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on the accuracy of turbulence measurements with inclined hot wires

Published online by Cambridge University Press:  20 April 2006

Udo R. Müller
Affiliation:
Aerodynamisches Institut, Technische Hochschule Aachen, West Germany

Abstract

Since the accuracy of mean velocities and Reynolds stresses measured with inclined hot wires depends on the accurate knowledge of the hot-wire cooling law, each hot wire used in the boundary-layer experiment of Müller (1982, hereinafter referred to as I) had to be calibrated individually with respect to the magnitude and direction of the flow vector. In the present paper details of the calibration procedure and an example of calibrated data are reported. The directional hot-wire response was described by an effective cooling velocity, which was then used for the data reduction. The errors in the measured Reynolds stresses evaluated with an empirical cooling law as opposed to the actual one were estimated analytically from the governing equations and were confirmed by corresponding recalculations from the same set of measurements. Additionally, the validity of the conventional linearized method for evaluating the Reynolds stress tensor from the root-expanded equation for the cooling velocity was checked for increasing turbulence levels. In the test measurements all triple velocity correlations, which are usually neglected compared with second-order ones, were measured and taken into account in the data reduction.

Type
Research Article
Copyright
© 1982 Cambridge University Press

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References

Berg, B. V. D. & Elsenaar, A. 1972 Measurements in a three-dimensional incompressible turbulent boundary layer in an adverse pressure gradient under infinite swept wing conditions. NLR Tech. Rep. no. 72092 U.Google Scholar
Bradshaw, P. 1972 The understanding and prediction of turbulent flow. Jahrbuch der Deutschen Gesellschaft für Luft-und Raumfahrt, p. 51.
Bruun, H. H. 1971a Interpretation of a hot-wire signal using a universal calibration law. J. Phys. E: Sci. Instrum. 4, 225.Google Scholar
Brunn, H. H. 1971b Linearisation and hot-wire anemometry., J. Phys. E: Sci. Instrum. 4, 815.Google Scholar
Bruun, H. H. 1972 Hot-wire data corrections in low and high turbulence intensity flows. J. Phys. E: Sci. Instrum. 5, 812.Google Scholar
Bruun, H. H. 1975 Interpretation of X-hot-wire signals. DISA Info. no. 18, p. 5.Google Scholar
Champagne, F. H., Sleicher, C. A. & Wehrmann, O. H. 1967 Turbulence measurements with inclined hot-wires. Part 1 and 2. J. Fluid Mech. 28, 153.Google Scholar
Dechow, R. 1977 Mittlere Geschwindigkeit und Reynoldsscher Spannungstensor in der dreidimensionalen turbulenten Wandgrenzschicht vor einem stehenden Zylinder. In Strömungsmechanik und Strömungsmaschinen, Heft 21. Mitteilungen des Instituts für Strömungslehre und Strömungsmaschinen, Univ. Karlsruhe.
Durst, F. 1971 Evaluation of hot-wire anemometer measurements in turbulent flows. Imperial College, Dept Mech. Engng Rep. ET/TN/A/9.Google Scholar
Elsenaar, A. & Boelsma, S. H. 1974 Measurements of the Reynolds stress tensor in a three-dimensional turbulent boundary layer under infinite swept wing conditions. NLR Tech. Rep. no. 74095 U.Google Scholar
Friehe, C. A. & Schwaez, W. H. 1968 Deviations from the cosine law for yawed cylindrical anemometer sensors. Trans. A.S.M.E. E, J. Appl. Mech. 35, 655.Google Scholar
Hfskestad, G. 1965 Hot-wire measurements in a plane turbulent jet. Trans. A.S.M.E. E, J. Appl. Mech. 32, 721.Google Scholar
Hinze, J. O. 1975 Turbulence. McGraw-Hill.
Horvatin, M. 1970 A contribution to the calibration of hot-wire dual probes. DISA Info. no. 10, p. 22.Google Scholar
Irwin, H. P. A. H. 1971 The longitudinal cooling correction for wires inclined to the prongs and some turbulence measurements in fully developed pipe flow. McGill Univ., Montreal, Mech. Engng Res. Lab. Tech. Note no. 72–1.Google Scholar
Johnston, J. P. 1970 Measurements in a three-dimensional turbulent boundary layer induced by a swept, forward facing step. J. Fluid Mech. 42, 823.Google Scholar
Jörgensen, F. E. 1971 Directional sensitivity of wire and fiber-film probes. DISA Info. no. 11, p. 31.Google Scholar
Kjellström, B. & Hedberg, S. 1970 Die Eichung eines DISA Hitzdrahtanemometers und Bestätigung der Eichung durch Messung in einem zylindrischen Kanal. DISA Info. no. 9, p. 8.Google Scholar
Krause, E. 1974 Analysis of viscous flow over swept wings. ICAS Paper no. 74–20.Google Scholar
Krause, E. 1975 Flow analysis through numerical techniques. In AGARD LS 73.
Marvin, J. G. 1977 Turbulence modeling for compressible flows. NASA Tech. Memo. X-73, 188.
Müller, U. R. 1982 Measurements of the Reynolds stresses and the mean-flow field in a three-dimensional pressure-driven boundary layer. J. Fluid Mech. 118, 121.Google Scholar
Müller, U. R. & Krause, E. 1979 Measurements of mean velocities and Reynolds stresses in an incompressible three-dimensional turbulent boundary layer. In Proc. 2nd Symp. on Turbulent Shear Flows, Imperial College, London, p. 15.36.
Rodi, W. 1975 A new method for analysing hot-wire signals in highly turbulent flows, and its evaluation in a round jet. DISA Info. no. 17, p. 9.Google Scholar
Rotta, J. C. 1977 A family of turbulence models for three-dimensional thin shear layers. In Proc. 1st Symp. on Turbulent Shear Flows, Pennsylvania State Univ., p. 10.27.
Vagt, J. D. 1972 Hot-wire measurement techniques in a highly turbulent flow and the calculation of intensities. In Heat and Mass Transfer in Boundary Layers (Proc. Int. Summer School Heat and Mass Transfer in Turbulent Boundary Layers, Herceg Novi, Sept. 1968, and selected papers and abstracts of the International Seminar Heat and Mass Transfer in Flows with Separated Regions, Herceg Novi, Sept. 1969) (eds. N. Afgan, Z. Zaric & P. Anastasijevic), vol. 2, p. 995, Pergamon.
Vagt, J. D. 1979 Hot-wire probes in low speed flow. Prog. Aero. Sci. 18, 271.Google Scholar
Webster, C. A. G. 1962 A note on the sensitivity to yaw of a hot-wire anemometer. J. Fluid Mech. 13, 307.Google Scholar