Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “curing kinetics”

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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Characterization of and sensor-model verification and control of the properties of PMR-13 during processing

This study presents an in situ sensor and a process-simulation model developed for monitoring and controlling the cure process of PMR-15. The time-temperature dependence of the buildup in the molecular network structure, extent of reaction, viscosity, flow, and consolidation during the cure of PMR-15 are discussed. The relationship of the time-temperature cycle used during imidization to the length of the endcapped chains formed is examined. The relationship of the time-temperature cure-processing cycle to the reaction kinetics, viscosity, flow, and consolidation during crosslinking is analyzed using frequency-dependent electromagnetic sensors and the Loos processing model. Application of the FDEMS sensing technique and the process-simulation model for quality assurance processing and automated on-line control of cure is discussed.

Kranbuehl, D.↗
DOE OSTI2026

Latent Catalysis as a Platform for Accessing Diverse Material Properties in Vat Photopolymerization 3D Printing

Vat photopolymerization (VP) 3D printing is an attractive strategy to manufacture customized polymer parts. The properties of printed materials are limited by the need to employ a low viscosity liquid resin and achieve rapid polymerization kinetics. To circumvent this limitation, dual‐cure methods have been developed using reagents embedded in the liquid resin formulation; however, the reagent‐based approach requires the discovery and optimization of new chemistry for each desired material. Here, in this work, we demonstrate a catalytic, dual‐cure platform that enables access to both Nylon‐6 and polyester interpenetrating networks through VP 3D printing under a universal approach. Structure–reactivity relationships of the latent NHC catalysts led to the identification of a magnesium chloride–NHC adduct as a latent catalyst that is orthogonal to radical polymerization and can be unmasked at elevated temperatures post‐printing to initiate ring‐opening polymerization of lactones and lactams. This strategy results in access to semicrystalline materials, which are a challenging morphology to access via VP 3D printing, that have attractive mechanical properties and can be printed at high resolution. This work represents the first photochemical‐based 3D printing of Nylon‐based materials and demonstrates the value of catalytic approaches to access new material properties in VP 3D printing.

Colliver, Cali N. [University of North Carolina, C↗
DOE OSTI2026

Effects of a Small Fraction of Norbornene Comonomers on the Frontal Ring Opening Metathesis Polymerization of Dicyclopentadiene and Dihydrofuran

Frontal ring-opening metathesis polymerization (FROMP) is an energy-efficient process for the construction of high performance polydicyclopentadiene (pDCPD) thermosets. A small fraction of norbornene (NBE) comonomer is often added to DCPD to liquify the resin, but their effects on the resin chemistry and frontal curing characteristics are not quantitatively understood, especially for recently developed deconstructable DCPD resins containing cleavable comonomers. 2,3-Dihydrofuran (DHF) is a commercially available, effective cleavable comonomer for ROMP of norbornenes, and it has been recently demonstrated to enable full deconstruction of pDCPD thermosets at 5% loading. Herein, we investigated deconstructable DCPD resins containing 5% of different (oxa)NBE derivatives and 5% DHF. We report the effects of such a small fraction of (oxa)NBE comonomers on the resin pot life (room temperature resin reactivity), front curing characteristics, degree of cure, crosslinking density, comonomer distribution, and deconstruction kinetics of the resulting pDCPD thermosets. These effects can be correlated to the metathesis reactivity of these comonomers. As a result, this study provides quantitative understanding that will guide the future development of new deconstructable FROMP resins with desired construction and deconstruction characteristics.

Luo, Xuyi [Stanford University, CA (United States)↗
DOE OSTI2024

Product-specific kinetics reveal effect of epoxy crystallization on thermoset thermal degradation

