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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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Parallel Implicit Hydrodynamics with Material Strength for High Explosive Burn Calculations

High explosives are almost always evolving in some form of metal containment vessel. This fact requires that a materials model for the evolution of the metal containment vessel be part of any simulation of the HE. Since the actual form of the strength model to be used is an open question, we incorporate the material strength properties in a relatively agnostic fashion, which will accommodate many strength models. The only restriction is that the stress components be a function of density, specific internal energy and velocities. In addition, the timescales and rates of the chemical reactions in the HE vary between thousands of seconds and nanoseconds. A hydrodynamics capable of operating in anticipation of the eventual violent release of energy via these chemical reactions is a necessity. The central issue in creating a hydrodynamics capable of spanning these timescales is to forgo the use of a Courant time step control necessary in an explicit hydrodynamics. The Courant time-step arises because of characteristic velocities associated with the material, such as the sound speed or, in materials with strength, characteristic longitudinal and transverse speeds associated with compression and shear. The method used to circumvent the need for a Courant time-step limit is to develop an implicit calculation of the advanced particle pressure and shear modulus derived from the conservation laws of mass, momentum and specific internal energy. This process creates the implicit hydrodynamics needed for the HE calculations of interest to this study.

36 MATERIALS SCIENCE↗
DOE OSTI2019

PBX-9501 High Explosive Infrared Thermography Test Report

High explosive safety requirements put in place by the Department of Defense necessitate that Los Alamos National Laboratory verify that high melting explosive-based plastic bonded explosive 9501 will not present a health or safety risk to personnel when exposed to various accident scenarios. The JT5R-14C test is being developed to validate this requirement in a scenario where PBX-9501 is exposed to a hydrocarbon fuel fire. Preliminary testing is required to establish benchmark data on the burning characteristics of PBX-9501. The PBX-9501 High Explosive Infrared Thermography test was designed to provide the benchmark burning characteristics of PBX-9501 in a simulated fuel fire environment using propane burners as a fuel source. The PBX-9501-HEIT was successfully completed using a 20.32 cm tall cylindrical sample of PBX-9501 with a radius of 10.16 cm, a volume of 6,589.63 cm 3 , a density of 1.83 g/cm 3 , and a mass of 1.2 kg. The PBX-9501-HEIT test was captured and recorded video sequence using a Telops Inc., Multispectral Infrared camera. The infrared sequence was reviewed to identify key events throughout the test and serves as a visual tool to cross reference against future testing to aid in the identification of PBX-9501 high explosive ignition and deflagration characteristics. The data obtained in the thermographic sequence confirmed that the temperatures emitted by the PBX-9501 were higher than the temperatures of the propane burner ignition source. The propane burner flames had a temperature range of 700-850 °C. The cylindrical sample of PBX-9501 burned at an average temperature of 1000-1200 °C on the surface with off-gassing temperatures averaging 1100-1250 °C. The heat map of the PBX-9501 obtained through the test was between 250-550 °C higher than the propane gas temperatures. The temperature differential between the PBX-9501 and the propane flame allowed for the identification of key burning features.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
DOE OSTI2025

Additive manufacturing of high explosives with inert dilution for wave shaping and detonation velocity grading

The performance of a high explosive charge is highly influenced by the detonation velocity and any inherent internal structure. Additively manufactured (AM) high explosive charges allow for a precisely engineered internal structure and the selective placement of discrete or graded volumes of a tailored material, which are unachievable by conventional means. The dilution of a solid explosive by an inert additive for detonation velocity reduction is herein evaluated for a method of material extrusion called a direct-ink-write AM, where an 1,3,5,7-tetranitro-1,3,5,7-tetrazoctane-based ultraviolet -curable energetic-binder paste explosive was diluted by the inert density mock 5-iodo-2′-deoxyuridine for use in the manufacture of multi-material explosive charges. The explosive ink was characterized for printing by rheological and particle size measurements, and the detonation velocities for 0–40 wt. % inert diluent were found to have a continuous linear reduction in detonation velocity down to 14.3% difference. A two-component 3D plane wave explosive lens with 8.038 km/s “fast” and 7.491 km/s “slow” diluted ink in an internal cone demonstrated a reduced time of breakout at the output face from 361 to 53 ns. A linearly graded “fast–slow–fast” cylinder was successfully printed and fired, showing engineered control along the length of the charge as the detonation velocity dropped from 7.851 to 6.700 km/s and then recovered to 7.241 km/s. The extreme control over the internal composition of a high explosive charge via a dual-material extruder/mixer challenges conventional manufacturing approaches and opens new avenues for engineered detonation wavefronts, high explosive charge performance, and new applications.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Spatio-Temporal Surrogates for Interaction of a Jet with High Explosives: Part II - Clustering Extremely High-Dimensional Grid-Based Data

