Highly turbulent solutions of the Lagrangian-averaged Navier-Stokes α model and their large-eddy-simulation potential (original) (raw)

Computational Models of Turbulence: The LANS-α Model and the Role of Global Analysis

Over the last 50 years, researchers have proposed numerous computational models of turbulence for obtaining closure. The objective of closure is to capture certain statistical features of the physical phenomenon of turbulence at computably low resolution by mimicking the average effects of the small scales on the larger ones, without calculating the former explicitly.

Anomalous Scaling of Structure Functions and Dynamic Constraints on Turbulence Simulations

Journal of Statistical Physics, 2005

The connection between anomalous scaling of structure functions (intermittency) and numerical methods for turbulence simulations is discussed. It is argued that the computational work for direct numerical simulations (DNS) of fully developed turbulence increases as Re 4 , and not as Re 3 expected from Kolmogorov's theory, where Re is a large-scale Reynolds number. Various relations for the moments of acceleration and velocity derivatives are derived. An infinite set of exact constraints on dynamically consistent subgrid models for Large Eddy Simulations (LES) is derived from the Navier-Stokes equations, and some problems of principle associated with existing LES models are highlighted.

Turbulent channel with slip boundaries as a benchmark for subgrid-scale models in LES

Most turbulent flows cannot be calculated by direct numerical simulation (DNS) of the Navier-Stokes equations because the range of scales of motion is so large that the computational cost becomes prohibitive. In large-eddy simulations (LES), only the large eddies are resolved and the effect of the small scales on the larger ones is supplied through a subgrid-scale (SGS) model in order to overcome most of the computational cost. In this sense, the role of SGS models is to provide the missing large-scale Reynolds stresses that can not be resolved in coarser LES computational grids. Given that accurate representation of turbulence and prediction of flow behavior are needed in almost all engineering and scientific applications, validation of SGS models must be considered a task of paramount importance. Common reference solutions for LES validation are simple hydrodynamic cases such as forced or decaying isotropic turbulence (Métais & Lesieur 1992), spatial or temporal mixing layers (Vreman et al. 1996, 1997) and plane turbulent channel flow (Germano et al. 1991), among others. See Bonnet et al. (1998) for an overview of LES validation. Most models explicitly or implicitly assume that the effective filter cutoff of the simulation lies within the inertial range, that is, far from the viscous effects but fine enough to represent the large-scale motions. This provides certain degree of universality to the flow and makes the modeling process more approachable. Hence, in order to properly evaluate a SGS model, the Reynolds number needs to be sufficiently large so the above conditions are reasonably well satisfied. In test cases without walls, like isotropic turbulence, LES can be computed at relatively coarse grid resolutions while still meeting the aforementioned conditions. However, this requirement is impossible to fulfill in the near-wall region of wall-bounded flows such as turbulent channels or boundary layers, where the flow is dominated by the small viscous scales. The root of the problem lies at the formation of thin viscous layers required to force the no-slip boundary condition. As a result, the viscous stress is the dominant term in the momentum balance equation and the near-wall physics scale in wall units defined in terms of the kinematic viscosity and friction velocity at the wall. Therefore, in wall-bounded simulations where the resolution close to the wall is not fine enough, the SGS model must also supply the corresponding viscous stress, that is not the usual way they are designed to work. The consequence is that most LES channel flows are wall-resolved and their Reynolds numbers are relatively low in order to reduce the computational cost of solving the near-wall region whose grid resolution requirements are not that far from DNS (Choi & Moin 2012). A possible solution is to incorporate wall-models that act as a surrogate of the near-wall dynamics, although this adds an extra modeling component that is intimately coupled with the SGS model under study and complicates the analysis. In this brief, we present and discuss a new benchmark case to assess the performance

Three regularization models as large-eddy simulations

We test three regularizations, the alpha-model, Leray-alpha, and Clark-alpha, as sub-grid models for LES by comparison with a 1024^3 direction numerical simulation (DNS), Rlambda 800, with a Taylor-Green forcing. Both the alpha-model and Clark-alpha are able to reproduce the large-scale anisotropy of the flow as well as the time scale of developing turbulence. Leray-alpha fails in both these regards. We study intermittency corrections through pdfs and the anomalous scaling of the velocity increment structure functions. Leray-alpha is somewhat less intermittent than the DNS and produces an energy spectrum that is too shallow in the inertial range, while Clark-alpha produces a broad k-5/3 spectrum and stronger intermittency corrections. Finally, the agreement of the DNS and alpha-model spectra, in disparity with results for lower Reynolds number simulations, is worse than in the Clark-alpha model. We conjecture that this enhanced intermittency in the alpha model is related to the stee...

