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Review Articles

On Direct Numerical Simulation of Turbulent Flows

[+] Author and Article Information
Giancarlo Alfonsi

 Mem. ASME Fluid Dynamics Laboratory, Dipartimento Difesa del Suolo, Università della Calabria, Via P. Bucci 42b, 87036 Rende (Cosenza), Italygiancarlo.alfonsi@unical.it

Appl. Mech. Rev 64(2), 020802 (Dec 07, 2011) (33 pages) doi:10.1115/1.4005282 History: Received May 19, 2010; Accepted October 03, 2011; Published December 07, 2011; Online December 07, 2011

The direct numerical simulation of turbulence (DNS) has become a method of outmost importance for the investigation of turbulence physics, and its relevance is constantly growing due to the increasing popularity of high-performance-computing techniques. In the present work, the DNS approach is discussed mainly with regard to turbulent shear flows of incompressible fluids with constant properties. A body of literature is reviewed, dealing with the numerical integration of the Navier-Stokes equations, results obtained from the simulations, and appropriate use of the numerical databases for a better understanding of turbulence physics. Overall, it appears that high-performance computing is the only way to advance in turbulence research through the front of the direct numerical simulation.

Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Mean-velocity profile in turbulent channel flow: (—) data from Ref. [31]; (+++) data from Ref. [22]; (- - -) law of the wall (u+=y+ and u+=2.5lny++5.5)

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Figure 2

Rms values of the velocity fluctuations in turbulent channel flow, (—) (u'rms), (- - -) (v'rms), (···) (w'rms), data from Ref. [31]; (+++) (u'rms), (×××) (v'rms), (***) (w'rms), data from Ref. [22]

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Figure 3

Reynolds shear stress in turbulent channel flow: (—) data from Ref. [31]; (+++) data from Ref. [22]

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Figure 4

Skewness factor (Su') in turbulent channel flow: (—) data from Ref. [31]; (+++) data from Ref. [22]

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Figure 5

Flatness factor (Fv') in turbulent channel flow: (—) data from Ref. [31]; (+++) data from Ref. [22]

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Figure 6

Terms in the budget of turbulent kinetic energy (data from Ref. [46])

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Figure 7

Terms in the budget of Reynolds stress (data from Ref. [46]): (a) budget for u'1u'1¯; (b) budget for u'2u'2¯; (c) budget for u'3u'3¯; (d) budget for u'1u'2¯ (1=x, 2=y, 3=z)

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Figure 8

Terms in the budget of rate of dissipation (data from Ref. [46])

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Figure 9

Mean-streamwise-velocity distribution (at three different Reynolds numbers) in turbulent channel flow with roughness on one wall. Lines are DNS results, symbols are experimental data (adapted from Ref. [51]).

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Figure 10

Sketch of drag-increase and drag-reduction mechanisms by riblets: (a) s+=40, drag increase; (b) s+=20, drag reduction (the gray areas denote regions of high skin friction due to downwash motions) (adapted from Ref. [81])

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Figure 11

Vortical structures in the computing domain at t+=1036.8 (adapted from Ref. [161])

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Figure 12

Single hairpin vortex (top view) at: (a) t+=1022.4; (b) t+=1036.8; (c) t+=1051.2; (d) t+=1065.6 (adapted from Ref. [161])

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Figure 13

Representation of hairpin vortices and quadrant events. Persistent hairpin at: (a) t+=1022.4; (b) t+=1044; (c) t+=1051.2; (d) t+=1058.4 (the hairpin is shown in green, isosurfaces of Q2-events are shown in black, isosurfaces of Q4-events are shown in gray, adapted from Ref. [161]).

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Figure 14

Representation of hairpin vortices and quadrant events. Ephemeral hairpin at: (a) t+=1029.6; (b) t+=1036.8 (the hairpin is shown in green, isosurfaces of Q2-events are shown in black, adapted from Ref. [161]).

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Figure 15

Representation of hairpin vortices and quadrant events at t+=1058.4: (a) ephemeral symmetric hairpin; (b) ephemeral nonsymmetric hairpin (the hairpin is shown in green, isosurfaces of Q2-events are shown in black, isosurfaces of Q4-events are shown in gray, adapted from Ref. [161])

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Figure 16

Surfaces of constant streamwise fluctuation reconstructed from the first three most energetic KL modes at: (a) t+=50.4; (b) t+=198 (light surfaces are positive, dark surfaces are negative, adapted from Ref. [172])

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Figure 17

Surfaces of constant streamwise fluctuation reconstructed from the second two most energetic KL modes at: (a) t+=25.2; (b) t+=61.2 (light surfaces are positive, dark surfaces are negative, adapted from Ref. [172])

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Figure 18

Surfaces of constant streamwise fluctuation reconstructed from the first five most energetic KL modes at: (a) t+=54; (b) t+=64.8; (c) t+=72; (d) t+=82.8 (red surfaces are positive, blue surfaces are negative, adapted from Ref. [172])

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Figure 19

Surfaces of constant streamwise fluctuation reconstructed from the first five most energetic KL modes at: (a) t+=136.8; (b) t+=165.8; (c) t+=172.8; (d) t+=190.8 (red surfaces are positive, blue surfaces are negative, adapted from Ref. [172])

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Figure 20

Option C. Characterization diagram with different sizes of the computational domain and number of processors: (×) N=32; (♦) N=64; (▴) N=96; (•) N=128 (adapted from Ref. [191]).

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Figure 21

Performance results on HP Exemplar 2000 computer in terms of speedup corresponding to different sizes of the computational domain and number of processors: (▴) 323; (•) 643; (▪) 963; (- - -) ideal (adapted from Ref. [191])

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Figure 22

Performance results on HP V-2500 computer in terms of speedup corresponding to different sizes of the computational domain and number of processors: (▴) 323; (•) 643; (▪) 963; (- - -) ideal (adapted from Ref. [191])

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