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 EE: Turbulence: Modeling I |
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Chair: J.M. McDonough, University of Kentucky Room: Salt Palace Convention Center 151 D-F |
Sunday, November 18, 2007 4:10PM - 4:23PM |
EE.00001: Studies of the NS-alpha model using a lid-driven cavity flow K.A. Scott, F.S. Lien The NS-alpha equations have a more compact energy spectrum than the Navier- Stokes equations. Hence, it has been proposed in the literature to use them as a turbulence model. Here we present results from our experience in applying the NS- alpha model to an anisotropic and inhomogeneous flow, namely, a lid-driven cavity flow. It was found that the isotropic NS-alpha model generated excessive backscatter near the lid. Following an LES methodology, where the smoothed velocity is used as the dependent variable, the anisotropic NS-alpha equations were then investigated as a subgrid model. As compared to the isotropic model, the anisotropic model is found to remove the excessive backscatter near the cavity lid, resulting in improved velocity profiles. The ability of the model to correctly reflect the turbulent state of the cavity, and to reproduce the anisotropy in the turbulent stresses near the cavity bottom will be discussed. [Preview Abstract] |
Sunday, November 18, 2007 4:23PM - 4:36PM |
EE.00002: Spectral scaling of the two-dimensional Navier-Stokes-$\alpha$ and Leray-$\alpha$ models Evelyn Lunasin, Susan Kurien, Mark Taylor, Edriss Titi The NS-$\alpha$ model of turbulence is a mollification of the Navier-Stokes equations, such that the vorticity is advected by a velocity field that is smoothed over spatial scales of size smaller than $\alpha$. The spectral properties of the smoothed velocity field match those of Navier-Stokes turbulence for wavenumbers $k$ such that $k\alpha\ll 1$. For $k\alpha \gg 1$ it is not possible to predict the scaling of the energy spectrum {\it a priori} since the smoothed and unsmoothed velocities provide several possible characteristic timescales for the problem. The same holds true for the other $\alpha$-models of turbulence. We measure the $k\alpha \gg 1$ scaling of the energy spectra from high-resolution simulations in two-dimensions, in the limit as $\alpha \rightarrow \infty$, for two models: the Navier-Stokes-$\alpha$ model and the Leray-$\alpha$ model. The spectrum of the smoothed velocity field scales as $k^{-7}$ in the former and as $k^{-5}$ in the latter. These scalings correspond to the direct cascade of the conserved enstrophy in each case, the governing time scales given by $(k |v_k|)^{-1}$ and $(k\sqrt{( u_k, v_k)}\;)^{-1}$ respectively, where $u_k$ and $v_k$ are the fourier components of the filtered (smoothed) velocity field $u$ and unfiltered velocity field $v$. [Preview Abstract] |
Sunday, November 18, 2007 4:36PM - 4:49PM |
EE.00003: Statistical properties of the 3-D poor man's Navier--Stokes equation J.M. McDonough The poor man's Navier--Stokes (PMNS) equation is an efficiently-evaluated discrete dynamical system (DDS) derived directly from the Navier--Stokes (N.--S.) equations via a Galerkin procedure. The 2-D version of this DDS was introduced by McDonough and Huang, {\it Int.\ J.\ Numer.\ Meth.\ Fluids} (2004), where it was thoroughly analyzed for values of bifurcation parameters that might be associated with isotropic turbulence. Yang {\it et al.}, {\it AIAA J.\ }(2003), demonstrated that the PMNS equation could be employed to accurately fit experimental data. These results suggest possible use of the PMNS equation as part of a subgrid-scale (SGS) model for LES formulated to capture effects of interactions between turbulence and other physics on unresolved scales. Here, we consider statistical properties of the 3-D PMNS equation to ascertain whether they are sufficiently close to those of physical N.--S.\ flows to warrant development of such models. In particular, we will present auto and cross correlation of velocity components, probability density functions, flatness and skewness of velocity derivatives, and scaling of longitudinal velocity structure functions of orders two, three, four and six. It will be demonstrated that PMNS equation statistics are generally in accord with those of the full N.--S.\ equations, and as a consequence this DDS could lead to very efficient LES SGS models able to replicate small-scale turbulence interactions with other physics. [Preview Abstract] |
Sunday, November 18, 2007 4:49PM - 5:02PM |
EE.00004: Empirical and Analytic Generalized Mean Field Model Gilead Tadmor, Bernd R. Noack, Oliver Lehmann, Marek Morzynski The generalized mean field model has been introduced by Noack \& al. (JFM, 2003) as a critical enabler for very low dimensional Galerkin fluid models of transient dynamics. As originally introduced, it uses a \emph{shift mode} to resolve the global state space direction of natural transient changes in the base flow. Here we highlight a physics interpretation, as a Galerkin representation of the Reynolds stress, and of energy exchanges between fast perturbations and the base flow. We thus explore and compare alternative concepts of local shift modes, including via empirical proper orthogonal decompositions of long and short term base flow transients, and an analytic definition, in terms of the Reynolds equation. [Preview Abstract] |
Sunday, November 18, 2007 5:02PM - 5:15PM |
