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]

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]

In 2013 the EU awarded a Marie Curie grant of 3.8M Euros for research and training of 13 young scientists and engineers in multiscale turbulence in order to further explore and apply the properties of these flows^[15]^[16]

Multiscale turbulence has also played an important role into probing the internal structure of turbulence.^[17] This sort of turbulence allowed researchers to unveil a novel dissipation law in which the parameter $C_{\epsilon }$ in

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

is not constant, as required by the Richardson-Kolmogorov energy cascade. This new law^[17] can be expressed as $C_{\epsilon }\propto {\frac {Re_{I}^{m}}{Re_{L}^{n}}}$ , with $m\approx 1\approx n$ , 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^[17]^[18]

References

^ Laizet, S.; Vassilicos, J. C. (January 2009). "Multiscale Generation of Turbulence". Journal of Multiscale Modelling. 01 (01): 177–196. doi:10.1142/S1756973709000098.
^ Mazzi, B.; Vassilicos, J. C. (10 March 2004). "Fractal-generated turbulence". Journal of Fluid Mechanics. 502: 65–87. doi:10.1017/S0022112003007249.
^ Hurst, D.; Vassilicos, J. C. (2007). "Scalings and decay of fractal-generated turbulence". Physics of Fluids. 19 (3): 035103. doi:10.1063/1.2676448.
^ 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. doi:10.1063/1.4811402.
^ Thormann, A.; Meneveau, C. (February 2014). "Decay of homogeneous, nearly isotropic turbulence behind active fractal grids". Physics of Fluids. 26 (2): 025112. doi:10.1063/1.4865232.
^ "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. 1 December 2013. doi:10.1088/0169-5983/45/6/061001.
^ Nedić, J., B. Ganapathisubramani, J. C. Vassilicos, J. Boree, L. E. Brizzi, A. Spohn. "Aeroacoustic performance of fractal spoilers". AIAA journal 2012.
^ 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.
^ 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. doi:10.1088/0169-5983/45/6/061406.
^ 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. doi:10.1017/jfm.2014.695.
^ 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. doi:10.1088/0031-8949/2010/T142/014065.
^ 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.
^ 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.
^ 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.
^ "Multisolve". Retrieved 25 February 2015.
^ "Multisolve Marie Curie grant".
^ ^a ^b ^c Vassilicos, J. C. (2015). "Dissipation in Turbulent Flows". Annual Review of Fluid Mechanics: 95–114. doi:10.1146/annurev-fluid-010814-014637.
^ Castro, Ian P. (2016). "Dissipative distinctions". Journal of Fluid Mechanics. 788: 1–4. doi:10.1017/jfm.2015.630. ISSN 0022-1120.

[1] Laizet, S.; Vassilicos, J. C. (January 2009). "Multiscale Generation of Turbulence". Journal of Multiscale Modelling. 01 (01): 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. doi:10.1017/S0022112003007249.

[3] Hurst, D.; Vassilicos, J. C. (2007). "Scalings and decay of fractal-generated turbulence". Physics of Fluids. 19 (3): 035103. 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. 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. doi:10.1063/1.4865232.

[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. 45 (6): 061001. 1 December 2013. 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. doi:10.1088/0169-5983/45/6/061406.

[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. doi:10.1017/jfm.2014.695.

[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. doi:10.1088/0031-8949/2010/T142/014065.

[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.

[15] "Multisolve". Retrieved 25 February 2015.

[16] "Multisolve Marie Curie grant".

[DissipationJCV15-17] Vassilicos, J. C. (2015). "Dissipation in Turbulent Flows". Annual Review of Fluid Mechanics: 95–114. doi:10.1146/annurev-fluid-010814-014637.

[18] Castro, Ian P. (2016). "Dissipative distinctions". Journal of Fluid Mechanics. 788: 1–4. doi:10.1017/jfm.2015.630. ISSN 0022-1120.

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