Scale-by-scale energy budget in fractal element grid-generated turbulence

Abstract

Measurements were conducted downstream of a square-fractal-element grid at , where L₀ is the size of the largest element in the grid. The scale-by-scale energy budget for grid turbulence is used to investigate the phenomenological change in the turbulence between the inhomogeneous and homogeneous regions downstream of the grid, providing greater insight into the evolution of the turbulence in these two regions. It is shown that in the far field, x/L₀ ≥ 20, where the flow is approximately homogeneous and isotropic, the scale-by-scale energy budget for grid turbulence is well balanced. In the near field, x/L₀ < 20, the same energy budget is not satisfied, with the imbalance of the budget occurring at scales in the range λ ≲ r ≲ L₀. It is proposed that the imbalance is caused by non-zero transverse transport of turbulent kinetic energy and production due to transverse mean velocity gradients. Approach of the spectra to k^−5/3 behaviour with a decade long scaling range in the inhomogeneous region is attributed to forcing by these non-zero transverse terms.

Keywords:

• grid turbulence
• homogeneous turbulence
• isotropic turbulence
• energy budget
• fractal grid

Acknowledgements

P. Lavoie is grateful to Prof. R.A. Antonia for his guidance and mentorship over the years. R. Jason Hearst would also like to thank Mr H. Sadeghi for the frequent and stimulating discussions that took place relating to the scale-by-scale energy budget analysis.

Additional information

Funding

This work is supported by the Natural Sciences and Research Council of Canada (NSERC).