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DOE OSTI2016

Ion-acoustic shocks with self-regulated ion reflection and acceleration

Here, an analytic solution describing an ion-acoustic collisionless shock, self-consistently with the evolution of shock-reflected ions, is obtained. The solution extends the classic soliton solution beyond a critical Mach number, where the soliton ceases to exist because of the upstream ion reflection. The reflection transforms the soliton into a shock with a trailing wave and a foot populated by the reflected ions. The solution relates parameters of the entire shock structure, such as the maximum and minimum of the potential in the trailing wave, the height of the foot, as well as the shock Mach number, to the number of reflected ions. This relation is resolvable for any given distribution of the upstream ions. In this paper, we have resolved it for a simple “box” distribution. Two separate models of electron interaction with the shock are considered. The first model corresponds to the standard Boltzmannian electron distribution in which case the critical shock Mach number only insignificantly increases from M ≈ 1:6 (no ion reflection) to M ≈ 1:8 (substantial reflection). The second model corresponds to adiabatically trapped electrons. They produce a stronger increase, from M ≈ 3:1 to M ≈ 4:5 . The shock foot that is supported by the reflected ions also accelerates them somewhat further. A self-similar foot expansion into the upstream medium is described analytically.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

Revisiting the Anisotropic Complex Refractive Indices of Sodium Nitrate for Interpretation of the Reflectance Spectrum of Pressed Pellets

Reflectance spectroscopy is notoriously confounding in that the measured spectral response is highly dependent upon the morphology of the sample. Fortunately, all such perturbations are neatly encoded by the complex refractive index of the sample. Herein, we seek to quantitatively model the measured infrared reflectance spectrum of a specularly flat pressed pellet sample of the birefringent compound, sodium nitrate. Single crystals of sodium nitrate were synthesized via a slow evaporation process and spectroscopically analyzed using polarization-dependent infrared single-angle reflectance spectroscopy. The anisotropic complex refractive index was measured from 7500 to 300 cm-1 (1.33 to 33.33 µm). The deduced anisotropic optical constants were found to be consistent with those previously reported. Once measured and validated, the optical constants were applied to model the pressed pellet reflectance spectrum. It was evident that an average of the anisotropic refractive indices was insufficient to account for the measured pellet reflectance. In order to account for contributions of all possible microcrystalline orientations within the pellet, the Python package PYELLI was used to calculate a basis set of orientation-dependent reflection spectra spanning the distinct ? and ? Euler rotations of the uniaxial crystal. When the population of orientations was allowed to vary freely in a spectral fit analysis, the fit-deduced orientations were tightly clustered along f = 45º, hinting at residual anisotropy in the pressed pellet sample. Conversely, an equally valid spectral fit (with marginally worse fit metric) was obtained when the population was constrained to an isotropic distribution of orientations. Subsequent non-zero cross-polarization reflectance measurements likewise suggested anisotropy in the pellet. However, both grazing incidence wide-angle x-ray scattering and scanning electron microscopy measurements revealed that the microcrystal orientations at the surface of the pressed pellet sample were isotropically distributed (and that the average crystallite size was larger than ?/10). Application of the measured complex refractive indices for modeling the reflectance spectrum of the pressed pellet, and rectification of these seemingly contradictory observations will be discussed.

Wilhelm, Michael J.↗

DOE OSTI2024

Retrofitting Buildings with Solar-Reflective Roofs and Walls and its Impact on Peak Power Demand

Buildings are a major consumer of electricity in the United States and a significant portion of the consumption comes from heating, ventilation, and air-conditioning (HVAC) applications. Passive cooling strategies in the building envelope help to reduce the energy consumption for HVAC as well as peak electricity demand. Although being one of the most cost-effective passive cooling strategies, modern reflective roofing and reflective exterior wall technology is not well documented for its impact on peak demand. This study utilized whole building energy simulations on residential and commercial building prototype models to quantify the impact of cool roofs and cool exterior walls. The analysis was performed in three climate zones with varying insulation levels and solar reflectances for roofs and exterior walls. For both the residential and commercial buildings, the baseline building had a roof solar reflectance value of 0.10 and an exterior wall solar reflectance value of 0.25. The results from the simulations show that roofs and exterior walls with higher reflectance values increase cooling energy savings but can also increase heating energy consumption. The impact of changes in solar reflectances was greater in buildings with low roof/wall insulation levels compared to roofs/walls with higher insulation levels. A baseline for the simulations was set with the roof and exterior wall solar reflectances set at 0.1 and 0.25, respectively and simulations having varying roof and exterior wall thermal resistances were compared to the baselines.

