Particle-in-cell Simulations of Decaying Plasma Turbulence: Linear Instabilities versus Nonlinear Processes in 3D and 2.5D Approximations
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S. Peter Gary↗
SEARCH · Engineering Papers
Results for “Turbulence simulation”
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Simulations of tokamak edge plasma turbulent fluctuations based on a minimal 3D model
In this study, a new simulation model for tokamak boundary plasma, SOLT3D, is implemented in the BOUT++ framework. The simulation model includes a set of dynamic equations describing collisional boundary plasma and neutral gas in the tokamak scrape-off layer and divertor region. The model is verified against standard linear plasma instabilities and available nonlinear results. For L-mode like conditions, SOLT3D reproduces characteristics of boundary plasma turbulent fluctuations that are similar to published experimental data, in terms of the amplitude and spatial dependence of the fluctuations. It also reproduces realistic plasma fluxes on material surfaces and expected Bohm-like effective radial transport. Plasma fluctuations inferred from the simulations imply inevitably a significant level of intrinsic 'noise' for axisymmetric tokamak plasma transport modeling, introducing errors on the order of unity. In particular, the toroidally averaged atomic rates below 5–10 eV are strongly modified by turbulent plasma fluctuations, which should significantly affect the standard axisymmetric modeling of the tokamak edge plasma and divertor.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Subgrid-scale backscatter in transitional and turbulent flows
Most subgrid-scale (SGS) models for large-eddy simulations are absolutely dissipative (that is, they remove energy from the large scales at each point in the physical space). The actual SGS stresses, however, may transfer energy to the large scales (backscatter) at a given location. Direct numerical simulations of turbulent channel flow and compressible isotropic turbulence are used to study the backscatter phenomena. In all flows considered roughly 50 percent of the grid points were experiencing backscatter when a Fourier cutoff filter was used. The backscatter fraction was less with a Gaussian filter, and intermediate with a box filter in physical space. Moreover, the backscatter and forward scatter contributions to the SGS dissipation were comparable, and each was often much larger than the total SGS dissipation. The SGS dissipation (normalized by total dissipation) increased with filter width almost independently of filter type and Reynolds number. The amount of backscatter showed an increasing trend with Reynolds numbers. In the near-wall region of the channel, events characterized by strong Reynolds shear stress correlated fairly well with areas of high SGS dissipation (both forward and backward). In compressible isotropic turbulence similar results were obtained, independent of fluctuation Mach number.
Piomelli, Ugo↗
On the Subgrid-Scale Modeling of Compressible Turbulence
A new sub-grid scale model is presented for the large-eddy simulation of compressible turbulence. In the proposed model, compressibility contributions have been incorporated in the sub-grid scale eddy viscosity which, in the incompressible limit, reduce to a form originally proposed by Smagorinsky (1963). The model has been tested against a simple extension of the traditional Smagorinsky eddy viscosity model using simulations of decaying, compressible homogeneous turbulence. Simulation results show that the proposed model provides greater dissipation of the compressive modes of the resolved-scale velocity field than does the Smagorinsky eddy viscosity model. For an initial r.m.s. turbulence Mach number of 1.0, simulations performed using the Smagorinsky model become physically unrealizable (i.e., negative energies) because of the inability of the model to sufficiently dissipate fluctuations due to resolved scale velocity dilations. The proposed model is able to provide the necessary dissipation of this energy and maintain the realizability of the flow. Following Zeman (1990), turbulent shocklets are considered to dissipate energy independent of the Kolmogorov energy cascade. A possible parameterization of dissipation by turbulent shocklets for Large-Eddy Simulation is also presented.
Squires, Kyle↗
Large eddy simulation of a supersonic lifted hydrogen flame: Impacts of Lewis, turbulent Schmidt and Prandtl numbers
Parametric large eddy simulations (LES) of a supersonic lifted hydrogen flame are reported. The emphases are on two aspects: impacts of (1) Lewis number (Lei of the ith species) and (2) turbulent Schmidt and Prandtl numbers (Sc t and Pr t ) on supersonic turbulent flame and flow structures. Five cases are considered: species-specific Le i , Sc t = Sr t = 1.0 (C 0 ); unity Le i , Sc t = Pr t = 1.0 (C 1 ); species-specific Sc t = 0.5, Pr t = 1.0 (C 2 ); species-specific Le i , Sc t = 1.0, Pr t = 0.5 (C 3 ); and species-specific Le i , Sc t = Pr t = 0.5 (C 4 ). Numerical results of instantaneous and/or time-averaged species mole fractions, mixture fraction, heat release rate, flame base location, and mixed modes of premixed and diffusion combustion are compared between cases C 0 and C 1 . Differences in auto-ignition locations and strengths and flame structures and stabilization specify the impacts of Lewis number. They are triggered by different predictions of species mass and thermal diffusions at fuel-coflow and/or coflow-ambient air mixing layers. These differences are rationalized by a scale analysis of mass/thermal diffusion and convection for case C 0 , which suggests the relatively low but non-negligible former against the latter. Cases C 0 and C 2 –C 4 barely see differences in terms of instantaneous and/or time-averaged temperature, velocity, and mixed combustion modes except for further downstream areas where combustion occurs. Both Sc t and Pr t impose less significant influences than Lewis number, as sub-grid scale mass/thermal diffusion is subordinate to its resolved counterpart according to their scale analysis for case C 4 .
