Subgrid-scale Fluxes Research Articles

Convection in Lorenz’s global energy cycle with the ECMWF model

Lorenz’s global energy cycle includes the conversion rate C between available potential and kinetic energy. In traditional estimates of C only gridscale processes were evaluated; subgridscale processes were lumped into dissipation. It is argued that this is inadequate; organized subgridscale heat fluxes like deep convection cannot be treated as molecular.Here both Cgrid and Csub are evaluated from the ECMWF Integrated Forecast System, for a 1-yr forecast in climate mode. The subgridscale fluxes are obtained from the model parametrization and the results tested for consistency; the largest contribution comes from the convection scheme. The integrand of Csub, the familiar ‘buoyancy flux’ −α′ω′¯ is locally much smaller than its gridscale counterpart −α′¯ω′¯. However, the buoyancy flux is upward throughout, and thus representative for, the global atmosphere. The global annual means are Cgrid = (3.4 ± 0.1)Wm−2 and Csub = (1.7 ± 0.1)Wm−2. Further, the gridscale generation rate of available potential energy is evaluated independently and found to be Ggrid = (3.0 ± 0.2)Wm−2.These results suggest that (i) the subgridscale processes contribute significantly to the Lorenz energy cycle and (ii) the cycle, represented by the total dissipation of D = (5.1 ± 0.2)Wm−2, is more intense than all earlier gridscale estimates have indicated.

Modelling of subgrid-scale phenomena in supercritical transitional mixing layers: an a priori study

A database of transitional direct numerical simulation (DNS) realizations of a supercritical mixing layer is analysed for understanding small-scale behaviour and examining subgrid-scale (SGS) models duplicating that behaviour. Initially, the mixing layer contains a single chemical species in each of the two streams, and a perturbation promotes roll-up and a double pairing of the four spanwise vortices initially present. The database encompasses three combinations of chemical species, several perturbation wavelengths and amplitudes, and several initial Reynolds numbers specifically chosen for the sole purpose of achieving transition. The DNS equations are the Navier-Stokes, total energy and species equations coupled to a real-gas equation of state; the fluxes of species and heat include the Soret and Dufour effects. The large-eddy simulation (LES) equations are derived from the DNS ones through filtering. Compared to the DNS equations, two types of additional terms are identified in the LES equations: SGS fluxes and other terms for which either assumptions or models are necessary. The magnitude of all terms in the LES conservation equations is analysed on the DNS database, with special attention to terms that could possibly be neglected. It is shown that in contrast to atmospheric-pressure gaseous flows, there are two new terms that must be modelled: one in each of the momentum and the energy equations. These new terms can be thought to result from the filtering of the nonlinear equation of state, and are associated with regions of high density-gradient magnitude both found in DNS and observed experimentally in fully turbulent high-pressure flows. A model is derived for the momentum-equation additional term that performs well at small filter size but deteriorates as the filter size increases, highlighting the necessity of ensuring appropriate grid resolution in LES. Modelling approaches for the energy-equation additional term are proposed, all of which may be too computationally intensive in LES. Several SGS flux models are tested on an a priori basis. The Smagorinsky (SM) model has a poor correlation with the data, while the gradient (GR) and scale-similarity (SS) models have high correlations. Calibrated model coefficients for the GR and SS models yield good agreement with the SGS fluxes, although statistically, the coefficients are not valid over all realizations. The GR model is also tested for the variances entering the calculation of the new terms in the momentum and energy equations; high correlations are obtained, although the calibrated coefficients are not statistically significant over the entire database at fixed filter size. As a manifestation of the small-scale supercritical mixing peculiarities, both scalar-dissipation visualizations and the scalar-dissipation probability density functions (PDF) are examined. The PDF is shown to exhibit minor peaks, with particular significance for those at larger scalar dissipation values than the mean, thus significantly departing from the Gaussian behaviour.

Experimental Determination of the Sub-grid Scale Scalar Flux in a Non-Reacting Jet-Flow

This work presents an experimental approach to the direct determination of the sub-grid scale scalar flux used in Large Eddy Simulation (LES). Two non-reacting jet-flow configurations were examined, one with the jet temperature similar to the ambient air temperature and one preheated jet. Hence data were obtained for varying viscosities. Each case was investigated for two different, high Reynolds numbers of 17,471 and 31,714. For the measurements of mixture fraction and flow velocity field a finest resolution of almost 100 μm was achieved. Thus both the sub-grid scale scalar flux as well as the spatially filtered quantities can be obtained from the same data set. The data were acquired by the simultaneous application of planar laser-induced fluorescence (LIF) and particle image velocimetry (PIV).

