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All sourcesNASA NTRSDOE OSTI
NASA NTRS1983

A survey of grid generation techniques in computational fluid dynamics

The use of numerically-generated body-conforming coordinate systems has become well-established in computational fluid dynamics, allowing general codes to be written which can treat boundaries of arbitrary shape. There is now a rapidly increasing interest in the dynamic coupling of the grid with the physical solution so that the grid lines continually move to achieve concentration in regions of strong variation of the physical solution and alignment with shocks, flame fronts, etc. Such adaptive coordinate systems have been developed using a variety of techniques for sensing and reacting to the developing regions of concentration and/or alignment. This paper reviews the techniques and applications of these dynamically adaptive systems and other systems.

Thompson, J. F.↗
NASA NTRS1983

Multiple transonic solutions with a new class of shock transitions in steady isothermal solar and stellar winds

It is shown that a new class of shock transitions arises in the transonic solutions of the steady isothermal solar wind equations when momentum deposition and/or nonradial flow tube divergence give rise to multiple critical points in the flow. These shock transitions between critical solutions occur for a certain range of the parameters which characterize the momentum deposition function. The isothermal wind equations allow multiple transonic solutions in the presence of such shock transitions, yielding a continuous solution passing through an inner critical point and solutions involving a shock transition between critical solutions. It is determined that these multiple transonic solutions have the same flow speed at the base but different supersonic flow speeds at infinity. It is found that the nonradial flow tube divergence and momentum addition are equivalent, which gives rise to multiple critical points and hence to multiple transonic solutions with shock transitions. In addition, the physical relevance of these properties are examined for astrophysical systems such as the inner solar wind, flows in extragalactic jets, and accretion discs.

Habbal, S. R.↗
NASA NTRS1990

One-dimensional hybrid continuum/particle simulation approach for rarefied hypersonic flows

A hybrid numerical technique, based on local application of continuum and particle methods, is applied to the one-dimensional normal shock structure in a monatomic gas. The methods are coupled iteratively via a flux boundary condition in a region where both are applicable. The validity of each method through the shock structure is quantified. The physical and numerical aspects of coupling are discussed and a variety of coupling methods are assessed. Results are presented to show the improvement in computational efficiency available via the hybrid approach.

Wadsworth, D. C.↗
NASA NTRS1991

High-order ENO schemes applied to two- and three-dimensional compressible flow

High order essentially non-oscillatory (ENO) finite difference schemes are applied to the 2-D and 3-D compressible Euler and Navier-Stokes equations. Practical issues, such as vectorization, efficiency of coding, cost comparison with other numerical methods, and accuracy degeneracy effects, are discussed. Numerical examples are provided which are representative of computational problems of current interest in transition and turbulence physics. These require both nonoscillatory shock capturing and high resolution for detailed structures in the smooth regions and demonstrate the advantage of ENO schemes.

Shu, Chi-Wang↗
NASA NTRS1994

Two-fluid simulations of galaxy formation

We investigate the formation of galaxies and larger structure with a simulation modeling two gravitationally coupled fluids representing dark matter and baryons. The baryon gas dynamics are calculated with a smoothed particle hydrodynamics (SPH) method, and the physics modeled includes thermal pressure, shock heating, and radiative cooling. We simulate a 16 Mpc periodic cube with 64(exp 3) particles in each fluid and 10% baryon mass fraction. We confirm, for the first time experimentally, disk formation as a natural consequence of hierarchical clustering in a large-scale cosmological environment. The majority of isolated galaxies exhibit centrifugally supported disks. A power-law relation between cold baryonic mass and maximum rotation velocity is found, M varies as nu(sub rot)(exp alpha) with alpha = 2.5 after correcting for differential numerical resolution. Both the spatial and velocity distributions of the simulated galaxies are biased with respect to the dark matter. A counts-in-cells analysis indicates that an unphysical degree of merging in the central cluster is likely responsible for the antibias signal in the correlation function. A robust, scale-dependent velocity bias is measured. The ratio of galaxy to dark matter pairwise velocity dispersions on a scale of 1 Mpc is 0.7. The amplitude is only mildly dependent on redshift or mass cutoff and scales with separation as r(exp 0.2). The degree to which these results depend on numerical parameters is discussed. Mass resolution plays a key role in controlling the resulting fraction of cold, dense baryons. The mass fraction associated with galaxies decreases by a factor of approximately greater than 3 when the mass per particle is increased by a factor 8. Photoionization and energy input from supernova will have to be included to determine more carefully the fraction of highly dissipated material and the characteristics of the stellar component of galaxies.

