Bulletin of the American Physical Society
2006 59th Annual Meeting of the APS Division of Fluid Dynamics
Sunday–Tuesday, November 19–21, 2006; Tampa Bay, Florida
Session EM: Turbulence Simulations I |
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Chair: Sharath Girimaji, Texas A&M University Room: Tampa Marriott Waterside Hotel and Marina Meeting Room 10 |
Sunday, November 19, 2006 4:15PM - 4:28PM |
EM.00001: Scaling of energy dissipation and enstrophy in high-resolution numerical simulations Diego Donzis, Pui-kuen Yeung, Katepalli Sreenivasan We present results from direct numerical simulations using grid resolution up to $2048^3$ with Taylor-scale Reynolds number ($R_\lambda$) up to 650 to study the scaling of energy dissipation rate $\epsilon$ and enstrophy $\Omega$. Almost all sources of data have suggested that enstrophy is more intermittent whereas theoretical arguments suggest identical scaling. Large values of $\epsilon$ and $\Omega$ imply large velocity gradients which must be well resolved in order to study their intermittent behavior. An examination of the statistics of velocity increments shows that the usual resolution criterion of $k_{max}\eta\approx 1.5$ (where $k_{max}=\sqrt{2}N/3$ is highest resolvable wavenumber on an $N^3$ grid and $\eta$ is Kolmogorov scale) is not sufficient for the smallest scales which contribute to high-order moments. By means of highly-resolved simulations at $R_\lambda$ up to 240, we show that $k_{max}\eta\approx 3$ is sufficient for moments of $\epsilon$ and $\Omega$ up to order 4 and attempt to separate effects of Reynolds number and resolution on the observed scaling differences. A tentative conclusion is that the correlation between dissipation and enstrophy increases with $R_\lambda$ while the tails of the PDFs of $\epsilon/\langle\epsilon\rangle$ and $\Omega/\langle\Omega\rangle$ approach each other. While the observed statistics of small scales are sensitive to resolution effects, results in the inertial range are less so. [Preview Abstract] |
Sunday, November 19, 2006 4:28PM - 4:41PM |
EM.00002: Spectral properties of passive scalars in MHD turbulence Maxime Kinet, Paolo Burattini, Daniele Carati, Bernard Knaepen Magnetohydrodynamics (MHD) --- which deals with the flow of an electrically conducting fluid in presence of a magnetic field --- finds applications in the steel industry (where magnetic fields are used to damp or to stir the turbulent motion) and in nuclear fusion devices (e.g. tokamaks). There, the liquid lithium, used as coolant, undergoes the effect of the plasma-confining magnetic field. Here, we focus on MHD at low magnetic Reynolds number, for a magnetic field applied in one direction only. In this case, the flow is known to become anisotropic, in that the velocity fluctuations parallel to the magnetic field are damped. Using direct numerical simulations in a cubic domain with periodic boundary conditions, we analyse the transport properties of a passive scalar embedded in the flow. Three cases, having increasing magnetic field strength, and two Schmidt numbers (0.1 and 1) are considered. The Fourier-space distributions of the scalar variance, mean dissipation rate, and transfer indicate that the anisotropy of the velocity field is reflected on the scalar. In order to evaluate the interchange between these quantities, their contributions in wavenumber space are decomposed in radial and angular directions. [Preview Abstract] |
Sunday, November 19, 2006 4:41PM - 4:54PM |
EM.00003: DNS of the thermal effects of plasma/turbulence interaction Shankar Ghosh, Krishnan Mahesh Direct numerical simulation is used to study the thermal effect of laser energy deposition in (i) quiescent air, and (ii) isotropic turbulence. In quiescent air, two idealizations of the plasma are considered -- spherical and tear--drop shaped. The spherical idealization is used to compare to classical solutions (Taylor 1950, Sedov 1959) for shock radius and velocity at the shock front, and to predict the behavior of density in the core of the plasma. The tear--drop shaped idealization resembles the initial shape of the plasma observed in experiments on laser induced breakdown of a gas. Shock radius and jumps in fluid properties at the shock front are compared to experiment. Budgets are computed for the vorticity transport equation, and physical behavior of vorticity will be discussed. For the turbulent simulations, the background flow is developed isotropic turbulence, and only the tear--drop shaped idealization is considered. Regions of compression and expansion are observed to be most intense normal to the axis of the plasma. The propagating blast wave is distorted by the background turbulence. Turbulence levels get suppressed in the core of the plasma and amplify across the blast wave. Turbulent simulations corresponding to the experiments of Comte--Bellot and Corrsin (1971) have been initiated, and will be presented. [Preview Abstract] |
Sunday, November 19, 2006 4:54PM - 5:07PM |
EM.00004: Decaying isotropic turbulence simulations in a binary mixture of different viscosities Kurnchul Lee, Sharath S. Girimaji Turbulence in mixtures differs from that in homogeneous medium due to two main reasons: (i) pressure-related effects manifesting through equation of state; and (ii) variable transport coefficient effect. In this study, we examine the variable transport co-efficient effect in isolation. We perform direct numerical simulation (DNS) of turbulence in a binary mixture of fluids with identical densities but vastly different viscosities. The initial turbulence field is isotropic with each fluid occupying one-half of the computational domain. A Boltzmann-equation based numerical scheme is employed for this simulation. The objective of the study is to investigate the various effects of viscosity on turbulence small scales: (i) the relation between viscosity, local dissipation and local strain rate; (ii) orientation of vorticity with the strain-rate eigen-vectors; and (iii) the magnitude of strain-rate eigen-values. [Preview Abstract] |
