Session A09: Turbulence: Large-Eddy Simulations

Assessment of a non-local subgrid scale model for LES

In this work we introduce a new approach assessing the LES models based on contrasting the eddy diffusivity operators obtained from the DNS and LES flow fields. Our analysis is based on the expectation that the mean field momentum obtained from a LES must be the same as the filtered mean field momentum obtained from a DNS. Using the macroscopic forcing method (Park and Mani 2021), we project both the LES and DNS equations onto the RANS space and obtain the respective operators that govern the mean fields of both systems. In this presentation, we consider homogeneous isotropic turbulence as a canonical setting to assess the LES models. We show that while the standard Smagorinsky model performs reasonably at low-wavenumbers when assessed against this criterion, it is over-dissipative in the high-wavenumbers limit. Inspired by these results we introduce an alternative non-local LES model and demonstrate its superior performance over the entire wavenumber spectrum. We have tested these LES models for as high as Re_λ=106.   

Advancements in dynamic subgrid-scale modeling for large-eddy simulations (LES) of turbulent flows

In LES methodology, one of the drawbacks of eddy-viscosity-based subgrid-scale(SGS) models is the misalignment between residual stresses and large-scale strain rate tensor. Further, since small-scale turbulence is generated from 3-D vortex stretching, it is desirable to include large-scale rotation rate tensor in phenomenological SGS models. Early attempts at developing higher-fidelity SGS models led to tuned model coefficients and/or under-dissipative models (Meneveau and Katz, Annu. Rev. Fluid Mech. 2000).

We propose novel dynamic formulations of the tensor-coefficient Smagorinsky model (Moin, Springer 1993), and a non-linear model characterized by the full velocity-gradient tensor (Lund and Novikov, Res. Briefs, CTR 1992) using the Germano identity while preserving the rotational invariance of the Navier Stokes equations. We also validate these models in decaying and forced Homogeneous Isotropic Turbulence at Re_λ = 70 & 410 respectively, followed by wall-modeled LES of channel flow at Re_τ = 4200. Results from simulations of complex-separated flows such as the Boeing Speed Bump using these models will also be reported and compared to that of other models.   

Toward autonomous large eddy simulations of turbulence based on interscale energy transfer among resolved scales

We show how the subgrid-scale (SGS) energy transfer among resolved scales in large eddy simulations (LES) can be used to obtain the total SGS energy transfer for unknown, full velocity field. The total transfer serves then as a physical constraint on several classical spectral SGS models and can be used to obtain and update model constants at each time step in actual LES. The performance of SGS models depends not only on their ability to capture the total SGS dissipation (which is enforced by the method) but also by distribution of the SGS dissipation among scales of motion (which is enforced by a model). Moreover, we show how the SGS transfer wave number distribution itself can be obtained from the evolving LES velocity fields. Information about the total SGS transfer and its wave number distribution, supplemented by a known asymptotic properties of energy flux in the inertial range, allows autonomous LES, i.e.,  self-contained simulations without use of extraneous SGS models. The method is tested in LES of isotropic turbulence at high Reynolds number where the inertial range dynamics is expected and for lower Reynolds number decaying turbulence under conditions of the classical Comte-Bellot and Corrsin experiments.   

A physics-inspired alternative to spatial filtering for large-eddy simulations of turbulent flows

Spatial filtering is commonly used to justify LES equations and inform closure modeling. However, spatial filtering theory for LES is not without its shortcomings, including the precise definition of filtering near boundaries, the presence of commutation errors for non-uniform resolution, and difficulties associated with additional physical complexity such as two-phase interfaces. This presentation will introduce a new theory for LES using a coarsening procedure that imitates nature. This physics-inspired approach is equivalent to Gaussian filtering for single-phase wall-free flows with uniform resolution but opens up new insights even in that simple case. An alternative to the Germano identity will be introduced and used to define a dynamic procedure without the need for a test filter. Boundaries and nonuniform resolution can be treated seamlessly in this framework without commutation errors, and the divergence-free condition is retained for incompressible flows. Preliminary results for simple flows will be shown and potential extensions to more complex physics will be briefly discussed.   

Optimal Eddy Viscosity in Closure Models for 2D Turbulent Flows

In this talk, we consider the question of fundamental limitations on the performance of eddy-viscosity closure models for turbulent flows, focusing on the Leith model for 2D Large-Eddy Simulation. Optimal eddy viscosities depending on the magnitude of the vorticity gradient are determined subject to minimum assumptions by solving PDE-constrained optimization problems defined such that the corresponding optimal Large-Eddy Simulation best matches the Direct Numerical Simulation. The main finding is that with a fixed cutoff wavenumber k_c, the performance of the Large-Eddy Simulation systematically improves as the regularization in the solution of the optimization problem is reduced and this is achieved with the optimal eddy viscosities exhibiting increasingly irregular behaviour with rapid oscillations. Since the optimal eddy viscosities do not converge to a well-defined limit as the regularization vanishes, we conclude that the problem of finding an optimal eddy viscosity does not in fact have a solution and is thus ill-posed. Moreover, while better behaved and hence practically more useful eddy viscosities can be obtained with stronger regularization, the corresponding Large-Eddy Simulations will not achieve their theoretical performance limits.   

