Multiscale turbulence: Difference between revisions

Content deleted Content added

Inline

Revision as of 15:13, 28 February 2015

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]. This is usually achieved by immersing a body in a moving fluid; the obstacle may have a specific arrangement of length scales^[2] or have it's geometry actively changed^[3] by some control system (as illustrated on YouTube).

Three examples of multiscale turbulence generators. From left to right, a fractal cross grid, a fractal square grid and a fractal I 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, such as reducing acoustic noise from wings modifying the geometry of spoilers^[4], enhancing heat transfer from impinging jets passing through grids^[5], increasing the drag of flows past normal plates^[6] or enhancing mixing ^[7]. Further research of multiscale turbulence is currently in place in order to further explore the properties of these flows^[8].

Multiscale turbulence has also played an important role into probing the internal structure of turbulence^[9]. This sort of turbulence allowed researchers to unveil a novel dissipation law in which the parameter $C_{\epsilon }$ in

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

is not constant, as required by the Richardson-Kolmogorov energy cascade. This new law^[10] can be expressed as $C_{\epsilon }\propto {\frac {Re_{I}^{m}}{Re_{L}^{n}}}$ , with $m\approx n$ , where $Re_{I}$ and $Re_{L}$ are respectively Reynolds numbers based on initial (such as free-stream velocity and the object's length scale) and local conditions (such as the rms velocity and integral length scale). The region of the flow where this new law holds is termed non-equilibrium turbulence^[11] as it implies an imbalance between the energy fed down the cascade by the large (energy containing) scales and that which is dissipated (at the smallest scales).

References

^ Laizet, S.; Vassilicos, J. C. (January 2009). "Multiscale Generation of Turbulence". Journal of Multiscale Modelling. 01 (01): 177–196. doi:10.1142/S1756973709000098.
^ Queiros-Conde, D., and J. C. Vassilicos. "Turbulent wakes of 3D fractal grids." Intermittency in turbulent flows (2001): 136-167.
^ Hideharu, M. (October 1991). "Realization of a large-scale turbulence field in a small wind tunnel". Fluid Dynamics Research. 8 (1–4): 53–64. doi:10.1016/0169-5983(91)90030-M.
^ 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., J. C. Vassilicos. "Fractal space-scale unfolding mechanism for energy-efficient turbulent mixing" Physical Review E 2012
^ "Multisolve". Retrieved 25 February 2015.
^ Vassilicos, J. C. (2015). "Dissipation in Turbulent Flows". Annual Review of Fluid Mechanics: 95-114. doi:10.1146/annurev-fluid-010814-014637.
^ Seoud, R. E.; Vassilicos, J. C. (2007). "Dissipation and decay of fractal-generated turbulence". Phys. Fluids. 19. doi:10.1063/1.2795211.
^ Valente, P. C.; Vassilicos, J. C. (May 2012). "Universal Dissipation Scaling for Nonequilibrium Turbulence". Physical Review Letters. 108 (21). doi:10.1103/PhysRevLett.108.214503.

[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] Queiros-Conde, D., and J. C. Vassilicos. "Turbulent wakes of 3D fractal grids." Intermittency in turbulent flows (2001): 136-167.

[3] Hideharu, M. (October 1991). "Realization of a large-scale turbulence field in a small wind tunnel". Fluid Dynamics Research. 8 (1–4): 53–64. doi:10.1016/0169-5983(91)90030-M.

[4] Nedić, J., B. Ganapathisubramani, J. C. Vassilicos, J. Boree, L. E. Brizzi, A. Spohn. "Aeroacoustic performance of fractal spoilers". AIAA journal 2012.

[5] 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.

[6] 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.

[7] Laizet, S., J. C. Vassilicos. "Fractal space-scale unfolding mechanism for energy-efficient turbulent mixing" Physical Review E 2012

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

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

[10] Seoud, R. E.; Vassilicos, J. C. (2007). "Dissipation and decay of fractal-generated turbulence". Phys. Fluids. 19. doi:10.1063/1.2795211.

[11] Valente, P. C.; Vassilicos, J. C. (May 2012). "Universal Dissipation Scaling for Nonequilibrium Turbulence". Physical Review Letters. 108 (21). doi:10.1103/PhysRevLett.108.214503.

