Search NASA⌕ Search

SEARCH · Search NASA

Results for “Fluid equations”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
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 OSTI2021

A multi-dimensional parametric study of variability in multi-phase flow dynamics during geologic CO 2 sequestration accelerated with machine learning

Successful geologic CO 2 storage projects depend on numerical simulations to predict reservoir performance during site selection, injection verification, and post-injection monitoring phases of the project. These numerical simulations solve non-linear sets of coupled partial differential equations, while accounting for multi-phase fluid dynamics on the basis of constitutive equations that are embedded into the solution scheme. As a consequence, individual simulations often require tens to hundreds of hours to complete on high-performance computing clusters. Moreover, laboratory experiments reveal that parametric functions for capillary pressure and relative permeability exhibit substantial variability, even within the same rock type. This combination of computational expense and wide-ranging parametric variability means that there remains substantial uncertainty in the behavior of multi-phase CO 2 -water systems, particularly in the context of feedbacks between relative permeability and capillary pressure. To bridge this knowledge gap, here we develop a novel workflow that utilizes physics-based numerical simulation to train an artificial neural network (ANN) emulator for interrogating the multivariate parameter space that governs both capillary pressure and relative permeability. With this approach, the ANN is trained to emulate both fluid pressure distribution and CO 2 saturation, which are then interrogated quantitatively to generate parametric response surface mappings with high-fidelity resolution. Results from this study initially show that capillary entry pressure is the dominant control on both CO 2 plume geometry and fluid pressure propagation when considering the combined effects of capillary pressure and relative permeability, particularly when phase interference is low and residual CO 2 saturation is high. Moreover, the ANN emulator provides tremendous computational speed-up by computing 2691 individual simulations in several minutes; whereas, the same simulation ensemble would have required ~3 years of simulation time using only physics-based simulation methods (25,000 times speed up).

58 GEOSCIENCES↗
DOE OSTI2025

Speed of Sound Measurements of Binary Mixtures of trans -1,2-Difluoroethylene (R-1132(E)) with Difluoromethane (R-32) or 2,3,3,3-Tetrafluoropropene (R-1234yf)

The speed of sound of two binary mixtures containing 0.336 mole fraction trans-1,2- difluoroethylene (R-1132(E)) with difluoromethane (R-32) and 0.435 mole fraction R-1132(E) with 2,3,3,3-tetrafluoropropene (R-1234yf) were measured with a dual-path pulse-echo instrument. The speed of sound was measured along several pseudo-isochores for each blend at temperatures ranging from 230 K to 325 K for blends with R-32 and to 342 K for blends with R- 1234yf. Measurements started at pressures just above each mixtures bubble point pressure and were limited to 8 MPa to avoid potential disproportionation reactions of the R-1132(E). The data were compared to multi-fluid models incorporating Helmholtz-energy-explicit equations of state (EOS) for each pure fluid.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Ephemeral antibubbles: Spatiotemporal evolution from direct numerical simulations

Antibubbles, which consist of a shell of a low-density fluid inside a high-density fluid, have several promising applications. We show, via extensive direct numerical simulations (DNSs), in both two and three dimensions, that the spatiotemporal evolution of antibubbles can be described naturally by the coupled Cahn-Hilliard-Navier-Stokes (CHNS) equations for a binary fluid. Our DNSs capture elegantly the gravity-induced thinning and breakup of an antibubble via the time evolution of the Cahn-Hilliard scalar-order-parameter field $\phi$, which varies continuously across interfaces, so we do not have to enforce complicated boundary conditions at the moving antibubble interfaces. To ensure that our results are robust, we supplement our CHNS simulations with sharp-interface volume-of-fluid DNSs. We track the thickness of the antibubble and calculate the dependence of the lifetime of an antibubble on several parameters; we show that our DNS results agree with various experimental results; in particular, the velocity with which the arms of the antibubble retract after breakup scales as σ 1/2 , where σ is the surface tension.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Data-driven recovery of hidden physics in reduced order modeling of fluid flows

