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DOE OSTI2020

An Assessment of the Drag Models in the Case of a Shock Interacting With a Fixed Bed of Point Particles

Abstract In this work, three-dimensional Euler–Lagrange (EL) point-particle simulations of a shock wave interacting with a fixed bed of particles are carried out. The results from the particle-resolved (PR) simulations are used to assess the performance of the point-particle drag models during short time scales. We demonstrate that in a one-way coupled regime, the point-particle simulations recover the dominant gas dynamic features of the flow and are in a good agreement with the exact Riemann solution of a shock traveling through a sudden area contraction. Although the PR simulations are inviscid, we show that a dissipative drag is necessary to predict the mean behavior of the gas. As a model for the inviscid shock-induced (SI) drag two different models are presented in lieu of the quasi-steady drag. Finally, two-way coupled simulations are performed at four different particle volume fractions {0.10, 0.15, 0.20, 0.25} and three different incident shock Mach numbers {1.22, 1.66, 3.0} and compared against the data from PR inviscid simulations. At a lower Mach number (1.22), averaged flow quantities from the two-way coupled simulations agree well with the PR simulations. As the Mach number increases, we observe that the discrepancies between the point-particle and the PR simulations grow. A sensitivity analysis of the drag models involved reveals a strong influence of the inviscid-unsteady force on the gas quantities especially in the case of a strong shock interacting with a dense bed of particles. The use of Mach correlation beyond the subcritical regime coupled with the model for volume fraction correction is identified as a probable cause for the additional drag.

Engineering↗

DOE OSTI2025

Microscopic changes governing melting anisotropy: Real-time nanosecond x-ray diffraction

To understand the microscopic origins governing melting anisotropy, in-situ x-ray diffraction (XRD) measurements were obtained in aluminum single crystals shocked along $\langle$100$\rangle$ and $\langle$110$\rangle$ to stresses below and above the melting threshold for each orientation. XRD results and analysis for the two orientations showed significant differences in the microstructure prior to the melting threshold stresses, demonstrating the key role of deformation induced microstructure – in addition to temperature and pressure – on the melting transition. As a result, our findings make a strong case for reconsidering theoretical approaches to melting, specifically for dislocation mediated melting, in shock compressed solids.

crystal melting↗

DOE OSTI2024

Laser Shock Modeling Archival Discussion

The purpose of this discussion is to provide archival information related to the Laser Shock finite element modeling effort. As discussed in Laser Shock System, Assessing bond strength in layered materials (see Section 8.0), the Laser Shock System creates a high-amplitude shockwave on the frontside of a structure (i.e. an aluminum 6061-T6 plate for this discussion) via a high-energy pulsed laser. The shock wave is monitored on the back surface of the structure as a velocity time history. It is a compressive wave as it comes to the back surface but reflects as a tensile wave. If a bond exists in the structure and the reflected tensile wave exceeds its interface threshold stress, then bond rupture occurs. The desire of the Laser Shock effort is to establish (with multiple tests) an ultimate bond strength which can be used for fuel plate design calculations. In this process, the finite element modeling effort is the catalyst to mimic the Laser Shock tests and provide the damage information at the bond that is useful for fuel plate design calculations.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

NASA NTRSDate not supplied

Progress on Transonic Flutter and Shock Buffet Computationsin Support of the Third Aeroelastic Prediction Workshop

This paper reports on the progress of the NASA Langley team contributions to the third Aeroelastic Pre-diction Workshop’s (AePW-3) High Angle Working Group (HAWG). The primary objectives of HAWG is to predict the fluter dynamic pressure of the NASA Benchmark Supercritical Wing (BSCW) configuration at Mach 0.8 and 5◦angle of attack. The secondary objective is to determine if a shock-buffet onset is present at or near that flow condition. The computational results are obtained using FUN3D, an unstructured grid Reynolds-averaged Navier-Stokes solver developed at the NASA Langley Research Center. The preliminary analysis results show a computationally-obtained flutter dynamic pressure of approximately 120 psf. Initial results describing unforced BSCW unsteady flow environment at flutter condition are also presented.