14 SOLAR ENERGY↗

DOE OSTI2022

Investigation of the impact of supplemental reflective films to improve micro-light climate within tomato plant canopy in solar greenhouses

The non-uniform growth and development of crops within Chinese Solar Greenhouses (CSG) is directly related to the micro-light climate within canopy. In practice, reflective films are used to improve micro-light climate within plant canopy by homogenizing light distribution and so increasing total plant light interception. However, as to our knowledge, the contributions to light distribution within canopy have not been investigated for passive reflector like reflective films. Field experiments dealing with light conditions and growth behavior over time, are complicated to carry out, time-consuming and hard to control, while however, accurate measurements of how reflective films influence the micro-light climate of canopy are an essential step to improve the growth conditions for any crop. Here, we propose a supplementary light strategy using reflective films to improve light distribution within plant canopy. Based on the example of CSG, a 3D greenhouse model including a detailed 3D tomato canopy structure was constructed to simulate the influence of supplementary reflective films to improve micro-light climate. Comparison of measured solar radiation intensity with predicted model data demonstrated that the model could precisely predict light radiation intensity over time with different time points and positions in the greenhouse. A series of reflective film configurations were investigated based on features analysis of light distribution in the tomato canopy on sunny days using the proposed model. The reflective film configuration scheme with the highest impact significantly improved the evenness of horizontal and vertical light distribution in tomato canopy. The strategy provided here can be used to configure reflective films that will enhance light conditions in CSG, which can be applied and extended in different scenarios.

Liu, Anhua↗

DOE OSTI2015

Nonlinear reflection of a spherically divergent N-wave from a plane surface: Optical interferometry measurements in air

Mach stem is a well-known structure typically observed in the process of strong (acoustic Mach numbers greater than 0.4) step-shock waves reflection from a rigid boundary. However, this phenomenon has been much less studied for weak shocks in nonlinear acoustic fields where Mach numbers are in the range from 0.001 to 0.01 and pressure waveforms have more complicated waveforms than step shocks. The goal of this work was to demonstrate experimentally how nonlinear reflection occurs in air for very weak spherically divergent acoustic spark-generated pulses resembling an N-wave. Measurements of reflection patterns were performed using a Mach-Zehnder interferometer. A thin laser beam with sub-millimeter cross-section was used to obtain the time resolution of 0.4 µs, which is 6 times higher than the time resolution of the condenser microphones. Pressure waveforms were reconstructed using the inverse Abel transform applied to the phase of the signal measured by the interferometer. The Mach stem formation was observed experimentally as a result of collision of the incident and reflected shock pulses. It was shown that irregular reflection of the pulse occurred in a dynamic way and the length of the Mach stem increased linearly while the pulse propagated along the surface. Since the front shock of the spark-generated pulse was steeper than the rear shock, irregular type of reflection was observed only for the front shock of the pulse while the rear shock reflection occurred in a regular regime.

42 ENGINEERING↗

DOE OSTI2024

Reconstructing the reflectivity of liquid surfaces from grazing incidence X-ray off-specular scattering data

The capillary wave model of a liquid surface predicts both the X-ray specular reflection and the diffuse scattering around it. A quantitative method is presented to obtain the X-ray reflectivity (XRR) from a liquid surface through the diffuse scattering data around the specular reflection measured using a grazing incidence X-ray off-specular scattering (GIXOS) geometry at a fixed horizontal offset angle with respect to the plane of incidence. With this approach the entire Q z -dependent reflectivity profile can be obtained at a single, fixed incident angle. This permits a much faster acquisition of the profile than with conventional reflectometry, where the incident angle must be scanned point by point to obtain a Q z -dependent profile. The XRR derived from the GIXOS-measured diffuse scattering, referred to in this paper as pseudo-reflectivity, provides a larger Q z range compared with the reflectivity measured by conventional reflectometry. Transforming the GIXOS-measured diffuse scattering profile to pseudo-XRR opens up the GIXOS method to widely available specular XRR analysis software tools. Here the GIXOS-derived pseudo-XRR is compared with the XRR measured by specular reflectometry from two simple vapor–liquid interfaces at different surface tension, and from a hexadecyltrimethylammonium bromide monolayer on a water surface. For the simple liquids, excellent agreement (beyond 11 orders of magnitude in signal) is found between the two methods, supporting the approach of using GIXOS-measured diffuse scattering to derive reflectivities. Pseudo-XRR obtained at different horizontal offset angles with respect to the plane of incidence yields indistinguishable results, and this supports the robustness of the GIXOS-XRR approach. The pseudo-XRR method can be extended to soft thin films on a liquid surface, and criteria are established for the applicability of the approach.

