Bulletin of the American Physical Society
60th Annual Meeting of the Divison of Fluid Dynamics
Volume 52, Number 12
Sunday–Tuesday, November 18–20, 2007; Salt Lake City, Utah
Session JO: Turbulence: Simulations III |
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Chair: Richard Kirkman, University of Utah Room: Salt Palace Convention Center 251 C |
Monday, November 19, 2007 3:35PM - 3:48PM |
JO.00001: Strong enstrophy events and maximal growth estimates in turbulence simulations Joerg Schumacher, Bruno Eckhardt, Charles R. Doering The temporal growth of enstrophy is a question of fundamental interest which is intimately related to the open problem of uniqueness and regularity of solutions of the Navier-Stokes equations. Recently, Lu and Doering derived a rigorous upper bound for the temporal growth of enstrophy and detected the optimal structures that can cause such events. Here, we study the temporal growth of large-amplitude vortices locally, in quasi-Lagrangian frames of reference which are moving with a swarm of Lagrangian tracers. The analysis is done in situ with highly-resolved direct numerical simulations of forced homogeneous isotropic turbulence at a Taylor microscale Reynolds number of 107 with N=2048 grid points in each direction. The most rapid growth events in the simulations are found to correspond with interacting Burgers vortices. [Preview Abstract] |
Monday, November 19, 2007 3:48PM - 4:01PM |
JO.00002: Return-to-isotropy of anisotropic dilatational turbulence Kurnchul Lee, Sharath S. Girimaji Turbulence in compressible flows differs from its incompressible counterpart due to the activation of thermal energy mode. In this study, we examine the return-to-isotropy process in initially anisotropic compressible turbulence. A Boltzmann Bhatnagar-Gross-Krook (BGK) equation based numerical scheme is employed for direct numerical simulations of the anisotropic compressible turbulence. The initial turbulence field is made of both solenoidal and dilatational components. The objective of the study is to investigate the various effects of compressibility: (i) the rate of return-to-isotropy of dilatational turbulence; (ii) the rate of return-to-isotropy of solenoidal turbulence; and (iii) the role of pressure dilatation in return-to-isotropy. [Preview Abstract] |
Monday, November 19, 2007 4:01PM - 4:14PM |
JO.00003: Numerical Simulations of Turbulence Subjected to a Straining and De-Straining Cycle Paolo Gualtieri, Charles Meneveau In most applications turbulent flows develop in geometrically complex devices where interactions between fluctuations and mean velocity gradients occur in non equilibrium conditions, i.e. turbulence is subjected to a significant large-scale deformation. The simplest flow which retains this physical aspect is turbulence subjected to homogenous straining flow. Non-equilibrium effects may be studied by varying the applied straining as function of time. To simulate such a flow numerically, a spectral code with the Rogallo transformation and stochastic forcing is employed. Direct and Large-Eddy Simulations of initially isotropic turbulence subjected to a straining and destraining cycle are performed. Numerical results are compared with experimental data obtained in similar conditions [Chen, Meneveau \& Katz, J. Fluid Mech.562 (2006)]. The role played by the initial energy spectra is discussed in relation with the position of the random forcing within the inertial range. The response of the system is characterized both in terms of velocity variances and turbulent kinetic energy production. In agreement with experimental data, numerical simulations provide significant backscatter of turbulent kinetic energy during the destraining phase explained in terms of anisotropy persistency in the Reynolds stresses. [Preview Abstract] |
Monday, November 19, 2007 4:14PM - 4:27PM |
JO.00004: On the Lagrangian study of circulations Minping Wan, Zuoli Xiao, Shiyi Chen, Gregory Eyink The conservation of circulations was argued by G. I. Taylor to play a key role in the production of dissipation in turbulent fluids, by the process of vortex line-stretching. We present evidence from a numerical simulation of high-Reynolds-number turbulence for violation of circulation conservation by Lagrangian tracking of material loops. Although violated in individual realizations, we find that the circulations are still conserved in some average sense. Taylor's vortex line-stretching picture is also examined by Lagrangian tracking of material lines. The difference between material lines and vortex lines is discussed with special attention to the role of viscosity. [Preview Abstract] |
Monday, November 19, 2007 4:27PM - 4:40PM |
JO.00005: Gradient statistics around particle tra jectory in turbulence Enrico Calzavarini, Luca Biferale, Massimo Cencini, Federico Toschi Fluid velocity increments at different spatial locations or times in a three-dimensional turbulent flow display both highly non-Gaussian fluctuations and long-range correlations. A statistical description of their properties represents one of the most intriguing problem of turbulence research. Theoretically, it has been suggested that a possible mechanism for their large fluctuations may be the nonlinear self-stretching that occurs during the Lagrangian evolution of the velocity gradients. We address here by Direct Numerical Simulations the fluid gradient temporal statistics along lagrangian trajectories of fluid tracers and of heavy/light inertial particles. High-resolution $Re_{\lambda} \simeq 180$ ($512^3$) and $Re_{\lambda} \simeq 380$ ($2048^3$) numerical results are employed. In particular, by computing velocity Lagrangian Structure Functions and coarse-grained moments of the energy dissipation rate and enstrophy field along the trajectories, we perform an analysis of the Refined Kolmogorov Similarity Hypothesis (Kolmogorov 1962) in the framework of Lagrangian turbulence. Statistics of the topological properties of the carrier flow along trajectories are also examined. Joint probability density between the Q-R invariants of the gradient tensor and their time evolutions along trajectories of tracers and inertial particles will be discussed. [Preview Abstract] |
