Sensitivity of turbulent stresses in boundary layers to cross-wire probe uncertainties in the geometry and calibration procedure

Abstract

The sensitivity of measured turbulent stresses to uncertainties in the probe geometry and calibration procedure is investigated for a cross-wire probe in a turbulent boundary layer using direct numerical simulation (DNS) data. The errors investigated are guided by experiments, and to replicate the full experimental procedure, the cross-wire calibration procedure is simulated to generate a voltage-tovelocity mapping function, which is then utilised to calculate the measured velocity from simulated cross-wire voltages. We show that wire misalignment can lead to an incorrect mean wall-normal velocity and Reynolds shear stress in the near-wall region due to the presence of shear. Furthermore, we find that misalignment in the wire orientation cannot be fully accounted for through the calibration procedure, presumably due to increased sensitivity to an out-of-plane velocity component. This has strong implications if using a generic commercial cross-wire probe, since inclining these probes to gain access to the near-wall region can lead to a large error (up to 10 %) in turbulent stresses and these errors can manifest in the log region and beyond to half the boundary layer thickness. For uncertainties introduced during the calibration procedure, the Reynolds shear stress is observed to exhibit an elevated sensitivity compared with other turbulent stresses. This is consistent with empirical observations where the repeatability in the Reynolds shear stress is found to be the poorest.

Spatial averaging effects on the streamwise and wall-normal velocity measurements in a wall-bounded turbulence using a cross-wire probe

“…D u 2 = u 2 measured −u 2 original ) at fixed z + due to finite sensor dimension effects should remain approximately the same in the near-wall region across all wall-bounded flow, provided that the sensor dimensions remain fixed in viscous units. Furthermore, the small-scale invariance when scaled by viscous units observed for the u velocity, also occurs for the v and w velocities (Baidya, 2016;Baidya et al, 2017). Consequently, Lee et al (2016) have shown that the deviations for the w 2 statistics observed in boundary layer particle image velocimetry experiments agree well with that predicted from the filtered channel DNS statistics when the averaging was performed across all three dimensions to match the spatial resolution expected from the experiments.…”

“…The qualitative trends observed in the simulation study are compared against the experimental results obtained using custom built sub-miniature ×-probes in the High Reynolds Number Boundary Layer Wind Tunnel (HRNBLWT), at the University of Melbourne. For further details of the experiment, the readers are referred to Baidya et al (2017).…”

“…Thus, while the uw statistics are robust to the finite sensor effects, it is found to be highly sensitive to other sources of errors such as those introduced by wire misalignment and calibration procedures. Since the focus of this paper is on investigating the effects of spatial averaging due to finite sensor dimensions, the other error sources are investigated in a companion paper (Baidya et al, 2019). In appendix A, for completeness we show the comparison of the statistics from the experimental u-v ×-probe with that from a simulation.…”

“…Misalignment of the sensor plane (a plane parallel to both hot-wires) and the streamwise-spanwise (x-y) or streamwise-wall-normal (x-z) planes should be avoided. Thus, the usage of inclined generic probe to allow nearwall access is strongly discouraged, as this can lead to a substantial error, up to 10 % for the turbulent stresses, to be introduced in the log region and beyond, until half the boundary layer thickness (Baidya et al, 2019). Instead, a custom ×-probe, where the sensor plane can be designed to accommodate the inclination angle, such that it remains parallel to the x-y or x-z planes should be considered.…”

“…A well-designed calibration procedure is vital. The Reynolds shear stress is found to be extremely sensitive (more than twice the other stresses) to any uncertainties introduced during the calibration procedure (Baidya et al, 2019). In this regard, an in situ two-dimensional calibration conducted with an articulated probe holder in the freestream region of the wind tunnel (e.g., Österlund, 1999) may be considered the best practise.…”