Subgrid Flux Research Articles

Prediction of finite chemistry effects using large eddy simulation

A large eddy simulation (LES) in three dimensions is applied to study flow, mixing, and combustion ina highly turbulent jet flame. Turbulence chemistry interactions, including finite rate chemistry effects, are investigated. The hydrogen fuel has been diluted with nitrogen to allow for both accurate numerical and accurate experimental investigation. In the numerical method, fluctuations of density in time and space are considered to depend only onthe chemical state, not on pressure. This low-Mach assumption greatly improves the efficiency of the code. Mixing and the effects of heat release are included by means of the mixture-fraction formulation. To model subgrid scale stresses and scalar fluxes, the Smagorinsky model is used since the dynamic Germano procedure did not show any particular advantage for this flame. To relate mixture fraction to density, temperature, and species concentrations, a steady flamelet model is used. To evaluate the performance of LES with steady flamelet chemistry, a comparison has been made to experimental data, as well as to the results of a probability density function simulation, with a five-step mechanism considering differential diffusion effects. This is done in terms of averaged quantities, scatter plots, and conditional averages. The LES results were found to be in good agreement with the existing data. For this stable flame, the influence of differential diffusion (inherent to hydrogen flames) seems to be negligible.

On the meridional circulation and balance of momentum in the Southern Ocean of POP

The circulation of the Southern Ocean is studied in the eddy-resolving model POP (Parallel Ocean Program) by an analysis of zonally integrated balances. The TEM formalism (Transformed Eulerian Mean) is extended to include topography and continental boundaries, thus deviations from a zonally integrated state involve transient and standing eddies. The meridional circulation is presented in terms of the Eulerian, eddy-induced, and residual streamfunctions. It is shown that the splitting of the meridional circulation into Ekman and geostrophic transports and the component induced by subgrid and Reynolds stresses is identical to a particular form of the zonally integrated balance of zonal momentum. In this balance, the eddy-induced streamfunctions represent the interfacial form stresses by transient and standing eddies and the residual streamfunction represents the acceleration of the zonal current by density fluxes in a zonally integrated frame. The latter acceleration term is directly related to the surface flux of density and interior fluxes due to the resolved and unresolved eddies. The eddy-induced circulation is extremely vigorous in POP. In the upper ocean a shallow circulation, reversed in comparison to the Deacon cell and mainly due to standing eddies, appears to the north of Drake Passage latitudes, and in the Drake Passage belt of latitudes a deep-reaching cell is induced by transient eddies. In the resulting residual circulation the Deacon cell is largely cancelled and the residual advection of the zonal mean potential density is balanced by diapycnal eddy and subgrid fluxes which are strong in the upper few hundred meters but small in the ocean interior. The balance of zonal momentum is consistent with other eddy-resolving models; a new aspect is the clear identification of density effects in the zonally integrated balance. We show that the wind stress and the stress induced by the residual circulation drive the eastward current, whereas both eddy species result in a braking. Finally, we extend the Johnson–Bryden model of zonal transport to incorporate all relevant terms from the zonal momentum balance. It is shown that wind stress and induction by the residual circulation carry an eastward transport while bottom form stress and the stress induced by standing eddies yield westward components of transport.

Optimal two-dimensional models for wake flows

In the case of nominally two-dimensional (2D) cylinders of arbitrary cross section in cross flow, the three-dimensionality of the wake manifests in the form of quasi-streamwise vortices. These three-dimensional (3D) features profoundly influence lift and drag forces. However, a two-dimensional projection of such a flow, where the effects of three-dimensionality are modeled, will be computationally very attractive. One can consider the two-dimensional projection as the limiting case of large eddy simulation, where the spanwise direction has been completely averaged out. The transport equation for the span-averaged spanwise component of vorticity, ω̄z, is considered; the 3D effects to be modeled appear as a subgrid scale flux of torque. It is shown that simple minded eddy viscosity type models that assume the flux vector to be proportional to the spatial gradient of ω̄z are inadequate. Here we extend the optimal modeling formalism [Moser, Balachandar, and Adrian, Turbulence and Internal Flow/Unsteady Aerodynamics and Hypersonics Conference, Annapolis, MD, pp. 269–274 (1998); Langford and Moser, J. Fluid Mech. 398, 321 (1999)] to address issues pertaining to complex flows with multiple directions of inhomogeneity. We present optimal closures for subgrid flux modeled in terms of ω̄z distribution, based on linear and quadratic stochastic approximations. These ideas are tested using the database of flow over a flat plate held normal to a cross flow. It is observed that even the optimal model has about 70% normalized error, indicating that the subgrid flux is only about 30% deterministic. Furthermore, it is observed that local models are inadequate, but there exists a region of nonlocality for model dependence, expanding beyond which does not improve the estimate. Higher order nonlinearities however do not seem to improve the model’s predictability.

