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At least 145 records · Page 8

Artificial viscosity: back to the basics

Summary In this paper, we take a different perspective on the derivation of artificial viscosity. Heretofore, the development of artificial viscosity has been based on the paper published in Journal of Applied Physics in 1950 authored by John von Neumann and Robert Richtmyer [1]. Earlier, in 1948, Richtmyer published a report at Los Alamos Scientific Laboratory documenting the original concept [2]. This report was the true origin of shock capturing methods and contains several key ideas that are conceptually different than the 1950 journal article. Unfortunately, this report (LA‐671) was classified until 1993. This has resulted in two issues: the misattribution of the invention of artificial viscosity as primarily being the work of von Neumann and the loss of the structurally different ideas in the original report. We seek to right the record of history here and use the ideas contained in Richtmyer's report to good effect in deriving a new shock viscosity. The focus of previous development has been the Hugoniot curve describing the locus of states connected by a single shock wave. Here we follow a path more focused upon the Rayleigh line, which is strongly guided by Richtmyer's line of development of the original artificial viscosity formulation. We provide an implementation of the method resulting from this perspective and computational results for simple shock problems. Copyright © 2014 John Wiley & Sons, Ltd.

Mattsson, Ann E.↗

Volume-translated cubic EoS and PC-SAFT density models and a free volume-based viscosity model for hydrocarbons at extreme temperature and pressure conditions

This research focuses on providing the petroleum reservoir engineering community with robust models of hydrocarbon density and viscosity at the extreme temperature and pressure conditions (up to 533 K and 276 MPa, respectively) characteristic of ultra-deep reservoirs, such as those associated with the deepwater wells in the Gulf of Mexico. Our strategy is to base the volume-translated (VT) Peng–Robinson (PR) and Soave–Redlich–Kwong (SRK) cubic equations of state (EoSs) and perturbed-chain, statistical associating fluid theory (PC-SAFT) on an extensive data base of high temperature (278–533 K), high pressure (6.9–276 MPa) density rather than fitting the models to low pressure saturated liquid density data. This high-temperature, high-pressure (HTHP) data base consists of literature data for hydrocarbons ranging from methane to C{sub 40}. The three new models developed in this work, HTHP VT-PR EoS, HTHP VT-SRK EoS, and hybrid PC-SAFT, yield mean absolute percent deviation values (MAPD) for HTHP hydrocarbon density of ~2.0%, ~1.5%, and <1.0%, respectively. An effort was also made to provide accurate hydrocarbon viscosity models based on literature data. Viscosity values are estimated with the frictional theory (f-theory) and free volume (FV) theory of viscosity. The best results were obtained when the PC-SAFT equation was used to obtain both the attractive and repulsive pressure inputs to f-theory, and the density input to FV theory. Both viscosity models provide accurate results at pressures to 100 MPa but experimental and model results can deviate by more than 25% at pressures above 200 MPa.

02 PETROLEUM↗

Viscosity-temperature relation based on the evolution of medium-range structures of silica

The viscosity of glass is the most important technological property to glass manufactures and various applications. Practically, finding an accurate equation to express the glass viscosity behavior in the entire glass transition temperature range is tremendously challenge because it spans more than ten orders of magnitude. After a brief review of existing empirical viscosity equations, this work focuses on the correlating silica viscosity behavior with the evolution of glass medium-range structure, based on the recently proposed nanoflake model. From this new model, a new equation is constructed, which correctly describes the Arrhenius-type behavior of silica viscosity η above the melting temperature Tm, and non-Arrhenius-type behavior from Tm to a critical temperature Tc. At temperature lower than Tc, the equation predicts Arrhenius-type behavior again for the viscous flow with increased activation energy. The new equation agrees with experimental data in the entire temperature spanned from extremely high to extremely low. Furthermore, the application of the new equation is shown to extend to sodium silicate glasses as well.