In this article, we introduce a modular hybrid analysis and modeling (HAM) approach to account for hidden physics in reduced order modeling (ROM) of parameterized systems relevant to fluid dynamics. The hybrid ROM framework is based on using first principles to model the known physics in conjunction with utilizing the data-driven machine learning tools to model the remaining residual that is hidden in data. This framework employs proper orthogonal decomposition as a compression tool to construct orthonormal bases and Galerkin projection (GP) as a model to build the dynamical core of the system. Our proposed methodology hence compensates structural or epistemic uncertainties in models and utilizes the observed data snapshots to compute true modal coefficients spanned by these bases. The GP model is then corrected at every time step with a data-driven rectification using a long short-term memory (LSTM) neural network architecture to incorporate hidden physics. A Grassmannian manifold approach is also adopted for interpolating basis functions to unseen parametric conditions. The control parameter governing the system's behavior is thus implicitly considered through true modal coefficients as input features to the LSTM network. The effectiveness of the HAM approach is then discussed through illustrative examples that are generated synthetically to take hidden physics into account. Furthermore, our approach thus provides insights addressing a fundamental limitation of the physics-based models when the governing equations are incomplete to represent underlying physical processes.

42 ENGINEERING↗
DOE OSTI2023

Improved analytic modeling of the linear Rayleigh–Taylor instability with plasma transport

The Rayleigh–Taylor (R–T) instability with transport effects has long been studied analytically in the neutral fluid regime. How this picture may differ in plasmas has been given less consideration, however. Leveraging previous numerical simulations with plasma viscosity and diffusion of R–T at a binary plasma interface, we show how plasma transport and kinetic effects alter the linear R–T dispersion relation. Our insight informs a much improved analytical dispersion relation, which better matches the simulation data than previously established models. Additionally, we demonstrate the importance of employing asymptotically correct viscosity coefficients in fluid codes for accurately capturing plasma R–T growth.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Experimental observation and numerical investigation of filamentary structures in magnetized plasmas

Filamentary structures in low-pressure, low-temperature plasmas are produced when strong magnetic fields are applied parallel to the electric field defined by parallel electrodes. Filamentary structures are regions within the plasma that have distinct properties such as optical brightness and extend along the magnetic field lines. In our experiments, an argon, radio frequency discharge is exposed to a strong background magnetic field in the magnetized dusty plasma experiment at Auburn University. Different forms of filamentary structures emerge in the plasma such as columns, target, or spiral-like structures. To investigate the origin and the characteristics of these patterns, we have developed a three-dimensional fluid model that can reproduce the experimental observations which enables us to investigate the underlying mechanisms of the filamentation process.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

On Two-Phase Pressure and Temperature Equilibration with Mie-Grüneisen Equations of State

In the course of reactive flow modeling, the phases of high explosive (HE) reactants and products introduce additional degrees of freedom to the underlying hydrodynamic equations of compressible reactive fluid mechanics. Hydrodynamic simulations track the bulk (mixture) conservation properties of mass, momentum and energy. When multiple phases are introduced, one must decide on appropriate closure rules to determine the relative phase volumes and energy distribution between the phases. One typical closure is to assume that the phases are in pressure and temperature equilibrium. Here, the requisite equations of p-T equilibration are explored for Mie-Grüneisen Equations of State (EOS). Examples with Davis reactants and Davis products EOSs will be given. The Davis forms are used in both the WSD and AWSD reactive flow models.

42 ENGINEERING↗
DOE OSTI2023

Two-fluid physical modeling of superconducting resonators in the ARTEMIS framework

In this work, we implement a new London equation module for superconductivity in the GPU-enabled ARTEMIS framework, and couple it to a finite-difference time-domain solver for Maxwell's equations. We apply this two-fluid approach to model a superconducting coplanar waveguide (CPW) resonator. We validate our implementation by verifying that the theoretical skin depth and reflection coefficients can be obtained for several superconductive materials, with different London penetration depths, over a range of frequencies. Our convergence studies show that the algorithm is second-order accurate in both space and time, except at superconducting interfaces where the approach is spatially first-order. In our CPW simulations, we leverage the GPU scalability of our code to compare the two-fluid model to more traditional approaches that approximate superconducting behavior and demonstrate that superconducting physics can show comparable performance to the assumption of quasi-infinite conductivity as measured by the Q-factor.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Online Machine Learning for Accelerating Molecular Dynamics Modeling of Cells

