The effect of Reynolds number on the scaling range along the centreline of a round turbulent jet

Abstract

In this paper, the effect of Reynolds number on the scaling range of the velocity spectra and structure functions along the centreline in a round turbulent jet is considered. Hot-wire measurements were taken over a range of exit Reynolds numbers (). Both axial (u) and transverse (v) energy spectra in the scaling range demonstrate considerable departure from the k^−5/3 (Kolmogorov inertial range scaling). Over the present range of Reynolds numbers, the scaling wave number exponent for axial, m₁, and transverse, m₂, spectra exhibit monotonic changes with Taylor Reynolds number: , . On the jet centreline, the data are in close agreement with the earlier findings for grid-generated turbulence. In addition, the structure functions are investigated. The scaling exponent for the second-order structure functions increases with in a power-law fashion () similar to the spectra. The peak value of the normalised third-order structure function C₃ asymptotically approaches 4/5 as the Reynolds numbers increases: . The present round jet data confirm that a proper inertial range is unlikely to be established along the jet axis unless a very high Reynolds number of can be reached.

Keywords:

• turbulent jet
• scaling range
• energy spectra
• structure functions
• Reynolds number

Additional information

Funding

The authors acknowledge the financial support of the Natural Sciences and Engineering Research Council of Canada under their discovery and RTI grant programmes.