36 MATERIALS SCIENCE↗

A study of overflow simulations using MPAS-Ocean: Vertical grids, resolution, and viscosity

MPAS-Ocean is used to simulate an idealized, density-driven overflow using the dynamics of overflow mixing and entrainment (DOME) setup. Additionally, numerical simulations are carried out using three of the vertical coordinate types available in MPAS-Ocean, including z-star with partial bottom cells, z-star with full cells, and sigma coordinates. The results are first benchmarked against other models, including the MITgcm’s z-coordinate model and HIM’s isopycnal coordinate model, which are used to set the base case used for this work. A full parameter study is presented that looks at how sensitive overflow simulations are to vertical grid type, resolution, and viscosity. Horizontal resolutions with 50 km grid cells are under-resolved and produce poor results, regardless of other parameter settings. Vertical grids ranging in thickness from 15 m to 120 m were tested. A horizontal resolution of 10 km and a vertical resolution of 60 m are sufficient to resolve the mesoscale dynamics of the DOME configuration, which mimics real-world overflow parameters. Mixing and final buoyancy are least sensitive to horizontal viscosity, but strongly sensitive to vertical viscosity. This suggests that vertical viscosity could be adjusted in overflow water formation regions to influence mixing and product water characteristics. In conclusion, the study shows that sigma coordinates produce much less mixing than z-type coordinates, resulting in heavier plumes that go further down slope. Sigma coordinates are less sensitive to changes in resolution but as sensitive to vertical viscosity compared to z-coordinates.

58 GEOSCIENCES↗

Revisiting the validity of eddy viscosity models for predicting airflow over water waves

In this study, we revisit the validity of eddy viscosity models for predicting wave-induced airflow disturbances over ocean surface waves. We first derive a turbulence curvilinear model for the phase-averaged Navier–Stokes equations, extending the work of Cao, Deng & Shen (2020 J. Fluid Mech. 901, A27), by incorporating turbulence stress terms previously neglected in the linearised viscous curvilinear model. To verify our formulation, we perform a priori tests by numerically solving the model using mean wind and turbulence stress profiles from large-eddy simulations (LES) of airflow over waves across various wave ages. Results show that including turbulence stress terms improves wave-induced airflow predictions compared with the previous viscous curvilinear model. We further show that using a standard mixing-length eddy viscosity yields inaccurate predictions at certain wave ages, as it fails to capture wave-induced turbulence, which fundamentally differs from mean shear-driven turbulence. The LES data show that accurate representations of wave-induced stresses require a complex-valued eddy viscosity. The maximum magnitude of this eddy viscosity scales as ∼𝑢 𝜏 ⁢𝜁 𝑖𝑛𝑛𝑒𝑟 , where 𝑢 𝜏 is the friction velocity and 𝜁 𝑖𝑛𝑛𝑒𝑟 is the inner-layer thickness, the height at which the eddy-turnover time matches the wave advection time scale. This scaling aligns with the prediction by Belcher & Hunt (1993 J. Fluid Mech. 251, 109–148). Overall, the findings demonstrate that traditional eddy viscosity models are inadequate for capturing wave-induced turbulence. More sophisticated turbulence models are essential for the accurate prediction of airflow disturbances and form drag in wind–wave interaction models.

16 TIDAL AND WAVE POWER↗

Effects of surface tension and viscosity on gold and silver sputtered onto liquid substrates

Here, we report on DC magnetron sputtering of gold and silver onto liquid substrates of varying viscosities and surface tensions. We were able to separate the effects of viscosity from surface tension by depositing the metals onto silicone oils with a range of viscosities. The effects of surface tension were studied by depositing the metals onto squalene, poly(ethylene glycol), and glycerol. It was discovered that dispersed nanoparticles were formed on liquids with low surface tension and low viscosity whereas dense films were formed on liquids with low surface tension and high viscosity. Nanoparticles were formed on both the liquid surface and within the bulk liquid for high surface tension liquids. Our findings can be used to tailor the metal and liquid interaction to fabricate particles and films for various applications in optics, electronics, and catalysis.