PIV Measurements in the Atmospheric Boundary Layer within and above a Mature Corn Canopy. Part I: Statistics and Energy Flux

Particle image velocimetry (PIV) measurements just within and above a mature corn canopy have been performed to clarify the small-scale spatial structure of the turbulence. The smallest resolved scales are about 15 times the Kolmogorov length scale (η ≈ 0.4 mm), the Taylor microscales are about 100η, and the Taylor scale Reynolds numbers range between Rλ = 2000 and 3000. The vertical profiles of mean flow and turbulence parameters match those found in previous studies. Frequency spectra, obtained using the data as time series, are combined with instantaneous spatial spectra to resolve more than five orders of magnitude of length scales. They display an inertial range spanning three decades. However, the small-scale turbulence in the dissipation range exhibits anisotropy at all measurement heights, in spite of apparent agreement with conditions for reaching local isotropy, following a high-Reynolds-number wind tunnel study. Directly calculated subgrid-scale (SGS) energy flux, determined by spatially filtering the PIV data, increases significantly with decreasing filter size, providing support for the existence of a spectral shortcut that bypasses the cascading process and injects energy directly into small scales. The highest measured SGS flux is about 40% of the estimated energy cascading rate as determined from a −5/3 fit to the spectra. Terms appearing in the turbulent kinetic energy budget that can be calculated from the PIV data are in agreement with previous results. Evidence of a very strong correlation between dissipation rate and out-of-plane component of the vorticity is demonstrated by a striking similarity between their time series.

Modeling and Scaling Coupled Energy, Water, and Carbon Fluxes Based on Remote Sensing: An Application to Canada’s Landmass

Abstract Land surface models (LSMs) need to be coupled with atmospheric general circulation models (GCMs) to adequately simulate the exchanges of energy, water, and carbon between the atmosphere and terrestrial surfaces. The heterogeneity of the land surface and its interaction with temporally and spatially varying meteorological conditions result in nonlinear effects on fluxes of energy, water, and carbon, making it challenging to scale these fluxes accurately. The issue of up-scaling remains one of the critical unsolved problems in the parameterization of subgrid-scale fluxes in coupled LSM and GCM models. A new distributed LSM, the Ecosystem–Atmosphere Simulation Scheme (EASS) was developed and coupled with the atmospheric Global Environmental Multiscale model (GEM) to simulate energy, water, and carbon fluxes over Canada’s landmass through the use of remote sensing and ancillary data. Two approaches (lumped case and distributed case) for handling subgrid heterogeneity were used to evaluate the effect of land-cover heterogeneity on regional flux simulations based on remote sensing. Online runs for a week in August 2003 provided an opportunity to investigate model performance and spatial scaling issues. Comparisons of simulated results with available tower observations (five sites) across an east–west transect over Canada’s southern forest regions indicate that the model is reasonably successful in capturing both the spatial and temporal variations in carbon and energy fluxes, although there were still some biases in estimates of latent and sensible heat fluxes between the simulations and the tower observations. Moreover, the latent and sensible heat fluxes were found to be better modeled in the coupled EASS–GEM system than in the uncoupled GEM. There are marked spatial variations in simulated fluxes over Canada’s landmass. These patterns of spatial variation closely follow vegetation-cover types as well as leaf area index, both of which are highly correlated with the underlying soil types, soil moisture conditions, and soil carbon pools. The surface fluxes modeled by the two up-scaling approaches (lumped and distributed cases) differ by 5%–15% on average and by up to 15%–25% in highly heterogeneous regions. This suggests that different ways of treating subgrid land surface heterogeneities could lead to noticeable biases in model output.

A General Dynamic Linear Tensor-Diffusivity Subgrid-Scale Heat Flux Model for Large-Eddy Simulation of Turbulent Thermal Flows

In this article, a general dynamic linear tensor diffusivity model is proposed for representing the subgrid-scale (SGS) heat flux (HF). The tensor diffusivity for the model is an inhomogeneous linear function of the resolved strain and rotation rate tensors, and includes three conventional dynamic SGS HF modeling approaches as special cases. In contrast to the dynamic SGS eddy diffusivity modeling approach, the proposed model admits more degrees of freedom for representing the SGS thermal diffusivity, allows for nonalignment between the SGS HF and resolved temperature gradient, and consequently provides a more realistic geometric representation of the SGS heat flux. To validate the proposed modeling approach, numerical simulations have been performed based on a combined forced- and natural-convention flow in a vertical channel with a Reynolds number and a Grashof number Gr = 9.6 × 105. In comparison with the reported direct numerical simulation data and the results obtained using the conventional dynamic SGS eddy diffusivity model, it is shown that the proposed model is able to provide good predictions of various flow quantities at the resolved scale and, more important, offer new insights into near-wall flow physics at the subgrid scale.

