Entropy Stable Methods for the Euler Equations Revisited
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HECC↗
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Entropy Stable Methods for the Euler Equations Revisited
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HECC↗
On the Behavior of Entropy-Stable Schemes in the Low Mach Regime
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STMD↗
Low Thermal Conductivity and Diffusivity at High Temperatures Using Stable High–Entropy Spinel Oxide Nanoparticles
The realization of low thermal conductivity at high temperatures (0.11 W m –1 K –1 800 °C) in ambient air in a porous solid thermal insulation material, using stable packed nanoparticles of high-entropy spinel oxide with 8 cations (HESO-8 NPs) with a relatively high packing density of ≈50%, is reported. The high-density HESO-8 NP pellets possess around 1000-fold lower thermal diffusivity than that of air, resulting in much slower heat propagation when subjected to a transient heat flux. The low thermal conductivity and diffusivity are realized by suppressing all three modes of heat transfer, namely solid conduction, gas conduction, and thermal radiation, via stable nanoconstriction and infrared-absorbing nature of the HESO-8 NPs, which are enabled by remarkable microstructural stability against coarsening at high temperatures due to the high entropy. Furthermore, this work can elucidate the design of the next-generation high-temperature thermal insulation materials using high-entropy ceramic nanostructures.
thermal insulation↗
Intrastep, Stage-Value Predictors for Diagonally-Implicit Runge-Kutta Methods
To better identify the necessary attributes of good stage-value predictors (SVPs), numerous SVPs are designed for an existing: ESDIRK4(3)7L[2]SA [26] and a new: ESDIRK4(3)8L[2]SA scheme.1 Both are stifflyaccurate, stage-order two, explicit, singly-diagonally implicit Runge–Kutta (ESDIRK) schemes. Tradeoffs are studied in the parameter spaces enforcing the constraints on accuracy, linear stability, nonlinear stability and coefficient size to determine which objectives correlate with effective predictors. The SVPs are tested on three challenging external aerodynamics problems [107 − 108 degrees of freedom (DoFs)], each with a different level of stiffness. The problems include two 3D airfoils simulations and one canonical turbulence simulation. All simulations use the compressible Navier-Stokes equations (CNSE). An entropy stable spectral collocation formulation is used for discretizing the spatial terms in the equations. Simulations are performed at a wide variety of temporal error tolerances. Problems that are sufficiently stiff (e.g., lax temporal error tolerances) benefit from SVPs designed with second-order accuracy and stability properties: A-stability, and L-stability, rather than high accuracy constraints. Simulations with modest stiffness (e.g., strict error tolerances) are better suited for SVPs designed using high accuracy constraints. Designing SVPs with enhanced stability properties is tedious but worthwhile. Simulation times are reduced with optimal SVPs by as much as 100% on some stages, with combined stepwise improvements of between 50 − 100% for both methods. A comparative study is performed with the two aforementioned methods as well as four other ESDIRKs. The newly designed ESDIRK4(3)8L[2]SA with γ ≈ 1/10, proves to be the most efficient of the six tested ESDIRK schemes simulating the CNSE.
Diagonally-Implicit Runge-Kutta↗
Entropy conservative finite element schemes
The question of entropy stability for discrete approximations to hyperbolic systems of conservation laws is studied. The amount of numerical viscosity present in such schemes is quantified and related to their entropy stability by means of comparison. To this end, two main ingredients are used: entropy variables and the construction of certain entropy conservative schemes in terms of piecewise-linear finite element approximations. It is then shown that conservative schemes are entropy stable, if and (for three-point schemes) only if, they contain more numerical viscosity than the abovementioned entropy conservation ones.
Tadmor, E.↗
DNS of Flow in a Low-Pressure Turbine Cascade Using a Discontinuous-Galerkin Spectral-Element Method
A new computational capability under development for accurate and efficient high-fidelity direct numerical simulation (DNS) and large eddy simulation (LES) of turbomachinery is described. This capability is based on an entropy-stable Discontinuous-Galerkin spectral-element approach that extends to arbitrarily high orders of spatial and temporal accuracy and is implemented in a computationally efficient manner on a modern high performance computer architecture. A validation study using this method to perform DNS of flow in a low-pressure turbine airfoil cascade are presented. Preliminary results indicate that the method captures the main features of the flow. Discrepancies between the predicted results and the experiments are likely due to the effects of freestream turbulence not being included in the simulation and will be addressed in the final paper.
