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Large eddy simulation and direct numerical simulation of high speed turbulent reacting flows

The objective of this research is to make use of Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS) for the computational analyses of high speed reacting flows. Our efforts in the first phase of this research conducted within the past three years have been directed in several issues pertaining to intricate physics of turbulent reacting flows. In our previous 5 semi-annual reports submitted to NASA LaRC, as well as several technical papers in archival journals, the results of our investigations have been fully described. In this progress report which is different in format as compared to our previous documents, we focus only on the issue of LES. The reason for doing so is that LES is the primary issue of interest to our Technical Monitor and that our other findings were needed to support the activities conducted under this prime issue. The outcomes of our related investigations, nevertheless, are included in the appendices accompanying this report. The relevance of the materials in these appendices are, therefore, discussed only briefly within the body of the report. Here, results are presented of a priori and a posterior analyses for validity assessments of assumed Probability Density Function (PDF) methods as potential subgrid scale (SGS) closures for LES of turbulent reacting flows. Simple non-premixed reacting systems involving an isothermal reaction of the type A + B yields Products under both chemical equilibrium and non-equilibrium conditions are considered. A priori analyses are conducted of a homogeneous box flow, and a spatially developing planar mixing layer to investigate the performance of the Pearson Family of PDF's as SGS models. A posteriori analyses are conducted of the mixing layer using a hybrid one-equation Smagorinsky/PDF SGS closure. The Smagorinsky closure augmented by the solution of the subgrid turbulent kinetic energy (TKE) equation is employed to account for hydrodynamic fluctuations, and the PDF is employed for modeling the effects of scalar fluctuations. The implementation of the model requires the knowledge of the local values of the first two SGS moments. These are provided by additional modeled transport equations. In both a priori and a posteriori analyses, the predicted results are appraised by comparison with subgrid averaged results generated by DNS. Based on these results, the paths to be followed in future investigations are identified.

Adumitroaie, V.↗

Multi-Layer Arctic Mixed-Phase Clouds Simulated by a Cloud-Resolving Model: Comparison with ARM Observations and Sensitivity Experiments

A cloud-resolving model (CRM) is used to simulate the multiple-layer mixed-phase stratiform (MPS) clouds that occurred during a three-and-a-half day subperiod of the Department of Energy-Atmospheric Radiation Measurement Program s Mixed-Phase Arctic Cloud Experiment (M-PACE). The CRM is implemented with an advanced two-moment microphysics scheme, a state-of-the-art radiative transfer scheme, and a complicated third-order turbulence closure. Concurrent meteorological, aerosol, and ice nucleus measurements are used to initialize the CRM. The CRM is prescribed by time-varying large-scale advective tendencies of temperature and moisture and surface turbulent fluxes of sensible and latent heat. The CRM reproduces the occurrences of the single- and double-layer MPS clouds as revealed by the M-PACE observations. However, the simulated first cloud layer is lower and the second cloud layer thicker compared to observations. The magnitude of the simulated liquid water path agrees with that observed, but its temporal variation is more pronounced than that observed. As in an earlier study of single-layer cloud, the CRM also captures the major characteristics in the vertical distributions and temporal variations of liquid water content (LWC), total ice water content (IWC), droplet number concentration and ice crystal number concentration (nis) as suggested by the aircraft observations. However, the simulated mean values differ significantly from the observed. The magnitude of nis is especially underestimated by one order of magnitude. Sensitivity experiments suggest that the lower cloud layer is closely related to the surface fluxes of sensible and latent heat; the upper cloud layer is probably initialized by the large-scale advective cooling/moistening and maintained through the strong longwave (LW) radiative cooling near the cloud top which enhances the dynamical circulation; artificially turning off all ice-phase microphysical processes results in an increase in LWP by a factor of 3 due to interactions between the excessive LW radiative cooling and extra cloud water; heating caused by phase change of hydrometeors could affect the LWC and cloud top height by partially canceling out the LW radiative cooling. It is further shown that the resolved dynamical circulation appears to contribute more greatly to the evolution of the MPS cloud layers than the parameterized subgrid-scale circulation.

