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A very high resolution minimal channel flow DNS was used to examine, virtually, the ability of various multi-sensor hot-wire probe configurations to measure the statistics of velocity gradient components. Various array and sensor configurations and the spatial resolution of probes with these configurations were studied, building on designs and investigations of various authors. In contrast to our previous studies, which focused on turbulent vorticity, vorticity- velocity correlations, dissipation and production rate, here the measurement accuracy of each component of the velocity vector gradient tensor is analyzed separately. The results of the study show that the virtual experiments compare well with a physical experiment, and that such virtual experiments are a powerful tool to examine the accuracy of velocity gradient measurements. The cross- stream gradients needed to determine the vorticity components can be measured with sufficient accuracy with most of the array and sensor configurations of vorticity probes used so far. A systematic error of some of the gradient measurements can appear due to the array or sensor configurations. None of the examined probe designs can measure, with sufficient accuracy, the streamwise velocity gradients, directly or indirectly, using the continuity equation.

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VUKOSLAVČEVIĆ, Petar V.; WALLACE, James M.. ON THE ACCURACY OF MEASUREMENT OF TURBULENT VELOCITY GRADIENT STATISTICS WITH HOT-WIRE PROBES. Thermal Science, [S.l.], mar. 2017. ISSN 2334-7163. Available at: <http://thermal-science.tech/journal/index.php/thsci/article/view/2282>. Date accessed: 24 feb. 2018. doi: https://doi.org/10.2298/TSCI160210116V.
Received 2017-03-07
Accepted 2017-03-14
Published 2017-03-14


[1] Taylor, G.I., Production and dissipation of vorticity in a turbulent fluid, Proc. R. Soc. London, Ser. A, 164 (1938), 916, pp. 15-23
[2] Wallace, J.M., Vukoslavčević, P.V., Measurement of the velocity gradient tensor in turbulent flows, Annu. Rev. Fluid Mech., 42 (2010), pp. 157-181
[3] Vukoslavčević, P.V, Wallace, J.M., The influence of the arrangements of multi-sensor probe arrays on the accuracy of simultaneously measured velocity and velocity gradient-based statistics in turbulent shear flows, Exp. Fluids, 54 (2013), Issue 6, 1537, DOI No: 10.1007/s00348-013-1537-z
[4] Vukoslavčević, P., et al., The velocity and vorticity vector fields of a turbulent boundary layer. Part 1. Simultaneous measurement by hot wire anemometry, J. Fluid Mech., 228 (1991), pp. 25-51
[5] Tsinober, A., et al., Experimental investigation of the field of velocity gradients in turbulent flows, J. Fluid Mech., 242 (1992), pp. 169-192
[6] Vukoslavčević, P., Wallace, J.M. A 12-sensor hot-wire probe to measure the velocity and vorticity vectors in turbulent flow, Meas. Sci. Technol., 7 (1996), pp. 1451-1461
[7] Honkan, A., Andreopoulos, Y., Vorticity, strain rate and dissipation characteristics in the near wall region of turbulent boundary layers, J. Fluid Mech., 350 (1997), pp. 29-96
[8] Galanti, B., et al., Velocity derivatives in turbulent flows in an atmospheric boundary layer without Taylor hypothesis, Proceedings (Eds. N. Kasagi et al.), Third International Symposium on Turbulence and Shear Flow Phenomena (TSFP3), Sendai, Japan, 2003, Vol. II, pp. 745-750
[9] Gulitski, G., et al., Velocity and temperature derivatives in high-Reynolds number turbulent flows in the atmospheric surface layer. Part1. Facilities, methods and some general results, J. Fluid Mech., 589 (2007), pp. 57-81
[10] Vukoslavčević, P.V., Wallace, J.M., On the accuracy of simultaneously measuring velocity component statistics in turbulent wall flows with arrays of three or four hot-wire sensors, Exp. Fluids, 51 (2011), pp. 1509-1519
[11] Vukoslavčević, P.V., A hot-wire probe configuration and data reduction method to minimize velocity gradient errors for simultaneous measurement of three velocity components in turbulent flows, Exp. Fluids, 53 (2012), pp. 481-488
[12] Vukoslavčević, P.V., Wallace, J.M., Using direct numerical simulation to analyze and improve hot-wire probe sensor and array configurations for simultaneous measurement of the velocity vector and the velocity gradient tensor, Phys. Fluids, 25 (2013), Issue 11, 110820
[13] Moin, P., Spalart, P.R., Contributions of numerical simulation data bases to the physics, modeling and measurement of turbulence, NASA-TM-100022, NASA Ames Research Center, Moffett Field, CA, United States, 1987
[14] Vukoslavčević, P.V., et al., On the spatial resolution of velocity and velocity gradient-based turbulence statistics measured with multi-sensor hot-wire probes, Exp. Fluids, 46 (2009), pp. 109-119
[15] Pompeo, L., Thomann, H., Quadruple hot-wire probes in a simulated wall flow, Exp. Fluids, 14 (1993), 3, pp. 145-152
[16] Antonia, R.A., et al., On the measurement of lateral velocity derivatives in turbulent flows, Exp. Fluids, 15 (1993), pp. 65-69
[17] Jiménez, J., Moin, P., The minimal flow unit in near-wall turbulence, J. Fluid Mech., 225 (1991), pp. 213-240
[18] Piomelli, U., et al., Turbulent structures in accelerating boundary layers, Journal of Turbulence, 1 (2000), 1, pp. 1-16, DOI No: 10.1088/1468-5248/1/1/001
[19] Vukoslavčević, P., Wallace, J.M., Influence of velocity gradients on measurements of velocity and streamwise vorticity with hot-wire X-array probes, Rev. Sci. Instrum., 52 (1981), 6, pp. 869-879
[20] Kastrinakis, E.G., Eckelmann, H., Measurements of streamwise vorticity fluctuations in a turbulent channel flow, J. Fluid Mech., 137 (1983), pp. 165-186
[21] Samet, M., Einav, S., A hot-wire technique for simultaneous measurement of instantaneous velocities in 3D flows, J. Phys. E: Sci. Instrum., 20 (1987), pp. 683-690
[22] Lekakis, I.C., et al., Measurement of velocity vectors with orthogonal and non-orthogonal triple-sensor probes, Exp. Fluids, 7 (1989), pp. 228-240
[23] Holzäpfel, F., et al., Assessment of a quintuple hot-wire technique for highly turbulent flows, Exp. Fluids, 18 (1994), 1, pp. 100-106
[24] Döbbeling, K., et al., Basic considerations concerning the construction and usage of multiple hot-wire probes for highly turbulent three-dimensional flows, Meas. Sci. Technol., 1 (1990), pp. 924-933
[25] Maciel, Y., Gleyzes, C., Survey of multi-wire probe data processing techniques and efficient processing of four wire probe velocity measurements in turbulent flows, Exp. Fluids, 29 (2000), pp. 66-78
[26] Geng, C., et al., Taylor’s hypothesis in turbulent channel flow considered using a transport equation analysis, Phys. Fluids, 27 (2015), Issue 2, 025111
[27] Balint, J.L., et al., The velocity and vorticity vector fields of a turbulent boundary layer. Part 2: Statistical properties, J. Fluid Mech., 228 (1991), pp. 53-86
[28] Ong, L., Wallace, J.M., Joint probability density analysis of the structure and dynamics of the vorticity field of a turbulent boundary layer, J. Fluid Mech., 367 (1997), pp. 291-328