Direct Numerical Simulation of Turbulent Channel Flow on High-Performance GPU Computing System
Abstract
:1. Introduction
- (i)
- the development of ejections distributed on spheric-like isosurfaces behind an initial -shaped vortex filament;
- (ii)
- the subsequent development of sweeps distributed on elongated isosurfaces adjacent to the external sides of hairpins’ heads and necks.
2. Numerical Techniques
3. Flow-Structure Extraction
4. Numerical Simulations
- (i)
- 2 Intel Xeon 5660 exa-core CPU processors (12 cores) at 2.8 GHz, with 48 GB GDDR3 RAM;
- (ii)
- 3 Nvidia C-1060 (Tesla) 240-core GPU boards (720 computing cores) at 1.3 GHz, each with 4 GB GDDR3 RAM at 102 GB/s (12 GB available);
- (iii)
- 1 Nvidia GTS-450 (GeForce) 192-core GPU board at 1804 MHz, with 1 GB GDDR5 RAM at 57.7 GB/s (mainly used for visualization);
- (iv)
- storage system including 5 Hard Drives at 7200 rpm, for a total supply of 5 TB.
5. Turbulence Statistics
6. Flow Structures
7. Concluding Remarks
- (i)
- the physical condition for the development and subsequent morphological evolution of a stable hairpin-like vortical structure is the occurrence of ejections distributed onto an isosurface almost equally developed along the streamwise, spanwise and normal-to-the-wall directions (a spheric-like isosurface) behind an initially connected Ω-shaped vortex filament, lying near the wall. These ejections actually constitute the physical mechanism according to which the head of the hairpin is raised upward;
- (ii)
- the physical condition for the development of a complete and persistent hairpin is the subsequent occurrence of sweeps, as distributed on elongated isosurfaces adjacent to the external sides of the neck and legs of the hairpin.
- (ii/a)
- the legs of the hairpin are stably kept near the wall;
- (ii/b)
- the right portion (leg and neck) of the hairpin is characterized by local clockwise particle rotation, the left portion (leg and neck) by counter clockwise local particle rotation.
Author Contributions
Conflicts of Interest
Nomenclature
Roman symbols (upper case) | |
velocity-gradient tensor | |
bulk-velocity friction coefficient | |
discriminant of characteristic equation | |
viscous-diffusion term of turbulent kinetic-energy transport equation | |
flatness factors of velocity fluctuations | |
peak value of | |
mean turbulent kinetic energy | |
domain dimensions along x,y,z (h units) | |
domain dimensions along x,y,z (wall units) | |
number of grid points along x,y,z | |
total number of grid points | |
production term of turbulent kinetic-energy transport equation | |
scalar invariants of velocity-gradient tensor | |
parameters in the grid-stretching law | |
second-quadrant event (ejection) | |
fourth-quadrant event (sweep) | |
friction-velocity Reynolds number | |
skewness factors of velocity fluctuations | |
peak value of | |
transport term of turbulent kinetic-energy transport equation | |
Roman symbols (lower case) | |
channel half-height | |
wavenumber | |
pressure | |
time coordinate | |
time coordinate (wall units) | |
total database calculated time | |
actually saved database calculated time (wall units) | |
velocity components along x,y,z | |
fluctuating-velocity components along x,y,z | |
rms velocity fluctuations | |
peak value of | |
Reynolds shear stress | |
peak value of | |
bulk velocity | |
centerline velocity | |
