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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
DOE OSTI2023

Multi-injection investigation of a high-volatility diesel in advanced compression ignition combustion for NO x control

Traditional selective catalytic reduction aftertreatment technologies used to reduce [Formula: see text] are very limited at exhaust temperatures below [Formula: see text]. Therefore, under these low engine load conditions, having effective in-cylinder control of [Formula: see text] emissions is important. Previous work by the authors explored the effect of fuel physical properties on the ability to control [Formula: see text] in-cylinder. That work was limited to one direct injection near top dead center. Modern diesel high-pressure fuel systems have the capability of five or more injections in one engine cycle. A higher-volatility diesel fuel and high amounts of exhaust gas recirculation to delay ignition could provide an opportunity for reduction in engine-out [Formula: see text] through an increased level of fuel premixing. By appropriately timing multiple short injections, a more optimal distribution of fuel in-cylinder may be achieved, which could reduce [Formula: see text] while maintaining an efficient combustion phasing. A computational fluid dynamics model previously validated against experimental data was used to explore several injection strategies with increased levels of fuel premixing to assess the potential trade-offs between [Formula: see text] and CO/unburned hydrocarbon (UHC) emissions and thus reduce reliance on the aftertreatment system for [Formula: see text] control. The results show that the devised injection strategies resulted in an increased level of fuel premixing. However, none of the attempted injection strategies resulted in significant [Formula: see text] reductions, and all strategies showed a significant increase in CO and UHC emissions.

33 ADVANCED PROPULSION SYSTEMS↗
NASA NTRSDate not supplied

Parametric Analysis of the Charge-Hold-Vent Method for Cryogenic Propellant Tank Chill Down

In the absence of external heat exchangers, the on-orbit transfer of cryogenic propellants requires the receiver tank to first be quenched to a sufficiently low energy state to allow for a continuous no-vent fill to avoid unnecessary venting of liquid. One proposed method for tank chilldown that minimizes the potential for venting liquid is the charge hold vent (CHV) method. CHV follows a cyclic process that gradually removes thermal energy from the receiver tank by injecting liquid with the vent valve closed and allowing the fluid and wall to reach near-thermal equilibrium before venting the superheated vapor. However, the CHV method must be optimized to minimize complexity, mass, and time. This paper presents a modular CHV analytical model used to quantify the number of cycles and propellant mass consumed based on first principles. The model is used to examine the effect of eight parameters: receiver tank material, volume, mass, maximum expected operating pressure, and initial pressure, liquid injection pressure and temperature, and the target temperature. The model is validated against the only two available CHV datasets. Based on results, the tank mass-to-volume ratio is the most important factor in determining the number of CHV cycles and thus degree of difficulty in tank chilldown. The model can easily be used for early-stage design, sizing, and analysis of cryogenic propellant transfer systems.

Tank Chilldown↗
NASA NTRSDate not supplied

Parametric Analysis of the Charge-Hold-Vent Method for Cryogenic Propellant Tank Chill Down

Abstract. In the absence of external heat exchangers, the on-orbit transfer of cryogenic propellants requires the receiver tank to first be quenched to a sufficiently low energy state to allow for a continuous no-vent fill to avoid unnecessary venting of liquid. One proposed method for tank chilldown that minimizes the potential for venting liquid is the charge hold vent (CHV) method. CHV follows a cyclic process that gradually removes thermal energy from the receiver tank by injecting liquid with the vent valve closed and allowing the fluid and wall to reach near-thermal equilibrium before venting the superheated vapor. However, the CHV method must be optimized to minimize complexity, mass, and time. This paper presents a modular CHV analytical model used to quantify the number of cycles and propellant mass consumed based on first principles. The model is used to examine the effect of eight parameters: receiver tank material, volume, mass, maximum expected operating pressure, and initial pressure, liquid injection pressure and temperature, and the target temperature. The model is validated against the only two available CHV datasets. Based on results, the tank mass-to-volume ratio is the most important factor in determining the number of CHV cycles and thus degree of difficulty in tank chilldown. The model can easily be used for early-stage design, sizing, and analysis of cryogenic propellant transfer systems. Keywords: tank chilldown, charge-hold-vent, no-vent fill

Tank Chilldown↗
NASA NTRS2008

Influence of Reduced Mass Flow Rate and Chamber Backpressure on Swirl Injector Fluid Mechanics

