Channel flow with friction Reynolds number Reτ as high as 80 000 is treated by large-eddy simulation at a moderate cost, using the subgrid-scale model designed for detached-eddy simulations. It includes wall modeling, and was not adjusted for this flow. The grid count scales with the logarithm of the Reynolds number. Three independent codes are in fair agreement with each other. Reynolds-number variations and grid refinement cause trades between viscous, modeled, and resolved shear stresses. The skin-friction coefficient is too low, on the order of 15%. The velocity profiles contain a “modeled” logarithmic layer near the wall and some suggest a “resolved” logarithmic layer farther up, but the two layers have a mismatch of several units in U+.

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Abstract-In this paper we present numerical techniques suitable for a direct numerical simulation in the spatial setting. We demonstrate the application to the simulation of compressible flat plate flow instabilities. We compare second and fourth order accurate spatial discretization schemes in combination with explicit multistage time stepping for the simulation of the 2D Navier-Stokes equations. We consider Mach numbers 0.5 and 4.5. In the vicinity of the outflow boundary, an efficient buffer domain treatment is introduced, which is suitable in conjunction with an explicit time integration scheme. This treatment requires only a short buffer domain to damp wave reflections at the outflow boundary. Results for the instability of Tollmien-Schlichting (T-S) waves are compared with two instability theories, linear stability theory (LST) and linear parabolized stability equations (PSE). The growth rates of T-S waves for parallel base flow at both Mach numbeis compare well with LST results. Moreover, the growth rates of T-S waves for nonparallel base flow compare well with results obtained by solving the PSE at Mach number 0.5. The second order discretization scheme requires, however, considerably higher grid resolution than the fourth order method to achieve accurate results. High amplitude disturbances were also considered to activate nonlinear terms. The nonlinearity strongly affects the form of the T-S waves and the growth rate of the disturbance:. The results obtained here support the use of these numerical techniques in flow simulations with increasing complexity such as flat plate flow simulations up to the turbulent regime and with separation regions in 3D. The results also encourage the use of perturbations derived from the compressible PSE as inlet perturbations for nonparallel flow. 0 1997

This paper introduces a new approach to Large-Eddy Simulation (LES) where subgrid-scale (SGS) dissipation is applied proportionally to the degree of local spectral broadening, hence mitigated or deactivated in regions dominated by large-scale and/or laminar vortical motion. The proposed coherentvorticity preserving (CvP) LES methodology is based on the evaluation of the ratio of the test-filtered to resolved (or grid-filtered) enstrophy, σ. Values of σ close to 1 indicate low sub-test-filter turbulent activity, justifying local deactivation of the SGS dissipation. The intensity of the SGS dissipation is progressively increased for σ < 1 which corresponds to a small-scale spectral broadening. The SGS dissipation is then fully activated in developed turbulence characterized by σ ≤ σ eq , where the value σ eq is derived assuming a Kolmogorov spectrum. The proposed approach can be applied to any eddy-viscosity model, is algorithmically simple and computationally inexpensive. LES of Taylor-Green vortex breakdown demonstrates that the CvP methodology improves the performance of traditional, non-dynamic dissipative SGS models, capturing the peak of total turbulent kinetic energy dissipation during transition. Similar accuracy is obtained by adopting Germano's dynamic procedure albeit at more than twice the computational overhead. A CvP-LES of a pair of unstable periodic helical vortices is shown to predict accurately the experimentally observed growth rate using coarse resolutions.The ability of the CvP methodology to dynamically sort the coherent, large-scale motion from the smaller, broadband scales during transition is demonstrated via flow visualizations. Finally, the CvP methodology is also shown to improve the accuracy of subrid models in LES of compressible turbulent channel flow.

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This paper investigates the transient regime and turbulent wake characteristics of temporally developing double helical vortices via high-fidelity large-eddy simulation (LES) for circulation Reynolds numbers in the range $Re_{\unicode[STIX]{x1D6E4}}=7000{-}70\,000$, vortex-core radii between $r_{c}=0.06R$ and $0.2R$ and helical pitches in the range $h=0.36R{-}0.61R$, where $R$ is the initial helix radius. The present study achieves three objectives: (i) assess the influence of $Re_{\unicode[STIX]{x1D6E4}}$, $r_{c}$ and $h$ on the growth rates of the helical vortex instability driven by mutual inductance; (ii) characterize the type of vortex reconnection events that appear during transition; (iii) study the characteristics of turbulence in the far wake, and in particular quantify the anisotropy in the flow. The initial transient dynamics is conveniently described in terms of the non-dimensional time $t^{\star }=t\unicode[STIX]{x1D6E4}/h^{2}$, yielding the dimensionless growth rate of $\unicode[STIX]{x1D6FC}^{\ast }\sim 20$ and collapsing of all the LES data for a given $r_{c}/h$ ratio. The vortex-core displacement growth rate is found to be Reynolds-number independent, and decreases for larger $r_{c}/h$ ratios. Several vortex reconnection events are identified during the transition, mostly initiated by the leap frogging of helical vortices. This phenomenon causes the entanglement of orthogonal vortex filaments, leading to their separation, followed by the creation of elongated threads in the axial direction. The turbulent wake generated by the breakdown of the helical vortices is found to be highly anisotropic with the axial fluctuations being dominant compared to the radial and azimuthal fluctuations (near one-dimensional turbulence). The study of integral length scales shows the presence of a strong large-scale anisotropy, retaining the memory of the initial helical pitch $h$, in particular for the integral scale in the axial direction. The large-scale anisotropy is propagated through the inertial and dissipative ranges, determined from the computation of the moments of velocity gradients in the three directions.