Crystallization is a common problem for epoxy resins, which are ubiquitous in industrial and commercial use. Integration of crystallized epoxy monomers into cured thermosets has been shown to alter the thermosets’ final mechanical properties. However, no studies have investigated the impact of these crystals on the thermal stability of the thermoset. Here we investigate the degradation kinetics of a bisphenol F–based epoxy thermoset with and without crystallized monomers using Product-Specific Kinetic (PSK) analysis coupled with Evolved Gas Analysis-Mass Spectrometry (EGA-MS). PSK analysis revealed significant differences in evolved product ion kinetics, suggesting changes in the degradation kinetics between thermoset configurations. Further, it was concluded that early stages of degradation are influenced most by crystal presence due to the high concentration of unreacted epoxy monomers and lower cross-linking density of the cured network. After post-cure annealing, significant changes are observed in the degradation kinetics of thermosets without crystal inclusions. Conversely, post-cure annealing procedures of crystal integrated thermosets showed little change in the thermoset degradation kinetics across all conversion extents. These findings suggest that post-cure annealing of thermosets with crystals present at the onset does not alter the cross-linking density of the polymer network enough to significantly change the degradation kinetics. We hypothesize this is because the excess monomers from the melted crystals are unable to find suitable reaction sites for complete binding into the polymer network, which has direct implications for the material properties and final thermal stability of the thermoset.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1987

A cure-rate model for the Shuttle filament-wound case

An epoxy and carbon fiber composite has been used to produce a light-weight rocket case for the Space Shuttle. A kinetic model is developed which can predict the extent of epoxy conversion during the winding and curing of the case. The model accounts for both chemical and physical kinetics. In the model, chemical kinetics occur exclusively up to the time the transition temperature equals the reaction temperature. At this point the resin begins to solidify and the rate of this process limits the rate of epoxy conversion. A comparison of predicted and actual epoxy conversion is presented for isothermal and temperature programmed cure schedules.

Cagliostro, D. E.↗
NASA NTRS1989

Process modeling for carbon-phenolic nozzle materials

A thermochemical model based on the SINDA heat transfer program is developed for carbon-phenolic nozzle material processes. The model can be used to optimize cure cycles and to predict material properties based on the types of materials and the process by which these materials are used to make nozzle components. Chemical kinetic constants for Fiberite MX4926 were determined so that optimization of cure cycles for the current Space Shuttle Solid Rocket Motor nozzle rings can be determined.

Letson, Mischell A.↗
NASA NTRS2004

Curing Composite Materials Using Lower-Energy Electron Beams

In an improved method of fabricating composite-material structures by laying up prepreg tapes (tapes of fiber reinforcement impregnated by uncured matrix materials) and then curing them, one cures the layups by use of beams of electrons having kinetic energies in the range of 200 to 300 keV. In contrast, in a prior method, one used electron beams characterized by kinetic energies up to 20 MeV. The improved method was first suggested by an Italian group in 1993, but had not been demonstrated until recently. With respect to both the prior method and the present improved method, the impetus for the use of electron- beam curing is a desire to avoid the high costs of autoclaves large enough to effect thermal curing of large composite-material structures. Unfortunately, in the prior method, the advantages of electron-beam curing are offset by the need for special walls and ceilings on curing chambers to shield personnel from x rays generated by impacts of energetic electrons. These shields must be thick [typically 2 to 3 ft (about 0.6 to 0.9 m) if made of concrete] and are therefore expensive. They also make it difficult to bring large structures into and out of the curing chambers. Currently, all major companies that fabricate composite-material spacecraft and aircraft structures form their layups by use of automated tape placement (ATP) machines. In the present improved method, an electron-beam gun is attached to an ATP head and used to irradiate the tape as it is pressed onto the workpiece. The electron kinetic energy between 200 and 300 keV is sufficient for penetration of the ply being laid plus one or two of the plies underneath it. Provided that the electron-beam gun is properly positioned, it is possible to administer the required electron dose and, at the same time, to protect personnel with less shielding than is needed in the prior method. Adequate shielding can be provided by concrete walls 6 ft (approximately equal to 1.8 m) high and 16 in. (approximately equal to 41 cm) thick, without a ceiling. The success of the present method depends on the use of a cationic epoxy as the matrix material in the prepreg tape, heating the prepreg tape to a temperature of 50 C immediately prior to layup, and exposing the workpiece to an electron-beam dose of approximately 2 Mrad. Experiments have shown that structures fabricated by the present method have the same mechanical properties as those of nominally identical structures fabricated by the prior method with electron beams of 3 to 4 MeV.

Byrne, Catherine A.↗
NASA NTRS1971

Molecular configuration and pyrolysis reactions of phenolic-novolaks.

