Bulletin of the American Physical Society
66th Annual Meeting of the APS Division of Fluid Dynamics
Volume 58, Number 18
Sunday–Tuesday, November 24–26, 2013; Pittsburgh, Pennsylvania
Session D22: Turbulence Modeling III |
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Chair: Reetesh Ranjan, Georgia Institute of Technology Room: 317 |
Sunday, November 24, 2013 2:15PM - 2:28PM |
D22.00001: On the accuracy of simulations of a 2D boundary layer with RANS models implemented in OpenFoam Benjamin J. Graves, Sebastian Gomez, Svetlana V. Poroseva The OpenFoam software is an attractive Computational Fluid Dynamics solver for evaluating new turbulence models due to the open-source nature, and the suite of existing standard model implementations. Before interpreting results obtained with a new model, a baseline for performance of the OpenFoam solver and existing models is required. In the current study we analyze the RANS models in the OpenFoam incompressible solver for two planar (two-dimensional mean flow) benchmark cases generated by the AIAA Turbulence Model Benchmarking Working Group (TMBWG): a zero-pressure-gradient flat plate and a bump-in-channel. The OpenFoam results are compared against both experimental data and simulation results obtained with the NASA CFD codes CFL3D and FUN3D. Sensitivity of simulation results to the grid resolution and model implementation are analyzed. Testing is conducted using the Spalart-Allmaras one-equation model, Wilcox's two-equation k-omega model, and the Launder-Reece-Rodi Reynolds-stress model. Simulations using both wall functions and wall-resolved (low Reynolds number) formulations are considered. [Preview Abstract] |
Sunday, November 24, 2013 2:28PM - 2:41PM |
D22.00002: A hybrid RANS closure scheme for the near-wall turbulence Farid Karimpour, Subhas K. Venayagamoorthy In this study, we propose a parameterization for the eddy viscosity ($\nu_t$) that can be employed in a wall-resolving standard $k$-$\epsilon$ closure model. To this end, we use the equilibrium assumption between the production rate of the turbulent kinetic energy $(P)$ and $\epsilon$ in a wall-bounded turbulent flow. Using this assumption and the linear shear stress distribution, the appropriate velocity scale is $U_S=(\epsilon/S)^{1/2}$ while the corresponding length scale is $L_S=f_\mu \kappa y (1-y/\delta)^{3/4}$, where $\kappa$ is von K\'{a}rm\'{a}n's constant, $f_\mu$ is van Driest's damping function, $y$ represents the vertical distance from the wall and $\delta$ is one half of the channel depth. Consequently, $\nu_t$ results as a product of these two characteristic scales, i.e. $\nu_t=U_SL_S$. {\it `A priori'} tests are performed to assess the validity of the proposed eddy viscosity and the corresponding characteristic scales using the direct numerical simulation (DNS) data of unstratified channel flow. Furthermore, a one-dimensional standard $k$-$\epsilon$ model was developed and `{\it a posteriori}' tests were performed. The comparison of both `{\it a priori}' and `{\it a posteriori}' tests with DNS data show excellent agreement. [Preview Abstract] |
Sunday, November 24, 2013 2:41PM - 2:54PM |
D22.00003: Application of the order-of-magnitude analysis to a fourth-order RANS closure for simulating a 2D boundary layer Svetlana V. Poroseva Simulations of turbulent boundary-layer flows are usually conducted using a set of the simplified Reynolds-Averaged Navier-Stokes (RANS) equations obtained by order-of-magnitude analysis (OMA) of the original RANS equations. The resultant equations for the mean-velocity components are closed using the Boussinesq approximation for the Reynolds stresses. In this study OMA is applied to the fourth-order RANS (FORANS) set of equations. The FORANS equations are chosen as they can be closed on the level of the 5th-order correlations without using unknown model coefficients, i.e. no turbulent diffusion modeling is required. New models for the 2nd-, 3rd- and 4th-order velocity-pressure gradient correlations are derived for the current FORANS equations. This set of FORANS equations and models are analyzed for the case of two-dimensional mean flow. The equations include familiar transport terms for the mean-velocity components along with algebraic expressions for velocity correlations of different orders specific to the FORANS approach. Flat plate DNS data (Spalart, 1988) are used to verify these expressions and the areas of the OMA applicability within the boundary layer. [Preview Abstract] |
Sunday, November 24, 2013 2:54PM - 3:07PM |