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

@@ Line 3: / Line 3: @@
 '''Multiscale turbulence''' is a class of [[Turbulence | turbulent]] flows in which the chaotic motion of the [[Fluid|fluid]] is forced at different length and/or time scales<ref>{{cite journal|last1=Laizet|first1=S.|last2=Vassilicos|first2=J. C.|title=Multiscale Generation of Turbulence|journal=Journal of Multiscale Modelling|date=January 2009|volume=01|issue=01|pages=177–196|doi=10.1142/S1756973709000098}}</ref>. This is usually achieved by immersing a body in a moving fluid; the obstacle may have a specific arrangement of length scales<ref>Queiros-Conde, D., and J. C. Vassilicos. "Turbulent wakes of 3D fractal grids." Intermittency in turbulent flows (2001): 136-167.</ref> or have it's geometry actively changed<ref>{{cite journal|last1=Hideharu|first1=M.|title=Realization of a large-scale turbulence field in a small wind tunnel|journal=Fluid Dynamics Research|date=October 1991|volume=8|issue=1-4|pages=53–64|doi=10.1016/0169-5983(91)90030-M}}</ref> by some [[Control system | control system]] ({{YouTube| id= CU8qg9Jo8o4 | title= as illustrated }}).
-[[File:Fractalgrids.pdf|thumb|Three examples of multiscale turbulence generators. From left to right, a fractal cross grid, a fractal square grid and a fractal I grid.]]
+[[File:Fractalgrids.pdf|thumb|Three examples of multiscale [[Turbulence | turbulence]] generators. From left to right, a [[Fractal|fractal]] cross [[Grid (spatial index)|grid]], a [[Fractal|fractal]] square [[Grid (spatial index)|grid]] and a [[Fractal|fractal]] I [[Grid (spatial index)|grid]].]]
 As [[Turbulence | turbulent]] flows contain [[Eddy (fluid dynamics) | eddies]] with a wide range of scales, exciting the [[Turbulence | 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, such as reducing [[Noise (acoustic)|acoustic noise]] from wings modifying the geometry of [[Spoiler (aeronautics)|spoilers]]<ref> Nedić, J., B. Ganapathisubramani, J. C. Vassilicos, J. Boree, L. E. Brizzi, A. Spohn. [http://arc.aiaa.org/doi/pdf/10.2514/1.J051387 "Aeroacoustic performance of fractal spoilers"]. ''[[AIAA journal]]'' 2012.</ref>, enhancing [[Heat transfer|heat transfer]] from impinging jets passing through grids<ref>{{cite journal|last1=Cafiero|first1=G.|last2=Discetti|first2=S.|last3=Astarita|first3=T.|title=Heat transfer enhancement of impinging jets with fractal-generated turbulence|journal=International Journal of Heat and Mass Transfer|date=August 2014|volume=75|pages=173–183|doi=10.1016/j.ijheatmasstransfer.2014.03.049}}</ref>, increasing the [[Drag (physics)|drag]] of flows past normal plates<ref>{{cite journal|last1=Nedić|first1=J.|last2=Ganapathisubramani|first2=B.|last3=Vassilicos|first3=J. C.|title=Drag and near wake characteristics of flat plates normal to the flow with fractal edge geometries|journal=Fluid Dynamics Research|date=1 December 2013|volume=45|issue=6|pages=061406|doi=10.1088/0169-5983/45/6/061406}}</ref> or enhancing mixing <ref>Laizet, S., J. C. Vassilicos. [http://journals.aps.org/pre/pdf/10.1103/PhysRevE.86.046302 "Fractal space-scale unfolding mechanism for energy-efficient turbulent mixing"] ''[[Physical Review E]]'' 2012</ref>. Further research of multiscale turbulence is currently in place in order to further explore the properties of these flows<ref>{{cite web|url=http://www.multisolve.eu|accessdate=25 February 2015|title=Multisolve}}</ref>.
@@ Line 11: / Line 11: @@
 <math>\epsilon = C_\epsilon \frac{\mathcal{U}^3}{\mathcal{L}}</math>
-is not constant, as required by the [[Lewis Fry Richardson|Richardson]]-[[Andrey Kolmogorov|Kolmogorov]] [[Energy cascade|energy cascade]]. This new law<ref>{{cite journal|last1=Seoud|first1=R. E.|last2=Vassilicos|first2=J. C.|title=Dissipation and decay of fractal-generated turbulence|journal=Phys. Fluids|date=2007|volume=19|doi=10.1063/1.2795211|url=http://scitation.aip.org/content/aip/journal/pof2/19/10/10.1063/1.2795211}}</ref> can be expressed as <math>C_\epsilon \propto \frac{Re_I^m}{Re_L^n}</math>, with <math>m \approx n</math>, where <math>Re_I</math> and <math>Re_L</math> are respectively [[Reynolds number|Reynolds numbers]] based on initial (such as [[Freestream|free-stream velocity]] and the object's [[Length scale|length scale]]) and local conditions (such as the [[Root mean square|rms]] velocity and integral length scale). The region of the flow where this new law holds is termed non-equilibrium turbulence<ref>{{cite journal|last1=Valente|first1=P. C.|last2=Vassilicos|first2=J. C.|title=Universal Dissipation Scaling for Nonequilibrium Turbulence|journal=Physical Review Letters|date=May 2012|volume=108|issue=21|doi=10.1103/PhysRevLett.108.214503}}</ref> as it implies an imbalance between the energy fed down the [[Energy cascade|cascade]] by the large (energy containing) scales and that which is dissipated (at the [[Kolmogorov microscales|smallest scales]]).
+is not constant, as required by the [[Lewis Fry Richardson|Richardson]]-[[Andrey Kolmogorov|Kolmogorov]] [[Energy cascade|energy cascade]]. This new law<ref>{{cite journal|last1=Seoud|first1=R. E.|last2=Vassilicos|first2=J. C.|title=Dissipation and decay of fractal-generated turbulence|journal=Phys. Fluids|date=2007|volume=19|doi=10.1063/1.2795211|url=http://scitation.aip.org/content/aip/journal/pof2/19/10/10.1063/1.2795211}}</ref> can be expressed as <math>C_\epsilon \propto \frac{Re_I^m}{Re_L^n}</math>, with <math>m \approx n</math>, where <math>Re_I</math> and <math>Re_L</math> are respectively [[Reynolds number|Reynolds numbers]] based on initial (such as [[Freestream|free-stream velocity]] and the object's [[Length scale|length scale]]) and local conditions (such as the [[Root mean square|rms]] velocity and integral length scale). The region of the flow where this new law holds is termed non-equilibrium turbulence<ref>{{cite journal|last1=Valente|first1=P. C.|last2=Vassilicos|first2=J. C.|title=Universal Dissipation Scaling for Nonequilibrium Turbulence|journal=Physical Review Letters|date=May 2012|volume=108|issue=21|doi=10.1103/PhysRevLett.108.214503}}</ref> as it implies an imbalance between the energy fed down the [[Energy cascade|cascade]] by the large ([[Turbulence kinetic energy|energy]] containing) scales and that which is [[Dissipation |dissipated]] (at the [[Kolmogorov microscales|smallest scales]]).