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

/pdf/development-of-a-turbulent-boundary-layer-beneath-finite-2qvrceeegu.pdf

Development of a turbulent boundary layer beneath finite-amplitude continuous freestream turbulence

: The interaction of a shock wave with a turbulent boundary layer is a central problem in supersonic inlet flows. This work uses numerical and analytical techniques to study shock/turbulence interaction in order to identify and explain factors important in shock/boundary layer interaction. Direct numerical simulation of a normal shock wave with an isotropic turbulent field of vorticity and entropy fluctuations showed that negative upstream correlation between the vorticity and entropy fluctuations enhances the turbulence across the shock. Positive upstream correlation has a suppressing effect. A new numerical method providing excellent high wavenumber resolution while reducing the computational cost was developed. A model with no adjustable constants was developed to study the vortex breakdown resulting from the interaction of canard or forbody vortices with the shock waves in a supersonic inlet flow. Very good agreement with both experiment and computation was obtained. A numerical method to compute shock/turbulence interaction using a conservative form of the Large Eddy Simulation (LES) equations has been developed and validated. LES of the interaction of isotropic turbulence with a normal shock was performed and comparisons with direct numerical simulation (DNS) results were favorable. A new Fortran 90 code has been developed for the computation of shock/turbulence interaction. The code is an improved version of codes used previously in shock/turbulence interaction simulations.

Large Eddy Simulation of Supersonic Inlet Flows

We investigate the performance of wall-modeled LES for external aerodynamics in the NASA Juncture Flow. We characterize the errors in the prediction of mean velocity profiles and pressure coefficient for three different locations over the aircraft: the upstream region of the fuselage, the wing-body juncture, and the wing-body juncture close to the trailing-edge. The last two locations are characterized by strong mean-flow three-dimensionality and separation. The message conveyed by our error analysis is that WMLES performs as expected in regions where the flow resembles a zero-pressure-gradient flat plate boundary layer. However, there is a clear decline of the current models in the presence of wing-body junctions and, more acutely, in separated zones. The slow convergence to the solution in these regions renders the brute-force grid-refinement approach to improve the accuracy of the solution unfeasible. The results reported above pertain to the mean velocity profile predicted using the typical grid resolution for external aerodynamics applications, i.e., 5--20 points per boundary-layer thickness. The prediction of the pressure coefficient is below 5\% error for all grid sizes considered, even when boundary layers were marginally resolved. The latter accuracy can be attributed to the outer-layer nature of the mean pressure, which becomes less sensitive to flow details within the turbulent boundary layer. Finally, we show that boundary-layer-conforming grids (i.e., grids maintaining a constant number of points per boundary-layer thickness) allow for a more efficient distribution of grid points and smaller errors. Our results suggest that novel modeling venues encompassing physical insights, together with numerical and gridding advancements, must be exploited to attain predictions within the tolerance required for Certification by Analysis.

Parviz Moin

Papers

Development of a turbulent boundary layer beneath finite-amplitude continuous freestream turbulence

Large Eddy Simulation of Supersonic Inlet Flows

Performance of wall-modeled LES for external aerodynamics in the NASA Juncture Flow

Optimal and robust control and estimation of transition and turbulence.

Computational Study of Aero-Optical Distortion by Turbulent Wake