36 MATERIALS SCIENCE↗

Numerical minimization of neoclassical poloidal viscosity for supersonic equilibria in tokamak geometry

Extensive experimental evidence has shown that the presence of poloidal flow in tokamaks can dramatically improve transport properties. However, theory indicates that poloidal flows are damped by poloidal viscosity, thus necessitating external drivers, such as neutral beam injection or radio frequency heating. In this work, ideal magnetohydrodynamic equilibria are calculated via the FORTRAN code FLOW [Guazzotto et al., Phys. Plasmas 11, 604 (2004)] and a postprocessor is used to estimate the neoclassical poloidal viscosity. The equilibrium inputs, which correspond to intuitive physical quantities, are then numerically optimized to reduce a viscosity figure of merit. We present supersonic equilibria in tokamak geometry with minimized neoclassical poloidal viscosities for various velocity free function inputs, plasma aspect ratios, and collisionality regimes. Benchmarks are made against an analytic theory as well as a classical expression of poloidal viscosity. Numerical confirmation of the analytic theory is obtained in the high aspect ratio and high collisionality limit. Good agreement is also seen near the plasma core and edge, with discrepancies arising in the intermediate region. Outside of these limits, rotation input function profiles are found that provide ∼order of magnitude improvements over the analytic theory, with additional progress being made toward predictions for tokamak-relevant equilibria.

Physics↗

Taking control of compressible modes: bulk viscosity and the turbulent dynamo

Many polyatomic astrophysical plasmas are compressible and out of chemical and thermal equilibrium, introducing a bulk viscosity into the plasma via the internal degrees of freedom of the molecular composition, directly impacting the decay of compressible modes, $\mathrm{{\boldsymbol {\mathit {v}}}}_{\parallel }(\boldsymbol {k})$. This is especially important for small-scale, turbulent dynamo processes in the interstellar medium (ISM), which are known to be sensitive to the effects of compression. To control the viscous properties of $\mathrm{{\boldsymbol {\mathit {v}}}}_{\parallel }(\boldsymbol {k})$, we perform trans-sonic, visco-resistive dynamo simulations with additional bulk viscosity $\nu _{\text{bulk}}$, deriving a new $\nu _{\text{bulk}}$ Reynolds number $\text{Re}_{\text{bulk}}$, and viscous Prandtl number $\text{P}\nu \equiv \text{Re}_{\text{bulk}}/ \text{Re}_{\text{shear}}$, where $\text{Re}_{\text{shear}}$ is the shear viscosity Reynolds number. We derive a framework for decomposing $E_{\rm mag}$ growth rates into incompressible and compressible terms via orthogonal tensor decompositions of $\boldsymbol {\nabla }\otimes \mathrm{{\boldsymbol {\mathit {v}}}}$, where $\mathrm{{\boldsymbol {\mathit {v}}}}$ is the fluid velocity. We find that $\mathrm{{\boldsymbol {\mathit {v}}}}_{\parallel }(\boldsymbol {k})$ play a dual role, growing and decaying $E_{\rm mag}$, and that field-line stretching is the main driver of growth, even in compressible dynamos. In the absence of $\nu _{\text{bulk}}$ ($\text{P}\nu \rightarrow \infty$), $\mathrm{{\boldsymbol {\mathit {v}}}}_{\parallel }(\boldsymbol {k})$ pile up on small-scales, creating a spectral bottleneck, which disappears for $\text{P}\nu \approx 1$. As $\text{P}\nu$ decreases, $\mathrm{{\boldsymbol {\mathit {v}}}}_{\parallel }(\boldsymbol {k})$ are dissipated at increasingly larger scales, in turn suppressing incompressible modes through a coupling between high-k modes. We emphasize the importance of further understanding the role of $\nu _{\text{bulk}}$ in compressible astrophysical plasmas, which we estimate could be as strong as the shear viscosity in the cold ISM, and highlight that compressible direct numerical simulations without bulk viscosity have unresolved compressible mode dissipation scales.

