Bulletin of the American Physical Society
2005 58th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 20–22, 2005; Chicago, IL
Session KP: Turbulence Simulations: DNS III |
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Chair: Daniele Carati, Universite Libre de Bruxelles Room: Hilton Chicago Stevens 1 |
Monday, November 21, 2005 4:10PM - 4:23PM |
KP.00001: Anisotropy of scalar transport in conductive flows at low magnetic Reynolds numbers. Bernard Knaepen, Maxime Kinet, Daniele Carati Conductive flows at low magnetic Reynolds numbers are encountered in many industrial applications. For example, in the steel industry, applied magnetic fields can be used to damp turbulence in the casting process. In nuclear fusion devices (Tokamaks), liquid lithium flows are used as coolant blankets and interact with the surrounding magnetic field that drives and confines the fusion plasma. An important characteristic of such flows is the development of a strong anisotropy. This anisotropy can be twofold. Firstly, flows structures tend to elongate in the direction of the magnetic field (morphological anisotropy). Secondly, the magnetic field can severely alter the partition of energy between the components of the velocity field parallel or orthogonal to its direction (even in the case of homogeneous turbulence). In this work we study numerically how the transport of a passive scalar is affected by those two kinds of flow anisotropies. For the regimes considered, it is shown that the morphological anisotropy is the factor that is most influential on the anisotropic scalar transport. [Preview Abstract] |
Monday, November 21, 2005 4:23PM - 4:36PM |
KP.00002: Energy transfers in MHD turbulence Daniele Carati, Olivier Debliquy, Mahendra Verma The knowledge of the interactions between resolved and unresolved scales is required to design accurate subgrid-scale models for large-eddy simulations (LES). Although these interactions have been extensively studied for Navier-Stokes turbulence, much less has been done for turbulent conducting fluids. The objective of this study is to analyze the triad interactions in magneto-hydrodynamic (MHD) turbulence and more specifically the shell-to-shell interactions which are more complex in MHD. Indeed, the total energy can be split into the kinetic and the magnetic energy. The characterization of energy fluxes thus requires a detailed analysis of the energy transfers, not only between different length scales but also between the velocity and magnetic fields. Simulations of isotropic decaying and forced MHD turbulence using $512^3$ Fourier modes have been analyzed. The energy transfers appear to be very much local, i.e. the transfers are dominated by exchanges of energy between structures that have similar sizes. Shell-to-shell interactions have also been decomposed into forward and backward energy transfers. Such a decomposition is not unique and two possible strategies to identify the energy backscatter are suggested. They lead to fairly different diagnostics. [Preview Abstract] |
Monday, November 21, 2005 4:36PM - 4:49PM |
KP.00003: Anisotropy of MHD turbulence at low magnetic Reynolds number. Oleg Zikanov, Anatoly Vorobev, Peter Davidson, Bernard Knaepen Turbulent fluctuations in MHD flows are known to become anisotropic under the action of a sufficiently strong magnetic field. We investigate this phenomenon in the case of low magnetic Reynolds number using DNS and LES of a forced flow in a periodic box. A series of simulations is performed with different strengths of the magnetic field, varying Reynolds number, and two types of forcing, one of which is isotropic and the other limited to two-dimensional flow modes. We find that both the velocity anisotropy (difference in the relative amplitude of the velocity components) and the anisotropy of the velocity gradients are predominantly determined by the value of the magnetic interaction parameter. The effects of the Reynolds number and the type of forcing are much weaker. We also find that the anisotropy varies only slightly with the length scale. The work was supported by the DOE Office of Basic Energy Science and NSF-MRI program. [Preview Abstract] |
Monday, November 21, 2005 4:49PM - 5:02PM |
KP.00004: MHD Shallow-Water Turbulence on the Sphere Erica Staehling, James Cho Motivated by astrophysical-geophysical applications, we have performed a series of high Reynolds number simulations of freely- evolving, magnetohydrodynamic shallow-water turbulence (MHDSWT) on a rotating sphere. MHDSWT is the simplest turbulence model that includes the effects of stratification, differential rotation, and magnetic field that can be studied over long durations. A systematic exploration of the full physical and numerical parameter-space shows novel as well as consistent behavior, compared to those of pure hydrodynamic (HD) and 2-D MHD counterparts. In the case without rotation, our simulations show that the turbulent evolution is sensitive to initial conditions, most strongly to the peak of the energy spectrum. With increasing magnetic field strength, the flow field is more susceptible to loss of balance; the field blows up in finite time. In addition, the pronounced anisotropic structures (jets and vorticity bands) observed in differentially-rotating HD systems do not form. An application of the model to the solar tachocline is also presented. [Preview Abstract] |
Monday, November 21, 2005 5:02PM - 5:15PM |