Monday, November 19, 2007 4:40PM - 4:53PM |
JO.00006: Exit-time statistics and the inference of Richardson scaling in numerical simulations of turbulent dispersion. J.F. Hackl, B.L. Sawford, P.K. Yeung Unambiguous observation of Richardson inertial-range behavior for particle-pair dispersion and the associated scaling constant ($g$) in turbulence is often difficult in both experiment and computation, because of limitations in Reynolds number, effects of initial separation, and other factors. The concept of exit-time (time taken for the distance $l$ between two fluid particles to increase by a prescribed factor) has attracted recent interest in dispersion statistics viewed as functions of instantaneous length scale instead of time of travel. We consider both mean-squared dispersion and mean exit time, obtained from direct numerical simulations of forced isotropic turbulence up to Taylor-scale Reynolds numbers of about 650 on a $2048^3$ grid. Moments of exit time at fixed thresholds of particle pair separation are computed, and estimates of $g$ are inferred by assuming that the probability density function of $l$ follow self-similar forms such as that predicted by Richardson (1926). Subject to uncertainties due to temporal variability of space-averaged dissipation rate in the simulations, the present analyses suggest a trend towards $g$ in the range 0.4--0.6. However, high-Reynolds-number simulations longer than recently reported in the literature are needed. [Preview Abstract] |
Monday, November 19, 2007 4:53PM - 5:06PM |
JO.00007: Large-eddy simulations of the turbulent oscillating boundary layer Senthil Radhakrishnan, Ugo Piomelli A turbulent boundary layer subjected to an oscillating pressure gradient has been computed using Large-Eddy Simulation with wall-layer models. Two types of wall-layer models were tested, one group based on log-law, another on the DES methodology. For the calculations using log-law wall model, the subgrid scale stresses were computed with the Smagorinsky, Lagrangian Dynamic and Scale-Dependent Lagrangian Dynamic models. Simulations were carried out for a Stokes Reynolds number $Re_{\delta_s}=3500$. All the calculations predict the response of the wall-shear stress to the applied pressure gradient qualitatively well but with an error in the phase. The mean velocity is predicted reasonably well by all the calculations. During the late acceleration and early deceleration, the calculations based on DES methodology and those using the Smagorinsky model underpredict the streamwise and wall-normal Reynolds stresses whereas the Lagrangian Dynamic model gives improved agreement with the experiments. [Preview Abstract] |
Monday, November 19, 2007 5:06PM - 5:19PM |
JO.00008: Computational study on the statistics of turbulent pipe flow Xiaohua Wu, Parviz Moin Fully developed turbulent pipe flow at $Re_{D}$ 44000 was simulated with finite difference method on 630 million grid points. The corresponding pipe radius R based Karman number $R^{+}$ is 1142 and the domain length is 15R. Simulation results agree well with the experimental data of Lawn (1971), Zagarola et al (1997) and McKeon et al (2004). Near the wall the gradient of $\mbox{ln}U^{+}$ with respect to $\mbox{ln}(1-r)^{+}$ is approximately constant for the narrow region of $70<(1-r)^{+}<120$. Thus the DNS is consistent with the limited power-law of Zagarola et al for $R^{+}<5000$. Similarly, the near-wall gradient of $U^{+}$ with respect to $\mbox{ln}(1-r)^{+} $ can only be considered constant for $50<(1-r)^{+}<90$ thereby indicating limited log-law. The gradient of U with respect to $1-r$ at $Re_{D}$ 44000 is found to nearly collapse with that at $Re_{D}$ 5300 for the central region of $1-r>0.4$. An explanation for the existence of logarithmic mean pipe flow velocity profile even at very low Reynolds numbers is given. Budgets of the mean axial velocity balance show that at $Re_{D}$ 44000 only within a very narrow range of approximately 10 wall units ($0.003<1- r<0.015$) do the effects of viscous shear stress gradient and turbulent shear stress gradient overwhelm other contributions. Away from the pipe surface for $1-r>0.2$ all terms in the mean axial momentum transport equation remain nearly unchanged. Flow visualizations at both Reynolds numbers will also be presented. [Preview Abstract] |
Monday, November 19, 2007 5:19PM - 5:32PM |
