Measurement of velocity vectors with orthogonal and non-orthogonal triple-sensor probes

Abstract

Abstract.A new method of interpreting the signals from triplesensor thermal anemometer probes has been developed based on fast solution for all the roots of the non-linear Jorgensen (1971) equations describing the directional response of each cylindrical sensor. The sensors can be oriented at arbitrary angles to each other, but always within a range of probe geometries that keep prong interference and thermal wake interference below acceptable levels. The properties of a class of non-orthogonal symmetric tetrahedral probe geometries are studied in relation to the range of flow vector angles that can be measured, the sensitivity of the probe with respect to changes in flow angle, and the sensitivity of the computed velocity components due to angular errors associated with the construction of the probe. The solutions of Jorgensen's equations are inherently multiple-valued, but if the velocity vector is restricted to be within a cone of angles, they are unique. It is shown that measurements with non-orthogonal triple sensor signals are sensitive to angular deviations of a few degrees of the sensor angles from the nominally orthogonal probe geometry, indicating the need of a non-orthogonal algorithm. The mean, rms, Reynolds stress, and power spectrum of the velocity in fully developed turbulent pipe flow were measured using a specially designed triple sensor probe and the proposed algorithm.

An experimental approach to the calibration and use of triple hot-wire probes

“…This method provides a way to optimize the constants in the conventionally accepted response model and to include additional terms in the model to further reduce the errors. This procedure decouples the angular calibration from the sensitivity to the velocity magnitude, in a manner similar to that used by Lekakis et al 1989. The 315 decoupling considerably reduces the complexity of the calibration and velocity extraction procedures.…”

“…Tables with a resolution of 200 x 200 are sufficient to insure and accuracy in all velocity components of the order of 0.03% for the average error with maxima of the order of 0.1%. When comparing the table look-up method to iterative (Chang et al 1988;Choi, 1989; and others) and analytical (Lekakis et al 1989) approaches, the errors noted above are those which are most relevant. These approaches, like the table look-up method, provide a nearly exact inversion of assumed or experimentally determined response models.…”

“…This approach is possible since the form of the response models was selected such that the velocity magnitude could be scaled out, yielding a two-dimensional problem which depends only on the flow direction. Similar variable transformations were used by Lekakis et al (1988Lekakis et al ( , 1989 to solve Jorgensen's equation. Their procedure is an exact inversion of the cooling velocity equations, but it is computationally complex and limited to the response model given in Eq.…”

“…Few algorithms have been developed (Chang, Adrian and Jones, 1984;Vukoslavcevic, Balint and Wallace, 1987;Lekakis, 1988;Choi, 1989;Lekakis, Adrian and Jones, 1989;Russ and Simon, 1990; and others) to extract velocity components from triple hot-wire measurements and most rely on certain simplifying assumptions. The most crucial assumption is the choice of the model to describe how the heat transfer from each wire depends on the direction and magnitude of the impinging velocity vector.…”

“…Once again, the governing model equations had to be simple and the use of the circuits was limited to a specific arrangement of wires. Lekakis (1988) and Lekakis, Adrian, and Jones (1989) developed a method to analytically invert the three response equations making use of variable transformations very similar to the transformations used in the present analysis. Their inversion procedure requires that the form of the wire response model, or cooling law, be the Jorgensen's form.…”