Weak solutions of the three-dimensional vorticity equation with vortex singularities

The use of a modified scheme for the dynamics of vortex singularities is shown to lead to a weak solution of the three-dimensional inviscid incompressible vorticity equation

Some Progress in Large-Eddy Simulation using the 3-D Vortex Particle Method

This two-month visit at CTR was devoted to investigating possibilities in LES modeling in the context of the 3-D vortex particle method (=vortex element method, VEM) for unbounded flows. A dedicated code was developed for that purpose. Although O(N(sup 2)) and thus slow, it offers the advantage that it can easily be modified to try out many ideas on problems involving up to N approx. 10(exp 4) particles. Energy spectrums (which require O(N(sup 2)) operations per wavenumber) are also computed. Progress was realized in the following areas: particle redistribution schemes, relaxation schemes to maintain the solenoidal condition on the particle vorticity field, simple LES models and their VEM extension, possible new avenues in LES. Model problems that involve strong interaction between vortex tubes were computed, together with diagnostics: total vorticity, linear and angular impulse, energy and energy spectrum, enstrophy. More work is needed, however, especially regarding relaxation schemes and further validation and development of LES models for VEM. Finally, what works well will eventually have to be incorporated into the fast parallel tree code

Vortex Particle-Mesh with Immersed Lifting Lines for Aerospace and Wind Engineering

AbstractWe present the treatment of lifting lines with a Vortex Particle-Mesh (VPM) methodology. The VPM method relies on the Lagrangian discretization of the Navier-Stokes equations in vorticity-velocity formulation. The use of this hybrid discretization offers several advantages. The particles are used solely for the advection, thereby waiving classical time stability constraints. They also exploit the compactness of vorticity support, leading to high computational gains for external flow simulations. The mesh, on the other hand, handles all the other computationally intensive tasks, such as the evaluation of the differential operators and the use of fast Fourier-based Poisson solvers, which allow the combination of unbounded directions and inlet/outlet boundaries. Both discretizations communicate through high order interpolation. The mesh and the interpolation also allow for additional advances; they are used to handle Lagrangian distortion by reinitializing the particle positions onto a regular grid. This crucial step, referred to as remeshing, guarantees the accuracy of the method. In addition, the resulting methodology provides computational efficiency and scalability to massively parallel architectures.Sources of vorticity are accounted for through a lifting line approach. This line handles the attached and shed vorticity contributions in a Lagrangian manner. Its immersed treatment efficiently captures the development of vorticity from thin sheets into a three-dimensional field. We apply this approach to the simulation of wake flows encountered in aeronautical and wind energy applications. An important aspect in these fields is the handling of turbulent inflows. We have developed a technique for the introduction of pre-computed or synthetic turbulent flow fields in vorticity form. Our treatment is based on particles as well and consistent with the Lagrangian character of the method. We apply here our method to the investigation of wind turbine wakes over very large distances, reaching cluster or wind farm sizes

Discontinuous Galerkin methodology for Large-Eddy Simulations of wind turbine airfoils

peer reviewedThis paper aims at evaluating the potential of the Discontinuous Galerkin (DG) methodology for Large-Eddy Simulation (LES) of wind turbine airfoils. The DG method has shown high accuracy, excellent scalability and capacity to handle unstructured meshes. It is however not used in the wind energy sector yet. The present study aims at evaluating this methodology on an application which is relevant for that sector and focuses on blade section aerodynamics characterization. To be pertinent for large wind turbines, the simulations would need to be at low Mach numbers (M ≤ 0.3) where compressible approaches are often limited and at large Reynolds numbers (Re ≥ 106) where wall-resolved LES is still unaffordable. At these high Re, a wall-modeled LES (WMLES) approach is thus required. In order to first validate the LES methodology, before the WMLES approach, this study presents airfoil flow simulations at low and high Reynolds numbers and compares the results to state-of-the-art models used in industry, namely the panel method (XFOIL with boundary layer modeling) and Reynolds Averaged Navier-Stokes (RANS). At low Reynolds number (Re = 6 x 104), involving laminar boundary layer separation and transition in the detached shear layer, the Eppler 387 airfoil is studied at two angles of attack. The LES results agree slightly better with the experimental chordwise pressure distribution than both XFOIL and RANS results. At high Reynolds number (Re = 1.64 x 106), the NACA4412 airfoil is studied close to stall condition. In this case, although the wall model approach used for the WMLES is very basic and not supposed to handle separation nor adverse pressure gradients, all three methods provide equivalent accuracy on averaged quantities. The present work is hence considered as a strong step forward in the use of LES at high Reynolds numbers