Reexamination of a scale-similarity model for the subgrid-scale flux in the Earth's core

The effects of small-scales (subgrid-scales) on large-scales (grid-scales) must be properly estimated in large eddy simulation. We reexamine a scale-similarity model based on spatial filter-width dependence in a small region of the Earth's core with periodic boundary conditions proposed by Matsushima (2004). The model, which has been found not to well reproduce spatial distribution of subgrid-scale fluxes, is then improved. Spatial distribution and amplitude of subgrid-scale fluxes estimated by the new model are compared with those obtained through direct numerical simulations (DNS) in confirmation of substantial improvement of the model. Numerical simulations at lower resolution with and without some subgrid-scale models are carried out to demonstrate that the present model is reliable and robust. Heat flux, kinetic energy and magnetic energy averaged over space and time are compared among results of DNS at high and low resolution and of numerical simulations with subgrid-scale models. The present model is found to perform better than the others examined in this study.

Modelling of subgrid-scale fluxes

Abstract Both necessary and sufficient conditions are derived in a systematic, rigorous way for a subgrid-scale (SGS) flux vector model to preserve the frame-indifference of the vector and to satisfy both the principle of material frame-indifference (PMFI) and the second law of thermodynamics. This leads to the results either confirming the previous intuitive arguments or offering new insights into turbulence modeling, and is of significance in clarifying some controversies in the literature, examining how well existing models preserve the physics, and developing new models.

On the Application of the Dynamic Smagorinsky Model to Large-Eddy Simulations of the Cloud-Topped Atmospheric Boundary Layer

Abstract In this paper the dynamic Smagorinsky model originally developed for engineering flows is adapted for simulations of the cloud-topped atmospheric boundary layer in which an anelastic form of the governing equations is used. The adapted model accounts for local buoyancy sources, vertical density stratification, and poor resolution close to the surface and calculates additional model coefficients for the subgrid-scale fluxes of potential temperature and total water mixing ratio. Results obtained with the dynamic model are compared with those obtained using two nondynamic models for simulations of a nocturnal marine stratocumulus cloud deck observed during the first research flight of the second Dynamics and Chemistry of Marine Stratocumulus (DYCOMS-II) field experiment. The dynamic Smagorinsky model is found to give better agreement with the observations for all parameters and statistics. The dynamic model also gives improved spatial convergence and resolution independence over the nondynamic models. The good results obtained with the dynamic model appear to be due primarily to the fact that it calculates minimal subgrid-scale fluxes at the inversion. Based on other results in the literature, it is suggested that entrainment in the DYCOMS-II case is due predominantly to isolated mixing events associated with overturning internal waves. While the behavior of the dynamic model is consistent with this entrainment mechanism, a similar tendency to switch off subgrid-scale fluxes at an interface is also observed in a case in which gradient transport by small-scale eddies has been found to be important. This indicates that there may be problems associated with the application of the dynamic model close to flow interfaces. One issue here involves the plane-averaging procedure used to stabilize the model, which is not justified when the averaging plane intersects a deforming interface. More fundamental, however, is that the behavior may be due to insufficient resolution in this region of the flow. The implications of this are discussed with reference to both dynamic and nondynamic subgrid-scale models, and a new approach to turbulence modeling for large-eddy simulations is proposed.

Dynamic subgrid‐scale models for momentum and scalar fluxes in large‐eddy simulations of neutrally stratified atmospheric boundary layers over heterogeneous terrain

