Nonlinear Large Eddy Simulation Research Articles

Large-Eddy Simulation of High-Speed Vaporizing Liquid-Fuel Spray Using Mixed Gradient-Type Structural Subgrid-Scale Model

ABSTRACT The accuracy of the large-eddy simulation (LES) of high-speed vaporizing sprays is highly dependent on the choice of subgrid-scale (SGS) models. This study adopts a nonlinear SGS stress model to simulate a well-known high-speed non-reacting vaporizing liquid-fuel spray case, Spray A. An advantage of using the nonlinear structural SGS model is that it can provide reverse energy transfer from small to large scales, and thus, the model can be more accurate than traditional eddy-viscosity models at capturing cross-scale interactions between turbulence and spray. Also, the adopted gradient-type approach is very computationally efficient. To understand the performance of the nonlinear LES framework, this study presents comprehensive comparisons against experimental data and results obtained using the Smagorinsky model and the sub-grid kinetic energy model. In particular, we compare the general structure of the flows, liquid and vapor penetrations, and mass fraction profiles. Results using the nonlinear structural SGS stress model show minimal dependence on the grid size regarding the capture of flow structures. Using the same mesh resolution, the statistics of the simulated field exhibit both good agreement with measurements and a significant improvement over simulations based on the other two types of models. Results support the assertion that the proposed nonlinear LES framework can accurately achieve direct injection simulations with reasonable computational costs.

Large-eddy simulation of Sandia Flame F using structural subgrid-scale models and partially-stirred-reactor approach

Owing to the strong interaction between turbulence and combustion, it is particularly challenging to accurately predict local flame extinctions in a turbulent flame at high Reynolds numbers. Subgrid-scale (SGS) parameterization and model for calculating the filtered reaction rates are the main determinants of an accurate large-eddy simulation (LES) of turbulent flow. This study integrates the recently introduced gradient-type structural SGS models with a simplified partially-stirred-reactor approach to simulate a piloted partially premixed jet flame, Sandia Flame F. An advantage of using the nonlinear SGS models is that they can provide reverse energy transfer from subgrid to resolved scales. To quantitatively understand the performance of the LES framework, we have comprehensively compared temperature and mass fractions of major and minor species with experimental data. The statistics of the simulated field show good agreement with measurements and a notable improvement over previous simulations. Results support the assertion that the proposed nonlinear LES framework can capture extinction and re-ignition in turbulent flames with reasonable computational cost.

Large-eddy simulation of MILD combustion using partially stirred reactor approach

Subgrid-scale (SGS) parameterization and method for calculating filtered reaction rate are critical components of an accurate large-eddy simulation (LES) of turbulent flames. In this study, we integrate gradient-type structural SGS models with a partially stirred reactor approach by using detailed chemical kinetics to simulate a turbulent methane/hydrogen jet flame under moderate or intense low-oxygen dilution (MILD) conditions. The study examines two oxygen dilution levels. The framework is assessed through a systematic and comprehensive comparison of temperature, and mass fractions of major and minor species with experimental data and other reference simulation results. Overall, the statistics of the combustion field show excellent agreement with measurements at different axial locations, and a significant improvement compared to some previous simulations. It suggests that the proposed nonlinear LES framework is able to accurately model MILD combustion with reasonable computational cost.

Publisher’s note: “Study of ultrahigh Atwood-number Rayleigh–Taylor mixing dynamics using the nonlinear large-eddy simulation method” [Phys. Fluids 23, 045106 (2011)

Publisher’s note: “Study of ultrahigh Atwood-number Rayleigh–Taylor mixing dynamics using the nonlinear large-eddy simulation method” [Phys. Fluids 23, 045106 (2011)

LES of heat transfer in electronics

Numerical methods based on the Reynolds Averaged Navier–Stokes (RANS) and Large Eddy Simulation (LES) equations are applied to the thermal prediction of flows representative of those found in and around electronics systems and components. Low Reynolds number flows through a heated ribbed channel, around a heated cube and within a complex electronics system case are investigated using linear and nonlinear LES models, hybrid RANS–LES and RANS–Numerical-LES (RANS–NLES) methods. Flow and heat transfer predictions using these techniques are in good agreement with each other and experimental data for a range of grid resolutions. Using second order central differences, the RANS–NLES method performs well for all simulations.

Study of ultrahigh Atwood-number Rayleigh–Taylor mixing dynamics using the nonlinear large-eddy simulation method

