Bulletin of the American Physical Society
62nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 54, Number 19
Sunday–Tuesday, November 22–24, 2009; Minneapolis, Minnesota
Session EB: Turbulence Modelling I |
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Chair: Ugo Piomelli, Queen's University Canada Room: 101B |
Sunday, November 22, 2009 4:15PM - 4:28PM |
EB.00001: Modeling the pressure term in finite-volume LES with unresolved wall layers Henry Chang, Robert Moser In the incompressible Navier-Stokes equations, the fluctuating pressure term serves to keep the velocity field divergence-free. Here we consider the role of incompressibility and the pressure in LES with finite-volume filter and unresolved wall layers. In particular, we use a uniform staggered-grid finite-volume discretization, where ${\Delta y}^+=50$ in the wall-normal direction. The standard treatment of pressure in such a finite-volume discretization results in an LES field that satisfies a discrete divergence-free condition. However, solutions to the incompressible Navier-Stokes equations--when volume-averaged--are not discretely divergence-free. In fact, the discrete divergence increases sharply close to the wall. It is also found that the resulting discrete pressure does not represent well the pressure contribution to the evolution of the filtered Reynolds stress tensor. It appears, therefore, that the standard pressure solution is not appropriate for finite volume LES of wall-bounded turbulence. Using the techniques of optimal LES, alternative pressure models are being developed which: (1) do not strictly impose the discrete divergence-free condition and (2) correctly represent the contribution of pressure to the evolution of Reynolds stress. [Preview Abstract] |
Sunday, November 22, 2009 4:28PM - 4:41PM |
EB.00002: Characterizing Finite Volume Operators for LES Jeremy Hira, Nicholas Malaya, Venkat Raman, Robert Moser Optimal large eddy simulation (OLES) is an approach to LES sub-grid modeling that requires multi-point correlation data as input. Until now, this has been obtained by analyzing DNS statistics. In the finite-volume OLES formulation studied here, under the assumption of small-scale homogeneity and isotropy, these correlations can be theoretically determined from Kolmogorov inertial-range theory and the quasi-normal approximation. Resulting models are expressed as generalized quadratic and linear finite volume operators that represent the convective momentum flux, and they have been found to produce accurate LES results. The operators have been analyzed to determine their characteristics as numerical approximation operators and as models of subgrid effects. In addition, the dependence of the model operators on the anisotropy of the grid and on the size of the stencils is analyzed to develop idealized general operators that can be used on general grids. These constitute finite volume turbulence operators applicable in a wide range of LES problems. [Preview Abstract] |
Sunday, November 22, 2009 4:41PM - 4:54PM |
EB.00003: A grid-independent length scale for large-eddy simulations U. Piomelli, B.J. Geurts In most large-eddy simulations a length-scale related to the grid size is used in the subgrid-scale models. Rapid variations of the mesh may cause errors and unphysical results. We propose a new length scale for small-scale turbulence models that is decoupled from the grid, and is determined dynamically from the velocity field itself. It is based on an approximation to a local integral scale used in turbulence models. The resulting eddy-viscosity model has many features of dynamic models (it vanishes near a wall or in laminar flows, and senses the local small scales of the flow) but does not require the use of spatial filtering operations, which are costly and may be difficult to perform on unstructured grids. The model coefficient is determined by a Successive Inverse Polynomial Interpolation procedure (Geurts \& Meyers, 2006), in which the coefficient is optimized computationally to minimize a specified cost function. Since this procedure can be performed on coarse grids, it adds little to the computational cost of the method. A set of 4-6 coarse simulations with the new model is required to approximate the optimum with fair accuracy, and the total cost of a simulation is comparable to that of a single simulation with a dynamic model. The new length scale also has the desirable feature that refining the mesh does not result in a DNS, but in a grid-converged LES. Applications to plane channel and mixing layers will be presented. [Preview Abstract] |
Sunday, November 22, 2009 4:54PM - 5:07PM |