The accuracy of large‐eddy simulations (LESs) of the atmospheric boundary layer (ABL) over complex terrain relies on the ability of the subgrid‐scale (SGS) models to capture the effect of subgrid turbulent fluxes on the resolved fields of velocity and scalars (e.g., heat, water vapor, and pollutants). A common approach consists of parameterizing the SGS stresses and fluxes using eddy viscosity and eddy diffusivity models, respectively. These models require the specification of two parameters: the Smagorinsky coefficient in the eddy viscosity model and, in addition, the SGS Schmidt/Prandtl number in the eddy diffusivity model. This is complicated by the dependence of the coefficients on local conditions such as distance to the ground, mean shear, and atmospheric stability. In this study, scale‐dependent dynamic SGS models are used in conjunction with Lagrangian averaging to compute both the Smagorinsky coefficient and the SGS Schmidt (or Prandtl) number dynamically as the flow evolves in both space and time based on the local dynamics of the resolved scales. These tuning‐free models are implemented in LES of both homogeneous and heterogeneous neutral atmospheric boundary layers with surface fluxes of a passive scalar. In the homogeneous simulations the models are shown to accurately predict the resolved flow statistics (mean profiles and spectra of velocity and scalar concentration) and spatial distributions of the SGS model coefficients and parameters. In simulations over heterogeneous surfaces both coefficients adjust in a self‐consistent way to horizontal flow inhomogeneities associated with changes in surface conditions. For smooth‐to‐rough (rough‐to‐smooth) abrupt changes in surface roughness the Smagorinsky coefficient decreases (increases) in response to increased (decreased) mean shear and flow anisotropy associated with these transitions. The SGS Schmidt number also adjusts to inhomogeneities in the scalar field associated with changes in surface scalar flux. This illustrates the need for local calculation of model coefficients and brings into question the common practice of using a constant SGS Schmidt/Prandtl number in LES of the ABL.

A scale-similarity model for the subgrid-scale flux with application to MHD turbulence in the Earth’s core

Turbulent motions in the Earth’s core have a strong influence on diffusive processes for large-scale fields through the eddy diffusion. They are highly anisotropic due to the influence of the Earth’s rotation and the magnetic field. It is therefore of significance to estimate the eddy diffusivity and to model subgrid-scale processes properly. A scale-similarity model, being one of the subgrid-scale models used in large-eddy simulation, is found to reproduce anisotropy. The purpose of this study is to reexamine scale similarity of magnetohydrodynamic (MHD) turbulence in the core and to demonstrate the validity of the subgrid-scale model developed by Matsushima [Matsushima, M., 2004. Scale similarity in the Earth’s core. Earth Planets Space 56, 599–605.] in two ways. First, spatial correlation and root-mean-square amplitude of the turbulent flux estimated through use of the model are compared with those obtained through direct numerical simulations at the same time step. The model appears valid from the result. Second, numerical simulations of MHD turbulence including the model of subgrid scales are carried out, and their results of time evolution are compared with those obtained through numerical simulations excluding the model. The result also indicates the subgrid-scale model holds valid.

Implication of Mismatch Between Stress and Strain-Rate in Turbulence Subjected to Rapid Straining and Destraining on Dynamic LES Models

Abstract Planar straining and destraining of turbulence is an idealized form of turbulence-meanflow interaction that is representative of many complex engineering applications. This paper studies experimentally the response of turbulence subjected to a process involving planar straining, a brief relaxation and destraining. Subsequent analysis quantifies the impact of the applied distortions on model coefficients of various eddy viscosity subgrid-scale models. The data are obtained using planar particle image velocimetry (PIV) in a water tank, in which high Reynolds number turbulence with very low mean velocity is generated by an array of spinning grids. Planar straining and destraining mean flows are produced by pushing and pulling a rectangular piston towards and away from the bottom wall of the tank. The velocity distributions are processed to yield the time evolution of mean subgrid dissipation rate, the Smagorinsky and dynamic model coefficients, as well as the mean subgrid-scale momentum flux during the entire process. It is found that the Smagorinsky coefficient is strongly scale dependent during periods of straining and destraining. The standard dynamic approach overpredicts the dissipation based Smagorinsky coefficient, with the model coefficient at scale Δ in the standard dynamic Smagorinsky model being close to the dissipation based Smagorinsky coefficient at scale 2Δ. The scale-dependent Smagorinsky model, which is designed to compensate for such discrepancies, yields unsatisfactory results due to subtle phase lags between the responses of the subgrid-scale stress and strain-rate tensors to the applied strains. Time lags are also observed for the SGS momentum flux at the larger filter scales considered. The dynamic and scale-dependent dynamic nonlinear mixed models do not show a significant improvement. These potential problems of SGS models suggest that more research is needed to further improve and validate SGS models in highly unsteady flows.