Pawel Chwalowski↗

NASA NTRS1974

The ratio of specific heats for postshock plasmas of a detached bow shock - An MHD model

The empirical relationship between the standoff distance of a detached bow shock (generated by the flow of a supersonic gas past an impenetrable obstacle), the size of the obstacle, the Mach number of the gas, and the ratio of specific heats has been generalized to include the magnetic field. The value of the ratio of specific heats (gamma-prime) in the postshock plasma has been calculated in terms of the preshock Alfvenic and sonic Mach numbers and orientation of the magnetic field. The empirical relationship is further generalized by taking into consideration the normal momentum and energy flux due to waves and/or turbulence and/or heat flow in association with high Mach number shocks. The computed value of gamma prime is substantially modified in comparison with that given by the MHD or the gas dynamic model. For this generalized model the computed gamma prime can be considered to be a more precise thermodynamic quantity, since the macroscopic parameters of the plasma have been separated out. Application of this empirical relationship to the earth's bow shock has been given.

Chao, J. K.↗

NASA NTRS1985

Nonlinear shock acceleration. III - Finite wave velocity, wave pressure, and entropy generation via wave damping

The nonlinear theory of shock acceleration developed in earlier papers, which treated the waves as being completely frozen into the fluid, is generalized to include wave dynamics. In the limit where damping keeps the wave amplitude small, it is found that a finite phase velocity (V sub ph) of the scattering waves through the background fluid, tempers the acceleration generated by high Mach number shocks. Asymptotic spectra proportional to 1/E sq are possible only when the ratio of wave velocity to shock velocity is less than 0.13. For a given asymptotic spectrum, the efficiency of relativistic particle production is found to be practically independent of the value of V sub ph, so that earlier results concerning its value remain valid for finite V sub ph. In the limit where there is no wave damping, it is shown that for modest Alfven Mach numbers, approximately greater than 4 and less than 6, the magnetic field is amplified by the energetic particles to the point of being in rough equipartition with them, as models of synchrotron emission frequently take the field to be. In this case, the disordering and amplification of field energy may play a major role in the shock transition.

Eichler, D.↗

NASA NTRS1994

Two-dimensional hydrodynamical simulations of wind-compressed disks around rapidly rotating B stars

We use a two-dimensional piecewise parabolic method (PPM) code to simulate numerically the hydrodynamics of a radiation-driven stellar wind from a rapidly rotating Be star. The results generally confirm predictions of the semianalytic 'wind-compressed disk' model recently proposed by Bjorkman and Cassinelli to explain the circumstellar disks inferred observationally to exist around such rapidly rotating stars. However, this numerical simulation is able to incorporate several important effects not accounted for in the simple model, including a dynamical treatment of the outward radiative driving and gas pressure, as well as a rotationally distorted, oblate stellar surface. This enables us to model quantitatively the compressed wind and shock that forms the equatorial disk. The simulation results thus do differ in several important details from the simple method, showing, for example, an inner disk inflow not possible in the heuristic approach of assuming a fixed outward velocity law. There is also no evidence for the predicted detachment of the disk that arises in the fixed outflow picture. The peak equatorward velocity in the dynamical models is furthermore about a factor of 2 smaller than the lytically predicted value of approximately 50% of the stellar equatorial rotation speed. As a result, the dynamical disks are somewhat weaker than predicted, with a wider opening angle, lower disk/pole density ratio, and smaller shock velocity jump. The principal cause of these latter differences appears to be an artificially strong equatorward drift of the subsonic outflow in the original analytic model. Much better agreement with the dynamical results can be obtained, however, from a slightly modified, analytic wind-compression model with a more detailed specification of the fixed wind outflow and a lower boundary set to the sonic radius along a rotationally oblate stellar surface. Hence, despite these detailed differences, the general predicted effect of disk formation by wind compression toward the equator is substantially confirmed.