Building an accurate surrogate model for the spatio-temporal outputs of a computer simulation is a challenging task. A simple approach to improve the accuracy of the surrogate is to cluster the outputs based on similarity and build a separate surrogate model for each cluster. This clustering is relatively straightforward when the output at each time step is of moderate size. However, when the spatial domain is represented by a large number of grid points, numbering in the millions, the clustering of the data becomes more challenging. In this report, we consider output data from simulations of a jet interacting with high explosives. These data are available on spatial domains of different sizes, at grid points that vary in their spatial coordinates, and in a format that distributes the output across multiple files at each time step of the simulation. We first describe how we bring these data into a consistent format prior to clustering. Borrowing the idea of random projections from data mining, we reduce the dimension of our data by a factor of thousand, making it possible to use the iterative k-means method for clustering. We show how we can use the randomness of both the random projections, and the choice of initial centroids in k-means clustering, to determine the number of clusters in our data set. Our approach makes clustering of extremely high dimensional data tractable, generating meaningful cluster assignments for our problem, despite the approximation introduced in the random projections.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Explosion Detection Using Smartphones: Ensemble Learning with the Smartphone High-Explosive Audio Recordings Dataset and the ESC-50 Dataset

Explosion monitoring is performed by infrasound and seismoacoustic sensor networks that are distributed globally, regionally, and locally. However, these networks are unevenly and sparsely distributed, especially at the local scale, as maintaining and deploying networks is costly. With increasing interest in smaller-yield explosions, the need for more dense networks has increased. To address this issue, we propose using smartphone sensors for explosion detection as they are cost-effective and easy to deploy. Although there are studies using smartphone sensors for explosion detection, the field is still in its infancy and new technologies need to be developed. We applied a machine learning model for explosion detection using smartphone microphones. The data used were from the Smartphone High-explosive Audio Recordings Dataset (SHAReD), a collection of 326 waveforms from 70 high-explosive (HE) events recorded on smartphones, and the ESC-50 dataset, a benchmarking dataset commonly used for environmental sound classification. Two machine learning models were trained and combined into an ensemble model for explosion detection. The resulting ensemble model classified audio signals as either “explosion”, “ambient”, or “other” with true positive rates (recall) greater than 96% for all three categories.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2019

Eulerian Applications Project - xRage: High Explosives Package [Slides]

At the most elementary level, the high explosive model in xRage (or many other hydro codes) computes the amount of material that changes from a high explosive reactant to a high explosive product during a time step and accounts for the energy added to the flow by this reaction. The actual chemical reactions that occur during this conversion are not modeled. These processes are very complicated and involve levels of spatial and temporal resolution that are generally not practical for an application code. They would also require a state variable representation that includes all of the chemical species that are produced by the reaction and account for multiple stage chemical reactions. Instead the explosive models we generally use are phenomenological and try to represent the most important physics that drive the explosive wave in a very simplified way. These models generally have a number of tunable parameters that must be calibrated to experiment.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2026

Critical Review of Brazil Disk Techniques for Tensile Strength Characterization With an Emphasis on High Explosive Materials