Low-Pressure Turbine Cascade↗
DNS of Low-Pressure Turbine Cascade Flows with Elevated Inflow Turbulence Using a Discontinuous-Galerkin Spectral-Element Method
Recent progress towards developing a new computational capability for accurate and efficient high-fidelity direct numerical simulation (DNS) and large-eddy simulation (LES) of turbomachinery is described. This capability is based on an entropy- stable Discontinuous-Galerkin spectral-element approach that extends to arbitrarily high orders of spatial and temporal accuracy, and is implemented in a computationally efficient manner on a modern high performance computer architecture. An inflow turbulence generation procedure based on a linear forcing approach has been incorporated in this framework and DNS conducted to study the effect of inflow turbulence on the suction- side separation bubble in low-pressure turbine (LPT) cascades. The T106 series of airfoil cascades in both lightly (T106A) and highly loaded (T106C) configurations at exit isentropic Reynolds numbers of 60,000 and 80,000, respectively, are considered. The numerical simulations are performed using 8th-order accurate spatial and 4th-order accurate temporal discretization. The changes in separation bubble topology due to elevated inflow turbulence is captured by the present method and the physical mechanisms leading to the changes are explained. The present results are in good agreement with prior numerical simulations but some expected discrepancies with the experimental data for the T106C case are noted and discussed.
Garai, Anirban↗
Scale-Resolving Simulations of Low-Pressure Turbine Cascades with Wall Roughness Using A Spectral-Element Method
The accurate prediction of wall-roughness effects in turbomachinery is becoming critical as turbine designers address airfoil surface quality and degradation concerns arising from the shift to advanced ceramic matrix composite (CMC) or additively-manufactured airfoils operating in higher temperature environments. In this paper, a recently developed computational capability for accurate and efficient scale-resolving simulations of turbomachinery is extended to analyze the boundary- layer separation and transition characteristics in a rough-wall low-pressure turbine (LPT) cascade. The computational capability is based on an entropy-stable discontinuous-Galerkin spectral-element approach that extends to arbitrarily high orders of spatial and temporal accuracy, and is implemented in an efficient manner for a modern high performance computer architecture. Results from the scale-resolving simulations of both smooth and rough airfoil cascades are presented and compared to previous experiments and numerical simulations. The results show that the suction surface boundary layer undergoes laminar separation, transition, and turbulent reattachment for the smooth airfoil cascade, while in the presence of roughness the separation and transition behavior of the suction surface boundary layer is substantially modified. The differences between the smooth and rough airfoil cascades are then highlighted by a detailed analysis of their respective turbulent flow fields.
Spectral-Element↗
Scale–Resolving Simulations of a Fundamental Trailing–Edge Cooling Slot Using a Discontinuous–Galerkin Spectral–Element Method
The accurate prediction of turbulent mixing in high-pressure turbines that incorporate various airfoil surface-cooling strategies is becoming increasing critical to the design of modern gas turbine engines where the quest for improved efficiency is driving compressor overall pressure ratios and turbine inlet temperatures to much higher levels than ever before. In the present paper, a recently developed computational capability for accurate and efficient scale–resolving simulations of turbomachinery is extended to study the turbulent mixing mechanism of a simplified abstraction of an airfoil trailing-edge cooling slot - a plane wall jet with finite lip thickness discharging into an ambient flow. The computational capability is based on an entropy– stable, discontinuous–Galerkin approach that extends to arbitrarily high orders of spatial and temporal accuracy. The numerical results show that the present simulations capture the trends observed in the experiments. Discrepancies between the simulations and experiments are believed to be due to differences in the inflow profiles and tunnel side–wall effects. The thick lip configuration leads to a thicker wake and higher unsteadiness in the wall jet compared to the thin lip. A detailed comparison of the turbulent flowfields is presented to highlight differences arising due to lip thickness variations.
