A-priori testing of an eddy viscosity model for the density-weighted subgrid scale stress tensor in turbulent premixed flames

In this study, the behaviours of subgrid-scale (SGS) turbulence are investigated with direct numerical simulations when an isotropic turbulence is brought to interact with imposed rapid waves. A partition of the velocity field is used to decompose the SGS stress into three parts, namely, the turbulent part $\unicode[STIX]{x1D749}^{T}$, the wave-induced part $\unicode[STIX]{x1D749}^{W}$ and the cross-interaction part $\unicode[STIX]{x1D749}^{C}$. Under strong wave straining, $\unicode[STIX]{x1D749}^{T}$ is found to follow the Kolmogorov scaling $\unicode[STIX]{x1D6E5}_{c}^{2/3}$, where $\unicode[STIX]{x1D6E5}_{c}$ is the filter width. Based on the linear Airy wave theory, $\unicode[STIX]{x1D749}^{W}$ and the filtered strain-rate tensor due to the wave motion, $\tilde{\unicode[STIX]{x1D64E}}^{W}$, are found to have different phases, posing a difficulty in applying the usual eddy-viscosity model. On the other hand, $\unicode[STIX]{x1D749}^{T}$ and the filtered strain-rate tensor due to the turbulent motion, $\tilde{\unicode[STIX]{x1D64E}}^{T}$, are only weakly wave-phase-dependent and could be well related by an eddy-viscosity model. The linear wave theory is also used to describe the vertical distributions of SGS statistics driven by the wave-induced motion. The predictions are in good agreement with the direct numerical simulation results. The budget equation for the turbulent SGS kinetic energy shows that the transport terms related to turbulence are important near the free surface and they compensate the imbalance between the energy flux and the SGS energy dissipation.

Download Full-text

A Priori Direct Numerical Simulation Modeling of Scalar Dissipation Rate Transport in Head-On Quenching of Turbulent Premixed Flames

Combustion Science and Technology ◽

10.1080/00102202.2016.1195823 ◽

2016 ◽

Vol 188 (9) ◽

pp. 1440-1471 ◽

Cited By ~ 11

Author(s):

Jiawei Lai ◽

Nilanjan Chakraborty

Keyword(s):

Numerical Simulation ◽

Direct Numerical Simulation ◽

Simulation Modeling ◽

Dissipation Rate ◽

A Priori ◽

Premixed Flames ◽

Scalar Dissipation ◽

Scalar Dissipation Rate ◽

Turbulent Premixed Flames ◽

Turbulent Premixed

Download Full-text

On the properties of similarity subgrid-scale models as deduced from measurements in a turbulent jet

Journal of Fluid Mechanics ◽

10.1017/s0022112094002296 ◽

1994 ◽

Vol 275 ◽

pp. 83-119 ◽

Cited By ~ 465

Author(s):

Shewen Liu ◽

Charles Meneveau ◽

Joseph Katz

Keyword(s):

Stress Tensor ◽

Eddy Viscosity ◽

Weighting Function ◽

A Priori ◽

Scale Model ◽

Solid Boundary ◽

Strain Rate Tensor ◽

Subgrid Scale ◽

The Real ◽

Subgrid Scale Model

The properties of turbulence subgrid-scale stresses are studied using experimental data in the far field of a round jet, at a Reynolds number of Rλ ≈ 310. Measurements are performed using two-dimensional particle displacement velocimetry. Three elements of the subgrid-scale stress tensor are calculated using planar filtering of the data. Using a priori testing, eddy-viscosity closures are shown to display very little correlation with the real stresses, in accord with earlier findings based on direct numerical simulations at lower Reynolds numbers. Detailed analysis of subgrid energy fluxes and of the velocity field decomposed into logarithmic bands leads to a new similarity subgrid-scale model. It is based on the ‘resolved stress’ tensor Lij, which is obtained by filtering products of resolved velocities at a scale equal to twice the grid scale. The correlation coefficient of this model with the real stress is shown to be substantially higher than that of the eddy-viscosity closures. It is shown that mixed models display similar levels of correlation. During the a priori test, care is taken to only employ resolved data in a fashion that is consistent with the information that would be available during large-eddy simulation. The influence of the filter shape on the correlation is documented in detail, and the model is compared to the original similarity model of Bardina et al. (1980). A relationship between Lij and a nonlinear subgrid-scale model is established. In order to control the amount of kinetic energy backscatter, which could potentially lead to numerical instability, an ad hoc weighting function that depends on the alignment between Lij and the strain-rate tensor, is introduced. A ‘dynamic’ version of the model is shown, based on the data, to allow a self-consistent determination of the coefficient. In addition, all tensor elements of the model are shown to display the correct scaling with normal distance near a solid boundary.

Download Full-text

Application of a Dynamic Global-Coefficient Subgrid-Scale Model for Large-Eddy Simulation in Complex Geometries

Volume 1: Symposia, Parts A and B ◽

10.1115/fedsm2007-37486 ◽

2007 ◽

Cited By ~ 1

Author(s):

Donghyun You ◽

Parviz Moin

Keyword(s):

Large Eddy Simulation ◽

Eddy Viscosity ◽

Viscosity Model ◽

Scale Model ◽

Complex Geometries ◽

Subgrid Scale ◽

Eddy Simulation ◽

Eddy Viscosity Model ◽

Large Eddy ◽

Model Coefficient

The application of a dynamic global-coefficient subgrid-scale eddy-viscosity model for large-eddy simulation in complex geometries is presented. The model employs a dynamic procedure for closure of the subgrid-scale eddy-viscosity model developed by Vreman [Phys. Fluids 16, 3670 (2004)]. The model coefficient which is globally constant in space but varies in time is dynamically determined assuming the “global equilibrium” between the subgrid-scale dissipation and the viscous dissipation of which utilization was proposed by Park et al. [Phys. Fluids 18, 125109 (2006)]. Like the Vreman’s model with a fixed coefficient and the dynamic-coefficient model of Park et al., the present model predicts zero eddy-viscosity in regions where the vanishing eddy viscosity is theoretically expected. The present dynamic model is especially suitable for large-eddy simulation in complex geometries since it does not require any ad hoc spatial and temporal averaging or clipping of the model coefficient for numerical stabilization and requires only a single-level test filter.

Download Full-text