D22.00004: An implicit turbulence model for Preconditioned-Roe scheme by using Truncated Navier-Stokes Equations ChungGang Li, Makoto Tsubokura A new turbulence model named dissipative model for Preconditioned-Roe scheme is proposed. The original Roe scheme employs the Roe upwinding dissipation term to stabilize the simulations. In this study, a free parameter $\varepsilon $ is used to adjust the Roe upwinding dissipation term appropriately. Based on the procedure developed previously for the Truncated Navier Stokes (TNS) equations and the energy level of small resolved scales, the extra dissipation provided by the dissipative model for the turbulence is meaningful and of physical fundamental, which is the most different from other implicit turbulence models. With the advantages of easy implementation because no extra terms are needed to the equations and the availability on the curvilinear coordinate, the dissipative model is expected to be a promising tool for practical applications. [Preview Abstract] |
Sunday, November 24, 2013 3:07PM - 3:20PM |
D22.00005: Optimal Turbulence Closures in Galerkin Models Bartosz Protas, Bernd Noack In the present study we propose a variational optimization technique to determine an optimal eddy viscosity for a Galerkin model of a fluid flow. Analogously to LES and RANS, such models require suitable closure strategies to account for the effects of unresolved dynamics and ensure stability of long-time integration. A commonly used ansatz involves a linear dissipation term with the magnitude controlled by an eddy viscosity. While the eddy viscosity is often assumed constant or a linear function of the state, there is in fact a lot of evidence that nonlinear eddy viscosities perform better. We show how an optimal form of a nonlinear eddy viscosity can be determined such that the corresponding trajectories of the Galerkin model best match available data. The eddy viscosity is assumed to depend on the fluctuating kinetic energy only, so that our optimal closure results in an autonomous dynamical system. The eddy viscosity is reconstructed in the continuous setting using a non-parametric structure identification method which does not involve any assumptions other than smoothness. The method is applied to a reduced-order model of a mixing layer and the optimal eddy viscosities found reveal nontrivial insights about the behavior of the model. [Preview Abstract] |
Sunday, November 24, 2013 3:20PM - 3:33PM |
D22.00006: A three-equation bypass transition model based on the intermittency function Xuan Ge, Paul Durbin An intermittency model that is formulated in local variables is proposed for representing bypass transition in Reynolds-Averaged Navier-Stokes (RANS) computations. No external data correlation is used to fix transition. Transition is initiated by diffusion and a source term carries it to completion. A sink term is created to predict the laminar region before transition and vanishes in turbulent region. For validation of this model, a group of test cases based on flat plate experiments have been set up for numerical simulations in OpenFOAM. It turns out that the current model is capable to predict boundary layer transition on a flat plate both with and without pressure gradients. Decent agreement with the available experiment data is observed. [Preview Abstract] |
Sunday, November 24, 2013 3:33PM - 3:46PM |
D22.00007: Use of DNS Data for the Evaluation of Closure Models for Rotating Turbulent Channel Flow Alan Hsieh, Sedat Biringen, Alec Kucala A direct numerical simulation (DNS) of a turbulent channel flow rotating about the spanwise axis was conducted at a Reynolds number (based on the centerline velocity and channel half height) 8000, Prandtl number 0.71, and Rossby number 26. Several Reynolds-Averaged Navier-Stokes (RANS) based turbulence models for rotating flows were analyzed and tested. It was shown that the closure approximations in the pressure-strain correlation term proposed by the Speziale, Sarkar, and Gatski (SSG) RSM model were more accurate than the Girimaji EARSM model. The Reynolds stresses, primarily the shear stresses, produced by the Girimaji model were compared to the DNS data and revealed an evident discontinuity in the modeled Reynolds stress profiles; consequently, a smoothing function was generated and applied as a correction so that there is significantly better agreement between the Reynolds shear stress profiles produced by the DNS data and the modified Girimaji model. [Preview Abstract] |
Sunday, November 24, 2013 3:46PM - 3:59PM |