Industry interest in variable-thrust liquid rocket engines places a demand on engine injector technology to operate over a wide range of liquid mass flow rates and chamber backpressures. One injection technology of current interest for variable thrust applications is an injector design with swirled fluids. Current swirl injector design methodologies do not take into account how swirl injector design parameters respond to elevated chamber backpressures at less than design mass flow rates. The current work was created to improve state-of-the-art swirl injector design methods in this area. The specific objective was to study the effects of elevated chamber backpressure and off-design mass flow rates on swirl injector fluid mechanics. Using a backpressure chamber with optical access, water was flowed through a swirl injector at various combinations of chamber backpressure and mass flow rates. The film thickness profile down the swirl injector nozzle section was measured through a transparent nozzle section of the injector. High speed video showed measurable increases in the film thickness profile with application of chamber backpressure and mass flow rates less than design. At prescribed combinations of chamber backpressure and injected mass flow rate, a discrete change in the film thickness profile was observed. Measured injector discharge coefficient values showed different trends with increasing chamber backpressure at low mass flow rates as opposed to near-design mass flow rates. Downstream spray angles showed classic changes in morphology as the mass flow rate was decreased below the design value. Increasing chamber backpressure decreased the spray angle at any injection mass flow rate. Experimental measurements and discussion of these results are reported in this paper.

Kenny, R Jeremy↗
NASA NTRS2008

Effect of Chamber Backpressure on Swirl Injector Fluid Mechanics

A common propellant combination used for high thrust generation is GH2/LOX. Historical GH2/LOX injection elements have been of the shear-coaxial type. Element type has a large heritage of research work to aid in element design. The swirl-coaxial element, despite its many performance benefits, has a relatively small amount of historical, LRE-oriented work to draw from. Design features of interest are grounded in the fluid mechanics of the liquid swirl process itself, are based on data from low-pressure, low mass flow rate experiments. There is a need to investigate how high ambient pressures and mass flow rates influence internal and external swirl features. The objective of this research is to determine influence of varying liquid mass flow rate and ambient chamber pressure on the intact-length fluid mechanics of a liquid swirl element.

Kenny, R. Jeremy↗
DOE OSTI2015

Reaction-space analysis of homogeneous charge compression ignition combustion with varying levels of fuel stratification under positive and negative valve overlap conditions

Full-cycle computational fluid dynamics simulations with gasoline chemical kinetics were performed to determine the impact of breathing and fuel injection strategies on thermal and compositional stratification, combustion and emissions during homogeneous charge compression ignition combustion. The simulations examined positive valve overlap and negative valve overlap strategies, along with fueling by port fuel injection and direct injection. The resulting charge mass distributions were analyzed prior to ignition using ignition delay as a reactivity metric. The reactivity stratification arising from differences in the distributions of fuel–oxygen equivalence ratio (Φ FO ), oxygen molar fraction (χ O2 ) and temperature (T) was determined for three parametric studies. In the first study, the reactivity stratification and burn duration for positive valve overlap valve events with port fuel injection and early direct injection were nearly identical and were dominated by wall-driven thermal stratification. nitrogen oxide (NO) and carbon monoxide (CO) emissions were negligible for both injection strategies. In the second study, which examined negative valve overlap valve events with direct injection and port fuel injection, reactivity stratification increased for direct injection as the Φ FO and T distributions associated with direct fuel injection into the hot residual gas were positively correlated; however, the latent heat absorbed from the hot residual gas by the evaporating direct injection fuel jet reduced the overall thermal and reactivity stratification. These stratification effects were offsetting, resulting in similar reactivity stratification and burn durations for the two injection strategies. The higher local burned gas temperatures with direct injection resulted in an order of magnitude increase in NO, while incomplete combustion of locally over-lean regions led to a sevenfold increase in CO emissions compared to port fuel injection. The final study evaluated positive valve overlap and negative valve overlap valve events with direct injection. Furthermore, relative to positive valve overlap, the negative valve overlap condition had a wider reactivity stratification, a longer burn duration and higher NO and CO emissions associated with reduced fuel–air mixing.

