Scaling Behavior of a Turbulent Kinetic Energy Closure Scheme for the Stably Stratified Atmosphere: A Steady-State Analysis
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Michael MacDonald↗
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Results for “kinetic closures”
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Closure of a kinetic model of plasma in strong turbulence by relaxation
A Fokker-Planck kinetic equation for a turbulent plasma is derived by a repeated cascade decomposition. Calculation of the propagator and the kinetic equation determine the transport coefficients (diffusivity and turbulent viscosity) by means of a closure based on a relaxation procedure governing the approach to equilibrium. The k to the minus third power spectral law is obtained, which governs the coupling between the velocity and the electrostatic field fluctuations.
Tchen, C. M.↗
Intercomparison of Martian Lower Atmosphere Simulated Using Different Planetary Boundary Layer Parameterization Schemes
We use the mesoscale modeling capability of Mars Weather Research and Forecasting (MarsWRF) model to study the sensitivity of the simulated Martian lower atmosphere to differences in the parameterization of the planetary boundary layer (PBL). Characterization of the Martian atmosphere and realistic representation of processes such as mixing of tracers like dust depend on how well the model reproduces the evolution of the PBL structure. MarsWRF is based on the NCAR WRF model and it retains some of the PBL schemes available in the earth version. Published studies have examined the performance of different PBL schemes in NCAR WRF with the help of observations. Currently such assessments are not feasible for Martian atmospheric models due to lack of observations. It is of interest though to study the sensitivity of the model to PBL parameterization. Typically, for standard Martian atmospheric simulations, we have used the Medium Range Forecast (MRF) PBL scheme, which considers a correction term to the vertical gradients to incorporate nonlocal effects. For this study, we have also used two other parameterizations, a non-local closure scheme called Yonsei University (YSU) PBL scheme and a turbulent kinetic energy closure scheme called Mellor- Yamada-Janjic (MYJ) PBL scheme. We will present intercomparisons of the near surface temperature profiles, boundary layer heights, and wind obtained from the different simulations. We plan to use available temperature observations from Mini TES instrument onboard the rovers Spirit and Opportunity in evaluating the model results.
Natarajan, Murali↗
Finite element analysis of aeroacoustic jet-flap flows
A computational analysis was performed on the steady, turbulent aerodynamic flowfields associated with a jet-blown flap. For regions devoid of flow separation, a parabolic approximation to the governing time-averaged Navier-Stokes equations was applied. Numerical results are presented for the symmetry plane flow of a slot-nozzle planar jet flap geometry, including prediction of flowfield evolution within the secondary mixing region immediately downstream of the trailing edge. Using a two equation turbulence kinetic energy closure model, rapid generation and decay of large spatial gradients in mean and correlated fluctuating velocity components within the immediate wake region were predicted. Modifications to the turbulent flow structure, as induced by porous surface treatment of the flap, were evaluated. The recirculating flow within a representative discrete slot in the surface was evaluated, using the two dimensional, time-averaged Navier-Stokes equations.
Baker, A. J.↗
Single-column Model Intercomparison for a Stably Stratified Atmospheric Boundary Layer
The parameterization of the stably stratified atmospheric boundary layer is a difficult issue, which has a large impact on the medium-range weather forecasts and on climate integrations. A non-strongly stratified arctic case is simulated by nineteen single-column turbulence schemes. The statistics from the Large-eddy simulation (LES) intercomparison made for the same case by eight different models are used as a guiding reference. The single-column parameterizations include research schemes and operational schemes from major forecast and climate research centres. First order schemes, a large number of turbulence kinetic energy closures, and other proposals have submitted results. There is a large spread in the results; in general, the operational schemes mix more efficiently than the research ones, and the TKE and other higher order closures give results closer to the LES statistics. The sensitivities of the schemes to the parameters of their turbulence closures are partially explored.
