A novel method for extending the calibration range of five-hole probe for highly three-dimensional flows
Introduction
Five-hole probes [1] are commonly used to obtain the scalar and vector properties of complicated flow fields such as those encountered around complex bodies or turbomachines in terms of static and total pressure and three-dimensional (3D) velocity components respectively. The probe can be used in both nulling and non-nulling mode, however, space and wind tunnel blockage often require the probe to be small [2], and the difficulty associated with traversing and data acquisition encountered when the probe is used in a nulling fashion, make a non-nulling method a better alternative.
Available calibration techniques [1], [2], [3], [4], [5] of a five-hole probe in a non-nulling mode are unfortunately either difficult to conduct and require a complex procedural method for use, encounter singularity, or are restricted to lower flow angle ranges, preventing their use in highly 3D flows. Attempts to extend the range of a five-hole probe [6], [7], have had limited success, due to their complexity or limitations.
The most common method of calibration is by using the technique proposed by Treaster and Yocum [1]. Although elegant in its simplicity, the technique encounters singularity when calibration for large angle of pitch or yaw is sought.
A closer examination suggests that the technique is essentially an adaptation of five-hole probe calibration procedure used in a nulling mode where P1 is considered as the total pressure, and P̄ is considered as the static pressure. Consequently the difference of the two pressures, , is taken to represent the dynamic pressure, which is used to non-dimensionalise the calibration pressure coefficients. However, in a non-nulling mode, for large angles of both yaw and pitch, P1 and P̄ deviate significantly from the actual total and static pressure, and therefore, their difference no longer represents the dynamic pressure. To illustrate this point, a plot of the pitch angle, α, against Cpden is presented (Fig. 1), where Cpden is the traditional denominator [1], non-dimensionalised with the dynamic pressure of the freestream, q. The variation in Cpden is significant, with the value much less than unity, e.g. at −25° pitch and −25° yaw, the value of Cpden is 0.55. However, problem arises when there is a change in sign in the denominator, or more precisely when the denominator goes to zero producing a singularity that in turn makes the coefficients of pitch, yaw, total, and static pressure become infinite.
It thus appears that the problem lies in the definition of the denominator used in the non-dimensionalisation of calibration coefficients. A modification to the denominator of the method of Treaster and Yocum [1] is, therefore, developed, which successfully allows calibration to much higher angles of pitch and yaw, while maintaining the simplicity of the original procedure.
Section snippets
Calibration experiment
In order to explore for an improved method of calibration that avoids singularity and extends the range of calibration to higher pitch and yaw angles, a calibration experiment was performed. Calibration of these probes are often carried out in an open jet wind tunnel because of the large blockage errors that occur when the calibration set up is placed in a closed wind tunnel test section. The air quality in terms of low turbulence and uniformity of flow within a closed test section is, however,
Preliminary investigations
In this section we examine various options for avoiding singularity in the denominator of the pressure coefficients.
Discussion
The error in repeated Cppitch and Cpyaw values gathered on different days, was found to be on average, within ±1.5%. This neglects those values that are close to zero, which cause a singularity in the error calculation. Great care [8] must be taken to reduce error in the calibration process, as the error in calibration is effectively added to the overall error when the probe is in use. It was for this reason that the calibration was conducted for only half the calibration range, namely negative
Conclusion
A novel method that is simple and easy to implement, and successfully overcomes the problem of singularity encountered in the traditional method has been detailed in this paper. The new calibration procedure should allow five-hole probes, when used in a non-nulling mode, to provide useful information when applied to highly 3D flows. A calibration experiment performed using this technique demonstrates that the calibration range can be easily extended up to angles of ±75°.
Acknowledgements
The authors wish to thank the Australian Research Council, and Edmonds Australia Ltd. for funding this project.
References (9)
- et al.
Five-hole pressure probe analysis technique
Flow Meas. Instrum.
(1998) - et al.
The calibration and application of five-hole probes
ISA Trans.
(1979) - et al.
Miniature five-hole pressure probe for measurement of three mean velocity components in low-speed flows
J. Phys. E.
(1989) The evaluation of a simplified form of presentation for five-hole spherical and hemispherical pitometer calibration data
J. Phys. E.
(1970)