The present paper reports the development and nonnulling calibration technique to calibrate a cantilever type cylindrical fourhole probe of 2.54 mm diameter to measure threedimensional flows. The probe is calibrated at a probe Reynolds number of 9525. The probe operative angular range is extended using a zonal method by dividing into three zones, namely, center, left, and right zone. Different calibration coefficients are defined for each zone. The attainable angular range achieved using the zonal method is ±60 degrees in the yaw plane and −50 to +30 degrees in the pitch plane. Sensitivity analysis of all the four calibration coefficients shows that probe pitch sensitivity is lower than the yaw sensitivity in the center zone, and extended left and right zones have lower sensitivity than the center zone. In addition, errors due to the data reduction program for the probe are presented. The errors are found to be reasonably small in all the three zones. However, the errors in the extended left and right zones have slightly larger magnitudes compared to those in the center zone.
Turbomachinery flows are highly unsteady and three dimensional. The key to further improvement in turbomachinery is through understanding the threedimensional flow through their components such as rotors and stators. Such three dimensional flows encountered in turbomachines can be analyzed by flow visualization, computational methods, and direct measurements of the flow field. However, flow visualization has limitations since the techniques serve only to the locate regions of interest in the flow, and computational methods are expensive and are not fully reliable. Only direct measurement of the flow can provide quantitative data of flow parameters, such as total and static pressures, velocities and Mach numbers, and flow angles to understand the flow better. Pressure probes are one of the options to measure the flow parameters directly by inserting them into the flow field of turbomachines [
Since Henri Pitot used a simple bent tube to measure the total pressure in fluid flow in 1732, a broad variety of pneumatic probes have been developed over years. Recently, Telionis et al. [
Ostowari and Wentz Jr. [
As previously stated, a multihole probe having four pressure holes can be used to measure threedimensional flows. The size of the fivehole probe, sevenhole probe, and probe of higher number of holes is larger, causing larger velocity gradient and blockage errors. Shepherd [
The objective of the present work is to develop a miniature fourhole probe with a hemispherical shape on top of the probe tip, as opposed to an elliptical shape [
The fourhole probe used in the present investigation is fabricated using stainless steel tube of 2.54 mm diameter to which a probe head of 2.54 mm diameter and 8 mm length is silver brazed. Figure
Orthogonal views of the fourhole pressure probe head and schematic of the probe.
The fourhole probe is calibrated in an openjet, low speed calibration tunnel facility of Thermal Turbomachines Laboratory, Department of Mechanical Engineering, IIT, Madras, which is shown in Figure
Calibration tunnel, calibration device, probe, and instrumentation.
The probe is mounted in a calibration device. The calibration device consists of a base plate, a cclamp, and protractors with pointers for measurement of the pitch (
The fourhole probe is calibrated at a Reynolds number of 9525 (60 m/s velocity), based on the probe head diameter. A total of 425 (25 × 17 in the yaw and pitch planes, resp.) of calibration points were obtained over a yaw angle range of ±60 degrees and a pitch angle range of 30 to −50 degrees, at an interval of 5 degrees in the yaw and pitch angle range.
The pressure data recorded during calibration was used to plot calibration curves using the traditional calibration coefficients defined for one such probe earlier [
The traditional normalized calibration coefficients for the fourhole probe are defined as follows:
The calibration curve
Pressure distributions of the fourhole probe and zone division.
The calibration coefficients and normalizing factor are calculated using the pressures measured by the four holes of the probe. Hence, it is necessary to analyze the pressure data of each hole of the probe at various flow angles for discrimination of zones based on their behavior. In this section, an effort has been made to analyze the pressure coefficient distributions of the four probe holes over an angular range of ±60 degrees in yaw and +30 to −50 degrees in pitch. Figure
For the present fourhole probe,
Figure
Zone division including extended zones.
The calibration space is divided into three zones, namely, center (yaw angle range of ±30°), left (yaw angle range of −60° to −20°), and right (yaw angle range of 20° to 60°) zones, with zones overlapping so that no yaw region is left without calibration coefficients. Calibration coefficients are defined for each zone and computed. The calibration coefficients for each zone are defined as shown in Table
Definition of calibration coefficients.
Zone 