KP.00005: Acceleration statistics of heavy particles in turbulence Federico Toschi, Jeremie Bec, Luca Biferale, Guido Boffetta, Antonio Celani, Massimo Cencini, Alessandra Lanotte, Stefano Musacchio We study, by means of direct numerical simulations, the dynamics of heavy particle transport in homogeneous, isotropic, fully developed turbulence, up to resolution $512^3$ ($R_\lambda\approx 185$). Following the trajectories of up to 120 million particles with Stokes numbers, $St$, in the range from $0.16$ to $3.5$ we are able to characterize in full detail the statistics of particle acceleration. We will show that the root-mean-squared acceleration $a_{\rm rms}$ sharply falls off from the fluid tracer value already at quite small Stokes numbers, that at a given $St$ the normalised acceleration $a_{\rm rms}/(\epsilon^3/\nu)^{1/4}$ increases with $R_\lambda$ consistently with the trend observed for fluid tracers and that the tails of the probability density function of the normalised acceleration $a/a_{\rm rms}$ decrease with $St$. Two concurrent mechanisms lead to the above results: particle clustering, very effective at small $St$, and filtering induced by the particle response time, that takes over at larger $St$. [Preview Abstract] |
Monday, November 21, 2005 5:15PM - 5:28PM |
KP.00006: Dispersion of heavy particles in isotropic turbulence Jaedal Jeong, Kyongmin Yeo, Changhoon Lee Particle-laden turbulence is frequently observed in nature such as in the atmosphere or the ocean as well as in many engineering flows. Recently, airbourne micro or nano-scale particles in the atmosphere draw much attention from environmental societies since such small particles cause a lot of environmental problems in the industrialized areas. In order to predict disperion of small particles, we have to understand the mechanism by which laden particles disperses in turbulent environment. In this study, we carried out direct numerical simulation of isotropic turbulence with particles under the Stokes drag assumption for a spherical particle. We consider only oneway interaction so that modification of turbulence by the particles is not taken into account. Particularly, we investigate the evolution of flow varialbe along the trajectory of a heavy particle with and without the influence of gravity. Comparisonal study of statistics between Lagrangian fluid dispersion and heavy particle dispersion is made. These results can be used in the development of a stochastic model for particle dispersion. Detailed results including correlation or time scales associated with dispersion will be presented in the meeting. [Preview Abstract] |
Monday, November 21, 2005 5:28PM - 5:41PM |
KP.00007: Direct numerical simulation of confined turbulent thermal convection at high Rayleigh numbers Roberto Verzicco, Katepalli Sreenivasan Results from direct numerical simulations of turbulent Boussinesq convection are presented. The flow is computed for a cylindrical cell of aspect ratio 1/2 in order to compare with the results from recent experiments. The results span eight decades of the Rayleigh number, $Ra$, from $2 \times 10^6$ to $2 \times 10^{14}$, and are unique because the Prandtl number is held constant at 0.7 and Boussinesq conditions are strictly enforced. One of the conclusions is that the Nusselt number varies nearly as the 1/3 power of $Ra$ for about 4 decades towards the upper end of the $Ra$-range covered. Another important observation is that, in same range of $Ra$, the large-scale recirculation, often called the mean wind, first weakens and eventually disappears. In the absence of the mean wind, the thermal boundary layers on the lower and upper plates become disconnected from each other, and the heat transfer scaling becomes essentially independent of the plate distance $h$. This is one of the basic assumptions of Malkus (1954) leading to the 1/3 power law of the relation between the Nusselt and Rayleigh numbers. [Preview Abstract] |
Monday, November 21, 2005 5:41PM - 5:54PM |
KP.00008: Viscoelastic nonlinear traveling waves and drag reduction in plane Poiseuille flow Wei Li, Philip Stone, Michael Graham Nonlinear traveling wave solutions to the Navier-Stokes equations in the plane Poiseuille geometry come into existence at a Reynolds number $Re$ very close to the experimentally observed value for transition to turbulence. These ``exact coherent states'' (ECS) capture the dominant streamwise-aligned counter-rotating pairs of vortices of the near-wall buffer layer. The present work considers the effect of viscoelasticity on these states, using the FENE-P constitutive model of polymer solutions. These effects mirror many experimental observations in fully turbulent flows near the onset of turbulent drag reduction. The mechanism underlying these changes is suppression of streamwise vortices by the polymer forces. Moreover, all mean velocity profiles on the ECS existence curves collapse onto a universal profile, which is insensitive to polymer extensibility, concentration, Weissenberg number or Reynolds number. In experiments with a given fluid, Reynolds and Weissenberg numbers ($Wi$) are linearly related. In this situation, we predict that there exist experimental conditions where these states cannot exist at all. Since polymer additives do not relaminarize turbulent flow, these results imply that there must exist other nontrivial states in turbulent viscoelastic flow that exist at high $Wi$. [Preview Abstract] |
Monday, November 21, 2005 5:54PM - 6:07PM |