Evrard, August E.↗
NASA NTRS1995

Two-dimensional structure of slow shocks

The two-dimensional (2-D) structure of switch-off slow magnetosonic shocks is investigated using an electromagnetic hybrid (fluid electrons, kinetic ions) code. It is shown that the basic physical processes occurring at 1-D slow shocks are also operative in 2-D. Specifically, the interaction between the upstream ions and those streaming away from the shock results in the excitation of Alfven/ions-cyclotron (AIC) waves. Depending on the plasma parameters, these waves may either stay in the upstream or convect back into the shock resulting in a non-steady shock behavior which prevents the formation of a trailing wave train. Despite this similarity, some slow shocks which are steady in 1-D are found to be non-steady in 2-D. Fourier analysis of the waves downstream of non-steady shocks identifies them as AIC, demonstrating that the waves remain on the same branch as they convect from upstream into the downstream region.

Omidi, N.↗
NASA NTRS2022

Snapping Shrimp Have Helmets That Protect Their Brains By Dampening Shock Waves

Shock waves are supersonic high-amplitude pressure waves that cause barotrauma when they transfer kinetic energy to the tissues of animals.1–4 Snapping shrimp (Alpheidae) produce shock waves and are exposed to them frequently, so we asked if these animals have evolved mechanisms of physical protection against them. Snapping shrimp generate shock waves by closing their snapping claws rapidly enough to form cavitation bubbles that release energy as an audible ‘‘snap’’ and a shock wave when they collapse.5–8 We tested if snapping shrimp are protected from shock waves by a helmet-like extension of their exoskeleton termed the orbital hood. Using behavioral trials, we found shock wave exposure slowed shelterseeking and caused a loss of motor control in Alpheus heterochaelis from which we had removed orbital hoods but did not significantly affect behavior in shrimp with unaltered orbital hoods. Shock waves thus have the potential to harm snapping shrimp but may not do so under natural conditions because of protection provided to shrimp by their orbital hoods. Using pressure recordings, we discovered the orbital hoods of A. heterochaelis dampen shock waves. Sealing the anterior openings of orbital hoods diminished how much they altered the magnitudes of shock waves, which suggests these helmet-like structures dampen shock waves by trapping and expelling water so that kinetic energy is redirected and released away from the heads of shrimp. Our results indicate orbital hoods mitigate blast-induced neurotrauma in snapping shrimp by dampening shock waves, making them the first biological armor system known to have such a function.

Alexandra C.N. Kingston↗
DOE OSTI2020

Electron acceleration in laboratory-produced turbulent collisionless shocks

Astrophysical collisionless shocks are among the most powerful particle accelerators in the Universe. Generated by violent interactions of supersonic plasma flows with the interstellar medium, supernova remnant shocks are observed to amplify magnetic fields and accelerate electrons and protons to highly relativistic speeds. In the well-established model of diffusive shock acceleration, relativistic particles are accelerated by repeated shock crossings. However, this requires a separate mechanism that pre-accelerates particles to enable shock crossing. This is known as the ‘injection problem’, which is particularly relevant for electrons, and remains one of the most important puzzles in shock acceleration. In most astrophysical shocks, the details of the shock structure cannot be directly resolved, making it challenging to identify the injection mechanism. In this letter we report results from laser-driven plasma flow experiments, and related simulations, that probe the formation of turbulent collisionless shocks in conditions relevant to young supernova remnants. We show that electrons can be effectively accelerated in a first-order Fermi process by small-scale turbulence produced within the shock transition to relativistic non-thermal energies, helping overcome the injection problem. Our observations provide new insight into electron injection at shocks and open the way for controlled laboratory studies of the physics underlying cosmic accelerators.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Outflow Boundary Conditions for Turbine-Integrated Rotating Detonation Combustors