Description of a statistical method for characterizing the structure of an average phenolic-novolak prepolymer molecule in terms of the total number of phenolic nuclei that compose the molecule and the number of these nuclei that are pendent. It is only necessary to resort to experimental pyrolysis to evaluate the thermokinetic parameters for pyrolysis for the ablator. In addition, the fraction of phenolic involved in the major pyrolysis reactions can be estimated in terms of the parameters previously evaluated. It is shown that the overlapping reactions which occur during pyrolysis of a phenolic-novolak can be resolved by pyrolyzing samples with different extents of cure. It is then possible to determine the kinetic parameters for pyrolysis for the major reactions by well-known methods which often fail when reactions are not well resolved.

Winkler, E. L.↗
NASA NTRS1993

Verification of a two-dimensional infiltration model for the resin transfer molding process

A two-dimensional finite element model for the infiltration of a dry textile preform by an injected resin was verified. The model, which is based on the finite element/control volume technique, determines the total infiltration time and the pressure increase at the mold inlet associated with the RTM process. Important input data for the model are the compaction and permeability behavior of the preform along with the kinetic and rheological behavior of the resin. The compaction behavior for several textile preforms was determined by experimental methods. A power law regression model was used to relate fiber volume fraction to the applied compaction pressure. Results showed a large increase in fiber volume fraction with the initial application of pressure. However, as the maximum fiber volume fraction was approached, the amount of compaction pressure required to decrease the porosity of the preform rapidly increased. Similarly, a power law regression model was used to relate permeability to the fiber volume fraction of the preform. Two methods were used to measure the permeability of the textile preform. The first, known as the steady state method, measures the permeability of a saturated preform under constant flow rate conditions. The second, denoted the advancing front method, determines the permeability of a dry preform to an infiltrating fluid. Water, corn oil, and an epoxy resin, Epon 815, were used to determine the effect of fluid type and viscosity on the steady state permeability behavior of the preform. Permeability values measured with the different fluids showed that fluid viscosity had no influence on the permeability behavior of 162 E-glass and TTI IM7/8HS preforms. Permeabilities measured from steady state and advancing front experiments for the warp direction of 162 E-glass fabric were similar. This behavior was noticed for tests conducted with corn oil and Epon 815. Comparable behavior was observed for the warp direction of the TTI IM7/8HS preform and corn oil. Mold filling and flow visualization experiments were performed to verify the analytical computer model. Frequency dependent electromagnetic sensors were used to monitor the resin flow front as a function of time. For the flow visualization tests, a video camera and high resolution tape recorder were used to record the experimental flow fronts. Comparisons between experimental and model predicted flow fronts agreed well for all tests. For the mold filling tests conducted at constant flow rate injection, the model was able to accurately predict the pressure increase at the mold inlet during the infiltration process. A kinetics model developed to predict the degree of cure as a function of time for the injected resin accurately calculated the increase in the degree of cure during the subsequent cure cycle.

Hammond, Vincent H.↗
DOE OSTI2024

Investigating the Crosslinking, Degradation, and Adhesion Behavior of Photovoltaic Encapsulants Under Thermal Accelerated Aging

Degradation of photovoltaic (PV) module encapsulant characteristics that lead to mechanical embrittlement and delamination remains a cause of failure in solar installations. A multiscale reliability model connecting the encapsulant mechanical and fracture properties to the degraded molecular structure and interfacial bonding to adjacent solar cell and glass substrates was previously published. The model, developed primarily for poly(ethylene-co-vinyl acetate) acetate (EVA) encapsulants, remains to be experimentally validated. Determining the degradation and crosslinking kinetics of alternative encapsulants, such as polyolefin elastomer (POE) and EVA/POE/EVA composites (EPE), can generalize the model. In this work, we subject fully cured EVA, POE, and EPE encapsulants to accelerated thermal aging to determine how high temperatures impact reaction kinetics. An increase in gel content (crosslinking) and decrease in crystallinity of the encapsulants under hot-aerobic (90 degrees C, 22% RH) and hot-anaerobic (90 degrees C, sealed in N 2 air) aging were observed, even in the absence of UV and crosslinking initiators. Fourier transform infrared spectroscopy (FTIR)-attenuated total reflectance analysis showed insignificant encapsulant degradation, demonstrating the critical role of UV and moisture in accelerating degradation. Adhesion testing performed on coupon-level specimens (cell/encapsulant/glass laminates) showed decreases in adhesion energy, Gc , from 5000 h of hot-dry (90 degrees C, ~1% RH) and hot-humid (90 degrees C, 60% RH) aging. POE coupons demonstrated the best stability, followed by EPE then EVA. For EVA and POE, hot-humid aged coupons experienced a larger decrease in Gc due to enhanced hydrolytic degradation. Hot-dry aging condition demonstrated that thermal degradation of the interface could be significant even if the encapsulant experiences negligible degradation in the absence of UV and elevated humidity.