Luo, Yali↗

Transport models for numerical forecast

The explosive growth of computing power, coupled with scientific and technological emphasis on a national scale, has led to significant major advances in operational numerical weather prediction (NWP) during the last two decades. There are about half a dozen major centers around the world running global NWP models operationally. Many more countries have operational hemispheric or limited-area models which provide weather forecasts. The global models typically have several hundred kilometer resolution, while the limited-area models usually have horizontal spacing of 50 to 100 km. Given the pace of burgeoning growth in this area, it seems warranted to occasionally take an overview of aspects of the field common to all modelers. Here, a brief look is taken at the nature of subgrid scale turbulence transport parameterization, and some of the difficulties pertaining thereto, with particular emphasis on operational NWP models.

Burk, Stephen D.↗

Large Eddy Simulation of Cirrus Clouds

The Regional Atmospheric Modeling System (RAMS) with mesoscale interactive nested-grids and a Large-Eddy Simulation (LES) version of RAMS, coupled to two-moment microphysics and a new two-stream radiative code were used to investigate the dynamic, microphysical, and radiative aspects of the November 26, 1991 cirrus event. Wu (1998) describes the results of that research in full detail and is enclosed as Appendix 1. The mesoscale nested grid simulation successfully reproduced the large scale circulation as compared to the Mesoscale Analysis and Prediction System's (MAPS) analyses and other observations. Three cloud bands which match nicely to the three cloud lines identified in an observational study (Mace et al., 1995) are predicted on Grid #2 of the nested grids, even though the mesoscale simulation predicts a larger west-east cloud width than what was observed. Large-eddy simulations (LES) were performed to study the dynamical, microphysical, and radiative processes in the 26 November 1991 FIRE 11 cirrus event. The LES model is based on the RAMS version 3b developed at Colorado State University. It includes a new radiation scheme developed by Harrington (1997) and a new subgrid scale model developed by Kosovic (1996). The LES model simulated a single cloud layer for Case 1 and a two-layer cloud structure for Case 2. The simulations demonstrated that latent heat release can play a significant role in the formation and development of cirrus clouds. For the thin cirrus in Case 1, the latent heat release was insufficient for the cirrus clouds to become positively buoyant. However, in some special cases such as Case 2, positively buoyant cells can be embedded within the cirrus layers. These cells were so active that the rising updraft induced its own pressure perturbations that affected the cloud evolution. Vertical profiles of the total radiative and latent heating rates indicated that for well developed, deep, and active cirrus clouds, radiative cooling and latent heating could be comparable in magnitude in the cloudy layer. This implies that latent heating cannot be neglected in the construction of a cirrus cloud model. The probability density function (PDF) of w was analyzed to assist in the parameterization of cloud-scale velocities in large-scale models. For the more radiatively-driven, thin cirrus case, the PDFs are approximately Gaussian. However, in the interior of the deep, convectively unstable case, the PDFs of w are multi-modal and very broad, indicating that parameterizing cloud-scale motions for such clouds can be very challenging. The results of this research are described in detail in a paper submitted to the Journal of Atmospheric Science (Wu and Cotton, 1999), which is enclosed as Appendix 2. Using soundings extracted from a mesoscale simulation of the November 26, 1991 cirrus event, the radiative effects on vapor deposition/sublimation of ice crystals was studied using a two-dimensional cloud-resolving model (CRM) version of RAMS, coupled to an explicit bin-resolving microphysics. The CRM simulations of the November 26, 1991 cirrus event demonstrate that the radiative impact on the diffusional growth (or sublimation) of ice crystals is significant. In this case, the ice particles experienced radiative warming. Model results show that radiative feedbacks in the diffusional growth of ice particles can be very complex. Radiative warming of an ice particle will restrict the particle's diffusional growth. In the case of radiative warming, ice particles larger than a certain size will experience so much radiative warming that surface ice saturation vapor pressures become large enough to cause sublimation of the larger crystals, while smaller crystals are growing by vapor deposition. However, ice mass production can be enhanced in the case of radiative cooling of an ice particle. For the November 26, 1991 cirrus event, radiative feedback results in significant reduction in the total ice mass, especially in the production of large ice crystals, and consequently, both radiative and dynamic properties of the cirrus cloud are significantly affected. A complete description of this research has been submitted as a paper to the Journal of Atmospheric Science (Wu et al., 1999), and included as Appendix 3.