Mechanical properties are a critical performance metric for many high explosive (HE) materials and tensile strength properties are particularly important. Direct tensile measurements using dogbone shaped samples are the gold standard but they have the disadvantage that they are fairly large and require samples machined from billets. Diametral compression, more commonly known as Brazil disk (BD) testing, is an indirect method for measuring tensile strength on smaller and more easily fabricated samples. A review of the BD literature is presented with an emphasis on tensile strength measurements in high explosive materials. BD literature is reviewed in three primary areas: (i) rocks and concrete, (ii) pharmaceutical materials, and (iii) high explosive materials. The literature for rocks/concrete is extensive and dates back over 80 years; despite this there is no consensus on the validity/accuracy of the BD technique or the optimal variant of the BD technique to employ. The pharmaceutical literature is the opposite, being limited in scope and quantity of studies. BD literature on high explosive materials falls in between, not as impressive as in the rocks/concrete community but more substantiative than in the pharmaceutical community. After the review of the literature practical parameters for HE BD testing and recommended future work is discussed.

Brazil disk↗
DOE OSTI2020

An Eulerian multimaterial framework for simulating high-explosive aquarium tests

Aquarium tests of cylindrical high-explosive charges provide optical data of the detonation front velocity and shape, propagation of the shock wave in the surrounding water, and expansion rates of the detonation products behind the front. Data from aquarium experiments is often used for calibration of reactive burn models based on phenomenological equations of state (EOS) and reaction rate laws. This paper presents a multimaterial numerical modeling framework to solve the 2D axisymmetric reactive Euler equations for high-explosive aquarium tests, in particular for ammonium nitrate - fuel oil (ANFO) explosives. An extension of the Ghost Fluid Method (GFM) is used to handle the dynamic material interfaces for the ANFO explosion products, the charge-confining material (polymethyl methacrylate PMMA), and the surrounding water. This study analyzes the sensitivity of calculations (both computational efficiency and numerical accuracy) to different algorithms for the material interface models including the original GFM versus Riemann solver-based strategies. A novel method for defining the left and right states in the interfacial Riemann problem eliminates the need for sorting or nodal interpolation during the projection along the material interface. Numerical tests indicate that populating the interface node values using the Riemann solution mitigate the overheating error observed in steady-state calculations. Solution convergence and computational efficiency are explored as a function of the spatial and temporal order of the schemes. Results from the computational model with analytical equations of state and fitted reaction rate parameters show very good quantitative agreement with experimentally observed detonation front velocity, reaction products expansion, and shock wave propagation in the surrounding water for a cylindrical ANFO charge encased in PMMA. Finally, the proposed modeling framework, in conjunction with experimental tests, provides a reliable tool to assess equations of state and reaction rate expressions for reactive burn models of confined high explosives.

42 ENGINEERING↗
DOE OSTI2016

High-order shock-fitted detonation propagation in high explosives

In this paper, a highly accurate numerical shock and material interface fitting scheme composed of fifth-order spatial and third- or fifth-order temporal discretizations is applied to the two-dimensional reactive Euler equations in both slab and axisymmetric geometries. High rates of convergence are not typically possible with shock-capturing methods as the Taylor series analysis breaks down in the vicinity of discontinuities. Furthermore, for typical high explosive (HE) simulations, the effects of material interfaces at the charge boundary can also cause significant computational errors. Fitting a computational boundary to both the shock front and material interface (i.e. streamline) alleviates the computational errors associated with captured shocks and thus opens up the possibility of high rates of convergence for multi-dimensional shock and detonation flows. Several verification tests, including a Sedov blast wave, a Zel'dovich–von Neumann–Döring (ZND) detonation wave, and Taylor–Maccoll supersonic flow over a cone, are utilized to demonstrate high rates of convergence to nontrivial shock and reaction flows. Comparisons to previously published shock-capturing multi-dimensional detonations in a polytropic fluid with a constant adiabatic exponent (PF-CAE) are made, demonstrating significantly lower computational error for the present shock and material interface fitting method. For an error on the order of 10 m / s , which is similar to that observed in experiments, shock-fitting offers a computational savings on the order of 1000. In addition, the behavior of the detonation phase speed is examined for several slab widths to evaluate the detonation performance of PBX 9501 while utilizing the Wescott–Stewart–Davis (WSD) model, which is commonly used in HE modeling. It is found that the thickness effect curve resulting from this equation of state and reaction model using published values is dramatically more steep than observed in recent experiments. Utilizing the present fitting strategy, in conjunction with a nonlinear optimizer, a new set of reaction rate parameters improves the correlation of the model to experimental results. In conclusion, this new model is tested against two dimensional slabs as a validation test.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2025