This study examines outflow boundary conditions (BCs) in computational fluid dynamics (CFD) simulations of a transition duct with and without guide vanes that converts supersonic flow exiting a rotating detonation combustor (RDC) to subsonic flow to drive a turbine. Since the flow exiting the transition duct has swirling shock waves with significant spatial and temporal variations in pressure, temperature, and Mach number, imposing proper BCs poses a challenge. To ensure all swirling shock waves exit the transition duct without creating non-physical reflected waves at its outlet, this study examined three outflow BCs: (1) the average pressure imposed at the duct’s outlet, (2) a nonreflecting BC (NRBC) with a specified average pressure imposed at the duct’s outlet, (3) the average pressure imposed at the outlet of an extension duct made up of a buffer layer and a sponge layer. This study is based on the three-dimensional, unsteady density-weighted-ensemble-averaged continuity, Navier–Stokes, and energy equations for a thermally perfect gas closed by the realizable k–ε model and “enhanced” wall functions. The results obtained show that imposing an average pressure at the transition duct’s outlet produces spurious waves that degrade the physical meaningfulness of the solution. When the NRBC was applied, swirling shock waves exited the duct’s outlet without creating spurious waves. However, its usage requires the gas to be thermally, as well as calorically, perfect, which this study shows could be a concern. By imposing the average pressure at the outlet of an extension duct, the gas does not need to be calorically perfect. The results obtained show the effects of the sponge layer’s length and coarsening ratio on damping nonuniformities in non-physical reflected waves to ensure the flow exiting the transition duct’s outlet can do so as if there are no boundaries present and has the desired average pressure—even though the BC is applied at the extension duct’s outlet.

gas turbines↗
NASA NTRSDate not supplied

An Improved Approach to the Predictability & Reliability of the Onset of Turbulence With Shocks

The construction of numerical schemes for (a) stable and accurate simulation of turbulence with strong shocks, and for (b) obtaining correct propagation speed of discontinuities in the presence of stiff source terms share one important ingredient – minimization of numerical dissipation while maintaining numerical stability. The dual requirements to achieve both numerical stability and minimal numerical dissipation are often conflicting since existing shock capturing schemes were designed mainly to be robust for rapidly developed turbulence-free flows and for shock waves without stiff source term. For the past two decades, Yee and collaborators have focused on an improved understanding of the nonlinear behavior of different high order shock-capturing methods. It was found that even very high order methods without proper nonlinear stability and numerical dissipation control can either numerically smear the onset of turbulence due to excess numerical dissipation, or induce (onset) numerical turbulence that is not physical turbulence due to lack of proper numerical dissipation to improve nonlinear stability for long time integration. Our approach is to combine (I) and (II) below for obtaining the physically correct onset of turbulence with shocks, including problems with stiff source terms: (I) Nonlinear dynamics is utilized to complement the traditional linearized stability theory (Yee & Sweby, Yee et al., Griffiths et al., Lafon & Yee, Yee, Wang et al., Kotov et al. 1990- 2015) in order to (i) Minimize numerically induced false transition to turbulence, (ii) Minimize numerical instability due to long time integration of turbulent flows, (iii) Minimize numerically induced standing wave solutions, and (iv) Minimize wrong propagation of speed of discontinuities due to the presence of stiff source terms. (II) Our recently developed physical preserving (structural preserving) high order methods with improved nonlinear stability & accuracy that are essential in minimizing spurious numerics are used.