42 ENGINEERING↗
Turbulence Effects on Shaped Booms: Propagation Simulations Using KZKFourier
Upcoming X-59 aircraft flight tests as part of NASA’s Quesst Mission are expected to occur in a range of atmospheric conditions. Sensitivity of ground waveform acoustic metrics to turbulent perturbations during propagation complicates the determination of noise levels. A series of simulations through turbulence was executed using the KZKFourier model of Stout et al. to develop a database of results for expanding the functionality of NASA tools for estimating turbulence effects on shaped-boom ground waveforms. For 45 cases covering a seven-factor design space, multiple realizations of turbulence were generated to characterize statistical turbulence effects on levels of six acoustic metrics. An individual simulation in the study produced over one thousand waveforms across a virtual microphone array. Different measures were used to evaluate refinement of results with increasing number of simulations. Data suggest that mean effects and variability were most strongly influenced by propagation distance and velocity fluctuation intensity. Although local increases in acoustic metrics were common, the overall average result in all cases was a reduction in metric levels. Sensitivity of acoustic metrics varied, with mean reductions of up to 2 dB in Perceived Level occurring across the 45 cases.
turbulence↗
Simulation and modeling of homogeneous compressible turbulence under isotropic mean compression
Compressible homogeneous turbulence subjected to isotropic mean compression is simulated numerically for high and low turbulent Mach numbers, at various compression rates. It is found that at low Mach numbers, the effects of viscosity variations on the development of the turbulent kinetic energy can be significant. A model consistent with the invariance of the Navier-Stokes equations to spherical compression, that takes into account variable viscosity effects is proposed. At high Mach numbers, the distribution of energy between the acoustic and solenoid fields is found to depend upon initial conditions. The simulation results are also used to evaluate two-equation compressible turbulence models.
Coleman, G. N.↗
Investigation of grid-based vorticity-velocity large eddy simulation off-body solvers for application to overset CFD
Accurately predicting unsteady wakes and vortex-dominated flows is essential to a wide range of engineering applications, including aircraft, rotorcraft, shipboard operations, bio-inspired unsteady flight and propulsion, wind turbines, and urban flows. While current CFD software can model the complete flow field and wake system, the computational costs incurred in high Reynolds number unsteady turbulent flow simulations often remain prohibitive for routine engineering use, particularly for applications involving moving components. Prior work has demonstrated that by adopting a vorticity-velocity formulation in a grid-based off-body flow solver (VorTran-M and VorTran-M2) one can lower these costs by several orders of magnitude when compared to conventional approaches. This paper describes the extensions made to VorTran-M2 to support turbulent flows, and associated benchmarking activity to assess its performance for problems involving strong stretching and diffusion processes, whose competing contributions to the vorticity field are core drivers of turbulent flow evolution. Predictions are presented for: (i) the Kida-Pelz problem whose inviscid form is of mathematical interest due to its apparent formation of singular flow in finite time; and (ii) the Taylor Green vortex arrangement, which has been extensively studied as a fundamental simulation challenge in the turbulent modeling community. Here, the results are used to evaluate the overall predictive ability and performance of two sub-grid scale models incorporated into VorTran-M2. Results indicate that the computational cost savings seen previously for inviscid and convection dominated problems extend to turbulent flow simulations supporting the viability of VorTran-M2 as a low cost means for accurately modeling the far-field and background flow, particularly when long duration vorticity evolution is of interest.
