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DOE OSTI2017

Generalized fluid theory including non-Maxwellian kinetic effects

The results obtained by the plasma physics community for the validation and the prediction of turbulence and transport in magnetized plasmas come mainly from the use of very central processing unit (CPU)-consuming particle-in-cell or (gyro)kinetic codes which naturally include non-Maxwellian kinetic effects. To date, fluid codes are not considered to be relevant for the description of these kinetic effects. Here, after revisiting the limitations of the current fluid theory developed in the 19th century, we generalize the fluid theory including kinetic effects such as non-Maxwellian super-thermal tails with as few fluid equations as possible. The collisionless and collisional fluid closures from the nonlinear Landau Fokker–Planck collision operator are shown for an arbitrary collisionality. Indeed, the first fluid models associated with two examples of collisionless fluid closures are obtained by assuming an analytic non-Maxwellian distribution function. One of the main differences with the literature is our analytic representation of the distribution function in the velocity phase space with as few hidden variables as possible thanks to the use of non-orthogonal basis sets. These new non-Maxwellian fluid equations could initiate the next generation of fluid codes including kinetic effects and can be expanded to other scientific disciplines such as astrophysics, condensed matter or hydrodynamics. As a validation test, we perform a numerical simulation based on a minimal reduced INMDF fluid model. The result of this test is the discovery of the origin of particle and heat diffusion. The diffusion is due to the competition between a growing INMDF on short time scales due to spatial gradients and the thermalization on longer time scales. Here, the results shown here could provide the insights to break some of the unsolved puzzles of turbulence.

42 ENGINEERING↗

DOE OSTI2024

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↗

DOE OSTI2020

Grassy ELM regime at low pedestal collisionality in high-power tokamak plasma

Spontaneous mitigation of giant ELMs and appearance of grassy ELMs have been observed repeatedly at low pedestal collisionality (${\nu }_{\mathrm{e},\mathrm{p}\mathrm{e}\mathrm{d}}^{{\ast}}\sim 0.15$) in the high-power (P inj > 13 MW) hybrid scenario in DIII-D. Higher β p and higher q 95 appear to be beneficial to achieving the grassy ELM regime. The grassy ELM H-mode plasma shows high energy confinement performance (H 98y2 up to over 1.5) under the conditions of high neutral beam torque and high core rotation. The pedestal width appears to exceed the EPED1.0 model prediction by more than 50%. Pedestal stability analysis performed with the ELITE code indicates that the stability against low-n kink/peeling modes is improved with increased auxiliary heating power and the operational point in the grassy ELM regime is located near the ballooning boundary. The pedestal stability characteristics during the grassy ELM crashes have been investigated in comparison with the giant ELM crashes based on plasma profiles experimentally measured with high resolution and accuracy. It has been found that the underlying mechanism for the observed small-amplitude ELM crashes is mainly the expansion of the ballooning stability boundary induced by an initial radially localized collapse in the pedestal, which helps to stop the growth of instabilities and further collapse of the pedestal. The effect of electron density pedestal on mitigating edge localized instabilities has been analyzed by numerical simulation, suggesting that the electron density pedestal characterized by high n e,sep /n e,ped and low density gradient helps to stabilize peeling-ballooning modes because of a low pressure pedestal gradient and to lower the ballooning boundary mainly because of a low ion diamagnetic frequency in the pedestal region, thus triggering ballooning instabilities and producing the intrinsic grassy ELMs. Numerical simulation of the Chinese fusion engineering test reactor (CFETR) with the SOLPS code indicates that the separatrix density might be insensitive to the electron diffusivity in the pedestal region and increase with the power flowing from the core region to the edge region. Furthermore, pedestal stability analysis suggests that the flat density pedestal with high separatrix density obtained in the high-power plasma in CFETR would make the operational point close to the ballooning boundary, which is considered to help destabilize ballooning instabilities and facilitate the access to the grassy ELM regime.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Randomized Sketching Algorithms for Low-Memory Dynamic Optimization