MHD↗

Shear viscosity from perturbative quantum chromodynamics to the hadron resonance gas at finite baryon, strangeness, and electric charge densities

Through model-to-data comparisons from heavy-ion collisions, it has been shown that the quark gluon plasma has an extremely small shear viscosity at vanishing densities. At large baryon densities, significantly less is known about the nature of the shear viscosity from quantum chromodynamics (QCD). Within heavy-ion collisions, there are three conserved charges: baryon number (B), strangeness (S), and electric charge (Q). Here we calculate the shear viscosity in two limits using perturbative QCD (pQCD) and an excluded-volume hadron resonance gas at finite BSQ densities. We then develop a framework that interpolates between these two limits such that shear viscosity is possible to calculate across a wide range of finite BSQ densities. We find that the pQCD and hadron resonance gas calculations have different BSQ density dependencies such that a rather nontrivial shear viscosity appears at finite densities.

Phenomenology↗

Phenomenological consequences of enhanced bulk viscosity near the QCD critical point

In the proximity of the QCD critical point the bulk viscosity of quark-gluon matter is expected to be proportional to nearly the third power of the critical correlation length, and become significantly enhanced. Here, this work is the first attempt to study the phenomenological consequences of enhanced bulk viscosity near the QCD critical point. For this purpose, we implement the expected critical behavior of the bulk viscosity within a non-boost-invariant, longitudinally expanding 1 + 1 dimensional causal relativistic hydrodynamical evolution at nonzero baryon density. We demonstrate that the critically enhanced bulk viscosity induces a substantial nonequilibrium pressure, effectively softening the equation of state, and leads to sizable effects in the flow velocity and single-particle distributions at the freeze-out. In conclusion, the observable effects that may arise due to the enhanced bulk viscosity in the vicinity of the QCD critical point can be used as complementary information to facilitate searches for the QCD critical point.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Bulk viscosity from Urca processes: npeμ matter in the neutrino-trapped regime

In this work, we extend our previous study of the bulk viscosity of hot and dense npe matter induced by the Urca process in the neutrino trapped regime to npeμ matter by adding the muonic Urca processes as well as the purely leptonic electroweak processes involving electron-muon transition. Here, the nuclear matter is modeled in a relativistic density functional approach with two different parametrizations which predict neutrino dominated matter (DDME2 model) and anti-neutrino dominated matter (NL3 model) at temperatures for which neutrinos/anti-neutrinos are trapped. In the case of neutrino-dominated matter, the main equilibration mechanism is lepton capture, whereas in the case of antineutrino-dominated matter this is due to neutron decay. We find that the equilibration rates of Urca processes are higher than that of the pure leptonic processes, which implies that the Urca bulk viscosity can be computed with the leptonic reactions assumed to be frozen. We find that the bulk viscosity decreases with temperature as ζ~T –2 at moderate temperatures. At high temperatures this scaling breaks down by sharp drops of the bulk viscosity close to the temperature where the proton fraction is density-independent and the matter becomes scale-invariant. This occurs also when the matter undergoes a transition from the antineutrino-dominated regime to the neutrino-dominated regime where the bulk viscosity attains a local maximum. We also estimate the bulk viscous dissipation timescales and find that these are in the range ≳ 1 s for temperatures above the neutrino trapping temperature. These timescales would be relevant only for long-lived objects formed in binary neutron star mergers and hot proto-neutron stars formed in core-collapse supernovas.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Effects of particle size and briquetting of soda-lime-silicate glass batch on viscosity during batch-to-melt conversion

