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Results for “equations of fluid dynamics”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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DOE OSTI2020

Anti-symmetric representation of the extended magnetohydrodynamic equations

We introduce the anti-symmetric representation of the extended magnetohydrodynamic (MHD) equations. In this representation, the use of the anti-symmetric flux operator (∇·ν+ν·∇) results in conservation theorems with discrete analogs. Inherently robust numerical applications are achieved with little effort, and conservation to machine precision is possible with simple numerical schemes. Starting from the two-fluid equations, we construct a single-fluid MHD model based on generalized center-of-mass variables for the mass (√ρ), momentum (√ρν), and pressure (√ p ). This model is shown to possess identical conservation properties to the two-fluid system, with the only restriction being the use of a single temperature. Common approximations to the Braginskii heat fluxes and to the gyroviscous stress tensor are cast into our representation for convenience. The discrete conservation properties are verified using the classic Orszag–Tang vortex problem. In addition to the favorable mass, momentum, and energy conservation properties, the time reversibility of the simulations is demonstrated.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

A boundary value “reservoir problem” and boundary conditions for multi-moment multifluid simulations of sheaths

Multifluid simulations of plasma sheaths are increasingly used to model a wide variety of problems in plasma physics ranging from global magnetospheric flows around celestial bodies to plasma–wall interactions in thrusters and fusion devices. For multifluid problems, accurate boundary conditions to model an absorbing wall that resolves a classical sheath remain an open research area. This work justifies the use of vacuum boundary conditions for absorbing walls to show comparable accuracy between a multifluid sheath and lower moments of a continuum-kinetic sheath.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Generation of excited species in a streamer discharge

At or near atmospheric pressure, most transient discharges, particularly in molecular gases or gas mixture containing molecular gases result in a space-charge dominated transport called a streamer discharge. The excited species generation in such discharges forms the basis for plasma chemistry in most technological applications. In this paper we simulate the propagation of streamers in atmospheric pressure N 2 to understand the energy partitioning in the formation of various excited species and compare the results to a uniform Townsend discharge. The model is fully two-dimensional with azimuthal symmetry. Results show a significantly larger fraction of the energy goes into vibrational excitation of the N 2 ground state in a streamer-type discharge in comparison to a Townsend discharge. For lower applied voltages, the anode-directed (negative) steamer is slightly more efficient in channeling energy for excited species production in comparison to a cathode-directed (positive) streamer. Near 70% overvoltage both types of streamers show very similar energy partitioning but quite different from a Townsend discharge.

42 ENGINEERING↗

DOE OSTI2021

Laser-plasma acceleration beyond wave breaking

Laser wakefield accelerators rely on the extremely high electric fields of nonlinear plasma waves to trap and accelerate electrons to relativistic energies over short distances. When driven strongly enough, plasma waves break, trapping a large population of the background electrons that support their motion. Aside from limiting the maximum electric field, this trapping can lead to accelerated electron bunches with large energy spreads. Here we introduce a novel regime of plasma wave excitation and wakefield acceleration that allows for arbitrarily high electric fields while avoiding the deleterious effects of unwanted trapping. Here, the regime, enabled by spatiotemporal shaping of laser pulses, exploits the property that nonlinear plasma waves with superluminal phase velocities cannot trap charged particles and are therefore immune to wave breaking.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Multi-fluid and kinetic models of partially ionized magnetic reconnection

