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

The tip-leakage flow in axial turbomachines is studied using large-eddy simulation with an emphasis on understanding the underlying mechanisms for low-pressure fluctuations and cavitations downstream of the tip-gap. Simulation results are validated against experimental measurements, and reasonable agreements are obtained. Dominant vortical structures such as the tip-leakage vortex and tip-separation vortices are examined, and their effects on the turbulent flow characteristics as well as on the low-pressure statistics are investigated. Analysis of the velocity and pressure fields suggests a high correlation between cavitations inception and the tip-leakage vortex. To suppress the tip-leakage vortex and the associated low-pressure events, the use of a grooved casing wall is explored, and preliminary simulation results show good promise. Additional simulations to investigate the effects of inflow vortices and tip-gap size are also discussed.

Large-eddy simulation and analysis of tip-clearance flows in turbomachinery applications

An incompressible, time developing 3-D mixing layer with idealized initial conditions was simulated numerically. Consistent with the suggestions from experimental measurements, the braid region between the dominant spanwise vortices or rolls develops longitudinal vortices or ribs, which are aligned upstream and downstream of a roll and produce spanwise distortion of the rolls. The process by which this distortion occurs is explained by studying a variety of quantities of dynamic importance (e.g., production of enstrophy, vortex stretching). Other quantities of interest (dissipation, helicity density) are also computed and discussed. The currently available simulation only allows the study of the early evolution (before pairing) of the mixing layer. New simulations in progress will relieve this restriction.

/pdf/dynamics-of-coherent-structures-in-a-plane-mixing-layer-12c2sc9dvy.pdf

Dynamics of coherent structures in a plane mixing layer

The effects of transverse curvature are investigated by means of direct numerical simulations of turbulent axial flow over cylinders. Two cases of Reynolds number of about 3400 and layer-thickness-to-cylinder-radius ratios of 5 and 11 were simulated. All essential turbulence scales were resolved in both calculations, and a large number of turbulence statistics were computed. The results are compared with the plane channel results of Kim et al. (1987) and with experiments. With transverse curvature the skin friction coefficient increases and the turbulence statistics, when scaled with wall units, are lower than in the plane channel. The momentum equation provides a scaling that collapses the cylinder statistics, and allows the results to be interpreted in light of the plane channel flow. The azimuthal and radial length scales of the structures in the flow are of the order of the cylinder diameter. Boomerang-shaped structures with large spanwise length scales were observed in the flow.

Numerical study of axial turbulent flow over long cylinders

: Large eddy simulations (LES) have been performed for two massively separated flows: a planar backward-facing step and a coaxial jet combustor. The backward-facing step case was used to develop and validate both the numerical method and the subgrid-scale model. Backward-facing step simulations were performed at Reynolds numbers 5100 and 28000. Both cases agree well with experimental data; the low Reynolds number case is also in excellent agreement with DNS data. Two versions of the dynamic subgrid-scale model as well as the classical Smagorinsky model were tested and little difference was found among them. The coaxial jet combustor simulations were used as a first step to study the flame stability problem known as lean blow-out. The study focused on the entrainment and mixing of fuel and air within the combustion chamber, using a passive scalar tracking technique. Chemical reactions and the effects of heat release were ignored in this initial study. Mean statistics at Reynolds number 38000 are in good agreement with experimental data. A motion picture of the unsteady motion revealed intermittent pockets of fuel-rich fluid crossing the annular air jet and becoming entrained in the recirculation zone. A larger source of entrainment, however, was found to be the upstream redirection of the fuel jet near the instantaneous impingement point on the combustor wall.

Large Eddy Simulation of Backward-Facing Stop Flow with Application to Coaxial Jet Combustors.

Large-eddy simulation is a promising technique for accurate prediction of reacting multiphase flows in practical gas-turbine combustion chambers involving complex physical phenomena of turbulent mixing and combustion dynamics. Development of advanced models for liquid fuel atomization, droplet evaporation, droplet deformation and drag, and turbulent combustion is discussed specifically for gas-turbine applications. The nondissipative, yet robust numerical scheme for arbitrary shaped unstructured grids developed by Mahesh et al. (Mahesh, K., Constantinescu, G., and Moin, P., "A New Time-Accurate Finite-Volume Fractional-Step Algorithm for Prediction of Turbulent Flows on Unstructured Hybrid Meshes," Journal of Computational Physics, Vol. 197, No. 1, 2004, pp. 215-240) is modified to account for density variations due to chemical reactions. A systematic validation and verification study of the individual spray models and the numerical scheme is performed in canonical and complex combustor geometries. Finally, a multiscale, multi physics, turbulent reacting flow simulation in a real gas-turbine combustor is performed to assess the predictive capability of the solver.

/pdf/large-eddy-simulation-of-realistic-gas-turbine-combustors-1d7wkqffhq.pdf

Parviz Moin

Papers

Large-eddy simulation and analysis of tip-clearance flows in turbomachinery applications

Dynamics of coherent structures in a plane mixing layer

Numerical study of axial turbulent flow over long cylinders

Large Eddy Simulation of Backward-Facing Stop Flow with Application to Coaxial Jet Combustors.

Large-Eddy Simulation of Realistic Gas Turbine Combustors