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

We discuss development of a numerical algorithm, and solver capable of performing large-eddy simulation (LES) in geometries as complex as the combustor of a gas-turbine engine. The algorithm is developed for unstructured grids, is non-dissipative, yet robust at high Reynolds numbers on highly skewed grids. Results from validation in simple geometries is shown along with simulation results in the exceedingly complex geometry of a Pratt & Whitney gas turbine combustor.© 2003 ASME

Simulating Turbulent Flows in Complex Geometries

: The turbulent flow over a NACA 4412 airfoil at angle of incidence corresponding to maximum lift (12 degree) has been computed via large-eddy simulation Two different numerical approaches, one based on a conventional structured mesh and one with a more economical unstructured mesh, have been employed Results from both simulations differ considerably from each other and from the available experimental data Differences are found with respect to occurrence of transition near the suction peak and with respect to the amount of backflow (incipient separation) near the trailing edge The unstructured mesh code predicts rapid boundary layer growth and separation near the trailing edge, whereas the flow remains attached in the structured mesh simulation It was concluded that a better matching of the transition mechanism (boundary layer tripping) which was employed in the experiments is paramount for an accurate simulation of this flow and for convergence of solutions from the two codes (AN)

Large Eddy Simulation of Turbulent Flow Over an Airfoil.

Osborne reynolds' pipe flow: Direct computation from laminar through transition to fully-developed turbulence

While great progress is being made in characterizing the 3-D structure of organized turbulent motions using conditional averaging analysis, there is a lack of theoretical guidance regarding the interpretation and utilization of such information. Questions concerning the significance of the structures, their contributions to various transport properties, and their dynamics cannot be answered without recourse to appropriate dynamical governing equations. One approach which addresses some of these questions uses the conditional fields as initial conditions and calculates their evolution from the Navier-Stokes equations, yielding valuable information about stability, growth, and longevity of the mean structure. To interpret statistical aspects of the structures, a different type of theory which deals with the structures in the context of their contributions to the statistics of the flow is needed. As a first step toward this end, an effort was made to integrate the structural information from the study of organized structures with a suitable statistical theory. This is done by stochastically estimating the two-point conditional averages that appear in the equation for the one-point probability density function, and relating the structures to the conditional stresses. Salient features of the estimates are identified, and the structure of the one-point estimates in channel flow is defined.

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Dynamical interpretation of conditional patterns

: Space-time characteristics of pressure fluctuations were analyzed using the databases generated from the direct numerical simulation. In the separated flow, the wall-pressure fluctuations are significantly reduced in the separation zone. However, they are significantly enhanced in the reattachment region. The streamwise and spanwise vorticities are lifted away from the wall in the separation zone and the pressure fluctuations are significantly enhanced in this shear layer. The contours of space-time correlations show that the convection velocities of wall-pressure fluctuations are reduced significantly inside the separation bubble. The reattachment region is characterized by large scale structures which are formed in the shear layer above the separation bubble. Frequency spectra downstream of incipient detachment shows that maximum turbulent shearing stress appears to be the proper scale to normalize wall-pressure fluctuations in the turbulent boundary layers in the presence of large adverse pressure gradient. (AN)

Parviz Moin

Papers

Simulating Turbulent Flows in Complex Geometries

Large Eddy Simulation of Turbulent Flow Over an Airfoil.

Osborne reynolds' pipe flow: Direct computation from laminar through transition to fully-developed turbulence

Dynamical interpretation of conditional patterns

Direct and large eddy simulation of separated turbulent boundary layers