friction velocity | |
Cartesian coordinates | |
Cartesian coordinates (wall units) | |
y-position of (wall units) | |
y-position of (wall units) | |
y-position of (wall units) | |
y-position of (wall units) | |
Greek symbols (upper case) | |
time resolution of calculations (wall units) | |
space resolution of calculations along x,z (wall units) | |
space resolution of calculations along y at channel wall (wall units) | |
space resolution of calculations along y at channel center (wall units) | |
Greek symbols (lower case) | |
average rate of dissipation of turbulent kinetic energy per unit mass | |
dissipation term of mean turbulent kinetic-energy transport equation | |
Kolmogorov space microscale (wall units) | |
eigenvalue | |
real eigenvalue | |
real part of complex eigenvalue | |
imaginary part of complex eigenvalue | |
threshold value of swirling strength | |
fluid kinematic viscosity | |
fluid density | |
mean shear stress at wall | |
Kolmogorov time microscale (wall units) | |
Acronyms | |
CPU | Central Processing Unit |
DNS | Direct Numerical Simulation (of turbulence) |
GPU | Graphic Processing Unit |
References
- Kim, J.; Moin, P.; Moser, R. Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 1987, 177, 133–166. [Google Scholar] [CrossRef]
- Lyons, S.L.; Hanratty, T.J.; McLaughlin, J.B. Large-scale computer simulation of fully developed turbulent channel flow with heath transfer. Int. J. Num. Meth. Fluids 1991, 13, 999–1028. [Google Scholar] [CrossRef]
- Antonia, R.A.; Teitel, M.; Kim, J.; Browne, L.W.B. Low-Reynolds-number effects in a fully developed turbulent channel flow. J. Fluid Mech. 1992, 236, 579–605. [Google Scholar] [CrossRef]
- Kasagi, N.; Tomita, Y.; Kuroda, A. Direct numerical simulation of passive scalar field in a turbulent channel flow. ASME J. Heat Transf. 1992, 114, 598–606. [Google Scholar] [CrossRef]
- Rutledge, J.; Sleicher, C.A. Direct simulation of turbulent flow and heat transfer in a channel. Part I: Smooth walls. Int. J. Num. Meth. Fluids 1993, 16, 1051–1078. [Google Scholar] [CrossRef]
- Moser, R.D.; Kim, J.; Mansour, N.N. Direct numerical simulation of turbulent channel flow up to . Phys. Fluids 1999, 11, 943–945. [Google Scholar] [CrossRef]
- Abe, H.; Kawamura, H.; Matsuo, Y. Direct numerical simulation of a fully developed turbulent channel flow with respect to the Reynolds number dependence. ASME J. Fluids Eng. 2001, 123, 382–393. [Google Scholar] [CrossRef]
- Iwamoto, K.; Suzuki, Y.; Kasagi, N. Reynolds number effect on wall turbulence: Toward effective feedback control. Int. J. Heat Fluid Flow 2002, 23, 678–689. [Google Scholar] [CrossRef]
- Del Alamo, J.C.; Jiménez, J. Spectra of the very large anisotropic scales in turbulent channels. Phys. Fluids 2003, 15, L41–L44. [Google Scholar] [CrossRef]
- Del Alamo, J.C.; Jiménez, J.; Zandonade, P.; Moser, R.D. Scaling of the energy spectra of turbulent channels. J. Fluid Mech. 2004, 500, 135–144. [Google Scholar] [CrossRef]
- Tanahashi, M.; Kang, S.J.; Miyamoto, T.; Shiokawa, S.; Miyauchi, T. Scaling law of the fine-scale eddies in turbulent channel flows up to . Int. J. Heat Fluid Flow 2004, 25, 331–340. [Google Scholar] [CrossRef]
- Iwamoto, K.; Kasagi, N.; Suzuki, Y. Direct numerical simulation of turbulent channel flow at . Available online: http://www.nmri.go.jp/turbulence/PDF/symposium/FY2004/Iwamoto.pdf (accessed on 17 February 2016).