Updating Critical Temperature Calculations for Several Secondary High Explosives

In designing experiments where high explosives (HEs) are heated, it is important to have an understanding of where thermal runaway may occur. This determination is often done by using the Frank-Kamenetskii (FK) equation. For several highly-studied HEs, the parameters necessary for FK calculations are typically referenced from decades-old literature, and more recent experimental data have shown that these values require adjustment. For example, some of the legacy parameters dangerously overpredict the critical temperature by tens of degrees relative to more recent observed values. Herein, we first summarize historical results and highlight the importance of insulation effects when estimating critical temperatures for small samples, which is especially relevant to small-scale aging, compatibility, and characterization experiments. Here, we then present updated FK parameters for several common secondary CHNO HEs like RDX, HMX, PETN, and TATB, as well as the first reported values for 2,6-Diamino-3,5-dinitropyrazine-1-oxide (LLM-105). Our updated parameters produce critical-temperature curves that are consistent with both mm-scale differentical scanning calorimetry (DSC) measurements and cm-scale data from the Lawrence Livermore National Laboratory one-dimensional time-to-explosion (ODTX) experiment. In analyzing the critical temperature versus sample size curves derived from the transcendental FK equation, we discovered that these curves are remarkably well described by a simple power-law function with a universal power of 0.142 and a HE-specific scaling factor.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2022

Effect of lot microstructure variations on detonation performance of the triaminotrinitrobenzene (TATB)-Based insensitive high explosive PBX 9502

PBX 9502 is an important insensitive high explosive due to its combination of safety properties and detonation performance. It is a polymer-bonded formulation consisting of 95 wt.% 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) as the high explosive crystal, bound with Kel F-800 (FK-800), a co-polymer of chlorotrifluoroethylene and vinylidene-fluoride. Two different types are used, one known as virgin that uses only pristine manufactured TATB, and a second known as recycled that has 50 wt.% of its TATB reclaimed from machining scraps of previously pressed virgin PBX 9502. Recycled lots have a higher percentage of fine particles compared to virgin lots, due to the fracturing and damage sustained by TATB crystals during pressing. We examine the influence that this TATB microstructure difference between virgin and recycled PBX 9502 has on detonation performance properties. New rate-stick geometry diameter effect, detonation front shape and cylinder expansion test data are obtained for two previously uncharacterized virgin lots and one recycled lot of PBX 9502. This is combined with previously published data for one virgin and one recycled lot for evaluation purposes. Detonation shock dynamics model calibrations are conducted on each of the five lots to provide an assessment of the detonation timing characteristics of virgin versus recycled PBX 9502 lots. For two of the virgin lots, detonations propagate slower in the rate-stick geometry than those in the two recycled lots. However, the other virgin lot tested has propagation rates comparable to that of the recycled lots for larger diameter rate-sticks. The latter result, though, is shown to be geometry dependent and depends on the range of detonation curvatures accessed in different geometries. New copper-confined, cylinder expansion tests are conducted on each of the three virgin and two recycled lots to obtain detonation product Jones-Wilkins-Lee equations of state, enabling an assessment of the metal push capabilities for each of the five lots. We find that the metal push capabilities, characterized by the evolution of the heat of detonation with volume, are similar between the virgin and recycled lots. Thus, changes in microstructure between different PBX 9502 lots seemingly affect the rate of reaction, but not the overall energy content.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Structural Transformation and Chemical Stability of a Shock-Compressed Insensitive High Explosive Single Crystal: Time-Resolved Raman Spectroscopy