To assess the effects of grain size and briquetting on glass-batch melting, we measured the viscosity (?b) of an industrial glass batch during its conversion to molten simulated architectural glass within the temperature interval of 1050 °C to 1300 °C and at a shear rate of 0.02 s-1. On the basis of the mass fraction of undissolved sand (xs), which was determined using X-ray diffraction analysis on quenched batch samples, and the gas-phase fraction (p), which was obtained from volumetric measurements, we established the relationship ln(?b/?m) = a0 + bsxs + app, where ?m is the transition melt viscosity, a0 is the melt homogeneity coefficient, bs is the coefficient for undissolved sand, and ap is the coefficient for bubbles. The obtained values, bs = 8.756 and ap = 0.658, indicate that undissolved silica sand strongly influences batch viscosity. Consequently, compared with coarse-grained batches, fine raw materials and briquetting resulted in lower batch viscosity during conversion. Owing to their lower viscosities and higher heat conductivities, batches from finer raw materials or batches shaped into briquettes are expected to enhance the melting rate of batch blankets in industrial glass-melting furnaces.

Doi, Yoji↗

Verification study of xRAGE’s multi-ion viscosity model

This report on the adequacy of the plasma viscosity model implemented in LANL’s ASC program code, xRAGE is organized as follows. Section I provides a brief introduction on the kinetic theory which underpins plasma viscosity, and Section II describes how plasma kinetic theory can be used to calculate plasma viscosity coefficients accurate within the hydrodynamic limit. Section III describes the existing model for calculating the plasma viscosity coefficient in xRAGE. Next, Section IV shows tests of the xRAGE viscosity model against established hydrodynamic theory in the case of binary and trinary plasma mixtures.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Optimization of artificial viscosity in production codes based on Gaussian Regression surrogate models

To accurately model flows with shock waves using staggered-grid Lagrangian hydrodynamics, artificial viscosity has to be introduced to convert kinetic energy into internal energy, thereby increasing the entropy across shocks. Determining the appropriate strength of the artificial viscosity is an art and strongly depends on the particular problem and experience of the researcher. The objective of this study is to pose the problem of finding the appropriate strength of artificial viscosity as an optimization problem and solve this problem using machine learning (ML) tools, specifically using surrogate models based on Gaussian Process regression and Bayesian analysis. We describe the optimization method and discuss various practical details of its implementation. The shock-containing problems for which we apply this method all have been implemented in the LANL code FLAG. First, we apply ML to find optimal values to isolated shock problems of different strengths. Second, we apply ML to optimize viscosity for a 1D propagating detonation problem based on Zel’dovich-von Neumann-Doring (ZND) detonation theory using a reactive burn model. We compare results for default (currently used values in FLAG) and optimized values of artificial viscosity for these problems demonstrating the potential for significant improvement in the accuracy of computations.

42 ENGINEERING↗

Effect of varying experimental conditions on the viscosity of α -pinene derived secondary organic material

Knowledge of the viscosity of particles containing secondary organic material (SOM) is useful for predicting reaction rates and diffusion in SOM particles. In this study we investigate the viscosity of SOM particles as a function of relative humidity and SOM particle mass concentration, during SOM synthesis. The SOM was generated via the ozonolysis of α -pinene at < 5 % relative humidity (RH). Experiments were carried out using the poke-and-flow technique, which measures the experimental flow time ( τ exp, flow ) of SOM after poking the material with a needle. In the first set of experiments, we show that τ exp, flow increased by a factor of 3600 as the RH increased from < 0.5 RH to 50 % RH, for SOM with a production mass concentration of 121 µg m -3 . Based on simulations, the viscosities of the particles were between 6 × 10 5 and 5 × 10 7 Pa s at < 0.5 % RH and between 3 × 10 2 and 9 × 10 3 Pa s at 50 % RH. In the second set of experiments we show that under dry conditions τ exp, flow decreased by a factor of 45 as the production mass concentration increased from 121 to 14 000 µg m -3 . From simulations of the poke-and-flow experiments, the viscosity of SOM with a production mass concentration of 14 000 µg m -3 was determined to be between 4 × 10 4 and 1.5 × 10 6 Pa s compared to between 6 × 10 5 and 5 × 10 7 Pa s for SOM with a production mass concentration of 121 µg m -3 . The results can be rationalized by a dependence of the chemical composition of SOM on production conditions. Lastly, these results emphasize the shifting characteristics of SOM, not just with RH and precursor type, but also with the production conditions, and suggest that production mass concentration and the RH at which the viscosity was determined should be considered both when comparing laboratory results and when extrapolating these results to the atmosphere.