This paper develops a novel limited-memory method to solve dynamic optimization problems. The memory requirements for such problems often present a major obstacle, particularly for problems with PDE constraints such as optimal flow control, full waveform inversion, and optical tomography. In these problems, PDE constraints uniquely determine the state of a physical system for a given control; the goal is to find the value of the control that minimizes an objective. While the control is often low dimensional, the state is typically more expensive to store. This paper suggests using randomized matrix approximation to compress the state as it is generated and shows how to use the compressed state to reliably solve the original dynamic optimization problem. Concretely, the compressed state is used to compute approximate gradients and to apply the Hessian to vectors. The approximation error in these quantities is controlled by the target rank of the sketch. This approximate first- and second-order information can readily be used in any optimization algorithm. As an example, we develop a sketched trust-region method that adaptively chooses the target rank using a posteriori error information and provably converges to a stationary point of the original problem. Numerical experiments with the sketched trust-region method show promising performance on challenging problems such as the optimal control of an advection-reaction-diffusion equation and the optimal control of fluid flow past a cylinder.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Semi-Analytic Functions to Calculate the Deposition Coefficients for Ice Crystal Vapor Growth in Bin and Bulk Microphysical Models

Numerical cloud models require estimates of the vapor growth rate for ice crystals. Current bulk and bin microphysical parameterizations generally assume that vapor growth is diffusion limited, though some parameterizations include the influence of surface attachment kinetics through a constant deposition coefficient. A parameterization for variable deposition coefficients is provided herein. The parameterization is an explicit function of the ambient ice supersaturation and temperature, and an implicit function of crystal dimensions and pressure. The parameterization is valid for variable surface types including growth by dislocations and growth by step nucleation. Deposition coefficients are predicted for the two primary growth directions of crystals, allowing for the evolution of the primary habits. Comparisons with benchmark calculations of instantaneous mass growth indicate that the parameterization is accurate to within a relative error of 1%. Parcel model simulations using Lagrangian microphysics as a benchmark indicate that the bulk parameterization captures the evolution of mass mixing ratio and fall speed with typical relative errors of less than 10%, whereas the average axis lengths can have errors of up to 20%. The bin model produces greater accuracy with relative errors often less that 10%. The deposition coefficient parameterization can be used in any bulk and bin scheme, with low error, if an equivalent volume spherical radius is provided.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Improved Prediction of Cold-Air Pools in the Weather Research and Forecasting Model Using a Truly Horizontal Diffusion Scheme for Potential Temperature

The terrain-following vertical coordinate system used by many atmospheric models, including the Weather Research and Forecasting (WRF) Model, is prone to errors in regions of complex terrain. These errors stem, in part, from the calculation of horizontal gradients within the diffusion term of the momentum or scalar evolution equations. In WRF, such gradients can be calculated along coordinate surfaces, or using metric terms that help account for grid skewness. However, neither of these options ensures a truly horizontal gradient calculation, especially if a grid cell is skewed enough that the heights of the neighboring grid points used in the calculation fall outside the vertical range of the cell. In this work, an improved scheme that uses Taylor series approximations to vertically interpolate variables to the level necessary for a truly horizontal gradient calculation is implemented in WRF for the diffusion of potential temperature. The scheme is validated using an atmosphere-at-rest configuration, in which spurious flows develop only as a result of numerical errors and can thus be used as a proxy for model performance. Following validation, the method is applied to the simulation of cold-air pools (CAPs), which occur in regions of complex terrain and are characterized by strong near-surface temperature gradients. Using the truly horizontal scheme, idealized simulations demonstrate reduced numerical mixing in a quiescent CAP, and a realistic case study in the Columbia River basin shows a reduction in positive wind speed bias by up to roughly 20% compared to observations from the Second Wind Forecast Improvement Project.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2018

