Abstract
The supersonic multi-hole probe is an essential test tool for wind tunnel experiments, which is necessary to develop the basic research of improving the measurement accuracy and expanding the application of the probes.
This paper theoretically derived a gas compression factor δs∼f(p*, ps, κ, λ) to expand the scope of application of Bernoulli’s equation, and discussed the reliability issues of using this factor to solve the velocity and Mach number of the supersonic flow. The research results show that the calculation method of aerodynamic parameters of the supersonic flow proposed in this paper has credibility within one ten-thousandth of the calculation error compared with the calculation of aerodynamic theory. Compared with the algorithm in this paper and the other three algorithms, the calculation errors of the velocity and Mach number of the supersonic flow and the static pressure ratio before and after the shock are all within the range of one ten-thousandth based on the experimental data of a transonic turbine linear cascade. However, the error of the post-wave Mach number is relatively large. Finally, a universal supersonic multi-hole probe calibration algorithm proposed in this paper is suitable for automated non-opposing measurement. It has generally credible and fully considers the shock wave factor. It will improve the theoretical system of multi-hole probes, and provide theoretical guidance and technical support for the supersonic wind tunnel experiment.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Abbreviations
- a :
-
sound velocity
- h :
-
gas enthalpy
- K:
-
calibration coefficient
- Ma :
-
Mach number
- P :
-
pressure
- q :
-
heat transfer per unit mass of fluid
- T :
-
flow temperature
- v :
-
flow velocity
- γ :
-
specific heat ratio
- δ s :
-
gas compression factor
- ε(λ):
-
aerodynamic function of density
- κ :
-
adiabatic index
- λ :
-
velocity factor
- π(λ):
-
aerodynamic function of pressure
- ρ :
-
flow density
- τ(λ):
-
aerodynamic function of temperature
- s:
-
static value
- α :
-
angle of pitch
- β :
-
deflection angle
- 1:
-
before the shock wave
- 2:
-
behind the shock wave
- *:
-
total value
References
Vergine F., Maddalena L., Stereoscopic particle image velocimetry measurements of super-sonic, turbulent, and interacting streamwise vortices: challenges and application. Progress in Aerospace Sciences, 2014, 66: 1–16.
Johansen E.S., Rediniotis O.K., Jones G., The compressible calibration of miniature multi-hole probes. Journal of Fluids Engineering, 2001, 123(1): 128–138.
Delhaye D., Paniagua G., Fernández Oro J.M., et al., Enhanced performance of fast-response 3-hole wedge probes for transonic flows in axial turbomachinery. Experiments in Fluids, 2011, 50(1): 163–177.
Payne F.M., Ng T.T., Nelson R.C., Seven-hole probe measurement of leading-edge vortex flows. Experiments in Fluids, 1989, 7(1): 1–8.
Sumner D., Heseltine J.L., Dansereau O.J.P., Wake structure of a finite circular cylinder of small aspect ratio. Experiments in Fluids, 2004, 37(5): 720–730.
Gilarranz J.L., Ranz A.J., Kopko J.A., et al., On the use of five-hole probes in the testing of industrial centrifugal compressors. Journal of Turbomachinery, 2005, 127(1): 91–106.
Kan X.X., Huang G.F., Wu W.Y., Zhong J.J., Research on solving flow velocity method of a high subsonic probe. Academic Conference on Thermomechanical and Aerodynamics of Chinese Society of Engineering Thermophysics; Baoding, Hebei, China, 2020, Oct 23–25, No. 202446. (in Chinese)
Goodyer M.J., A stagnation pressure probe for supersonic and subsonic flows. Aeronautical Quarterly, 1974, 25(02): 91–100.
Hsieh T., Flow-field study about a hemi-sphere-cylinder in the transonic and low supersonic Mach number range. AIAA Paper, 1975, 75–83: 1–11.
Zhao B., Zhao J., Numerical simulation of pressure probe calibration based on CFD under supersonic condition. Metrology & Measurement Technology, 2017, 37(2): 15–18, 36. (in Chinese)
Pisasale A.J., Ahmed N.A., Theoretical calibration for highly three-dimensional low-speed flows of a five-hole probe. Measurement Science & Technology, 2002, 13(7): 1100.
Anderson J.D., Fundamentals of aerodynamics. Beijing: Aviation industry press, 2010, 3: 549–550.
Zhong J.J., Kan X.X., Wu W.Y., et al., A composite pressure-temperature probe and flow velocity calculation method. China, 202010599342.5.
Luo W.W., Wang H.S., Zhao X.L., Experiment investigation on the flow characteristic in a transonic convergent-divergent turbine cascade. Journal of Engineering Thermophysics, 2013, 34(7): 1229–1233. (in Chinese)
Acknowledgments
This study was co-supported by the National Natural Science Foundation of China (No. 51906134 and 51436002).
Author information
Authors and Affiliations
Corresponding author
Additional information
Article type: Contributed by Asian Congress on Gas Turbines 2020 (August 18–19, 2021, China).
Rights and permissions
About this article
Cite this article
Zhong, J., Huang, G., Wu, W. et al. Research on Calculation Method of Aerodynamic Parameters of Supersonic Probe Based on Gas Compressibility Factor. J. Therm. Sci. 31, 111–119 (2022). https://doi.org/10.1007/s11630-022-1514-9
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11630-022-1514-9