Bulletin of the American Physical Society
61st Annual Meeting of the APS Division of Fluid Dynamics
Volume 53, Number 15
Sunday–Tuesday, November 23–25, 2008; San Antonio, Texas
Session PC: Turbulence Modeling III |
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Chair: Dietmar Rempfer, Illinois Institute of Technology Room: 002A |
Tuesday, November 25, 2008 11:35AM - 11:48AM |
PC.00001: Further Analysis of Hybrid-Filtered Navier-Stokes Equations Bernie Rajamani, John Kim We have shown that Germano's hybrid-filter approach is both a physically and mathematically correct method of blending the Reynolds-Averaged Navier-Stokes (RANS) and large-eddy simulation (LES). The hybrid-filtered Navier-Stokes (HFNS) equations provides correct behavior in the crossover region via three means: (1) presence of extra terms in the governing equations, (2) presence of a fluctuation-like term in the modeled part of the Reynolds shear stress, and (3) presence of a smooth blending function. In many existing hybrid methods, the governing equations were modified in an {\it ad hoc} manner in order to achieve improved behavior at the RANS-LES crossover. We have shown that such a fix is not necessary in the current approach. For example, our full simulation of HFNS equations showed that the extra terms enhanced the wall-normal transport of resolved turbulence fluctuations, thus alleviating the need for an artificial backscatter-like term. Further investigations of the effects of grid and blending function revealed no evidence of deterioration of the solution upon progressive refinement of the grid, contrary to many conventional hybrid methods. We also found that the blending function -- its magnitude near the wall and its shape in the crossover region -- must be chosen to be consistent with the grid used in these regions. Otherwise, the solution deteriorates, primarily due to its inability to resolve the LES part. [Preview Abstract] |
Tuesday, November 25, 2008 11:48AM - 12:01PM |
PC.00002: A poor man's compressible Navier--Stokes equation J.M. McDonough, J.P. Strodtbeck We outline derivation of a ``poor man's compressible Navier--Stokes'' (PMCNS) equation, a discrete dynamical system (DDS) extending analyses of McDonough and Huang (Int.\ J.\ Numer. Meth.\ Fluids 44, 545, 2004) for the 2-D incompressible Navier--Stokes (N.--S.) equation to the 3-D compressible counterpart, and we indicate a method for computing bifurcation parameters of the DDS directly from those of the original differential equations, along with known physical parameters such as transport properties. We briefly provide a mathematical characterization of the PMCNS equation, in particular noting an approximate relationship to micro-local analysis of a pseudo-differential operator of the compressible N.--S. equation. We then investigate time series, power spectra and bifurcation diagrams of this DDS for various combinations of bifurcation parameters, including those most closely corresponding to homogeneous, isotropic turbulence; and we present comparisons of PMCNS calculations with extant experimental and DNS compressible flow data. We conclude by discussing application of this discrete dynamical system to construction of subgrid-scale models for LES of compressible flows within a synthetic-velocity/multi-scale framework. [Preview Abstract] |
Tuesday, November 25, 2008 12:01PM - 12:14PM |
PC.00003: Assessment of regularization models for LES of high-$Re$ turbulent flows Abhilash Chandy, Steven Frankel Regularization-based SGS turbulence models for LES are quantitatively assessed for decaying homogeneous turbulence (DHT) and transition to turbulence for the Taylor-Green vortex (TGV) through comparisons to laboratory measurements and DNS respectively. LES predictions using the Leray-$\alpha$, LANS-$\alpha$, and Clark-$\alpha$ regularization-based SGS models are compared to the classic non-dynamic Smagorinsky model. Regarding the regularization models, this work represents their first application to relatively high $Re$ decaying turbulence with comparison to the active-grid-generated decaying turbulence measurements of Kang {\sl et al.} (JFM, 2003) at $Re_\lambda \approx 720$ and the $Re=3000$ DNS of transition to turbulence in the TGV of Drikakis {\sl et al.} (J. Turb., 2007). For DHT the non-dynamic Smagorinsky model is in excellent agreement with measurements for t.k.e., but higher-order moments show slight discrepancies and for TGV, the energy decay rates agree reasonably well with DNS. Regarding the regularization models stable results are not obtained as compared to Smagorinsky at the same grid resolution for various values of $\alpha$, and at higher resolutions, they are in worse agreement. However, with additional dissipation such as in mixed $\alpha$-Smagorinsky models, results are acceptable, but show slight deviations from Smagorinsky. [Preview Abstract] |
Tuesday, November 25, 2008 12:14PM - 12:27PM |
PC.00004: Comparative study of SGS scalar models for LES of turbulent mixing O.S. Sun, L.K. Su For LES of applications involving scalar transport and mixing, the smallest scales of the molecular mixing process are unresolved, so understanding the effects of SGS modeling on the resulting concentration fields is particularly important. Comprehensive analyses of the range of modeling approaches for scalar transport and mixing have yet to be conducted. The present objective is to analyze the impact of different modeling approaches on the statistics of the resolved-scale scalar concentration. We perform LES of passive scalar mixing in a turbulent, round jet. The SGS scalar flux term in the scalar transport equation is closed using four different models, including: the dynamic eddy diffusivity and mixed models, the dynamic structure model (Chumakov, 2004) and the multi-fractal model (Burton, 2008). Results are analyzed by comparing mean concentration profiles and scaling, fluctuating quantities at the grid scale, scalar PDFs and spectra, and individual terms in the resolved-scale scalar transport equations. Particular attention is paid to the performance and behavior of SGS scalar models through analyses of model parameters, energy transfer, and structural fidelity. [Preview Abstract] |