36 MATERIALS SCIENCE↗

DOE OSTI2017

Measurement of the infrared optical constants for spectral modeling: n and k values for (NH4)2SO4 via single-angle reflectance and ellipsometric methods

The optical constants n and k can be used to model infrared spectra, including refraction, absorption, reflectance, and emissivity, but obtaining reliable values for solid materials (pure or otherwise) presents a challenge: In the past, the best results for n and k have been obtained from bulk, homogeneous materials, free of defects. That is, materials where the Fresnel equations are operant since there is no light scattering. Since it is often not possible to obtain a pure macroscopic (crystalline) material, it may be possible to press the material into a (uniform, void-free) disk. We have recently been able to do this with ammonium sulfate powder and then measured the n & k values via two independent methods: 1) Ellipsometry - which measures the changes in amplitude and phase of light reflected from the material of interest as a function of wavelength and angle of incidence, and 2) Single angle specular reflectance with an FT spectrometer using a specular reflectance device within an FT instrument which measures the change in amplitude of light reflected from the material of interest as a function of wavelength and angle of incidence over a wide wavelength range. The quality of the derived n & k values was tested by generating the reflectance spectra of the pellet and comparing to the calculated to measured reflectance spectra of the pure material which has been previously published. The comparison to literature values showed good accuracy and good agreement, indicating promise to measure other materials by such methods.

ammonium sulfate↗

DOE OSTI2020

Measurements of angle-resolved reflectivity of PTFE in liquid xenon with IBEX

Abstract Liquid xenon particle detectors rely on excellent light collection efficiency for their performance. This depends on the high reflectivity of polytetrafluoroethylene (PTFE) at the xenon scintillation wavelength of 178 nm, but the angular dependence of this reflectivity is not well-understood. IBEX is designed to directly measure the angular distribution of xenon scintillation light reflected off PTFE in liquid xenon. These measurements are fully described by a microphysical reflectivity model with few free parameters. Dependence on PTFE type, surface finish, xenon pressure, and wavelength of incident light is explored. Total internal reflection is observed, which results in the dominance of specular over diffuse reflection and a reflectivity near 100% for high angles of incidence.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Anomalous dips in reflection spectra of optical polymers deposited on plasmonic metals

Abstract We have studied reflection spectra of dye-doped and undoped polymers deposited onto Ag and Au substrates and found anomalous dips in the UV spectral range. On top of Ag substrates, the λ ∼ 375 nm dips were observed in undoped PMMA, PVP, and PS polymers as well as PMMA doped with Rh590 and HITC laser dyes. In silver-based samples, the spectral positions of the observed reflection dips were close to singularities in the refractive indexes of surface plasmon polaritons (SPPs) propagating at the interface between Ag and polymer. The latter singularities can tentatively explain the λ ∼ 375 nm reflection dips, if the scattering of Ag and polymeric films is large enough to launch SPP without any prism or grating. The dips observed in reflection of Rh590:PMMA and HITC:PMMA on top of Au, were more pronounced than those on Ag, broader, shifted to shorter wavelengths, and their spectral positions had large standard deviations. Furthermore, no anomalous dips in gold-based samples were observed in the reflection spectra of undoped PMMA, PVP, and PS polymers, and a modest singularity in the SPP refractive index, predicted theoretically at λ ∼ 500 nm, cannot explain the dips in the UV reflection spectra observed experimentally. It appears likely that the origin of the reflection dips on top of Au substrates is different from that on top of Ag substrates.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Hyperspectral leaf reflectance of grasses varies with evolutionary lineage more than with site