Wu, Ting↗

Annual Research Briefs - 1996, Center for Turbulence Research

Partial contents include: (1) Simulation of jet impingement heat transfer with the k-e-V2 model; (2) A new methodology for turbulence modelers using Direct Numerical Simulation (DNS) database analysis; (3) A particle representation model for the deformation of homogeneous turbulence; (4) Modeling of inhomogeneous compressible turbulence using a two-scale statistical theory; (5) Lewis number effects on partially premixed flames; (6) Conditional moment closure of mixing and reaction in turbulent non-premixed combustion; (7) Dynamic models for LES of turbulent front propagation with a spectral method; (8) Jet noise using large eddy simulation; (9) Towards numerical simulations of trailing-edge aeroacoustics; (10) A model for the onset of vortex breakdown; (11) Compressing an elliptic vortex: transition to turbulence by tumble breakdown; (12) A new method for the adaptive control of vortex-wall interactions; (13) Symmetries in turbulent boundary layer flows; (14) Near-wall models in large eddy simulations of flow behind a backward-facing step; (15) Assessment of the subgrid-scale models at low and high Reynolds numbers; (16) Large-eddy simulations of flow around a NACA 4412 airfoil using unstructured grids; (17) Progress on LES of flow past a circular cylinder; (18) Experimental investigation of flow through an asymmetric plane diffuser; (19) Progress in the large-eddy simulation of an asymmetric plane diffuser; (20) A numerical study of self-similarity in a turbulent plane wake using large-eddy simulation; (21) On the generation of turbulent inflow conditions for boundary layer simulations, and (22) A new class of finite difference schemes.

COMPUTATIONAL FLUID DYNAMICS↗

Kinetic energy budgets in areas of convection

Synoptic scale budgets of kinetic energy are computed using 3 and 6 h data from three of NASA's Atmospheric Variability Experiments (AVE's). Numerous areas of intense convection occurred during the three experiments. Large kinetic energy variability, with periods as short as 6 h, is observed in budgets computed over each entire experiment area and over limited volumes that barely enclose the convection and move with it. Kinetic energy generation and transport processes in the smaller volumes are often a maximum when the enclosed storms are near peak intensity, but the nature of the various energy processes differs between storm cases and seems closely related to the synoptic conditions. A commonly observed energy budget for peak storm intensity indicates that generation of kinetic energy by cross-contour flow is the major energy source while dissipation to subgrid scales is the major sink. Synoptic scale vertical motion transports kinetic energy from lower to upper levels of the atmosphere while low-level horizontal flux convergence and upper-level horizontal divergence also occur. Spatial fields of the energy budget terms show that the storm environment is a major center of energy activity for the entire area.

Fuelberg, H. E.↗

Stably stratified shear turbulence: A new model for the energy dissipation length scale

A model is presented to compute the turbulent kinetic energy dissipation length scale l(sub epsilon) in a stably stratified shear flow. The expression for l(sub epsilon) is derived from solving the spectral balance equation for the turbulent kinetic energy. The buoyancy spectrum entering such equation is constructed using a Lagrangian timescale with modifications due to stratification. The final result for l(sub epsilon) is given in algebraic form as a function of the Froude number Fr and the flux Richardson number R(sub f), l(sub epsilon) = l(sub epsilon)(Fr, R(sub f). The model predicts that for R(sub f) less than R(sub fc), l(sub epsilon) decreases with stratification. An attractive feature of the present model is that it encompasses, as special cases, some seemingly different models for l(sub epsilon) that have been proposed in the past by Deardorff, Hunt et al., Weinstock, and Canuto and Minotti. An alternative form for the dissipation rate epsilon is also discussed that may be useful when one uses a prognostic equation for the heat flux. The present model is applicable to subgrid-scale models, which are needed in large eddy simulations (LES), as well as to ensemble average models. The model is applied to predict the variation of l(sub epsilon) with height z in the planetary boundary layer. The resulting l(sub epsilon) versus z profile reproduces very closely the nonmonotonic profile of l(sub epsilon) exhibited by many LES calculations, beginning with the one by Deardorff in 1974.