HECC↗
NASA NTRS1994

The physics of grain-grain collisions and gas-grain sputtering in interstellar shocks

Grain-grain collisions and ion sputtering destroy dust grains in interstellar shocks. An analytical theory is developed for the propagation of shock waves in solids driven by grain-grain collisions, which compares very favorably with detailed numerical calculations. This theory is used to determine the fraction of grain vaporized by a grain-grain collision. Our results predict much less vaporization of colliding grains in interstellar shocks than previous estimates. This theory can also be used to determine the fraction of a colliding grain that melts, shatter, or undergoes a phase transformation to a higher density phase. In particular, the latter two processes can be much more important in interstellar shocks than vaporization. The sputtering of grains by impacting gas ions is reanalyzed based upon extensive laboratory studies and a theoretically derived 'universal'sputtering relation. The analytical results are compared to available experimental studies of sputtering of graphite/amorphous carbon, SiO2, SiC, Fe, and H2O. Sputtering yields for astrophysically relevant materials as a function of impact energy and ion mass are derived. These yields are also averaged over thermal impact spectrum and simple polynomial fits to the resulting yields as a function of temperature are presented. The derived sputtering yields are similar to those adopted in previous studies, except for graphite near threshold where the new yields are much larger due to a lower adopted binding energy. The ion bombardment will amorphitize the surface layers of interstellar grains. It will also convert graphite into hydrogenated amorphous carbon (HAC) to a depth of 10-20 A. It is suggested that these HAC surfaces are the carriers of the 3.4 micrometer absorption feature in the interstellar medium.

Tielens, A. G. G. M.↗
NASA NTRS1980

Theoretical interpretation of Traveling Interplanetary Phenomena and their solar origins

A review is made of recent theoretical studies on Traveling Interplanetary Phenomena (TIP) and their possible solar origins in the context of mathematical methods and physical processes. Flare-generated interplanetary shocks are used as examples to illustrate the following set of contrasting approaches to the phenomena: analytical vs numerical, hydrodynamic vs magnetohydrodynamic, dissipative vs non-dissipative, continuum/macroscopic vs kinetic/microscopic. It is suggested in conclusion that future research should emphasize continuum/macroscopic physical processes together with the kinetic approach to deepen understanding of microscopic interactions.

Wu, S. T.↗
DOE OSTI2023

Polyimide dynamically compressed to decomposition pressures: Two-wave structures captured by velocimetry and modeling

We performed a series of six plate impact experiments on polyimide and modeled them using new reactant and products equations of state combined with an Arrhenius rate model. The first experiment was diagnosed with embedded electromagnetic velocity gauges through which we directly observed attenuation of the lead shock to an approximately constant state over a propagation distance of roughly 4 mm. Simulated gauge profiles were in excellent qualitative agreement with experiment and suggested a sluggish chemical reaction that did not proceed to completion. The remaining five experiments were conducted in a transmission geometry and diagnosed velocimetrically at the sample/window interface. All five of these yielded profiles with a sharp shock followed by a more gradual approach to maximum interface velocity that was “rounded” to varying degree. These profiles proved difficult to interpret unambiguously due to the convolution of the reactive wave upon first shock with reflection of the lead wave and reshock or release by the window. Comparison with thermochemical calculations strongly suggests that the point of maximum interface velocity corresponds to the equilibrium reshock or release locus. We discuss the implications of this point for the practice of impedance matching based on the reflected Hugoniot of reactive materials such as polymers. The reactant and thermochemical products equations of state are developmental SESAME tables 97710 and 97720, respectively.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1973

Unique characterization of lunar samples by physical properties

The measurement of compressional velocity, shear velocity, static compressibility, and thermal expansion of (1) a suite of shocked rocks fron the Ries impact in Germany, (2) a suite of samples cracked by thermal cycling to high temperatures, (3) many terrestrial igneous rocks, and (4) lunar basalts, gabbroic anorthosites, and breccias, indicate that shock metamorphism is the primary cause for values of physical properties of lunar rocks being diffferent from their intrinsic values. Large scale thermal metamorphism, thermal cycling between temperatures of lunar day and night, large thermal gradients, or thermal fatigue could possibly cause minor cracking in the top few centimeters of the lunar regolith, but are probably not important mechanism for extensively changing values of physical properties of lunar rocks.-