Scale Resolving↗
Intrastep, Stage-Value Predictors for Diagonally-Implicit Runge-Kutta Methods
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Diagonally-Implicit Runge-Kutta↗
High‐Entropy Lithium Argyrodite Solid Electrolytes Enabling Stable All‐Solid‐State Batteries
Abstract Superionic solid electrolytes (SEs) are essential for bulk‐type solid‐state battery (SSB) applications. Multicomponent SEs are recently attracting attention for their favorable charge‐transport properties, however a thorough understanding of how configurational entropy (ΔS conf ) affects ionic conductivity is lacking. Here, we successfully synthesized a series of halogen‐rich lithium argyrodites with the general formula Li 5.5 PS 4.5 Cl x Br 1.5‐x (0≤x≤1.5). Using neutron powder diffraction and 31 P magic‐angle spinning nuclear magnetic resonance spectroscopy, the S 2− /Cl − /Br − occupancy on the anion sublattice was quantitatively analyzed. We show that disorder positively affects Li‐ion dynamics, leading to a room‐temperature ionic conductivity of 22.7 mS cm −1 (9.6 mS cm −1 in cold‐pressed state) for Li 5.5 PS 4.5 Cl 0.8 Br 0.7 (ΔS conf =1.98R). To the best of our knowledge, this is the first experimental evidence that configurational entropy of the anion sublattice correlates with ion mobility. Our results indicate the possibility of improving ionic conductivity in ceramic ion conductors by tailoring the degree of compositional complexity. Moreover, the Li 5.5 PS 4.5 Cl 0.8 Br 0.7 SE allowed for stable cycling of single‐crystal LiNi 0.9 Co 0.06 Mn 0.04 O 2 (s‐NCM90) composite cathodes in SSB cells, emphasizing that dual‐substituted lithium argyrodites hold great promise in enabling high‐performance electrochemical energy storage.
Chemistry↗
A New Approach for a Wider Class of Entropy Split Methods for Compressible Gas Dynamics and MHD
The high order entropy split methods of Sjögreen & Yee [1, 2] by entropy splitting of the compressible Euler (inviscid) flux derivatives for a thermally-perfect gas are based on Harten’s entropy function [3, 4, 5]. Their derivation takes advantage of the homogeneity property of Euler flux, symmetrizable Euler flux derivatives and energy-norm stability in conjunction with high order classical spatial central, DRP (dispersion relation-preserving) [6, 7, 8] or Padé (compact) spatial discretizations [9] with summation-by-parts (SBP) operators [10]. Our entropy split methods have been proven entropy conserving and stable [1, 11, 12]. Our proofs do not rely on a two-point numerical flux, but rather only a linear difference operator is required to derive these methods. To extend the entropy split method for the MHD, we used the Godunov symmetrizable non-conservative MHD form [12, 13, 14]. These high order entropy split methods not only preserve certain physical properties of the chosen governing equations but are also known to either improve numerical stability, and/or minimize aliasing errors in long time integration of turbulent flow computations without the aid of added numerical dissipation. In our previous published work, extensive error norm comparison with grid refinement was performed to show the high accuracy performance of these methods. These studies also showed how well the entropy split methods conserve the entropy, momentum and mass, and preserve the kinetic energy for long time integration of the various flows [1, 2, 12, 13, 14]. The objective of the present work is to use a new approach to obtain a wider class of entropy split methods consisting of a two-point numerical flux portion and a non-conservative portion in such a way that the homogeneity property of the compressible Euler flux is not required. For high order classical spatial central, DRP (dispersion relation-preserving) or Padé (compact) spatial discretizations, this new approach can be proven to be entropy conservative with conservative spatial dsicretizations while at the same time allowing a wider class of symmetrizable inviscid flux derivatives. We also use this generalization to derive an entropy split scheme that is entropy conserving for the equations of MHD without the homogeneity property using the Godunov symmetrizable ideal MHD formulation [15].
