intermittency, mixing, and dispersion High-Resolution Simulations of Turbulence: Supported by NSF (CTS)

Size: px

Start display at page:

Download "intermittency, mixing, and dispersion High-Resolution Simulations of Turbulence: Supported by NSF (CTS)"

Tyler Harper
5 years ago
Views:

1 High-Resolution Simulations of Turbulence: intermittency, mixing, and dispersion P.K. Yeung and Diego A. Donzis School of Aero. Engr., Georgia Tech, Atlanta, GA Close collaborators: K.R. Sreenivasan (ICTP, Italy), S.B. Pope (Cornell), B.L. Sawford (Monash, Australia) ASC Flash Center Turbulence Mini-Workshop University of Chicago, June 8, 2006 Supported by NSF (CTS) Resources & Consulting: NERSC, SDSC, PSC High-Resolution Simulations of Turbulence p.1/??

2 The meaning of High-Resolution grid, for isotropic turbulence): in 1990 s; in 2000 s Size of computation ( in 1980 s; World-record: on 40-Teraflop Earth Simulator (Kaneda etal. Phys. Fluids 2003) Using state-of-the-art cyberinfrastructure: Thousands (or tens of thousands) of processors Petascale computing power to come by Are the smallest scales resolved sufficiently well? (The answer depends..) High-Resolution Simulations of Turbulence p.2/??

3 Direct Numerical Simulation (DNS) 3-D incompressible Navier-Stokes equations for conservation of mass and momentum: (And chemical species or heat) For fundamental understanding (canonical flows) For model development (share the data) High-Resolution Simulations of Turbulence p.3/??

4 DNS: scales and requirements To resolve full range of scales in space and time: (largest length scale) (Kolmogorov length scale) size of domain grid spacing (large-eddy time scale) length of simulation (Kolmogorov time scale), time step further subjected to numerical stability constraints Basic estimates for DNS at high Reynolds number: and Fourier pseudo-spectral in space (FFTs), 2nd order in time High-Resolution Simulations of Turbulence p.4/??

5 Historical Evolution of Computers and DNS Adapted from NRC Report Figure originally by K.R. Sreenivasan (1999) BlueGene/W (IBM) Earth Simulator Seaborg (NERSC) DataStar (SDSC) Lemeiux (PSC) Cray XT3 (PSC) DNS now gives Reynolds no. comparable to or higher than in many laboratory experiments IBM 704 MANIAC SEAC Electro mechanical Intel Delta, CM 200, etc Intel Gamma, CM 2, etc Easy commercial CDC 7600 CDC 6600 IBM 7030 Cray T3D CM 1,etc Cray Y MP Cray 1 Cray X MP Origin 2000 CM 5 J 90 series Earth Simulator NERSC/SDSC/PSC 3D Navier Stokes turbulence Year R λ And can offer more (tremendous detail, quantities difficult to measure) High-Resolution Simulations of Turbulence p.5/?? Operations per second

6 Some Questions and Issues? Intermittency at the Small Scales: Do dissipation and enstrophy scale the same at high Resolution effects on higher-order moments? Mixing of passive scalars: Do deviations from local isotropy persist at high ) effects, over a wide range Schmidt number ( Dispersion in a Lagrangian frame: How can we incorporate intermittency in stochastic modeling intended for high Reynolds numbers? Statistics conditioned on local relative motion High-Resolution Simulations of Turbulence p.6/??

7 Our work on High-resolution DNS Stationary, isotropic turbulence: idealized geometry, with numerical forcing yet justified by at least approximate small-scale universality (Kolmogorov 1941) simulations using large CPU allocations at: Three NERSC facility at Lawrence Berkeley (DOE: INCITE) San Diego Supercomputer Center (NSF) Pittsburgh Supercomputing Center (NSF) Code development and benchmarking for future (IBM BGW, 32k processors) High-Resolution Simulations of Turbulence p.7/??

8 Intermittency at the Small Scales Intense fluctuations localized in space and time (topology of such regions in space is of interest) Structure functions and scaling exponents at viscous and inertial scales Non-Gaussian statistics: higher-order moments and far tails of PDF (subject to resolution and sampling) Statistics of local box averages (Kolmogorov 1962) and multifractal properties High-Resolution Simulations of Turbulence p.8/??

9 Dissipation and enstrophy Second-order invariants of strain-rate and rotation-rate vs. Fluctuations of are responsible for: anomalous scaling of velocity structure functions intermittency corrections to inertial-range spectrum Most data sources show enstrophy to be more intermittent limit but theories suggest same scaling in high- High-Resolution Simulations of Turbulence p.9/??

10 Effects of Resolution ) (large which gives Most simulations in literature aim at high usual criterion is analytic behavior (at small ) often not well achieved in structure functions of higher order Under-resolution tends to miss extreme, localized events: does underestimation of high-order moments affect conclusion on same scaling at high for and? Yakhot & Sreenivasan (2005) suggests a need for smaller (or higher ) than in usual practice High-Resolution Simulations of Turbulence p.10/??

11 !! Dissipation vs Enstrophy: Effect of Reynolds no. and PDFs of Same mean value, but larger higher moments for enstrophy ) ) and 700 ( ( Tails of the PDFs: 10 1 stretched-exponential fit, e.g better than log-normal theory Stretched-exponential parameters versus Reynolds, etc. number: is there an asymptotic trend? High-Resolution Simulations of Turbulence p.11/??