Tuesday, November 25, 2008 12:27PM - 12:40PM |
PC.00005: Investigation of turbulent transport in hybrid PANS model Dasia Reyes, Sharath Girimaji Partially Averaged Navier-Stokes (PANS) turbulence method provides a closure model for any degree of velocity field filtering - ranging from completely resolved Direct Numerical Simulation (DNS) to completely averaged Reynolds Averaged Navier-Stokes (RANS) method. The physical closure investigation of PANS presented here is the validation of closure model chosen to describe the transport of the unresolved kinetic energy, k$_{u}$, and unresolved dissipation, $\varepsilon _{u}$, due to the resolved velocity fluctuations. The three models presented are the Zero Transport Model (ZTM), the Maximum Transport Model (MTM) and the Boundary Layer Transport Model (BLTM). In the ZTM it is assumed that the resolved velocity fluctuations do not contribute to the transport of the turbulent quantities. The MTM suggests that the transport of the unresolved scales of the turbulent quantities is proportional to the ratio of the unresolved to total viscosity. The BLTM is developed from the physics of the boundary layer. These models are tested against experimental results for flow past a circular cylinder. [Preview Abstract] |
Tuesday, November 25, 2008 12:40PM - 12:53PM |
PC.00006: Assessment of the {\it t}-model as a SGS model for LES of high-$Re$ turbulent flows Abhilash Chandy, Steven Frankel The recently developed optimal prediction-based {\it t}-model (PNAS, 2007) is quantitatively assessed as a SGS turbulence model for LES of decaying homogeneous turbulence (DHT) and transition to turbulence for the Taylor-Green vortex (TGV) through comparisons to laboratory measurements and DNS. The {\it t}-model is based on the idea the motion of a vortex at one scale is influenced by the past history of motion of vortices in other scales (``long memory'' effects). {\it t}-model predictions are compared to the classic non-dynamic Smagorinsky model. Regarding the {\it t}-model, this work represents its first application to decaying turbulence with comparison to active-grid-generated decaying turbulence measurements of Kang {\sl et al.} (J. Fluid Mech., 2003) at $Re_\lambda \approx 720$ and $Re=3000$ DNS of transition to turbulence in the TGV of Drikakis {\sl et al.} (J. Turb., 2007). For DHT non-dynamic Smagorinsky is in excellent agreement with measurements for t.k.e. but higher-order moments show slight discrepancies and for TGV, energy decay rates agree reasonably well with DNS. Regarding the {\it t}-model, predictions are worse than Smagorinsky at the same grid resolution due to the insufficient resolution of small scales. Improved results are obtained at higher resolutions, but are still not as good as Smagorinsky. [Preview Abstract] |
Tuesday, November 25, 2008 12:53PM - 1:06PM |
PC.00007: Implementation of a Spectral Decomposition of the Boltzmann Equation with the Streaming in the Lattice-Boltzmann Method Jacques Richard, Terry McCullum, Robert Fievisohn Recent developments in mathematics have allowed for the collision process of the Boltzmann equation to be discretized using spectral methods. This new method has the potential for replacing the Bhatnagar-Gross-Krook (BGK) approximation used in approaches such as the lattice-Boltzmann method (LBM). This would end the need for a low Mach approximation to the linearized Boltzmann equation in LBM. This allows solving the full Boltzmann equation and should therefore avoid many of the limitations of current approxima- tions. This paper shows a derivation for the spectral method as well as an implementation for a 2-D and 3-D test cases with results. A simulation of decaying isotropic turbulence is also presented. [Preview Abstract] |
Tuesday, November 25, 2008 1:06PM - 1:19PM |
PC.00008: Towards understanding of near wall behavior in two-equation models for supersonic flows Sunil Lakshmipathy, Sriram Arasanipalai, Sharath Girimaji The standard two-equation models over-predict the turbulent viscosity and turbulent kinetic energy in the near wall region for supersonic flows. There are several approaches to tune the model behavior to agree with experimental values. In the present approach we modify C$_{\mu}$ along the lines of Durbin stagnation point correction. The influence of the turbulent Prandtl numbers - $\sigma _{k}$, $\sigma _{\varepsilon}$, $\sigma _{\omega}$-- are also examined. [Preview Abstract] |
Tuesday, November 25, 2008 1:19PM - 1:32PM |
PC.00009: Modeling Low Reynolds Number Homogeneous Decaying Turbulence Blair Perot Very low Reynolds number nearly homogeneous turbulence can occur in the free-stream outside of a turbulent boundary layer. It is also found in nocturnal atmospheric and oceanic boundary layers. Low Reynolds number turbulence represent the interesting situation where the nonlinear terms in the Navier-Stokes equations are weak, and therefore negligible or linearizable, and yet a turbulence model is still required because the initial conditions are unknown and a variety of length scales are still present. This work considers the behavior of two-equation turbulence models in the low Reynolds number limit. It is shown that some models are unstable in this limit and others result in inconsistent or incorrect decay rates. Perhaps most importantly, all current models involve an ad hoc blending function to include the low Re limit. In this work a low Reynolds number correction to classic two-equation models is proposed which requires no blending functions, which obtains the correct decay limits (for any low wavenumber spectra), and which is simple. The performance of the model is compared with a variety of experiments and simulations over a range of Reynolds numbers. [Preview Abstract] |
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