Direct measurement of vorticity by optical probe

Abstract

An optical method for the direct measurement of vorticity in liquid flows is described. At the present state of development it is capable of responding to vorticity fluctuations with a response time of about 1 msec and a spatial resolution of better than 50 μm. Small spherical particles suspended in the flow rotate with angular velocity accurately equal to half the local vorticity; thus measurements of the rotation rates of such particles indicate the vorticity. Transparent spherical particles of less than 50 μm diameter, each containing embedded planar crystal mirrors, have been developed for this purpose and are suspended in a refractive-index-matched liquid. Measurements of the times required for laser reflections from the mirrors to rotate through the small angle defined by a pair of slits yields the rotation rate, and thus the vorticity. Production and physical properties of the probe particles are reported. Theoretical capabilities and limitations of the method, including accuracy, spatial and temporal resolution, data rate, and background noise are calculated and found to be coupled to the optical geometry and flow field. Analysis yields procedures for selective optimization of each parameter as dictated by the particular application. Measurements of steady-state, laminar, two-dimensional Poiseuille flows demonstrate the effectiveness of the technique and confirm theoretical predictions.

Measurements of Vorticity Vectors in Couette Flow with the Vorticity Optical Probe

“…Frish at Cornell University as part of his doctoral thesis research (1981). The first direct optical vorticity measurements were single component measurements in laminar Poiseuille flow and in a transitional boundary layer (Frish and Webb, 1981). This work was continued at Cornell by Ferguson, who developed the multi-component VOP sensor based upon a dual-axis position-sensing photodiode detector.…”

“…To pertorm these measurements, Frish (1981) invented a method of encasing microscopic plane mirrors carbonate crystal platelets) in 20 to 30 Am clear plastic spheres having refractive indices that match the w fluid in which they are dispersed as probes. Each particle is mechanically spherical, but optically planar reflections and refractions are effectively eliminated at the particle surface by index matching.…”

“…Autocorrelations for discrete random data have been described by Frish (1981) and others and will not Irecounted here, except to note that the time axis is simply divided uniformly into bins of sufficient widt, obtain reasonable statistics in each bin (properly normalized including statistical weights) and still insure adequate time resolution. A necessary refinement of discrete auto-correlations for finite time events is time weighting (Buchhave, et al, 1979), which is the auto-correlation anaolog of transit time weighting umformly spaced bins are then suitable for Fourier transformation in order to estimate the power spectrn the random signal.…”

“…The VOP technique was developed by Frish and Webb (1981) specifically to address the problem of resolving the smallest scales of intense turbulence, even in the presence of powerful mean shear. In its present form, the VOP measures three components of vorticity in virtually any geometry, in liquid flows including water.…”

Fluid flow vorticity measurement using laser beams with orbital angular momentum

“…The first direct measurement of vorticity was attempted more than three decades ago by measuring the rotation rate of planar mirrors embedded in 25μm transparent spherical beads that were suspended in a refractive-index-matched liquid. 4 The implementation of this method is very complex and requirement of index matching significantly limits its use and prohibits its application …”