Cheng, Y.↗

Preliminary large-eddy simulations of flow around a NACA 4412 airfoil using unstructured grids

Large-eddy simulation (LES) has matured to the point where application to complex flows is desirable. The extension to higher Reynolds numbers leads to an impractical number of grid points with existing structured-grid methods. Furthermore, most real world flows are rather difficult to represent geometrically with structured grids. Unstructured-grid methods offer a release from both of these constraints. However, just as it took many years for structured-grid methods to be well understood and reliable tools for LES, unstructured-grid methods must be carefully studied before we can expect them to attain their full potential. In the past two years, important building blocks have been put into place making possible a careful study of LES on unstructured grids. The first building block was an efficient mesh generator which allowed the placement of points according to smooth variation of physical length scales. This variation of length scales is in all three directions independently, which allows a large reduction in points when compared to structured-grid methods, which can only vary length scales in one direction at a time. The second building block was the development of a dynamic model appropriate for unstructured grids. The principle obstacle was the development of an unstructured-grid filtering operator. In the past year, some of the new filters developed by Jansen have been implemented into a highly parallelized finite element code based on the Galerkin/least-squares finite element method. We have chosen the NACA 4412 airfoil at maximum lift as the first simulation for a variety of reasons. First, it is a problem of significant interest since it would be the first LES of an aircraft component. Second, this flow has been the subject of three experimental studies. The third reason for considering this flow is the variety of flow features which provide an important test of the dynamic model. Only the dynamic model can be expected to perform satisfactorily in this variety of situations: from the laminar regions where it must not modify the flow at all to the turbulent boundary layers and wake where it must represent a wide variety of subgrid-scale structures. The flow configuration we have chosen is that of Wadcock (1987) at Reynolds number based on chord Re(sub c) = u(sub infinity)c/v = 1.64 x 10(exp 6), Mach number M = 0.2, and 12 deg angle of attack.

Jansen, Kenneth↗

The helical decomposition and the instability assumption

Direct numerical simulations show that the triadic transfer function T(k,p,q) peaks sharply when q (or p) is much smaller than k. The triadic transfer function T(k,p,q) gives the rate of energy input into wave number k from all interactions with modes of wave number p and q, where k, p, q form a triangle. This observation was thought to suggest that energy is cascaded downscale through non-local interactions with local transfer and that there was a strong connection between large and small scales. Both suggestions were in contradiction with the classical Kolmogorov picture of the energy cascade. The helical decomposition was found useful in distinguishing between kinematically independent interactions. That analysis has gone beyond the question of non-local interaction with local transfer. In particular, an assumption about the statistical direction of triadic energy transfer in any kinematically independent interaction was introduced (the instability assumption). That assumption is not necessary for the conclusions about non-local interactions with local transfer recalled above. In the case of turbulence under rapid rotation, the instability assumption leads to the prediction that energy is transferred in spectral space from the poles of the rotation axis toward the equator. The instability assumption is thought to be of general validity for any type of triad interactions (e.g. internal waves). The helical decomposition and the instability assumption offer detailed information about the homogeneous statistical dynamics of the Navier-Stokes equations. The objective was to explore the validity of the instability assumption and to study the contributions of the various types of helical interactions to the energy cascade and the subgrid-scale eddy-viscosity. This was done in the context of spectral closures of the Direct Interaction or Quasi-Normal type.

Waleffe, Fabian A.↗

A regional analysis of cloudy mean spherical albedo over the marine stratocumulus region and the tropical Atlantic Ocean