54 ENVIRONMENTAL SCIENCES↗

Viscosity Determination of Molten Ash from Low-Grade US Coals

In entrained slagging gasifiers, the fluidity of the molten ash is a critical factor for process control since it affects slag formation, the capture of inorganic constituents, refractory wear, and slag drainage along the gasification chamber walls. The use of western coal, or mixtures of eastern and western coals as gasifier feedstock, is likely to occur as western coals become available and technological issues that hinder their use are being resolved. In the present work, the viscosity of synthetic slags with ash chemistries simulating the western U.S. coals, was experimentally measured at a Po 2 = 10 - 8 atm in the temperature range of 1773–1573 K (1500–1300 °C) using a rotating-bob viscometer. Alumina spindles and containment crucibles of both alumina and zirconia were used. Crystallization studies of this slag using a confocal scanning laser microscope found that a (Mg,Fe)Al 2 O 4 -based spinel precipitated at temperatures below 1723 K (1450 °C), and this agreed with FactSage equilibrium phase prediction. The same spinels were observed in the post-viscometry experiment slags when ZrO 2 crucibles were used and assumed to be in equilibrium with the slag at the higher temperatures. Zirconia dissolution resulted in a slight increase in the solid fraction present in slags at lower temperatures, compared to spinel fraction. Crystal precipitation changed the apparent activation energy and required a longer stabilization times for viscosity measurements. The viscosity results were used in predictive equations based on Veytsman and Einstein's models, with critical nucleation temperatures and the solid fraction calculated with FactSage. In the simulated eastern/western coal feedstock blends based on ash compositions, the fractions of the solid precipitates were also calculated using the thermodynamic program FactSage for each blend composition, and the plastic viscosity of each eastern/western coal slag blend was predicted using Veytsman's model and compared to available experimental data.

01 COAL, LIGNITE, AND PEAT↗

Viscosity of Heterogeneous Silicate Melts: A Non-Newtonian Model

The recently published viscosity data of heterogeneous silicate melts with well-documented structure and experimental conditions are critically re-analyzed and tabulated. By using these data, a non-Newtonian viscosity model incorporating solid fraction, solid shape, and shear rate is proposed on the basis of the power-law equation. This model allows calculating the viscosity of the heterogeneous silicate melts with solid fraction up to 34 vol pct. The error between the calculated and measured data is evaluated to be 32 pct, which is acceptable considering the large error in viscosity measurement of the completely liquid silicate melt.

36 MATERIALS SCIENCE↗

Effects of Fluorine on Solidification, Viscosity, Structure, and Heat Transfer of CaO-Al{sub 2}O{sub 3}-Based Mold Fluxes

To mitigate the chemical reaction between mold fluxes and high-Al steel, CaO-Al{sub 2}O{sub 3}-based mold fluxes were proposed to replace the conventional CaO-SiO{sub 2}-based mold fluxes. However, the high viscosity of CaO-Al{sub 2}O{sub 3}-based mold fluxes is harmful to the lubrication to the strand. In this article, the effects of fluorine on solidification, viscosity, structure, and heat transfer of CaO-Al{sub 2}O{sub 3}-based mold fluxes were evaluated. The addition of fluorine increased the break temperature and decreased the heat transfer rate of mold fluxes. It also reduced the flux viscosity at 1673 K (1400 °C) when fluorine content increased from 4.0 to 6.9 mass pct; but a further increase of fluorine to 12.5 mass pct did not notably change the flux viscosity. This phenomenon was correlated to the synergic effects of the dissociation of flux network and the increased potential of nucleation at high temperature with the fluorine addition.

36 MATERIALS SCIENCE↗