On the large eddy simulation of scalar transport with prandtl number up to 10 using dynamic mixed model

The dynamic mixed model (DMM) combined with a box filter of Zang et al(1993) has been generalized for passive scalar transport and applied to large eddy simulation of turbulent channel flows with Prandtl number up to 10 Results from a priot test showed that DMM is capable of predicting both subgrid-scale (SGS) scalar flux and dissipation rather accurately for the Prandtl number considered . This would suggest that the favorable feature of DMM, originally developed for the velocity field, works equally well for scalar transport problem. The validity of the DMM has also been tested a posteriori. The results of the large eddy simulation showed that DMM is superior to the dynamic Smagrinsky model in the prediction of scalar field and the model performance of DMM depends to a lesser degree on the ratio of test to grid filter widths, unlike in the a priori test.

Consistent large-eddy simulation of a temporal mixing layer laden with evaporating drops. Part 2. A posteriori modelling

Large-eddy simulation (LES) is conducted of a three-dimensional temporal mixing layer whose lower stream is initially laden with liquid drops which may evaporate during the simulation. The gas-phase equations are written in an Eulerian frame for two perfect gas species (carrier gas and vapour emanating from the drops), while the liquid-phase equations are written in a Lagrangian frame. The effect of drop evaporation on the gas phase is considered through mass, species, momentum and energy source terms. The drop evolution is modelled using physical drops, or using computational drops to represent the physical drops. Simulations are performed using various LES models previously assessed on a database obtained from direct numerical simulations (DNS). These LES models are for: (i) the subgrid-scale (SGS) fluxes and (ii) the filtered source terms (FSTs) based on computational drops. The LES, which are compared to filtered-and-coarsened (FC) DNS results at the coarser LES grid, are conducted with 64 times fewer grid points than the DNS, and up to 64 times fewer computational than physical drops. It is found that both constant-coefficient and dynamic Smagorinsky SGS-flux models, though numerically stable, are overly dissipative and damp generated small-resolved-scale (SRS) turbulent structures. Although the global growth and mixing predictions of LES using Smagorinsky models are in good agreement with the FC-DNS, the spatial distributions of the drops differ significantly. In contrast, the constant-coefficient scale-similarity model and the dynamic gradient model perform well in predicting most flow features, with the latter model having the advantage of not requiring a priori calibration of the model coefficient. The ability of the dynamic models to determine the model coefficient during LES is found to be essential since the constant-coefficient gradient model, although more accurate than the Smagorinsky model, is not consistently numerically stable despite using DNS-calibrated coefficients. With accurate SGS-flux models, namely scale-similarity and dynamic gradient, the FST model allows up to a 32-fold reduction in computational drops compared to the number of physical drops, without degradation of accuracy; a 64-fold reduction leads to a slight decrease in accuracy.

Effects of subgrid-scale turbulence on resolvable-scale velocity–scalar statistics

The effects of subgrid-scale (SGS) velocity and scalar and SGS models on the resolvable-scale velocity-scalar joint probability density function (JPDF) are studied. It is shown that the SGS stress and SGS scalar flux evolve the JPDF though the conditional mean SGS stress and flux, their production rates, and the SGS scalar variance production rate. The mean SGS stress and SGS scalar flux production rate are predicted using Lumley's assumption (Lumley, J. 1967 Physics of Fluids, 16, 3859–3867), which is consistent with Kolmogorov's hypothesis. Analyses of these statistics using data obtained in a slightly heated turbulent jet show that the mean SGS stress, SGS scalar flux, and their production rates have filter-scale dependences consistent with our predictions, suggesting that the SGS turbulence has diminishing influences on the lower-order resolvable-scale statistics for inertial-range filter scales. The Smagorinsky model predictions also have similar filter-scale dependences, suggesting that the models have diminishing effects on lower-order LES statistics. The measured conditional SGS stress and SGS flux as well as the conditional production rates decrease much slower than the predicted filter dependences, indicating that the SGS turbulence has non-trivial effects on the high-order resolvable-scale statistics even for inertial-range filter scales. The Smagorinsky models predictions of these conditional statistics decrease slower with the filter scale than our predictions but do not agree with measurements; therefore the models are likely to influence the high-order LES statistics but in ways different from that of the SGS turbulence.