Extension du modèle d'échelles mixtes à la diffusivité de sous-maille

In the large-eddy simulation frame for non-isothermal turbulent flow, the Mixed Scale Model is extended to the subgrid diffusivity, in order to dissociate the computation of subgrid viscosity and diffusivity. The identification of the subgrid thermal dissipation term in the subgrid flux transport equation leads to an algebraic expression of the subgrid diffusivity. This diffusive model, as the Smagorinsky one, is weighted by a model based on scale similarity. This expression leads to satisfactory results when applied to a buoyant turbulent flow in a differentially heated cavity.

A vortex-based model for the subgrid flux of a passive scalar

A model for the flux of a passive scalar by the subgrid motions in the large-eddy simulation of turbulent flow is proposed within the framework of the stretched-vortex subgrid stress model. The model is based on an analytical solution for the winding of a scalar field by an elemental subgrid vortex. This gives a tensor gradient-diffusion expression for the local flux of the scalar with subgrid turbulent diffusivity which depends upon the subgrid energy, the local cell size, and the vortex orientation in space. The scalar-flux subgrid model is tested by comparison of the results of 323 large-eddy simulation of passive-scalar transport by forced isotropic turbulence in the presence of a mean scalar gradient, with the direct-numerical simulation results of Overholt and Pope [Phys. Fluids 8, 2128 (1996)]. The present large-eddy simulation results predict that at large Taylor–Reynolds numbers, the ratio of the scalar variance to the squared product of the scalar gradient with the dissipation length of the turbulence, is asymptotic to a nearly constant value c′2/(α1 Lε)2≈0.36.

Subgrid Surface Fluxes in Fair Weather Conditions during TOGA COARE: Observational Estimates and Parameterization

Abstract Bulk aerodynamic formulas are applied to meteorological data from low-altitude aircraft flights to obtain observational estimates of the subgrid enhancement of momentum, sensible heat, and latent heat exchange at the atmospheric–oceanic boundary in light wind, fair weather conditions during TOGA COARE (Tropical Ocean Global Atmosphere Coupled Ocean–Atmosphere Response Experiment). Here, subgrid enhancement refers to the contributions of unresolved disturbances to the grid-box average fluxes at the lower boundary of an atmospheric general circulation model. The observed subgrid fluxes increase with grid-box area, reaching 11%, 9%, 24%, and 12% of the total sensible heat, latent heat, scalar wind stress, and vector wind stress magnitude, respectively, at a grid-box size of 2° × 2° longitude and latitude. Consistent with previous observational and modeling studies over the open ocean, most of the subgrid flux is explained by unresolved directional variability in the near-surface wind field. The auth...

Large-eddy simulation of high-Schmidt number mass transfer in a turbulent channel flow

Mass transfer through the solid boundary of a turbulent channel flow is analyzed by means of large-eddy simulation (LES) for Schmidt numbers Sc=1, 100, and 200. For that purpose the subgrid stresses and fluxes are closed using the Dynamic Mixed Model proposed by Zang et al. [Phys. Fluids A 5, 3186 (1993)]. At each Schmidt number the mass transfer coefficient given by the LES is found to be in very good quantitative agreement with that measured in the experiments. At high Schmidt number this coefficient behaves like Sc−2/3, as predicted by standard theory and observed in most experiments. The main statistical characteristics of the fluctuating concentration field are analyzed in connection with the well-documented statistics of the turbulent motions. It is observed that concentration fluctuations have a significant intensity throughout the channel at Sc=1 while they are negligible out of the wall region at Sc=200. The maximum intensity of these fluctuations depends on both the Schmidt and Reynolds numbers and is especially influenced by the intensity of the velocity fluctuations present in the buffer layer of the concentration field. At Sc=1, strong similarities are observed between the various terms contributing to the turbulent kinetic energy budget and their counterpart in the budget of the variance of concentration fluctuations. At high Schmidt number, the latter budget is much more influenced by the small turbulent structures subsisting in the viscous sublayer. The instantaneous correlation between the spatial characteristics of the concentration field and those of the velocity field is clearly demonstrated by the presence of low- and high-concentration streaks close to the wall. The geometrical characteristics of these structures are found to be highly Sc dependent. In particular their spanwise wavelength is identical to that of the streamwise velocity streaks at Sc=1 while it is reduced by half at Sc=200. Analysis of the co-spectra between concentration and normal velocity fluctuations emphasizes the fact that the large-scale structures play an essential role in the turbulent mass transfer process at high Schmidt number. Overall the picture that emerges from this investigation fully confirms the conclusions of Campbell and Hanratty [AIChE J. 29, 221 (1983)]: high-Schmidt-number mass transfer at a solid wall is governed by the low-frequency part of the normal velocity fluctuation gradient at the wall, i.e., by the large-scale structures observed in planes parallel to the wall in the viscous sublayer.