33 ADVANCED PROPULSION SYSTEMS↗
NASA NTRS1993

Particle injection and the structure of energetic-particle-modified shocks

A macroscopic 'self-consistent' nonlinear two-fluid model is developed for energetic-particle-modeled shocks. The model incorporates particle exchange between a thermal gas and an energetic population via a 'thermal leakage' mechanism. In the model, injection is regarded as a process whereby particles in the cooler thermal core of a total particle distribution are energized sufficiently to cross a 'momentum boundary' into the wings of the distribution. Particles in the wings are identified as 'energetic particles' or 'cosmic rays' and are assumed to propagate according to the diffusive transport equation of cosmic ray theory. Thermal particles are energized either as a result of adiabatic compression in a decelerating flow or directly via anomalous heating within a subshock. It is shown that the nature and model of particle injection directly affects the nature and dynamics of the shock, and hence the efficiency of particle acceleration, and that the shock itself regulates particle injection dynamically.

Zank, G. P.↗
DOE OSTI2020

Multi-physics modeling of injected nanoparticles effect on remediation of CO 2 leakage through cracks

One potential risk in CO 2 sequestration is the leakage of carbon dioxide, which can result in contamination of underground water, creating potential threats to existing ecosystems. The common leakage pathway is through the pre-existing fractures or discontinuities within cement in the wellbore, incurred by the environmental conditions imposed on the cement. Injecting nanoparticles into pre-existing cracks is one of the most recently proposed ideas for mitigating fracture propagation in cement CO 2 sequestration. To demonstrate the feasibility of this new technology, a numerical approach was taken in this work, as it is challenging to investigate it in a laboratory setting. We proposed a coupled ALE (Arbitrary Lagrangian–Eulerian)–DEM (Discrete Element Method)–peridynamic modeling strategy within the LS-Dyna package to investigate the intertwined interaction among the CO 2 fluid flow, native fluid (e.g., brine), particle clusters, and cracks within the cement. The numerical results demonstrate that injected nanoparticles can effectively reduce the pressure exerted on the crack surface. Accordingly, the potential fracture propagation at the crack tip would be reduced compared to corresponding cases without nanoparticels as pressurized by fluid flow. This result verifies the effectiveness of proposed nanoparticle injection technology. Finally, using this established modeling strategy, the effect of filling particles on the fracture mitigation for different crack geometries (e.g. particle cluster patterns, aspect ratio of crack aperture and length) and CO 2 reservoir pressure are examined. The result shows that injected particles successfully reduce the fracture propagation in these scenarios.

42 ENGINEERING↗
DOE OSTI2018

Geologic CO 2 sequestration monitoring design: A machine learning and uncertainty quantification based approach

Monitoring is a crucial aspect of geologic carbon dioxide (CO 2 ) sequestration risk management. Effective monitoring is critical to ensure CO 2 is safely and permanently stored throughout the life-cycle of a geologic CO 2 sequestration project. Effective monitoring involves deciding: (i) where is the optimal location to place the monitoring well(s), and (ii) what type of data (pressure, temperature, CO 2 saturation, etc.) should be measured taking into consideration the uncertainties at geologic sequestration sites. We have developed a filtering-based data assimilation procedure to design effective monitoring approaches. To reduce the computational cost of the filtering-based data assimilation process, a machine-learning algorithm: Multivariate Adaptive Regression Splines is used to derive computationally effcient reduced order models from results of full-physics numerical simulations of CO 2 injection in saline aquifer and subsequent multi-phase fluid flow. We use example scenarios of CO 2 leakage through legacy wellbore and demonstrate a monitoring strategy can be selected with the aim of reducing uncertainty in metrics related to CO 2 leakage. We demonstrate the proposed framework with two synthetic examples: a simple validation case and a more complicated case including multiple monitoring wells. The examples demonstrate that the proposed approach can be effective in developing monitoring approaches that take into consideration uncertainties.