12 Dissipation vs Enstrophy: Moments and Resolution ),, ( and, 140, on Three simulations at resolution resolution resolution Higher-order moments are underestimated at, but ( ) seems to be sufficient up to order 4. show less sensitivity and Ratios of moments of High-Resolution Simulations of Turbulence p.12/??

13 Mixing of Passive Scalars of scalar varies: Schmidt number, for gaseous flames 0.7 for heat in air, in some liquids 7 for heat and salinity in water, ) is more difficult: Weakly diffusive regime ( fluctuations arise at smaller scales than velocity field, at expense of resolve Batchelor scale, Some engineering literature use the Peclet no. but effects of increasing Reynolds no. and increasing Schmidt no. are different High-Resolution Simulations of Turbulence p.13/??

14 Inertial-convective range at high Reynolds no. (higher than needed for velocity field), at Clear demonstration of both Obukhov-Corrsin scaling and Yaglom relation, better than in the past, and consistent with experiment High-Resolution Simulations of Turbulence p.14/??

15 Scalar Gradients: Local Anisotropy Component along mean gradient has positive skewness factor at Low Increasing Increasing at 10 1 R 8 λ R 38 λ R 140 µ λ Sc=1/8 Sc= : local anisotropy is sustained (contrast to velocity) High : return to local isotropy (beyond threshold depending High ) on High-Resolution Simulations of Turbulence p.15/??

16 Scalar Gradients: Intermittency PDF of component along mean gradient at Increasing at Increasing 10 0 Sc=1/ R λ = : increasing intermittency (more than velocity field) : saturation of intermittency occurs beyond High High High-Resolution Simulations of Turbulence p.16/??

17 Energy and Scalar Dissipation Rates Energy dissipation Scalar dissipation Scalar dissipation has higher peaks, and is more intermittent High-Resolution Simulations of Turbulence p.17/??

18 3D visualization High-Resolution Simulations of Turbulence p.18/??

19 Dispersion: Lagrangian viewpoint Lagrangian frame: observer moving with the fluid Pollutant cloud : position, linear size, surface area, volume via motions of fluid particles singly and up to four DNS gives full instantaneous velocity field, hence can provide much more comprehensive data than experiment Inertial-range similarity more difficult than for Eulerian statistics, because range of time scales increase more slowly Reynolds number dependence is very important for use of data in stochastic modeling High-Resolution Simulations of Turbulence p.19/??

20 Statistics of the Acceleration (Lagrangian) force/mass (Eulerian) Modeling: model the acceleration, recover velocity and position by integration Variance departs from Kolmogorov universaliity Highly intermittent, closely related to local relative motion (strain or rotation) From Sawford etal. Phys. Fluids 2003 Solid: our data+gotoh. Open: experiments. High-Resolution Simulations of Turbulence p.20/??

21 Lagrangian conditional statistics In regions of large velocity Conditional velocity autocorrelation gradients: decorrelates faster, while gets large Statistics conditioned on local pseudo-dissipation captures both strain and rotation is almost a Gaussian process conditional acceleration is less intermittent High-Resolution Simulations of Turbulence p.21/??

22 Flow structure: conditioning on enstrophy Analyses in local axes and to vorticity vector suggest behavior for large at low is an indication of vortex-trapping effects : effect is weak because of rapid changes in vorticity vector orientation High High-Resolution Simulations of Turbulence p.22/??

23 Algorithms and Data Structure Pencils ( 2-D decomposition ) Slabs ( 1-D decomposition ) More communication calls, but among fewer processors MPI_ALLTOALL communication for transposes Scales better for larger problems; necessary for No. of processors must be integer factor of High-Resolution Simulations of Turbulence p.23/??

24 Performance Measures IBM SP Power 4 at SDSC and Blue-Gene W at IBM Watson Machine SP4 (1D) BGW (2D) Problem size No. of procs CPU/step/proc Mflop/s/proc Aggreg. Tflop/s Mem/proc(Mb) Perfect scaling would be in some cases ): excellent, Weak scaling (vary Strong scaling (vary PROCS): very good, 86% between 16 and 32 K procs for High-Resolution Simulations of Turbulence p.24/??

25 Outlook: our database for passive scalars and Lagrangian statistics Large database achieved for: highest for scalars at low/moderate highest Potential for many fields of study: reacting flows: intermittency, differential diffusion droplet dynamics, zooplankton behavior subgrid modeling, wavelet analyses, cosmology... Maintain the data, and share with the community High-Resolution Simulations of Turbulence p.25/??

26 Outlook: future computations and higher: towards Petascale computing Simulations to resolve small scales better Simulations to sample large scales better Active scalars: reacting flow, thermal stratification Lagrangian statistics in more complex flows: homogeneous shear, fully-developed channel High-Resolution Simulations of Turbulence p.26/??

P. K. Yeung Georgia Tech,

Progress in Petascale Computations of Turbulence at high Reynolds number P. K. Yeung Georgia Tech, pk.yeung@ae.gatech.edu Blue Waters Symposium NCSA, Urbana-Champaign, May 2014 Thanks... NSF: PRAC and