Center zone 





Left zone 





Right zone 




( 
In Table
The calibration curves for the center, left, and right zones are shown in Figures
Calibration curves of the fourhole probe for the center zone.
Calibration curves of the fourhole probe for the left and right zones.
This severe distortion from a rectangular shape may result in an error of flow angle determination. From the calibration curves of
A sensitivity analysis of the calibration coefficients was carried out for the three zones to quantify the accuracy of the measurements. Sensitivity graphs show the variation of the dependent quantities as a function of the independent quantities. The dependent quantities here are the four calibration coefficients,
The sensitivity coefficients for the center, left, and right zones are shown in Figures
Sensitivity curves of the calibration coefficients in the center zone.
Sensitivity curves of the calibration coefficients in the left and right zones.
A look up table method has been developed for a fivehole probe by Sitaram and Kumar [
Histograms of interpolation errors of the fourhole probe in different zones.
The maximum, minimum, RMS, and SD values of errors in yaw and pitch angles and total, static, and dynamic pressures are also presented in Table
Errors in yaw and pitch angles and total and static pressure coefficients.
Zone  Error in yaw angle, Δ 
Error in total pressure coefficient, Δ  

Max  Min  RMS  SD  Max  Min  RMS  SD  
Center  1.00  −1.27  0.36  0.35  0.020  −0.029  0.012  0.008 
Left  0.85  −1.27  0.32  0.32  0.020  −0.029  0.008  0.008 
Right  0.61  −2.03  0.54  0.54  0.022  −0.015  0.008  0.008 


Zone  Error in pitch angle, Δ 
Error in static pressure coefficient, 

Max  Min  RMS  SD  Max  Min  RMS  SD  


Center  0.89  −1.34  0.59  0.38  0.028  −0.028  0.011  0.010 
Left  0.89  −1.14  0.33  0.33  0.028  −0.028  0.010  0.010 
Right  0.85  −2.11  0.53  0.50  0.027  −0.039  0.015  0.014 
Except for yaw and pitch angles and the static pressure coefficient in the right zone, the errors are very small. The large values of errors occur near the extreme range of the calibration zones. The errors are due to the data reduction program only. All other measurement errors such as instrumentation errors, errors due to the calibration (zero angle settings, pitch and yaw angle measurements during calibration, etc.), are not included. For Table
From the present investigation, the following major conclusions are drawn:
The calibration range of a cantilever type fourhole probe is extended to ±60 degrees in the yaw plane and −50 to +30 degrees in the pitch plane. This is achieved by dividing the calibration space into three zones, namely, center, left, and right zones. The zones are overlapping so that no point in the calibration space is left without calibration coefficients. In each of the zones, the calibration coefficients are defined differently.
The probe pitch sensitivity is lower than the yaw sensitivity in the center zone. Extended left and right zones have lower sensitivity than the center zone.
Errors due to the data reduction program for the probe are presented for all the zones and the errors are found to be reasonably low in all three zones. However the errors in the extended left and right zones have slightly larger magnitudes compared to those in the center zone.
From the present investigation, it can be concluded that the probe can be used for measurement of highly threedimensional flows that occur in turbomachinery and other aerodynamic flows, particularly in confined measurement spaces.
It is important to emphasize that measurements by multihole probes are affected by flow Mach and Reynolds numbers. Hence it is essential that the probes be calibrated at different Mach and Reynolds numbers and methods be developed to account for these effects on the probe measurements. The calibration is presented at only one velocity to establish the extended calibration technique. The probe will be calibrated at different Mach and Reynolds numbers and methods will be developed to include these effects on the probe measurements. These results will be presented in a future paper.
Center, left, and right zones of calibration space (see Figures
Pitch coefficient (defined in text)
Static pressure coefficient (defined in text)
Total pressure coefficient (defined in text)
Yaw coefficient (defined in text)
Probe dynamic pressure, Pa (defined in text)
Maximum, minimum, root mean square, and standard deviation values of interpolation error
Total pressure, Pa
Static pressure, Pa
Pressures measured by probe holes 1 to 4, Pa
Pressures measured by probe holes 1 to 4, nondimensionalized with
Dynamic pressure =
Yaw angle, deg.
Pitch angle, deg.
Interpolation error of yaw angle, deg.
Interpolation error of pitch angle, deg.
Sensitivity of calibration coefficient,
Interpolation error of static pressure coefficient
Interpolation error of total pressure coefficient.
The authors declare that there is no conflict of interests regarding the publication of this paper.