Adaptive Scale-Similar Closure of the Subgrid Stress and Subgrid Scalar Flux in Large Eddy Simulations

We demonstrate an adaptive scale-similar closure approach that represents subgrid terms accurately and stably even at the smallest resolved scales of a simulation. This is based on scale similarity and generalized representations of subgrid terms from the complete and minimal tensor representation theory of Smith (1971). Tensor polynomial coefficients adapt to the local turbulence state via system identification at a test-filter scale. The local test-scale coefficients are rescaled to the LES-scale to evaluate the subgrid term. Resulting stress and production fields, and scalar flux and scalar dissipation fields, are nearly identical to corresponding true fields. Even in a low-dissipation pseudo-spectral code, this closure is stable without any added dissipation, and with only minor added dissipation shows E(k) ~ k-5/3 scaling to the smallest resolved scales. A posteriori tests show greatly improved accuracy in inner-scale statistics compared to traditional closure with a prescribed subgrid model. When accuracy is needed even at the smallest resolved scales, the 3X longer run-time compared to traditional closure with the dynamic Smagorinsky model may be acceptable, and this new closure approach can provide stable and accurate simulations across all resolved scales.   

A Predictive Near-Wall Model For Large Eddy Simulations

Spectral analysis of the DNS data indicates that thin-layer asymptotics is a

promising approach to model the interactions between the near-wall layer and

the outer flow. For this approach an asymptotic analysis of the filtered

Navier-Stokes equations is pursued in the limit in which the horizontal filter

scale is large compared to the thickness of the wall layer.  It is shown in

this limit that the filtered velocities in the near-wall layer are

determined to zeroth order by filtered velocities at the boundary of the wall

layer. Further, the asymptotics suggest that there is a scaled universal

velocity profile in the near-wall region. The profile is evaluated

through analysis of DNS data from channel flow at Re_{\tau}=5200. The

resulting profile is used along with asymptotically relevant terms

to formulate a predictive near-wall model. This model is a PDE solved on the

boundary plane for the LES domain to represent the integrated effects of

the wall on the LES.  We present results from a coarse LES using this wall

model.   

Wall modelled LES for variable viscosity turbulence

Modification of turbulence by temperature-dependent fluid properties is not ignorable when a relatively large temperature difference is imposed on the flow fields. It is true particularly for high Prandtl number flows heated/cooled from the wall boundaries. Since most of the algebraic wall models simply assume constant fluid properties, it is required to provide an alternative model to simulate such a flow field. Indeed, models based on the equilibrium logarithmic law cannot describe the effects of variable viscosity. This study hence proposes a wall-modelled LES method by introducing a temperature-dependent near-wall layer for the viscosity. With a simple model function for the viscosity, the steep near-wall variation of the temperature-dependent viscosity is described. We then integrate the Favre averaged thin boundary layer equations for the momentum and the temperature to construct an algebraic non-equilibrium wall model. The present LES shows that the proposed model successfully reproduces the skewed mean velocity and temperature profiles owing to the temperature-dependent variable viscosity.   

Impact of numerical hydrodynamics in turbulent mixing transition simulations

Underresolved simulations are unavoidable in high Reynolds (Re) and Mach (Ma) number turbulent flow applications at scale. Implicit large-Eddy simulation (ILES) often becomes the effective strategy to capture the dominating effects of convectively driven flow instabilities. We evaluate the impact of three distinct numerical strategies in simulations of transition and turbulence decay with ILES: the HLL Riemann solver applying Strang splitting and a Lagrange-plus-Remap formalism to solve the directional sweep -- denoted split; the HLLC solver using a directionally unsplit strategy and parabolic reconstruction -- denoted unsplit; and the HLLC solver using unsplit and a low-Ma correction (LMC) -- denoted unsplit*. Three case studies are considered: shock tube problems prototyping shock-driven turbulent mixing, the Taylor–Green Vortex (TGV) prototyping transition to turbulence, and homogeneous isotropic turbulence.  Significantly more accurate predictions are provided by the unsplit schemes, in particular, when augmented with the LMC.  For given resolution, only the unsplit schemes predict the turbulent mixing transition after reshock observed in the shock tube experiments – exhibiting higher simulated turbulence Re and increased small-scale content associated with the unsplit discretizations.  Unsplit* schemes are also instrumental in allowing to capture the spatial development of the TGV flow and its validation at prescribed Re with significantly less resolution.  -- Selected as Editor’s Pick, Phys. Fluids 33, 035126, 2021.