A posteriori tests of subgrid-scale models in an isothermal turbulent channel flow (original) (raw)
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Testing of subgrid scale (SGS) models for large-eddy simulation (LES) of turbulent channel flow
2015
Sub-grid scale (SGS) models are required in order to model the influence of the unresolved small scales on the resolved scales in large-eddy simulations (LES), the flow at the smallest scales of turbulence. In the following work two SGS models are presented and deeply analyzed in terms of accuracy through several LESs with different spatial resolutions, i.e. grid spacings. The first part of this thesis focuses on the basic theory of turbulence, the governing equations of fluid dynamics and their adaptation to LES. Furthermore, two important SGS models are presented: one is the Dynamic eddy-viscosity model (DEVM), developed by \cite{germano1991dynamic}, while the other is the Explicit Algebraic SGS model (EASSM), by \cite{marstorp2009explicit}. In addition, some details about the implementation of the EASSM in a Pseudo-Spectral Navier-Stokes code \cite{chevalier2007simson} are presented. The performance of the two aforementioned models will be investigated in the following chapters, ...
Physics of Fluids
We study the construction of subgrid-scale models for large-eddy simulation of incompressible turbulent flows. In particular, we aim to consolidate a systematic approach of constructing subgrid-scale models, based on the idea that it is desirable that subgrid-scale models are consistent with the mathematical and physical properties of the Navier-Stokes equations and the turbulent stresses. To that end, we first discuss in detail the symmetries of the Navier-Stokes equations, and the near-wall scaling behavior, realizability and dissipation properties of the turbulent stresses. We furthermore summarize the requirements that subgrid-scale models have to satisfy in order to preserve these important mathematical and physical properties. In this fashion, a framework of model constraints arises that we apply to analyze the behavior of a number of existing subgrid-scale models that are based on the local velocity gradient. We show that these subgrid-scale models do not satisfy all the desired properties, after which we explain that this is partly due to incompatibilities between model constraints and limitations of velocity-gradient-based subgrid-scale models. However, we also reason that the current framework shows that there is room for improvement in the properties and, hence, the behavior of existing subgrid-scale models. We furthermore show how compatible model constraints can be combined to construct new subgrid-scale models that have desirable properties built into them. We provide a few examples of such new models, of which a new model of eddy viscosity type, that is based on the vortex stretching magnitude, is successfully tested in large-eddy simulations of decaying homogeneous isotropic turbulence and turbulent plane-channel flow.
A priori tests of subgrid-scale models in an anisothermal turbulent channel flow at low mach number
International Journal of Thermal Sciences
The subgrid-scale modelling of a low Mach number strongly anisothermal turbulent flow is investigated using direct numerical simulations. The study is based on the filtering of the low Mach number equations, suited to low Mach number flows with highly variable fluid properties. The results are relevant to formulations of the filtered low Mach number equations established with the classical filter or the Favre filter. The two most significant subgrid terms of the filtered low Mach number equations are considered. They are associated with the momentum convection and the densityvelocity correlation. We focus on eddy-viscosity and eddy-diffusivity models. Subgridscale models from the literature are analysed and two new models are proposed. The subgrid-scale models are compared to the exact subgrid term using the instantaneous flow field of the direct numerical simulation of a strongly anisothermal fully developed turbulent channel flow. There is no significant differences between the use of the classical and Favre filter regarding the performance of the models. We suggest that the models should take into account the asymptotic near-wall behaviour of the filter length. Eddy-viscosity and eddy-diffusivity models are able to represent the energetic contribution of the subgrid term but not its effect in the flow governing equations. The AMD and scalar AMD models are found to be in better agreement with the exact subgrid terms than the other investigated models in the a priori tests.
A dynamic subgrid-scale eddy viscosity model
Physics of Fluids A: Fluid Dynamics, 1991
One major drawback of the eddy viscosity subgrid-scale stress models used in large-eddy simulations is their inability to represent correctly with a single universal constant different turbulent fields in rotating or sheared flows, near solid walls, or in transitional regimes. In the present work a new eddy viscosity model is presented which alleviates many of these drawbacks. The model coefficient is computed dynamically as the calculation progresses rather than input apriori. The model is based on an algebraic identity between the subgrid-scale stresses at two different filtered levels and the resolved turbulent stresses. The subgrid-scale stresses obtained using the proposed model vanish in laminar flow and at a solid boundary, and have the correct asymptotic behavior in the near-wall region of a turbulent boundary layer. The results of large-eddy simulations of transitional and turbulent channel flow that use the proposed model are in good agreement with the direct simulation data.
Physics of Fluids, 2001
It is well known that the correlation between the Smagorinsky model and the subgrid scale stress is low, while the model based on the scale similarity assumption has considerably higher correlation. However, the scale similarity model by itself was found to be insufficiently dissipative. Therefore, the model is usually used together with the Smagorinsky model. Model coefficients are commonly computed using the two-parameter dynamic procedure. Nevertheless, the dynamic two-parameter mixed model still does not work well for wall bounded flows, since the model predicts a high value of the wall shear stress. In this study, we propose a modification to the two-parameter dynamic procedure for wall bounded flows, which removes that defect: the Smagorinsky parameter, C S ,i s computed exactly the same way as in the dynamic Smagorinsky model, then the other parameter, C L , is computed dynamically as C S is known. This ensures that the mixed model provides proper wall shear stress and mean velocity profile. Computational tests are done for turbulent channel flow where the Reynolds numbers based on the channel half-width and wall friction velocity are 395 and 1400. To remove the ambiguity regarding the accuracy of the finite difference scheme, we use high ͑up to 12th͒ order accurate fully conservative finite difference schemes in a staggered grid system.