accelerated aging↗
DOE OSTI2026

Suppressing proximity effects during rapid serial two-photon lithography through tuning of reaction–diffusion kinetics

The ability of two-photon lithography (TPL) to print deterministic nanoporous 3D structures is highly valuable for many applications. However, it is challenging to print such structures rapidly due to the proximity effects that cause closely spaced features to enlarge and merge. A key challenge is the limited understanding of the origins and spatiotemporal dynamics of the long-range proximity effects that extend beyond the optical focal spot. Here, we empirically investigate these proximity effects in serial TPL using custom-made acrylate-based photoresists. We demonstrate that the complex spatiotemporal dynamics of the proximity effects can be explained through the kinetics of the reaction–diffusion photopolymerization mechanisms that underlie the curing process. Specifically, we show that the proximity effects arise due to comparable timescales of reaction and diffusion of oxygen. Furthermore, we demonstrate that long-range proximity effects can be suppressed by introducing phenolic inhibitors, which reduce oxygen consumption through non-inhibiting side reactions and promote faster termination of curing reactions. These insights enabled improving the linewidths from >400 to 260 nm during printing of nanoporous 3D woodpiles at scanning speeds of 50 mm s −1 . Thus, the knowledge generated here can be applied to deterministically tune the proximity effects and enable rapid printing of high-resolution nanoporous 3D structures.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Solvent Impregnated Polymers Loaded with Liquid-Like Nanoparticle Organic Hybrid Materials for Enhanced Kinetics of Direct Air Capture and Point Source CO 2 Capture

Hybrid CO 2 capture materials, solvent impregnated polymers (SIPs), are developed based on a simple and scalable encapsulation technique to enhance CO 2 capture kinetics of water-lean solvents with high viscosity. Liquid-like nanoparticle organic hybrid materials functionalized with polyethylenimine (NOHM-I-PEI) are incorporated into a shell material and UV-cured to produce gas-permeable solid sorbents with uniform NOHMs loading (NPEI-SIPs). The CO 2 capture kinetics of NPEI-SIPs show a remarkable 50-fold increase compared to that of neat NOHM-I-PEI due to a large increase in the NOHMs-CO 2 interfacial surface area provided by the SIP design. The optimum NOHM-I-PEI loading and sorption temperature are found to be ≈49 wt% and 50 °C, respectively, and NPEI-SIPs exhibit great thermal stability over 20 CO 2 capture/sorbent regeneration temperature swing cycles. The pseudoequilibrium CO 2 loadings of NPEI-SIPs under humid conditions are as high as 3.1 mmol CO 2 g -1 NPEI - SIPs for 15 vol% CO 2 (postcombustion capture) and 1.7 mmol CO 2 g -1 NPEI - SIPs for 400 ppm (direct air capture). Overall, these findings suggest that NPEI-SIPs can effectively capture CO 2 from a wide range of CO 2 concentrations including direct air capture while allowing the flexible design of CO 2 capture reactors by combining the benefits of liquid solvents and solid sorbents.

36 MATERIALS SCIENCE↗
NASA NTRS1995

Verification of a three-dimensional resin transfer molding process simulation model

