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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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At least 793 records · Page 44
All sourcesNASA NTRSDOE OSTI
NASA NTRS1999

Computations of Boiling in Microgravity

The absence (or reduction) of gravity, can lead to major changes in boiling heat transfer. On Earth, convection has a major effect on the heat distribution ahead of an evaporation front, and buoyancy determines the motion of the growing bubbles. In microgravity, convection and buoyancy are absent or greatly reduced and the dynamics of the growing vapor bubbles can change in a fundamental way. In particular, the lack of redistribution of heat can lead to a large superheat and explosive growth of bubbles once they form. While considerable efforts have been devoted to examining boiling experimentally, including the effect of microgravity, theoretical and computational work is limited to very simple models. In this project, the growth of boiling bubbles is studied by direct numerical simulations where the flow field is fully resolved and the effects of inertia, viscosity, surface deformation, heat conduction and convection, as well as the phase change, are fully accounted for. The proposed work is based on previously funded NASA work that allowed us to develop a two-dimensional numerical method for boiling flows and to demonstrate the ability of the method to simulate film boiling. While numerical simulations of multi-fluid flows have been advanced in a major way during the last five years, or so, similar capability for flows with phase change are still in their infancy. Although the feasibility of the proposed approach has been demonstrated, it has yet to be extended and applied to fully three-dimensional simulations. Here, a fully three-dimensional, parallel, grid adaptive code will be developed. The numerical method will be used to study nucleate boiling in microgravity, with particular emphasis on two aspects of the problem: 1) Examination of the growth of bubbles at a wall nucleation site and the instabilities of rapidly growing bubbles. Particular emphasis will be put on accurately capturing the thin wall layer left behind as a bubble expands along a wall, on computing instabilities on bubble surfaces as bubbles grow, and on quantifying the effects of both these phenomena on heat transfer; and 2) Examination of the effect of shear flow on bubble growth and heat transfer.

Tryggvason, Gretar↗
NASA NTRS2018

Cryogenic Selective Surfaces

There are many challenges involved in deep-space exploration, but several of these can be mitigated, or even solved, by the development of a coating that reflects most of the Sun’s energy, yet still provides far-infrared heat emission. Such a coating would allow non-heat-generating objects in space to reach cryogenic temperatures without using an active cooling system. This would benefit deep-space sensors that require low temperatures, such as the James Webb Telescope focal plane array. It would also allow the use of superconductors in deep space, which could lead to magnetic energy storage rings, lossless power delivery, or perhaps a large-volume magnetic shield against galactic cosmic radiation. However, perhaps the most significant enablement achieved from such a coating would be the long-term, deep space storage of cryogenic liquids, such as liquid oxygen (LOX). In our Phase I NIAC study, we realized that a combination of scattering particles and a silver backing could yield a highly effective, very broadband, reflector that could potentially reflect more than 99.9% of the Sun’s irradiant power. We developed a sophisticated model of this reflector and theoretically showed that cryogenic temperatures could be achieved in deep space at one astronomical unit (1 AU) from the Sun. We showed how this new reflector could minimize heat conduction into the cryogenic tanks by coating the tank support struts. We then modelled a strawman architecture for a mission to Mars, using a coated LOX tank, coated struts, and infrared shields, to show that with our new coating it would be possible to maintain liquid oxygen passively. As a result of this work a patent application was generated and a paper published in Optics Letters. Our Phase II NIAC study had two primary goals, to develop a rigid version of the cryogenic selective surface proposed in Phase I and to test its performance in a simulated deep space environment. During the first year of the project the work concentrated on developing rigid tiles of BaF2, leading to tiles as large as 4 inches in diameter that transmitted very little visible light. In addition, during the first year a simulated deep space environment was created using a vacuum chamber and cryocooler. Using this facility, we showed that our BaF2 tiles absorbed less than ¼% of 375 nm radiation, a significant milestone for the work. During the second year of the project, we continued to develop the BaF2 tiles and we put significant effort into the construction of a deep space environment where we could project simulated solar radiation onto a sample. In the spring of 2018, we conducted our first solar simulator test with BaF2 and saw about 3.6% absorption. This is better than the state-of-the-art, but disappointing since predictions were for much lower absorption. We, erroneously, attributed this absorption to water retention by the BaF2, and decided to change materials. We considered several oxides and settled on yttrium oxide (Y2O3) for further development, because it is broadband, lightweight, has high index, and is hydrophobic. In July 2018 we conducted our first test of a rigid tile of Y2O3 in the simulated deep space environment and saw significant absorption again. We then realized that the issue was not water, but mid-wave radiation passing through the tile and being absorbed by the temperature sensor and the varnish used to hold it in place. We wrapped the sensor in silver foil, re-ran the test, and saw much lower absorption; only 1.1%. We then re-ran the BaF2 tile and saw 1.4% absorption. These values are almost adequate to maintain LOX in deep space, but we suspect that there are still issues in our test apparatus; we suspect thermocouple wires may be absorbing radiation. Further, post-NIAC, testing will better determine the performance of our new solar reflector. In order to restrict the size of this report, we will only briefly describe topics that we have previously published, allowing us to devote more time to new material. So minimal material will be devoted to modeling the material and deep space cryogenic storage, while longer sections will cover our material development, simulated deep space testing, and new applications. The Launch Service Program (LSP) requested that we explore ways to use this new coating to maintain LOX in low Earth Orbit and that work is described. In addition, the Nuclear Thermal Propulsion (NTP) Program asked us to explore ways to reduce the heat load for liquid hydrogen, resulting in the development of a spray-on version of the coating that should significantly improve in-space multi-layer insulation performance.