EB.00004: A modulated gradient model for large-eddy simulation: application to a neutral atmospheric boundary layer Hao Lu, Fernando Porte-Agel It is known that in LES of high-Re atmospheric boundary layer (ABL), standard eddy-viscosity models poorly predict mean shear in the near-wall region and yield erroneous velocity profiles. A modulated gradient model is proposed. It is based on the Taylor expansion of the SGS stress and uses local equilibrium hypothesis to evaluate the SGS kinetic energy. To ensure numerical stability, a clipping procedure is used to avoid local backscatter. Two approaches are considered to specify the model coefficient: a constant value of 1, and a simple correction to account for the effects of the clipping procedure on the SGS energy production rate. The model is assessed through a systematic comparison with well-established empirical formulations and theoretical predictions of a variety of flow statistics in a neutral ABL. The statistics of the simulated velocity field obtained with the model show good agreement with reference results and a significant improvement compared to simulations with standard models. For instance, it is capable to reproduce the expected log-law profile and power-law energy spectra. It also yields streaky structures and near-Gaussian PDFs of velocity in the near-wall region. [Preview Abstract] |
Sunday, November 22, 2009 5:07PM - 5:20PM |
EB.00005: Progress Towards Specifying Initial Conditions for Variable Density Turbulence Models Bertrand Rollin, Malcolm J. Andrews It is now well accepted in the turbulence community that variable density turbulence can be affected at late time by the initial perturbations. This important property has opened an opportunity for prediction and ``design'' of late-time turbulence of particular interest for many engineering purposes. Specifically, our study aims at defining the rules for properly accounting for the initial conditions in variable density turbulence models. We report our latest advancement in this direction. A nonlinear ODE model is used to compute the evolution of bubbles/spikes in Rayleigh-Taylor/Richtmyer-Meshkov mixing after carefully formulated initial perturbations. We investigate the relations between the composition of the initial conditions, key characteristics, and quantities of the bubble/spikes evolution. Properties and possible scalings that dictate the late-time behavior of the flow will be discussed. [Preview Abstract] |
Sunday, November 22, 2009 5:20PM - 5:33PM |
EB.00006: Recovery of subgrid-scale kinetic energy in large-eddy simulations of incompressible wall-bounded flows Yifeng Tang, Rayhaneh Akhavan A method is presented for recovering the subgrid-scale kinetic energy in large-eddy simulations (LES) of wall-bounded flows. The formulation is based on extending the one-dimensional energy spectra obtained in LES using the filtered one-dimensional energy spectra derived from the theoretical formulations of Pao (1965) or Meyers and Meneveau (2008) for the three-dimensional energy spectrum in isotropic turbulence. To allow for application of these formulations to wall-bounded flows, the LES spectra are re-normalized into an isotropic space. Once the SGS kinetic energy is recovered, the individual components of turbulence intensities are computed using the formulation of Winckelmans {\em et al.} (2002). The entire procedure is applied as a post-processing step and can be combined with any SGS model. In tests performed using filtered DNS databases of turbulent channel flow at a $Re_\tau \approx 570$, the method recovered the SGS kinetic energy with errors of less than 10\% and the total kinetic energy with errors of less than 1\%. In application to LES data obtained using the Dynamic Smagorinsky Model, the individual components of turbulence intensities were recovered with an accuracy comparable to that with which the filtered statistics were predicted in LES. [Preview Abstract] |
Sunday, November 22, 2009 5:33PM - 5:46PM |
EB.00007: SGS model based on spatial correlation between turbulence structure and energy transfer Hiromichi Kobayashi In LES, it is well known that the spatial correlation between the energy transfer term obtained from filtered DNS and that from the Smagorinsky model is rather poor, especially in channel flows. Recently, several references showed that the local equilibrium proposed by Smagorinsky between the subgrid-scale (SGS) energy production and the SGS energy dissipation in the SGS kinetic energy equation seems to be not valid. The energy transfer from grid-scale (GS) to SGS is called the forward scatter. The energy transfer term is often called the SGS energy production term. The spatial correlation between the energy transfer term with the forward scatter and turbulence structure is examined. It is found that the negative second invariant of a velocity gradient tensor surrounding a vortex gives relatively high correlation in not only homogeneous turbulence but also a channel flow. A SGS model based on the correlation is proposed. [Preview Abstract] |