Since clouds are the largest variable in Earth's radiation budget, it is critical to determine both the spatial and temporal characteristics of their radiative properties. The relationships between cloud properties and cloud fraction are studied in order to supplement grid scale parameterizations. The satellite data used is from three hourly ISCCP (International Satellite Cloud Climatology Project) and monthly ERBE (Earth Radiation Budget Experiment) data on a 2.5 deg x 2.5 deg latitude-longitude grid. Mean cloud spherical albedo, the mean optical depth distribution, and cloud fraction are examined and compared off the coast of California and the mid-tropical Atlantic for July 1987 and 1988. Individual grid boxes and spatial averages over several grid boxes are correlated to Coakley's theory of reflection for uniform and broken layered cloud and to Kedem, et al.'s findings that rainfall volume and fractional area of rain in convective systems is linear. Kedem's hypothesis can be expressed in terms of cloud properties. That is, the total volume of liquid in a box is a linear function of cloud fraction. Results for the marine stratocumulus regime indicate that albedo is often invariant for cloud fractions of 20% to 80%. Coakley's satellite model of small and large clouds with cores (1 km) and edges (100 m) is consistent with this observation. The cores maintain high liquid water concentrations and large droplets while the edges contain low liquid water concentrations and small droplets. Large clouds are just a collection of cores. The mean optical depth (TAU) distributions support the above observation with TAU values of 3.55 to 9.38 favored across all cloud fractions. From these results, a method based upon Kedem, et al's theory is proposed to separate the cloud fraction and liquid water path (LWP) calculations in a general circulation model (GCM). In terms of spatial averaging, a linear relationship between albedo and cloud fraction is observed. For tropical locations outside the Intertropical Convergence Zone (ITCZ), results of cloud fraction and albedo spatial averaging followed that of the stratus boxes containing few overcast scenes. Both the ideas of Coakley and Kedem, et al. apply. Within the ITCZ, the grid boxes tended to have the same statistical properties as stratus boxes containing many overcast scenes. Because different dynamical forcing mechanisms are present, it is difficult to devise a method for determining subgrid scale variations. Neither of the theories proposed by Kedem, et al. or Coakley works well for the boxes with numerous overcast scenes.

Ginger, Kathryn M.↗

A Regional Analysis of Cloudy Mean Spherical Albedo over the Marine Stratocumulus Region and the Tropical Atlantic Ocean

Since clouds are the largest variable in Earth's radiation budget, it is critical to determine both the spatial and temporal characteristics of their radiative properties. This study examines the relationships between cloud properties and cloud fraction in order to supplement grid scale parameterizations. The satellite data used in this study is from three hourly ISCCP (International Satellite Cloud Climatology Project) and monthly ERBE (Earth Radiation Budget Experiment) data on a 2.50 x 2.50 latitude-longitude grid. Mean cloud spherical albedo, the mean optical depth distribution and cloud fraction are examined and compared off the coast of California and the mid-tropical Atlantic for July 1987 and 1988. Individual grid boxes and spatial averages over several grid boxes are correlated to Coakleys (1991) theory of reflection for uniform and broken layered cloud and to Kedem, et al.(1990) findings that rainfall volume and fractional area of rain in convective systems is linear. Kedem's hypothesis can be expressed in terms of cloud properties. That is, the total volume of liquid in a box is a linear function of cloud fraction. Results for the marine stratocumulus regime indicate that albedo is often invariant for cloud fractions of 20% to 80%. Coakley's satellite model of small and large clouds with cores (1 km) and edges (100 in) is consistent with this observation. The cores maintain high liquid water concentrations and large droplets while the edges contain low liquid water concentrations and small droplets. Large clouds are just a collection of cores. The mean optical depth (TAU) distributions support the above observation with TAU values of 3.55 to 9.38 favored across all cloud fractions. From these results, a method based upon Kedem, et al. theory is proposed to separate the cloud fraction and liquid water path (LWP) calculations in a general circulation model (GCM). In terms of spatial averaging, a linear relationship between albedo and cloud fraction is observed. For tropical locations outside the Intertropical Convergence Zone (ITCZ), results of cloud fraction and albedo spatial averaging followed that of the stratus boxes containing few overcast scenes. Both the ideas of Coakley and Kedem, et al. apply. Within the ITCZ, the grid boxes tended to have the same statistical properties as stratus boxes containing many overcast scenes. Because different dynamical forcing mechanisms are present, it is difficult to devise a method for determining subgrid scale variations. Neither of the theories proposed by Kedem, et al. or Coakley works well for the boxes with numerous overcast scenes.