Robert C. Youngquist,↗
DOE OSTI2023

Self-consistent integrated modeling of combined hybrid discharge-laser produced plasma devices for extreme ultraviolet metrology

Discharge- and laser-produced plasma (DLPP) devices are being used as light sources for extreme ultraviolet (EUV) generation. A key challenge for both, DPP and LPP, is achieving sufficient brightness to support the throughput requirements of nanometrology tools. To simulate the environment of a hybrid DLPP device and optimize the EUV output, we have developed an integrated HEIGHTS-DLPP computer simulation package. The package integrates simulation of two evolving plasmas (DPP and LPP) and includes modeling of a set of integrated self-consistent processes: external power source and plasma energy balance, plasma resistive magnetohydrodynamics, plasma heat conduction, detailed radiation transport (RT), and laser absorption and refraction. We simulated and optimized DLPP devices using Xe gas as a target material. We synchronized the external circuit parameters, chamber gas parameters, and laser beam temporal and spatial profiles to achieve maximum EUV output. The full 3D Monte Carlo scheme was integrated for detailed RT and EUV output calculations in Xe using more than 3600 spectral groups. The modeling results are in good agreement with Julich Forschungszentrum experimental data. Theoretical models, developed and integrated into the HEIGHTS package, showed wide capabilities and flexibility. In conclusion, the models and package can be used for optimization of the experimental parameters and settings, investigation of DLPP devices with complex design, analyzing the impact of integrated spatial effects and working timeline arrangement on the final EUV output, and EUV source size, shape, and angular distribution.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Effect of self-generated magnetic fields on x-ray emission in Kr-filled targets at the National Ignition Facility

We examine the effects of self-generated magnetic fields in a Kr gas pipe x-ray source platform. X-ray emission from Kr plasma is dependent on the plasma conditions, as the ionization state is largely a function of temperature. Magnetic fields are known to limit heat conduction, which increases temperature. We show that the emission in simulations of the gas pipe x-ray source is dependent on how self-generated magnetic fields are modeled. The inclusion of self-generated magnetic fields in simulations more accurately captures the emission of lower energy x-ray emission (L-shell), bringing results closer to experiments. The modeled x-ray emission and self-generated magnetic fields are shown to be particularly sensitive to the inclusion of the Nernst effect in simulations. Severely limiting the Nernst effect leads to a hotter Kr plasma, which can account for the discrepancy seen in earlier studies. By modifying the Nernst effect multiplier, we can achieve better experimental agreement in x-ray emission from gas pipes; the value of the multiplier that leads to the best agreement is dependent on the laser power of the drive. Currently, the suppression factor of the Nernst effect needed for high power drives (PL>200 TW) is more restrictive than what is currently put forward by non-local models.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Wide‐Field Bond Quality Evaluation Using Frequency Domain Thermoreflectance with Deep Neural Network Feature Reconstruction

