Development of a nanoscale hot-wire probe for supersonic flow applications


A new nanoscale thermal anemometry probe (NSTAP) was designed and fabricated to measure mass flux in supersonic flows. This sensor was evaluated in the Trisonic Wind Tunnel Munich (TWM) at both subsonic and supersonic speeds. Subsonic compressible flow tests were performed to confirm the new sensor’s repeatability and to compare its behaviour to measurements from a conventional cylindrical hot-wire, while supersonic tests were performed to investigate the nature of the convective heat transfer from the nanoscale sensor at those conditions. For the range of mass fluxes tested in the supersonic regime, a linear relationship between the Nusselt number and the Reynolds number fit the data well. A linear relationship has previously been noticed at length scales close to the molecular mean free path of the flow and has been attributed to the free-molecule flow regime, where the Knudsen number is on the order of unity.

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  1. Bailey SCC, Kunkel GJ, Hultmark M, Vallikivi M, Hill JP, Meyer KA, Tsay C, Arnold CB, Smits AJ (2010) Turbulence measurements using a nanoscale thermal anemometry probe. J Fluid Mech 663:160–179

    Article  Google Scholar 

  2. Bruun HH (1996) Hot-wire anemometry: principles and signal analysis

  3. Byers CP (2018) Theoretical and experimental investigations of similarity solutions in turbulent flows. PhD thesis, Princeton University

  4. Comte-Bellot G (1976) Hot-wire anemometry. Annu Rev Fluid Mech 8(1):209–231

    Article  Google Scholar 

  5. Dewey CF Jr (1965) A correlation of convective heat transfer and recovery temperature data for cylinders in compressible flow. Int J Heat Mass Transfer 8(2):245–252

    Article  Google Scholar 

  6. Fan Y, Arwatz G, Van Buren T, Hoffman D, Hultmark M (2015) Nanoscale sensing devices for turbulence measurements. Exp Fluids 56(7):138

    Article  Google Scholar 

  7. Hultmark M, Ashok A, Smits AJ (2011) A new criterion for end-conduction effects in hot-wire anemometry. Meas Sci Technol 22(5):055401

    Article  Google Scholar 

  8. Hultmark M, Vallikivi M, Bailey SCC, Smits AJ (2012) Turbulent pipe flow at extreme Reynolds numbers. Phys Rev Lett 108(9):094501

    Article  Google Scholar 

  9. Hutchins N, Monty JP, Hultmark M, Smits AJ (2015) A direct measure of the frequency response of hot-wire anemometers: temporal resolution issues in wall-bounded turbulence. Exp Fluids 56(1):18

    Article  Google Scholar 

  10. King LV (1914) XII. On the convection of heat from small cylinders in a stream of fluid: Determination of the convection constants of small platinum wires with applications to hot-wire anemometry. Phil Trans R Soc Lond A 214(509–522):373–432

    Article  Google Scholar 

  11. Kovasznay LS (1950) The hot-wire anemometer in supersonic flow. J Aeronaut Sci 17(9):565–572

    Article  Google Scholar 

  12. Kovasznay LS (1953) Turbulence in supersonic flow. J Aeronaut Sci 20(10):657–674

    Article  Google Scholar 

  13. Laufer J, McClellan R (1956) Measurements of heat transfer from fine wires in supersonic flows. J Fluid Mech 1(3):276–289

    Article  Google Scholar 

  14. Li JD, McKeon BJ, Jiang W, Morrison JF, Smits AJ (2004) The response of hot wires in high Reynolds-number turbulent pipe flow. Meas Sci Technol 15(5):789

    Article  Google Scholar 

  15. Morkovin MV (1956) Fluctuations and hot-wire anemometry in compressible flows. North Atlantic Treaty Organization Advisory Group for Aeronautical Research and Development

  16. Oppenheim A (1953) Generalized theory of convective heat transfer in a free-molecule flow. J Aeronaut Sci 20(1):49–58

    Article  Google Scholar 

  17. Raffel M, Willert CE, Scarano F, Kähler CJ, Wereley ST, Kompenhans J (2018) Particle image velocimetry: a practical guide. Springer, New York

    Book  Google Scholar 

  18. Rapp BE (2016) Microfluidics: modeling, mechanics and mathematics. William Andrew, Amsterdam

    MATH  Google Scholar 

  19. Sarma GR (1993) Analysis of a constant voltage anemometer circuit. In: 1993 IEEE instrumentation and measurement technology conference, IEEE, pp 731–736

  20. Scharnowski S, Bross M, Kähler CJ (2019) Accurate turbulence level estimations using PIV/PTV. Exp Fluids 60(1):1

    Article  Google Scholar 

  21. Sheplak M, Spina EF, McGinley CB (1996) Progress in hot-film anemometry for hypersonic flow. Exp Thermal Fluid Sci 13(1):21–28

    Article  Google Scholar 

  22. Smits AJ, Hayakawa K, Muck KC (1983) Constant temperature hot-wire anemometer practice in supersonic flows. Exp Fluids 1(2):83–92

    Article  Google Scholar 

  23. Stalder JR, Goodwin G, Creager MO (1951) A comparison of theory and experiment for high-speed free-molecule flow

  24. Stalder JR, Goodwin G, Creager MO (1952) Heat transfer to bodies in a high-speed rarified-gas stream

  25. Vallikivi M, Smits AJ (2014) Fabrication and characterization of a novel nanoscale thermal anemometry probe. J Microelectromech Syst 23(4):899–907

    Article  Google Scholar 

  26. Vallikivi M, Hultmark M, Bailey SCC, Smits AJ (2011) Turbulence measurements in pipe flow using a nano-scale thermal anemometry probe. Exp Fluids 51(6):1521–1527

    Article  Google Scholar 

  27. Wallace JM, Foss JF (1995) The measurement of vorticity in turbulent flows. Annu Rev Fluid Mech 27(1):469–514

    Article  Google Scholar 

  28. Wittmer KS, Devenport WJ, Zsoldos JS (1998) A four-sensor hot-wire probe system for three-component velocity measurement. Exp Fluids 24(5–6):416–423

    Article  Google Scholar 

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This work was supported by the AFOSR FA9550-16-1-0170 (program manager: Ivett Leyva) and by the German Research Foundation (DFG). This work was also partly supported by the DFG Priority Programme SPP 1881 Turbulent Superstructures project number KA1808/21-1. The authors are grateful for having participated in the Sonderforschungsbereich Transregio 40 program as this initiated collaboration between both institutions. The authors particularly thank Dr. Christian Stemmer for his support throughout the program. The authors are also grateful to Princeton University’s clean room staff for their advice regarding certain manufacturing processes. In particular, the authors thank David S. Barth for his assistance using the scanning electron microscope. Finally, the authors thank Prof. Alexander J. Smits for his helpful discussions.

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Kokmanian, K., Scharnowski, S., Bross, M. et al. Development of a nanoscale hot-wire probe for supersonic flow applications. Exp Fluids 60, 150 (2019).

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