Dynamical Analysis of Three Distant Trans-Neptunian Objects with Similar Orbits

Here, this paper reports the discovery and orbital characterization of two extreme trans-Neptunian objects (ETNOs), 2016 QV 89 and 2016 QU 89 , which have orbits that appear similar to that of a previously known object, 2013 UH 15 . All three ETNOs have semimajor axes a ≈ 172 au and eccentricities e ≈ 0.77. The angular elements (i, ω, Ω) vary by 6°, 15°, and 49°, respectively, between the three objects. The two new objects add to the small number of TNOs currently known to have semimajor axes between 150 and 250 au, and they serve as an interesting dynamical laboratory to study the outer realm of our solar system. Using a large ensemble of numerical integrations, we find that the orbits are expected to reside in close proximity in the (a, e) phase plane for roughly 100 Myr before diffusing to more separated values. We find that an explanation for the orbital configuration of the bodies as a collision product is disfavored. We then explore other scenarios that could influence their orbits. With aphelion distances over 300 au, the orbits of these ETNOs extend far beyond the classical Kuiper Belt and an order of magnitude beyond Neptune. As a result, their orbital dynamics can be affected by the proposed new solar system member, referred to as Planet Nine in this work. With perihelion distances of 35–40 au, these orbits are also influenced by resonant interactions with Neptune. Furthermore, a full assessment of any possible new solar system planets must thus take into account this emerging class of TNOs.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1971

Recent radial turbine research at the NASA Lewis Research Center

The high efficiencies of small radial turbines led to their application in space power systems and numerous APU and shaft power engines. Experimental and analytical work associated with these systems included examination of blade-shroud clearance, blade loading, and exit diffuser design. Results indicate high efficiency over a wide range of specific speed and also insensitivity to clearance and blade loading in the radial part of the rotor. The exit diffuser investigation indicated that a conventional conical outer wall may not provide the velocity variation consistent with minimum overall diffuser loss.

Rohlik, H. E.↗

NASA NTRS1981

A general method for computing the total solar radiation force on complex spacecraft structures

The method circumvents many of the existing difficulties in computational logic presently encountered in the direct analytical or numerical evaluation of the appropriate surface integral. It may be applied to complex spacecraft structures for computing the total force arising from either specular or diffuse reflection or even from non-Lambertian reflection and re-radiation.

Chan, F. K.↗

NASA NTRS1981

Numerical experiments on the role of radiative processes in the development and maintenance of upper level clouds

A time-dependent, two-dimensional Eulerian model is presented whose purpose is to obtain more realistic parameterizations of extended high level cloudiness, and the results of a numerical experiment using the model are reported. The model is anelastic and the Bousinesque assumption is invoked. Unresolved subgrid scale processes are parameterized as eddy diffusion processes. Two phases of water are incorporated and equilibrium between them is assumed. The effects of infrared radiative processes are parametrically represented. Two simulations were conducted with identical initial conditions; in one of them, the radiation term was never turned on. The mean values of perturbation potential temperature at each level in the domain are plotted versus height after 15, 30, and 60 minutes of simulated time. The influence of the radiative term is seen to impose a cooling trend, leading to an increased generation of ice water and an increased generation of turbulent kinetic energy in the cloud layer.

Starr, D. O'C.↗

NASA NTRS1982

Single-mode theory of diffusive layers in thermohaline convection

A two-layer configuration of thermohaline convection is studied, with the principal aim of explaining the observed independence of the buoyancy-flux ratio on the stability parameter when the latter is large. Temperature is destabilizing and salinity is stabilizing, so diffusive interfaces separate the convecting layers. The convection is treated in the single-mode approximation, with a prescribed horizontal planform and wavenumber. Surveys of numerical solutions are presented for a selection of Rayleigh numbers R, stability parameters lambda and horizontal wavenumbers. The solutions yield a buoyancy flux ratio chi that is insensitive to lambda, in accord with laboratory experiments. However chi increases with increasing R, in contradiction to laboratory observations.