58 GEOSCIENCES↗
DOE OSTI2012

Antimicrobial properties of analgesic kyotorphin peptides unraveled through atomic force microscopy

Highlights: Black-Right-Pointing-Pointer New kyotorphin derivatives have antimicrobial properties against S. aureus. Black-Right-Pointing-Pointer Atomic force microscopy show membrane disturbing effects of KTP-NH{sub 2} and IbKTP-NH{sub 2}. Black-Right-Pointing-Pointer None of the KTP derivatives are hemolytic. Black-Right-Pointing-Pointer The minimal peptidic sequence with antimicrobial activity is Tyr-Arg, if amidated. -- Abstract: Antimicrobial peptides (AMPs) are promising candidates as alternatives to conventional antibiotics for the treatment of resistant pathogens. In the last decades, new AMPs have been found from the cleavage of intact proteins with no antibacterial activity themselves. Bovine hemoglobin hydrolysis, for instance, results in AMPs and the minimal antimicrobial peptide sequence was defined as Tyr-Arg plus a positively charged amino acid residue. The Tyr-Arg dipeptide alone, known as kyotorphin (KTP), is an endogenous analgesic neuropeptide but has no antimicrobial activity itself. In previous studies new KTP derivatives combining C-terminal amidation and Ibuprofen (Ib) - KTP-NH{sub 2}, IbKTP, IbKTP-NH{sub 2} - were designed in order to improve KTP brain targeting. Those modifications succeeded in enhancing peptide-cell membrane affinity towards fluid anionic lipids and higher analgesic activity after systemic injection resulted therefrom. Here, we investigated if this affinity for anionic lipid membranes also translates into antimicrobial activity because bacteria have anionic membranes. Atomic force microscopy revealed that KTP derivatives perturbed Staphylococcus aureus membrane structure by inducing membrane blebbing, disruption and lysis. In addition, these peptides bind to red blood cells but are non-hemolytic. From the KTP derivatives tested, amidated KTP proves to be the most active antibacterial agent. The combination of analgesia and antibacterial activities with absence of toxicity is highly appealing from the clinical point of view and broadens the therapeutic potential and application of kyotorphin peptides.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2019

Numerical simulation of Water-alternating-gas Process for Optimizing EOR and Carbon Storage

Carbon dioxide (CO 2 ) generated by fossil fuel combustion can have serious consequences for humans and environments. Carbon capture, utilization and geological storage (CCUS) is a key approach to reduce the emissions of the anthropogenic CO 2 into the atmosphere. Of those, sequestering the CO 2 into depleted hydrocarbon reservoirs with associated enhanced oil recovery is the most achievable approach under current economic constraints since it increases recovery of existing oil reserves, and bridges the gap between nonprofit geological CO 2 sequestration and profit CO 2 -EOR. The Upper Devonian fluvial sandstone reservoir in Jacksonburg-Stringtown oil field in West Virginia, which has produced over 22 million barrels of oil since 1895, is an ideal candidate for CO 2 sequestration coupled with EOR. This research illustrates an example of CCUS, in which CO 2 is sequestered into underground meanwhile enhanced oil recovery from the depleted hydrocarbon reservoir by water alternating gas (WAG) strategy. Three CO 2 storage mechanisms including structural/stratigraphic trapping, dissolution trapping, and residual trapping are considered. A 3D geological model is constructed based on existing geological data from the Jacksonburg-Stringtown oil field. A 3D composition fluid model with 0.4 pore volume (PV) of water injection before WAG process is considered as a benchmark of this study. Several factors including WAG cycle period, injection time ratio, CO 2 injection rate are evaluated. After injection wells are completely shut-in, stored CO 2 is monitored for additional 200 years as a function of various storage mechanisms. The result shows that over 6 years of WAG injection, total 12 - 40 MMlb-mol CO 2 is sequestrated and oil recovery factor can achieve 28%. As a conclusion, this research constructs a basic workflow for CO 2 storage coupled with CO 2 -EOR which can be applied to other super-mature oil fields.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2021

A Critical Review of the Physicochemical Impacts of Water Chemistry on Shale in Hydraulic Fracturing Systems

Hydraulic fracturing of unconventional hydrocarbon resources involves the sequential injection of a high-pressure, particle-laden fluid with varying pH’s to make commercial production viable in low permeability rocks. This process both requires and produces extraordinary volumes of water. The water used for hydraulic fracturing is typically fresh, whereas “flowback” water is typically saline with a variety of additives which complicate safe disposal. As production operations continue to expand, there is an increasing interest in treating and reusing this high-salinity produced water for further fracturing. Here in this paper we review the relevant transport and geochemical properties of shales, and critically analyze the impact of water chemistry (including produced water) on these properties. We discuss five major geochemical mechanisms that are prominently involved in the temporal and spatial evolution of fractures during the stimulation and production phase: shale softening, mineral dissolution, mineral precipitation, fines migration, and wettability alteration. A higher salinity fluid creates both benefits and complications in controlling these mechanisms. For example, higher salinity fluid inhibits clay dispersion, but simultaneously requires more additives to achieve appropriate viscosity for proppant emplacement. In total this review highlights the nuances of enhanced hydrogeochemical shale stimulation in relation to the choice of fracturing fluid chemistry.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2011