Ginger, Kathryn M.↗

Chapter 10 - Remote Sensing Measurements of Aerosol Properties

Satellite instruments have proven especially capable at monitoring the quantity of airborne particles in columns of atmosphere, globally. This chapter describes the principles of satellite measurements and retrieval algorithms, and surveys current instruments and their capabilities. We outline the issues associated with retrieval algorithms, such as surface characterization and aerosol proximity to clouds, and the challenges with interpretation of the results. The relationship between measured aerosol properties and climate-relevant aerosol properties simulated in models is outlined, as well as how measurements are used to evaluate models. Most space-based aerosol instruments are passive sensors that measure reflected sunlight at multiple wavelengths, some at multiple viewing angles. A few are active sensors that send out their own laser light and measure the returned signal. Except when clouds are present, the excess amount of light scattered back to space, beyond that expected from the surface and atmospheric gas, is attributed to aerosol. Satellite measurements are used in many ways in aerosol research. They often provide the only method for monitoring hazardous phenomena such as major wildfire and volcanic eruption plumes, especially in remote areas. Stable, long-term, near-global-scale satellite data records make it possible to identify regional and global aerosol trends. Aerosol radiative effects on climate can be quantified on a near-global scale and used to estimate the strength of aerosol–radiation and aerosol–cloud interactions as well as to evaluate climate model simulations of these interactions. Aerosol-type mapping from satellite imagery is helpful for source attribution, model validation, and to constrain particle light-absorption properties that are essential for radiative forcing calculations. The range of aerosol properties retrieved from satellite observations has grown considerably since the first global estimates of aerosol optical depth (τ a) over ocean were made in the late 1970s. Methods for retrieving particle size and light-absorption properties were explored in the 1990s using multispectral, multi-angle observations, and polarization in visible and near-infrared wavelengths. Sensitivity to particle light absorption, primarily from black or brown carbon content, improved with the inclusion of UV channels, and sensitivity to very thin aerosol layers in the upper troposphere and lower stratosphere was advanced with the use of limb-sounding instruments and active sensors. There are limitations to every measurement technique, including satellite aerosol remote sensing. For wide-swath, passive instruments, aerosol retrievals near clouds can present substantial challenges as far as 15 km away due to cloud-scattered light contaminating the signal. In nearly all cases, retrievals over bright snow and ice surfaces are precluded because surface reflectance uncertainties can overwhelm the aerosol signal. Similarly, meteorological cloud is identified and masked out where possible. Data from passive sensors also lack vertical resolution except those that view toward the limb or where multi-angle imagery is acquired over plumes from wildfires, erupting volcanoes, and wind-blown dust. Yet, passive sensors provide vastly more coverage than the active instruments that mitigate these issues. Particle microphysical information is qualitative from all remote sensing techniques, relying on proxies to infer particle composition, hygroscopicity, and the amount of light-absorbing material. Further, particles smaller than about 200 nm diameter cannot be distinguished from atmospheric gas molecules with remote sensing, which hinders studies of cloud condensation nuclei and their effects on clouds. Most satellite instruments dedicated to aerosol observations are in low-Earth, near-polar, sun-synchronous orbits, which means they cross the equator at the same local time each day. Most are set on cycles that repeat approximately every 16 days, which makes it difficult to monitor aerosol evolution locally. Geostationary satellites make it possible to observe changes occurring from minutes to hours over regions up to 8000 km in size, but lack coverage of high latitudes, and often provide more limited constraints on aerosol properties. Ground-truth data are vital for satellite aerosol-retrieval validation. The AErosol RObotic NETwork (AERONET) of sun photometers was created in 1993 and has become an established global network of over 350 instruments for validating satellite measurements. The network, as well as global networks of ground-based lidars, solar flux radiometers and other sun photometers, are widely used for evaluating global satellite retrievals and model simulations. NASA's Earth Observing System (EOS) program beginning in 1999 led to improvements in reliability, spatial resolution, and spectral resolution (and hence, to improved particle size discrimination and light absorption properties). Satellite payloads include advanced broad-swath and multi-angle imagers, along with the first space-based active sensor focused largely on long-term aerosol monitoring. Since about 2002, Europe's SENTINEL and operational meteorological satellite fleets are also providing sustained aerosol observations, with planned continuation until at least 2030. Satellite remote sensing instruments offer valuable data for evaluating aerosol representations in global climate models. They have been used to assess aerosol optical and physical properties, trends and distributions, and are applied increasingly as direct model constraints in data assimilation to create global aerosol reanalysis products. Aerosol optical depth is the most common quantity adopted for routine model evaluation, including multiwavelength data to loosely constrain particle-size distributions. These evaluations of multiple models have revealed general biases in their regional aerosol amounts and seasonal patterns of transport and removal. Although satellite measurements have near-global coverage, substantial errors can be introduced into the model observation comparison unless attention is paid to spatial and temporal collocation, cloud screening, subgrid-scale variability, and measurement uncertainties that vary with retrieval conditions.