We developed a biomechanics-informed online learning framework to learn the dynamics with ground truth generated with multiscale modeling simulation. It was built on Summit-like supercomputers, which were also used to benchmark and validate our framework on one physiologically significant modeling of deformable biological cells. We generalized the century-old equation of Jeffery orbits to a new equation of motion with additional parameters to account for the flow conditions and the cell deformability. Using simulation data at particle-based resolutions for flowing cells and the learned parameters from our framework, we validated the new equation by the motions, mostly rotations, of a human platelet in shear blood flow at various shear stresses and platelet deformability. Our online framework, which surrogates redundant computations in the conventional multiscale modeling by solutions of our learned equation, accelerates the conventional modeling by three orders of magnitude without visible loss of accuracy.

multiscale modeling↗
DOE OSTI2025

Turbulence in Core-collapse Supernovae

It is understood in a general sense that turbulent fluid motion below the shock front in a core-collapse supernova stiffens the effective equation of state of the fluid and aids in the revival of the explosion. However, when one wishes to be precise and quantify the amount of turbulence in a supernova simulation, one immediately encounters the problem that turbulence is difficult to define and measure. Using the 3D magnetohydrodynamic code ELEPHANT, we study how different definitions of turbulence change one’s conclusions about the amount of turbulence in a supernova and the extent to which it helps the explosion. We find that, while all the definitions of turbulence we use lead to a qualitatively similar growth pattern over time of the turbulent kinetic energy in the gain region, the total amount of turbulent kinetic energy, and especially the ratios of turbulent to total kinetic energy, distinguish them. Some of the definitions appear to indicate turbulence is a necessary contributor to the explosion, and others indicate it is not. The different definitions also produce turbulence maps with different correlations with maps of the enstrophy, a quantity widely regarded as also indicating the presence of turbulence. We also compute the turbulent adiabatic index and observe that, in regions of low enstrophy, this quantity is sensitive to the definition used. As a consequence, the effective adiabatic index depends upon the method used to measure the turbulence, and thus it alters one’s conclusions regarding the impact of turbulence within the supernova.

computational astronomy↗
DOE OSTI2025

Type-II spacetimes and the double copy for fluids metrics

In our previous paper [Keeler , From Navier-Stokes to Maxwell via Einstein, .] we discussed type-D and type-N fluid-dual spacetimes and provided their associated single copies in the context of the Weyl double copy. In this work we extend our analysis to more general fluids thereby requiring the application of the double-copy picture to type-II spacetimes. By combining our previous type-D and type-N fluids via their associated stream functions we construct an example of a viable type-II double copy. We show that the gravity duals of these fluids perturbatively satisfy Einstein’s equations. We use a near-horizon expansion to identify the type-II double copy for the fluid-dual spacetimes. We show a Maxwell spinor ansatz containing a heterogeneous bispinor component is necessary to provide a viable type-II double copy at the lowest order.

Fluid-gravity correspondence↗
DOE OSTI2024

Self-organization in collisionless, high- β turbulence

The magnetohydrodynamic (MHD) equations, as a collisional fluid model that remains in local thermodynamic equilibrium (LTE), have long been used to describe turbulence in myriad space and astrophysical plasmas. Yet, the vast majority of these plasmas, from the solar wind to the intracluster medium (ICM) of galaxy clusters, are only weakly collisional at best, meaning that significant deviations from LTE are not only possible but common. Recent studies have demonstrated that the kinetic physics inherent to this weakly collisional regime can fundamentally transform the evolution of such plasmas across a wide range of scales. Here, we explore the consequences of pressure anisotropy and Larmor-scale instabilities for collisionless, β $\gg$ 1, turbulence, focusing on the role of a self-organizational effect known as ‘magneto-immutability’. We describe this self-organization analytically through a high-β, reduced ordering of the Chew–Goldberger–Low-MHD (CGL-MHD) equations, finding that it is a robust inertial-range effect that dynamically suppresses magnetic-field-strength fluctuations, anisotropic-pressure stresses and dissipation due to heat fluxes. As a result, the turbulent cascade of Alfvénic fluctuations continues below the putative viscous scale to form a robust, nearly conservative, MHD-like inertial range. These findings are confirmed numerically via Landau-fluid CGL-MHD turbulence simulations that employ a collisional closure to mimic the effects of microinstabilities. We find that microinstabilities occupy a small (~5%) volume-filling fraction of the plasma, even when the pressure anisotropy is driven strongly towards its instability thresholds. We discuss these results in the context of recent predictions for ion-vs-electron heating in low-luminosity accretion flows and observations implying suppressed viscosity in ICM turbulence.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