Magnetic reconnection in partially ionized plasmas is a ubiquitous and important phenomenon in both laboratory and astrophysical systems. Here, simulations of partially ionized magnetic reconnection with well-matched initial conditions are performed using both multi-fluid and fully-kinetic approaches. Despite similar initial conditions, the time-dependent evolution differs between the two models. In multi-fluid models, the reconnection rate locally obeys either a decoupled Sweet–Parker scaling, where neutrals are unimportant, or a fully coupled Sweet–Parker scaling, where neutrals and ions are strongly coupled, depending on the resistivity. In contrast, kinetic models show a faster reconnection rate that is proportional to the fully-coupled, bulk Alfvén speed, $v^*_A$. In this work, these differences are interpreted as the result of operating in different collisional regimes. Multi-fluid simulations are found to maintain $ν_{ni}L/v^*_A$ ≳1, where $ν_{ni}$ is the neutral–ion collision frequency and L is the time-dependent current sheet half-length. This strongly couples neutrals to the reconnection outflow, while kinetic simulations evolve to allow $ν_{ni}L/v^*_A$ <1, decoupling neutrals from the reconnection outflow. Differences in the way reconnection is triggered may explain these discrepancies.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Scaling of the mean transverse flow and Reynolds shear stress in turbulent plane jet

Here, proper scaling for the mean transverse flow and Reynolds shear stress in a turbulent plane jet is determined using a scaling patch approach. By seeking an admissible scaling, a key concept in the scaling patch approach, for the mean continuity equation, a proper scale for the mean transverse flow in a turbulent plane jet is found as V ref = –δdU ctr /dx, where δ is the jet half width and dU ctr /dx is the decay rate of the mean axial velocity at the jet centerline. By seeking an admissible scaling for the mean axial momentum equation, a proper scale for the kinematic Reynolds shear stress is found as R uv,ref =U ctr V ref , which is a mix of the velocity scales in the axial and transverse directions. Approximation functions for the scaled mean transverse flow and Reynolds shear stress are developed and found to agree well with experimental and numerical data. Similarities and differences between the scales of the mean transverse flow and Reynolds shear stress in turbulent plane jets and zero-pressure-gradient turbulent boundary layer flows are clarified.

42 ENGINEERING↗

DOE OSTI2021

On the mechanism of ionization oscillations in Hall thrusters

Low-frequency ionization oscillations involving plasma and neutral density (breathing modes) are the most violent perturbations in Hall thrusters for electric propulsion. Because of its simplicity, the zero-dimensional (0D) predator–prey model of two nonlinearly coupled ordinary differential equations for plasma and neutral density has often been used for the characterization of such oscillations and scaling estimates. In this work, we investigate the properties of its continuum analog, the one-dimensional (1D) system of two nonlinearly coupled equations in partial derivatives (PDEs) for plasma and neutral density. This is a more general model, of which the standard 0D predator–prey model is a special limit case. We show that the 1D model is stable and does not show any oscillations for the boundary conditions relevant to Hall thrusters and the uniform ion velocity. We then propose a reduced 1D model based on two coupled PDEs for plasma and neutral densities that is unstable and exhibit oscillations if the ion velocity profile with the near-the-anode back-flow (toward the anode) region is used. Comparisons of the reduced model with the predictions of the full model that takes into account the self-consistent plasma response show that the main properties of the breathing mode are well captured. In particular, it is shown that the frequency of the breathing mode oscillations is weakly dependent on the final ion velocity but shows a strong correlation with the width of the ion back-flow region.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Scaling patch analysis of turbulent planar plume

Proper scaling in turbulent planar plumes is investigated in this study using a scaling patch approach. Based on the scaled boundary conditions, a proper velocity scale for the mean axial flow is the plume centerline velocity U ref = U ctr , and a proper temperature scale for the temperature excess is Θ ref = T ctr – T ∞ , where T ctr is the plume centerline temperature and T ∞ is the ambient fluid temperature. By seeking an admissible scaling, a key concept in the scaling patch approach, for the mean continuity, mean momentum, and mean energy equations, respectively, the following is found: (1) a proper scale for the mean transverse flow is V ref = ( d δ / d x ) U ctr , where d δ / d x is the growth rate of the plume width. (2) A proper scale for the Reynolds shear stress is R vu , ref = U ctr V ref = ( d δ / d x ) U ctr 2 , a mix of the scales for the mean axial and transverse flows. (3) A proper scale for the turbulent heat flux is R v θ , ref = V ref Θ ctr , a mix of the scales for the mean transverse flow and mean temperature excess. The mean transverse flow thus plays a critical role in the scaling of turbulent planar plumes. Approximate functions are developed for the scaled mean transverse flow, Reynolds shear stress, and turbulent temperature flux, and are found to agree favorably with experimental and numerical simulation data. The integral analysis of the mean momentum equation yields a Richardson number Ri, which remains invariant in the axial direction. The Richardson number is defined as Ri = def g β Θ ctr δ t / ( U ctr V ref ) ≈ 1 / 2 , where g is the gravitational acceleration, β is the thermal expansion coefficient, and δ t is the plume half-width based on the mean temperature profile. This Richardson number arises directly from the scaling patch analysis of the mean momentum equation, including both the streamwise and transverse velocity scales.