Heterogeneous integration of microelectronic components provides a pathway to improve circuit/component performance; however, this comes with assembly challenges, in particular due to complex interfaces via subsurface bump bonds. The ability of these bonds to transmit electrical signals and conduct heat to the carrier substrate limits component performance. In this work, hyperspectral frequency‐domain thermoreflectance (FDTR) imaging is demonstrated as a robust technique for evaluating the quality of subsurface indium bump bonds in a surrogate microelectronic sample. By performing microscale FDTR imaging with coarse motion image stitching, thermal phase maps that cover a 4 mm by 4 mm field‐of‐view with subsurface feature sensitivity at depths greater than 50 µm are obtained. The resulting FDTR hyperspectral data contains more than three million pixels and reveal the quality of subsurface microbump arrays. Wide‐field analysis of bonded versus gap regions is enabled by deep neural network feature reconstruction, that after training, rapidly provides an interpretable representation of bond quality. Utility of noisy higher frequency FDTR phase maps, i.e., near the computationally predicted sensing depth limit, results in an average prediction error of 11%. Taken together, FDTR with neural network‐based analysis demonstrates subsurface bond monitoring at length scales relevant for heterogeneously integrated microelectronics.

FDTR↗
DOE OSTI2021

Multi-physics Peridynamic Modeling of Damage Processes in Protective Coatings

Protective coatings can revolutionize the aerospace industry by providing a way to build a fuel-efficient and low-emission gas turbine engine operating at elevated temperature. Currently, significant challenges persist in the multi-physics modeling of damage processes in protective coatings exposed to the hot corrosive environment of gas turbine engine. Examples of such detrimental processes include an interface damage between different material layers forming protective coating, a formation of the through-the-thickness vertical cracks, a diffusion of oxygen and moisture through those cracks, an oxidation, and a delamination. In this paper, a feasibility of a multi-physics peridynamic model to provide insight to these detrimental processes has been demonstrated. 3-Dimensional peridynamic equations which are valid everywhere, including dynamically evolving discontinuities, have been presented. In conclusion, validation and demonstration have been shown for conduction heat transfer, reactive oxidation, and delamination of protective coating with a composition borrowed from the open literature.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Layer structured bifunctional monolith catalysts for energy-efficient conversion of CO 2 to dimethyl ether

A monolith supported bifunctional catalyst for the direct conversion of CO 2 to dimethyl ether was developed and evaluated. The catalyst consists of a layer structured configuration, in which a CuO/ZnO/ZrO 2 component for methanol synthesis using CO 2 as feedstock and a Ferrierite zeolite component for the subsequent dehydration reaction are washcoated onto the channel surfaces of a metallic monolith substrate as two consecutive layers. The metal substrate provides heat conduction to regulate the catalyst bed temperature. The layered configuration significantly improves the synergistic effects of the two components, resulting in a 20% increase in the productivity for dimethyl ether at 240 °C as compared with the conventional catalysts with the two components being blended in various levels of proximity. Furthermore, the layer structured design minimizes the undesirable interaction between the two components and drastically improves the on-stream durability of the catalyst. No activity decline was observed in a 146-h performance test.

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

LaSDI: Parametric Latent Space Dynamics Identification

Enabling fast and accurate physical simulations with data has become an important area of computational physics to aid in inverse problems, design-optimization, uncertainty quantification, and other various decision-making applications. This paper presents a data-driven framework for parametric latent space dynamics identification procedure that enables fast and accurate simulations. The parametric model is achieved by building a set of local latent space model and designing an interaction among them. An individual local latent space dynamics model achieves accurate solution in a trust region. By letting the set of trust region to cover the whole parameter space, our model shows an increase in accuracy with an increase in training data. Herein we introduce two different types of interaction mechanisms, i.e., point-wise and region-based approach. Both linear and nonlinear data compression techniques are used. We illustrate the framework of Latent Space Dynamics Identification (LaSDI) enable a fast and accurate solution process on various partial differential equations, i.e., Burgers’ equations, radial advection problem, and nonlinear heat conduction problem, achieving 0 (100)x speed-up and 0 (1)% relative error with respect to the corresponding full order models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Weak-form latent space dynamics identification