Experimental evidence was obtained to complete the verification of the parameters needed for input to a three-dimensional finite element model simulating the resin flow and cure through an orthotropic fabric preform. The material characterizations completed include resin kinetics and viscosity models, as well as preform permeability and compaction models. The steady-state and advancing front permeability measurement methods are compared. The results indicate that both methods yield similar permeabilities for a plain weave, bi-axial fiberglass fabric. Also, a method to determine principal directions and permeabilities is discussed and results are shown for a multi-axial warp knit preform. The flow of resin through a blade-stiffened preform was modeled and experiments were completed to verify the results. The predicted inlet pressure was approximately 65% of the measured value. A parametric study was performed to explain differences in measured and predicted flow front advancement and inlet pressures. Furthermore, PR-500 epoxy resin/IM7 8HS carbon fabric flat panels were fabricated by the Resin Transfer Molding process. Tests were completed utilizing both perimeter injection and center-port injection as resin inlet boundary conditions. The mold was instrumented with FDEMS sensors, pressure transducers, and thermocouples to monitor the process conditions. Results include a comparison of predicted and measured inlet pressures and flow front position. For the perimeter injection case, the measured inlet pressure and flow front results compared well to the predicted results. The results of the center-port injection case showed that the predicted inlet pressure was approximately 50% of the measured inlet pressure. Also, measured flow front position data did not agree well with the predicted results. Possible reasons for error include fiber deformation at the resin inlet and a lag in FDEMS sensor wet-out due to low mold pressures.

Fingerson, John C.↗
NASA NTRS1989

Chemoviscosity modeling for thermosetting resin systems, 4

An experimental study on the changes of chemorheological properties has been conducted and analyzed on commercial Hercules 3501-6 resin system cured under several isothermal conditions between 375 and 435 K. For the cure temperatures equal to or greater than 385 K, the storage modulus curing curves, G prime (t), exhibited abrupt changes in slope which occurred at various times depending on the curing temperatures and were attributed to the onset of gelation reactions. The crossover points between G prime (t) and G double prime (t) curves were observed for curing temperatures equal to or greater than 400 K. The gelation and the crossover points obtained from the chemorheological measurements, therefore, defined two characteristic resin states during cure. Approximately the same value for the degree of cure was reached by the advancement of the reaction at each of these states. The temperature dependency of the viscosities for the characteristic resin states and the rate constants of increase in moduli at different stages of curing were analyzed. Various G prime (t) and G double prime (t) isothermal curing curves were also shown to be capable of being superimposed on one another by the principle of time-temperature superposition. The resultant shift factors a sub t(t) and a Eta(T) were shown to follow the Arrhenius type relationship. Values of the activation energy suggested that the reaction kinetics, instead of the diffusion mechanism, was the limiting step in the overall resin advancement for the cure at temperatures equal to or greater than 385 K.

Hou, T. H.↗
DOE OSTI2021

Mechanisms of internal curing water release from retentive and non-retentive superabsorbent polymers in cement paste

This paper examines the mechanisms of desorption within cement pastes for superabsorbent polymers (SAP) with different sorption kinetics: retentive and non-retentive (self-releasing). Despite the different behavior in solution, both SAP types mitigated the autogenous shrinkage of cement pastes. {sup 1}H NMR and X-ray tomography showed that the cavities formed by both SAP types were saturated until 9–11 h after mixing, while the entrained water in the cavities redistributed to the cement matrix afterwards. In particular, the non-retentive SAP might have rapidly released the absorbed water, but the released water stayed in the original cavities. Therefore, the behavior of the SAP in the pore solution may not completely determine their internal curing performance in cement pastes. In particular, the initial absorption that forms the solution-filled cavities might be more important than whether the SAP are able to retain the solution for extended periods of time or not.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Controlled patterning of crystalline domains by frontal polymerization

Materials with hierarchical architectures that combine soft and hard material domains with coalesced interfaces possess superior properties compared with their homogeneous counterparts. These architectures in synthetic materials have been achieved through deterministic manufacturing strategies such as 3D printing, which require an a priori design and active intervention throughout the process to achieve architectures spanning multiple length scales. Here we harness frontal polymerization spin mode dynamics to autonomously fabricate patterned crystalline domains in poly(cyclooctadiene) with multiscale organization. This rapid, dissipative processing method leads to the formation of amorphous and semi-crystalline domains emerging from the internal interfaces generated between the solid polymer and the propagating cure front. The size, spacing and arrangement of the domains are controlled by the interplay between the reaction kinetics, thermochemistry and boundary conditions. Small perturbations in the fabrication conditions reproducibly lead to remarkable changes in the patterned microstructure and the resulting strength, elastic modulus and toughness of the polymer. Furthermore, this ability to control mechanical properties and performance solely through the initial conditions and the mode of front propagation represents a marked advancement in the design and manufacturing of advanced multiscale materials. Drawing inspiration from biological systems in which structural complexity develops through dissipative reaction–diffusion processes, this study explores a transformative synthetic manufacturing strategy aimed at harnessing the principles underpinning morphogenic growth, unlocking new avenues for advanced materials design and fabrication. Synthetic coupled reaction-transport processes offer a versatile yet relatively underexplored method to manipulate the spatial attributes of synthetic materials10. Here we introduce an innovative manufacturing approach based on frontal ring-opening metathesis polymerization (FROMP) that draws parallels with morphogenic growth and development, enabling the formation of patterned microstructures within polymeric materials.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Determining the Crosslinking and Degradation Reaction Kinetics in Photovoltaic Encapsulants Using Accelerated Aging: Preprint