The Nonlinear Large-Eddy Simulation (nLES) method [G. C. Burton, “The nonlinear large-eddy simulation method (nLES) applied to Sc≈1 and Sc⪢1 passive-scalar mixing,” Phys. Fluids 20, 035103 (2008)] is employed in the first numerical study of multimode miscible Rayleigh–Taylor instability (RTI) in the ultrahigh Atwood-number regime above A≥0.90. The present work focuses on the dynamics of turbulent mixing at the large density ratios that may be encountered in certain astrophysical contexts and engineering applications. Using the initial condition from the landmark (N=30723) direct numerical study of Cabot and Cook [W. Cabot and A. W. Cook, “Reynolds number effects on Rayleigh-Taylor instability with possible implications for type-Ia supernovae,” Nat. Phys. 2, 562 (2006)], the nLES method is first validated in simulations of A=0.5 RTI mixing and is shown to recover important statistical measures of the mixing process, such as bubble and spike growth rates and mixing efficiency reported in that study, but at the significantly coarser resolutions typical of most large-eddy simulations. The first simulations of RTI at Atwood numbers A>0.90 are then used to explore the effects of varying the density ratio on mixing dynamics at very high Atwood numbers 0.75≤A≤0.96. Spike heights and mixing layer growth rates are shown to be strongly affected by the initial density ratio. An empirical power-law scaling relationship is shown to predict nearly exactly the variation in the ratio of spike to bubble heights as a function of Atwood number. Mixing efficiency is shown to be influenced by the initial density difference but the competition between increased molecular mixing and entrainment largely cancel, producing a relatively modest variation in these flow parameters when compared with the intermediate Atwood-number case. Late-time power spectra show the appearance of an inertial range, indicating that the mixing layer has transitioned to a fully turbulent state. The role of bubble and spike structures in the interscale transfer of kinetic energy is explored for the first time for high Atwood-number RTI flows. Bubble heads (stems) are shown to produce forward (reverse) transfer due to compressive (extensional) straining at intermediate Atwood number. At high Atwood number, however, spike stems are shown to produce forward transfer due to compressive straining generated from the larger spike penetration velocity and the differing spike morphology produced at the higher Atwood number. The study indicates that stable and accurate simulations of ultrahigh Atwood-number mixing may be conducted using the nLES method on grids significantly coarser than used previously to examine RTI flows.

Scalar-energy spectra in simulations of Sc⪢1 mixing by turbulent jets using the nonlinear large-eddy simulation method

The nonlinear large-eddy simulation (nLES) method is applied to the first numerical study of passive-scalar mixing by a turbulent shear flow at a high Schmidt number (Sc⪢1). The work is intended to address inconsistencies between previous studies concerning the formation of power-law scaling in the scalar-energy spectra at viscous-convective scales. Results are reported for LES of a round turbulent jet at Sc=1024 and ReD=2000. The nLES method is first shown to recover the large-scale jet structure, including the self-similarity of far-field scalar moments. Scalar timeseries and spatial data produce the first power spectra from a LES shear-flow study that exhibits k−1 scaling at viscous-convective scales, consistent with the analysis of Batchelor [J. Fluid Mech. 5, 113 (1959)] and recent direct numerical studies of simpler Sc⪢1 flows.

The nonlinear large-eddy simulation method applied to Sc≈1 and Sc⪢1 passive-scalar mixing

The nonlinear large-eddy simulation (nLES) method is extended here to simulations of Sc≈1 and Sc⪢1 turbulent mixing of passive-scalar fields. These are the first LES studies to reproduce the instantaneous structure of the scalar-energy field ϕ¯2(x,t) at viscous-convective scales in the high Schmidt-number regime. The simulations employ a refinement of the nLES method with multifractal modeling first proposed by G. C. Burton and W. J. A. Dahm [Phys. Fluids 17, 075111 (2005)]. In this approach, the nonlinear inertial stresses uiuj¯ in the filtered Navier–Stokes equation and the nonlinear scalar fluxes ujϕ¯ in the filtered advection-diffusion equation are calculated directly, using multifractal models for the subgrid velocity and scalar fields, ujsgs and ϕsgs. Resolved energy levels are controlled by a new adaptive backscatter limiter that adjusts locally to changing flow conditions consistent with the mechanism governing energy transfer in actual hydrodynamic turbulence. No artificial viscosity or diffusivity closures are applied and no explicit de-aliasing is performed. The nLES approach is shown to simulate accurately Sc≈1 mixing for flows between Reλ≈35 and 4100, the highest Reλ tested. Characteristics of the resulting scalar field are examined, including the turbulence-to-scalar time-scale ratio and total scalar variance ⟨ϕ′2⟩, indicating good agreement with prior studies. Simulations between Sc=8 and 8192 produce the first scalar-energy spectra from an LES that exhibit k−1 scaling in the viscous-convective range, consistent with the analytical prediction of G. K. Batchelor [J. Fluid Mech. 5, 113 (1959)]. The simulations indicate decreasing scalar anisotropy and increasing intermittency with increasing Schmidt number, also consistent with prior studies.

Unified turbulence models for LES and RANS, FDF and PDF simulations

A review of existing basic turbulence modeling approaches reveals the need for the development of unified turbulence models which can be used continuously as filter density function (FDF) or probability density function (PDF) methods, large eddy simulation (LES) or Reynolds-averaged Navier–Stokes (RANS) methods. It is then shown that such unified stochastic and deterministic turbulence models can be constructed by explaining the dependence of the characteristic time scale of velocity fluctuations on the scale considered. The unified stochastic model obtained generalizes usually applied FDF and PDF models. The unified deterministic turbulence model that is implied by the stochastic model recovers and extends well-known linear and nonlinear LES and RANS models for the subgrid-scale and Reynolds stress tensor.