42 ENGINEERING↗

DOE OSTI2022

Effects of Coulomb collisions on lower hybrid drift waves inside a laboratory reconnection current sheet

We have developed a local, linear theoretical model for lower hybrid drift waves that can be used for plasmas in the weakly collisional regime. Two cases with typical plasma and field parameters for the current sheet of the magnetic reconnection experiment have been studied. For a case with a low electron beta (β e =0.25, high guide field case), the quasi-electrostatic lower hybrid drift wave is unstable, while the electromagnetic lower hybrid drift wave has a positive growth rate for a high-β e case (β e =8.9, low guide field case). For both cases, including the effects of Coulomb collisions reduces the growth rate but collisional impacts on the dispersion and growth rate are limited (≲20%).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Model fusion with physics-guided machine learning: Projection-based reduced-order modeling

The unprecedented amount of data generated from experiments, field observations, and large-scale numerical simulations at a wide range of spatiotemporal scales has enabled the rapid advancement of data-driven and especially deep learning models in the field of fluid mechanics. Although these methods are proven successful for many applications, there is a grand challenge of improving their generalizability. This is particularly essential when data-driven models are employed within outer-loop applications like optimization. In this work, we put forth a physics-guided machine learning (PGML) framework that leverages the interpretable physics-based model with a deep learning model. Leveraging a concatenated neural network design from multi-modal data sources, the PGML framework is capable of enhancing the generalizability of data-driven models and effectively protects against or inform about the inaccurate predictions resulting from extrapolation. We apply the PGML framework as a novel model fusion approach combining the physics-based Galerkin projection model and long- to short-term memory (LSTM) network for parametric model order reduction of fluid flows. We demonstrate the improved generalizability of the PGML framework against a purely data-driven approach through the injection of physics features into intermediate LSTM layers. Our quantitative analysis shows that the overall model uncertainty can be reduced through the PGML approach, especially for test data coming from a distribution different than the training data. Moreover, we demonstrate that our approach can be used as an inverse diagnostic tool providing a confidence score associated with models and observations. The proposed framework also allows for multi-fidelity computing by making use of low-fidelity models in the online deployment of quantified data-driven models.

42 ENGINEERING↗

DOE OSTI2021

Benchmarking NIMROD continuum kinetic formulations through the steady-state poloidal flow

In this work, continuum kinetic formulations are employed as a mechanism to include closure physics in an extended magnetohydrodynamics model. Two continuum kinetic approaches have been implemented in the plasma fluid code NIMROD [Sovinec et al., “Nonlinear magnetohydrodynamics with high-order finite elements,” J. Comput. Phys. 195, 355 (2004)] including a Chapman–Enskog-like (CEL) formulation and a more conventional df approach. Ion kinetic closure schemes are employed to describe the neoclassical flow properties in axisymmetric toroidal geometry. In particular, predictions for steady-state values of poloidal flow profiles in tokamak geometry are provided using both the df formulation and two different solution techniques for the CEL approach. These results are benchmarked against analytic theory predictions as well as results from the drift kinetic code DK4D. The continuum kinetic formulations employed here show agreement with both the analytic theory and DK4D results, and offer a novel velocity space representation involving higher-order finite elements in pitch angle.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Development of five-moment two-fluid modeling for Z-pinch physics