A priori testing of subgrid-scale models for the velocity-pressure and vorticity-velocity formulations

Subgrid-scale models for Large Eddy Simulation (LES) in both the velocity-pressure and the vorticity-velocity formulations were evaluated and compared in a priori tests using spectral Direct Numerical Simulation (DNS) databases of isotropic turbulence: 128(exp 3) DNS of forced turbulence (Re(sub(lambda))=95.8) filtered, using the sharp cutoff filter, to both 32(exp 3) and 16(exp 3) synthetic LES fields; 512(exp 3) DNS of decaying turbulence (Re(sub(Lambda))=63.5) filtered to both 64(exp 3) and 32(exp 3) LES fields. Gaussian and top-hat filters were also used with the 128(exp 3) database. Different LES models were evaluated for each formulation: eddy-viscosity models, hyper eddy-viscosity models, mixed models, and scale-similarity models. Correlations between exact versus modeled subgrid-scale quantities were measured at three levels: tensor (traceless), vector (solenoidal 'force'), and scalar (dissipation) levels, and for both cases of uniform and variable coefficient(s). Different choices for the 1/T scaling appearing in the eddy-viscosity were also evaluated. It was found that the models for the vorticity-velocity formulation produce higher correlations with the filtered DNS data than their counterpart in the velocity-pressure formulation. It was also found that the hyper eddy-viscosity model performs better than the eddy viscosity model, in both formulations

Peripheral blood mitochondrial DNA content in relation to circulating metabolites and inflammatory markers: a population study

Mitochondrial DNA (mtDNA) content might undergo significant changes caused by metabolic derangements, oxidative stress and inflammation that lead to development and progression of cardiovascular diseases. We, therefore, investigated in a general population the association of peripheral blood mtDNA content with circulating metabolites and inflammatory markers. We examined 310 subjects (50.6% women; mean age, 53.3 years) randomly selected from a Flemish population. Relative mtDNA content was measured by quantitative real-time PCR in peripheral blood cells. Peak circulating metabolites were quantified using nuclear magnetic resonance spectroscopy. The level of inflammation was assessed via established inflammatory markers. Using Partial Least Squares analysis, we constructed 3 latent factors from the 44 measured metabolites that explained 62.5% and 8.5% of the variance in the contributing metabolites and the mtDNA content, respectively. With adjustments applied, mtDNA content was positively associated with the first latent factor (P = 0.002). We identified 6 metabolites with a major impact on the construction of this latent factor including HDL3 apolipoproteins, tyrosine, fatty acid with αCH2, creatinine, β-glucose and valine. We summarized them into a single composite metabolite score. We observed a negative association between the composite metabolic score and mtDNA content (P = 0.001). We also found that mtDNA content was inversely associated with inflammatory markers including hs-CRP, hs-IL6, white blood cell and neutrophil counts as well as neutrophil-to-lymphocyte ratio (P≤0.0024). We demonstrated that in a general population relative peripheral blood mtDNA content was associated with circulating metabolites indicative of perturbed lipid metabolism and with inflammatory biomarkers

Nonlinear subgrid-scale models for large-eddy simulation of rotating turbulent flows

We aim to design subgrid-scale models for large-eddy simulation of rotating turbulent flows. Rotating turbulent flows form a challenging test case for eddy viscosity models due to the presence of the conservative Coriolis force. We therefore propose a new subgrid-scale model that, in addition to a dissipative eddy viscosity term, contains a nondissipative nonlinear model term that can capture transport processes, such as those due to rotation. We show that the addition of this nonlinear model term leads to improved predictions of the Reynolds stress anisotropy in large-eddy simulations of a spanwise-rotating plane-channel flow, while maintaining the prediction of the mean velocity profile that is obtained when only using an eddy viscosity model.<br/

When Does Eddy Viscosity Damp Subfilter Scales Sufficiently?