Recent work in data-driven modeling has demonstrated that a weak formulation of model equations enhances the noise robustness of a wide range of computational methods. In this paper, we demonstrate the power of the weak form to enhance the LaSDI (Latent Space Dynamics Identification) algorithm, a recently developed data-driven reduced order modeling technique. We introduce a weak form-based version WLaSDI (Weak-form Latent Space Dynamics Identification). WLaSDI first compresses data, then projects onto the test functions and learns the local latent space models. Notably, WLaSDI demonstrates significantly enhanced robustness to noise. With WLaSDI, the local latent space is obtained using weak-form equation learning techniques. Compared to the standard sparse identification of nonlinear dynamics (SINDy) used in LaSDI, the variance reduction of the weak form guarantees a robust and precise latent space recovery, hence allowing for a fast, robust, and accurate simulation. We demonstrate the efficacy of WLaSDI vs. LaSDI on several common benchmark examples including viscid and inviscid Burgers', radial advection, and heat conduction. For instance, in the case of 1D inviscid Burgers' simulations with the addition of up to 100% Gaussian white noise, the relative error remains consistently below 6% for WLaSDI, while it can exceed 10,000% for LaSDI. Similarly, for radial advection simulations, the relative errors stay below 15% for WLaSDI, in stark contrast to the potential errors of up to 10,000% with LaSDI. Moreover, speedups of several orders of magnitude can be obtained with WLaSDI. For example applying WLaSDI to 1D Burgers' yields a 140X speedup compared to the corresponding full order model.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Real-time cure monitoring of fiber-reinforced polymer composites using infrared thermography and recursive Bayesian filtering

Despite the desirable characteristics of fiber-reinforced polymer (FRP) composites, their utilization in high volume production industries is limited by a lack of efficient manufacturing techniques. Monitoring the curing process of these composites can help with improving the quality and efficiency of the manufacturing process. This article discusses a method that uses Kalman-filter-based fusion of the information obtained from infrared thermography (surface temperature measurements) and a heat conduction model to estimate degrees of cure and internal temperatures of curing FRP composite parts in real time. The effectiveness of the methodology is demonstrated by successfully monitoring the curing of an FRP composite part in a laboratory experiment. Finally, the proposed methodology is a crucial step towards identifying anomalies in the curing process that negatively impact the quality of FRP composite parts.

36 MATERIALS SCIENCE↗
DOE OSTI2023

A conservative, interface-resolved, compressible framework for the modeling and simulation of liquid/gas phase change

This paper presents a method for simulating evaporation in a compressible, interface-resolved framework appropriate for modeling problems of engineering interest. In order to achieve robustness and broad applicability, the method has been designed to discretely enforce consistent mass and thermal energy transport at the phase interface, to globally conserve mass, momentum, and energy, and to be capable of modeling compressible and incompressible systems. Verification is performed via the Sod-shock test, one-dimensional heat conduction, evaporation from a planar interface, and evaporation of three-dimensional droplets. Convergence with increasing mesh resolution is demonstrated in all tested configurations, and conservation is maintained near machine precision for a translating droplet. Conservation and accurate phase change rates are preserved at the low numerical resolutions commonly encountered in engineering calculations. Following verification, the method is validated by comparison to an empirical correlation for evaporating droplets in high temperature crossflow, and the presentation concludes with the simulation of an iso-octane spray at conditions representative of gasoline direct injection. In conclusion, successful verification, validation, and demonstrated practical utility suggest the method to be an accurate, efficient, and robust approach for the study of phase change in engineering systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

