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 KE: Turbulence: Modeling II |
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Chair: Ivan Marusic, University of Minnesota Room: Salt Palace Convention Center 151 D-F |
Tuesday, November 20, 2007 8:00AM - 8:13AM |
KE.00001: Progress in the Variational Multiscale Formulation of Large Eddy Simulation Zhen Wang, Assad Oberai In the variational multiscale (VMS) formulation of large eddy simulation subgrid models are introduced in the variational (or weak) formulation of the Navier Stokes equations and a-priori scale separation is accomplished using projection operators to create coarse and fine scales. This separation also leads to two sets of evolution equations: one for the coarse scales and another for the fine scales. The coarse scale equations are solved numerically while the fine scale equations are solved analytically to obtain an expression for the fine scales in terms of the coarse scales and hence achieve closure. Till date, the VMS formulation has lead to accurate results in the simulation of canonical turbulent flow problems. It has been implemented using spectral, finite element and finite volume methods. In this talk, for the incompressible Navier Stokes equations, we willpresent some new ideas for modeling the fine scales within the context of the VMS formulation and discuss their impact on the coarse scale solution. We will present a simple residual-based approximation for the fine scales that accurately models the cross-stress term and demonstrate that when this term is append with an eddy viscosity model for the Reynolds stress, a new mixed-model is obtained. The application of these ideas will be illustrated through some simple numerical examples. [Preview Abstract] |
Tuesday, November 20, 2007 8:13AM - 8:26AM |
KE.00002: Scaling properties of subgrid-scale energy dissipation rate in Large Eddy Simulation Sergei Chumakov In Large Eddy Simulation (LES), the dissipation rates of subgrid-scale (SGS) kinetic energy and SGS scalar variance are arguably the two most elusive quantities to model. In the literature it is customary to model them using assumed power-law correlations between the SGS energy and its dissipation, and between SGS scalar variance and its dissipation. We use DNS of forced homogeneous isotropic turbulence with 512$^3$ and 1024$^3$ grid points with Reynolds number based on Taylor microscale up to 400 to examine a priori the scaling properties of the SGS kinetic energy, SGS variance of a passive scalar and their dissipation rates. It is found that the two pairs of quantities are strongly correlated and a power-law scaling assumption holds reasonably well for both pairs. However, the scaling exponent for the power-law approximation of correlation between SGS energy and its dissipation was found to change considerably with the LES filter size, while it was assumed to be varying weakly in previous studies. The scaling between SGS scalar variance and its dissipation, on the other hand, was found to be extremely close to the power-law scaling with an exponent that does not vary with the LES filter size. [Preview Abstract] |
Tuesday, November 20, 2007 8:26AM - 8:39AM |
KE.00003: Constrained Dynamic Subgrid-scale Model for Large Eddy Simulation Zuoli Xiao, Yipeng Shi, Shiyi Chen In traditional dynamic subgrid-scale (SGS) stress models of large eddy simulation (LES), the model coefficients are determined by a least square procedure which minimizes the error between the resolved stress and the model stress using the Germano identity. We propose to impose physical constraints in this dynamic procedure and to calculate the SGS model coefficients using a constrained variation. Based on the scale-invariance of the turbulence flow, we deduce a SGS energy dissipation constraint. Numerical simulations demonstrate that the constrained dynamic model predicts well the energy evolution and the SGS energy dissipation and the results are more accurate than those from the non-constrained models. The constrained SGS model also shows a strong correlation with the real stress and predicts well the energy backscatter, which is a desirable feature of combining the advantages of dynamics Smagorinsky and mixed models. [Preview Abstract] |
Tuesday, November 20, 2007 8:39AM - 8:52AM |
