Multiplane particle shadow velocimetry to quantify integral length scales
The integral length scale can be calculated from planar particle image velocimetry (PIV) data by integrating a two-point velocity correlation over a range of in-plane spatial separations. However, the field of view restricts the integral scale that can be measured by limiting the integration domain. This limitation can be overcome if multiple planes are imaged, and velocity is correlated along the out-of-plane direction. Multiplane particle shadow velocimetry (PSV) is introduced for this purpose. A backlight is used to illuminate particles in the flow field, rather than a laser sheet as in PIV. These illuminated particles obstruct light from entering the camera, thus appearing dark. The combination of two colors in the backlight and a dichroic mirror makes possible the simultaneous imaging of two planes. Separated along the the out-of-plane direction (the optical axis), the multiple imaged planes allow for an integral length scale to be measured independent of the field of view. Experiments were conducted in the axisymmetric 285 mm diameter glycerin tunnel at Penn State’s Applied Research Laboratory. Turbulence statistics calculated using multiplane PSV are consistent with those obtained using planar PSV and laser Doppler velocimetry (LDV) at the same facility. The temporal autocorrelation and the integral timescale, measured with planar and multiplane PSV, agree within 95% confidence. The two-point velocity correlation separated spatially along the in-plane radial direction is the same, within 95% confidence, as that separated spatially along the out-of-plane radial direction. The former is insufficient for calculating an integral length scale due to its limited domain. Integrating the latter yields an integral length scale equal to 11% of the radius of the tunnel.
The authors would like to thank the many sponsors who motivated and funded this work, the Walker Fellowship program, and ISSI for initially developing the measurement method. Discussions with Michael McPhail are also gratefully acknowledged.
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