Fixed-scale statistics and the geometry of turbulent dispersion at high reynolds number via numerical simulation

Turbulent mixing;Turbulence;Relative dispersion;Direct numerical simulation;Fluid particles;Lagrangian statistics

Hackl, Jason F. ; Aerospace Engineering

University:Georgia Institute of Technology

Department:Aerospace Engineering

关键词: Turbulent mixing;    Turbulence;    Relative dispersion;    Direct numerical simulation;    Fluid particles;    Lagrangian statistics;   

Others  :  https://smartech.gatech.edu/bitstream/1853/41100/1/hackl_jason_f_201108_phd.pdf

美国|英语

来源: SMARTech Repository

【 摘 要 】

The relative dispersion of one fluid particle with respect to another isfundamentally related to the transport and mixing of contaminant species inturbulent flows. The most basic consequence of Kolmogorov's 1941 similarityhypotheses for relative dispersion, the Richardson-Obukhov law that mean-squarepair separation distance grows with the cube of timeat intermediate times in the inertial subrange, is notoriously difficult toobserve in the environment, laboratory, and direct numerical simulations (DNS).Inertial subrange scaling in size parameters like the mean-square pair separation requirescareful adjustment for the initial conditions of the dispersion process as wellas a very wide range of scales (high Reynolds number) in the flow being studied.However, the statistical evolution of the shapes of clusters of more than twoparticles has already exhibited statistical invariance at intermediate times inexisting DNS. This invariance is identified with inertial-subrange scaling andis more readily observed than inertial-subrange scaling for seemingly simpler quantities such as the mean-square pair separationResults from dispersion of clusters of four particles (called tetrads) inlarge-scale DNS at grid resolutions up to 4096 points in each of three directions and Taylor-scale Reynoldsnumbers from 140 to 1000 are used to explore the question ofstatistical universality in measures of the size and shape of tetrahedra inhomogeneous isotropic turbulence in distinct scaling regimes at very small times(ballistic), intermediate times (inertial) and very late times (diffusive).Derivatives of fractional powers of the mean-square pair separation with respect to time normalized by thecharacteristic time scale at the initial tetrad size constitute a powerfultechnique in isolating cubic time scaling in the mean-square pair separation. This techniqueis applied to the eigenvalues of a moment-of-inertia-like tensor formed from theseparation vectors between particles in the tetrad. Estimates of theproportionality constant "g" in the Richardson-Obukhov law from DNS at aTaylor-scale Reynolds number of 1000 converge towards the value g=0.56 reported inprevious studies. The exit time taken by a particle pair to first reachsuccessively larger thresholds of fixed separation distance is also brieflydiscussed and found to have unexplained dependence on initial separationdistance for negative moments, but good inertial range scaling for positivemoments. The use of diffusion models of relative dispersion in the inertialsubrange to connect mean exit time to "g" is also tested and briefly discussedin these simulations.Mean values and probability density functions of shapeparameters including the triangle aspect ratio "w," tetrahedronvolume-to-gyration radius ratio, and normalized moment-of-inertiaeigenvalues are all found to approach invariant forms in the inertial subrangefor a wider range of initial separations than size parameters such asmean-square gyration radius. These results constitute theclearest evidence to date that turbulence has atendency to distort and elongate multiparticle configurations more severely inthe inertial subrange than it does in the diffusive regime at asymptoticallylate time. Triangle statistics are found to be independent ofinitial shape for all time beyond the ballistic regime.The development and testing of different schemes for parallelizing the cubicspline interpolation procedure for particle velocities needed to track particles in DNS is also covered. A "pipeline" method of moving batches of particlesfrom processor to processor is adopted due to its low memory overhead, but there are challenges in achieving good performance scaling.