Gough, D. O.↗

NASA NTRS1985

Features of a reattaching turbulent shear layer in divergent channel flow

Experimental data have been obtained in an incompressible turbulent flow over a rearward-facing step in a diverging channel flow. Mean velocities, Reynolds stresses, and triple products that were measured by a laser Doppler velocimeter are presented for two cases of tunnel wall divergence. Eddy viscosities, production, convection, turbulent diffusion, and dissipation (balance of kinetic energy equation) terms are extracted from the data. These data are compared with various eddy-viscosity turbulence models. Numerical calculations incorporating the k-epsilon and algebraic-stress turbulence models are compared with the data. When determining quantities of engineering interest, the modified algebraic-stress model (ASM) is a significant improvement over the unmodified ASM and the unmodified k-epsilon model; however, like the others, it dramatically overpredicts the experimentally determined dissipation rate.

Driver, D. M.↗

NASA NTRS1986

Middle Atmosphere Program. Handbook for MAP, volume 20

Various topics related to investigations of the middle atmosphere are discussed. Numerical weather prediction, performance characteristics of weather profiling radars, determination of gravity wave and turbulence parameters, case studies of gravity-wave propagation, turbulence and diffusion due to gravity waves, the climatology of gravity waves, mesosphere-stratosphere-troposphere radar, antenna arrays, and data management techniques are among the topics discussed.

Bowhill, S. A.↗

NASA NTRS1992

Navier-Stokes analysis and experimental data comparison of compressible flow within ducts

Many aircraft employ ducts with centerline curvature or changing cross-sectional shape to join the engine with inlet and exhaust components. S-ducts convey air to the engine compressor from the intake and often decelerate the flow to achieve an acceptable Mach number at the engine compressor by increasing the cross-sectional area downstream. Circular-to-rectangular transition ducts are used on aircraft with rectangular exhaust nozzles to connect the engine and nozzle. To achieve maximum engine performance, the ducts should minimize flow total pressure loss and total pressure distortion at the duct exit. Changes in the curvature of the duct centerline or the duct cross-sectional shape give rise to streamline curvature which causes cross stream pressure gradients. Secondary flows can be caused by deflection of the transverse vorticity component of the boundary layer. This vortex tilting results in counter-rotating vortices. Additionally, the adverse streamwise pressure gradient caused by increasing cross-sectional area can lead to flow separation. Vortex pairs have been observed in the exit planes of both duct types. These vortices are due to secondary flows induced by pressure gradients resulting from streamline curvature. Regions of low total pressure are produced when the vortices convect boundary layer fluid into the main flow. The purpose of the present study is to predict the measured flow field in a diffusing S-duct and a circular-to-rectangular transition duct with a full Navier-Stokes computer program, PARC3D, and to compare the numerical predictions with new detailed experimental measurements. The work was undertaken to extend previous studies and to provide additional CFD validation data needed to help model flows with strong secondary flow and boundary layer separation. The S-duct computation extends the study of Smith et al, and Harloff et al, which concluded that the computation might be improved by using a finer grid and more advanced turbulence models. The present study compares results for both the Baldwin-Lomas and k-epsilon turbulence models and is conducted with a refined grid. For the transition duct, two inlet conditions were considered, the first with straight flow and the second with swirling flow. The first case permits examination of the effects of the geometric transition on the flow field, while the second case includes the rotational flow effect characteristic of a gas turbine engine.

Harloff, G. J.↗

NASA NTRS1992

Constraints on the thermal evolution of Venus inferred from Magellan data

The impact craters with diameters from 1.5 to 280 km compiled from Magellan observations indicate that the crater population on Venus has a completely spatially random distribution and the size/density distribution of craters with diameters greater than or equal to 35 km is consistent with a 'production' population with an age of 500 plus or minus 250 m.y. The similarity in size distribution from area to area indicates that the crater distribution is independent of crater size. Also, the forms of the modified craters are virtually identical to those of the pristine craters. These observations imply that Venus reset its cratering record by global resurfacing 500 m.y. ago, and resurfacing declined relatively fast. The fact that less than 40 percent of all craters have been modified and that the few volcanically embayed craters are located on localized tectonic regions indicate that only minor and localized volcanism and tectonism have occurred since the latest vigorous resurfacing event approximately 500 m.y. ago and the interior of Venus has been solid and possibly colder than Earth's. This is because the high-temperature lithosphere of Venus would facilitate upward ascending of mantle plumes and result in extensive volcanism if the venusian upper mantle were as hot as or hotter than Earth's. Therefore, the present surface morphology of Venus may provide useful constraints on the pattern of that vigorous convection, and possibly on the thermal state of the venusian mantle. We examine this possibility through numerical calculations of three-dimensional thermal convection models in a spherical shell with temperature- and pressure-dependent Newtonian viscosity, temperature-dependent thermal diffusivity, pressure-dependent thermal expansion coefficient, and time-dependent internal heat production rate solar magnitude.