Cuxart, J.↗
Demonstration of Capability to Simulate Particle Irregular Shape and Poly-Disperse Mixtures Within Lunar Lander Plume-Surface Interaction
Plume-Surface Interaction (PSI) between lander engine plumes and regolith soil creates hazards in obscuration and contamination by particle clouds, high-energy ejecta streams, and landing area cratering damage. The MSFC Fluid Dynamics Branch is developing simulation tools to offer a predictive PSI capability to NASA customers such as the Human Lander System (HLS) and Commercial Lunar Payload Services (CLPS). The Gas-Granular Flow Solver (GGFS) is the main application tool for coupled gas-particle two-phase flow simulations to predict the range of PSI effects from onset of surface erosion to deep crater formation. GGFS features an Eulerian-Eulerian modeling approach, treating both gas and granular material as interacting continuum phases. Modeling the lunar regolith granular material fluidic characteristics poses special challenges due to complex particle shapes and mixture composition. The lunar regolith is poorly sorted with broad particle size distributions and large fines content. It has significant cohesion, due to interlocking jagged particle shapes. Eulerian granular material flow modeling requires closure formulations for the granular material constitutive models (stress, friction, collisional and kinetic energy dissipation, drag, etc.). While closure models for spherical particles are available from particle kinetic theory, closure models for realistic non-spherical particles must be extracted from unit physics Discrete Element Model (DEM) particle interaction simulations and provided in the form of tabular datasets. The effects of particle irregular shape (non-spherical shape factors, angular particle surface roughness, and interlocking features) are simulated by approximating the particle features in the form of grouped elemental spheres to form composite particles in the DEM simulations. The effects of the wide range of regolith mixture particle sizes and the strong effects of the presence of the small particle sizes results in high cohesion and low porosity of the regolith mixture. The range of particle sizes is simulated by binning the particle sizes into an appropriate finite number of particle-size species and solving the problem as a species mixture. Combining these two modeling approaches enables simulations to capture both, the contributions of the irregular particle shape and the particle size distribution. The integration and maturation of the DEM-based constitutive model database generation process and poly-disperse mixture binning approach into the GGFS simulation framework are proceeding under funding by the NASA Game Changing Development program. The status of current capabilities will be presented in comparisons of crater characteristics resulting for spherical and irregular shape particles, and for mono-, bi-, and tri-disperse mixture simulations of Apollo LM plume-surface interaction. The computational results confirm the significance of including the particle shape and mixture effects. Going forward plans for the full implementation of the general poly-disperse regolith modeling capability and maturation towards NASA project application readiness under the GCD program will be presented.
Peter A Liever↗
Demonstration of Capability to Simulate Particle Irregular Shape and Poly-Disperse Mixtures Within Lunar Lander Plume-Surface Interaction
Plume-Surface Interaction (PSI) between lander engine plumes and regolith soil creates hazards in obscuration and contamination by particle clouds, high-energy ejecta streams, and landing area cratering damage. The MSFC Fluid Dynamics Branch is developing simulation tools to offer a predictive PSI capability to NASA customers such as the Human Lander System (HLS) and Commercial Lunar Payload Services (CLPS). The Gas-Granular Flow Solver (GGFS) is the main application tool for coupled gas-particle two-phase flow simulations to predict the range of PSI effects from onset of surface erosion to deep crater formation. GGFS features an Eulerian-Eulerian modeling approach, treating both gas and granular material as interacting continuum phases. Modeling the lunar regolith granular material fluidic characteristics poses special challenges due to complex particle shapes and mixture composition. The lunar regolith is poorly sorted with broad particle size distributions and large fines content. It has significant cohesion, due to interlocking jagged particle shapes. Eulerian granular material flow modeling requires closure formulations for the granular material constitutive models (stress, friction, collisional and kinetic energy dissipation, drag, etc.). While closure models for spherical particles are available from particle kinetic theory, closure models for realistic non-spherical particles must be extracted from unit physics Discrete Element Model (DEM) particle interaction simulations and provided in the form of tabular datasets. The effects of particle irregular shape (non-spherical shape factors, angular particle surface roughness, and interlocking features) are simulated by approximating the particle features in the form of grouped elemental spheres to form composite particles in the DEM simulations. The effects of the wide range of regolith mixture particle sizes and the strong effects of the presence of the small particle sizes results in high cohesion and low porosity of the regolith mixture. The range of particle sizes is simulated by binning the particle sizes into an appropriate finite number of particle-size species and solving the problem as a species mixture. Combining these two modeling approaches enables simulations to capture both, the contributions of the irregular particle shape and the particle size distribution. The integration and maturation of the DEM-based constitutive model database generation process and poly-disperse mixture binning approach into the GGFS simulation framework are proceeding under funding by the NASA Game Changing Development program. The status of current capabilities will be presented in comparisons of crater characteristics resulting for spherical and irregular shape particles, and for mono-, bi-, and tri-disperse mixture simulations of Apollo LM plume-surface interaction. The computational results confirm the significance of including the particle shape and mixture effects. Going forward plans for the full implementation of the general poly-disperse regolith modeling capability and maturation towards NASA project application readiness under the GCD program will be presented.