The Z-pinch m = 0 instability as well as its stabilization by radially sheared axial flow is studied using the nonlinear ideal five-moment twofluid (5M2F) model with an extension of that model to include Braginskii heat and momentum transport. Using the ideal 5M2F model, linear growth rate results are compared with prior work using MHD and Hall MHD. At small normalized wavenumber, 1 < k a < 4 , where a is the effective pinch radius, 5M2F results agree with Hall MHD within 20% in scenarios without radially sheared axial flow. With the sheared flow and focusing on ka = 10/3, agreement with Hall MHD is excellent. In the limit of small ion inertial length, results also match with MHD. A comparison with PIC modeling of shear-free m = 0 stability focuses on a plasma scenario based on recent experimental results. In a scan of mode wavenumber, ideal 5M2F results are qualitatively similar to PIC: the growth rate rises to a peak at a moderate wavenumber and declines at a large wavenumber in contrast to MHD results, which show the saturation of the growth rate with the increasing wavenumber rather than a decline. The peak normalized 5M2F growth rate is γ τ A = 1.5 , where sA is the Alfven transit time across the pinch. The peak occurs at normalized wavenumber ka = 10. For comparison, PIC results have a peak growth of γ τ A = 0.77 at ka = 5. Including Braginskiibased closure of the 5M2F model does not qualitatively change the ideal results in this particular case. Nonlinear saturation is studied using the 5M2F model with the dissipative Braginskii-based closure in cases with pinch-edge sheared-flow speed equal to half the Alfven speed. Nonlinear mixing due to the sheared flow yields a quasi-steady state after modest losses of pinch ion inventory and pinch thermal energy, approximately 30% and 10%, respectively. 5M2F modeling captures the essential physics of m = 0 instability and offers a computationally tractable route to high-fidelity modeling of 3D Z-pinch behavior, including m = 1 instability.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

On the merit of hot ion mode for tearing mode stabilization

The stabilization of tearing modes with rf driven current benefits from the cooperative feedback loop between rf power deposition and electron temperature within the island. This effect, termed rf current condensation, can greatly enhance and localize the current driven within magnetic islands. It has previously been shown that the condensation effect opens the possibility of passive stabilization with broad rf profiles, as would be typical of LHCD for steady state operation. Here, we show that this self-healing effect can be dramatically amplified by operation in a hot ion mode, due to the additional electron heat source provided by the hotter ions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

On closures for reduced order models - A spectrum of first-principle to machine-learned avenues

For over a century, reduced order models (ROMs) have been a fundamental discipline of theoretical fluid mechanics. Early examples include Galerkin models inspired by the Orr–Sommerfeld stability equation and numerous vortex models, of which the von Karman vortex street is one of the most prominent. Subsequent ROMs typically relied on first principles, like mathematical Galerkin models, weakly nonlinear stability theory, and two- and three-dimensional vortex models pioneered the data-driven proper orthogonal decomposition (POD) modeling. In early POD modeling, available data were used to build an optimal basis, which was then utilized in a classical Galerkin procedure to construct the ROM, but data have made a profound impact on ROMs beyond the Galerkin expansion. In this paper, we take a modest step and illustrate the impact of data-driven modeling on one significant ROM area. Specifically, we focus on ROM closures, which are correction terms that are added to the classical ROMs in order to model the effect of the discarded ROM modes in under-resolved simulations. Through simple examples, we illustrate the main modeling principles used to construct the classical ROMs, motivate and introduce modern ROM closures, and show how data-driven modeling, artificial intelligence, and machine learning have changed the standard ROM methodology over the last two decades. Finally, we outline our vision on how the state-of-the-art data-driven modeling can continue to reshape the field of reduced order modeling.