- Hoyas, S.; Jiménez, J. Scaling of the velocity fluctuations in turbulent channels up to . Phys. Fluids 2006, 18, 011702. [Google Scholar] [CrossRef]
- Hu, Z.W.; Morfey, C.L.; Sandham, N.D. Wall pressure and shear stress spectra from direct simulations of channel flow. AIAA J. 2006, 44, 1541–1549. [Google Scholar] [CrossRef]
- Alfonsi, G.; Primavera, L. Direct numerical simulation of turbulent channel flow with mixed spectral-finite difference technique. J. Flow Visual. Image Proc. 2007, 14, 225–243. [Google Scholar]
- Lozano-Durán, A.; Flores, O.; Jiménez, J. The three-dimensional structure of momentum transfer in turbulent channels. J. Fluid Mech. 2012, 694, 100–130. [Google Scholar] [CrossRef]
- Lozano-Durán, A.; Jiménez, J. Effect of the computational domain on direct simulations of turbulent channels up to . Phys. Fluids 2014, 26, 011702. [Google Scholar] [CrossRef]
- Vreman, A.W.; Kuerten, J.G.M. Comparison of direct numerical simulation databases of turbulent channel flow at . Phys. Fluids 2014, 26, 015102. [Google Scholar] [CrossRef]
- Vreman, A.W.; Kuerten, J.G.M. Statistics of spatial derivatives of velocity and pressure in turbulent channel flow. Phys. Fluids 2014, 26, 085103. [Google Scholar] [CrossRef]
- Bernardini, M.; Pirozzoli, S.; Orlandi, P. Velocity statistics in turbulent channel flow up to . J. Fluid Mech. 2014, 742, 171–191. [Google Scholar] [CrossRef]
- Lee, M.; Moser, R.D. Direct numerical simulation of turbulent channel flow up to . J. Fluid Mech. 2015, 774, 395–415. [Google Scholar] [CrossRef]
- Kim, J.; Moin, P. Application of a fractional-step method to incompressible Navier-Stokes equations. J. Comput. Phys. 1985, 59, 308–323. [Google Scholar] [CrossRef]
- Alfonsi, G.; Passoni, G.; Pancaldo, L.; Zampaglione, D. A spectral-finite difference solution of the Navier-Stokes equations in three dimensions. Int. J. Numer. Meth. Fluids 1998, 28, 129–142. [Google Scholar] [CrossRef]
- Alfonsi, G. On direct numerical simulation of turbulent flows. Appl. Mech. Rev. 2011, 64, 020802. [Google Scholar] [CrossRef]
- Marusic, I.; McKeon, B.J.; Monkewitz, P.A.; Nagib, H.M.; Smits, A.J.; Sreenivasan, K.R. Wall-bounded turbulent flows at high Reynolds numbers: Recent advances and key issues. Phys. Fluids 2010, 22, 065103. [Google Scholar] [CrossRef]
- Smits, A.J.; McKeon, B.J.; Marusic, I. High-Reynolds number wall turbulence. Annu. Rev. Fluid Mech. 2011, 43, 353–375. [Google Scholar] [CrossRef]
- Kim, J. Progress in pipe and channel flow turbulence, 1961–2011. J. Turbul. 2012, 13. [Google Scholar] [CrossRef]
- Jiménez, J. Cascades in wall-bounded turbulence. Annu. Rev. Fluid Mech. 2012, 44, 27–45. [Google Scholar] [CrossRef]
- Alfonsi, G.; Primavera, L. Temporal evolution of vortical structures in the wall region of turbulent channel flow. Flow Turbul. Combust. 2009, 83, 61–79. [Google Scholar] [CrossRef]
- Zhou, J.; Adrian, R.J.; Balachandar, S.; Kendall, T.M. Mechanisms for generating coherent packets of hairpin vortices in channel flow. J. Fluid Mech. 1999, 387, 353–396. [Google Scholar] [CrossRef]
- Le, H.; Moin, P. An improvement of fractional step methods for the incompressible Navier-Stokes equations. J. Comput. Phys. 1991, 92, 369–379. [Google Scholar] [CrossRef]
- Passoni, G.; Alfonsi, G.; Tula, G.; Cardu, U. A wavenumber parallel computational code for the numerical integration of the Navier-Stokes equations. Parall. Comput. 1999, 25, 593–611. [Google Scholar] [CrossRef]
- Passoni, G.; Cremonesi, P.; Alfonsi, G. Analysis and implementation of a parallelization strategy on a Navier-Stokes solver for shear flow simulations. Parall. Comput. 2001, 27, 1665–1685. [Google Scholar] [CrossRef]