Peter A. Liever↗
An explicit three-dimensional nonhydrostatic numerical simulation of a tropical cyclone
A nonhydrostatic numerical simulation of a tropical cyclone is performed with explicit representation of cumulus on a meso-beta scale grid and for a brief period on a meso-gamma scale grid. Individual cumulus plumes are represented by a combination of explicit resolution and a 1.5 level closure predicting turbulent kinetic energy (TKE).
Tripoli, G. J.↗
Discontinuous Galerkin Methods for NonLinear Differential Systems
This talk considers simplified finite element discretization techniques for first-order systems of conservation laws equipped with a convex (entropy) extension. Using newly developed techniques in entropy symmetrization theory, simplified forms of the discontinuous Galerkin (DG) finite element method have been developed and analyzed. The use of symmetrization variables yields numerical schemes which inherit global entropy stability properties of the PDE (partial differential equation) system. Central to the development of the simplified DG methods is the Eigenvalue Scaling Theorem which characterizes right symmetrizers of an arbitrary first-order hyperbolic system in terms of scaled eigenvectors of the corresponding flux Jacobian matrices. A constructive proof is provided for the Eigenvalue Scaling Theorem with detailed consideration given to the Euler equations of gas dynamics and extended conservation law systems derivable as moments of the Boltzmann equation. Using results from kinetic Boltzmann moment closure theory, we then derive and prove energy stability for several approximate DG fluxes which have practical and theoretical merit.
Barth, Timothy↗
Formulation and closure of compressible turbulence equations in the light of kinetic theory
Fluid-dynamic moment equations, based on a kinetic hierarchy system, are derived governing the interaction between turbulent and thermal fluctuations. The kinetic theory is shown to reduce the inherent complexity of the conventional formalism of compressible turbulence theory and to minimize arbitrariness in formulating the closure condition.
Tsuge, S.↗
Turbulence kinetic energy equation for dilute suspensions
A multiphase turbulence closure model is presented which employs one transport equation, namely the turbulence kinetic energy equation. The proposed form of this equation is different from the earlier formulations in some aspects. The power spectrum of the carrier fluid is divided into two regions, which interact in different ways and at different rates with the suspended particles as a function of the particle-eddy size ratio and density ratio. The length scale is described algebraically. A mass/time averaging procedure for the momentum and kinetic energy equations is adopted. The resulting turbulence correlations are modeled under less retrictive assumptions comparative to previous work. The closures for the momentum and kinetic energy equations are given. Comparisons of the predictions with experimental results on liquid-solid jet and gas-solid pipe flow show satisfactory agreement.
Abou-Arab, T. W.↗
Prediction and measurement of turbulent aerodynamic trailing edge flows
A viscous-inviscid interaction algorithm is developed for prediction of two-dimensional mean and fluctuating velocity distributions in the wake immediately downstream of an airfoil trailing edge. A composite pressure field is defined, and a Poisson equation solved for transverse pressure variations. A parabolized form of the time-averaged steady Navier-Stokes equations are solved in conjunction with a viscous-augmented two-dimensional inviscid potential flow analysis. A tensor constitutive equation is employed to predict Reynolds stress distributions from solutions of a turbulence kinetic energy two equation closure model. Numerical predictions compared favorably with detailed experimental data for mean and fluctuating velocities, and Reynolds shear stress distributions, in the trailing edge region of a NACA 63-012 airfoil.
Baker, A. J.↗
Subgrid Combustion Modeling for the Next Generation National Combustion Code
In the first year of this research, a subgrid turbulent mixing and combustion methodology developed earlier at Georgia Tech has been provided to researchers at NASA/GRC for incorporation into the next generation National Combustion Code (called NCCLES hereafter). A key feature of this approach is that scalar mixing and combustion processes are simulated within the LES grid using a stochastic 1D model. The subgrid simulation approach recovers locally molecular diffusion and reaction kinetics exactly without requiring closure and thus, provides an attractive feature to simulate complex, highly turbulent reacting flows of interest. Data acquisition algorithms and statistical analysis strategies and routines to analyze NCCLES results have also been provided to NASA/GRC. The overall goal of this research is to systematically develop and implement LES capability into the current NCC. For this purpose, issues regarding initialization and running LES are also addressed in the collaborative effort. In parallel to this technology transfer effort (that is continuously on going), research has also been underway at Georgia Tech to enhance the LES capability to tackle more complex flows. In particular, subgrid scalar mixing and combustion method has been evaluated in three distinctly different flow field in order to demonstrate its generality: (a) Flame-Turbulence Interactions using premixed combustion, (b) Spatially evolving supersonic mixing layers, and (c) Temporal single and two-phase mixing layers. The configurations chosen are such that they can be implemented in NCCLES and used to evaluate the ability of the new code. Future development and validation will be in spray combustion in gas turbine engine and supersonic scalar mixing.