Sunday, November 22, 2009 5:46PM - 5:59PM |
EB.00008: Possible modifications to implicit large-eddy simulation J.M. McDonough Implicit large-eddy simulation (ILES) provides an advantage over more usual LES approaches in that its construction does not involve filtering of the governing equations and, as a consequence, removal of the need to develop sub-grid scale (SGS) models to represent artificial stresses arising from this filtering. At the same time, it is clear that ILES is simply an under-resolved direct numerical simulation with advanced treatments of advection terms to better control numerical stability via dissipation that otherwise would have been provided by a SGS model. As such it cannot be expected to accurately predict interactions of fluid turbulence with other physical phenomena ({\it e.g.}, heat and mass transfer, chemical kinetics) on subgrid scales---as is also true of usual forms of LES. In this talk we describe a straightforward technique, based on formal multi-scale methods, whereby SGS interactions can be introduced to enhance resolved-scale results computed as in ILES, and we discuss derivation of a class of efficient models based on the ``poor man's Navier--Stokes equation'' (McDonough, {\it Phys.Rev.\ E} {\bf 79}, 2009; McDonough and Huang, {\it Int.J.Numer.\ Meth.\ Fluids} {\bf 44}, 2004). Properties of these models will be presented for a moderate-$Re$ 3-D lid-driven cavity problem. [Preview Abstract] |
Sunday, November 22, 2009 5:59PM - 6:12PM |
EB.00009: Evaluation of Leray, LANS and Verstappen regularizations in LES, without and with added SGS modeling G. Winckelmans, N. Bourgeois, Y. Collet, M. Duponcheel Regularization approaches (Leray, LANS and Verstappen) for the ``restriction in the production of small-scales'' in turbulence simulations have regained some interest in the LES community, because of their potentially appealing properties due to filtering. Their potential is here investigated using the best possible numerics (dealiased pseudo-spectral code) and on simple problems: transition of the Taylor-Green vortex (TGV) and its ensuing turbulence, developed homogeneous isotropic turbulence (HIT). The filtered velocity field is obtained using discrete filters, also of various orders (2 and 6). Diagnostics include energy, enstrophy, and spectra. The performance of the regularizations on the TGV is first evaluated in inviscid mode ($96^3$ Euler), then in viscous mode at $Re=1600$ ($256^3$ DNS and $48^3$ LES). Although they delay the production of small scales, none of the regularizations can perform LES when the flow has become turbulent: the small scales are still too energized, and thus added subgrid-scale (SGS) modeling is required. The combination of regularization and SGS modeling (here using the RVM multiscale model) is then also evaluated. Finally, $128^3$ LES of fully developed HIT at very high $Re$ is also investigated, providing the asymptotic behavior. In particular, it is found that the regularization helps increase a bit the true inertial subrange obtained with the RVM model. [Preview Abstract] |
Sunday, November 22, 2009 6:12PM - 6:25PM |
EB.00010: On Closure Model for Accurate Reduced-Order Modeling in 3-D Flows Imran Akhtar, Jeff Borggaard, Traian Iliescu, Zhu Wang Reduced-order models based on the proper orthogonal decomposition (POD) can be used to represent and understand complex dynamical systems such as the Navier-Stokes equations. These models give insight to the flow physics, reproduce the data, and may be used for control purposes. However, most successful applications of this approach involve low Reynolds number, 2-D flows. For most 3-D flows, a large number of POD modes are required to accurately represent the flow field. The large dimension of the resulting model contradicts the essence of model reduction. Furthermore, the resulting reduced-order model is usually numerically unstable. In this study, we suggest an LES-type closure model within the POD-based reduced-order modeling framework. We simulate the flow past a 3-D cylinder at Re=1000 and collect a large set of snapshots to capture turbulent structures in the wake. We develop a reduced-order model using a small number of POD modes and introduce an additional term within the model to capture the effects of high frequencies (e.g. discarded modes) in the system. We compare the results of the model with the DNS data to establish accuracy of the modified reduced-order model. [Preview Abstract] |
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