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 a priori. 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.

A dynamic subgrid‐scale eddy viscosity model

We present an overview of the lattice Boltzmann method (LBM), a parallel and efficient algorithm for simulating single-phase and multiphase fluid flows and for incorporating additional physical complexities. The LBM is especially useful for modeling complicated boundary conditions and multiphase interfaces. Recent extensions of this method are described, including simulations of fluid turbulence, suspension flows, and reaction diffusion systems.

Lattice boltzmann method for fluid flows

Considerable confusion surrounds the longstanding question of what constitutes a vortex, especially in a turbulent flow. This question, frequently misunderstood as academic, has recently acquired particular significance since coherent structures (CS) in turbulent flows are now commonly regarded as vortices. An objective definition of a vortex should permit the use of vortex dynamics concepts to educe CS, to explain formation and evolutionary dynamics of CS, to explore the role of CS in turbulence phenomena, and to develop viable turbulence models and control strategies for turbulence phenomena. We propose a definition of a vortex in an incompressible flow in terms of the eigenvalues of the symmetric tensor ${\bm {\cal S}}^2 + {\bm \Omega}^2$ are respectively the symmetric and antisymmetric parts of the velocity gradient tensor ${\bm \Delta}{\bm u}$. This definition captures the pressure minimum in a plane perpendicular to the vortex axis at high Reynolds numbers, and also accurately defines vortex cores at low Reynolds numbers, unlike a pressure-minimum criterion. We compare our definition with prior schemes/definitions using exact and numerical solutions of the Euler and Navier–Stokes equations for a variety of laminar and turbulent flows. In contrast to definitions based on the positive second invariant of ${\bm \Delta}{\bm u}$ or the complex eigenvalues of ${\bm \Delta}{\bm u}$, our definition accurately identifies the vortex core in flows where the vortex geometry is intuitively clear.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112095000462

On the identification of a vortex

http://home.eps.hw.ac.uk/~ab226/tmp/implicit/lele_92.pdf

Compact finite difference schemes with spectral-like resolution

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Turbulence and the dynamics of coherent structures. I. Coherent structures

Large-eddy simulation is currently very expensive for high Reynolds number attached flows due to the need to resolve the wall layer. In order to reduce this expense, wall modeling has been proposed to provide approximate boundary conditions to the LES that allow the wall layer to be unresolved. Unfortunately, subgrid scale modeling errors and numerical errors are important in this region when a coarse grid is used, necessitating a wall model that can compensate for their effects. Optimal control theory has been used to provide such models in the past, but is impractical for complex flows due to the need to provide a target mean velocity profile and the computational expense involved with solving gradient-based optimization problems. In this paper we address the latter issue by reformulation of the optimization problem to include only data near the wall. Further approximations have been made to the Navier-Stokes and adjoint equations used in the optimization process that significantly reduce the computational cost. Results will be presented comparing this method with other control-based and standard wall models.

An efficient wall model for large-eddy simulation based on optimal control theory

Feedback control equations were developed and tested for computing wall normal control velocities to control turbulent flow in a channel with the objective of reducing drag. The technique used is the minimization of a 'cost functional' which is constructed to represent some balance of the drag integrated over the wall and the net control effort. A distribution of wall velocities is found which minimizes this cost functional some time shortly in the future based on current observations of the flow near the wall. Preliminary direct numerical simulations of the scheme applied to turbulent channel flow indicates it provides approximately 17 percent drag reduction. The mechanism apparent when the scheme is applied to a simplified flow situation is also discussed.

/pdf/optimal-feedback-control-of-turbulent-channel-flow-1kjdatqyjc.pdf

Optimal feedback control of turbulent channel flow

The effects of convex transverse curvature on the wall pressure fluctuations were studied through direct numerical simulations. The flow regime of interest is characterized by large ratio of the shear-layer thickness to the radius of curvature (γ = δ/a) and by small a+, the radius of curvature in wall units. Two direct numerical simulations of a model problem approximating axial flow boundary layers on long cylinders were performed for γ = 5 (a+ ≈ 43) and γ = 11 (a+ ≈ 21). The space-time characteristics of the wall pressure fluctuations of the plane channel flow simulation of Kim, Moin & Moser (1987), which were studied by Choi & Moin (1990) are used to assess the effects of curvature.
 As the curvature increases the root-mean-square (r.m.s.) pressure fluctuations decrease and the ratio of the streamwise to spanwise lengthscales of the wall pressure fluctuations increases. Fractional contributions from various layers in the flow to the wall r.m.s. pressure fluctuations are marginally affected by the curvature. Curvature-dependent timescales and lengthscales are identified that collapse the high-frequency range of the wall pressure temporal spectra and the high wave-number range of the wall pressure streamwise spectra of flows with different curvatures. Taylor's hypothesis holds for the wall pressure fluctuations with a lower convection velocity than in the planar case.

Effects of convex transverse curvature on wall-bounded turbulence. Part 2. The pressure fluctuations

In wall-bounded turbulent flows, the wall-normal gradient in turbulence intensity causes inertial particles to move preferentially toward the wall, leading to elevated concentration levels in the viscous sublayer. At first glance, wall-modelled large-eddy simulations may seem ill suited for accurately simulating this behaviour, given that the sharp gradients and coherent structures in the viscous sublayer and buffer region are unresolved in this approach. In this paper, a detailed inspection of conservation equations describing the influence of turbophoresis and near-wall structures on particle concentration profiles reveals a more nuanced view depending on the friction Stokes number. The dynamics of low and moderate Stokes number particles indeed depends strongly on the complex spatio-temporal details of streaks, ejections, and sweeps in the near-wall region. This significantly impacts the near-wall particle concentration through a biased sampling effect which provides a net force away from the wall on the particle ensemble caused by the tendency of inertial particles to accumulate in low-speed ejection regions. At higher Stokes numbers, however, this biased sampling is of minimal importance, and the particle concentration becomes inversely proportional to the wall-normal particle velocity variance at a given distance from the wall. As a result, wall-modelled large-eddy simulations can predict concentration profiles with more accuracy in the high Stokes number regime than low Stokes numbers simply by modifying the interpolation scheme for particles between the first grid point and the boundary. However, accurate representation of low and moderate Stokes number particles depends critically on information not present in standard wall-modelled large-eddy simulations.

Turbophoresis of small inertial particles: theoretical considerations and application to wall-modelled large-eddy simulations

Two kinds of linear analysis, rapid distortion theory (RDT) and linear interaction analysis (LIA), were used to investigate the effects of a shock wave on turbulence. Direct numerical simulations of two-dimensional isotropic turbulence interaction with a normal shock were also performed. The results from RDT and LIA are in good agreement for weak shock waves, where the effects of shock front curvature and shock front unsteadiness are not significant in producing vorticity. The linear analyses predict wavenumber-dependent amplification of the upstream one-dimensional energy spectrum, leading to turbulence scale length scale decrease through the interaction. Instantaneous vorticity fields show that vortical structures are enhanced while they are compressed in the shock normal direction. Entrophy amplfication through the shock wave compares favorably with the results of linear analyses.

Parviz Moin

Papers

An efficient wall model for large-eddy simulation based on optimal control theory

Optimal feedback control of turbulent channel flow

Effects of convex transverse curvature on wall-bounded turbulence. Part 2. The pressure fluctuations

Turbophoresis of small inertial particles: theoretical considerations and application to wall-modelled large-eddy simulations

Direct numerical simulation and analysis of shock turbulence interaction