Menon, Suresh↗
The development and preliminary application of an invariant coupled diffusion and chemistry model
In many real-world pollution chemical reaction problems, the rate of reaction problems, the rate of reaction may be greatly affected by unmixedness. An approximate closure scheme for a chemical kinetic submodel which conforms to the principles of invariant modeling and which accounts for the effects of inhomogeneous mixing over a wide range of conditions has been developed. This submodel has been coupled successfully with invariant turbulence and diffusion models, permitting calculation of two-dimensional diffusion of two reacting (isothermally) chemical species. The initial calculations indicate the ozone reactions in the wake of stratospheric aircraft will be substantially affected by the rate of diffusion of ozone into the wake, and in the early wake, by unmixedness.
Hilst, G. R.↗
Simulations of Magnetic Reconnection - Kinetic Mechanisms Underlying the Fluid Description of Ions
Because of its ability to transfer the energy stored in magnetic field together with the breaking of the flux freezing constraint, magnetic reconnection is considered as one of the most important phenomena in plasma physics. When it happens in a collision less environment such as the terrestrial magnetosphere, it should a priori be modelled with in the framework of kinetic physics. The evidence of kinetic features has incidentally for a long time, been shown by researchers with the help of both numerical simulations and satellite observations. However, most of our understanding of the process comes from the more intuitive fluid interpretation with simple closure hypothesis which do not include kinetic effects. To what extent are these two separate descriptions of the same phenomenon related? What is the role of kinetic effects in the averaged/fluid dynamics of reconnection? This thesis addresses these questions for the proton population in the particular case of anti parallel merging with the help of 2D Hybrid simulations. We show that one can not assume, as is usually done, that the acceleration of the proton flow is only due to the Laplace force. Our results show, for symmetric and asymmetric connection, the importance of the pressure force, opposed to the electric one on the separatrices, in the decoupling region. In the symmetric case, we emphasize the kinetic origin of this force by analyzing the proton distribution functions and explain their structure by studying the underlying particle dynamics. Protons, as individual particles, are shown to bounce in the electric potential well created by the Hall effect. The spatial divergence of this well results in a mixing in phase space responsible for the observed structure of the pressure tensor. A detailed energy budget analysis confirms the role of the pressure force for the acceleration; but, contrary to what is sometimes assumed, it also reveals that the major part of the incoming Poynting flux is transferred to the thermal energy flux rather than to the convective kinetic energy flux, although the latter is generally supposed dominant. In the symmetric case, we propose the pressure tensor to be an additional proxy of the ion decoupling region in satellite data and verify this suggestion by studying a reconnection event encountered by the Cluster spacecrafts. Finally, the last part of this thesis is devoted to the study of the kinetic structure of asymmetric tangential current sheets where connection can develop. This theoretical part consists in finding a steady state solution to the Vlasov-Maxwell system for the protons in such a configuration. We present the theory and its first confrontation to numerical tests.
Aunai, icolas↗
Dynamics and structure of turbulent premixed flames
In earlier work (Mantel & Bilger, 1994) the structure of the turbulent premixed flame was investigated using statistics based on conditional averaging with the reaction progress variable as the conditioning variable. The DNS data base of Trouve and Poinsot (1994) was used in this investigation. Attention was focused on the conditional dissipation and conditional axial velocity in the flame with a view to modeling these quantities for use in the conditional moment closure (CMC) approach to analysis of kinetics in premixed flames (Bilger, 1993). Two remarkable findings were made: there was almost no acceleration of the axial velocity in the flame front itself; and the conditional scalar dissipation remained as high, or higher, than that found in laminar premixed flames. The first finding was surprising since in laminar flames all the fluid acceleration occurs through the flame front, and this could be expected also for turbulent premixed flames at the flamelet limit. The finding gave hope of inventing a new approach to the dynamics of turbulent premixed flames through use of rapid distortion theory or an unsteady Bernoulli equation. This could lead to a new second order closure for turbulent premixed flames. The second finding was contrary to our measurements with laser diagnostics in lean hydrocarbon flames where it is found that conditional scalar dissipation drops dramatically below that for laminar flamelets when the turbulence intensity becomes high. Such behavior was not explainable with a one-step kinetic model, even at non-unity Lewis number. It could be due to depletion of H2 from the reaction zone by preferential diffusion. The capacity of the flame to generate radicals is critically dependent on the levels of H2 present (Bilger, et al., 1991). It seemed that a DNS computation with a multistep reduced mechanism would be worthwhile if a way could be found to make this feasible. Truly innovative approaches to complex problems often come only when there is the opportunity to work close at hand with the (in this case numerical) experimental data. Not only can one spot patterns and relationships in the data which could be important, but one can also get to know the limitations of the technique being used, so that when the next experiment is being designed it will address resolvable questions. A three-year grant from the Australian Research Council has enabled us to develop a small capability at the University of Sydney to work on DNS of turbulent reacting flow, and to analyze data bases generated at CTR. Collaboration between the University of Sydney and CTR is essential to this project and finding a workable modus operandum for this collaboration, given the constraints involved, has been a major objective of the past year's effort. The overall objectives of the project are: (1) to obtain a quantitative understanding of the dynamics of turbulent premixed flames at high turbulence levels with a view to developing improved second order closure models; and (2) to carry out new DNS experiments on turbulent premixed flames using a carefully chosen multistep reduced mechanism for the chemical kinetics, with a view to elucidating the laser diagnostic findings that are contrary to the findings for DNS using one-step kinetics. In this first year the objectives have been to make the existing CTR data base more accessible to coworkers at the University of Sydney, to make progress on understanding the dynamics of the flame in this existing CTR data base, and to carefully construct a suitable multistep reduced mechanism for use in a new set of DNS experiments on turbulent premixed flames.