42 ENGINEERING↗
Modeling of Alkane Oxidation Using Constituents and Species
It is currently not possible to perform simulations of turbulent reactive flows due in particular to complex chemistry, which may contain thousands of reactions and hundreds of species. This complex chemistry results in additional differential equations, making the numerical solution of the equation set computationally prohibitive. Reducing the chemical kinetics mathematical description is one of several important goals in turbulent reactive flow modeling. A chemical kinetics reduction model is proposed for alkane oxidation in air that is based on a parallel methodology to that used in turbulence modeling in the context of the Large Eddy Simulation. The objective of kinetic modeling is to predict the heat release and temperature evolution. This kinetic mechanism is valid over a pressure range from atmospheric to 60 bar, temperatures from 600 K to 2,500 K, and equivalence ratios from 0.125 to 8. This range encompasses diesel, HCCI, and gas-turbine engines, including cold ignition. A computationally efficient kinetic reduction has been proposed for alkanes that has been illustrated for n-heptane using the LLNL heptane mechanism. This model is consistent with turbulence modeling in that scales were first categorized into either those modeled or those computed as progress variables. Species were identified as being either light or heavy. The heavy species were decomposed into defined 13 constituents, and their total molar density was shown to evolve in a quasi-steady manner. The light species behave either in a quasi-steady or unsteady manner. The modeled scales are the total constituent molar density, Nc, and the molar density of the quasi-steady light species. The progress variables are the total constituent molar density rate evolution and the molar densities of the unsteady light species. The unsteady equations for the light species contain contributions of the type gain/loss rates from the heavy species that are modeled consistent with the developed mathematical forms for the total constituent molar density rate evolution; indeed, examination of these gain/loss rates shows that they also have a good quasi-steady behavior with a functional form resembling that of the constituent rate. This finding highlights the fact that the fitting technique provides a methodology that can be repeatedly used to obtain an accurate representation of full or skeletal kinetic models. Assuming success with the modified reduced model, the advantage of the modeling approach is clear. Because this model is based on the Nc rate rather than on that of individual heavy species, even if the number of species increases with increased carbon number in the alkane group, providing that the quasi-steady rate aspect persists, then extension of this model to higher alkanes should be conceptually straightforward, although it remains to be seen if the functional fits would remain valid or would require reconstruction.
Bellan, Jasette↗
DPM: A deep learning PDE augmentation method with application to large-eddy simulation
A framework is introduced that leverages known physics to reduce overfitting in machine learning for scientific applications. The partial differential equation (PDE) that expresses the physics is augmented with a neural network that uses available data to learn a description of the corresponding unknown or unrepresented physics. Training within this combined system corrects for missing, unknown, or erroneously represented physics, including discretization errors associated with the PDE's numerical solution. For optimization of the network within the PDE, an adjoint PDE is solved to provide high-dimensional gradients, and a stochastic adjoint method (SAM) further accelerates training. Additionally, the approach is demonstrated for large-eddy simulation (LES) of turbulence. High-fidelity direct numerical simulations (DNS) of decaying isotropic turbulence provide the training data used to learn sub-filter-scale closures for the filtered Navier–Stokes equations. Out-of-sample comparisons show that the deep learning PDE method outperforms widely-used models, even for filter sizes so large that they become qualitatively incorrect. It also significantly outperforms the same neural network when a priori trained based on simple data mismatch, not accounting for the full PDE. Measures of discretization errors, which are well-known to be consequential in LES, point to the importance of the unified training formulation's design, which without modification corrects for them. For comparable accuracy, simulation runtime is significantly reduced. A relaxation of the typical discrete enforcement of the divergence-free constraint in the solver is also successful, instead allowing the DPM to approximately enforce incompressibility physics. Since the training loss function is not restricted to correspond directly to the closure to be learned, training can incorporate diverse data, including experimental data.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Development and application of a non-Gaussian atmospheric turbulence model for use in flight simulators
A method is described for generating time histories which model the frequency content and certain non-Gaussian probability characteristics of atmospheric turbulence including the large gusts and patchy nature of turbulence. Methods for time histories using either analog or digital computation are described. A STOL airplane was programmed into a 6-degree-of-freedom flight simulator, and turbulence time histories from several atmospheric turbulence models were introduced. The pilots' reactions are described.
Reeves, P. M.↗
Numerical investigation of supersonic turbulent boundary layers with high wall temperature
A direct numerical approach has been developed to simulate supersonic turbulent boundary layers. The mean flow quantities are obtained by solving the parabolized Reynolds-averaged Navier-Stokes equations (globally). Fluctuating quantities are computed locally with a temporal direct numerical simulation approach, in which nonparallel effects of boundary layers are partially modeled. Preliminary numerical results obtained at the free-stream Mach numbers 3, 4.5, and 6 with hot-wall conditions are presented. Approximately 5 million grid points are used in all three cases. The numerical results indicate that compressibility effects on turbulent kinetic energy, in terms of dilatational dissipation and pressure-dilatation correlation, are small. Due to the hot-wall conditions the results show significant low Reynolds number effects and large streamwise streaks. Further simulations with a bigger computational box or a cold-wall condition are desirable.
Guo, Y.↗
Computed Turbulent Free Shear Flow Of Air
Standard k-epsilon model of turbulence yields fairly accurate results. Symposium paper discusses numerical simulation of turbulent free shear flow of nonreacting compressible fluid. Ability to compute such flows essential to advances in design.