Todd, T.↗
DOE OSTI2024

Richtmyer–Meshkov instability when a shock is reflected for fluids with arbitrary equation of state

First predicted by Richtmyer in 1960 and experimentally confirmed by Meshkov in 1969, the Richtmyer–Meshkov instability (RMI) is crucial in fields such as physics, astrophysics, inertial confinement fusion and high-energy-density physics. These disciplines often deal with strong shocks moving through condensed materials or high-pressure plasmas that exhibit non-ideal equations of state (EoS), thus requiring theoretical models with realistic fluid EoS for accurate RMI simulations. Approximate formulae for asymptotic growth rates, like those proposed by Richtmyer, are helpful but rely on heuristic prescriptions for compressible materials. These prescriptions can sometimes approximate the RMI growth rate well, but their accuracy remains uncertain without exact solutions, as the fully compressible RMI growth rate is influenced by both vorticity deposited during shock refraction and multiple sonic wave refractions. This study advances previous work by presenting an analytic, fully compressible theory of RMI for reflected shocks with arbitrary EoS. It compares theoretical predictions with heuristic prescriptions using ideal gas, van der Waals gas and three-term constitutive equations for simple metals, the latter being analysed with detailed and simplified ideal-gas-like EoS. We additionally offer an alternative explicit approximate formula for the asymptotic growth rate. The comprehensive model also incorporates the effects of constant-amplitude acoustic waves at the interface, associated with the D'yakov–Kontorovich instability in shocks.

Napieralski, Mario (ORCID:0009000692344901)↗
NASA NTRS2021

Direct Multipoint Observations Capturing the Reformation of a Supercritical Fast Magnetosonic Shock

Using multipoint Magnetospheric Multiscale (MMS) observations in an unusual string-of-pearls configuration, we examine in detail observations of the reformation of a fast magnetosonic shock observed on the upstream edge of a foreshock transient structure upstream of Earth’s bow shock. The four MMS spacecraft were separated by several hundred km, comparable to suprathermal ion gyro-radius scales or several ion inertial lengths. At least half of the shock reformation cycle was observed, with a new shock ramp rising up out of the “foot” region of the original shock ramp. Using the multipoint observations, we convert the observed time-series data into distance along the shock normal in the shock’s rest frame. That conversion allows for a unique study of the relative spatial scales of the shock’s various features, including the shock’s growth rate, and how they evolve during the reformation cycle. Analysis indicates that: the growth rate increases during reformation, electron-scale physics play an important role in the shock reformation, and energy conversion processes also undergo the same cyclical periodicity as reformation. Strong, thin electron-kinetic-scale current sheets and large-amplitude electrostatic and electromagnetic waves are reported. Evidence is also presented of nonlinear wave decay from electromagnetic whistler-mode “lion roars” to electrostatic solitary waves in the downstream plasma regime. Results highlight the critical cross-scale coupling between electron-kinetic-and ion-kinetic-scale processes and details of the nature of nonstationarity, shock-front reformation at collisionless, fast magnetosonic shocks.

D L Turner↗
DOE OSTI2026

On how avalanches penetrate the SOL and broaden heat loads

Recent experiments reported a correlation between power law core temperature spectra and Dα emission, suggesting that heat avalanches penetrate the SOL. This paper derives a threshold criterion for avalanche penetration using a reduced model. Avalanches with ($\bigtriangledown$$\tilde{T}$) rms > $\bigtriangledown$$\tilde{T}$ crit at the separatrix are predicted to penetrate, and so broaden the SOL and heat load distribution. $\bigtriangledown$$\tilde{T}$ crit is ~ 1/$τ$ ∥ , where $τ$ ∥ is the parallel heat flow time through the SOL. Penetration occurs when avalanches are strong enough to steepen sufficiently to shock at the separatrix. A positive correlation is found between the nonlinear drive for steepening and the penetration depth. In particular, penetration depth exceeds that of the heuristic drift limit when shocks form. Implications for numerical and physical experiments are also discussed.

SOL heat load↗