Conceptual Model Summary Report Simulation Framework for Regional Geologic CO 2 Storage Along Arches Province of Midwestern United States

A conceptual model was developed for the Arches Province that integrates geologic and hydrologic information on the Eau Claire and Mt. Simon formations into a geocellular model. The conceptual model describes the geologic setting, stratigraphy, geologic structures, hydrologic features, and distribution of key hydraulic parameters. The conceptual model is focused on the Mt. Simon sandstone and Eau Claire formations. The geocellular model depicts the parameters and conditions in a numerical array that may be imported into the numerical simulations of carbon dioxide (CO 2 ) storage. Geophysical well logs, rock samples, drilling logs, geotechnical test results, and reservoir tests were evaluated for a 500,000 km2 study area centered on the Arches Province. The geologic and hydraulic data were integrated into a three-dimensional (3D) grid of porosity and permeability, which are key parameters regarding fluid flow and pressure buildup due to CO 2 injection. Permeability data were corrected in locations where reservoir tests have been performed in Mt. Simon injection wells. The final geocellular model covers an area of 600 km by 600 km centered on the Arches Province. The geocellular model includes a total of 24,500,000 cells representing estimated porosity and permeability distribution. CO 2 injection scenarios were developed for on-site and regional injection fields at rates of 70 to 140 million metric tons per year.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1995

Integrated Microreactor for Chemical and Biochemical Applications

A completely integrated microreactor was developed that allows for the processing of very small amounts of chemical solutions. The entire system comprises several pumps and valves arranged in different branches as well as a mixing unit and a reaction chamber. The streaming path of each branch contains two valves and one pump each. The pumps are driven by piezoelectric elements mounted on thin glass membranes. Each pump is about 3.5 mm x 3.5 mm x 0.7 mm. A pumping rate up to 25 microliters per hour can be achieved. The operational voltage ranges between 40 and 200 V. A volume stroke up to 1.5 millimeter is achievable from the membrane structures. The valves are designed as passive valves. Sealing is by thin metal films. The dimension of a valve unit is 0.8 x 0.8. 07 mm. The ends of the separate streaming branches are arranged to meet in one point. This point acts as the beginning of a mixer unit which contains several fork-shaped channels. The arrangement of these channels allows for the division of the whole liquid stream into partial streams and their reuniting. A homogeneous mixing of solutions and/or gases can be observed after having passed about 10 of the fork elements. A reaction chamber is arranged behind the mixing unit to support the chemical reaction of special fluids. This unit contains heating elements placed outside of the chamber. The complete system is arranged in a modular structure and is built up of silicon. It comprises three silicon wafers bonded together by applying the silicon direct bonding technology. The silicon structures are made only by wet chemical etching processes. The fluid connections to the outside are realized using standard injection needles glued into v-shaped structures on the silicon wafers. It is possible to integrate other components, like sensors or electronic circuits using silicon as the basic material.

Schwesinger, N.↗
NASA NTRS1998

Development of Tripropellant CFD Design Code

A tripropellant, such as GO2/H2/RP-1, CFD design code has been developed to predict the local mixing of multiple propellant streams as they are injected into a rocket motor. The code utilizes real fluid properties to account for the mixing and finite-rate combustion processes which occur near an injector faceplate, thus the analysis serves as a multi-phase homogeneous spray combustion model. Proper accounting of the combustion allows accurate gas-side temperature predictions which are essential for accurate wall heating analyses. The complex secondary flows which are predicted to occur near a faceplate cannot be quantitatively predicted by less accurate methodology. Test cases have been simulated to describe an axisymmetric tripropellant coaxial injector and a 3-dimensional RP-1/LO2 impinger injector system. The analysis has been shown to realistically describe such injector combustion flowfields. The code is also valuable to design meaningful future experiments by determining the critical location and type of measurements needed.

