Session: 05-07 Advanced Topics in Instrumentation (I)

Paper Number: 101320

101320 - Reynolds Number Calibration Coefficient for Multi-Hole Pneumatic Probes 

To acquire high accuracy measurement data in transonic turbomachinery flows, pneumatic multi-hole probes are commonly calibrated in a known, homogenous flow. Typically, this entails recording the probe pressures while varying flow angles and the Mach number. Another parameter affecting the probe pressures is the Reynolds number. However, there are additional requirements regarding the calibration facility to achieve Reynolds number similarity between probe calibration and operation. Either the pressure or temperature must be varied independently of the Mach number. Achieving Reynolds number similarity is further complicated as the same probes are often used at different positions in the turbomachinery and thus at different Reynolds numbers. Consequently, the question arises how to deal with Reynolds number effects in a way that ensures high accuracy measurements while limiting calibration effort.

Although the significance of the Reynolds number effect has been investigated in literature, a generally accepted approach how to incorporate it into probe measurements seems to be missing so far. In comparison, there is a widespread consensus that, at least in compressible flows, the effect of the Mach number should be accounted for. This is usually done by defining a dimensionless calibration coefficient that can be used to interpolate between the discrete Mach numbers of the probe calibration. A similar approach seems desirable for the Reynolds number as well. Probes equipped with a temperature sensor are suitable to determine the complete thermodynamic state of the flow. Consequently, it seems feasible to derive a calibration coefficient from the directly measured probe pressures and temperatures to consider the Reynolds number effect. This would help to reduce the number of discrete Reynolds numbers required during probe calibration and simplify the evaluation of measurements.

In the present study, a calibration coefficient is introduced that can be used to take the Reynolds number effect into account. The calibration of a cone-shaped five-hole probe equipped with an additional pressure hole for measurements in transonic flows and a thermocouple is presented to demonstrate the suitability of the coefficient. The calibrations were conducted in the Probe Calibration Wind Tunnel (SKG) at the German Aerospace Center (DLR) in Göttingen. A Mach number range from 0.3 to 1.3 is covered. The total pressure is varied independently of the Mach number resulting in a probe Reynolds number range from 12,000 to 93,000. Additionally, 1,200 test points were recorded at randomly chosen flow angles and six different total pressures as well as four different Mach numbers. The measurement deviations between interpolated values of the flow parameters based on the calibration data and the reference values were calculated for each test point. In order to assess the performance of the coefficient, three different measurement evaluation approaches are considered in the study. Firstly, the effect of the Reynolds number is neglected. Secondly, the calibration data from the Reynolds number closest to the test point is selected for interpolation. Finally, the proposed Reynolds number coefficient is used.

The data show a clear increase of the measurement deviations with increasing differences of the Reynolds number between the test and calibration points. This demonstrates the Reynolds number effect. The standard deviations of the measurement deviations for flow angles increase up to a factor of three if the calibration data at a differing Reynolds number is used. For the Mach number, the increase is up to six-fold. In low subsonic and high transonic flow, the proposed calibration coefficient performs very well, almost completely eliminating the effect of the Reynolds number on measurement deviations. However, in high subsonic flow and near Mach number unity, the coefficient leads to an increase of the measurement deviations of the pitch angle and Mach number at some Reynolds numbers. Still, the study shows the suitability of the coefficient for interpolations between calibration data taken at different Reynolds numbers that is easy to incorporate into most probe measurement evaluation routines.

Presenting Author: Johannes R. Bachner German Aerospace Center (DLR)

Presenting Author Biography: Jan. 2018 - present: Research Assistent at German Aerospace Center (DLR)
Tasks:
- Calibration of multi-hole pneumatic probes
- Evaluation of measurement uncertainties for multi-hole pneumatic probes in research turbines
- Development of multi-hole pneumatic probes

Apr. 2014 - May 2017: Master Studies of Mechanical Engineering at KIT Karlsruhe
Focus on thermal turbomachinery

Authors:

Johannes R. Bachner German Aerospace Center (DLR)
Andreas Pahs German Aerospace Center (DLR)