gLaSDI: Parametric physics-informed greedy latent space dynamics identification

A parametric adaptive physics-informed greedy Latent Space Dynamics Identification (gLaSDI) method is proposed for accurate, efficient, and robust data-driven reduced-order modeling of high-dimensional nonlinear dynamical systems. In the proposed gLaSDI framework, an autoencoder discovers intrinsic nonlinear latent representations of high-dimensional data, while dynamics identification (DI) models capture local latent-space dynamics. Here, an interactive training algorithm is adopted for the autoencoder and local DI models, which enables identification of simple latent-space dynamics and enhances accuracy and efficiency of data-driven reduced-order modeling. To maximize and accelerate the exploration of the parameter space for the optimal model performance, an adaptive greedy sampling algorithm integrated with a physics-informed residual-based error indicator and random-subset evaluation is introduced to search for the optimal training samples on the fly. Further, to exploit local latent-space dynamics captured by the local DI models for an improved modeling accuracy with a minimum number of local DI models in the parameter space, a -nearest neighbor convex interpolation scheme is employed. The effectiveness of the proposed framework is demonstrated by modeling various nonlinear dynamical problems, including Burgers equations, nonlinear heat conduction, and radial advection. The proposed adaptive greedy sampling outperforms the conventional predefined uniform sampling in terms of accuracy. Compared with the high-fidelity models, gLaSDI achieves 17 to 2,658× speed-up with 1 to 5% relative errors.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Numerical evaluation of AGR-2 fission product release

The AGR-2 experiment produced normal operation and accident condition fuel performance data for tri-structural isotropic (TRISO) particles with UCO and UO 2 kernels. Data for compacts with no failed particles and for compacts with one or more failed particles are available. To model the fission product diffusion and release from these compacts, it is important to consider the computational mesh as well as the heat conduction and mass diffusion properties of the materials in a TRISO particle. Code and solution verification studies with the Bison fuel performance code were performed to show that the code is computing correct solutions. Bison comparisons to post-irradiation examination data and PARFUME predictions were made for several sets of compacts. Furthermore, these comparisons considered silver, cesium, strontium, and krypton with and without failed particles. Bison predictions closely match those of PARFUME, while both codes generally overpredict post-irradiation examination data.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Picosecond laser generated plasma as a source of singly charged ions for external injection into an EBIS

The focus of this paper is on practical aspects of ion generation by picosecond lasers as a source of low charge state ions for external injection of ions into an electron beam ion source (EBIS). For a ps-laser, compared to a ns-laser currently used at Relativistic Heavy Ion Collier Electron Beam Ion Source (RHIC EBIS), the influence of heat conductivity in the solid target is almost negligible, which results in a lower target consumption rate and less vacuum pressure rise. By using a laser with high repetition rate, it is possible to produce quasi continuous 1+ ion beams for periods of tens of milliseconds, making it possible to take advantage of the ability of the EBIS to accumulate ions in the “slow” injection capture mode. Producing such an ion pulse train is now feasible since ps-lasers with pulse energy up to 10 mJ and rep-rate up to 10 kHz have recently become commercially available. The advantages of this lower current accumulation scheme include: (1) easier beam transport due to lower space charge of lower beam currents required compared to the present single pulse fast injection scheme, (2) better EBIS pulse to pulse ion output stability since pulse to pulse ion variations of the laser source are averaged over a long train of laser pulses, and (3) the possible addition of an isotope separator in which rare beams could be produced and selected at run time from less expensive (unenriched) targets. We studied the properties of plasmas generated by a ps-laser with 1.27 mJ energy within an 8 ps pulse and a repetition rate up to 400 Hz at Argonne National Laboratory to investigate feasibility and specify parameters for a laser ion source for RHIC EBIS using a “slow” injection mode. Al, Ti, Cu, Nb, and Ta targets were tested with various target translation speeds. Here, we demonstrated that a both “slow” and “fast” injection modes are accessible with a single ion source geometry and single injection line, providing the most attractive option for an ion source for external injection into RHIC EBIS trap based on a ps-laser.

43 PARTICLE ACCELERATORS↗
DOE OSTI2023

Development of an in situ ion irradiation scanning electron microscope

An in situ ion irradiation scanning electron microscope (I 3 SEM) has been developed, installed, and integrated into the Ion Beam Laboratory at Sandia National Laboratories. The I 3 SEM facility combines a field emission, variable pressure, scanning electron microscope, a 6 MV tandem accelerator, high flux low energy ion source, an 808 nm-wavelength laser, and multiple stages to control the thermal and mechanical state of the sample observed. The facility advances real-time understanding of materials evolution under combined environments at the mesoscale. As highlighted in multiple examples, this unique combination of tools is optimized for studying mesoscale material response in overlapping extreme environments, allowing for simultaneous ion irradiation, implantation, laser bombardment, conductive heating, cooling, and mechanical deformation.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