Arkani-Hamed, Jafar↗

NASA NTRS1993

A numerical treatment of geodynamic viscous flow problems involving the advection of material interfaces

Effective numerical treatment of multicomponent viscous flow problems involving the advection of sharp interfaces between materials of differing physical properties requires correction techniques to prevent spurious diffusion and dispersion. We develop a particular algorithm, based on modern shock-capture techniques, employing a two-step nonlinear method. The first step involves the global application of a high-order upwind scheme to a hyperbolic advection equation used to model the distribution of distinct material components in a flow field. The second step is corrective and involves the application of a global filter designed to remove dispersion errors that result from the advection of discontinuities (e.g., material interfaces) by high-order, minimally dissipative schemes. The filter introduces no additional diffusion error. Nonuniform viscosity across a material interface is allowed for by the implementation of a compositionally weighted-inverse interface viscosity scheme. The combined method approaches the optimal accuracy of modern shock-capture techniques with a minimal increase in computational time and memory. A key advantage of this method is its simplicity to incorporate into preexisting codes be they finite difference, element, or volume of two or three dimensions.

Lenardic, A.↗

NASA NTRS2009

Uncertain Representations of Sub-Grid Pollutant Transport in Chemistry-Transport Models and Impacts on Long-Range Transport and Global Composition

Sub-grid transport, by convection and turbulence, is known to play an important role in lofting pollutants from their source regions. Consequently, the long-range transport and climatology of simulated atmospheric composition are impacted. This study uses the Goddard Earth Observing System, Version 5 (GEOS-5) atmospheric model to study pollutant transport. The baseline model uses a Relaxed Arakawa-Schubert (RAS) scheme that represents convection through a sequence of linearly entraining cloud plumes characterized by unique detrainment levels. Thermodynamics, moisture and trace gases are transported in the same manner. Various approximate forms of trace-gas transport are implemented, in which the box-averaged cloud mass fluxes from RAS are used with different numerical approaches. Substantial impacts on forward-model simulations of CO (using a linearized chemistry) are evident. In particular, some aspects of simulations using a diffusive form of sub-grid transport bear more resemblance to space-biased CO observations than do the baseline simulations with RAS transport. Implications for transport in the real atmosphere will be discussed. Another issue of importance is that many adjoint/inversion computations use simplified representations of sub-grid transport that may be inconsistent with the forward models: implications will be discussed. Finally, simulations using a complex chemistry model in GEOS-5 (in place of the linearized CO model) are underway: noteworthy results from this simulation will be mentioned.

Pawson, Steven↗

NASA NTRS2015

Investigation of Unsteady Flow Interaction Between an Ultra-Compact Inlet and a Transonic Fan

In the present study, unsteady flow interaction between an ultra-compact inlet and a transonic fan stage is investigated. Future combat aircraft require ultra-compact inlet ducts as part of an integrated, advanced propulsion system to improve air vehicle capability and effectiveness to meet future mission needs. The main purpose of the study is to advance the current understanding of the flow interaction between two different ultra-compact inlets and a transonic fan for future design applications. Both URANS and LES approaches are used to calculate the unsteady flow field and are compared with the available measured data. The present study indicates that stall inception is mildly affected by the distortion pattern generated by the inlet with the current test set-up. The numerical study indicates that the inlet distortion pattern decays significantly before it reaches the fan face for the current configuration. Numerical results with a shorter distance between the inlet and fan show that counter-rotating vortices near the rotor tip due to the serpentine diffuser affects fan characteristics significantly.

Inlet↗