Design and implementation of a hot-wire probe for simultaneous velocity and vorticity vector measurements in boundary layers

Abstract

A multi-sensor hot-wire probe for simultaneously measuring all three components of velocity and vorticity in boundary layers has been designed, fabricated and implemented in experiments up to large Reynolds numbers. The probe consists of eight hotwires, compactly arranged in two pairs of orthogonal ×-wire arrays. The ×-wire sub-arrays are symmetrically configured such that the full velocity and vorticity vectors are resolved about a single central location. During its design phase, the capacity of this sensor to accurately measure each component of velocity and vorticity was first evaluated via a synthetic experiment in a set of well-resolved DNS fields. The synthetic experiments clarified probe geometry effects, allowed assessment of various processing schemes, and predicted the effects of finite wire length and wire separation on turbulence statistics. The probe was subsequently fabricated and employed in large Reynolds number experiments in the Flow Physics Facility (FPF) wind tunnel at the University of New Hampshire. Comparisons of statistics from the actual probe with those from the simulated sensor exhibit very good agreement in trend, but with some differences in magnitude. These comparisons also reveal that the use of gradient information in processing the probe data can significantly improve the accuracy of the spanwise velocity measurement near the wall.

A comparative study of the velocity and vorticity structure in pipes and boundary layers at friction Reynolds numbers up to

“…The advantage of the systems given by (2.2) and (2.3) compared to a typical ×-array method is that the assumption of uniform flow across ×-wire pairs is relaxed to one that allows a linear velocity gradient across the measurement volume. This reduces the aliasing associated with non-uniform flow across the ×-wire domain (Zimmerman et al 2017). The remaining shear gradients not given by (2.2) or (2.3) (i.e.…”

“…All of the data presented herein were acquired via a multi-element hot-wire anemometry probe consisting of 8 independent sensing elements. The design of this probe and its capacity to capture key aspects of the velocity and vorticity time-series in turbulent boundary layers are discussed in detail in Zimmerman et al (2017). The arrangement of the sensing elements, shown in figure 2, is similar to the arrangement deployed by Antonia et al (1998) in a grid-generated turbulent flow.…”

“…Another advantage of the present design is the focus on resolving the vorticity vector specifically rather than the entire velocity gradient tensor. Forgoing measurement of two normal gradients (∂u 2 /∂x 2 and ∂u 3 /∂x 3 ) eliminates the practical requirement for each sub-array to estimate all three components of velocity simultaneously, the merits of which are evidenced by the velocity component variances reported in Zimmerman et al (2017).…”

“…where u e is the 'effective' cooling velocity and u i is either u 2 or u 3 (depending on the orientation of the sensor), and the subscripts N and T refer to the directions normal and tangential to the sensor, respectively. The original expression suggested by Jorgensen (1971) includes another term that describes the effect of 'bi-normal' cooling velocity, but this term is neglected here (Zimmerman et al 2017). The use of (2.1) with speeddependent cooling coefficients collapses the jet calibration data onto a single curve with errors typically less than 1% for speeds above 2 m/s.…”

“…the first step). First, it was shown in Zimmerman et al (2017) that even very minor misalignment of the jet relative to the mean flow could result in substantial errors in reported Reynolds shear stress components. Second, the fan which generates the calibrating jet flow can heat the air by several degrees Celsius, resulting in a shifted speed response curve.…”