Large eddy simulation (LES) seeks to predict the dynamics of spatially filtered turbulent flows. The very essence is that the LES-solution contains only scales of size ≥Δ, where Δ denotes some user-chosen length scale. This property enables us to perform a LES when it is not feasible to compute the full, turbulent solution of the Navier-Stokes equations. Therefore, in case the large eddy simulation is based on an eddy viscosity model we determine the eddy viscosity such that any scales of size <Δ are dynamically insignificant. In this paper, we address the following two questions: how much eddy diffusion is needed to (a) balance the production of scales of size smaller than Δ; and (b) damp any disturbances having a scale of size smaller than Δ initially. From this we deduce that the eddy viscosity νe has to depend on the invariants q = ½tr(S^2) and r =−⅓tr(S^3) of the (filtered) strain rate tensor S. The simplest model is then given by νe = 3/2(Δ/π)^2|r|/q. This model is successfully tested for a turbulent channel flow (Reτ = 590).

On the Clark-alpha model of turbulence: global regularity and long--time dynamics

In this paper we study a well-known three--dimensional turbulence model, the filtered Clark model, or Clark-alpha model. This is Large Eddy Simulation (LES) tensor-diffusivity model of turbulent flows with an additional spatial filter of width alpha ($\alpha$). We show the global well-posedness of this model with constant Navier-Stokes (eddy) viscosity. Moreover, we establish the existence of a finite dimensional global attractor for this dissipative evolution system, and we provide an anaytical estimate for its fractal and Hausdorff dimensions. Our estimate is proportional to $(L/l_d)^3$, where $L$ is the integral spatial scale and $l_d$ is the viscous dissipation length scale. This explicit bound is consistent with the physical estimate for the number of degrees of freedom based on heuristic arguments. Using semi-rigorous physical arguments we show that the inertial range of the energy spectrum for the Clark-$\aa$ model has the usual $k^{-5/3}$ Kolmogorov power law for wave numbers $k\aa \ll 1$ and $k^{-3}$ decay power law for $k\aa \gg 1.$ This is evidence that the Clark$-\alpha$ model parameterizes efficiently the large wave numbers within the inertial range, $k\aa \gg 1$, so that they contain much less translational kinetic energy than their counterparts in the Navier-Stokes equations.Comment: 11 pages, no figures, submitted to J of Turbulenc

Leray and LANS-α\alpha modeling of turbulent mixing

Mathematical regularisation of the nonlinear terms in the Navier-Stokes equations provides a systematic approach to deriving subgrid closures for numerical simulations of turbulent flow. By construction, these subgrid closures imply existence and uniqueness of strong solutions to the corresponding modelled system of equations. We will consider the large eddy interpretation of two such mathematical regularisation principles, i.e., Leray and LANS$-\alpha$ regularisation. The Leray principle introduces a {\bfi smoothed transport velocity} as part of the regularised convective nonlinearity. The LANS$-\alpha$ principle extends the Leray formulation in a natural way in which a {\bfi filtered Kelvin circulation theorem}, incorporating the smoothed transport velocity, is explicitly satisfied. These regularisation principles give rise to implied subgrid closures which will be applied in large eddy simulation of turbulent mixing. Comparison with filtered direct numerical simulation data, and with predictions obtained from popular dynamic eddy-viscosity modelling, shows that these mathematical regularisation models are considerably more accurate, at a lower computational cost.Comment: 42 pages, 12 figure