Bulletin of the American Physical Society
64th Annual Meeting of the APS Division of Fluid Dynamics
Volume 56, Number 18
Sunday–Tuesday, November 20–22, 2011; Baltimore, Maryland
Session M12: Turbulence Simulation V |
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Chair: Ugo Piomelli, Queens University Room: 315 |
Tuesday, November 22, 2011 8:00AM - 8:13AM |
M12.00001: Stochastic quantification of errors in large-eddy simulations of a spatially-evolving mixing layer Maria-Vittoria Salvetti, Marcello Meldi, Pierre Sagaut The development of methodologies aimed at obtaining new insights in the behavior of the error in Large-Eddy Simulation (LES) has recently gained considerable attention. A possible approach to estimate the error at moderate computational cost is to combine the response surface methodology with the generalized Polynomial Chaos (gPC) theory, in which statistical information on the system response can be obtained by modeling the uncertain quantities through input random variables with given statistics. The gPC approach is used herein to quantify the error in LES of a spatially-evolving mixing layer and its sensitivity to different simulation parameters, viz. the grid stretching in the streamwise and lateral directions and the subgrid scale model constant. The error is evaluated with respect to the results of a highly-resolved LES and for different quantities of interest. The considered spatially-evolving flow is characterized by the progressive transition from a laminar regime, highly dependent on the inlet conditions, to a fully-developed turbulent one. Therefore the computational domain is divided in two different zones (inlet dependent and fully turbulent)and the gPC error analysis is carried out for these two zones separately. An optimization of the parameters is also carried out for both zones. [Preview Abstract] |
Tuesday, November 22, 2011 8:13AM - 8:26AM |
M12.00002: Constrained Large Eddy Simulation of Separated Turbulent Flows Zhenhua Xia, Yipeng Shi, Jianchun Wang, Zuoli Xiao, Yantao Yang, Shiyi Chen Constrained Large-eddy Simulation (CLES) has~been recently proposed to simulate turbulent flows with massive separation. Different from traditional large eddy simulation (LES) and hybrid RANS/LES approaches, the CLES simulates the whole flow domain by large eddy simulation while enforcing a RANS Reynolds stress constraint on the subgrid-scale (SGS) stress models in the near-wall region. Algebraic eddy-viscosity models and one-equation Spalart-Allmaras (S-A) model have been used to constrain the Reynolds stress. The CLES approach is validated \textit{a posteriori} through simulation of flow past a circular cylinder and periodic hill flow at high Reynolds numbers. The simulation results are compared with those from RANS, DES, DDES and other available hybrid RANS/LES methods. It is shown that the capability of the CLES method in predicting separated flows is comparable to that of DES. Detailed discussions are also presented about the effects of the RANS models as constraint~in the near-wall layers. Our results demonstrate that the CLES method is a promising alternative towards engineering applications. [Preview Abstract] |
Tuesday, November 22, 2011 8:26AM - 8:39AM |
M12.00003: Dynamic Lagrangian model for LES on unstructured grids Krishnan Mahesh, Aman Verma We discuss a dynamic Lagrangian averaging approach applied in conjunction with the dynamic model for large-eddy simulation. Unlike Meneveau's Lagrangian dynamic model where the Lagrangian time scale contains an adjustable parameter $\theta$, we propose a dynamic time scale based on a ``surrogate-correlation'' of the Germano-identity error (GIE). Also, a simple material derivative relation is used to calculate GIE at different events along a pathline instead of Lagrangian tracking. The absence of any multi-linear interpolation makes this approach particularly suitable for unstructured grids. The proposed model is applied to LES of turbulent channel flow at various Reynolds numbers and grid resolutions. Significant improvement over the dynamic Smagorinsky model is observed, especially at coarse resolutions. The model is also applied to external flow over a cylinder at high Reynolds numbers. This work was supported by the United States Office of Naval Research under ONR Grant N00014-08-1-0433. [Preview Abstract] |
Tuesday, November 22, 2011 8:39AM - 8:52AM |
M12.00004: Dynamic time scale for the Lagrangian subgrid-scale model based on Rice's formula Claire Verhulst, Charles Meneveau The dynamic formulation of Smagorinsky's subgrid-scale model for Large Eddy Simulations (LES) requires averaging to avoid instability due to extreme fluctuations. For complex-geometry flows a Lagrangian approach is often useful [see Meneveau, Lund, and Cabot, JFM 319 (1996)]. However, an ad-hoc choice of the relaxation timescale must be made, often based on resolved strain-rates and stresses at the grid- scale. Recently, Park and Mahesh [Phys. Fluids 21, 065106 (2009)] proposed the attractive notion of using statistics of the error signal itself to determine a timescale dynamically. We extend this approach by using Rice's formula to dynamically estimate the time between mean-crossings of the error signal and set the averaging timescale to be twice this value. The approach requires accumulating Lagrange-averaged square error and its time-derivative squared, which is done using the Eulerian approximation as proposed in the original model. For validation, LES of flow in a channel and through an array of cubes are compared with experimental results. Distributions of the dynamic coefficient, error, and dynamic timescale are shown as a function of distance from the wall. Computational efficiency and memory requirements are also discussed. [Preview Abstract] |
Tuesday, November 22, 2011 8:52AM - 9:05AM |