Farmer, Richard C.↗
NASA NTRS2003

Calculation of Supersonic Combustion Using Implicit Schemes

One of the technology goals of NASA for advanced space transportation is to develop highly efficient propulsion systems to reduce the cost of payload for space missions. Developments of rockets for the second generation Reusable Launch Vehicle (RLV) in the past several years have been focused on low-cost versions of conventional engines. However, recent changes in the Integrated Space Transportation Program to build a crew transportation vehicle to extend the life of the Space Shuttle fleet might suggest that air-breathing rockets could reemerge as a possible propulsion system for the third generation RLV to replace the Space Shuttle after 2015. The weight of the oxygen tank exceeds thirty percent of the total weight of the Space Shuttle at launch while the payload is only one percent of the total weight. The air-breathing rocket propulsion systems, which consume oxygen in the air, offer clear advantages by making vehicles lighter and more efficient. Experience in the National Aerospace Plane Program in the late 1980s indicates that scramjet engines can achieve high specific impulse for low hypersonic vehicle speeds. Whether taking a form of Rocket Based Combined Cycle (RBCC) or Turbine Based Combined Cycle (TBCC), the scramjet is an essential mode of operation for air-breathing rockets. It is well known that fuel-air mixing and rapid combustion are of crucial importance for the success of scramjet engines since the spreading rate of the supersonic mixing layer decreases as the Mach number increases. A factored form of the Gauss-Seidel relaxation method has been widely used in hypersonic flow research since its first application to non-equilibrium flows. However, difficulties in stability and convergence have been encountered when there is strong interaction between fluid motion and chemical reaction, such as multiple fuel injection problems. The present paper reports the results from investigation of the effect of modifications to the original algorithm on the performance for multiple injectors.

Yoon, Seokkwan↗
NASA NTRS1998

Non-NMDA receptor antagonist-induced drinking in rat

Glutamate has been implicated in the central control of mechanisms that maintain body fluid homeostasis. The present studies demonstrate that intracerebroventricular (i.c.v.) injections of the non-N-methyl-d-aspartate (NMDA) receptor antagonists 6, 7-dinitroquinoxaline-2,3-dione (DNQX) and 6-cyano-7-nitroquinoxaline-2,3 dione (CNQX) induce drinking in rats. The dipsogenic effect of i.c.v. DNQX was antagonized by the non-NMDA receptor agonist alpha-amino-3-hydroxy-5-methylisoxazole-4-propionic acid (AMPA). The water intake induced by DNQX was also blocked by pretreatment with a NMDA receptor antagonist, MK-801, but not by angiotensin type 1 (AT1) or acetylcholine muscarinic receptor antagonists (losartan and atropine). The results indicate that non-NMDA receptors may exert a tonic inhibitory effect within brain circuits that control dipsogenic activity and that functional integrity of NMDA receptors may be required for the non-NMDA receptor antagonists to induce water intake. Copyright 1998 Published by Elsevier Science B.V.

Non-NASA Center↗
DOE OSTI2015

SIMULATIONS AND THEORY OF ION INJECTION AT NON-RELATIVISTIC COLLISIONLESS SHOCKS

We use kinetic hybrid simulations (kinetic ions-fluid electrons) to characterize the fraction of ions that are accelerated to non-thermal energies at non-relativistic collisionless shocks. We investigate the properties of the shock discontinuity and show that shocks propagating almost along the background magnetic field (quasi-parallel shocks) reform quasi-periodically on ion cyclotron scales. Ions that impinge on the shock when the discontinuity is the steepest are specularly reflected. This is a necessary condition for being injected, but it is not sufficient. Also, by following the trajectories of reflected ions, we calculate the minimum energy needed for injection into diffusive shock acceleration, as a function of the shock inclination. We construct a minimal model that accounts for the ion reflection from quasi-periodic shock barrier, for the fraction of injected ions, and for the ion spectrum throughout the transition from thermal to non-thermal energies. This model captures the physics relevant for ion injection at non-relativistic astrophysical shocks with arbitrary strengths and magnetic inclinations, and represents a crucial ingredient for understanding the diffusive shock acceleration of cosmic rays.

79 ASTRONOMY AND ASTROPHYSICS↗