KP.00009: Energy Analysis of Turbulent Flow Using Bi-Orthogonal Wavelets Joshi Vivek, Dietmar Rempfer Turbulent flow exhibits many different length and time scales. Hence in order to have a deeper insight into turbulence it is important to study energy transfer at discrete scales and between scales. Wavelets offer some potential for the analysis of energy transfer in turbulent flow. This is mainly due to their locality and scalability property. Wavelet representations have a natural built-in adaptivity through their ability to express and separate structures in a flow at different scales. Combined with the concept of the energy cascade, this feature makes wavelets a powerful tool for analysis compared to conventional discretizations. Wavelets are traditionally associated with orthonormal bases. A closer look reveals that orthogonality is often convenient but not essential. So in order to have more flexibility we have used the concept of bi-orthogonality for resolving different energy terms in the turbulent kinetic energy equation. This approach appears sometimes better suited, and offers interesting new combinations of concepts. The present work involves a wavelet decomposition of the terms in the turbulent kinetic energy transport equation of a fully developed channel flow, and a study of the behavior of the important terms. A detailed study of the energy transfer term is performed. An attempt is made to identify some well-known structures in turbulent channel flow at different scales of decomposition. The dynamics of these coherent structures is studied based on their contribution to energy transfer in the flow at discrete scales and over a period of time. [Preview Abstract] |
Monday, November 21, 2005 6:07PM - 6:20PM |
KP.00010: Parametric Dependence of Homogeneous Turbulent Shear Flow on Reynolds Number and Shear Parameter Juan Isaza, T. Vaithianathan, Lance Collins The combined role of the Shear Parameter, $S^{*} = S k / \epsilon$, and the Reynolds number in homogeneous turbulent shear flow is studied using direct numerical simulations (DNS). The parametric investigation involves DNS of $256^{3}$, $512^{3}$ and $1024^{3}$ with a constant shear parameter, $S^{*}$, between 1 and 100. Particular attention is given to velocity derivatives (strain and rotation) and higher-order structure functions and their scaling with the two parameters. This study is in line with some recent results reported by Schumacher, [Phys. Fluids 16, 2004]. Due to the high level of shear investigated, a new algorithm that avoids the remeshing step is used. The 20\% - 40\% loss in kinetic energy and dissipation rate reported by Lee \emph{et al.} [JFM, 216, 1990] using the Rogallo code is consequently avoided. [Preview Abstract] |
Monday, November 21, 2005 6:20PM - 6:33PM |
KP.00011: Numerical Methods for Scalar Transport Equation Yaser Khalighi, Vincent Terrapon, Parviz Moin Scalar transport phenomenon is known to generate small scale fluctuations. Consequently, in high Schmidt number regime it creates numerical difficulties in computer simulations. Besides that, the dissipative and dispersive nature of most numerical schemes aggravates the inaccuracy of such simulations. In the present work, two second order non-dissipative numerical schemes are implemented. These methods are optimized for the scalar transport equation and consider dispersion characteristics of numerical schemes, stability and computational efficiency. In addition, the advection of passive scalar is studied in Lagrangian framework. It is demonstrated that Lagrangian approach is very suitable for this problem when the Schmidt number is infinity. To ensure adequate resolution a particle destruction and creation algorithm is implemented. The effect this algorithm is studied in terms of overall accuracy and numerical dissipation. Passive scalar transport in a 2D Green-Taylor vortex is chosen as a benchmark problem where these new numerical techniques are applied. Results are compared in terms of dispersion, energy cascade and computational efficiency. [Preview Abstract] |
Monday, November 21, 2005 6:33PM - 6:46PM |
KP.00012: A numerical scheme to simulate arbitrary shaped resolved particles in complex flows Sourabh Apte, Neelesh Patankar We present a numerical scheme for the simulation of freely moving rigid particles in complex flows. The approach is based on the work by Patankar (2001) and Sharma \& Patankar (2004). The entire fluid-particle domain is assumed to be a fluid and the flow inside the particle domain is constrained to be a rigid body motion using an additional rigidity constraint in the context of a fractional step scheme. The particle is assumed to be made of material points moving on a fixed background mesh where the fluid flow equations are solved. The original scheme is further modified by introducing mollification kernels typically used in particle methods to interpolate between the particle material points and the fixed mesh. We evaluate the accuracy of the scheme together with the interpolation operator. This scheme is used to simulate a range of single and multiple particle problems in laminar flows. Some preliminary computations of particles in turbulent flows will also be presented. Application and extension of the scheme for the simulation of large number of resolved/deformable particles in complex turbulent flows will be discussed. [Preview Abstract] |
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