Owocki, Stanley P.↗

DOE OSTI2020

Global Prompt Proton Sensor Network: Monitoring Solar Energetic Protons Based on GPS Satellite Constellation

Energetic particle instruments on board Global Positioning System (GPS) satellites form a powerful global prompt proton sensor network (GPPSn) that provides an unprecedented opportunity to monitor and characterize solar energetic protons targeting the Earth. The medium-Earth orbits of the GPS constellation have the unique advantage of allowing solar energetic protons to be simultaneously measured from multiple points in both open- and closed-field line regions. Examining two example intervals of solar proton events, we showcase in this study how GPS proton data are prepared, calibrated, and utilized to reveal important features of solar protons, including their source, acceleration/scattering by interplanetary shocks, the relative position of Earth when impinged by these shocks, the shape of solar particle fronts, the access of solar protons inside the dynamic geomagnetic field, and temporally varying proton distributions in both energy and space. By comparing to Van Allen Probes data, GPS proton observations are further demonstrated not only to be useful for qualitatively monitoring the dynamics of solar protons but also for quantitative scientific research including determining cutoff L-shells. Finally, our results establish that this GPPSn can join forces with other existing solar proton monitors and contribute to observing, warning, understanding, and ultimately forecasting the incoming solar energetic proton events.

47 OTHER INSTRUMENTATION↗

DOE OSTI2026

Revealing the Formation of the <20 MeV Inner Proton Radiation Belt at L ∼ 2 During the 10–11 May 2024 Superstorm

A new proton radiation belt was identified during the geomagnetic superstorm of 10–11 May 2024. To investigate its origin, we use an MHD-test particle simulation to model solar energetic proton (SEP) trapping and the evolution of the initial trapped proton population during the storm. The simulation weights the injected SEP population with interplanetary proton measurements and the initial trapped proton radial profile with energy-resolved Weather System Follow-on-Microwave (WSF-M) proton data, enabling quantitative comparison with observations. Results show that SEP contributions are minimal; the new ∼2–18 MeV belt at L ∼ 2 forms mainly through redistribution and energization of the initial trapped population within hours of the CME shock, driven by subsequent electric field impulses, rather than the initial shock alone. These results provide quantitative evidence based on realistic, plasma-dependent field dynamics and significantly advance understanding of inner radiation belt formation.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2026

Titanium alloy response sensitivity to variations in spectral reconstructions of National Ignition Facility xenon line-emission x-ray sources

Thermomechanical shock experiments on the National Ignition Facility (NIF) aim to study high strain rate dynamic material response. In such experiments, the NIF laser is used to generate high fluence x-ray emission sources, which irradiate material samples of interest. Under sufficiently high x-ray energy deposition, thermomechanical impulses are generated in the materials. While it is known that the characteristics of x-ray generated impulses vary as a function of incident x-ray spectra, it remains unclear how spectral assumptions and uncertainties in NIF spectral reconstructions affect our interpretation of impulsive loading. Here, in this paper, we simulate the response of a standard titanium alloy baseline sample to synthetic analytically derived and measured NIF xenon line-emission x-ray sources with a radiation hydrodynamics code. We vary the source spectral characteristics based on different source reconstruction techniques to understand the resulting variation in baseline sample response and compare the simulated response with experimental results. We find that the response is highly sensitive to assumptions made about the spectral contents and that knowledge of spectral uncertainties bounds our understanding of the resulting material response. The results of this effort help to extend our ability to use baseline material samples to extract quantitative properties from x-ray experiments on the NIF.

Alloys↗

DOE OSTI2021

Visualizations of direct fuel injection effects in a supersonic cavity flameholder

Not Available

MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Comparative analysis of internal energy excitation and dissociation of nitrogen predicted by independently developed ab initio potential energy surfaces

In this article we present a comparative atomic level study analyzing the vibrational excitation and dissociation of molecular nitrogen due to N 2 ⁢( 1 Σ g ⁢ + )+N⁢( 4 S u ) and N 2 ⁢( 1 Σ g ⁢ + )+N 2 ⁢( 1 Σ g ⁢+ ) interactions governed by independently developed potential energy surfaces at the University of Minnesota and NASA Ames Research Center. Further, vibrational excitation was studied for N 2 +N 2 interactions from T=10000 to 25000 K and for N 2 +N from T=5000 to 30000 K. Nonequilibrium dissociation is studied from T=10000 to 30000 K under the quasi-steady-state condition for N 2 +N 2 and N 2 +N interactions. Finally, an inviscid Mach 20 dissociating nitrogen flow over a cylinder with a Knudsen number of 0.015 is carried out to study the impact of molecular interactions predicted by independently developed potential energy surfaces on a canonical hypersonic flow.