Degradation of photovoltaic (PV) module encapsulant mechanical characteristics that lead to embrittlement and delamination remains a cause of failure in solar installations. A multiscale reliability model based on detailed molecular degradation reaction kinetics was previously published, connecting the encapsulant mechanical properties (elastic modulus, yield strength, and adhesion energy) to the degraded molecular structure and interfacial bond density to adjacent solar cell and glass substrates. The model, developed primarily for poly(ethylene-co-vinyl acetate) (EVA) encapsulants, remains to be experimentally validated. Determining the degradation and crosslinking kinetics of alternative encapsulants, such as polyolefin elastomer (POE) and EVA/POE/EVA composites (EPE), can further generalize the model. Importantly, the activation energy for crosslinking of fully cured PV encapsulant products from temperature or UV is presently unknown or unavailable. In this work, we subject EVA, POE, and EPE encapsulants to a set of accelerated aging conditions, varying the temperature, UV intensity, and relative humidity. We use DSC, FTIR, and Soxhlet extraction (gel content) to characterize the encapsulants' changing molecular structure. This allows for determination of the photochemical degradation and crosslinking kinetics of the encapsulants. Preliminary results show an increase in gel content (crosslinking) and a decrease in crystallinity of EVA, POE, and EPE encapsulants under hot-aerobic (90 deg C, 22% RH) and hot-anaerobic (90oC, sealed in N2 air) accelerated aging, even in the absence of UV and crosslinking initiating agents. For a least squares regression with an assumed first-order crosslinking kinetics, the crosslinking rate parameters were computed for the three encapsulants under hot-aerobic and hot-anaerobic aging conditions. FTIR analysis showed insignificant encapsulant degradation for hot-aerobic and hot-anaerobic aging, demonstrating the critical role of UV and moisture in accelerating degradation. Aging conditions with UV exposure and elevated humidity are presently in progress.

adhesion↗
DOE OSTI2021

A positivity-preserving and conservative intersection-distribution-based remapping algorithm for staggered ALE hydrodynamics on arbitrary meshes

In this study, we introduce new intersection-distribution-based remapping tools for indirect staggered arbitrary Lagrangian-Eulerian (ALE) simulations of multi-material shock hydrodynamics on arbitrary meshes. In addition to conserving momentum and total energy, the three-stage remapper proposed in this work preserves non-negativity of the internal energy. At the first stage, we construct slope-limited piecewise-linear reconstructions of all conserved quantities on zones of the source mesh and perform intersection-based remap to obtain bound-preserving zonal quantities on the target mesh. At the second stage, we define bound-preserving nodal quantities of the staggered ALE discretization as convex combinations of corner quantities. The nodal internal energy is corrected in a way which keeps it non-negative, while providing exact conservation of total energy. At the final stage, we distribute the non-negative nodal internal energy to corners, zones and materials using non-negative weights. Proofs of positivity preservation are provided for each stage. This work is a natural extension of our paper [14] in which a similar intersection-distribution-based remapping procedure was employed. The original version used a nodal kinetic energy fix which did not provably ensure positivity preservation for the zonal internal energy after the final distribution stage. The new algorithm cures this potential drawback by using ‘coordinated’ limiters for piecewise-linear reconstructions, remapping the internal energy to nodes and correcting it before redistribution. The effectiveness of the new nodal fix is illustrated by numerical examples.

97 MATHEMATICS AND COMPUTING↗