Robust procedure for multi-hole probe data processing

Abstract

Multi-hole probes represent a durable and economic option to measure flow angles, total and static pressures in complex flow environments. The pressure readings are converted into flow direction using pressure calibration maps. However, depending on the geometry or manufacturing imperfections, conventional flow angle data reduction methods cannot guarantee uniqueness in the solution. This paper presents and demonstrates a novel data processing approach in a turbine measurement campaign. The new technique relies on a database of non-dimensional pressures (one per hole) instead of differential pressure levels. In addition, the new approach allows computing flow direction when a hole is blocked during the test campaign.

Introduction

Aerodynamic probes have been extensively used since 1960s [1] due to their robustness, simplicity and reduced cost. Experimental calibration is still essential because of manufacturing errors. Calibration maps are obtained in a wind tunnel varying the yaw and pitch angles, while recording the hole-pressures. With the advent of powerful computers, researchers have introduced numerical approaches to process the calibration data online.

To maximize the measurement accuracy the probe geometry should procure high sensitivity to angle variation, and low dependence between pressure coefficients. Bryer and Pankhurst [2] provided an extensive overview on multi-hole pressure probes for the investigation of three-dimensional flows. Fig. 1 displays a classification of 5-hole probes with increasing manufacturing complexity from left to right. Houtman and Bannink [3] recommended the use of hemispherical heads only for flow angles above 30°. Forward facing tubes or holes were the first type of three-dimensional probes [1]. Due to the simpler production, such geometries continue to enjoy some popularity. At a given yaw angle, Galliard [4] observed that increasing the pitch angle from 0 to 20 deg. the lateral pressure trace exhibited a non-monotonic evolution. Moreover, Dominy and Hodson [5] observed at lower Reynolds a separation bubble at the leading edge.

Fig. 2 displays the conical shape probe with perpendicular holes, used in the current research. Based on the extensive cone angle sensitivity studies of Galliard [4], an angle of 60 deg. was selected. More recently, several researchers [6], [7], [8] have developed seven-hole probe technology, for large angles of attack ±70 deg.

A directional probe can be operated in two different ways. In the yaw-null method, the probe is mounted on an actuator that rotates the probe until the pressure readings obtained on the two opposite pressure taps are equal. The second strategy is the so-called differential pressure method, in which the probe is held stationary during the test and the angle is obtained from the differential pressure across the opposite pressure taps by a careful calibration. In both methods, calibration is required to determine total and static pressure. Each technique has its advantages and drawbacks. Calibration and data reduction require less effort with the yaw-null method, but it requires sophisticated actuator devices and a minimum time to adjust the probe setting angle to the flow angle. In the differential pressure method, a large amount of data can be sampled and flow variations can be resolved up to the frequency limit of the probe. The yaw-null method cannot be used in transient tests or to resolve high frequency flow angles.

The probe calibration is usually carried out in a closed wind tunnel [9] or a free jet [10] at multiple flow directions. The probe is rotated to vary the flow incidence; while the probe is kept stationary the pressure level of each hole is recorded [11]. The flow direction is generally expressed by a pressure difference between the probe holes. Then, the non-dimensional pressure differences are presented in calibration maps. Potential flow theory may be used to model the flow around the probe head [12], allowing examining the map limitations and enhancing the calibration range. In case of supersonic flows, numerical simulations could assist the calibration. For instance, Milanovic and Kalkhoran [13] used a three-dimensional thin layer Navier–Stokes code to calibrate a five-hole probe at Mach numbers from 1.75 to 2.75.

Previously in the open literature, differential pressure readings were reduced to non-dimensional numbers that are then compared to calibration maps. Dudzinsky and Krause [1] used graphical methods to obtain the angles and pressures from those calibration maps. Morrison et al. [14] explained the calibration and data processing procedure using four non-dimensional parameters. Reichert and Wendt [15] performed a two-dimensional Taylor series decomposition of the calibration map. Gallington [16] proposed a polynomial curve fitting method for the data reduction; a third order least-square fitting was employed between flow conditions and calibration coefficients. Similarly, Johansen et al. [17] used a least-square curve fitting technique. Alternatively, a direct interpolation technique was introduced [6], [18], [19] for post-processing of the data. Sumner [20] compared the curve fitting method and direct interpolation technique for a seven-hole probe, concluding that both techniques provided similar accuracy when the flow incidence is below 30 deg. Baskaran et al. [21] and Rediniotis and Vijayagopal [22] proposed a technique using artificial neural networks to obtain directly the unknowns from the calibration map.

The accuracy of the data processing technique can be improved applying different methods. Wenger and Devenport [23] utilized a two-step data reduction technique. First they applied, a least-square surface fitting on the global calibration data, followed by a local interpolation. The definitions of the non-dimensional pressure parameters were modified in order to have a linear variation with the flow angle [24]. This modification improves the interpolation accuracy in the calibration domain. The accuracy of the direct interpolation is increased when the calibration region is divided into smaller portions [25]. Pisasale and Ahmed [26] improved the direct-interpolation technique for an extreme flow angles up to $\pm$75 deg. by applying additional parameters for the range of extreme flow incidences. Argüelles Díaz et al. [27] proposed a zonal definition of the calibration coefficients in order to prevent singular points occurrence. This technique discriminates several zones for the angular range of the calibration, which are identified using the pressures measured in the holes. Alternatively, Dambach and Hodson [28] suggested the use of a least-square method of the raw pressures.

In the current paper, a new methodology that uses a database of non-dimensional pressures and a minimization routine is proposed. The current data reduction approach is still valid even when one of the holes is clogged.