M12.00005: Convergence and scaling of large-eddy simulations of a turbulent free jet flow Haifeng Wang, Stephen Pope A large set of large-eddy simulations (LES) is performed for a turbulent free jet flow with Reynolds number 21,000 to investigate systemically the convergence and scaling of the LES results with respect to the turbulence resolution scale (the filter width $\Delta$) and the grid size $h$. Four convergence problems are considered: (a) convergence of the numerical error with $h$, for the Smagorinsky model with fixed $\Delta$; (b) convergence of the Smagorinsky model error with $\Delta$, for fixed $h$ ($h\le\Delta$); (c) convergence of the Smagorinsky model with $\Delta=h$; (d) convergence of the dynamic Smagorinsky model with $\Delta=h$. The convergence results are analyzed for the different LES quantities: the sub- filter eddy viscosity, the sub-filter shear stress, the resolved first, second and third order statistics. The scaling laws of the different LES quantities are analyzed based on the Kolmogorov energy-spectrum, and the LES convergence results agree with the scaling very well. [Preview Abstract] |
Tuesday, November 22, 2011 9:05AM - 9:18AM |
M12.00006: Grid-point requirement for large eddy simulation: Chapman's estimation revisited Haecheon Choi, Parviz Moin Resolution requirements for large eddy simulation (LES), estimated by Chapman [AIAA J. Vol. 17, p. 1293 (1979)], are modified using accurate formulae for high Reynolds number boundary layer flow. This correction indicates that the number of grid points ($N)$ required for wall-modeled LES is proportional to $Re_L^{\raise0.7ex\hbox{$2$} \!\mathord{\left/ {\vphantom {2 7}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$7$}} $, but a wall-resolving LES requires $N\sim Re_L^{\raise0.7ex\hbox{${13}$} \!\mathord{\left/ {\vphantom {{13} 7}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$7$}} $, where $L$ is the flat-plate length in the streamwise direction. The number of grid points required for the flow over an aircraft using LES with and without modeling the viscous wall region is estimated: the number of grid points for the wall-modeled LES is one to three orders of magnitude smaller than that for the wall-resolving LES, indicating the practical importance of wall modeling in LES for high Reynolds number flows. [Preview Abstract] |
Tuesday, November 22, 2011 9:18AM - 9:31AM |
M12.00007: Explicitly filtered LES on unstructured grids Sanjeeb Bose, Parviz Moin, Frank Ham Prior investigations using explicitly filtered LES have demonstrated that grid- independent solutions can be obtained by decoupling the filtering operator from the underlying grid. Dynamic, mixed SGS models were then derived from the explicitly filtered LES governing equations and showed good accuracy in coarse simulations of high Reynolds number wall-bounded flows. The explicitly filtered framework and SGS models are now implemented in a second order, unstructured, finite volume solver. Filtering on unstructured grids is decoupled from the mesh by utilizing differential filters. LES, using the proposed dynamic mixed models, of a Re=50000 rectangular duct flow (aspect ratio = 3.33) is performed. The grid is anisotropically refined in the near-wall region in the vicinity of the duct midplane away from the side walls. The regions of grid refinement are selected by processing the mean statistics of $\overline{u'}_i\overline{u'}_i$, which measures the smoothness of the LES solution with respect to the filter width. The overall resolution of the LES remains coarse ($\Delta x^+_f \approx 150$, maximum $\Delta z^+_f \approx 60$). Streamwise mean velocity profiles are predicted within a few percent of the experimental measurements of Kolade and Eaton (2010). Preliminary simulations of a three dimensional stalled diffuser will also be presented. [Preview Abstract] |
Tuesday, November 22, 2011 9:31AM - 9:44AM |
M12.00008: ABSTRACT WITHDRAWN |
Tuesday, November 22, 2011 9:44AM - 9:57AM |
M12.00009: The effects of extended stencil sizes and mildly anisotropic grids on finite volume OLES Sigfried Haering, Nicholas Malaya, Jeremy Hira, Robert Moser Optimal large eddy simulations (OLES) utilize stochastic estimation to approximate the convective terms and produce statistically accurate LES. This formulation requires multi-point velocity correlations as input for the sub-grid model. Rather than relying on DNS data, these correlations can be completely determined from Kolmogorov inertial-range theory, small-scale isotropy, and the quasi-normal approximation. Initially, these models were developed for a particular stencil ($4\times 1 \times 1$) on an isotropic grid, and produced accurate LES results. However, for OLES to become generally useful, it must be developed for anisotropic and inhomogeneous grids. Additionally, the optimal extent of correlation information to include must be determined. Here, we examine the effects of extending stencil sizes and introducing mild anisotropy. We present results from simulations characterizing the dependence of the model operators on a wide range of stencils and grid sizes. Modestly sized stencils are found to produce results nearly identical to the larger sets. These results provide evidence of ideal OLES operators for generic grids. [Preview Abstract] |
Tuesday, November 22, 2011 9:57AM - 10:10AM |
M12.00010: Wavelet-based adaptive LES with explicit-filtering. Giuliano De Stefano, Oleg V. Vasilyev Wavelet-based adaptive large-eddy simulation is a novel approach to the numerical simulation of turbulence, where the coherent energetic eddies are solved for, while modelling the influence of the less energetic coherent/incoherent background flow. The formal separation between resolved and unresolved turbulent velocity field is obtained by wavelet threshold filtering that is inherent to the adaptive wavelet collocation numerical method. A new explicit wavelet filtering strategy is introduced and tested, by considering two different filtering levels: the physical level, which controls the turbulence model, and the numerical level that is responsible for the accuracy of numerical calculations. The theoretical basis for wavelet-based adaptive large-eddy simulation with explicit filtering and consistent dynamic modelling is given. Some numerical experiments are presented for unsteady homogeneous turbulence, demonstrating the existence of grid-independent solutions. [Preview Abstract] |
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