aerosol properties↗

Improved methods for large-eddy simulations of turbulence

By using Fourier transforms for evaluating spatial derivatives, the accuracy of the large-eddy simulation of homogeneous isotropic turbulence is improved. Especially, the treatment of certain terms that arise in filtering the equations is considerably improved in both speed and accuracy. Use of vorticity as the principal variable is shown to be a viable and potentially useful alternative to the primitive variables. A method of deriving conservation properties of numerical schemes is given which is much simpler than previous methods and is widely applicable. The methods are applied to the computation of homogeneous isotropic turbulence, and it is found that the subgrid scale model is improved by using finite differences in place of 'exact' derivatives.

Mansour, N. N.↗

Large eddy simulation of homogeneous isotropic turbulence

This paper presents results from a comprehensive investigation of large-eddy simulations of homogeneous isotropic turbulence. Calculations have been made using grid meshes, a number of flowfield filters, and two simple subgrid scale turbulence models. Particular attention has been paid to the degree of isotropy and the ability of the approach to predict higher-order statistical quantities (skewness and flatness). Directions for needed improvement in the simulation approach are indicated, and a plea is made to experimenters to process their data in a way which will facilitate comparison with large eddy simulations.

Ferziger, J. H.↗

Large eddy simulation - A predictive approach to turbulent flow computation

The filtering approach (Leonard, 1974) to large eddy simulation is described. Large eddy simulation is then surveyed with reference to subgrid scale models, numerical methods, channel flow, and free shear flows. It is concluded that the premise of LES (i.e., that the small eddies are much easier to model than the large ones) seems to be borne out by computational experience to date. The greatest obstacle in LES at present is the lack of computer power which effectively denies the ability to simulate all the significant eddies in flows of interest.

Ferziger, J. H.↗

Kinetic energy budget during strong jet stream activity over the eastern United States

Kinetic energy budgets are computed during a cold air outbreak in association with strong jet stream activity over the eastern United States. The period is characterized by large generation of kinetic energy due to cross-contour flow. Horizontal export and dissipation of energy to subgrid scales of motion constitute the important energy sinks. Rawinsonde data at 3 and 6 h intervals during a 36 h period are used in the analysis and reveal that energy fluctuations on a time scale of less than 12 h are generally small even though the overall energy balance does change considerably during the period in conjunction with an upper level trough which moves through the region. An error analysis of the energy budget terms suggests that this major change in the budget is not due to random errors in the input data but is caused by the changing synoptic situation. The study illustrates the need to consider the time and space scales of associated weather phenomena in interpreting energy budgets obtained through use of higher frequency data.

Fuelberg, H. E.↗

Three-dimensional simulation of the free shear layer using the vortex-in-cell method

We present numerical simulations of the evolution of a mixing layer from an initial state of uniform vorticity with simple two- and three-dimensional small perturbations. A new method for tracing a large number of three-dimensional vortex filaments is used in the simulations. Vortex tracing by Biot-Savart interaction originally implied ideal (non-viscous) flow, but we use a 3-d mesh, Fourier transforms and filtering for vortex tracing, which implies 'modeling' of subgrid scale motion and hence some viscosity. Streamwise perturbations lead to the usual roll-up of vortex patterns with spanwise uniformity maintained. Remarkably, spanwise perturbations generate streamwise distortions of the vortex filaments and the combination of both perturbations leads to patterns with interesting features discernable in the movies and in the records of enstrophy and energy for the three components of the flow.

Couet, B.↗

Large Eddy Simulation of turbulent shear flows

The conceptual foundation underlying Large Eddy Simulation (LES) is summarized, and the numerical methods developed for simulation of the time-developing turbulent mixing layer and turbulent plane Poiseuille flow are discussed. Computational results show that the average Reynolds stress profile nearly attains the equilibrium shape which balances the downstream mean pressure gradient in the regions away from the walls. In the vicinity of the walls, viscous stresses are shown to be significant; together with the Reynolds stresses, these stresses balance the mean pressure gradient. It is stressed that the subgrid scale contribution to the total Reynolds stress is significant only in the vicinity of the walls. The continued development of LES is urged.

Moin, P.↗