- Passoni, G.; Alfonsi, G.; Galbiati, M. Analysis of hybrid algorithms for the Navier-Stokes equations with respect to hydrodynamic stability theory. Int. J. Numer. Meth. Fluids 2002, 38, 1069–1089. [Google Scholar] [CrossRef]
- Wallace, J.M. Twenty years of experimental and direct numerical simulation access to the velocity gradient tensor: What have we learned about turbulence? Phys. Fluids 2009, 21, 021301. [Google Scholar] [CrossRef]
- Alfonsi, G. Coherent structures of turbulence: Methods of eduction and results. Appl. Mech. Rev. 2006, 59, 307–323. [Google Scholar] [CrossRef]
- Alfonsi, G.; Primavera, L. The structure of turbulent boundary layers in the wall region of plane channel flow. Proc. R. Soc. A 2007, 463, 593–612. [Google Scholar] [CrossRef]
- Alfonsi, G.; Primavera, L. On identification of vortical structures in turbulent shear flow. J. Flow Visual. Image Proc. 2008, 15, 201–216. [Google Scholar]
- Alfonsi, G. Numerical simulations of wave-induced flow fields around large-diameter surface-piercing vertical circular cylinder. Computation 2015, 3, 386–426. [Google Scholar] [CrossRef]
- Alfonsi, G.; Primavera, L. Determination of the threshold value of the quantity chosen for vortex representation in turbulent flow. J. Flow Visual. Image Proc. 2009, 16, 41–49. [Google Scholar]
- Bakewell, H.P.; Lumley, J.L. Viscous sublayer and adjacent wall region in turbulent pipe flow. Phys. Fluids 1967, 10, 1880–1889. [Google Scholar] [CrossRef]
- Alfonsi, G.; Ciliberti, S.A.; Mancini, M.; Primavera, L. GPGPU implementation of mixed spectral-finite difference computational code for the numerical integration of the three-dimensional time-dependent incompressible Navier-Stokes equations. Comput. Fluids 2014, 102, 237–249. [Google Scholar] [CrossRef]
- Ciliberti, S.A. Coherent Structures of Turbulence in Wall-Bounded Turbulent Flows. Ph.D. Thesis, Università della Calabria, Rende, Italy, 2011. [Google Scholar]
- Dean, R.B. Reynolds number dependence of skin friction and other bulk flow variables in two-dimensional rectangular duct flow. ASME J. Fluids Eng. 1978, 100, 215–223. [Google Scholar] [CrossRef]
- Mochizuki, S.; Nieuwstadt, F.T.M. Reynolds-number-dependence of the maximum of the streamwise velocity fluctuations in wall turbulence. Exp. Fluids 1996, 21, 218–226. [Google Scholar] [CrossRef]
- Alfonsi, G. Analysis of streamwise velocity fluctuations in turbulent pipe flow with the use of an ultrasonic Doppler flowmeter. Flow Turbul. Combust. 2001, 67, 137–142. [Google Scholar] [CrossRef]
- Xu, C.; Zhang, Z.; den Toonder, J.M.J.; Nieuwstadt, F.T.M. Origin of high kurtosis level in the viscous sublayer. Direct numerical simulation and experiment. Phys. Fluids 1996, 8, 1938–1944. [Google Scholar] [CrossRef]
- Alfonsi, G. Evaluation of radial velocity fluctuations in turbulent pipe flow by means of an ultrasonic Doppler velocimeter. J. Flow Visual. Image Proc. 2003, 10, 155–161. [Google Scholar] [CrossRef]
- Kline, S.; Reynolds, W.C.; Schraub, F.A.; Rundstadler, P.W. The structure of turbulent boundary layers. J. Fluid Mech. 1967, 30, 741–773. [Google Scholar] [CrossRef]
Author(s) | Year | Numerical Technique |
---|---|---|
Kim et al. [1] | 1987 | Spectral |
Lyons et al. [2] | 1991 | Spectral |
Antonia et al. [3] | 1992 | Spectral |
Kasagi et al. [4] | 1992 | Spectral |
Rutledge and Sleicher [5] | 1993 | Spectral |
Moser et al. [6] | 1999 | Spectral |
Abe et al. [7] | 2001 | Finite Difference |
Iwamoto et al. [8] | 2002 | Spectral |
Del Alamo and Jiménez [9] | 2003 | Spectral |