EE.00005: Robust Real-Time Solutions of Velocity Fields from Predictive Estimation P. Mokhasi, D. Rempfer We want to predict 3-D velocity fields in complex geometries with applications to real-time solutions of the contaminant dispersion problem in an urban setting. Proper Orthogonal Decomposition is used to extract a set of optimal basis functions from an ensemble of snapshots. If the temporal coefficients can be computed, then combined with the basis functions one can get a good approximation to the velocity field. In this study, we explore the idea of using scalar measurements near the wall to construct the temporal POD coefficients. We look at the method of Linear Stochastic Estimation (LSE) and compare it to a few other regression methods for its prediction capabilities. Tests show that Principal Component Regression (PCR), and Least-Squares Support Vector Machines consistently outperform LSE in predicting POD coefficients outside the ensemble. We also develop state space equations that govern the short- term evolution of the POD coefficients. Using nonlinear Kalman filtering, we combine the regression methods with the state space equations to generate a robust method that can give accurate predictions in the presence of noisy measurements. The methods are tested on a numerical experiment of a wall- mounted cube in a channel. We demonstrate their effectiveness by predicting complete flow fields using only a handful of pressure measurements with and without noise. [Preview Abstract] |
Sunday, November 18, 2007 5:15PM - 5:28PM |
EE.00006: A Convectively Filtered Regularization of Multi-Dimensional Burgers Equation Gregory Norgard, Kamran Mohseni Multi-dimensional Burgers equation, $\textbf{u}_t+\textbf{u} \cdot \nabla \textbf{u}=\nu \triangle \textbf{u}$, can be considered as a simplified model of fluid dynamics. By sharing the convective nonlinear terms, it exhibits characteristics similar to those in the Euler and Navier-Stokes equations, particularly shocks and turbulence. Shocks and turbulence can both be attributed to the accumulation of energy in the high frequency wave modes, caused by the nonlinear term $\textbf{u} \cdot\nabla \textbf{u}$. Typically this energy cascade is halted by introducing viscosity, balancing the nonlinearity with dissipation. An alternative solution is replacing the convective velocity with a low pass filtered velocity, $\bar{\textbf{u}}$. The filtering reduces the energy in the higher wave modes, reducing the rate of the energy cascade. This method has been shown to regularize shocks in one-dimensional inviscid Burgers, $u_t+\bar{u}u_x=0$. This research extends this result into multiple dimensions with the equation, $\textbf{u}_t+\bar{\textbf{u}} \cdot\nabla \textbf{u}=0$. The existence and uniqueness of a continuously differentiable solution is proven for a general class of filters. This regularization is then compared and contrasted with viscous Burgers in areas such as constants of motion, energy decay, shock thickness, and spectral energy decompositions. [Preview Abstract] |
Sunday, November 18, 2007 5:28PM - 5:41PM |
EE.00007: Coherent Vortex Simulations of linearly forced homogeneous turbulence Oleg V. Vasilyev, Daniel E. Goldstein, Giuliano De Stefano This is the first of two talks on the wavelet based eddy capturing computational methodology that is capable of identifying and tracking on an adaptive mesh energetic coherent vortical structures in a turbulent flow field. This talk focuses on Coherent Vortex Simulations (CVS) approach, where the velocity field is decomposed into two parts: a coherent, inhomogeneous, non-Gaussian component and an incoherent, homogeneous, Gaussian component. This separation of coherent and incoherent components is achieved by wavelet thresholding, which can be viewed as a non-linear filter that depends on each flow realization. The essence of the CVS approach is to solve for the coherent non-Gaussian component of a turbulent flow field. It has been shown previously that second generation bi-orthogonal wavelet threshold filtering is able to decompose a turbulent velocity field such that the total resulting SGS dissipation is approximately zero. The results of Coherent Vortex Simulations of linearly forced incompressible 3D homogeneous turbulence for different Reynolds numbers demonstrated that CVS with no SGS model is capable to recover not only low order statistics, but also energy and, more importantly, enstrophy spectra up to the dissipative wavenumber range. [Preview Abstract] |
Sunday, November 18, 2007 5:41PM - 5:54PM |
EE.00008: Stochastic Coherent Adaptive Large Eddy Simulation of linearly forced homogeneous turbulence Giuliano De Stefano, Oleg V. Vasilyev In this talk we present the application of the Stochastic Coherent Adaptive Large Eddy Simulation (SCALES) method to the simulation of forced isotropic turbulence. In the SCALES approach, an explicit wavelet filtering procedure is applied in order to localize in space and follow in time the flow structures of significant energy. A suitable subgrid-scale (SGS) model is exploited to represent the effect un unresolved less energetic eddies upon the dynamics of resolved motions. Local dynamic SGS models based upon the kinetic energy content of the unresolved motions are employed in this work. An evolution model equation for the additional energy variable is solved along with the wavelet-filtered incompressible Navier-Stokes equations. The forcing scheme recently proposed by Lundgren, according to which the forcing term is proportional to the velocity field, is directly applied in physical space. Good results are obtained in terms of low order flow statistics, when compared to pseudo-spectral reference solution, as well as grid compression, which is a fundamental parameter for wavelet-based numerical simulation of turbulence. In particular, the grid compression converges to a (statistically) steady high value that allows to simulate moderately high Reynolds number flows with affordable computational cost. [Preview Abstract] |
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