An eddy‐diffusivity/mass‐flux parametrization for dry and shallow cumulus convection

AbstractRecently, a new consistent way of parametrizing simultaneously local and non‐local turbulent transport for the convective atmospheric boundary layer has been proposed and tested for the clear boundary layer. This approach assumes that in the convective boundary layer the subgrid‐scale fluxes result from two different mixing scales: small eddies, that are parametrized by an eddy‐diffusivity approach, and thermals, which are represented by a mass‐flux contribution. Since the interaction between the cloud layer and the underlying sub‐cloud layer predominantly takes place through strong updraughts, this approach offers an interesting avenue of establishing a unified description of the turbulent transport in the cumulus‐topped boundary layer. This paper explores the possibility of such a new approach for the cumulus‐topped boundary layer. In the sub‐cloud and cloud layers, the mass‐flux term represents the effect of strong updraughts. These are modelled by a simple entraining parcel, which determines the mean properties of the strong updraughts, the boundary‐layer height, the lifting condensation level and cloud top. The residual smaller‐scale turbulent transport is parametrized with an eddy‐diffusivity approach that uses a turbulent kinetic energy closure. The new scheme is implemented and tested in the research model MesoNH. Copyright © 2004 Royal Meteorological Society

Assimilating Coherent Doppler Lidar Measurements into a Model of the Atmospheric Boundary Layer. Part I: Algorithm Development and Sensitivity to Measurement Error

Abstract A four-dimensional variational data assimilation (4DVAR) algorithm for retrieval of spatially and temporally resolved velocity and thermodynamic fields within the atmospheric boundary layer (ABL) is described and applied to a coherent Doppler lidar dataset. The adjoint method is used to find the initialization of an ABL model that gives the best fit to radial velocity measurements from the Doppler lidar. The adjoint equations are derived by assuming that subgrid-scale fluxes can be represented as general functions of the resolved-scale rates of strain and potential temperature gradients. For this study, particular attention is paid to the treatment of real measurement error. Radial velocity precision as a function of the signal-to-noise ratio (SNR) is estimated from time series analysis of real fixed beam data, and this information is used in the evaluation of the cost function. The cost function is evaluated by interpolating the model output to the observation coordinates. As a result, the error...

Scale similarity of MHD turbulence in the Earth’s core

Turbulent motions in the core, being highly anisotropic because of the influence of the Earth’s rotation and its magnetic field, cause the eddy diffusion of large-scale fields much more effectively than the molecular diffusion. Reliable estimates of the eddy diffusivities, or the subgrid-scale fluxes, are therefore of significance. In this paper, scale similarity of magnetohydrodynamic turbulence in a rapidly rotating system is investigated to model subgrid-scale processes, as used in large-eddy simulations. The turbulent flux has been computed by taking an ensemble average of results of direct numerical simulations, which are to be employed in this paper, over the computational box which represents a small region in the Earth’s core. The anisotropy of turbulent flux computed after averaging over segments into which the box is divided remains unchanged even when the size of segments changes. Dependence of turbulent flux computed from fields to which a spatial filter is applied on its width indicates that subgrid-scale flux can be evaluated through extrapolation. This method will be useful for performing global geodynamo simulations taking into account subgrid-scale processes.

Dynamic Structure Models for Scalar Flux and Dissipation in Large Eddy Simulation

A new class of subgrid scale models (dynamic structure models) for large eddy simulation is proposed for subgrid scalar flux and dissipation terms. The structure of the modeled terms is taken from the corresponding Leonard terms by the use of the test filter size equal to the base filter size, and a particular form of the scaling factor is proposed. The models are evaluated using available direct numerical simulation data. The evaluation results compare well with viscosity and similarity models. The dynamic structure models have been found to be robust and to work well under various conditions, including various test-to-base filter size ratios and filter skewnesses. Models for both terms employ the subgrid scalar variance as a part of the scaling factor

On the large eddy simulation of high prandtl number scalar transport using dynamic subgrid-scale model

The present study investigates passive scalar transport using an eddy viscosity/diffusivity model in turbulent channel flow with Prandtl number range 1-10. Dynamic subgrid-scale model (DSM) was applied to the transport equation for passive scalar to determine the eddy diffusivity dynamically. To assess the feasibility of the DSM model applied for passive scalar,a priori test on direct numerical simulation data was conducted and the results are compared with those obtained from a large eddy simulation that uses DSM modela posteriori. As the Prandtl number increases, the discrepancy in subgrid-scale (SGS) heat flux amplifies but the shape of SGS temperature dissipation profiles shows reasonable agreement. This suggests that energy transfer between resolved and subgrid-scales are reasonably predicted regardless of the accuracy in SGS heat flux vectors. Whilea priori test shows that SGS turbulent Prandtl number changes significantly with Prandtl number, the actual LES results are found to be insensitive to Prandtl number away from the wall. Thus, the DSM model has some limitations in the prediction of high Prandtl number flows.