Despite the considerable interest in insensitive high explosives (IHE) as a safer alternative to conventional high explosives, a good understanding of the low sensitivity of IHEs to shock initiation is lacking. In particular, real-time measurements to directly probe the molecular-level response of shock compressed IHE single crystals constitute an important need. To address this need, plate impact experiments were conducted to determine time-resolved changes in the Raman spectra of 1,1-diamino-2,2-dinitroethene (FOX-7) single crystals – a representative IHE crystal – shock compressed up to 20 GPa longitudinal stress. The Raman measurements examined vibrational frequencies from 800 cm-1 to 1500 cm-1 with 15 nanosecond time resolution and were conducted at several peak stresses. At 4 – 6 GPa, two new Raman peaks appeared, in addition to the original peaks, consistent with onset of the α' – ε structural transformation reported previously in static compression work. The measured spectra indicated completion of the transformation at 10 GPa. Raman data to 20 GPa showed neither additional transformations nor any indication of chemical decomposition. This finding, though consistent with recent continuum measurements, is in marked contrast to the chemical decomposition observed at lower stresses in shock compressed conventional high explosive single crystals. Our Raman results support the previous suggestion that strengthening of intra- and inter-molecular bonds, due to the α' – ε structural transformation, plays a significant role in the insensitivity of FOX-7 single crystals to shock initiation. In conclusion, the present work, in conjunction with previous static compression studies, provides the first experimental insight into the molecular-level response of a shock compressed IHE single crystal and can serve as a bench mark for theoretical studies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Photoactive High Explosives: Substituents Effects on Tetrazine Photochemistry and Photophysics

High explosives that are photoactive, i.e., can be initiated with light, offer significant advantages in reduced potential for accidental electrical initiation. In this study, we examined a series of structurally related tetrazine based photoactive high explosive materials to detail their photochemical and photophysical properties. Using photobleaching infrared absorption, we determined quantum yields of photochemistry for nanosecond pulsed excitation at 355 and 532 nm. Changes in mass spectrometry during laser irradiation in vacuum measured the evolution of gaseous products. Fluorescence spectra, quantum yields, and lifetimes were measured to observe radiative channels of energy decay that compete with photochemistry. For the 6 materials studied, quantum yields of photochemistry ranged from <10 –5 to 0.03 and quantum yield of fluorescence ranged from <10 –3 to 0.33. In all cases, the photoexcitation nonradiatively relaxed primarily to heat, appropriate for supporting photothermal initiation processes. Lastly, the photochemistry observed was dominated by ring scission of the tetrazine, but there was evidence of more extensive multistep reactions as well.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Fine Tuning the CJ Detonation Speed of a High Explosive products Equation of State

For high explosive (HE) simulations, inaccuracies of a per cent or two in the detonation wave speed can result from not suficiently resolving the reaction zone width or from small inaccuracies in calibrating the products equation of state (EOS) or from variation of HE lots. More accurate detonation speeds can be obtained by ne tuning the equation of state to compensate. Here we show that two simple EOS transformations can be used to adjust the CJ detonation speed by a couple of per cent with minimal effect on the CJ release isentrope. The two transformations are (1) a shift in the energy origin and (2) a linear scaling of the speci c volume. The effectiveness of the transformations is demonstrated with simulations of the cylinder test for PBX 9502 starting with a products EOS for which the CJ detonation speed is 1 per cent too low.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2019

Measurements of the Dielectric Properties of Thin High-Explosive Samples Using a Parallel Plate Test Fixture

