Discrete filter operators for large‐eddy simulation using high‐order spectral difference methods

The combination of a high‐order unstructured spectral difference (SD) spatial discretization scheme with sub‐grid scale (SGS) modeling for large‐eddy simulation is investigated with particular focus on the consistent implementation of a structural mixed model based on the scale similarity hypothesis. The difficult task of deriving a consistent formulation for the discrete filter within the SD element of arbitrary order led to the development of a new class of three‐dimensional constrained discrete filters. The discrete filters satisfy a set of selected criteria and are completely local within the SD element. Their weights can be automatically computed at run time from the number of solution points within each element and the expected filter cutoff length scale. The novel discrete filters can be applied to any SGS model involving explicit filtering and to a broad class of high‐order discontinuous finite element numerical schemes. The code is applied to the computation of turbulent channel flows at three Reynolds numbers, namely Re_τ = 180, 395, and 590 (based on the friction velocity u_τ and channel half‐width δ). Results from computations with and without the SGS model are compared against results from direct numerical simulation. The numerical experiments suggest that the results are sensitive to the use of the SGS model, even when a high‐order numerical scheme is used, especially when the grid resolution is kept relatively low and mostly in terms of resolved Reynolds stresses. Results obtained using existing filters based on the projection of the solution over lower‐order polynomial bases are also shown and demonstrate that these filters are inadequate for SGS modeling purposes, mostly because of their inability to enforce the selected cutoff length scale with sufficient accuracy. The use of the similarity mixed formulation proved to be particularly accurate in reproducing SGS interactions, confirming that its well‐known potential can be realized in conjunction with state‐of‐the‐art high‐order numerical schemes.Copyright © 2012 John Wiley & Sons, Ltd.     

Structural Wall-modeled LES Using a High-order Spectral Difference Scheme for Unstructured Meshes

The combination of the high-order unstructured Spectral Difference (SD) spatial discretization scheme with Sub-Grid Scale (SGS) modeling for Wall-Modeled Large-Eddy Simulation (WMLES) is investigated. Particular focus is given to the use of wall-function approaches and to the relevant optimal coupling with the numerical scheme and the SGS model, a similarity mixed type model featuring newly designed discrete filters with specified cutoff length scale. To take full advantage of the discontinuous Finite Element (FE) structure which characterizes the SD scheme, wall-modeling is accomplished within the first wall element by using the information from the farthest solution points from the wall. Compared to the customary used first off-wall node, this point provides more accurate information to the wall-function, thus improving the quality of the solution. Two different law-of-the-wall are tested, a classical three-layers wall-function based on the equilibrium assumption and a more general formulation to account for the pressure gradient in more complex configurations. Moreover, the mixed scale-similarity SGS model is used in the entire computational domain without any particular adjustment inside the wall-modeled region. Numerical tests on the classical test case of the turbulent channel flow at different Reynolds numbers and on the channel with periodic constrictions at Re _h = 10,595 give evidence that the results are extremely sensitive to the choice of the solution points used to provide the informations to the law-of-the-wall. In particular, it is shown that significant improvements in the results can be attained by solving the wall-function away from the wall, rather than at the first off-wall solution point as customary done. The combination of the selected wall-modeling strategies and the similarity mixed formulation proves to be remarkably accurate, even in the presence of boundary layer separation, thus opening the path to further exploit the high-order SD platform, as well as a broad range of other similar methodologies, for WMLES. Extensions of the methodology are envisaged to include more sophisticated wall-modeling approaches incorporating turbulent sensors to switch to no-slip conditions in laminar regions.     

Zinc-porphyrin phosphonate coordination: structural control through a zinc phosphoryl-oxygen interaction

Inter- and intramolecular zinc-porphyrin phosphonate coordination in the cis and trans isomers of zinc tetraphenylporphyrinstyryldiphosphonate is reported, demonstrating the potential of the zinc phosphoryl-oxygen interaction for structural control.     

Estimation of three-dimensional flame surface densities from planar images in turbulent premixed combustion

Turbulence motions are, by nature, three-dimensional while planar imaging techniques, widely used in turbulent combustion, give only access to two-dimensional information. For example, to extract flame surface densities, a key ingredient of some turbulent combustion models, from planar images implicitly assumes an instantaneously two-dimensional flow, neglecting the unresolved flame front wrinkling. The objective here is to estimate flame surface densities from two-dimensional measurements assuming that (1) the flow is statistically two dimensional; (2) the measuring plane is a plane of symmetry of the mean flow, either by translation (homogeneous third direction as in slot burners for example) or by rotation (axi-symmetrical flows such as jets) and (3) flame movements in transverse directions are similar. The unknown flame front wrinkling is then modelled from known quantities. An excellent agreement is achieved against direct numerical simulation (DNS) data where all three-dimensional quantities are known, but validations in other conditions (larger DNS, experiments) are required.     

Analysis of High-order Explicit LES Dynamic Modeling Applied to Airfoil Flows

A high-order low dissipative numerical framework is discussed to tackle simultaneously the modeling of unresolved sub-grid scale flow turbulence and the capturing of shock waves. The flows around two different airfoil profiles are simulated using a Spectral Difference discretisation scheme. First, a transitional, almost incompressible, low Reynolds number flow over a Selig-Donovan 7003 airfoil. Second, a high Reynolds number flow over a RAE2822 airfoil under transonic conditions. These flows feature both laminar and turbulent flow physics and are thus particularly challenging for turbulence sub-grid scale modeling. The accuracy of the recently developed Spectral Element Dynamic Model, specifically capable of detecting spatial under-resolution in high-order flow simulations, is evaluated. Concerning the test in transonic conditions, the additional complexity due to the presence of shock waves has been handled using an artificial viscosity shock-capturing technique based on bulk viscosity. To mitigate the impact of the shock-capturing on turbulence dissipation, it was necessary to combine the high-order modal-type shock detection with a usual sensor measuring the local flow compressibility.

     

Evaluation of the Spectral Element Dynamic Model for Large-Eddy Simulation on Unstructured,Deformed Meshes

In this paper, the Spectral-Element Dynamic Model (SEDM), suited for Large-Eddy Simulation (LES) using Discontinuous Finite Element Methods (DFEM), is assessed using unstructured meshes. Five test cases of increasing complexity are considered, namely, the Taylor-Green vortex at Re =?5000, the turbulent channel flow at Re_τ =?587, the circular cylinder in cross-flow at Re_D =?3900, the square cylinder in cross-flow at Re_D =?22400 and the channel with periodic constrictions at Re_h =?10595. Various discretization parameters such as the grid spacing, polynomial degree and numerical flux are assessed and very accurate results are reported in all cases. This consistency in the results demonstrates the versatility of the SEDM approach and its ability to gage the actual resolution and quality of the mesh and, accordingly, to introduce an amount of sub-grid dissipation which is adapted to the spatial discretization considered.