Viegas, J. R.↗
Comment on "Heterodyne Lidar Returns in the Turbulent Atmosphere: Performance Evaluation of Simulated Systems"
The explanation for the difference between simulation and the zero-order theory for heterodyne lidar returns in a turbulent atmosphere proposed by Belmonte and Rye is incorrect. The theoretical expansion is not developed under a square- law-structure function approximation (random wedge atmosphere). Agreement between the simulations and the zero-order term of the theoretical expansion is produced for the limit of statistically independent paths (bi-static operation with large transmitter-receiver separation) when the simulations correctly include the large-scale gradients of the turbulent atmosphere.
Frehlich, Rod↗
Physical considerations governing computation of turbulent flows over bodies at large incidence
The physical aspects governing accurate numerical simulation of turbulent flows having large regions of crossflow separation are re-examined. Time-accurate, three-dimensional fine-grid Navier-Stokes solutions were obtained for turbulent subsonic and supersonic flows over a slender ogive-cylinder body of revolution at large angles of attack. These flowfields are complex and contain regions of crossflow separation and an organized leeward-side vortex structure. An algebraic eddy-viscosity turbulence model has been modified to correctly account for the effects of the vortices on the underlying viscous layers. The numerical results show that the vortical flow structure of both subsonic and supersonic high incidence flows are similar, and can be accurately treated by the turbulence model. As the angle of attack is increased, the effectiveness of the model increases since the influence of the vortices on the underlying boundary layer decreases.
Degani, David↗
An Improved Approach to the Predictability & Reliability of the Onset of Turbulence With Shocks
The construction of numerical schemes for (a) stable and accurate simulation of turbulence with strong shocks, and for (b) obtaining correct propagation speed of discontinuities in the presence of stiff source terms share one important ingredient – minimization of numerical dissipation while maintaining numerical stability. The dual requirements to achieve both numerical stability and minimal numerical dissipation are often conflicting since existing shock capturing schemes were designed mainly to be robust for rapidly developed turbulence-free flows and for shock waves without stiff source term. For the past two decades, Yee and collaborators have focused on an improved understanding of the nonlinear behavior of different high order shock-capturing methods. It was found that even very high order methods without proper nonlinear stability and numerical dissipation control can either numerically smear the onset of turbulence due to excess numerical dissipation, or induce (onset) numerical turbulence that is not physical turbulence due to lack of proper numerical dissipation to improve nonlinear stability for long time integration. Our approach is to combine (I) and (II) below for obtaining the physically correct onset of turbulence with shocks, including problems with stiff source terms: (I) Nonlinear dynamics is utilized to complement the traditional linearized stability theory (Yee & Sweby, Yee et al., Griffiths et al., Lafon & Yee, Yee, Wang et al., Kotov et al. 1990- 2015) in order to (i) Minimize numerically induced false transition to turbulence, (ii) Minimize numerical instability due to long time integration of turbulent flows, (iii) Minimize numerically induced standing wave solutions, and (iv) Minimize wrong propagation of speed of discontinuities due to the presence of stiff source terms. (II) Our recently developed physical preserving (structural preserving) high order methods with improved nonlinear stability & accuracy that are essential in minimizing spurious numerics are used.
HECC↗
Numerical Study of a Convective Turbulence Encounter
A numerical simulation of a convective turbulence event is investigated and compared with observational data. The specific case was encountered during one of NASA's flight tests and was characterized by severe turbulence. The event was associated with overshooting convective turrets that contained low to moderate radar reflectivity. Model comparisons with observations are quite favorable. Turbulence hazard metrics are proposed and applied to the numerical data set. Issues such as adequate grid size are examined.
Proctor, Fred H.↗
Numerical simulation of the generation of turbulence from cometary ion pick-up
Observations of magnetic field fluctuations near Comet Halley have revealed a rapid development of a Kolmogoroff-like turbulence spectrum extending from below 0.01 Hz to above 0.1 Hz. Spectra obtained far from the comet have a strong peak in power near the Doppler-shifted ion-cyclotron frequency of singly ionized water. Closer to the comet, the spectrum at higher frequencies is enhanced in power level over the background solar wind spectrum by approximately an order of magnitude. The equations of incompressible MHD are solved using a two-dimensional 256 x 256 mode spectral method code to simulate this spectral evolution as an inertial range turbulent cascade. The initial conditions contained a constant magnetic field and a single coherent wave mode at a low wave number. The solar wind turbulence was modeled by a background noise spectrum having a Kolmogoroff spectral index. The coherent mode decayed into an inertial range spectrum with Kolmogoroff slope within a few eddy-turnover times. Both the time scale and the increase in power level of the turbulence seen in the simulation are in accord with the Giotto observations.
Goldstein, M. L.↗