A whole-core steady-state thermal-hydraulic model for annular fuel type fluoride-salt-cooled reactors

A whole-core, steady-state thermal-hydraulic model is developed for the fluoride-salt-cooled small modular advanced high-temperature reactor (SmAHTR) that employs an annular fuel configuration. This pre-conceptual reactor design by Oak Ridge National Laboratory (ORNL) has the annular fuel and moderator pins arranged in a hexagonal layout. The FLiBe coolant flows from the bottom to the top of the core, parallel to the hexagonal bundle. The fuel and moderator pins in the core are discretized into finite volumes and the 3-D heat conduction equation is solved to obtain the temperature profile. Inter-fuel assembly conduction is also addressed. For this fuel assembly configuration, the coolant flows through two distinct regions – the hexagonal pin bundle and the annulus between the fuel pin and the tie rod. The fluid flow through the hexagonal bundles is modeled using the subchannel approach, in which the coolant region is discretized into corner, edge and interior subchannels and the resulting conservation equations are systematically solved. The 1-D mass, momentum and energy equations are solved for the annulus channels between the fuel pin and the tie rod. Pertinent closure models from the literature are employed to close the system of equations. We also performed a preliminary code-to-code comparison between the present model and a CFD model.. The resulting thermal-hydraulic model can provide temperature, flow rate and pressure drop profiles for the different solid and fluid regions throughout the entire core. Whole-core thermal-hydraulic results for a representative power profile are presented and discussed.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Design of a prototypical natural circulation water-based reactor cavity cooling system (RCCS) for a pebble-bed generic FHR

A prototypical natural circulation water-based reactor cavity cooling system (RCCS) for the UC Berkeley Mark-1 pebble-bed gFHR is designed based on one-dimensional thermal hydraulics modeling and optimization implemented in an in-house MATLAB code. The model employs a lumped core consisting of fuel pebble and graphite pebble regions, while the graphite reflector, vessel, and RCCS are represented as separate but energy-coupled regions. The model is derived based on steady state energy balance equations accounting for conductive heat transfer from the lumped core to the vessel and subsequent radiative heat transfer to the RCCS and convective heat transfer in the water. Further, mass flow rate is calculated based on momentum and thermal energy balance in the RCCS. Starting with ANL’s water NSTF as baseline, effects of RCCS design parameters such as size of the plate between pipes, pipe diameter, source-to-sink distance, surface emissivity, and pitch from the core are examined in an integral effects framework which accounts for subsequent variation of the mass flow rate, number of pipes, convection coefficient, mean region and surface temperatures, radiative view factors, and water outlet temperature. The importance of including a prototypical reactor design in RCCS design calculations is emphasized as the calculations show that temperature drops from the core to the RCCS fluid to transfer the heat tend to be the limitation not the heat removal capacity of the fluid. A closed-loop design is obtained with capability to safely remove up to 0.72% of the nominal reactor power at maximum estimated peak conditions and 0.40% at shutdown. The design is based on physics calculations and does not account for economic optimization.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2024

Thermodynamically consistent Cahn–Hilliard–Navier–Stokes equations using the metriplectic dynamics formalism

Cahn–Hilliard–Navier–Stokes (CHNS) systems describe flows with two-phases, e.g., a liquid with bubbles. Obtaining constitutive relations for general dissipative processes for such systems, which are thermodynamically consistent, can be a challenge. We show how the metriplectic 4-bracket formalism (Morrison and Updike, 2024) achieves this in a straightforward, in fact algorithmic, manner. First, from the noncanonical Hamiltonian formulation for the ideal part of a CHNS system we obtain an appropriate Casimir to serve as the entropy in the metriplectic formalism that describes the dissipation (e.g. viscosity, heat conductivity and diffusion effects). General thermodynamics with the concentration variable and its thermodynamics conjugate, the chemical potential, are included. Having expressions for the Hamiltonian (energy), entropy, and Poisson bracket, we describe a procedure for obtaining a metriplectic 4-bracket that describes thermodynamically consistent dissipative effects. The 4-bracket formalism leads naturally to a general CHNS system that allows for anisotropic surface energy effects. Furthermore, this general CHNS system reduces to cases in the literature, to which we can compare.

Cahn–Hilliard↗