Abstract To predict ecological responses at broad environmental scales, grass species are commonly grouped into two broad functional types based on photosynthetic pathway. However, closely related species may have distinctive anatomical and physiological attributes that influence ecological responses, beyond those related to photosynthetic pathway alone. Hyperspectral leaf reflectance can provide an integrated measure of covarying leaf traits that may result from phylogenetic trait conservatism and/or environmental conditions. Understanding whether spectra‐trait relationships are lineage specific or reflect environmental variation across sites is necessary for using hyperspectral reflectance to predict plant responses to environmental changes across spatial scales. We measured hyperspectral leaf reflectance (400–2400 nm) and 12 structural, biochemical, and physiological leaf traits from five grass‐dominated sites spanning the Great Plains of North America. We assessed if variation in leaf reflectance spectra among grass species is explained more by evolutionary lineage (as captured by tribes or subfamilies), photosynthetic pathway (C 3 or C 4 ), or site differences. We then determined whether leaf spectra can be used to predict leaf traits within and across lineages. Our results using redundancy analysis ordination (RDA) show that grass tribe identity explained more variation in leaf spectra (adjusted R 2 = 0.12) than photosynthetic pathway, which explained little variation in leaf spectra (adjusted R 2 = 0.00). Furthermore, leaf reflectance from the same tribe across multiple sites was more similar than leaf reflectance from the same site across tribes (adjusted R 2 = 0.12 and 0.08, respectively). Across all sites and species, trait predictions based on spectra ranged considerably in predictive accuracies ( R 2 = 0.65 to <0.01), but R 2 was >0.80 for certain lineages and sites. The relationship between Vc max , a measure of photosynthetic capacity, and spectra was particularly promising. Chloridoideae, a lineage more common at drier sites, appears to have distinct spectra‐trait relationships compared with other lineages. Overall, our results show that evolutionary relatedness explains more variation in grass leaf spectra than photosynthetic pathway or site, but consideration of lineage‐ and site‐specific trait relationships is needed to interpret spectral variation across large environmental gradients.

Pau, Stephanie [Department of Geography University↗

DOE OSTI2018

A dual-layer structure with record-high solar reflectance for daytime radiative cooling

We demonstrate a diffusive solar reflector with record high reflectance when integrated over the wavelength region from 0.28-4.0 μm. The reflector has a dual-layer structure consisting of a polytetrafluoroethylene (PTFE) sheet on top of a silver film. The thickness of the PTFE varies from 0.25 mm to 1 mm. Spectral reflectance and transmittance of the PTFE sheets (with and without a silver film) were measured using a monochromator and a Fourier-transform infrared spectrometer, with integrating spheres, at wavelengths from 0.28 μm to 15 μm. The scattering and absorption coefficients of the PTFE samples were obtained by fitting the reflectance and transmittance spectra. Integration over the solar irradiation spectrum (AM1.5) reveals that the total solar reflectance is approximately 0.99 for the reflector. This is the highest solar reflectance reported to date. A Monte Carlo ray-tracing method and a modified two-flux model were used to calculate the reflectance and compare with the experiments to shed light on mechanisms for the high reflectance. Our measurements also suggest that PTFE has a high emittance around 0.9 in the mid-infrared region. Therefore, we conclude the proposed structure holds promise for passive daytime radiative cooling.

14 SOLAR ENERGY↗

DOE OSTI2020

Reflectivity and PDE of VUV4 Hamamatsu SiPMs in liquid xenon

Considering reflective properties of materials and photodetection efficiency (PDE) of photodetectors is important for optimizing energy resolution and sensitivity of the next generation neutrinoless double beta decay, direct detection dark matter, and neutrino oscillation experiments that will use noble liquid gases, such as nEXO, DARWIN, DarkSide-20k, and DUNE . Little information is currently available about reflectivity and PDE in liquid noble gases, because such measurements are difficult to conduct in a cryogenic environment and at short enough wavelengths. Here we report a measurement of specular reflectivity and relative PDE of Hamamatsu VUV4 silicon photomultipliers (SiPMs) with 50 μ m micro-cells conducted with xenon scintillation light ( ~ 175 nm) in liquid xenon. The specular reflectivity at 15 o incidence of three samples of VUV4 SiPMs is found to be 30.4 ± 1.4%, 28.6 ± 1.3%, and 28.0 ± 1.3%, respectively. The PDE at normal incidence differs by ± 8% (standard deviation) among the three devices. The angular dependence of the reflectivity and PDE was further measured for one of the SiPMs. Both the reflectivity and PDE decrease as the angle of incidence increases. This is the first measurement of an angular dependence of PDE and reflectivity of a SiPM in liquid xenon.