Journal of Physics: Conference Series, 2014
The paper presents a consistent large eddy simulation (LES) framework which is particularly suited for implicitly filtered LES with unstructured finite volume (FV) codes. From the analysis of the subgrid-scale (SGS) stress tensor arising in this new LES formulation, a novel form of scale-similar SGS model is proposed and combined with a classical eddy viscosity term. The constants in the resulting mixed model are then computed trough a new, cheaper, dynamic procedure based on a consistent redefinition of the Germano identity within the new LES framework. The dynamic mixed model is implemented in a commercial, unstructured, finite volume solver and numerical tests are performed on the turbulent pipe flow at Reτ = 320−1142, showing the flexibility and improvements of the approach over classical modeling strategies. Some limitations of the proposed implementation are also highlighted.
Large Eddy Simulation of High-Reynolds-Number Free and Wall-Bounded Flows
Journal of Computational Physics, 2002
The ability to simulate complex unsteady flows is limited by the current state of the art of subgrid-scale (SGS) modeling, which invariably relies on the use of Smagorinsky-type isotropic eddy-viscosity models. Turbulent flows of practical importance involve inherently three-dimensional unsteady features, often subjected to strong inhomogeneous effects and rapid deformation, which cannot be captured by isotropic models. Although some available improved SGS models can outperform the isotropic eddy-viscosity models, their practical use is typically limited because of their complexity. Development of more-sophisticated SGS models is actively pursued, and it is desirable to also investigate alternative nonconventional approaches. In ordinary large eddy simulation (LES) approaches models are introduced for closure of the low-pass filtered Navier-Stokes equations (NSE). A promising LES approach is the monotonically integrated LES (MILES), which involves solving the unfiltered NSE using high-resolution monotone algorithms; in this approach, implicit SGS models, provided by intrinsic nonlinear high-frequency filters built into the convection discretization, are coupled naturally to the resolvable scales of the flow. Formal properties of the effective SGS modeling using MILES are documented using databases of simulated free and wall-bounded inhomogeneous flows, including isotropic decaying turbulence, transitional jets, and channel flows. Mathematical and physical aspects of (implicit) SGS modeling through the use of nonlinear flux limiters are addressed using a formalism based on the modified LES equations.
An approach to wall modeling in large-eddy simulations
Physics of Fluids, 2000
Channel flow with friction Reynolds number Re as high as 80 000 is treated by large-eddy simulation at a moderate cost, using the subgrid-scale model designed for detached-eddy simulations. It includes wall modeling, and was not adjusted for this flow. The grid count scales with the logarithm of the Reynolds number. Three independent codes are in fair agreement with each other. Reynolds-number variations and grid refinement cause trades between viscous, modeled, and resolved shear stresses. The skin-friction coefficient is too low, on the order of 15%. The velocity profiles contain a ''modeled'' logarithmic layer near the wall and some suggest a ''resolved'' logarithmic layer farther up, but the two layers have a mismatch of several units in U ϩ .
Development of Large Eddy Simulation Turbulence Models
2000
A new approach for a non-viscosity one-equation large eddy simulation (LES) subgrid stress model is presented. The new approach uses a tensor coefficient obtained from the dynamic modeling approach of Germano (1991) and scaling that is provided by the sub-grid kinetic energy. Mathematical and conceptual issues motivating the development of this new model are explored. The basic equations that originate in dynamic modeling approaches are Fredholm integral equations of the second kind. These equations have solvability requirements that have not been previously addressed in the context of LES. These conditions are examined for traditional dynamic Smagorinsky modeling (i.e. zeroequation approaches) and the one-equation sub-grid model of Ghosal et al. (1995). It is shown that standard approaches do not always satisfy the integral equation solvability condition. It is also shown that traditional LES models that use the resolved scale strainrate to estimate the sub-grid stresses scale poorly with filter level leading to significant errors in the modeling of the sub-grid scale stress. The poor scaling in traditional LES I would like to express my sincere gratitude to my advisor, Professor Christopher Rutland, for his guidance, technical assistance, encouragement and freedom provided to me during the past five years. I also would like to thank Professor Frederick Elder and Professor David Foster for their assistance in the graduate school admission process.
Is plane-channel flow a friendly case for the testing of large-eddy simulation subgrid-scale models?
2007
We present the grid-convergence behavior of channel-flow direct numerical simulations ͑DNS͒ at coarse resolutions typically encountered in large-eddy simulation subgrid-model testing. An energy-conservative discretization method is used to systematically vary the streamwise ͑N x ͒ and spanwise ͑N z ͒ resolution. We observe that the skin friction does not converge monotonously, and at coarse resolutions, a line of N x-N z combinations is found where the error on the skinfriction is zero. Along this line, mean profiles are evaluated and found to fit surprisingly well fully resolved DNS results. The location of this line is shown to depend on the Reynolds number and the wall-normal resolution.