D22.00008: Separated shear-layer instability reproduction by a Reynolds stress model of turbulence Suad Jakirlic, Robert Maduta A boundary layer separating from a solid wall transforms into a `separated shear layer' exhibiting a broader frequency range. Such a highly-unsteady shear layer separating the mean stream from the flow reversal is dominated by the organized, large-scale coherent structures, influencing to a large extent the overall flow behavior. Unlike in the case of a flat-plate boundary layer separating at a fixed point characterizing a backward-facing step geometry, which can be reasonably well captured by a statistical model of turbulence, the separation process pertinent to continuous curved surfaces as well as some fence- or rib-shaped configurations is beyond the reach of any RANS (Reynolds-Averaged Navier Stokes) model independent of the modeling level. The latter issue motivated the present work, dealing with an appropriate extension of a near-wall Second-Moment Closure (SMC) model towards an instability-sensitive formulation. The production term in the corresponding scale-supplying equation is selectively enhanced through introduction of the ratio of the first to the second derivative of the velocity field, the latter representing the integral part of the von Karman length scale, enabling appropriate capturing of the fluctuating turbulence and accordingly the reproduction of the separated shear-layer instability. The analysis is performed by simulating the flow separated from a fence, an axisymmetric hill and a cylinder configuration. [Preview Abstract] |
Sunday, November 24, 2013 3:59PM - 4:12PM |
D22.00009: Experimental verification of turbulence models for pressure diffusion process in plane turbulent jet Osamu Terashima, Yasuhiko Sakai, Kouji Nagata, Yasumasa Ito We performed simultaneous measurement of the three velocity components and the pressure in a plane turbulent jet, and examined turbulence models related to the pressure diffusion process, such as gradient-diffusion model and the model for the rapid/slow terms of the pressure diffusion term. The results show that the gradient-diffusion model developed in the previous studies are valid only in the region where the turbulent intensity and the turbulent/non-turbulent intermittency are high and the production of the turbulent energy is dominant in comparison with other processes such as the convection and diffusion of the turbulent energy in the turbulent energy budget. In addition, it is found that the pressure diffusion of the turbulent energy cannot be modeled accurately by using only the slow term, and its accuracy is improved by considering both rapid and slow terms in the model. This result indicates that modeling the pressure diffusion process using only the slow term has a certain risk leading to a misunderstanding of the turbulent energy transport process. [Preview Abstract] |
Sunday, November 24, 2013 4:12PM - 4:25PM |
D22.00010: An alternative eddy-viscosity representation and its implication to turbulence modeling Suad Jakirlic, Jovan Jovanovic, Branislav Basara Large majority of turbulence models in the RANS framework (it holds also in the case of the LES method) is based on the eddy-viscosity rationale. The principle task of modeling the Reynolds stress tensor reduces to modeling the eddy-viscosity, representing, according to Boussinesq (1877), the ``coefficient of proportionality'' between the Reynolds stress and mean rate of strain tensors. In the present contribution an extended formulation based on the least square approach applied to the Boussinesq's correlation is presented. Furthermore, a Taylor-microscale-based formulation is derived originating from the equilibrium assumption related to the equality between the production and dissipation rates of kinetic energy of turbulence. Finally, an expression is proposed reflecting the Reynolds stress anisotropy influence on the eddy-viscosity damping by approaching the solid wall as well as including an appropriate length-scale switch accounting for the viscosity effects through inclusion of the Kolmogorov scales blended with those of the energy-containing eddies. The latter formulation is successfully applied in the framework of an instability-sensitive Reynolds stress model of turbulence. The afore-mentioned eddy-viscosity definitions are comparatively assessed in a series of wall-bounded flow configurations (including separation) in a Reynolds number range. [Preview Abstract] |
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