47 OTHER INSTRUMENTATION↗

DOE OSTI2024

Validation of the VUV-reflective coating for next-generation liquid xenon detectors

Abstract Coating detector materials with films highly reflective in the vacuum ultraviolet region improves sensitivity of the next-generation rare-event detectors that use liquid xenon. In this work, we investigate the MgF 2 -Al-MgF 2 coating designed to achieve high reflectance at 175 nm, the mean wavelength of liquid xenon (LXe) scintillation. The coating was applied to an unpolished, passivated copper substrate mimicking a realistic detector component of the proposed nEXO experiment, as well as to two unpassivated substrates with “high” and “average” levels of polishing. After confirming the composition and morphology of the thin-film coating using TEM and EDS, the samples underwent reflectance measurements in LXe and gaseous nitrogen (GN2). Measurements in LXe exposed the coated samples to -100°C for several hours. No peeling of the coatings was observed after several thermal cycles. Polishing is found to strongly correlate with the measured specular reflectance (R spec ). In particular, 5.8(5)% specular spike reflectance in LXe was measured for the realistic sample at 20° of incidence, while the values for similar angles of incidence on the high and average polish samples are 62.3(1.3)% and 27.4(7)%, respectively. At large angles (66°–75°), theR spec in LXe for the three samples increases to 23(5)%, 80(8)%, and 84(18)%, respectively. The R spec at around 45° was measured in both GN2 and LXe for average polish sample and shows a reasonable agreement. Importantly, the total reflectance of the samples is comparable and estimated to be 92(8)%, 85(8)%, and 83(8)% in GN2 for the realistic, average, and high polish samples, respectively. This is considered satisfactory for the next-generation LXe experiments that could benefit from using reflective films, such as nEXO and DARWIN, thus validating the design of the coating.

Instruments & Instrumentation↗

DOE OSTI2022

Quasielastic least-squares reverse time migration of PS reflections

Conventional analysis of amplitude variation with offset for elastic PS reflections is based on analytical reflection coefficients in a layered medium, and wave-equation-based PS migration is mainly used to produce a structural image. To overcome this problem, we have developed a least-squares reverse time migration (LSRTM) method for elastic PS reflections based on a quasielastic wave equation. Here, the quasielastic wave equation can accurately model PS reflections with elastic amplitudes under the first-order Born approximation. Our LSRTM method inverts for perturbations of the S-wave velocity and density by minimizing the L 2 norm of the difference between recorded and predicted PS reflections modeled using a quasielastic wave equation. We refer to our new method as quasielastic LSRTM of PS reflections. Numerical tests on synthetic and field data indicate that our method can properly handle the amplitudes of elastic PS reflections and provides an accurate estimate of the perturbations of S-wave velocity and density. Extending the method to the 3D case is not straightforward and might require incorporating certain PS data processing techniques into the inversion itself.

58 GEOSCIENCES↗

DOE OSTI2024

Thermally reflective membrane apparatuses, and related fluid treatment systems and methods

A thermally reflective membrane apparatus comprises a housing structure, and a thermally reflective membrane contained within the housing structure. The thermally reflective membrane comprises a semipermeable structure, and a porous, thermally reflective structure physically contacting the semipermeable structure. The porous, thermally reflective structure comprises discrete thermally reflective particles, and a binder material coupling the discrete thermally reflective particles to one another and the semipermeable structure. A fluid treatment system and method of treating a fluid are also described.

Klaehn, John R.↗

DOE OSTI2020

Infrared Optical Constants from Pressed Pellets of Powders: I. Improved n and k Values of (NH4)(2)SO(4)from Single-Angle Reflectance

