Multiscale turbulence explained

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]

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

C _{\epsilon} in\varepsilon = C _{\varepsilon} (l{U)/(^{3}{l{L}}})

is not constant, as required by the Richardson-Kolmogorov energy cascade. This new law^[15] can be expressed as

C _{\epsilon} \propto (Re ^{m} _{I})/(Re ^{n} _{L}) , with m ≈ 1 ≈ n , where Re _{I} and 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]}

Notes and References

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