y)[m/s], are determined from the displacements fields, knowing the time step between image pairs, ΔT[s], and the image magnification, M[meter/pixel], i.e., u(x,y) = MD(x,y)/ΔT. The time step between images ΔT = 1/fps + D(x,y)/B, where B[pixels/s] is the time it takes for the ultrasound probe to sweep across the image width. In the present study, M = 77[μm/pixel], fps = 49.5[1/s], and B = 25,047[pixels/s]. Once acquired, the velocity fields can be analyzed to compute flow quantities of interest.
1. Create a Measurable Flow
2. Calibrate the Ultrasound
3. Data Collection
4. Converting Filetype
5. Computing Displacement Fields, D(x, y), Using DaVis
6. Analyzing Vector Fields
An instantaneous echo particle image velocimetry (EPIV) vector field is shown in Figure 3. The vector plot shows velocity vectors every fourth column, and the background color contour map corresponds to velocity magnitude. An ensemble average vector plot averaged over 1000 instantaneous EPIV vector plots is shown in Figure 4. Consistent with pipe flow, the velocity vectors are primarily in the streamwise direction, the largest velocities occur at the pipe centerline, and the velocities decrease to zero at the pipe walls. The root-mean-square (rms) velocity magnitude fluctuation is shown in Figure 5. Since in Hagen-Poiseuille flow, the rms velocities should be identically zero, the non-zero rms velocities provide a measure of the noise in the EPIV measurements. The high rms values near the upper wall results from strong reflection and refraction of the ultrasound beam from the pipe wall that produce high image intensities in this region (see Figure 2). These high intensities near the walls obscure particle intensities leading to measurement errors. The wall-normal profile of mean streamwise velocity computed by averaging the ensemble-averaged vector plot along the rows (horizontal direction) is plotted in Figure 6. The solid black line is the expected mean streamwise velocity profile for Hagen-Poiseuille (laminar pipe) flow for the given experimental conditions. The agreement between the EPIV measurements and the expected Hagen-Poiseuille profile is best near the pipe centerline and worst near the pipe walls, with the largest deviations occurring near the top wall. We are presently working on methods to reduce the ultrasound reflection and refraction at the pipe wall and to improve the near-wall EPIV measurements.
Figure 1. Schematic of the experimental setup. An aquarium pump drives the fluid (seeded with 10 μm glass microspheres) in a closed loop piping system. The linear ultrasound probe is affixed to the exterior pipe wall and transmits ultrasound waves through the pipe and receives echoes reflected from the 10 μm glass microspheres and the pipe walls. The ultrasound machine processes the reflected ultrasound waves to form an ultrasound B-mode image. The ultrasound B-mode images are exported to a PC running commercial PIV software.
Figure 2. Raw ultrasound B-mode image of pipe flow. The high intensity band of lines at the top and bottom of the image correspond to the pipe wall and the ellipsoids interior to the wall correspond to the 10 m hollow glass microspheres.
Figure 3. An instantaneous vector plot showing vector arrows every fourth column. The background color contour map corresponds to velocity magnitude. D is the pipe diameter, x is the streamwise position measured from the pipe inlet, and d is the radial position measured from the upper wall.
Figure 4. Ensemble average vector plot averaged over 1000 instantaneous EPIV vector plots. The vector plot shows velocity vectors every fourth column, and the background color contour map corresponds to velocity magnitude. Consistent with pipe flow, the velocity vectors point in the streamwise direction, the largest velocities occur at the pipe centerline, and the velocities decrease to zero at the pipe walls.
Figure 5. Contour plot of the root-mean-square (rms) velocity fluctuation computed over 1000 instantaneous EPIV vector plots. In Hagen-Poiseuille flow, the rms velocity fluctuations provide a measure of noise in the EPIV measurements.
Figure 6. The experimental measured mean streamwise velocity profile computed from the ensemble-averaged EPIV vector field shown in Figure 4. The solid black line is the theoretically expected profile for a Hagen-Poiseuille flow with the same volumetric flow rate as measured experimentally. The radial position measured from the pipe centerline is denoted by r, where the upper wall corresponds to r/D = -0.5. Differences between the experimental profile and the expected profile illustrate the difficulty of near-wall EPIV measurements.
The operating protocol for an echo particle image velocimetry (EPIV) system capable of acquiring two-dimensional fields of velocity in optically opaque fluids or through optically opaque geometries was described. Practical application of EPIV is well-suited for the study of industrial and biological flow systems, where the flow of opaque fluids occurs in a great many application. The particular system presented here was purposefully built to study the flow properties of liquefied biomass fluids used in the production of lignocellulosic ethanol. The capabilities of EPIV were demonstrated using representative measurements in pipe flow. In particular, mean and rms velocity profiles were computed from EPIV vector fields, Hagen-Poiseuille (laminar) pipe flow was shown to be measurable and quantifiable. The limitations of EPIV are the inherently low frame rates (limited by the imaging capabilities of the commercial ultrasound system) and low spatial resolution, which limits the range of velocities and transient flow behavior that can be measured. Lastly, although we have strived to make the article self-contained, the user manuals for the commercial ultrasound machine7 and the PIV software8 should be consulted for completeness. The reader is also referred to 9 and 10 for a comprehensive review of ultrasound imaging fundamentals and particle image velocimetry, respectively.
Authors have nothing to disclose.
The authors gratefully acknowledge support by the National Science Foundation, CBET0846359, grant monitor Horst Henning Winter.
|Ultrasound Machine||GE||Vivid 7 Pro|
|Linear Ultrasound Array||GE||10 L|
|DC Water Pump||KNF||NF 10 KPDC|
|Vector Processing Software||Lavision||DaVis 7.2|
|Post Processing Software||Mathworks||MATLAB 7.12|
|Ultrasound Gel||Parker||Aquasonic 100|
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