42 ENGINEERING↗

DOE OSTI2022

Hybrid-gyrokinetic simulations of low- n toroidal Alfvén eigenmodes using gKPSP

Here, we report a benchmark study of toroidal Alfvén eigenmode (TAE) simulation using the hybrid-gyrokinetic code GyroKinetic Plasma Simulation Program (gKPSP). A simulation capability for energetic particles based on the gyrokinetic δf method has been newly implemented in the gKPSP code. Benchmark simulations have been performed in both circular and realistic tokamak geometries. Good agreement has been found with previously reported results, demonstrating the new capability of the gKPSP code. We have investigated the effects of the distribution function on TAE stability by examining both isotropic and anisotropic slowing-down distributions of energetic particles. The slowing-down distribution produces a higher linear growth rate than a Maxwellian distribution, while a growth rate scan with the anisotropy shows an opposite trend. This can be attributed to competition between Landau damping and the linear drive, which are correlated with the fraction of resonant passing particles and their distribution in phase space.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Fluid and hybrid simulations of the ionization instabilities in Hall thruster

Low-frequency axial oscillations in the range of 5–50 kHz stand out as a pervasive feature observed in many types of Hall thrusters. While it is widely recognized that the ionization effects play the central role in this mode, as manifested via the large-scale oscillations of neutral and plasma density, the exact mechanism(s) of the instabilities remain unclear. To gain further insight into the physics of the breathing mode and evaluate the role of kinetic effects, a one-dimensional time-dependent full nonlinear low-frequency model describing neutral atoms, ions, and electrons is developed in full fluid formulation and compared to the hybrid model in which the ions and neutrals are kinetic. Both models are quasi-neutral and share the same electron fluid equations that include the electron diffusion, mobility across the magnetic field, and the electron energy evolution. The ionization models are also similar in both approaches. Further, the predictions of fluid and hybrid simulations are compared for different test cases. Two main regimes are identified in both models: one with pure low-frequency behavior and the other one, where the low-frequency oscillations coexist with high-frequency oscillations in the range of 100–200 kHz, with the characteristic time scale of the ion channel fly-by time, 100–200 kHz. The other test case demonstrates the effect of a finite temperature of injected neutral atoms, which has a substantial suppression effect on the oscillation amplitude.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Design optimization of gap distance for the capillary limitation of a heat pipe with annular-type wick structure

In this study, an experimental investigation was conducted on the rising height and contact angle of fluid in an annular wick-type heat pipe. The annular wick-type heat pipe was characterized by a small gap between the wick structure and tube wall, which compensated for the pressure drop along the porous media and created additional capillary force. To describe and model the advantage of this gap, the rising of a wetting liquid in the gap between a vertical solid plate and a mesh (with a small angle between them) was experimentally measured and analyzed. An additional experiment was performed to investigate the effect of curvature on the capillary rise using tubes and meshes of varying radii. Resultantly, we confirmed that the linear combination of the contact angles of the solid plate and mesh could be applied to calculate the rising height from the Laplace–Young equation. Furthermore, the effect of curvature on the rising height of the liquid was negligible. These results were extended to the investigation of finding the optimal gap distance for the annular wick-type heat pipe by referring to previous studies. We observed that a gap distance of 1.27 mm provided the largest permeability (K) over the effective pore radius (r eff ) value for a heat pipe with ethanol, which in turn resulted in the highest capillary limitation. For a sodium heat pipe, a gap distance of 0.84 mm resulted in the highest capillary limitation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Fueling limits in a cylindrical viscosity-limited reactor

Recently, a method to achieve a “natural hot-ion mode” was suggested by utilizing ion viscous heating in a rotating plasma with a fixed boundary. We explore the steady-state solution to the Braginskii equations and find the parameter regime in which a significant temperature difference between ions and electrons can be sustained in a driven steady state. Here, the threshold for this effect occurs at ρ i ≳ 0.1R. An analytic, leading order low flow solution is obtained, and a numerical, moderate Mach number M ≲ 2 is investigated. The limitation is found to be at moderate Mach numbers.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