KE.00004: A near-wall model for LES of an oceanic bottom boundary layer Sutanu Sarkar, John Taylor The high-Reynolds number turbulent boundary layer over the ocean bottom takes the form of a rough Ekman layer that is subject to a stable stratification imposed from above. Since the LES grid cannot resolve the viscous length scale or the small-scale roughness elements, a near-wall model (NWM) is required in addition to the baseline subgrid model, the dynamic eddy viscosity model in this case. From field data and from our own DNS at lower Reynolds number, it is known that the mean velocity profile admits an overlap log layer. Thus, an approximate instantaneous boundary condition based on the mean log law can be formulated. However, in agreement with the experience of previous investigators, we find that such a boundary condition leads to an over-prediction of the near-boundary shear. A novel stochastic forcing of the vertical momentum equation with proportional control is proposed to correct the problem. The forcing is restricted to a narrow envelope, $0 < z < \Delta_f$, and has a small amplitude. The good performance of the NWM is demonstrated using three test cases: a $Re_* = 2000$ smooth channel flow where DNS data is available, rough channel flow with $z_0/\delta=2.8*10^{-3}$ and $Re_* = 5,600$ where laboratory data is available, and a rough Ekman layer with $z_0/\delta=5.7 *10^{-3}$, $Re_* = 60,000$, and $N/f = 75$ where field data is available. [Preview Abstract] |
Tuesday, November 20, 2007 8:52AM - 9:05AM |
KE.00005: Near-Wall Geometrical Analysis of the Resolved- and Subgrid-Scale Velocity and Temperature Fields Donald Bergstrom, Bing-Chen Wang In this research, we investigate wall anisotropic effects on the geometrical properties of the resolved and subgrid-scale (SGS) velocity and temperature fields based on both numerical and analytical approaches. Previous studies on geometrical statistics have primarily focused on either isothermal or isotropic turbulent flows; in this work, we extend the scope of research to investigate both isothermal and non-isothermal wall-bounded turbulent flows. We focus on studying the resolved enstrophy generation, local vortex stretching, and a variety of characteristic geometrical alignment patterns. The presence of the wall has a significant impact on the geometrical properties of the resolved velocity and temperature fields. Some probability density distributions associated with these alignment patterns converge to Dirac delta functions as the wall is approached. In addition, the relative rotation between the eigen-triad of the SGS stress tensor and that of the resolved strain rate tensor is studied using a novel parameterization method based on Euler's theorem. The proposed parameters are the natural invariants of the rotation matrix, and found to be very effective in assessing different SGS stress models in terms of their degree of nonlinearity and sensitivity to the near-wall anisotropy. [Preview Abstract] |
Tuesday, November 20, 2007 9:05AM - 9:18AM |
KE.00006: A Numerical Simulation of Hybrid-Filtered Navier-Stokes Equations Bernie Rajamani, John Kim Germano(2004) derived an additive filter, by adding an LES-like filter operator ($\mathcal F$) and a RANS-like statistical operator ($\mathcal E$) with a blending function $k$ to form a hybrid filter ($\mathcal H$). This filter, when applied to the Navier-Stokes equations, yields a $\mathcal H-$filtered Navier- Stokes equations (HFNS). The most interesting term of the HFNS is the hybrid turbulent stresses, which evolve as a second-order central moment of the velocity field. Previous studies, which blended two model equations, including DES-like models, have shown that there are problems near the RANS/LES transition zones. The additional stresses in the hybrid equations are expected to provide a smooth RANS/LES transition. However, the HFNS is somewhat difficult to solve, and the current study undertakes the task of solving numerically these equations. We will present, for a plane channel flow, \textit{a-priori} test results as well as those obtained from a full simulation of the HFNS. Numerical issues encountered in solving the HFNS will also be discussed. [Preview Abstract] |
Tuesday, November 20, 2007 9:18AM - 9:31AM |
KE.00007: Turbulent Viscosity Coefficient in Low-Reynolds-Number Turbulence Hiroshi Shibata A new model for the Large Eddy Simulation (LES) is proposed. The LES has been accepted as the standard formalism. In the application of the LES, several models are chosen. The purpose of this paper is for us to propose one of the most physical models. The LES is usually written down as \begin{equation} \label{eq1} \frac{\partial U_i }{\partial t}+(\vec {U}\cdot \vec {\nabla })U_i =-\frac{1}{\rho }\frac{\partial P}{\partial x_i }+\nu _0 \Delta U_i -\frac{\partial Q_{ij} }{\partial x_j }. \end{equation} The above equation is rewritten as \begin{equation} \label{eq2} \frac{\partial U_i }{\partial t}+(\vec {U}\cdot \vec {\nabla })U_i =-\frac{1}{\rho }\frac{\partial P}{\partial x_i }+\nu \Delta U_i \end{equation} and $\nu $ is referred to as turbulent viscosity coefficient. The statistical mechanical method by Helfand[1] is reformed by the replacement of the relationship between the local velocity and the kinetic viscosity coefficient by the one between the turbulent velocity and the turbulent viscosity coefficient. The major assumption here is the Gaussian statistics for the turbulent velocity. The concrete calculation using the lattice Boltzmann method is shown for the low-Reynolds-number turbulence. [1] E. Helfand, Phys. Rev. 119,1(1960). [Preview Abstract] |