Scale-similar models for large-eddy simulations

Physics of Fluids, 1999

Scale-similar models employ multiple filtering operations to identify the smallest resolved scales, which have been shown to be the most active in the interaction with the unresolved subgrid scales. They do not assume that the principal axes of the strain-rate tensor are aligned with those of the subgrid-scale stress (SGS) tensor, and allow the explicit calculation of the SGS energy. They can provide backscatter in a numerically stable and physically realistic manner, and predict SGS stresses in regions that are well correlated with the locations where large Reynolds stress occurs. In this paper, eddy viscosity and mixed models, which include an eddy-viscosity part as well as a scale-similar contribution, are applied to the simulation of two flows, a high Reynolds number plane channel flow, and a three-dimensional, nonequilibrium flow. The results show that simulations without models or with the Smagorinsky model are unable to predict nonequilibrium effects. Dynamic models provide a...

Convergence of large-eddy simulation in the outer region of wall-bounded turbulence

Most turbulent flows cannot be calculated by direct numerical simulation (DNS) of the Navier-Stokes equations because the range of scales of motions is so large that the computational cost becomes prohibitive. In large-eddy simulation (LES), only the large eddies are resolved and the effect of the small scales on the larger ones is modeled through a subgrid scale (SGS) model. This process enables a reduction of the computational cost by several orders of magnitude. Given that the accurate representation and prediction of turbulence is needed in many engineering and scientific applications, validation of SGS models must be considered a task of paramount importance. In particular, the analysis must be framed in the context of a convergence study, which is the cornerstone of validation in computational fluid dynamics. In addition, the grid requirements must be determined for LES to be deemed as a cost-saving approach when compared to DNS. Common benchmark solutions for LES are simple hydrodynamic cases such as forced or decaying isotropic turbulence (Métais & Lesieur 1992), spatial or temporal mixing layers (Vreman et al. 1996, 1997) and plane turbulent channel flow (Piomelli et al. 1988; Germano et al. 1991; Chung & McKeon 2010), among others. See Bonnet et al. (1998) for an overview of LES validation. Most SGS models assume that the effective filter cutoff lies within the inertial range, and the Reynolds number and grid resolutions must comply with this requirement in order to faithfully assess the performance of the models. In unbounded flows, like isotropic turbulence, LES can be computed at relatively coarse grid resolutions while still meeting this condition. However, this is not the case in the logarithmic region of wall-bounded flows, where the energy-containing eddies have sizes proportional to the distance to the wall (Jiménez 2012; Larsson et al. 2016). In this case, the LES grid must be accordingly reduced in all directions, increasing the computational cost. This approach is known as wall-resolved LES (WRLES) and can be achieved, for example, through nested grids (Sullivan et al. 1996) such as the one depicted in Figure 1. Actual WRLES are scarce, and typically, only the wall-normal resolution is properly refined according to the size of the energy-containing eddies, while the wall-parallel directions remain under-resolved. The grid requirements become more restrictive in the buffer layer, where the viscous effects are non-negligible. If the near-wall grid resolution does not suffice to capture the energy-containing eddies, most SGS models perform poorly (Jiménez & Moser 2000). The consequence is that the majority of validation studies in turbulent channel flows are WRLES and, hence, their Reynolds numbers tend to be relatively low to make the computational cost affordable (Choi & Moin 2012). However, it is not clear whether the SGS models are active enough at these low Reynolds numbers to adequately measure their performance. In order to test higher Reynolds numbers without the burden of the wall, a possible solution is the implementation of wall models that act as a surrogate of the near-wall dynamics, or the wall-less channel flow proposed by Lozano-Durán &