Bilger, R. W.↗
Parallel Simulation of Unsteady Turbulent Flames
Time-accurate simulation of turbulent flames in high Reynolds number flows is a challenging task since both fluid dynamics and combustion must be modeled accurately. To numerically simulate this phenomenon, very large computer resources (both time and memory) are required. Although current vector supercomputers are capable of providing adequate resources for simulations of this nature, the high cost and their limited availability, makes practical use of such machines less than satisfactory. At the same time, the explicit time integration algorithms used in unsteady flow simulations often possess a very high degree of parallelism, making them very amenable to efficient implementation on large-scale parallel computers. Under these circumstances, distributed memory parallel computers offer an excellent near-term solution for greatly increased computational speed and memory, at a cost that may render the unsteady simulations of the type discussed above more feasible and affordable.This paper discusses the study of unsteady turbulent flames using a simulation algorithm that is capable of retaining high parallel efficiency on distributed memory parallel architectures. Numerical studies are carried out using large-eddy simulation (LES). In LES, the scales larger than the grid are computed using a time- and space-accurate scheme, while the unresolved small scales are modeled using eddy viscosity based subgrid models. This is acceptable for the moment/energy closure since the small scales primarily provide a dissipative mechanism for the energy transferred from the large scales. However, for combustion to occur, the species must first undergo mixing at the small scales and then come into molecular contact. Therefore, global models cannot be used. Recently, a new model for turbulent combustion was developed, in which the combustion is modeled, within the subgrid (small-scales) using a methodology that simulates the mixing and the molecular transport and the chemical kinetics within each LES grid cell. Finite-rate kinetics can be included without any closure and this approach actually provides a means to predict the turbulent rates and the turbulent flame speed. The subgrid combustion model requires resolution of the local time scales associated with small-scale mixing, molecular diffusion and chemical kinetics and, therefore, within each grid cell, a significant amount of computations must be carried out before the large-scale (LES resolved) effects are incorporated. Therefore, this approach is uniquely suited for parallel processing and has been implemented on various systems such as: Intel Paragon, IBM SP-2, Cray T3D and SGI Power Challenge (PC) using the system independent Message Passing Interface (MPI) compiler. In this paper, timing data on these machines is reported along with some characteristic results.
Menon, Suresh↗
A critical comparison of turbulence models for homogeneous shear flows in a rotating frame
A variety of turbulence models, including five second-order closure models and four two equation models, are tested for the problem of homogeneous turbulent shear flow in a rotating frame. The model predictions for the time evolution of the turbulent kinetic energy and dissipation rate, as well as those for the equilibrium states, are compared with the results of physical and numerical experiments. Most of the two-equation models predict the same results for all rotation rates (omega/S) in which there is an exponential time growth of the turbulent kinetic energy and dissipation rate. The second-order closures are qualitatively superior since, consistent with physical and numerical experiments, they only predict this type of unstable flow for intermediate rotation rates in the range -0.1 less than or equal to omega/S less than or equal to 1.6. For rotation rates outside this range, there is an exchange of stabilities with a solution whose kinetic energy and dissipation rate decay with time. Although the second-order closures are superior to the two-equation models, there are still problems with the quantitative accuracy of their predictions.
Speziale, Charles G.↗