In combination with other parameters, the real, n(?), and imaginary, k(?), components of the complex refractive index, = n + ik, can be used to simulate the optical properties of a material in different forms, e.g. its infrared spectra. But obtaining reliable values of the optical constants n/k for solid materials is challenging due to the lack of optical quality specimens, usually crystals, large enough to measure. An alternative to crystals is to press the powder into a uniform disk. We have produced pellets from ammonium sulfate, (NH4)2SO4, powder and derived the pellets’ n and k values via single-angle reflectance using a specular reflectance device in combination with a Fourier transform infrared spectrometer. The single-angle technique measures amplitude of light reflected from the material as a function of wavelength over a wide spectral domain; the optical constants are determined from the reflectance data using the Kramers-Kronig relationship. We investigate several parameters associated with the pellets and pellet formation and their effects upon delivering the most reliable n/k values. Parameters studied include pellet diameter, mass and density (void space), drying, grinding, sieving and particle size in the pellet formation, as well as pressing pressure and duration. Of these parameters, using size-selected mixtures of dried, small (< 100 µm) particles and pressing at = 10 tons for at least 30 minutes were found key to forming highly reflective samples. Comparison to two sets of previous literature n(?) and k(?) values obtained from crystalline (NH4)2SO4 both as crystal reflectance as well as extinction spectra of aerosols measured in a flow tube show reasonable agreement, but suggests the present values, as confirmed from two independent techniques, represent a substantial improvement for n/k values for (NH4)2SO4, also demonstrating promise to measure the optical constants of other materials.

Optical constants, index of refraction, single-ang↗

DOE OSTI2022

Temperature-dependent diffuse reflectance measurements of ceramic powders in the near- and mid-infrared spectra

Radiative properties are critical to quantify radiative energy fluxes between surfaces and in participating media. However, there is limited experimental data on temperature-dependent radiative properties of materials. Herein, this work focuses on experimentally measuring temperature-dependent diffuse reflectance in the near- and mid-infrared spectra (1–20 μm) for ceramic particles with applications as heat-transfer and thermal-storage media in concentrated solar power (CSP) plants. Specifically, a commercially available sintered bauxite proppant, ACCUCAST ID80, and its primary chemical constituents—alumina (Al 2 O 3 ) and silica (SiO 2 )—are measured in powder form using a Fourier transform infrared spectrometer (FTIR) coupled with a specialized diffuse reflectance accessory and a heated stage. Room-temperature diffuse reflectance measurements show increased absorption in tests with greater mass fractions of the ceramic samples. There is a strong correlation in the measured reflectance spectra of ACCUCAST with alumina and silica in the spectral range 2000–500 cm –1 (5–20 μm). Whereas, for shorter wavelengths (< 5 μm), the absorptance for ACCUCAST is greater than the absorptance for alumina and silica, indicating contributions from other chemical species present in the composite material. For the first time, temperature-dependent diffuse reflectance measurements are reported for ACCUCAST up to 1000 °C. These results are compared against those of alumina and silica through the calculation of a thermal emittance. All three materials exhibit a calculated emittance of ~0.9 at room temperature. However, this value decreases to ~0.6 for ACCUCAST and drops to less than 0.4 for alumina and silica at 1000 °C. Thermal cycling in air at 1000 °C resulted in a visible color change from dark grey to light orange for ACCUCAST and a subsequent larger increase in reflectance for wavelengths less than 5 μm as compared to ACCUCAST thermally cycled at 1000 °C in vacuum. Alumina and silica spectra proved to be largely unaffected by thermal cycling under atmospheric conditions. Overall, this study establishes a powerful technique for the characterization of radiative properties of particulate materials as a function of temperature and presents a detailed case study of ACCUCAST, a candidate for next-generation particle-based CSP.

14 SOLAR ENERGY↗

DOE OSTI2016

Theory of Mach reflection of detonation at glancing incidence

In this paper, we present a theory for Mach reflection of a detonation undergoing glancing incidence reflection off of a rigid wall. Our focus is on condensed-phase explosives, which we describe with a constant adiabatic gamma equation of state and an irreversible and either state-independent or weakly state-dependent reaction rate. We consider two detonation models: (1) the instantaneous reaction heat-release Chapman–Jouguet (CJ) limit and (2) the spatially resolved reaction heat-release Zeldovich–von Neumann–D$\ddot{Ø}$ring (ZND) limit, where here we only consider that a small fraction of the detonation energy release is spatially resolved (the SRHR limit). We observe a three-shock reflection in the CJ limit case, with a Mach shock that is curved. In addition, we develop an analytical expression for the triple-point track angle as a function of the angle of incidence. For the SRHR model, we observe a smooth lead shock, akin to von Neumann reflection, with no reflected shock in the reaction zone. Only at larger angles of incidence is a three-shock Mach reflection observed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