Del Alamo et al. [10] | 2004 | Spectral |
Tanahashi et al. [11] | 2004 | Spectral-Finite Difference |
Iwamoto et al. [12] | 2005 | Spectral |
Hoyas and Jiménez [13] | 2006 | Spectral-Finite Difference |
Hu et al. [14] | 2006 | Spectral |
Alfonsi and Primavera [15] | 2007 | Spectral-Finite Difference |
Lozano-Durán et al. [16] | 2012 | Spectral |
Lozano-Durán and Jiménez [17] | 2014 | Spectral |
Vreman and Kuerten [18] | 2014 | Spectral |
Vreman and Kuerten [19] | 2014 | Spectral |
Bernardini et al. [20] | 2014 | Finite Difference |
Lee and Moser [21] | 2015 | Spectral |
Quantities | |||
---|---|---|---|
2513 | 5026 | 7540 | |
400 | 800 | 1200 | |
1256 | 2513 | 3770 | |
256 | 343 | 512 | |
181 | 321 | 451 | |
256 | 343 | 512 | |
9.82 | 14.65 | 14.73 | |
0.25 | 0.28 | 0.30 | |
3.87 | 4.36 | 4.66 | |
4.91 | 7.33 | 7.36 | |
1.89 | 2.19 | 2.42 | |
5.20 | 6.69 | 6.09 | |
0.13 | 0.13 | 0.12 | |
2.05 | 1.99 | 1.93 | |
2.6 | 3.35 | 3.04 | |
0.02 | 0.04 | 0.06 | |
50· | 50· | 50· | |
500· | 500· | 500· | |
3.56 | 4.79 | 5.87 | |
0.006 | 0.008 | 0.010 |
CPU/GPU Cores | |||
---|---|---|---|
1 CPU/240 GPU Cores | 0.37 | 1.71 | - |
3 CPU/720 GPU Cores | - | - | 3.32 |
Quantities | |||
---|---|---|---|
(nominal) | 200 | 400 | 600 |
(present work) | 200.23 | 399.94 | 600.55 |
(nominal, after Dean [44]) | 3390.71 | 7254.35 | 11,343.22 |
(present work) | 3197.67 | 6966.95 | 11,106.17 |
(nominal, after Dean [44]) | 3918.71 | 8310.35 | 12,927.22 |
(present work) | 3706.26 | 7978.80 | 12,701.63 |
(nominal, after Dean [44]) | 16.95 | 18.14 | 18.91 |
(present work) | 16.97 | 17.42 | 18.49 |
(nominal, after Dean [44]) | 19.59 | 20.78 | 21.55 |
(present work) | 18.51 | 19.95 | 21.15 |
(nominal, after Dean [44]) | 1.16 | 1.15 | 1.14 |
(present work) | 1.16 | 1.14 | 1.14 |
(nominal, after Dean [44]) | |||
(present work) | |||
(present work) | 0.739 | 0.828 | 0.866 |
(from Moser et al. [6]) | 0.723 | 0.837 | 0.864 |
(present work) | 30.238 | 40.170 | 43.938 |
(from Moser et al. [6]) | 30.019 | 41.882 | 44.698 |
(present work) | 2.680 | 2.720 | 2.751 |
(from Moser et al. [6]) | 2.660 | 2.740 | 2.770 |
(present work) | 14.909 | 14.199 | 13.444 |
(from Moser et al. [6]) | 15.281 | 14.209 | 13.268 |
(present work) | 1.003 | 1.096 | 1.141 |
(from Moser et al. [6]) | 0.922 | 1.013 | 1.066 |
(present work) | 1.315 | 1.423 | 1.504 |
(from Moser et al. [6]) | 1.339 | 1.446 | 1.591 |
(present work) | 26.679 at | 19.424 at | 20.882 at |
(from Moser et al. [6]) | 26.712 at | 34.757 at | 37.653 at |
© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons by Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).
Share and Cite
Alfonsi, G.; Ciliberti, S.A.; Mancini, M.; Primavera, L. Direct Numerical Simulation of Turbulent Channel Flow on High-Performance GPU Computing System. Computation 2016, 4, 13. https://doi.org/10.3390/computation4010013
Alfonsi G, Ciliberti SA, Mancini M, Primavera L. Direct Numerical Simulation of Turbulent Channel Flow on High-Performance GPU Computing System. Computation. 2016; 4(1):13. https://doi.org/10.3390/computation4010013
Chicago/Turabian StyleAlfonsi, Giancarlo, Stefania A. Ciliberti, Marco Mancini, and Leonardo Primavera. 2016. "Direct Numerical Simulation of Turbulent Channel Flow on High-Performance GPU Computing System" Computation 4, no. 1: 13. https://doi.org/10.3390/computation4010013
APA StyleAlfonsi, G., Ciliberti, S. A., Mancini, M., & Primavera, L. (2016). Direct Numerical Simulation of Turbulent Channel Flow on High-Performance GPU Computing System. Computation, 4(1), 13. https://doi.org/10.3390/computation4010013