Large eddy simulation of reacting flows applied to bluff body stabilized flames

The objective of this paper is to present a large eddy simulation model for chemically reacting flows. The large eddy simulation model, founded on a physical model based on modern continuum mechanics, includes a complete treatment of the subgrid stresses and fluxes including both backscatter and diffusion. To investigate the predictive capabilities of the large eddy simulation model, numerical simulations of a configuration corresponding to a rig consisting of a rectilinear channel with a triangular-shaped bluff body have been performed. Both nonreacting and reacting flows have been examined under a variety of operating conditions. This paper focuses on the reacting case, which is characterized as lean and premixed. The simulation results are compared to experimental measurements of temperature, constituent mass fraction, and velocity fields in the test rig. The results indicate that the large eddy simulation technique works well and mimics most of the significant flow features, including the typical unsteady flow structures. The results from the large eddy simulations are furthermore used to investigate the mechanisms responsible for the typical flowfield in a bluff body stabilized flame.

Large-eddy simulations of bluff body stabilized flames

The objective of this paper is to extend a previously developed large-eddy simulation (LES) model, originally developed for anisochoric high-Reynolds-(Re-) number flows, to include chemically reacting flows as well. The LES model, developed from a physical model founded on modern continuum-mechanical mixture theories, includes a complete treatment of the subgrid stresses and fluxes. Different multistep global reaction schemes have been adopted along with a combustion model that considers the influence of subgrid effects on the effective chemical reaction rates. In order to study the predictive capabilities of this LES model, numerical simulations of the flow behind a two-dimensional generic bluff body in a straight channel have been undertaken, and results are compared with measurements from experimental investigations. In the simulations of reacting flow situations, the fuel was propane, and premixed conditions were enforced. The measurements were done with nonintrusive methods such as the 2λ-CARS technique, giving temperature probability density functions (pdfs) and profiles, as well as traditional gas analysis, giving temperature profiles. Comparison of simulated and measured temperature pdfs and profiles indicates that the LES technique works well for unsteady premixed flows, and it mimics most of the significant flow features, including typical unsteady flow structures and the flame-front dynamics.

A simplified hydrodynamic mesoscale model suitable for use over high plateau regions

A simplified hydrodynamic primitive equation model in σ-coordinates is described. This model includes the main physical processes that influence development and motion of mesoscale vortices over plateau regions: elevated terrain effects, effects of large-scale and synoptic-scale systems on the mesoscale systems, sensible heating from the earth's surface, moisture cycle and condensation heating released by both large-scale stable precipitation and cumulus convective precipitation, evaporation and the feedback effect of precipitation on evaporation, friction in the planetary boundary layer, horizontal diffusion by subgrid scale eddies and vertical eddy flux of meteorological elements (momentum, temperature, moisture, etc.) due to turbulence, cumulus convection and other smaller-scale physical processes. The model incorporates observed data as much as possible and equations are simplified so that it may be run using either a high-speed computer or a desktop computer.

The Use of Subgrid Transport Equations in a Three-Dimensional Model of Atmospheric Turbulence

A three-dimensional numerical model of turbulence in an atmospheric boundary layer has been revised to utilize subgrid transport equations for the subgrid Reynolds stresses and fluxes rather than subgrid eddy coefficients. It was applied to a daytime boundary layer over heated ground in a region of horizontal area 8km square and 2km deep, utilizing 40×40×40 grid points. The constraints involved in selecting four important subgrid closure constants are discussed in some detail, along with maintenance of realizability on the subgrid scale. The results indicate that the subgrid transport equations produce subgrid Reynolds stresses and fluxes which realistically simulate the transfer of larger scale variance to subgrid scales, provided truncation errors due to advective terms are not too large. They also show the superiority of this method over the use of (nonstability dependent) nonlinear eddy coefficients in maintaining the sharpness of the inversion base which lies above the mixed layer.