Tuesday, November 20, 2007 9:31AM - 9:44AM |
KE.00008: The compressible hybrid RANS/LES governing equations Martin Sanchez-Rocha, Suresh Menon In this work, the compressible governing equations for hybrid Reynolds-Averaged/Large-eddy simulations are formally derived by applying a hybrid filter in the Navier-Stokes equations. This filter is constructed by linearly combining the Reynolds-Average (RANS) and Large-eddy simulation (LES) operators with a blending function. The derived equations include additional terms that represent the interactions between RANS and LES formulations. The importance of these new terms is investigated in flat-plate turbulent boundary layer simulations. Current results indicate that, the additional terms play a fundamental role modeling the turbulence that is neither modeled nor resolved when the hybrid model transits from RANS to LES. It is also indicated that when the additional terms are included, the calculations are not severely affected by the blending function implemented. However, if the new terms are not included, the hybrid calculations become dependent on the blending function. These results are important to hybrid RANS/LES models since they would indicate that the transition between formulations could be specified arbitrarily as long as the formal hybrid equations are solved. In contrast, current hybrid RANS/LES approaches rely on how this transition is specified. [Preview Abstract] |
Tuesday, November 20, 2007 9:44AM - 9:57AM |
KE.00009: Geometrical alignment between SGS stress and its production rate Chenning Tong, Xingshi Wang The conditional SGS stress and conditional SGS stress production rate evolve the joint probability density function of the resolvable-scale velocity. We examine the orientations of the eigenvectors of the SGS stress and the SGS stress production rate using data obtained in the atmospheric boundary layer. The results show that the pdf of the relative angles between the eigenvectors of these are concentrated in three regions representing three alignment modes: (a) Their corresponding eigenvectors are in near perfect alignment; (b) The eigenvectors for their largest eigenvalues are aligned; (c) The eigenvectors for the intermediate production and the smallest SGS stress eigenvalues are aligned. The overall alignment is better than that between the SGS stress and the resolved strain rate. The production of SGS energy is largest in (a) and is smallest in (c). The probability for mode (a) is larger for positive vertical velocity whereas that for (c) is larger for negative vertical velocity. Consequently, the two tensors are better aligned when the vertical velocity is positive. These three regions correspond to three modes of alignment between the SGS stress and the resolvable strain rate. The results are important for understanding the SGS dynamics and for SGS modeling involving the SGS stress production. [Preview Abstract] |
Tuesday, November 20, 2007 9:57AM - 10:10AM |
KE.00010: Shock-confining filters for LES of compressible turbulence Nathan Grube, M. Pino Martin Uniformly high-order-accurate filtering of fluid flow properties in the presence of shocks and shocklets is susceptible to the introduction of Gibbs-like overshoots and stability problems. An example is given in Taylor, Grube and Martin (2007)\footnote{AIAA paper 2007-4197}, who show that linear filtering of highly compressible turbulent flow fields creates antiphysical flow characteristics. To alleviate this problem, we develop shock-confining filters (SCF). These non-linear filters adapt in order to avoid filtering across discontinuities. When used in combination with WENO methods, the data smoothness is gaged by the shock-capturing method and used to control the SCF adaptation. In smooth turbulent regions, the SCF reduces to a desired linear filter, and a traditional LES is recovered. We assess the benefits of SCF in the simulation of shock/isotropic turbulence interactions using the dynamic mixed model and the approximate deconvolution model. [Preview Abstract] |
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