Multiscale turbulence

Multiscale turbulence is a class of turbulent flows in which the chaotic motion of the fluid is forced at different length and/or time scales.^[1][2] This is usually achieved by immersing in a moving fluid a body with a multiscale, often fractal-like, arrangement of length scales. This arrangement of scales can be either passive^[3][4] or active^[5]

Three examples of multiscale turbulence generators. From left to right, a fractal cross grid, a fractal square grid and a fractal I grid. See on YouTube the manufacturing of a fractal grid.

As turbulent flows contain eddies with a wide range of scales, exciting the turbulence at particular scales (or range of scales) allows one to fine-tune the properties of that flow. Multiscale turbulent flows have been successfully applied in different fields.,^[6] such as:

• Reducing acoustic noise from wings by modifying the geometry of spoilers;^[7]
• Enhancing heat transfer from impinging jets passing through grids;^[8]
• Reducing the vortex shedding intensity of flows past normal plates without changing the shedding frequency;^[9]
• Enhancing mixing by energy-efficient stirring;^[10][11]
• Improving flow metering and flow conditioning in pipes;^[12]
• Improving combustion.^[13][14]

Multiscale turbulence has also played an important role into probing the internal structure of turbulence.^[15] This sort of turbulence allowed researchers to unveil a novel dissipation law in which the parameter ${\displaystyle C_{\epsilon }}$ in

${\displaystyle \varepsilon =C_{\varepsilon }{\frac {{\mathcal {U}}^{3}}{\mathcal {L}}}}$

is not constant, as required by the Richardson-Kolmogorov energy cascade. This new law^[15] can be expressed as ${\displaystyle C_{\epsilon }\propto {\frac {Re_{I}^{m}}{Re_{L}^{n}}}}$, with ${\displaystyle m\approx 1\approx n}$, where ${\displaystyle Re_{I}}$ and ${\displaystyle Re_{L}}$ are Reynolds numbers based, respectively, on initial/global conditions (such as free-stream velocity and the object's length scale) and local conditions (such as the rms velocity and integral length scale). This new dissipation law characterises non-equilibrium turbulence apparently universally in various flows (not just multiscale turbulence) and results from non-equilibrium unsteady energy cascade. This imbalance implies that new mean flow scalings exist for free shear turbulent flows, as already observed in axisymmetric wakes^[15][16]

References

1. Laizet, S.; Vassilicos, J. C. (January 2009). "Multiscale Generation of Turbulence". Journal of Multiscale Modelling. 01 (1): 177–196. doi:10.1142/S1756973709000098.
2. Mazzi, B.; Vassilicos, J. C. (10 March 2004). "Fractal-generated turbulence". Journal of Fluid Mechanics. 502: 65–87. Bibcode:2004JFM...502...65M. CiteSeerX 10.1.1.475.2171. doi:10.1017/S0022112003007249. S2CID 58933525.
3. Hurst, D.; Vassilicos, J. C. (2007). "Scalings and decay of fractal-generated turbulence". Physics of Fluids. 19 (3): 035103–035103–31. Bibcode:2007PhFl...19c5103H. doi:10.1063/1.2676448.
4. Nagata, K.; Sakai, Y.; Inaba, T.; Suzuki, H.; Terashima, O.; Suzuki, H. (2013). "Turbulence structure and turbulence kinetic energy transport in multiscale/fractal-generated turbulence". Physics of Fluids. 25 (6): 065102–065102–26. Bibcode:2013PhFl...25f5102N. doi:10.1063/1.4811402.
5. Thormann, A.; Meneveau, C. (February 2014). "Decay of homogeneous, nearly isotropic turbulence behind active fractal grids". Physics of Fluids. 26 (2): 025112. Bibcode:2014PhFl...26b5112T. doi:10.1063/1.4865232.
6. Laizet, Sylvain; Sakai, Yasuhiko; Christos Vassilicos, J. (1 December 2013). "Special issue of selected papers from the second UK–Japan bilateral Workshop and First ERCOFTAC Workshop on Turbulent Flows Generated/Designed in Multiscale/Fractal Ways, London, March 2012". Fluid Dynamics Research. 45 (6): 061001. Bibcode:2013FlDyR..45f1001L. doi:10.1088/0169-5983/45/6/061001.
7. Nedić, J., B. Ganapathisubramani, J. C. Vassilicos, J. Boree, L. E. Brizzi, A. Spohn. "Aeroacoustic performance of fractal spoilers". AIAA journal 2012.
8. Cafiero, G.; Discetti, S.; Astarita, T. (August 2014). "Heat transfer enhancement of impinging jets with fractal-generated turbulence". International Journal of Heat and Mass Transfer. 75: 173–183. doi:10.1016/j.ijheatmasstransfer.2014.03.049.
9. Nedić, J.; Ganapathisubramani, B.; Vassilicos, J. C. (1 December 2013). "Drag and near wake characteristics of flat plates normal to the flow with fractal edge geometries". Fluid Dynamics Research. 45 (6): 061406. Bibcode:2013FlDyR..45f1406N. doi:10.1088/0169-5983/45/6/061406. S2CID 119569184.
10. Laizet, S.; Vassilicos, J. C. (23 December 2014). "Stirring and scalar transfer by grid-generated turbulence in the presence of a mean scalar gradient". Journal of Fluid Mechanics. 764: 52–75. Bibcode:2015JFM...764...52L. doi:10.1017/jfm.2014.695. hdl:10044/1/21530. S2CID 122885256.
11. Suzuki, H.; Nagata, K.; Sakai, Y.; Hayase, T. (1 December 2010). "Direct numerical simulation of turbulent mixing in regular and fractal grid turbulence". Physica Scripta. T142: 014065. Bibcode:2010PhST..142a4065S. doi:10.1088/0031-8949/2010/T142/014065. S2CID 120566583.
12. Manshoor, B.; Nicolleau, F. C. G. A.; Beck, S. B. M. (June 2011). "The fractal flow conditioner for orifice plate flow meters". Flow Measurement and Instrumentation. 22 (3): 208–214. doi:10.1016/j.flowmeasinst.2011.02.003.
13. Verbeek, A. A.; Bouten, T. W. F. M.; Stoffels, G. G. M.; Geurts, B. J.; van der Meer, T. H. (January 2015). "Fractal turbulence enhancing low-swirl combustion". Combustion and Flame. 162 (1): 129–143. doi:10.1016/j.combustflame.2014.07.003.
14. Goh, K. H. H.; Geipel, P.; Lindstedt, R. P. (September 2014). "Lean premixed opposed jet flames in fractal grid generated multiscale turbulence". Combustion and Flame. 161 (9): 2419–2434. doi:10.1016/j.combustflame.2014.03.010. hdl:10044/1/26010. S2CID 93650086.
15. Vassilicos, J. C. (2015). "Dissipation in Turbulent Flows". Annual Review of Fluid Mechanics. 47 (1): 95–114. Bibcode:2015AnRFM..47...95V. doi:10.1146/annurev-fluid-010814-014637.
16. Castro, Ian P. (2016). "Dissipative distinctions". Journal of Fluid Mechanics. 788: 1–4. Bibcode:2016JFM...788....1C. doi:10.1017/jfm.2015.630. ISSN 0022-1120.