This report presents results of a study of the dielectric properties of several high explosive materials, including Composition B, C-4, Detasheet, Semtex 1A, Semtex 1H, and Semtex 10. The capacitance and dispersion of samples up to ten mm thick were measured at 24 and 65°C using a parallel plate test fixture. In this configuration, capacitance is proportional to the real component of the complex dielectric constant (or permittivity) of the material, while the dispersion is equal to the imaginary component of the dielectric constant divided by the real component. Measurements were performed at two temperatures to determine whether these dielectric properties might be used to monitor moderate temperature changes within these materials using an external fringing field capacitor. It was found that the real dielectric constant of the high explosives generally changed by only about 1% on heating from 24 to 65°C, and that the externally measured capacitance is therefore not a reliable parameter for monitoring temperature changes in these explosives. Temperature- based changes in the dispersion were often 20% or greater, and for several materials (e.g., Composition B, Detasheet) the temperature and dispersion showed good correlation as the temperature of the explosive was cycled up and down. It is thus possible that for some high explosives the externally measured dispersion is a useful parameter for monitoring temperature changes. However, other factors may limit the usefulness of this technique, including the need to have the plates of a fringing field capacitor in direct contact with the high explosive to obtain measurements, and the limited penetration depth of the fringing field into the explosive material.

36 MATERIALS SCIENCE↗
DOE OSTI2016

The escape of high explosive products: An exact-solution problem for verification of hydrodynamics codes

This paper documents the escape of high explosive (HE) products problem. The problem, first presented by Fickett & Rivard, tests the implementation and numerical behavior of a high explosive detonation and energy release model and its interaction with an associated compressible hydrodynamics simulation code. The problem simulates the detonation of a finite-length, one-dimensional piece of HE that is driven by a piston from one end and adjacent to a void at the other end. The HE equation of state is modeled as a polytropic ideal gas. The HE detonation is assumed to be instantaneous with an infinitesimal reaction zone. Via judicious selection of the material specific heat ratio, the problem has an exact solution with linear characteristics, enabling a straightforward calculation of the physical variables as a function of time and space. Lastly, implementation of the exact solution in the Python code ExactPack is discussed, as are verification cases for the exact solution code.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

The Trinity High Explosive Implosion System: The Foundation for Precision Explosive Applications

This article is set during the 1944 and 1945 final push to complete Project Y—the Manhattan Project at Los Alamos—and focuses primarily on overcoming the challenge of creating and demonstrating a successful convergent explosive implosion to turn a subcritical quantity of plutonium into a critical mass. The critical mass would then efficiently yield kilotons of trinitrotoluene (TNT)-equivalent energy in about a microsecond, demonstrating the implosion atomic bomb concept. This work culminated in the Trinity atomic test near Alamogordo on July 16, 1945. This implosion effect demarcated the approach to explosive science and technology the Laboratory has followed ever since, including development of high-explosive synthesis and formulation, small and large test and diagnostic facilities, shock dynamics theory, high-explosive system design engineering, and three-dimensional implosion modeling and simulation using some of the fastest computers in the world. This work also ushered in a period of broader application of precision high explosives in conventional munitions, demolition, mining and oil exploration, and space travel.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2017

Characterization of detonation soot produced during steady and overdriven conditions for three high explosive formulations

The detonation of high explosives (HE) produces a dense fluid of molecular gases and solid carbon. The solid detonation carbon contains various carbon allotropes such as detonation nanodiamonds, onion-like carbon, graphite and amorphous carbon, with the formation of the different forms dependent upon pressure, temperature and the environmental conditions of the detonation. We have collected solid carbon residues from controlled detonations of three HE formulations (Composition B-3, PBX 9501, and PBX 9502). Soot was collected from experiments designed to produce both steady and overdriven conditions, and from detonations in both an ambient (air) atmosphere and in an inert Ar atmosphere. Differences in solid carbon residues were quantified using X-ray photoelectron spectroscopy and carbon isotope measurements. Environmental conditions, HE formulation, and peak pressures influenced the amount of and isotopic composition of the carbon in the soot. Detonations in an Ar atmosphere produced greater amounts of carbon soot with lower δ 13 C values than those in ambient air. Therefore, solid carbon residues continued to evolve after detonation due to excess oxygen in the ambient air detonations. As well, higher peak pressures in overdriven conditions produced less carbon soot with, in general, higher δ 13 C values. Consequently, while overdriven conditions only produced peak pressures for a limited duration, it was enough to influence the composition of the solid carbon residues.

36 MATERIALS SCIENCE↗