74 ATOMIC AND MOLECULAR PHYSICS↗

NASA NTRS1971

Numerical solution of flowfields behind rectangular wings

The numerical solution of flow fields behind rectangular wings is described. Subjects discussed are: (1) evaluation of various differencing methods applied to the hyperbolic partial differential equations encountered in gas dynamics, (2) application of the numerical differencing techniques to the wedge flow, two dimensional shock reflection for the three dimensional finite thickness wing at zero degrees angle of attack, and (3) calculation of preliminary results for wedge flows using optimum differencing methods.

Anderson, D.↗

NASA NTRS1977

Buffet characteristics of the F-8 supercritical wing airplane

The buffet characteristics of the F-8 supercritical wing airplane were investigated. Wing structural response was used to determine the buffet characteristics of the wing and these characteristics are compared with wind tunnel model data and the wing flow characteristics at transonic speeds. The wingtip accelerometer was used to determine the buffet onset boundary and to measure the buffet intensity characteristics of the airplane. The effects of moderate trailing edge flap deflections on the buffet onset boundary are presented. The supercritical wing flow characteristics were determined from wind tunnel and flight static pressure measurements and from a dynamic pressure sensor mounted on the flight test airplane in the vicinity of the shock wave that formed on the upper surface of the wing at transonic speeds. The comparison of the airplane's structural response data to the supercritical flow characteristics includes the effects of a leading edge vortex generator.

Deangelis, V. M.↗

NASA NTRS1983

Implicit Total Variation Diminishing (TVD) schemes for steady-state calculations

The application of a new implicit unconditionally stable high resolution total variation diminishing (TVD) scheme to steady state calculations. It is a member of a one parameter family of explicit and implicit second order accurate schemes developed by Harten for the computation of weak solutions of hyperbolic conservation laws. This scheme is guaranteed not to generate spurious oscillations for a nonlinear scalar equation and a constant coefficient system. Numerical experiments show that this scheme not only has a rapid convergence rate, but also generates a highly resolved approximation to the steady state solution. A detailed implementation of the implicit scheme for the one and two dimensional compressible inviscid equations of gas dynamics is presented. Some numerical computations of one and two dimensional fluid flows containing shocks demonstrate the efficiency and accuracy of this new scheme.

Yee, H. C.↗

NASA NTRS1983

Implicit total variation diminishing (TVD) schemes for steady-state calculations

Yee, H. C.↗

NASA NTRS1984

Homogeneous condensation of gaseous mixtures of Si, Fe, O, N, and C in relative cosmic abundance and implications for astronomical condensation

The pressure versus temperature curves for homogeneous nucleation and condensation of two gaseous mixtures with nearly relative solar abundance of Si, Fe, O, N, and C in an excess of H were determined experimentally. Mixtures of CO, Fe(CO)5, H2, SiH4, and N2O in Ar were heated behind reflected shocks in a shock tube. The nucleation and condensation, which took place in the subsequent gas-dynamic expansion (cooling phase), was monitored by light scattering and turbidity. Grain morphologies and crystalline phases present in the condensates were determined by electron microscopy. These data cast doubt on the validity of both equilibrium and classical nucleation theoretical approaches to predict homogeneous condensation in a solar nebula or stellar atmosphere.

Stephens, J. R.↗

NASA NTRS1988

Analysis and Optimization of Truncated Scarf Nozzles Subject to External Flow Conditions

Results of a calculation of an optimized truncated scarfed nozzle were compared. The truncated scarfed nozzle was designed for an exit Mach number of 6.0, i.e., the Mach number at the last nozzle characteristic is 6.0, with an external flow Mach number of 5.0. The nozzle was designed by the Rao method for optimum thrust nozzles modified for 2-D flow and truncated scarfed nozzle applications. This design was analyzed using a shock-fitting method for 2-D supersonic flows. Excellent agreement was achieved between the design and analysis. Truncation of the lower nozzle wall (cowl) revealed that there is an optimum length for truncating the cowl without degrading the nozzle performance. Truncation of the nozzle cowl past this optimal length should be analyzed in trade-off studies for thrust loss versus gross vehicle weight. Plots of the oblique shock wave equations were also identified which will allow computation of slip line angle, dynamic pressure coefficient, or ambient Mach number for various specific heat ratios.

Shyne, Rickey J.↗