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

/pdf/turbulence-and-the-dynamics-of-coherent-structures-i-1o6o6m60fm.pdf

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

A lower bound on the Liapunov dimenison, D-lambda, of the attractor underlying turbulent, periodic Poiseuille flow at a pressure-gradient Reynolds number of 3200 is calculated, on the basis of a coarse-grained (16x33x8) numerical solution, to be approximately 352. Comparison of Liapunov exponent spectra from this and a higher-resolution (16x33x16) simulation on the same spatial domain shows these spectra to have a universal shape when properly scaled. On the basis of these scaling properties, and a partial exponent spectrum from a still higher-resolution (32x33x32) simulation, it is argued that the actual dimension of the attractor underlying motion of the given computational domain is approximately 780. It is suggested that this periodic turbulent shear flow is deterministic chaos, and that a strange attractor does underly solutions to the Navier-Stokes equations in such flows.

The dimension of attractors underlying periodic turbulent Poiseuille flow

The deformation of a hairpin-shaped vortex filament under self-induction and in the presence of shear is studied numerically using the Biot-Savart law. It is shown that the tip region of an elongated hairpin vortex evolves into a vortex ring and that the presence of mean shear impedes the process. Evolution of a finite-thickness vortex sheet under self-induction is also investigated using the Navier-Stokes equations. The layer evolves into a hairpin vortex which in turn produces a vortex ring of high Reynolds stress content. These results indicate a mechanism for the generation of ring vortices in turbulent shear flows, and a link between the experimental and numerical observation of hairpin vortices and the observation of ring vortices in the outer regions of turbulent boundary layers.

/pdf/evolution-of-a-curved-vortex-filament-into-a-vortex-ring-1lu0u99akz.pdf

Evolution of a curved vortex filament into a vortex ring

The governing equations for large-eddy simulation are derived from the application of a low-pass filter to the Navier–Stokes equations. It is often assumed that discrete operations performed on a particular grid act as an implicit filter, causing results to be sensitive to the mesh resolution. Alternatively, explicit filtering separates the filtering operation, and hence the resolved turbulence, from the underlying mesh distribution alleviating some of the grid sensitivities. We investigate the use of explicit filtering in large-eddy simulation in order to obtain numerical solutions that are grid independent. The convergence of simulations using a fixed filter width with varying mesh resolutions to a true large-eddy simulation solution is analyzed for a turbulent channel flow at Reτ=180, 395, and 640. By using explicit filtering, turbulent statistics and energy spectra are shown to be independent of the mesh resolution used.

Grid-independent large-eddy simulation using explicit filtering

The effects of tip-gap size on the tip-leakage vortical structures and velocity and pressure fields are investigated using large-eddy simulation, with the objective of providing guidelines for controlling tip-leakage cavitation and viscous losses associated with the tip-leakage flow The effects of tip-gap size on the generation and evolution of the end-wall vortical structures are discussed by investigating their evolutionary trajectories and the mean velocity field The tip-leakage jet and tip-leakage vortex are found to produce significant mean velocity gradients, leading to the production of vorticity and turbulent kinetic energy Inside the cascade passage, the peak streamwise velocity deficit and magnitudes of vorticity and turbulent kinetic energy in the tip-leakage vortex are reduced as the tip-gap size decreases The present analysis indicates that the mechanisms for the generation of vorticity and turbulent kinetic energy are mostly unchanged by the tip-gap size variation However, larger tip-ga

Effects of tip-gap size on the tip-leakage flow in a turbomachinery cascade

The cost of large eddy simulation (LES) in the near-wall region of attached turbulent boundary layers scales as the square of the friction Reynolds number, thus limiting LES to moderate Reynolds numbers. Wall stress boundary conditions are frequently used to alleviate this resolution requirement, but commonly used models are shown to perform poorly at high Reynolds numbers even in turbulent channel flow. Techniques from optimal control theory are used to find wall stresses that yield much better results in turbulent channel flow at high Reynolds numbers than existing models even on extremely coarse grids. In this approach, a suboptimal control strategy is used in which the objective is to force the outer LES towards a desired solution by using the wall stress boundary conditions as control. The suboptimal wall stresses are not necessarily physical, rather they are whatever is necessary to overcome the numerical and modeling errors present in the near-wall region to yield the correct mean velocity profile. Furthermore, the suboptimal control strategy generates reference data for comparing and deriving new wall models. Using linear stochastic estimation it is shown that the dynamically relevant part of the suboptimal wall stresses can be predicted from the local velocity field. A wall model derived from linear stochastic estimation yields good mean flow predictions in LES of turbulent channel flow on a 323 uniform grid for friction velocity Reynolds numbers from 640 to 20 000.

/pdf/large-eddy-simulation-wall-modeling-based-on-suboptimal-1u79ikes37.pdf

Parviz Moin

Papers

The dimension of attractors underlying periodic turbulent Poiseuille flow

Evolution of a curved vortex filament into a vortex ring

Grid-independent large-eddy simulation using explicit filtering

Effects of tip-gap size on the tip-leakage flow in a turbomachinery cascade

Large eddy simulation wall-modeling based on suboptimal control theory and linear stochastic estimation