JO.00009: Large eddy simulation of flow around a three-dimensional model vehicle Jung-Il Lee, Haecheon Choi, Noma Park Large eddy simulation of turbulent flow around a three- dimensional model vehicle is conducted at $Re=170,000$ based on the vehicle height. The three-dimensional shape of this model vehicle is realized by an immersed boundary method in a Cartesian coordinate (Kim et al., JCP 2001). As a subgrid-scale (SGS) model, we consider the Smagorinsky and Vreman (Vreman, PoF 2004) models with constant model coefficients ($C_s = 0.16$ and $C_v = 0.07$, respectively), and a dynamic Vreman model developed by Park et al. (PoF 2006). The issue on how to dynamically obtain the Vreman model coefficient is re-investigated based on the Germano identity and the global equilibrium between the SGS dissipation and viscous dissipation. The results of simulations are compared with the experimental results by Khalighi et al. (SAE 2001) and will be shown in the final presentation. [Preview Abstract] |
Monday, November 19, 2007 5:32PM - 5:45PM |
JO.00010: Dynamic K-L analysis of coherent structures based on DNS of turbulent Newtonian and viscoelastic flows Gaurab Samanta, Antony Beris, Robert Handler, Kostas Housiadas Direct Numerical Simulation (DNS) data of a Newtonian and a viscoelastic turbulent channel flow is analyzed here through a projection of a time sequence of velocity fields into a set of Karhunen-Loeve (K-L) modes, large enough to contain, on the average, more than 90{\%} of the fluctuating turbulence energy. The enhanced importance of large coherent structures in viscoelastic turbulent flows is exploited here, using K-L modes dynamically, to gain further quantitative insights into the behavior of the overall flow dynamics. A representational entropy is used in conjunction with fluctuating kinetic energy to show that viscoelastic turbulent flow is better organized than in the Newtonian limit. Dynamic correlations of pairs of K-L coefficients are used to quantify time scales that show an unsystematic increase with viscoelasticity. Calculating these correlations for K-L modes corresponding to different wavenumbers in the principal flow direction, in a moving frame of reference, allows us to detect coherent flow structures, their mean convective velocity, and locate turbulent events. Dependence of Newtonian case data on mesh-resolution, domain size and time-step of integration is investigated. [Preview Abstract] |
Monday, November 19, 2007 5:45PM - 5:58PM |
JO.00011: Link between turbulence production and surface current for a horizontal rectangular surface jet. Robert Martinuzzi, Iftehkar Naqavi, Eric Savory, Roi Gurka The surface jet provides a case study for the interaction of turbulence with the free surface. In the present work the TKE budget will be discussed for a rectangular surface jet at a Reynolds number of 4420 and a Froude number of 0.49. The relevant terms in the TKE budget are calculated through direct numerical simulation (DNS) of surface jet. The DNS has been validated thoroughly through comparison with the experimental results. It is observed that all the terms involved in the TKE budget except the production show a sudden change on approaching the free surface at the jet plane of symmetry. It is also observed that TKE production $P=-\left\langle {{u}'_i {u}'_j } \right\rangle {\partial U_i } \mathord{\left/ {\vphantom {{\partial U_i } {\partial x_j }}} \right. \kern-\nulldelimiterspace} {\partial x_j }$ becomes negative near the free surface. A detailed analysis of the turbulent production term shows that the normal stresses component in the spanwise direction contributes negative values to the production. This is a direct consequence of the free surface, which is responsible for the high level of lateral fluctuations resulting in higher normal stress, $\left\langle {{v}'^2} \right\rangle $ while the entrainment and spread of the jet along the free surface, provides a positive value for the mean normal strain of the spanwise velocity $\frac{\partial V}{\partial y}$. The negative production drives the lateral mean flow along the surface, which contributes towards the development of the surface current. [Preview Abstract] |
Monday, November 19, 2007 5:58PM - 6:11PM |
JO.00012: Numerical Investigations of the Leray-$\alpha $ Turbulence Model for Large Eddy Simulations S. Frankel, Y. Kwan, A. Chandy, S. Varghese, J. Shen, P. Fischer Large eddy simulations (LES) of transition to turbulence for steady flow through a model eccentric stenotic blood vessel are reported featuring the use of the Leray-$\alpha $ model. The Leray-$\alpha $ model uses a filtered velocity field for fluid advection, modifying the nonlinear vortex stretching dynamics effectively suppressing scales smaller than $\alpha $, and reducing resolution requirements, in contrast to more traditional LES models which filter the entire velocity field and enhance viscous dissipation through a computed eddy viscosity. A Helmholtz differential filter, both with and without projection of the filtered field onto a divergence free space, is used to investigate the issue of incompressibility of the filtered field. The effect of filter size is also studied. The incompressible Navier-Stokes and differential filter equations are numerically integrated using an $h/p $spectral-element method on a grid with 2448 hexahedral cells on up to 1024 processors on the IBM Blue Gene/L at Argonne National Laboratory. Differences between instantaneous and statistical LES results (with polynomial order 7) and recent published direct numerical simulation (DNS) results (with polynomial order 13) are discussed. Additional results from Fourier pseudospectral homogeneous isotropic turbulence simulations may be employed to shed further light on the LES results. [Preview Abstract] |
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