A non-neutral generalized Ohm's law model for magnetohydrodynamics in the two-fluid regime

Here, a new non-neutral generalized Ohm's law (GOL) model for atomic plasmas is presented. This model differs from previous models of this type in that quasi-neutrality is not assumed at any point. Collisional effects due to ionization, recombination, and elastic scattering are included, and an expression for the associated plasma conductivity is derived. An initial set of numerical simulations are considered that compare the GOL model to a two-fluid model in the ideal (collisionless) case. The results demonstrate that solutions obtained from the two models are essentially indistinguishable in most cases when the ion–electron mass ratio is within the range of physical values for atomic plasmas. Additionally, some limitations of the model are discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Direct imaging of shock wave splitting in diamond at Mbar pressure

Understanding the behavior of matter at extreme pressures of the order of a megabar (Mbar) is essential to gain insight into various physical phenomena at macroscales—the formation of planets, young stars, and the cores of super-Earths, and at microscales—damage to ceramic materials and high-pressure plastic transformation and phase transitions in solids. Under dynamic compression of solids up to Mbar pressures, even a solid with high strength exhibits plastic properties, causing the induced shock wave to split in two: an elastic precursor and a plastic shock wave. This phenomenon is described by theoretical models based on indirect measurements of material response. The advent of x-ray free-electron lasers (XFELs) has made it possible to use their ultrashort pulses for direct observations of the propagation of shock waves in solid materials by the method of phase-contrast radiography. However, there is still a lack of comprehensive data for verification of theoretical models of different solids. Here, we present the results of an experiment in which the evolution of the coupled elastic–plastic wave structure in diamond was directly observed and studied with submicrometer spatial resolution, using the unique capabilities of the x-ray free-electron laser (XFEL). The direct measurements allowed, for the first time, the fitting and validation of the 2D failure model for diamond in the range of several Mbar. Our experimental approach opens new possibilities for the direct verification and construction of equations of state of matter in the ultra-high-stress range, which are relevant to solving a variety of problems in high-energy-density physics.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Drift reduced Landau fluid model for magnetized plasma turbulence simulations in BOUT++ framework

Recently the drift-reduced Landau fluid six-field turbulence model within the BOUT++ framework has been upgraded. In particular, this new model employs a new normalization, adds a volumetric flux-driven source option, the Landau fluid closure for parallel heat flux and a Laplacian inversion solver which is able to capture $n$ = 0 axisymmetric mode evolution in realistic tokamak configurations. As we report here, these improvements substantially extended model's capability to study a wider range of tokamak edge phenomena, and are essential to build a fully self-consistent edge turbulence model capable of both transient (e.g., ELM, disruption) and transport time-scale simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
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 OSTI2024

Rindler fluids from gravitational shockwaves

We study a correspondence between gravitational shockwave geometry and its fluid description near a Rindler horizon in Minkowski spacetime. Utilizing the Petrov classification that describes algebraic symmetries for Lorentzian spaces, we establish an explicit mapping between a potential fluid and the shockwave metric perturbation, where the Einstein equation for the shockwave geometry is equivalent to the incompressibility condition of the fluid, augmented by a shockwave source. Then we consider an Ansatz of a stochastic quantum source for the potential fluid, which has the physical interpretation of shockwaves created by vacuum energy fluctuations. Under such circumstance, the Einstein equation, or equivalently, the incompressibility condition for the fluid, becomes a stochastic differential equation. By smearing the quantum source on a stretched horizon in a Lorentz invariant manner with a Planckian width (similarly to the membrane paradigm), we integrate fluctuations near the Rindler horizon to find an accumulated effect of the variance in the round-trip time of a photon traversing the horizon of a causal diamond.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