Эхо Velocimetry Particle Image

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.