Sunday, November 19, 2006 5:07PM - 5:20PM |
EM.00005: On the long time behavior of decaying 2D turbulence in bounded domains Kai Schneider, Marie Farge Two--dimensional turbulence in bounded domains has many applications in geophysical flows, {\it e.g.}, the prediction of coastal currents to study the transport and mixing of pollutants in oceans. We present Direct Numerical Simulations of 2D turbulence in bounded domains for different geometries. The Navier-Stokes equations are solved in a periodic square domain using the vorticity--velocity formulation. The bounded domain is imbedded in the periodic domain and the no--slip boundary conditions on the wall are imposed using a volume penalisation technique. The numerical integration is done with a Fourier pseudo-spectral method combined to a semi-implicit time discretization with adaptive time-stepping. The aim of the present paper is to study the influence of the geometry on the flow dynamics, and in particular on the long time flow behavior. We study different shapes for the bounded domain : a circle, a square, a triangle and a torus. The numerical results thus obtained are compared with theoretical predictions based on the eigenfunctions of the biharmonic operator of the corresponding domain shape. [Preview Abstract] |
Sunday, November 19, 2006 5:20PM - 5:33PM |
EM.00006: Direct numerical simulation of flow past cactus--shaped cylinders Pradeep Babu, Krishnan Mahesh The Saguaro cacti are tall, have short root systems and can withstand high wind velocities (Bulk 1984, Talley et al. 2002). Their trunks are essentially cylindrical with V--shaped longitudinal cavities. The size and number of cavities on the Saguaro cacti vary so that they have a near--constant fraction cavity depth ($l/D$ ratio of about $0.07$, Geller \& Nobel 1984). Direct numerical simulations is used to assess the aerodynamic effect of the grooves on the cactus. DNS is performed for cactus shaped cylinders with $l/d$ ratio's of $0.07$ and $0.105$, and smooth cylinders ($l/d$=$0$) at the same Reynolds number. Presence of the V--shaped cavities is found to decrease the drag on the cylindrical trunk as well as affect the fluctuating lift forces. The talk will quantify these differences, and discuss the physical mechanisms by which V--shaped cavities on the surface influence the flow. [Preview Abstract] |
Sunday, November 19, 2006 5:33PM - 5:46PM |
EM.00007: A minimal multiscale Lagrangian map approach to synthesize non-Gaussian turbulent vector fields Carlos Rosales, Charles Meneveau A simple method is proposed to generate synthetic vector fields as surrogates for turbulent velocity fields, based on a minimal Lagrangian map. An initial Gaussian field generated with random-phase Fourier modes is distorted by moving fluid particles of a sequence of low-pass filtered fields at their fixed velocity for some scale-dependent time interval, interpolating onto a regular grid, and imposing the divergence-free condition. Statistical analysis shows that the resultant non-Gaussian field displays many properties commonly observed in turbulence, such as skewed and intermittent velocity gradient and increment PDFs, preferential alignment of vorticity with intermediate strain-rate, and non-trivial vortex stretching statistics. Differences appear only for measures associated with intense vortex tubes that are absent in the synthesized field. These synthetic fields are used as initial conditions in DNS and LES of decaying isotropic turbulence, giving more realistic results with significantly shortened initial adjustment periods, compared with Gaussian fields initializations. [Preview Abstract] |
Sunday, November 19, 2006 5:46PM - 5:59PM |
EM.00008: Adaptive uncertainty quantification using adjoint method and generalized polynomial chaos Qiqi Wang, Tonkid Chantrasmi, Gianluca Iaccarino, Parviz Moin Uncertainty quantification of numerical results is a pacing item for numerical simulation of complex engineering systems. This work focuses on uncertainty quantification of complicated physical processes with a very large number of uncertain parameters. Since numerical simulations of complex flows are typically computationally intensive, a balance between the detail of the physical models and the complexity of uncertainty quantification model is critical. Without careful consideration, one can easily become the bottleneck in prediction quality or computational cost. We propose an adaptive procedure to address this challenge. In our uncertainty quantification framework, an adjoint based perturbation method is first used. From the result of the perturbation method, the uncertain parameters that have the largest magnitude and most heavily influence the quantities of interest are selected. Then a polynomial chaos based expansion is used for these critical parameters only. This allows to build accurate response surface without assumptions on the correlations between the uncertain parameters. We will discuss application of our method to the numerical solution of the Navier Stokes equations. [Preview Abstract] |
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