High Order Physical Preserving Methods↗
Extreme Temperature Cryptography Based On Nitrogen-Incorporated Ultrananocrystalline Diamond
Physical entropy sources that remain stable under extreme temperatures are essential for cryptography in emerging technological frontiers in deep space exploration, geothermal energy harvesting, and nuclear energy. However, conventional semiconductor platforms fail to generate stable and reliable cryptographic keys above 200 degrees C due to performance degradation. Here, we report a diamond-based cryptographic primitive that exploits the defect-rich sp 2 -bonded grain boundary network in nitrogen-incorporated ultrananocrystalline diamond (n-UNCD) film as a robust entropy source to generate cryptographic keys that remain operationally stable even after enduring extreme temperatures of 700 degrees C for 54 h while also surviving thermal cycling between room temperature and 700 degrees C for 48 h. The strength of the generated keys is assessed through several cryptographic metrics such as bit uniformity, entropy, hamming distances, and correlation coefficients, all of which are found to be near their respective ideal values. Moreover, the generated keys pass the NIST SP 800 and SP 800-90B tests and are also resilient to supply bias variations and a regression-based machine learning attack model based on the Fourier series. The robustness of the keys is attributed to the better thermal stability and chemical inertness of the n-UNCD film. This is supported by high-resolution energy-dispersive X-ray spectroscopy (EDS), which shows no significant lateral diffusion of metal atoms into the n-UNCD layer, and by Raman spectroscopy, which reveals no significant changes in the bonding configuration of the n-UNCD structure. Our findings highlight the remarkable potential of n-UNCD film for extreme environment cryptography by expanding the operational limits of conventional hardware security platforms.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Emergent Dimer-Model Topological Order and Quasiparticle Excitations in Liquid Crystals: Combinatorial Vortex Lattices
Liquid crystals have proven to provide a versatile experimental and theoretical platform for studying topological objects such as vortices, skyrmions, and hopfions. In parallel, in hard condensed matter physics, the concept of topological phases and topological order has been introduced in the context of spin liquids to investigate emergent phenomena like quantum Hall effects and high-temperature superconductivity. Here, we bridge these two seemingly disparate perspectives on topology in physics. Combining experiments and simulations, we show how topological defects in liquid crystals can be used as versatile building blocks to create complex, highly degenerate topological phases, which we refer to as “combinatorial vortex lattices” (CVLs). CVLs exhibit extensive residual entropy and support locally stable quasiparticle excitations in the form of charge-conserving topological monopoles, which can act as mobile information carriers and be linked via Dirac strings. CVLs can be rewritten and reconfigured on demand, endowed with various symmetries, and modified through laser-induced topological surgery—an essential capability for information storage and retrieval. We demonstrate experimentally the realization, stability, and precise optical manipulation of CVLs, thus opening new avenues for understanding and technologically exploiting higher-hierarchy topology in liquid crystals and other ordered media.
36 MATERIALS SCIENCE↗
Crystallographic Stability of Metastable Phase Formed by Containerless Processing in REFeO3 (RE: Rare-Earth Element)
Undercooling a melt often facilitates a metastable phase to nucleate preferentially. Although the classical nucleation theory shows that the most critical factor for forming a metastable phase is the interface free energy, the crystallographic stability is also indispensable for the phase to be frozen at ambient temperature. In compound materials such as oxides, authors have suggested that the decisive factors for forming a critical nucleus are not only the free energy difference but also the difference of the entropy of fusion between stable and metastable phases. In the present study, using REFeO3 (RE: rare-earth element) as a model material, we investigate the formation of a metastable phase from undercooled melts with respect to the competitive nucleation and crystallographical stabilities of both phases.
Kuribayashi, Kazuhiko↗
The Impact of Stable Layers on Downdrafts in Tropical Convection
While the idea that downdraft vertical velocity is influenced by thermodynamic stability may seem obvious, there remains a gap in the scientific literature surrounding the interaction between downdrafts and stable layers. A number of questions remain unanswered. Can a stable layer stop the downward progression of a downdraft or merely slow its velocity? Related to this, can a stable layer stop the injection of low entropy air into the boundary layer? Do downdrafts modify the environment in a way that removes pre-existing stable layers (limiting the influence of the stable layer)? Is it possible for evaporative cooling to generate and maintain a stable layer that is sufficiently strong to stop the downward progression of downdrafts?The present study aims to answer these questions using a combination of high-altitude airborne radar and dropsonde observations, both collected within four tropical cyclones (Gaston, Hermine, Karl, and Matthew) during the 2016 NOAA SHOUT field campaign, as well as idealized simulations of tropical deep convection. This presentation will focus on the potential for a stable layer to halt the downward progression of a downdraft (and the associated low entropy air) with particular attention given to conditions and processes that might enhance or mitigate the influence of the stable layer.
Helms, Charles N.↗